Subgroups — C₅₃×#61612 #27269124

Order 13568.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1832 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×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3320	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3316	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3313	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3312	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3301	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3299	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×#3277	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3269	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×#3202	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3201	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3191	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3127	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3121	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×#3004	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
33	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
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
41	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#563	—	2	1	no	—
43	C₅₃×#562	—	2	1	no	—
44	C₅₃×#556	C₂²	1	1	yes	characteristic
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
50	D₄×Q₈×C₅₃	—	2	1	no	—
51	D₄×Q₈×C₅₃	—	2	1	no	—
52	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
53	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
54	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
55	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
56	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#548	—	2	1	no	—
58	C₅₃×#548	—	2	1	no	—
59	C₅₃×#548	C₂²	1	1	yes	characteristic
60	C₅₃×#548	C₂²	1	1	yes	characteristic
61	C₅₃×#548	C₂²	1	1	yes	characteristic
62	C₅₃×#548	C₂²	1	1	yes	characteristic
63	C₅₃×#548	C₂²	1	1	yes	characteristic
64	C₅₃×#548	C₂²	1	1	yes	characteristic
65	C₅₃×#547	C₂²	1	1	yes	characteristic
66	C₅₃×#542	—	2	1	no	—
67	C₅₃×#542	C₂²	1	1	yes	characteristic
68	C₅₃×#541	C₂²	1	1	yes	characteristic
69	C₅₃×#539	—	2	1	no	—
70	C₅₃×#538	—	2	1	no	—
71	C₅₃×#538	—	2	1	no	—
72	C₅₃×#537	C₂²	1	1	yes	characteristic
73	C₅₃×#536	—	2	1	no	—
74	C₅₃×#536	—	2	1	no	—
75	C₅₃×#536	C₂²	1	1	yes	characteristic
76	C₅₃×#536	C₂²	1	1	yes	characteristic
77	C₅₃×#536	C₂²	1	1	yes	characteristic
78	C₅₃×#525	—	2	1	no	—
79	C₅₃×#525	—	2	1	no	—
80	C₅₃×#525	C₂²	1	1	yes	characteristic
81	C₅₃×#525	C₂²	1	1	yes	characteristic
82	C₅₃×#525	C₂²	1	1	yes	characteristic
83	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
84	C₅₃×#519	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
94	C₅₃×#485	C₂²	1	1	yes	characteristic
95	C₅₃×#485	C₂²	1	1	yes	characteristic
96	C₅₃×#485	C₂²	1	1	yes	characteristic
97	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#484	C₂²	1	1	yes	characteristic
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
103	C₅₃×#482	C₂²	1	1	yes	characteristic
104	C₅₃×#481	C₂²	1	1	yes	characteristic
105	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#470	C₂²	1	1	yes	characteristic
110	C₅₃×#470	C₂²	1	1	yes	characteristic
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#468	C₂²	1	1	yes	characteristic
115	C₅₃×#468	C₂²	1	1	yes	characteristic
116	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#467	C₂²	1	1	yes	characteristic
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
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×#464	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×#462	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, complemented
142	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#451	C₂²	1	1	yes	characteristic
147	C₅₃×#451	C₂²	1	1	yes	characteristic
148	C₅₃×#451	C₂²	1	1	yes	characteristic
149	C₅₃×#451	C₂²	1	1	yes	characteristic
150	C₅₃×#451	C₂²	1	1	yes	characteristic
151	C₅₃×#451	C₂²	1	1	yes	characteristic
152	C₅₃×#451	C₂²	1	1	yes	characteristic
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
157	C₅₃×#451	C₂²	1	1	yes	characteristic
158	C₅₃×#451	C₂²	1	1	yes	characteristic
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×#451	C₂²	1	1	yes	characteristic, complemented
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×#448	C₂²	1	1	yes	characteristic
168	C₅₃×#448	C₂²	1	1	yes	characteristic
169	C₅₃×#448	C₂²	1	1	yes	characteristic
170	C₅₃×#448	C₂²	1	1	yes	characteristic
171	C₅₃×#448	C₂²	1	1	yes	characteristic
