Subgroups — C₅₃×#61642 #27269154

Order 13568.

2042 conjugacy classes of subgroups.

The subgroup lattice has 1850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3320	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3313	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3300	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3269	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3269	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3225	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3223	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3203	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3201	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3190	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3120	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#563	—	2	1	no	—
43	C₅₃×#562	—	2	1	no	—
44	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#554	—	2	1	no	—
46	C₅₃×#554	C₂²	1	1	yes	characteristic
47	C₅₃×#553	—	2	1	no	—
48	C₅₃×#553	C₂²	1	1	yes	characteristic
49	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
52	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
53	C₅₃×#548	C₂²	1	1	yes	characteristic
54	C₅₃×#548	C₂²	1	1	yes	characteristic
55	C₅₃×#548	C₂²	1	1	yes	characteristic
56	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#547	—	2	1	no	—
58	C₅₃×#547	—	2	1	no	—
59	C₅₃×#547	C₂²	1	1	yes	characteristic
60	C₅₃×#547	C₂²	1	1	yes	characteristic
61	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#546	—	2	1	no	—
63	C₅₃×#546	—	2	1	no	—
64	C₅₃×#546	C₂²	1	1	yes	characteristic
65	C₅₃×#546	C₂²	1	1	yes	characteristic
66	C₅₃×#542	—	2	1	no	—
67	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#539	—	2	1	no	—
70	C₅₃×#538	—	2	1	no	—
71	C₅₃×#538	—	2	1	no	—
72	C₅₃×#537	—	2	1	no	—
73	C₅₃×#537	C₂²	1	1	yes	characteristic
74	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#536	—	2	1	no	—
76	C₅₃×#536	C₂²	1	1	yes	characteristic
77	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#525	—	2	1	no	—
79	C₅₃×#525	C₂²	1	1	yes	characteristic
80	C₅₃×#525	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
82	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
83	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
84	C₅₃×#520	C₂²	1	1	yes	characteristic
85	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#494	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#484	C₂²	1	1	yes	characteristic
97	C₅₃×#484	C₂²	1	1	yes	characteristic
98	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#467	C₂²	1	1	yes	characteristic
114	C₅₃×#467	C₂²	1	1	yes	characteristic
115	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#465	C₂²	1	1	yes	characteristic
123	C₅₃×#465	C₂²	1	1	yes	characteristic
124	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#452	C₂²	1	1	yes	characteristic
138	C₅₃×#452	C₂²	1	1	yes	characteristic
139	C₅₃×#452	C₂²	1	1	yes	characteristic
140	C₅₃×#452	C₂²	1	1	yes	characteristic
141	C₅₃×#452	C₂²	1	1	yes	characteristic
142	C₅₃×#452	C₂²	1	1	yes	characteristic
143	C₅₃×#452	C₂²	1	1	yes	characteristic
144	C₅₃×#452	C₂²	1	1	yes	characteristic
145	C₅₃×#452	C₂²	1	1	yes	characteristic
146	C₅₃×#452	C₂²	1	1	yes	characteristic
147	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#451	C₂²	1	1	yes	characteristic
154	C₅₃×#451	C₂²	1	1	yes	characteristic
155	C₅₃×#451	C₂²	1	1	yes	characteristic
156	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#450	C₂²	1	1	yes	characteristic
164	C₅₃×#449	C₂²	1	1	yes	characteristic
165	C₅₃×#449	C₂²	1	1	yes	characteristic
166	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#448	C₂²	1	1	yes	characteristic
169	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#447	C₂²	1	1	yes	characteristic
173	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#435	C₂²	1	1	yes	characteristic
182	C₅₃×#435	C₂²	1	1	yes	characteristic
183	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#416	C₂²	1	1	yes	characteristic
194	C₅₃×#416	C₂²	1	1	yes	characteristic
195	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
196	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
197	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
199	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
201	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
202	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
203	2₋¹⁺⁴×C₅₃	—	4	2	no	—
204	2₋¹⁺⁴×C₅₃	—	4	2	no	—
205	C₂×#41×C₅₃	—	2	1	no	—
206	C₂×#41×C₅₃	—	2	1	no	—
207	C₂×#41×C₅₃	—	2	1	no	—
208	C₂×#41×C₅₃	—	2	1	no	—
209	C₂×#41×C₅₃	—	2	1	no	—
210	C₂×#41×C₅₃	—	4	2	no	—
211	C₂×#41×C₅₃	—	4	2	no	—
212	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Q₈×C₅₃	—	2	1	no	—
222	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²×D₄×C₅₃	—	2	1	no	—
229	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂³×C₄×C₅₃	—	2	1	no	—
231	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
232	#137×C₅₃	—	4	2	no	—
233	#137×C₅₃	—	4	2	no	—
234	#135×C₅₃	—	4	2	no	—
235	#135×C₅₃	—	4	2	no	—
236	#135×C₅₃	—	4	2	no	—
237	C₂×Q₁₆×C₅₃	—	4	2	no	—
238	C₂×Q₁₆×C₅₃	—	4	2	no	—
239	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×SD₁₆×C₅₃	—	4	2	no	—
252	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
266	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
267	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
268	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
269	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
272	C₄⋊Q₈×C₅₃	—	2	1	no	—
273	C₄⋊Q₈×C₅₃	—	2	1	no	—
274	C₄⋊Q₈×C₅₃	—	2	1	no	—
275	C₄⋊Q₈×C₅₃	—	2	1	no	—
276	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
280	#126×C₅₃	—	2	1	no	—
281	#126×C₅₃	—	2	1	no	—
282	#126×C₅₃	—	2	1	no	—
283	#126×C₅₃	—	2	1	no	—
284	#126×C₅₃	—	2	1	no	—
285	#126×C₅₃	—	2	1	no	—
286	#126×C₅₃	—	2	1	no	—
287	#125×C₅₃	—	2	1	no	—
288	#125×C₅₃	—	2	1	no	—
289	#125×C₅₃	—	2	1	no	—
290	#125×C₅₃	—	2	1	no	—
291	#125×C₅₃	C₂³	1	1	yes	characteristic
292	#124×C₅₃	—	2	1	no	—
293	#124×C₅₃	—	2	1	no	—
294	#124×C₅₃	—	2	1	no	—
295	#124×C₅₃	—	2	1	no	—
296	#124×C₅₃	—	2	1	no	—
297	#124×C₅₃	—	2	1	no	—
298	#124×C₅₃	—	2	1	no	—
299	#124×C₅₃	C₂³	1	1	yes	characteristic
300	#124×C₅₃	C₂³	1	1	yes	characteristic
301	#124×C₅₃	C₂³	1	1	yes	characteristic
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	—	2	1	no	—
310	#123×C₅₃	—	2	1	no	—
311	#123×C₅₃	—	2	1	no	—
312	#123×C₅₃	—	2	1	no	—
313	#123×C₅₃	—	2	1	no	—
314	#123×C₅₃	—	2	1	no	—
315	#123×C₅₃	—	2	1	no	—
316	#123×C₅₃	—	2	1	no	—
317	#123×C₅₃	—	2	1	no	—
318	#123×C₅₃	D₄	1	1	yes	characteristic
319	#123×C₅₃	D₄	1	1	yes	characteristic
320	C₂²⋊Q₈×C₅₃	—	2	1	no	—
321	C₂²⋊Q₈×C₅₃	—	2	1	no	—
322	C₂²⋊Q₈×C₅₃	—	2	1	no	—
323	C₂²⋊Q₈×C₅₃	—	2	1	no	—
324	C₂²⋊Q₈×C₅₃	—	2	1	no	—
325	C₂²⋊Q₈×C₅₃	—	2	1	no	—
326	C₂²⋊Q₈×C₅₃	—	2	1	no	—
327	C₂²⋊Q₈×C₅₃	—	2	1	no	—
328	C₂²⋊Q₈×C₅₃	—	2	1	no	—
329	C₂²⋊Q₈×C₅₃	—	2	1	no	—
330	C₂²⋊Q₈×C₅₃	—	2	1	no	—
331	C₂²⋊Q₈×C₅₃	—	2	1	no	—
332	C₂²⋊Q₈×C₅₃	—	2	1	no	—
333	C₂²⋊Q₈×C₅₃	—	2	1	no	—
334	C₂²⋊Q₈×C₅₃	—	2	1	no	—
335	C₂²⋊Q₈×C₅₃	—	2	1	no	—
336	C₂²⋊Q₈×C₅₃	—	2	1	no	—
337	C₂²⋊Q₈×C₅₃	—	2	1	no	—
338	C₂²⋊Q₈×C₅₃	—	2	1	no	—
339	C₂²⋊Q₈×C₅₃	—	2	1	no	—
340	C₂²⋊Q₈×C₅₃	—	2	1	no	—
341	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
342	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
343	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
344	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
345	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
346	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
347	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
348	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
350	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
351	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
352	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
353	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
354	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
355	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
356	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
357	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
358	#121×C₅₃	—	2	1	no	—
359	#121×C₅₃	—	2	1	no	—
360	#121×C₅₃	—	2	1	no	—
361	#121×C₅₃	—	2	1	no	—
362	#121×C₅₃	—	2	1	no	—
363	#121×C₅₃	—	2	1	no	—
364	#121×C₅₃	—	2	1	no	—
365	#121×C₅₃	—	2	1	no	—
366	#121×C₅₃	—	2	1	no	—
367	#121×C₅₃	—	2	1	no	—
368	#121×C₅₃	—	2	1	no	—
369	#121×C₅₃	—	2	1	no	—
370	#121×C₅₃	—	2	1	no	—
371	#121×C₅₃	—	2	1	no	—
372	#121×C₅₃	—	2	1	no	—
373	#121×C₅₃	—	2	1	no	—
374	#121×C₅₃	D₄	1	1	yes	characteristic
375	#121×C₅₃	D₄	1	1	yes	characteristic
376	#121×C₅₃	C₂³	1	1	yes	characteristic
377	#121×C₅₃	C₂³	1	1	yes	characteristic
378	#121×C₅₃	C₂³	1	1	yes	characteristic
379	#121×C₅₃	C₂³	1	1	yes	characteristic
380	#121×C₅₃	C₂³	1	1	yes	characteristic
381	#120×C₅₃	—	2	1	no	—
382	#120×C₅₃	—	2	1	no	—
383	#120×C₅₃	—	2	1	no	—
384	#120×C₅₃	D₄	1	1	yes	characteristic
385	#120×C₅₃	D₄	1	1	yes	characteristic
386	C₄×Q₈×C₅₃	—	2	1	no	—
387	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
388	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
389	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
390	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
391	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
392	C₄×D₄×C₅₃	—	2	1	no	—
393	C₄×D₄×C₅₃	—	2	1	no	—
394	C₄×D₄×C₅₃	—	2	1	no	—
395	C₄×D₄×C₅₃	—	2	1	no	—
396	C₄×D₄×C₅₃	—	2	1	no	—
397	C₄×D₄×C₅₃	—	2	1	no	—
398	C₄×D₄×C₅₃	—	2	1	no	—
399	C₄×D₄×C₅₃	—	2	1	no	—
400	C₄×D₄×C₅₃	—	2	1	no	—
401	C₄×D₄×C₅₃	—	2	1	no	—
402	C₄×D₄×C₅₃	—	2	1	no	—
403	C₄×D₄×C₅₃	—	2	1	no	—
404	C₄×D₄×C₅₃	—	2	1	no	—
405	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
406	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
407	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
408	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
409	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
410	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
411	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
412	#117×C₅₃	—	2	1	no	—
413	#117×C₅₃	—	2	1	no	—
414	#117×C₅₃	C₂³	1	1	yes	characteristic
415	#117×C₅₃	C₂³	1	1	yes	characteristic
416	#117×C₅₃	C₂³	1	1	yes	characteristic
417	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
418	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
419	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
420	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
424	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
425	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
426	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
430	#107×C₅₃	C₂³	1	1	yes	characteristic
431	#107×C₅₃	C₂³	1	1	yes	characteristic
432	#107×C₅₃	C₂³	1	1	yes	characteristic
433	#107×C₅₃	C₂³	1	1	yes	characteristic
434	#107×C₅₃	C₂³	1	1	yes	characteristic
435	#107×C₅₃	C₂³	1	1	yes	characteristic
436	#106×C₅₃	C₂³	1	1	yes	characteristic
437	#106×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
441	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#103×C₅₃	C₂³	1	1	yes	characteristic
451	#103×C₅₃	C₂³	1	1	yes	characteristic
452	#103×C₅₃	C₂³	1	1	yes	characteristic
453	#103×C₅₃	C₂³	1	1	yes	characteristic
454	#103×C₅₃	C₂³	1	1	yes	characteristic
455	#103×C₅₃	C₂³	1	1	yes	characteristic
456	#103×C₅₃	C₂³	1	1	yes	characteristic
457	#103×C₅₃	C₂³	1	1	yes	characteristic
458	#103×C₅₃	C₂³	1	1	yes	characteristic
459	#103×C₅₃	C₂³	1	1	yes	characteristic
460	#103×C₅₃	C₂³	1	1	yes	characteristic
461	#103×C₅₃	C₂³	1	1	yes	characteristic
462	#103×C₅₃	C₂³	1	1	yes	characteristic
463	#103×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#102×C₅₃	C₂³	1	1	yes	characteristic
466	#102×C₅₃	C₂³	1	1	yes	characteristic
467	#102×C₅₃	C₂³	1	1	yes	characteristic
468	#102×C₅₃	C₂³	1	1	yes	characteristic
469	#102×C₅₃	C₂³	1	1	yes	characteristic
470	#102×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	#102×C₅₃	C₂³	1	1	yes	characteristic
473	#102×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
485	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
486	#97×C₅₃	C₂³	1	1	yes	characteristic
487	#97×C₅₃	C₂³	1	1	yes	characteristic
488	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
489	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
490	C₂⁴×C₅₃	—	2	1	no	—
491	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
492	#41×C₅₃	—	2	2	no	—
493	#41×C₅₃	—	2	2	no	—
494	#41×C₅₃	—	2	2	no	—
495	#41×C₅₃	—	2	2	no	—
496	#41×C₅₃	—	2	2	no	—
497	#41×C₅₃	—	2	2	no	—
498	#41×C₅₃	—	4	1	no	—
499	#41×C₅₃	—	4	1	no	—
500	#41×C₅₃	—	4	1	no	—
501	#41×C₅₃	—	4	1	no	—
502	#41×C₅₃	—	4	1	no	—
503	#41×C₅₃	—	4	1	no	—
504	#41×C₅₃	—	4	1	no	—
505	#41×C₅₃	—	4	1	no	—
506	#41×C₅₃	—	4	4	no	—
507	#41×C₅₃	—	4	4	no	—
508	#41×C₅₃	—	4	1	no	—
509	#41×C₅₃	—	4	1	no	—
510	#41×C₅₃	—	4	1	no	—
511	#41×C₅₃	—	4	1	no	—
512	#41×C₅₃	—	4	4	no	—
513	#41×C₅₃	—	4	4	no	—
514	#41×C₅₃	—	4	4	no	—
515	C₂×Q₈×C₅₃	—	2	1	no	—
516	C₂×Q₈×C₅₃	—	2	1	no	—
517	C₂×Q₈×C₅₃	—	2	1	no	—
518	C₂×Q₈×C₅₃	—	2	1	no	—
519	C₂×Q₈×C₅₃	—	2	1	no	—
520	C₂×Q₈×C₅₃	—	2	1	no	—
521	C₂×Q₈×C₅₃	—	2	1	no	—
522	C₂×Q₈×C₅₃	—	2	2	no	—
523	C₂×Q₈×C₅₃	—	2	2	no	—
524	C₂×Q₈×C₅₃	—	2	2	no	—
525	C₂×Q₈×C₅₃	—	4	1	no	—
526	C₂×Q₈×C₅₃	—	4	1	no	—
527	C₂×Q₈×C₅₃	—	4	1	no	—
528	C₂×Q₈×C₅₃	—	4	1	no	—
529	C₂×Q₈×C₅₃	—	4	1	no	—
530	C₂×Q₈×C₅₃	—	4	4	no	—
531	C₂×Q₈×C₅₃	—	4	1	no	—
532	C₂×Q₈×C₅₃	—	4	1	no	—
533	C₂×Q₈×C₅₃	—	4	1	no	—
534	C₂×Q₈×C₅₃	—	4	1	no	—
535	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
536	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
539	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
540	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂×D₄×C₅₃	—	2	1	no	—
544	C₂×D₄×C₅₃	—	2	2	no	—
545	C₂×D₄×C₅₃	—	2	1	no	—
546	C₂×D₄×C₅₃	—	2	1	no	—
547	C₂×D₄×C₅₃	—	2	1	no	—
548	C₂×D₄×C₅₃	—	2	1	no	—
549	C₂×D₄×C₅₃	—	2	1	no	—
550	C₂×D₄×C₅₃	—	2	1	no	—
551	C₂×D₄×C₅₃	—	2	1	no	—
552	C₂×D₄×C₅₃	—	2	1	no	—
553	C₂×D₄×C₅₃	—	2	1	no	—
554	C₂×D₄×C₅₃	—	2	1	no	—
555	C₂×D₄×C₅₃	—	2	1	no	—
556	C₂×D₄×C₅₃	—	2	1	no	—
557	C₂×D₄×C₅₃	—	2	1	no	—
558	C₂×D₄×C₅₃	—	4	1	no	—
559	C₂×D₄×C₅₃	—	4	4	no	—
560	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
561	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
562	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
563	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
564	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
565	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
566	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
567	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
568	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
569	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
570	C₂²×C₄×C₅₃	—	2	1	no	—
571	C₂²×C₄×C₅₃	—	2	1	no	—
572	C₂²×C₄×C₅₃	—	2	1	no	—
573	C₂²×C₄×C₅₃	—	2	1	no	—
574	C₂²×C₄×C₅₃	—	2	1	no	—
575	C₂²×C₄×C₅₃	—	2	1	no	—
576	C₂²×C₄×C₅₃	—	2	1	no	—
577	C₂²×C₄×C₅₃	—	2	1	no	—
578	C₂²×C₄×C₅₃	—	2	1	no	—
579	C₂²×C₄×C₅₃	—	2	1	no	—
580	C₂²×C₄×C₅₃	—	2	1	no	—
581	C₂²×C₄×C₅₃	—	2	1	no	—
582	C₂²×C₄×C₅₃	—	2	1	no	—
583	C₂²×C₄×C₅₃	—	2	1	no	—
584	C₂²×C₄×C₅₃	—	2	1	no	—
585	C₂²×C₄×C₅₃	—	2	1	no	—
586	C₂²×C₄×C₅₃	—	2	1	no	—
587	C₂²×C₄×C₅₃	—	2	1	no	—
588	C₂²×C₄×C₅₃	—	2	1	no	—
589	C₂²×C₄×C₅₃	—	2	1	no	—
590	C₂²×C₄×C₅₃	—	4	1	no	—
591	C₂²×C₄×C₅₃	—	4	1	no	—
592	C₂²×C₄×C₅₃	—	4	4	no	—
593	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
594	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
595	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
596	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
598	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