172	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#441	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×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#436	C₂²	1	1	yes	characteristic
182	C₅₃×#436	C₂²	1	1	yes	characteristic
183	C₅₃×#435	C₂²	1	1	yes	characteristic
184	C₅₃×#435	C₂²	1	1	yes	characteristic
185	C₅₃×#435	C₂²	1	1	yes	characteristic
186	C₅₃×#435	C₂²	1	1	yes	characteristic
187	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
188	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
189	C₅₃×#433	C₂²	1	1	yes	characteristic
190	C₅₃×#433	C₂²	1	1	yes	characteristic
191	C₅₃×#419	C₂²	1	1	yes	characteristic
192	C₅₃×#419	C₂²	1	1	yes	characteristic
193	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
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
198	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#408	C₂²	1	1	yes	characteristic
200	C₅₃×#408	C₂²	1	1	yes	characteristic
201	C₅₃×#407	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	C₂³	1	1	yes	characteristic
209	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×Q₈×C₅₃	—	2	1	no	—
215	C₂²×Q₈×C₅₃	—	2	1	no	—
216	C₂²×Q₈×C₅₃	—	2	1	no	—
217	C₂²×Q₈×C₅₃	—	2	1	no	—
218	C₂²×Q₈×C₅₃	—	4	2	no	—
219	C₂²×Q₈×C₅₃	—	4	2	no	—
220	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²×Q₈×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	#137×C₅₃	—	4	2	no	—
235	#137×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	—	4	2	no	—
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×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×Q₁₆×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×SD₁₆×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	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×M₁₆×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	—	2	1	no	—
277	C₄⋊Q₈×C₅₃	—	2	1	no	—
278	C₄⋊Q₈×C₅₃	—	2	1	no	—
279	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	#126×C₅₃	—	2	1	no	—
288	#126×C₅₃	—	2	1	no	—
289	#126×C₅₃	—	2	1	no	—
290	#125×C₅₃	—	2	1	no	—
291	#125×C₅₃	—	2	1	no	—
292	#125×C₅₃	—	2	1	no	—
293	#125×C₅₃	—	2	1	no	—
294	#125×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
300	#124×C₅₃	—	2	1	no	—
301	#124×C₅₃	—	2	1	no	—
302	#124×C₅₃	—	2	1	no	—
303	#124×C₅₃	—	2	1	no	—
304	#124×C₅₃	—	2	1	no	—
305	#124×C₅₃	C₂³	1	1	yes	characteristic
306	#124×C₅₃	C₂³	1	1	yes	characteristic
307	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
319	#123×C₅₃	—	2	1	no	—
320	#123×C₅₃	—	2	1	no	—
321	#123×C₅₃	D₄	1	1	yes	characteristic
322	#123×C₅₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
342	C₂²⋊Q₈×C₅₃	—	2	1	no	—
343	C₂²⋊Q₈×C₅₃	—	2	1	no	—
344	C₂²⋊Q₈×C₅₃	—	2	1	no	—
345	C₂²⋊Q₈×C₅₃	—	2	1	no	—
346	C₂²⋊Q₈×C₅₃	—	2	1	no	—
347	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
348	C₂²⋊Q₈×C₅₃	D₄	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	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
359	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
360	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
361	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
362	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
363	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
375	#121×C₅₃	D₄	1	1	yes	characteristic
376	#121×C₅₃	D₄	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	#121×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
388	C₄×Q₈×C₅₃	—	2	1	no	—
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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
393	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
394	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
395	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
406	C₄×D₄×C₅₃	—	2	1	no	—
407	C₄×D₄×C₅₃	—	2	1	no	—
408	C₄×D₄×C₅₃	—	2	1	no	—
409	C₄×D₄×C₅₃	—	2	1	no	—
410	C₄×D₄×C₅₃	—	2	1	no	—
411	C₄×D₄×C₅₃	—	2	1	no	—
412	C₄×D₄×C₅₃	—	2	1	no	—
413	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
414	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
415	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
416	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
417	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
418	#117×C₅₃	—	2	1	no	—
419	#117×C₅₃	—	2	1	no	—
420	#117×C₅₃	—	2	1	no	—
421	#117×C₅₃	C₂³	1	1	yes	characteristic
422	#117×C₅₃	C₂³	1	1	yes	characteristic
423	#117×C₅₃	C₂³	1	1	yes	characteristic
424	#117×C₅₃	C₂³	1	1	yes	characteristic
425	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