599	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
600	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
601	Q₁₆×C₅₃	—	2	2	no	—
602	Q₁₆×C₅₃	—	2	2	no	—
603	Q₁₆×C₅₃	—	2	2	no	—
604	Q₁₆×C₅₃	—	4	1	no	—
605	Q₁₆×C₅₃	—	4	1	no	—
606	Q₁₆×C₅₃	—	4	1	no	—
607	Q₁₆×C₅₃	—	4	1	no	—
608	Q₁₆×C₅₃	—	4	1	no	—
609	Q₁₆×C₅₃	—	4	1	no	—
610	Q₁₆×C₅₃	—	4	1	no	—
611	Q₁₆×C₅₃	—	4	1	no	—
612	Q₁₆×C₅₃	—	4	1	no	—
613	SD₁₆×C₅₃	—	2	2	no	—
614	SD₁₆×C₅₃	—	2	2	no	—
615	SD₁₆×C₅₃	—	2	2	no	—
616	SD₁₆×C₅₃	—	2	2	no	—
617	SD₁₆×C₅₃	—	4	1	no	—
618	SD₁₆×C₅₃	—	4	1	no	—
619	SD₁₆×C₅₃	—	4	1	no	—
620	SD₁₆×C₅₃	—	4	1	no	—
621	SD₁₆×C₅₃	—	4	1	no	—
622	SD₁₆×C₅₃	—	4	1	no	—
623	D₈×C₅₃	—	2	2	no	—
624	D₈×C₅₃	—	4	1	no	—
625	M₁₆×C₅₃	—	4	1	no	—
626	M₁₆×C₅₃	—	4	1	no	—
627	C₂×C₈×C₅₃	—	4	1	no	—
628	C₂×C₈×C₅₃	—	4	1	no	—
629	C₂×C₈×C₅₃	—	4	1	no	—
630	C₂×C₈×C₅₃	—	4	1	no	—
631	C₂×C₈×C₅₃	—	4	1	no	—
632	C₂×C₈×C₅₃	—	4	1	no	—
633	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
634	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
635	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
636	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
637	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
639	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
640	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	—	2	1	no	—
642	C₄⋊C₄×C₅₃	—	2	1	no	—
643	C₄⋊C₄×C₅₃	—	2	1	no	—
644	C₄⋊C₄×C₅₃	—	2	1	no	—
645	C₄⋊C₄×C₅₃	—	2	1	no	—
646	C₄⋊C₄×C₅₃	—	2	1	no	—
647	C₄⋊C₄×C₅₃	—	2	1	no	—
648	C₄⋊C₄×C₅₃	—	2	1	no	—
649	C₄⋊C₄×C₅₃	—	2	1	no	—
650	C₄⋊C₄×C₅₃	—	2	1	no	—
651	C₄⋊C₄×C₅₃	—	2	1	no	—
652	C₄⋊C₄×C₅₃	—	2	1	no	—
653	C₄⋊C₄×C₅₃	—	2	1	no	—
654	C₄⋊C₄×C₅₃	—	2	1	no	—
655	C₄⋊C₄×C₅₃	—	2	1	no	—
656	C₄⋊C₄×C₅₃	—	2	1	no	—
657	C₄⋊C₄×C₅₃	—	2	1	no	—
658	C₄⋊C₄×C₅₃	—	2	1	no	—
659	C₄⋊C₄×C₅₃	—	2	1	no	—
660	C₄⋊C₄×C₅₃	—	2	1	no	—
661	C₄⋊C₄×C₅₃	—	2	1	no	—
662	C₄⋊C₄×C₅₃	—	2	1	no	—
663	C₄⋊C₄×C₅₃	—	2	1	no	—
664	C₄⋊C₄×C₅₃	—	2	1	no	—
665	C₄⋊C₄×C₅₃	—	2	1	no	—
666	C₄⋊C₄×C₅₃	—	2	1	no	—
667	C₄⋊C₄×C₅₃	—	2	1	no	—
668	C₄⋊C₄×C₅₃	—	2	1	no	—
669	C₄⋊C₄×C₅₃	—	2	1	no	—
670	C₄⋊C₄×C₅₃	—	2	1	no	—
671	C₄⋊C₄×C₅₃	—	2	1	no	—
672	C₄⋊C₄×C₅₃	—	2	1	no	—
673	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
674	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
675	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
676	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
677	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
678	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
679	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
680	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
681	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
682	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
683	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
684	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
685	C₂²⋊C₄×C₅₃	—	2	1	no	—
686	C₂²⋊C₄×C₅₃	—	2	1	no	—
687	C₂²⋊C₄×C₅₃	—	2	1	no	—
688	C₂²⋊C₄×C₅₃	—	2	1	no	—
689	C₂²⋊C₄×C₅₃	—	2	1	no	—
690	C₂²⋊C₄×C₅₃	—	2	1	no	—
691	C₂²⋊C₄×C₅₃	—	2	1	no	—
692	C₂²⋊C₄×C₅₃	—	2	1	no	—
693	C₂²⋊C₄×C₅₃	—	2	1	no	—
694	C₂²⋊C₄×C₅₃	—	2	1	no	—
695	C₂²⋊C₄×C₅₃	—	2	1	no	—
696	C₂²⋊C₄×C₅₃	—	2	1	no	—
697	C₂²⋊C₄×C₅₃	—	2	1	no	—
698	C₂²⋊C₄×C₅₃	—	2	1	no	—
699	C₂²⋊C₄×C₅₃	—	2	1	no	—
700	C₂²⋊C₄×C₅₃	—	2	1	no	—
701	C₂²⋊C₄×C₅₃	—	2	1	no	—
702	C₂²⋊C₄×C₅₃	—	2	1	no	—
703	C₂²⋊C₄×C₅₃	—	2	1	no	—
704	C₂²⋊C₄×C₅₃	—	2	1	no	—
705	C₂²⋊C₄×C₅₃	—	2	1	no	—
706	C₂²⋊C₄×C₅₃	—	2	1	no	—
707	C₂²⋊C₄×C₅₃	—	2	1	no	—
708	C₂²⋊C₄×C₅₃	—	2	1	no	—
709	C₂²⋊C₄×C₅₃	—	2	1	no	—
710	C₂²⋊C₄×C₅₃	—	2	1	no	—
711	C₂²⋊C₄×C₅₃	—	2	1	no	—
712	C₂²⋊C₄×C₅₃	—	2	1	no	—
713	C₂²⋊C₄×C₅₃	—	2	1	no	—
714	C₂²⋊C₄×C₅₃	—	2	1	no	—
715	C₂²⋊C₄×C₅₃	—	2	1	no	—
716	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
717	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
718	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
719	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
720	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
721	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
722	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
723	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
724	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
725	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
726	C₄²×C₅₃	—	2	1	no	—
727	C₄²×C₅₃	—	2	1	no	—
728	C₄²×C₅₃	—	2	1	no	—
729	C₄²×C₅₃	—	2	1	no	—
730	C₄²×C₅₃	—	2	1	no	—
731	C₄²×C₅₃	—	2	1	no	—
732	C₄²×C₅₃	—	2	1	no	—
733	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
734	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
735	C₂³×C₅₃	—	2	1	no	—
736	C₂³×C₅₃	—	2	2	no	—
737	C₂³×C₅₃	—	2	1	no	—
738	C₂³×C₅₃	—	2	1	no	—
739	C₂³×C₅₃	—	4	1	no	—
740	C₂³×C₅₃	—	4	1	no	—
741	C₂³×C₅₃	—	4	2	no	—
742	C₂³×C₅₃	—	4	2	no	—
743	C₂³×C₅₃	—	8	1	no	—
744	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
745	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
746	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
747	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
748	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
749	Q₈×C₅₃	—	2	1	no	—
750	Q₈×C₅₃	—	2	1	no	—
751	Q₈×C₅₃	—	2	1	no	—
752	Q₈×C₅₃	—	2	1	no	—
753	Q₈×C₅₃	—	2	1	no	—
754	Q₈×C₅₃	—	2	1	no	—
755	Q₈×C₅₃	—	2	1	no	—
756	Q₈×C₅₃	—	2	1	no	—
757	Q₈×C₅₃	—	2	1	no	—
758	Q₈×C₅₃	—	2	1	no	—
759	Q₈×C₅₃	—	2	1	no	—
760	Q₈×C₅₃	—	2	1	no	—
761	Q₈×C₅₃	—	2	1	no	—
762	Q₈×C₅₃	—	4	1	no	—
763	Q₈×C₅₃	—	4	2	no	—
764	Q₈×C₅₃	—	4	2	no	—
765	Q₈×C₅₃	—	4	2	no	—
766	Q₈×C₅₃	—	4	2	no	—
767	Q₈×C₅₃	—	8	1	no	—
768	Q₈×C₅₃	—	8	1	no	—
769	Q₈×C₅₃	—	8	1	no	—
770	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
771	D₄×C₅₃	—	2	4	no	—
772	D₄×C₅₃	—	2	2	no	—
773	D₄×C₅₃	—	2	2	no	—
774	D₄×C₅₃	—	2	1	no	—
775	D₄×C₅₃	—	2	1	no	—
776	D₄×C₅₃	—	2	1	no	—
777	D₄×C₅₃	—	2	1	no	—
778	D₄×C₅₃	—	2	1	no	—
779	D₄×C₅₃	—	4	1	no	—
780	D₄×C₅₃	—	4	1	no	—
781	D₄×C₅₃	—	4	1	no	—
782	D₄×C₅₃	—	4	1	no	—
783	D₄×C₅₃	—	4	1	no	—
784	D₄×C₅₃	—	4	2	no	—
785	D₄×C₅₃	—	4	2	no	—
786	D₄×C₅₃	—	4	2	no	—
787	D₄×C₅₃	—	4	2	no	—
788	D₄×C₅₃	—	4	2	no	—
789	D₄×C₅₃	—	4	2	no	—
790	D₄×C₅₃	—	4	2	no	—
791	D₄×C₅₃	—	8	1	no	—
792	D₄×C₅₃	—	8	1	no	—
793	D₄×C₅₃	—	8	1	no	—
794	D₄×C₅₃	—	8	1	no	—
795	D₄×C₅₃	—	8	1	no	—
796	D₄×C₅₃	—	8	1	no	—
797	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
798	C₂×C₄×C₅₃	—	2	4	no	—
799	C₂×C₄×C₅₃	—	2	1	no	—
800	C₂×C₄×C₅₃	—	2	1	no	—
801	C₂×C₄×C₅₃	—	2	1	no	—
802	C₂×C₄×C₅₃	—	2	1	no	—
803	C₂×C₄×C₅₃	—	2	1	no	—
804	C₂×C₄×C₅₃	—	2	1	no	—
805	C₂×C₄×C₅₃	—	2	1	no	—
806	C₂×C₄×C₅₃	—	2	1	no	—
807	C₂×C₄×C₅₃	—	2	1	no	—
808	C₂×C₄×C₅₃	—	2	1	no	—
809	C₂×C₄×C₅₃	—	2	1	no	—
810	C₂×C₄×C₅₃	—	2	1	no	—
811	C₂×C₄×C₅₃	—	2	1	no	—
812	C₂×C₄×C₅₃	—	2	1	no	—
813	C₂×C₄×C₅₃	—	2	1	no	—
814	C₂×C₄×C₅₃	—	2	1	no	—
815	C₂×C₄×C₅₃	—	2	1	no	—
816	C₂×C₄×C₅₃	—	2	1	no	—
817	C₂×C₄×C₅₃	—	2	1	no	—
818	C₂×C₄×C₅₃	—	2	1	no	—
819	C₂×C₄×C₅₃	—	2	1	no	—
820	C₂×C₄×C₅₃	—	2	1	no	—
821	C₂×C₄×C₅₃	—	2	1	no	—
822	C₂×C₄×C₅₃	—	4	1	no	—
823	C₂×C₄×C₅₃	—	4	1	no	—
824	C₂×C₄×C₅₃	—	4	1	no	—
825	C₂×C₄×C₅₃	—	4	2	no	—
826	C₂×C₄×C₅₃	—	4	2	no	—
827	C₂×C₄×C₅₃	—	4	2	no	—
828	C₂×C₄×C₅₃	—	4	2	no	—
829	C₂×C₄×C₅₃	—	4	2	no	—
830	C₂×C₄×C₅₃	—	4	2	no	—
831	C₂×C₄×C₅₃	—	4	2	no	—
832	C₂×C₄×C₅₃	—	4	2	no	—
833	C₂×C₄×C₅₃	—	4	2	no	—
834	C₂×C₄×C₅₃	—	8	1	no	—
835	C₂×C₄×C₅₃	—	8	1	no	—
836	C₂×C₄×C₅₃	—	8	1	no	—
837	C₂×C₄×C₅₃	—	8	1	no	—
838	C₂×C₄×C₅₃	—	8	1	no	—
839	C₂×C₄×C₅₃	—	8	1	no	—
840	C₂×C₄×C₅₃	—	8	1	no	—
841	C₂×C₄×C₅₃	—	8	1	no	—
842	C₂×C₄×C₅₃	—	8	1	no	—
843	C₂×C₄×C₅₃	—	8	1	no	—
844	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
845	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
846	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
847	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
848	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
849	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
850	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
851	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
852	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
853	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
854	C₈×C₅₃	—	2	1	no	—
855	C₈×C₅₃	—	2	1	no	—
856	C₈×C₅₃	—	2	1	no	—
857	C₈×C₅₃	—	2	1	no	—
858	C₈×C₅₃	—	2	1	no	—
859	C₈×C₅₃	—	2	1	no	—
860	C₈×C₅₃	—	2	1	no	—
861	C₈×C₅₃	—	2	1	no	—
862	#61642	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
863	C₂²×C₅₃	—	2	1	no	—
864	C₂²×C₅₃	—	2	1	no	—
865	C₂²×C₅₃	—	2	1	no	—
866	C₂²×C₅₃	—	2	1	no	—
867	C₂²×C₅₃	—	2	1	no	—
868	C₂²×C₅₃	—	2	1	no	—
869	C₂²×C₅₃	—	2	1	no	—
870	C₂²×C₅₃	—	2	2	no	—
871	C₂²×C₅₃	—	2	1	no	—
872	C₂²×C₅₃	—	2	1	no	—
873	C₂²×C₅₃	—	2	1	no	—
874	C₂²×C₅₃	—	2	1	no	—
875	C₂²×C₅₃	—	2	1	no	—
876	C₂²×C₅₃	—	2	1	no	—
877	C₂²×C₅₃	—	2	1	no	—
878	C₂²×C₅₃	—	4	1	no	—
879	C₂²×C₅₃	—	4	1	no	—
880	C₂²×C₅₃	—	4	1	no	—
881	C₂²×C₅₃	—	4	1	no	—
882	C₂²×C₅₃	—	4	1	no	—
883	C₂²×C₅₃	—	4	1	no	—
884	C₂²×C₅₃	—	4	1	no	—
885	C₂²×C₅₃	—	4	1	no	—
886	C₂²×C₅₃	—	8	2	no	—
887	C₂²×C₅₃	—	8	4	no	—
888	C₂²×C₅₃	#578	1	2	yes	—
889	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
890	C₄×C₅₃	—	2	1	no	—
891	C₄×C₅₃	—	2	1	no	—
892	C₄×C₅₃	—	2	1	no	—
893	C₄×C₅₃	—	2	2	no	—
894	C₄×C₅₃	—	2	1	no	—
895	C₄×C₅₃	—	2	1	no	—
896	C₄×C₅₃	—	2	1	no	—
897	C₄×C₅₃	—	2	1	no	—
898	C₄×C₅₃	—	2	1	no	—
899	C₄×C₅₃	—	2	1	no	—
900	C₄×C₅₃	—	4	1	no	—
901	C₄×C₅₃	—	4	1	no	—
902	C₄×C₅₃	—	4	1	no	—
903	C₄×C₅₃	—	4	1	no	—
904	C₄×C₅₃	—	4	1	no	—
905	C₄×C₅₃	—	4	1	no	—
906	C₄×C₅₃	—	4	1	no	—
907	C₄×C₅₃	—	4	1	no	—
908	C₄×C₅₃	—	4	1	no	—
909	C₄×C₅₃	—	4	1	no	—
910	C₄×C₅₃	—	4	1	no	—
911	C₄×C₅₃	—	4	1	no	—
912	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
913	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
914	#3541	C₂×C₅₃	1	1	yes	characteristic, complemented
915	#3489	C₂×C₅₃	1	1	yes	characteristic, complemented
916	#3320	C₂×C₅₃	1	1	yes	characteristic, complemented
917	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
918	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
919	#3313	C₂×C₅₃	1	1	yes	characteristic, complemented
920	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
921	#3300	C₂×C₅₃	1	1	yes	characteristic, complemented
922	#3299	C₂×C₅₃	1	1	yes	characteristic, complemented
923	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
924	D₄×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
925	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
926	#3283	C₂×C₅₃	1	1	yes	characteristic, complemented
927	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
928	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
929	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
930	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
931	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
932	#3225	C₂×C₅₃	1	1	yes	characteristic, complemented
933	#3223	C₂×C₅₃	1	1	yes	characteristic, complemented
934	#3203	C₂×C₅₃	1	1	yes	characteristic, complemented
935	#3201	C₂×C₅₃	1	1	yes	characteristic, complemented
936	#3190	C₂×C₅₃	1	1	yes	characteristic, complemented
937	#3189	C₂×C₅₃	1	1	yes	characteristic, complemented
938	#3124	C₂×C₅₃	1	1	yes	characteristic, complemented
939	#3120	C₂×C₅₃	1	1	yes	characteristic, complemented
940	#3013	C₂×C₅₃	1	1	yes	characteristic, complemented
941	#3011	C₂×C₅₃	1	1	yes	characteristic, complemented
942	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
943	C₂×#452	C₂×C₅₃	1	1	yes	characteristic, complemented
944	#2977	C₂×C₅₃	1	1	yes	characteristic, complemented
945	C₂×C₅₃	—	2	2	no	—
946	C₂×C₅₃	—	4	1	no	—
947	C₂×C₅₃	—	4	1	no	—
948	C₂×C₅₃	—	4	1	no	—
949	C₂×C₅₃	—	4	1	no	—
950	C₂×C₅₃	—	4	2	no	—
951	C₂×C₅₃	—	8	1	no	—
952	C₂×C₅₃	—	8	1	no	—
953	C₂×C₅₃	#3484	1	1	yes	characteristic
954	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
955	C₂×C₅₃	#3584	1	1	yes	characteristic
956	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
957	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
958	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
961	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
962	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
964	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
966	#563	—	2	1	no	—
967	#562	—	2	1	no	—
968	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#554	—	2	1	no	—
970	#554	C₂²×C₅₃	1	1	yes	characteristic
971	#553	—	2	1	no	—
972	#553	C₂²×C₅₃	1	1	yes	characteristic
973	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
975	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
976	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
977	#548	C₂²×C₅₃	1	1	yes	characteristic
978	#548	C₂²×C₅₃	1	1	yes	characteristic
979	#548	C₂²×C₅₃	1	1	yes	characteristic
980	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#547	—	2	1	no	—
982	#547	—	2	1	no	—
983	#547	C₂²×C₅₃	1	1	yes	characteristic
984	#547	C₂²×C₅₃	1	1	yes	characteristic
985	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#546	—	2	1	no	—
987	#546	—	2	1	no	—
988	#546	C₂²×C₅₃	1	1	yes	characteristic
989	#546	C₂²×C₅₃	1	1	yes	characteristic
990	#542	—	2	1	no	—
991	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#539	—	2	1	no	—
994	#538	—	2	1	no	—
995	#538	—	2	1	no	—
996	#537	—	2	1	no	—
997	#537	C₂²×C₅₃	1	1	yes	characteristic
998	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#536	—	2	1	no	—
1000	#536	C₂²×C₅₃	1	1	yes	characteristic
1001	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#525	—	2	1	no	—
1003	#525	C₂²×C₅₃	1	1	yes	characteristic
1004	#525	C₂²×C₅₃	1	1	yes	characteristic
1005	C₂×C₂²⋊Q₈	—	2	1	no	—
1006	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1007	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1008	#520	C₂²×C₅₃	1	1	yes	characteristic
1009	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#484	C₂²×C₅₃	1	1	yes	characteristic
1021	#484	C₂²×C₅₃	1	1	yes	characteristic
1022	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#467	C₂²×C₅₃	1	1	yes	characteristic
1038	#467	C₂²×C₅₃	1	1	yes	characteristic
1039	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#465	C₂²×C₅₃	1	1	yes	characteristic
1047	#465	C₂²×C₅₃	1	1	yes	characteristic
1048	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#452	C₂²×C₅₃	1	1	yes	characteristic
1062	#452	C₂²×C₅₃	1	1	yes	characteristic
1063	#452	C₂²×C₅₃	1	1	yes	characteristic
1064	#452	C₂²×C₅₃	1	1	yes	characteristic
1065	#452	C₂²×C₅₃	1	1	yes	characteristic
1066	#452	C₂²×C₅₃	1	1	yes	characteristic
1067	#452	C₂²×C₅₃	1	1	yes	characteristic
1068	#452	C₂²×C₅₃	1	1	yes	characteristic
1069	#452	C₂²×C₅₃	1	1	yes	characteristic
1070	#452	C₂²×C₅₃	1	1	yes	characteristic
1071	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#451	C₂²×C₅₃	1	1	yes	characteristic
1078	#451	C₂²×C₅₃	1	1	yes	characteristic
1079	#451	C₂²×C₅₃	1	1	yes	characteristic
1080	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#450	C₂²×C₅₃	1	1	yes	characteristic
1088	#449	C₂²×C₅₃	1	1	yes	characteristic
1089	#449	C₂²×C₅₃	1	1	yes	characteristic
1090	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#448	C₂²×C₅₃	1	1	yes	characteristic
1093	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#447	C₂²×C₅₃	1	1	yes	characteristic
1097	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	#435	C₂²×C₅₃	1	1	yes	characteristic
1106	#435	C₂²×C₅₃	1	1	yes	characteristic
1107	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1110	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1111	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1115	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1116	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1117	#416	C₂²×C₅₃	1	1	yes	characteristic
1118	#416	C₂²×C₅₃	1	1	yes	characteristic
1119	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
1121	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1123	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1124	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1125	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
1126	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
1127	C₅₃	#61642	1	1	yes	characteristic, direct product factor, Sylow
1128	2₋¹⁺⁴	—	4	2	no	—
1129	2₋¹⁺⁴	—	4	2	no	—
1130	C₂×#41	—	2	1	no	—
1131	C₂×#41	—	2	1	no	—
1132	C₂×#41	—	2	1	no	—
1133	C₂×#41	—	2	1	no	—
1134	C₂×#41	—	2	1	no	—
1135	C₂×#41	—	4	2	no	—
1136	C₂×#41	—	4	2	no	—
1137	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂²×Q₈	—	2	1	no	—
1147	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1149	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1150	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1152	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂²×D₄	—	2	1	no	—
1154	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂³×C₄	—	2	1	no	—
1156	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1157	#137	—	4	2	no	—
1158	#137	—	4	2	no	—
1159	#135	—	4	2	no	—
1160	#135	—	4	2	no	—
1161	#135	—	4	2	no	—
1162	C₂×Q₁₆	—	4	2	no	—
1163	C₂×Q₁₆	—	4	2	no	—
1164	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1165	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1166	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1168	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1169	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂×SD₁₆	—	4	2	no	—
1177	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1186	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1187	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1188	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1189	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1190	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1191	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1192	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1193	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1194	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1195	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1196	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1197	C₄⋊Q₈	—	2	1	no	—
1198	C₄⋊Q₈	—	2	1	no	—
1199	C₄⋊Q₈	—	2	1	no	—
1200	C₄⋊Q₈	—	2	1	no	—
1201	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1202	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1203	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1204	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1205	#126	—	2	1	no	—
1206	#126	—	2	1	no	—
1207	#126	—	2	1	no	—
1208	#126	—	2	1	no	—
1209	#126	—	2	1	no	—
1210	#126	—	2	1	no	—
1211	#126	—	2	1	no	—
1212	#125	—	2	1	no	—
1213	#125	—	2	1	no	—
1214	#125	—	2	1	no	—
1215	#125	—	2	1	no	—
1216	#125	C₂³×C₅₃	1	1	yes	characteristic
1217	#124	—	2	1	no	—
1218	#124	—	2	1	no	—
1219	#124	—	2	1	no	—
1220	#124	—	2	1	no	—
1221	#124	—	2	1	no	—
1222	#124	—	2	1	no	—
1223	#124	—	2	1	no	—
1224	#124	C₂³×C₅₃	1	1	yes	characteristic
1225	#124	C₂³×C₅₃	1	1	yes	characteristic
1226	#124	C₂³×C₅₃	1	1	yes	characteristic
1227	#123	—	2	1	no	—
1228	#123	—	2	1	no	—
1229	#123	—	2	1	no	—
1230	#123	—	2	1	no	—
1231	#123	—	2	1	no	—
1232	#123	—	2	1	no	—
1233	#123	—	2	1	no	—
1234	#123	—	2	1	no	—
1235	#123	—	2	1	no	—
1236	#123	—	2	1	no	—
1237	#123	—	2	1	no	—
1238	#123	—	2	1	no	—
1239	#123	—	2	1	no	—
1240	#123	—	2	1	no	—
1241	#123	—	2	1	no	—
1242	#123	—	2	1	no	—
1243	#123	D₄×C₅₃	1	1	yes	characteristic
1244	#123	D₄×C₅₃	1	1	yes	characteristic
1245	C₂²⋊Q₈	—	2	1	no	—
1246	C₂²⋊Q₈	—	2	1	no	—
1247	C₂²⋊Q₈	—	2	1	no	—
1248	C₂²⋊Q₈	—	2	1	no	—
1249	C₂²⋊Q₈	—	2	1	no	—
1250	C₂²⋊Q₈	—	2	1	no	—
1251	C₂²⋊Q₈	—	2	1	no	—
1252	C₂²⋊Q₈	—	2	1	no	—
1253	C₂²⋊Q₈	—	2	1	no	—
1254	C₂²⋊Q₈	—	2	1	no	—
1255	C₂²⋊Q₈	—	2	1	no	—
1256	C₂²⋊Q₈	—	2	1	no	—
1257	C₂²⋊Q₈	—	2	1	no	—
1258	C₂²⋊Q₈	—	2	1	no	—
1259	C₂²⋊Q₈	—	2	1	no	—
1260	C₂²⋊Q₈	—	2	1	no	—
1261	C₂²⋊Q₈	—	2	1	no	—
1262	C₂²⋊Q₈	—	2	1	no	—
1263	C₂²⋊Q₈	—	2	1	no	—
1264	C₂²⋊Q₈	—	2	1	no	—
1265	C₂²⋊Q₈	—	2	1	no	—
1266	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1267	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1268	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1269	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1270	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1271	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1272	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1273	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1274	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1275	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1276	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1277	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1278	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1279	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1280	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1281	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1282	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1283	#121	—	2	1	no	—
1284	#121	—	2	1	no	—
1285	#121	—	2	1	no	—
1286	#121	—	2	1	no	—
1287	#121	—	2	1	no	—
1288	#121	—	2	1	no	—
1289	#121	—	2	1	no	—
1290	#121	—	2	1	no	—
1291	#121	—	2	1	no	—
1292	#121	—	2	1	no	—
1293	#121	—	2	1	no	—
1294	#121	—	2	1	no	—
1295	#121	—	2	1	no	—
1296	#121	—	2	1	no	—
1297	#121	—	2	1	no	—
1298	#121	—	2	1	no	—
1299	#121	D₄×C₅₃	1	1	yes	characteristic
1300	#121	D₄×C₅₃	1	1	yes	characteristic
1301	#121	C₂³×C₅₃	1	1	yes	characteristic
1302	#121	C₂³×C₅₃	1	1	yes	characteristic
1303	#121	C₂³×C₅₃	1	1	yes	characteristic
1304	#121	C₂³×C₅₃	1	1	yes	characteristic
1305	#121	C₂³×C₅₃	1	1	yes	characteristic
1306	#120	—	2	1	no	—
1307	#120	—	2	1	no	—
1308	#120	—	2	1	no	—
1309	#120	D₄×C₅₃	1	1	yes	characteristic
1310	#120	D₄×C₅₃	1	1	yes	characteristic
1311	C₄×Q₈	—	2	1	no	—
1312	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1313	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1314	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1315	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1316	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1317	C₄×D₄	—	2	1	no	—
1318	C₄×D₄	—	2	1	no	—
1319	C₄×D₄	—	2	1	no	—
1320	C₄×D₄	—	2	1	no	—
1321	C₄×D₄	—	2	1	no	—
1322	C₄×D₄	—	2	1	no	—
1323	C₄×D₄	—	2	1	no	—
1324	C₄×D₄	—	2	1	no	—
1325	C₄×D₄	—	2	1	no	—
1326	C₄×D₄	—	2	1	no	—
1327	C₄×D₄	—	2	1	no	—
1328	C₄×D₄	—	2	1	no	—
1329	C₄×D₄	—	2	1	no	—
1330	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1331	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1332	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1333	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1334	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1335	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1336	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1337	#117	—	2	1	no	—
1338	#117	—	2	1	no	—
1339	#117	C₂³×C₅₃	1	1	yes	characteristic
1340	#117	C₂³×C₅₃	1	1	yes	characteristic
1341	#117	C₂³×C₅₃	1	1	yes	characteristic
1342	C₂×C₄⋊C₄	—	2	1	no	—
1343	C₂×C₄⋊C₄	—	2	1	no	—
1344	C₂×C₄⋊C₄	—	2	1	no	—
1345	C₂×C₄⋊C₄	—	2	1	no	—
1346	C₂×C₄⋊C₄	—	2	1	no	—
1347	C₂×C₄⋊C₄	—	2	1	no	—
1348	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1349	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1350	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1351	C₂×C₂²⋊C₄	—	2	1	no	—
1352	C₂×C₂²⋊C₄	—	2	1	no	—
1353	C₂×C₂²⋊C₄	—	2	1	no	—
1354	C₂×C₂²⋊C₄	—	2	1	no	—
1355	#107	C₂³×C₅₃	1	1	yes	characteristic
1356	#107	C₂³×C₅₃	1	1	yes	characteristic
1357	#107	C₂³×C₅₃	1	1	yes	characteristic
1358	#107	C₂³×C₅₃	1	1	yes	characteristic
1359	#107	C₂³×C₅₃	1	1	yes	characteristic
1360	#107	C₂³×C₅₃	1	1	yes	characteristic
1361	#106	C₂³×C₅₃	1	1	yes	characteristic
1362	#106	C₂³×C₅₃	1	1	yes	characteristic
1363	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1364	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1365	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1366	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1367	#103	C₂³×C₅₃	1	1	yes	characteristic
1368	#103	C₂³×C₅₃	1	1	yes	characteristic
1369	#103	C₂³×C₅₃	1	1	yes	characteristic
1370	#103	C₂³×C₅₃	1	1	yes	characteristic
1371	#103	C₂³×C₅₃	1	1	yes	characteristic
1372	#103	C₂³×C₅₃	1	1	yes	characteristic
1373	#103	C₂³×C₅₃	1	1	yes	characteristic
1374	#103	C₂³×C₅₃	1	1	yes	characteristic
1375	#103	C₂³×C₅₃	1	1	yes	characteristic
1376	#103	C₂³×C₅₃	1	1	yes	characteristic
1377	#103	C₂³×C₅₃	1	1	yes	characteristic
1378	#103	C₂³×C₅₃	1	1	yes	characteristic
1379	#103	C₂³×C₅₃	1	1	yes	characteristic
1380	#103	C₂³×C₅₃	1	1	yes	characteristic
1381	#103	C₂³×C₅₃	1	1	yes	characteristic
1382	#103	C₂³×C₅₃	1	1	yes	characteristic
1383	#103	C₂³×C₅₃	1	1	yes	characteristic
1384	#103	C₂³×C₅₃	1	1	yes	characteristic
1385	#103	C₂³×C₅₃	1	1	yes	characteristic
1386	#103	C₂³×C₅₃	1	1	yes	characteristic
1387	#103	C₂³×C₅₃	1	1	yes	characteristic
1388	#103	C₂³×C₅₃	1	1	yes	characteristic
1389	#102	C₂³×C₅₃	1	1	yes	characteristic
1390	#102	C₂³×C₅₃	1	1	yes	characteristic
1391	#102	C₂³×C₅₃	1	1	yes	characteristic
1392	#102	C₂³×C₅₃	1	1	yes	characteristic
1393	#102	C₂³×C₅₃	1	1	yes	characteristic
1394	#102	C₂³×C₅₃	1	1	yes	characteristic
1395	#102	C₂³×C₅₃	1	1	yes	characteristic
1396	#102	C₂³×C₅₃	1	1	yes	characteristic
1397	#102	C₂³×C₅₃	1	1	yes	characteristic
1398	#102	C₂³×C₅₃	1	1	yes	characteristic
1399	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1400	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1401	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1402	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1403	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1404	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1405	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1406	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1407	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1408	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1409	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1410	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1411	#97	C₂³×C₅₃	1	1	yes	characteristic
1412	#97	C₂³×C₅₃	1	1	yes	characteristic
1413	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1414	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1415	C₂⁴	—	2	1	no	—
1416	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1417	#41	—	2	2	no	—
1418	#41	—	2	2	no	—
1419	#41	—	2	2	no	—
1420	#41	—	2	2	no	—
1421	#41	—	2	2	no	—
1422	#41	—	2	2	no	—
1423	#41	—	4	1	no	—
1424	#41	—	4	1	no	—
1425	#41	—	4	1	no	—
1426	#41	—	4	1	no	—
1427	#41	—	4	1	no	—
1428	#41	—	4	1	no	—
1429	#41	—	4	1	no	—
1430	#41	—	4	1	no	—
1431	#41	—	4	4	no	—
1432	#41	—	4	4	no	—
1433	#41	—	4	1	no	—
1434	#41	—	4	1	no	—
1435	#41	—	4	1	no	—
1436	#41	—	4	1	no	—
1437	#41	—	4	4	no	—
1438	#41	—	4	4	no	—
1439	#41	—	4	4	no	—
1440	C₂×Q₈	—	2	1	no	—
1441	C₂×Q₈	—	2	1	no	—
1442	C₂×Q₈	—	2	1	no	—
1443	C₂×Q₈	—	2	1	no	—
1444	C₂×Q₈	—	2	1	no	—
1445	C₂×Q₈	—	2	1	no	—
1446	C₂×Q₈	—	2	1	no	—
1447	C₂×Q₈	—	2	2	no	—
1448	C₂×Q₈	—	2	2	no	—
1449	C₂×Q₈	—	2	2	no	—
1450	C₂×Q₈	—	4	1	no	—
1451	C₂×Q₈	—	4	1	no	—
1452	C₂×Q₈	—	4	1	no	—
1453	C₂×Q₈	—	4	1	no	—
1454	C₂×Q₈	—	4	1	no	—
1455	C₂×Q₈	—	4	4	no	—
1456	C₂×Q₈	—	4	1	no	—
1457	C₂×Q₈	—	4	1	no	—
1458	C₂×Q₈	—	4	1	no	—
1459	C₂×Q₈	—	4	1	no	—
1460	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1461	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1462	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1463	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1464	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1465	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1466	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1467	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1468	C₂×D₄	—	2	1	no	—
1469	C₂×D₄	—	2	2	no	—
1470	C₂×D₄	—	2	1	no	—
1471	C₂×D₄	—	2	1	no	—
1472	C₂×D₄	—	2	1	no	—
1473	C₂×D₄	—	2	1	no	—
1474	C₂×D₄	—	2	1	no	—
1475	C₂×D₄	—	2	1	no	—
1476	C₂×D₄	—	2	1	no	—
1477	C₂×D₄	—	2	1	no	—
1478	C₂×D₄	—	2	1	no	—
1479	C₂×D₄	—	2	1	no	—
1480	C₂×D₄	—	2	1	no	—
1481	C₂×D₄	—	2	1	no	—
1482	C₂×D₄	—	2	1	no	—
1483	C₂×D₄	—	4	1	no	—
1484	C₂×D₄	—	4	4	no	—
1485	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1486	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1487	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1488	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1489	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1490	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1491	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1492	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1493	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1494	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1495	C₂²×C₄	—	2	1	no	—
1496	C₂²×C₄	—	2	1	no	—
1497	C₂²×C₄	—	2	1	no	—
1498	C₂²×C₄	—	2	1	no	—
1499	C₂²×C₄	—	2	1	no	—
1500	C₂²×C₄	—	2	1	no	—
1501	C₂²×C₄	—	2	1	no	—
1502	C₂²×C₄	—	2	1	no	—
1503	C₂²×C₄	—	2	1	no	—
1504	C₂²×C₄	—	2	1	no	—
1505	C₂²×C₄	—	2	1	no	—
1506	C₂²×C₄	—	2	1	no	—
1507	C₂²×C₄	—	2	1	no	—
1508	C₂²×C₄	—	2	1	no	—
1509	C₂²×C₄	—	2	1	no	—
1510	C₂²×C₄	—	2	1	no	—
1511	C₂²×C₄	—	2	1	no	—
1512	C₂²×C₄	—	2	1	no	—
1513	C₂²×C₄	—	2	1	no	—
1514	C₂²×C₄	—	2	1	no	—
1515	C₂²×C₄	—	4	1	no	—
1516	C₂²×C₄	—	4	1	no	—
1517	C₂²×C₄	—	4	4	no	—
1518	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1519	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1520	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1521	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1522	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1523	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1524	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1525	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1526	Q₁₆	—	2	2	no	—
1527	Q₁₆	—	2	2	no	—
1528	Q₁₆	—	2	2	no	—
1529	Q₁₆	—	4	1	no	—
1530	Q₁₆	—	4	1	no	—
1531	Q₁₆	—	4	1	no	—
1532	Q₁₆	—	4	1	no	—
1533	Q₁₆	—	4	1	no	—
1534	Q₁₆	—	4	1	no	—
1535	Q₁₆	—	4	1	no	—
1536	Q₁₆	—	4	1	no	—
1537	Q₁₆	—	4	1	no	—
1538	SD₁₆	—	2	2	no	—
1539	SD₁₆	—	2	2	no	—
1540	SD₁₆	—	2	2	no	—
1541	SD₁₆	—	2	2	no	—
1542	SD₁₆	—	4	1	no	—
1543	SD₁₆	—	4	1	no	—
1544	SD₁₆	—	4	1	no	—
1545	SD₁₆	—	4	1	no	—
1546	SD₁₆	—	4	1	no	—
1547	SD₁₆	—	4	1	no	—
1548	D₈	—	2	2	no	—
1549	D₈	—	4	1	no	—
1550	M₁₆	—	4	1	no	—
1551	M₁₆	—	4	1	no	—
1552	C₂×C₈	—	4	1	no	—
1553	C₂×C₈	—	4	1	no	—
1554	C₂×C₈	—	4	1	no	—
1555	C₂×C₈	—	4	1	no	—
1556	C₂×C₈	—	4	1	no	—
1557	C₂×C₈	—	4	1	no	—
1558	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1559	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1560	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1561	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1562	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1563	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1564	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1565	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1566	C₄⋊C₄	—	2	1	no	—
1567	C₄⋊C₄	—	2	1	no	—
1568	C₄⋊C₄	—	2	1	no	—
1569	C₄⋊C₄	—	2	1	no	—
1570	C₄⋊C₄	—	2	1	no	—
1571	C₄⋊C₄	—	2	1	no	—
1572	C₄⋊C₄	—	2	1	no	—
1573	C₄⋊C₄	—	2	1	no	—
1574	C₄⋊C₄	—	2	1	no	—
1575	C₄⋊C₄	—	2	1	no	—
1576	C₄⋊C₄	—	2	1	no	—
1577	C₄⋊C₄	—	2	1	no	—
1578	C₄⋊C₄	—	2	1	no	—
1579	C₄⋊C₄	—	2	1	no	—
1580	C₄⋊C₄	—	2	1	no	—
1581	C₄⋊C₄	—	2	1	no	—
1582	C₄⋊C₄	—	2	1	no	—
1583	C₄⋊C₄	—	2	1	no	—
1584	C₄⋊C₄	—	2	1	no	—
1585	C₄⋊C₄	—	2	1	no	—
1586	C₄⋊C₄	—	2	1	no	—
1587	C₄⋊C₄	—	2	1	no	—
1588	C₄⋊C₄	—	2	1	no	—
1589	C₄⋊C₄	—	2	1	no	—
1590	C₄⋊C₄	—	2	1	no	—
1591	C₄⋊C₄	—	2	1	no	—
1592	C₄⋊C₄	—	2	1	no	—
1593	C₄⋊C₄	—	2	1	no	—
1594	C₄⋊C₄	—	2	1	no	—
1595	C₄⋊C₄	—	2	1	no	—
1596	C₄⋊C₄	—	2	1	no	—
1597	C₄⋊C₄	—	2	1	no	—
1598	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1599	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1600	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1601	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1602	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1603	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1604	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1605	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1606	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1607	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1608	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1609	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1610	C₂²⋊C₄	—	2	1	no	—
1611	C₂²⋊C₄	—	2	1	no	—
1612	C₂²⋊C₄	—	2	1	no	—
1613	C₂²⋊C₄	—	2	1	no	—
1614	C₂²⋊C₄	—	2	1	no	—
1615	C₂²⋊C₄	—	2	1	no	—
1616	C₂²⋊C₄	—	2	1	no	—
1617	C₂²⋊C₄	—	2	1	no	—
1618	C₂²⋊C₄	—	2	1	no	—
1619	C₂²⋊C₄	—	2	1	no	—
1620	C₂²⋊C₄	—	2	1	no	—
1621	C₂²⋊C₄	—	2	1	no	—
1622	C₂²⋊C₄	—	2	1	no	—
1623	C₂²⋊C₄	—	2	1	no	—
1624	C₂²⋊C₄	—	2	1	no	—
1625	C₂²⋊C₄	—	2	1	no	—
1626	C₂²⋊C₄	—	2	1	no	—
1627	C₂²⋊C₄	—	2	1	no	—
1628	C₂²⋊C₄	—	2	1	no	—
1629	C₂²⋊C₄	—	2	1	no	—
1630	C₂²⋊C₄	—	2	1	no	—
1631	C₂²⋊C₄	—	2	1	no	—
1632	C₂²⋊C₄	—	2	1	no	—
1633	C₂²⋊C₄	—	2	1	no	—
1634	C₂²⋊C₄	—	2	1	no	—
1635	C₂²⋊C₄	—	2	1	no	—
1636	C₂²⋊C₄	—	2	1	no	—
1637	C₂²⋊C₄	—	2	1	no	—
1638	C₂²⋊C₄	—	2	1	no	—
1639	C₂²⋊C₄	—	2	1	no	—
1640	C₂²⋊C₄	—	2	1	no	—
1641	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1642	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1643	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1644	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1645	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1646	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1647	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1648	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1649	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1650	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1651	C₄²	—	2	1	no	—
1652	C₄²	—	2	1	no	—
1653	C₄²	—	2	1	no	—
1654	C₄²	—	2	1	no	—
1655	C₄²	—	2	1	no	—
1656	C₄²	—	2	1	no	—
1657	C₄²	—	2	1	no	—
1658	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1659	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1660	C₂³	—	2	1	no	—
1661	C₂³	—	2	2	no	—
1662	C₂³	—	2	1	no	—
1663	C₂³	—	2	1	no	—
1664	C₂³	—	4	1	no	—
1665	C₂³	—	4	1	no	—
1666	C₂³	—	4	2	no	—
1667	C₂³	—	4	2	no	—
1668	C₂³	—	8	1	no	—
1669	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1670	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1671	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1672	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1673	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1674	Q₈	—	2	1	no	—
1675	Q₈	—	2	1	no	—
1676	Q₈	—	2	1	no	—
1677	Q₈	—	2	1	no	—
1678	Q₈	—	2	1	no	—
1679	Q₈	—	2	1	no	—
1680	Q₈	—	2	1	no	—
1681	Q₈	—	2	1	no	—
1682	Q₈	—	2	1	no	—
1683	Q₈	—	2	1	no	—
1684	Q₈	—	2	1	no	—
1685	Q₈	—	2	1	no	—
1686	Q₈	—	2	1	no	—
1687	Q₈	—	4	1	no	—
1688	Q₈	—	4	2	no	—
1689	Q₈	—	4	2	no	—
1690	Q₈	—	4	2	no	—
1691	Q₈	—	4	2	no	—
1692	Q₈	—	8	1	no	—
1693	Q₈	—	8	1	no	—
1694	Q₈	—	8	1	no	—
1695	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1696	D₄	—	2	4	no	—
1697	D₄	—	2	2	no	—
1698	D₄	—	2	2	no	—
1699	D₄	—	2	1	no	—
1700	D₄	—	2	1	no	—
1701	D₄	—	2	1	no	—
1702	D₄	—	2	1	no	—
1703	D₄	—	2	1	no	—
1704	D₄	—	4	1	no	—
1705	D₄	—	4	1	no	—
1706	D₄	—	4	1	no	—
1707	D₄	—	4	1	no	—
1708	D₄	—	4	1	no	—
1709	D₄	—	4	2	no	—
1710	D₄	—	4	2	no	—
1711	D₄	—	4	2	no	—
1712	D₄	—	4	2	no	—
1713	D₄	—	4	2	no	—
1714	D₄	—	4	2	no	—
1715	D₄	—	4	2	no	—
1716	D₄	—	8	1	no	—
1717	D₄	—	8	1	no	—
1718	D₄	—	8	1	no	—
1719	D₄	—	8	1	no	—
1720	D₄	—	8	1	no	—
1721	D₄	—	8	1	no	—
1722	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1723	C₂×C₄	—	2	4	no	—
1724	C₂×C₄	—	2	1	no	—
1725	C₂×C₄	—	2	1	no	—
1726	C₂×C₄	—	2	1	no	—
1727	C₂×C₄	—	2	1	no	—
1728	C₂×C₄	—	2	1	no	—
1729	C₂×C₄	—	2	1	no	—
1730	C₂×C₄	—	2	1	no	—
1731	C₂×C₄	—	2	1	no	—
1732	C₂×C₄	—	2	1	no	—
1733	C₂×C₄	—	2	1	no	—
1734	C₂×C₄	—	2	1	no	—
1735	C₂×C₄	—	2	1	no	—
1736	C₂×C₄	—	2	1	no	—
1737	C₂×C₄	—	2	1	no	—
1738	C₂×C₄	—	2	1	no	—
1739	C₂×C₄	—	2	1	no	—
1740	C₂×C₄	—	2	1	no	—
1741	C₂×C₄	—	2	1	no	—
1742	C₂×C₄	—	2	1	no	—
1743	C₂×C₄	—	2	1	no	—
1744	C₂×C₄	—	2	1	no	—
1745	C₂×C₄	—	2	1	no	—
1746	C₂×C₄	—	2	1	no	—
1747	C₂×C₄	—	4	1	no	—
1748	C₂×C₄	—	4	1	no	—
1749	C₂×C₄	—	4	1	no	—
1750	C₂×C₄	—	4	2	no	—
1751	C₂×C₄	—	4	2	no	—
1752	C₂×C₄	—	4	2	no	—
1753	C₂×C₄	—	4	2	no	—
1754	C₂×C₄	—	4	2	no	—
1755	C₂×C₄	—	4	2	no	—
1756	C₂×C₄	—	4	2	no	—
1757	C₂×C₄	—	4	2	no	—
1758	C₂×C₄	—	4	2	no	—
1759	C₂×C₄	—	8	1	no	—
1760	C₂×C₄	—	8	1	no	—
1761	C₂×C₄	—	8	1	no	—
1762	C₂×C₄	—	8	1	no	—
1763	C₂×C₄	—	8	1	no	—
1764	C₂×C₄	—	8	1	no	—
1765	C₂×C₄	—	8	1	no	—
1766	C₂×C₄	—	8	1	no	—
1767	C₂×C₄	—	8	1	no	—
1768	C₂×C₄	—	8	1	no	—
1769	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1770	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1771	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1772	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1773	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1774	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1775	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1776	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1777	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1778	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1779	C₈	—	2	1	no	—
1780	C₈	—	2	1	no	—
1781	C₈	—	2	1	no	—
1782	C₈	—	2	1	no	—
1783	C₈	—	2	1	no	—
1784	C₈	—	2	1	no	—
1785	C₈	—	2	1	no	—
1786	C₈	—	2	1	no	—
1787	C₂²	—	2	1	no	—
1788	C₂²	—	2	1	no	—
1789	C₂²	—	2	1	no	—
1790	C₂²	—	2	2	no	—
1791	C₂²	—	2	1	no	—
1792	C₂²	—	2	1	no	—
1793	C₂²	—	2	1	no	—
1794	C₂²	—	2	1	no	—
1795	C₂²	—	2	1	no	—
1796	C₂²	—	2	1	no	—
1797	C₂²	—	2	1	no	—
1798	C₂²	—	2	1	no	—
1799	C₂²	—	2	1	no	—
1800	C₂²	—	2	1	no	—
1801	C₂²	—	2	1	no	—
1802	C₂²	—	4	1	no	—
1803	C₂²	—	4	1	no	—
1804	C₂²	—	4	1	no	—
1805	C₂²	—	4	1	no	—
1806	C₂²	—	4	1	no	—
1807	C₂²	—	4	1	no	—
1808	C₂²	—	4	1	no	—
1809	C₂²	—	4	1	no	—
1810	C₂²	—	8	2	no	—
1811	C₂²	—	8	4	no	—
1812	C₂²	C₅₃×#578	1	2	yes	—
1813	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1814	C₄	—	2	1	no	—
1815	C₄	—	2	2	no	—
1816	C₄	—	2	1	no	—
1817	C₄	—	2	1	no	—
1818	C₄	—	2	1	no	—
1819	C₄	—	2	1	no	—
1820	C₄	—	2	1	no	—
1821	C₄	—	2	1	no	—
1822	C₄	—	2	1	no	—
1823	C₄	—	2	1	no	—
1824	C₄	—	4	1	no	—
1825	C₄	—	4	1	no	—
1826	C₄	—	4	1	no	—
1827	C₄	—	4	1	no	—
1828	C₄	—	4	1	no	—
1829	C₄	—	4	1	no	—
1830	C₄	—	4	1	no	—
1831	C₄	—	4	1	no	—
1832	C₄	—	4	1	no	—
1833	C₄	—	4	1	no	—
1834	C₄	—	4	1	no	—
1835	C₄	—	4	1	no	—
1836	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1837	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1838	C₂	—	2	2	no	—
1839	C₂	—	4	1	no	—
1840	C₂	—	4	1	no	—
1841	C₂	—	4	1	no	—
1842	C₂	—	4	1	no	—
1843	C₂	—	4	2	no	—
1844	C₂	—	8	1	no	—
1845	C₂	—	8	1	no	—
1846	C₂	C₅₃×#3484	1	1	yes	characteristic
1847	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
1848	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#3541	C₂	semidirect
2. C₅₃×#3489	C₂	semidirect
3. C₅₃×#3320	C₂	semidirect
4. C₅₃×#3315	C₂	semidirect
5. C₅₃×#3314	C₂	semidirect
6. C₅₃×#3313	C₂	semidirect
7. C₅₃×#3302	C₂	semidirect
8. C₅₃×#3300	C₂	semidirect
9. C₅₃×#3299	C₂	semidirect
10. C₅₃×#3297	C₂	semidirect
11. D₄×Q₁₆×C₅₃	C₂	semidirect
12. C₅₃×#3285	C₂	semidirect
13. C₅₃×#3283	C₂	semidirect
14. C₅₃×#3282	C₂	semidirect
15. C₅₃×#3270	C₂	semidirect
16. C₅₃×#3269	C₂	semidirect
17. C₅₃×#3269	C₂	semidirect
18. C₅₃×#3266	C₂	semidirect
19. C₅₃×#3225	C₂	semidirect
20. C₅₃×#3223	C₂	semidirect
21. C₅₃×#3203	C₂	semidirect
22. C₅₃×#3201	C₂	semidirect
23. C₅₃×#3190	C₂	semidirect
24. C₅₃×#3189	C₂	semidirect
25. C₅₃×#3124	C₂	semidirect
26. C₅₃×#3120	C₂	semidirect
27. C₅₃×#3013	C₂	semidirect
28. C₅₃×#3011	C₂	semidirect
29. C₅₃×#3002	C₂	semidirect
30. C₂×C₅₃×#452	C₂	semidirect
31. C₅₃×#2977	C₂	semidirect
34. C₂×#137×C₅₃	C₂²	semidirect
35. C₂×#137×C₅₃	C₂²	semidirect
38. C₂×#135×C₅₃	C₂²	semidirect
40. C₂²×Q₁₆×C₅₃	C₂²	semidirect
44. C₅₃×#556	C₂²	semidirect
49. C₅₃×#552	C₂²	semidirect
56. C₅₃×#548	C₂²	semidirect
61. C₅₃×#547	C₂²	semidirect
67. C₅₃×#542	C₂²	semidirect
68. C₅₃×#541	C₂²	semidirect
74. C₅₃×#537	C₂²	semidirect
77. C₅₃×#536	C₂²	semidirect
85. C₅₃×#497	C₂²	semidirect
86. C₅₃×#497	C₂²	semidirect
87. C₅₃×#495	C₂²	semidirect
88. C₅₃×#494	C₂²	semidirect
89. C₅₃×#491	C₂²	semidirect
90. C₅₃×#489	C₂²	semidirect
91. C₅₃×#488	C₂²	semidirect
92. C₅₃×#487	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
98. C₅₃×#484	C₂²	semidirect
99. C₅₃×#484	C₂²	semidirect
100. C₅₃×#484	C₂²	semidirect
101. C₅₃×#483	C₂²	semidirect
102. C₅₃×#482	C₂²	semidirect
103. C₅₃×#480	C₂²	semidirect
104. C₅₃×#480	C₂²	semidirect
105. C₅₃×#479	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#477	C₂²	semidirect
108. C₅₃×#474	C₂²	semidirect
109. C₅₃×#470	C₂²	semidirect
110. C₅₃×#468	C₂²	semidirect
111. C₅₃×#468	C₂²	semidirect
112. C₅₃×#468	C₂²	semidirect
115. C₅₃×#467	C₂²	semidirect
116. C₅₃×#467	C₂²	semidirect
117. C₅₃×#467	C₂²	semidirect
118. C₅₃×#467	C₂²	semidirect
119. C₅₃×#467	C₂²	semidirect
120. C₅₃×#467	C₂²	semidirect
121. C₅₃×#466	C₂²	semidirect
124. C₅₃×#465	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#464	C₂²	semidirect
127. C₅₃×#464	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#463	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#462	C₂²	semidirect
132. C₅₃×#462	C₂²	semidirect
133. C₅₃×#462	C₂²	semidirect
134. C₅₃×#462	C₂²	semidirect
135. C₅₃×#461	C₂²	semidirect
136. C₅₃×#461	C₂²	semidirect
147. C₅₃×#452	C₂²	semidirect
148. C₅₃×#452	C₂²	semidirect
149. C₅₃×#452	C₂²	semidirect
150. C₅₃×#452	C₂²	semidirect
151. C₅₃×#452	C₂²	semidirect
152. C₅₃×#452	C₂²	semidirect
156. C₅₃×#451	C₂²	semidirect
157. C₅₃×#451	C₂²	semidirect
158. C₅₃×#451	C₂²	semidirect
159. C₅₃×#451	C₂²	semidirect
160. C₅₃×#451	C₂²	semidirect
161. C₅₃×#451	C₂²	semidirect
162. C₅₃×#451	C₂²	semidirect
166. C₅₃×#449	C₂²	semidirect
167. C₅₃×#449	C₂²	semidirect
169. C₅₃×#448	C₂²	semidirect
170. C₅₃×#448	C₂²	semidirect
171. C₅₃×#448	C₂²	semidirect
173. C₅₃×#441	C₂²	semidirect
174. C₅₃×#440	C₂²	semidirect
175. C₅₃×#440	C₂²	semidirect
176. C₅₃×#440	C₂²	semidirect
177. C₄×Q₁₆×C₅₃	C₂²	semidirect
178. C₄×Q₁₆×C₅₃	C₂²	semidirect
179. C₄×SD₁₆×C₅₃	C₂²	semidirect
180. C₄×D₈×C₅₃	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
187. C₈×D₄×C₅₃	C₂²	semidirect
188. C₈×D₄×C₅₃	C₂²	semidirect
189. C₅₃×#433	C₂²	semidirect
190. C₅₃×#433	C₂²	semidirect
191. C₅₃×#419	C₂²	semidirect
192. C₅₃×#417	C₂²	semidirect
195. C₅₃×#416	C₂²	semidirect
197. C₂×#103×C₅₃	C₂²	semidirect
199. C₅₃×#408	C₂²	semidirect
200. C₅₃×#408	C₂²	semidirect
862. #61642	C₅₃	direct (N × H)
914. #3541	C₂×C₅₃	semidirect
915. #3489	C₂×C₅₃	semidirect
916. #3320	C₂×C₅₃	semidirect
917. #3315	C₂×C₅₃	semidirect
918. #3314	C₂×C₅₃	semidirect
919. #3313	C₂×C₅₃	semidirect
920. #3302	C₂×C₅₃	semidirect
921. #3300	C₂×C₅₃	semidirect
922. #3299	C₂×C₅₃	semidirect
923. #3297	C₂×C₅₃	semidirect
924. D₄×Q₁₆	C₂×C₅₃	semidirect
925. #3285	C₂×C₅₃	semidirect
926. #3283	C₂×C₅₃	semidirect
927. #3282	C₂×C₅₃	semidirect
928. #3270	C₂×C₅₃	semidirect
929. #3269	C₂×C₅₃	semidirect
930. #3269	C₂×C₅₃	semidirect
931. #3266	C₂×C₅₃	semidirect
932. #3225	C₂×C₅₃	semidirect
933. #3223	C₂×C₅₃	semidirect
934. #3203	C₂×C₅₃	semidirect
935. #3201	C₂×C₅₃	semidirect
936. #3190	C₂×C₅₃	semidirect
937. #3189	C₂×C₅₃	semidirect
938. #3124	C₂×C₅₃	semidirect
939. #3120	C₂×C₅₃	semidirect
940. #3013	C₂×C₅₃	semidirect
941. #3011	C₂×C₅₃	semidirect
942. #3002	C₂×C₅₃	semidirect
943. C₂×#452	C₂×C₅₃	semidirect
944. #2977	C₂×C₅₃	semidirect
958. C₂×#137	C₂²×C₅₃	semidirect
959. C₂×#137	C₂²×C₅₃	semidirect
962. C₂×#135	C₂²×C₅₃	semidirect
964. C₂²×Q₁₆	C₂²×C₅₃	semidirect
968. #556	C₂²×C₅₃	semidirect
973. #552	C₂²×C₅₃	semidirect
980. #548	C₂²×C₅₃	semidirect
985. #547	C₂²×C₅₃	semidirect
991. #542	C₂²×C₅₃	semidirect
992. #541	C₂²×C₅₃	semidirect
998. #537	C₂²×C₅₃	semidirect
1001. #536	C₂²×C₅₃	semidirect
1009. #497	C₂²×C₅₃	semidirect
1010. #497	C₂²×C₅₃	semidirect
1011. #495	C₂²×C₅₃	semidirect
1012. #494	C₂²×C₅₃	semidirect
1013. #491	C₂²×C₅₃	semidirect
1014. #489	C₂²×C₅₃	semidirect
1015. #488	C₂²×C₅₃	semidirect
1016. #487	C₂²×C₅₃	semidirect
1017. #485	C₂²×C₅₃	semidirect
1018. #485	C₂²×C₅₃	semidirect
1019. #485	C₂²×C₅₃	semidirect
1022. #484	C₂²×C₅₃	semidirect
1023. #484	C₂²×C₅₃	semidirect
1024. #484	C₂²×C₅₃	semidirect
1025. #483	C₂²×C₅₃	semidirect
1026. #482	C₂²×C₅₃	semidirect
1027. #480	C₂²×C₅₃	semidirect
1028. #480	C₂²×C₅₃	semidirect
1029. #479	C₂²×C₅₃	semidirect
1030. #478	C₂²×C₅₃	semidirect
1031. #477	C₂²×C₅₃	semidirect
1032. #474	C₂²×C₅₃	semidirect
1033. #470	C₂²×C₅₃	semidirect
1034. #468	C₂²×C₅₃	semidirect
1035. #468	C₂²×C₅₃	semidirect
1036. #468	C₂²×C₅₃	semidirect
1039. #467	C₂²×C₅₃	semidirect
1040. #467	C₂²×C₅₃	semidirect
1041. #467	C₂²×C₅₃	semidirect
1042. #467	C₂²×C₅₃	semidirect
1043. #467	C₂²×C₅₃	semidirect
1044. #467	C₂²×C₅₃	semidirect
1045. #466	C₂²×C₅₃	semidirect
1048. #465	C₂²×C₅₃	semidirect
1049. #464	C₂²×C₅₃	semidirect
1050. #464	C₂²×C₅₃	semidirect
1051. #464	C₂²×C₅₃	semidirect
1052. #464	C₂²×C₅₃	semidirect
1053. #463	C₂²×C₅₃	semidirect
1054. #463	C₂²×C₅₃	semidirect
1055. #462	C₂²×C₅₃	semidirect
1056. #462	C₂²×C₅₃	semidirect
1057. #462	C₂²×C₅₃	semidirect
1058. #462	C₂²×C₅₃	semidirect
1059. #461	C₂²×C₅₃	semidirect
1060. #461	C₂²×C₅₃	semidirect
1071. #452	C₂²×C₅₃	semidirect
1072. #452	C₂²×C₅₃	semidirect
1073. #452	C₂²×C₅₃	semidirect
1074. #452	C₂²×C₅₃	semidirect
1075. #452	C₂²×C₅₃	semidirect
1076. #452	C₂²×C₅₃	semidirect
1080. #451	C₂²×C₅₃	semidirect
1081. #451	C₂²×C₅₃	semidirect
1082. #451	C₂²×C₅₃	semidirect
1083. #451	C₂²×C₅₃	semidirect
1084. #451	C₂²×C₅₃	semidirect
1085. #451	C₂²×C₅₃	semidirect
1086. #451	C₂²×C₅₃	semidirect
1090. #449	C₂²×C₅₃	semidirect
1091. #449	C₂²×C₅₃	semidirect
1093. #448	C₂²×C₅₃	semidirect
1094. #448	C₂²×C₅₃	semidirect
1095. #448	C₂²×C₅₃	semidirect
1097. #441	C₂²×C₅₃	semidirect
1098. #440	C₂²×C₅₃	semidirect
1099. #440	C₂²×C₅₃	semidirect
1100. #440	C₂²×C₅₃	semidirect
1101. C₄×Q₁₆	C₂²×C₅₃	semidirect
1102. C₄×Q₁₆	C₂²×C₅₃	semidirect
1103. C₄×SD₁₆	C₂²×C₅₃	semidirect
1104. C₄×D₈	C₂²×C₅₃	semidirect
1107. #435	C₂²×C₅₃	semidirect
1108. #435	C₂²×C₅₃	semidirect
1111. C₈×D₄	C₂²×C₅₃	semidirect
1112. C₈×D₄	C₂²×C₅₃	semidirect
1113. #433	C₂²×C₅₃	semidirect
1114. #433	C₂²×C₅₃	semidirect
1115. #419	C₂²×C₅₃	semidirect
1116. #417	C₂²×C₅₃	semidirect
1119. #416	C₂²×C₅₃	semidirect
1121. C₂×#103	C₂²×C₅₃	semidirect
1123. #408	C₂²×C₅₃	semidirect
1124. #408	C₂²×C₅₃	semidirect
1127. C₅₃	#61642	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3541	2
C₅₃×#3489	2
C₅₃×#3320	2
C₅₃×#3315	2
C₅₃×#3314	2
C₅₃×#3313	2
C₅₃×#3302	2
C₅₃×#3300	2
C₅₃×#3299	2
C₅₃×#3297	2
D₄×Q₁₆×C₅₃	2
C₅₃×#3285	2
C₅₃×#3283	2
C₅₃×#3282	2
C₅₃×#3270	2
C₅₃×#3269	2
C₅₃×#3266	2
C₅₃×#3225	2
C₅₃×#3223	2
C₅₃×#3203	2
C₅₃×#3201	2
C₅₃×#3190	2
C₅₃×#3189	2
C₅₃×#3124	2
C₅₃×#3120	2
C₅₃×#3013	2
C₅₃×#3011	2
C₅₃×#3002	2
C₂×C₅₃×#452	2
C₅₃×#2977	2
#61642	53

Subgroups — C53×#61642 #27269154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61642 #27269154