427	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
428	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	#106×C₅₃	C₂³	1	1	yes	characteristic
435	#106×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	#103×C₅₃	C₂³	1	1	yes	characteristic
465	#103×C₅₃	C₂³	1	1	yes	characteristic
466	#103×C₅₃	C₂³	1	1	yes	characteristic
467	#103×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	C₂×D₄	1	1	yes	characteristic
491	#41×C₅₃	—	2	2	no	—
492	#41×C₅₃	—	2	2	no	—
493	#41×C₅₃	—	4	1	no	—
494	#41×C₅₃	—	4	1	no	—
495	#41×C₅₃	—	4	1	no	—
496	#41×C₅₃	—	4	1	no	—
497	#41×C₅₃	—	4	1	no	—
498	#41×C₅₃	—	4	1	no	—
499	#41×C₅₃	—	4	4	no	—
500	#41×C₅₃	—	4	4	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	4	no	—
506	C₂×Q₈×C₅₃	—	2	2	no	—
507	C₂×Q₈×C₅₃	—	2	2	no	—
508	C₂×Q₈×C₅₃	—	2	1	no	—
509	C₂×Q₈×C₅₃	—	2	1	no	—
510	C₂×Q₈×C₅₃	—	2	1	no	—
511	C₂×Q₈×C₅₃	—	2	1	no	—
512	C₂×Q₈×C₅₃	—	2	1	no	—
513	C₂×Q₈×C₅₃	—	2	1	no	—
514	C₂×Q₈×C₅₃	—	2	1	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	2	no	—
520	C₂×Q₈×C₅₃	—	2	2	no	—
521	C₂×Q₈×C₅₃	—	2	2	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	1	no	—
531	C₂×Q₈×C₅₃	—	4	1	no	—
532	C₂×Q₈×C₅₃	—	4	1	no	—
533	C₂×Q₈×C₅₃	—	4	4	no	—
534	C₂×Q₈×C₅₃	—	4	1	no	—
535	C₂×Q₈×C₅₃	—	4	1	no	—
536	C₂×Q₈×C₅₃	—	4	1	no	—
537	C₂×Q₈×C₅₃	—	4	1	no	—
538	C₂×Q₈×C₅₃	—	4	4	no	—
539	C₂×Q₈×C₅₃	—	4	4	no	—
540	C₂×Q₈×C₅₃	—	4	4	no	—
541	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
542	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
544	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
545	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
546	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
547	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
548	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
549	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
559	C₂×D₄×C₅₃	—	2	1	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	C₂²×C₄×C₅₃	—	2	1	no	—
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	—	4	1	no	—
588	C₂²×C₄×C₅₃	—	4	1	no	—
589	C₂²×C₄×C₅₃	—	4	4	no	—
590	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
591	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
592	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
593	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
594	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
598	Q₁₆×C₅₃	—	2	2	no	—
599	Q₁₆×C₅₃	—	2	2	no	—
600	Q₁₆×C₅₃	—	2	2	no	—
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	—	4	1	no	—
616	SD₁₆×C₅₃	—	4	1	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	D₈×C₅₃	—	4	1	no	—
622	M₁₆×C₅₃	—	4	1	no	—
623	M₁₆×C₅₃	—	4	1	no	—
624	M₁₆×C₅₃	—	4	1	no	—
625	M₁₆×C₅₃	—	4	1	no	—
626	C₂×C₈×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	C₂⁴	1	1	yes	characteristic
631	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
632	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	—	2	1	no	—
639	C₄⋊C₄×C₅₃	—	2	1	no	—
640	C₄⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
672	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
678	C₄⋊C₄×C₅₃	C₂⁴	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	C₂²⋊C₄×C₅₃	—	2	1	no	—
684	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
714	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
715	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₅₃	—	2	1	no	—
724	C₄²×C₅₃	—	2	1	no	—
725	C₄²×C₅₃	—	2	1	no	—
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	2	no	—
736	C₂³×C₅₃	—	2	1	no	—
737	C₂³×C₅₃	—	2	1	no	—
738	C₂³×C₅₃	—	4	1	no	—
739	C₂³×C₅₃	—	4	1	no	—
740	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
741	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
742	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
743	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
744	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
745	Q₈×C₅₃	—	2	4	no	—
746	Q₈×C₅₃	—	2	1	no	—
747	Q₈×C₅₃	—	2	1	no	—
748	Q₈×C₅₃	—	2	1	no	—
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	—	4	1	no	—
761	Q₈×C₅₃	—	4	2	no	—
762	Q₈×C₅₃	—	4	2	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	—	4	2	no	—
768	Q₈×C₅₃	—	8	1	no	—
769	Q₈×C₅₃	—	8	1	no	—
770	Q₈×C₅₃	—	8	1	no	—
771	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
772	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
773	D₄×C₅₃	—	2	2	no	—
774	D₄×C₅₃	—	2	2	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	—	8	1	no	—
791	D₄×C₅₃	—	8	1	no	—
792	D₄×C₅₃	—	8	1	no	—
793	D₄×C₅₃	—	8	1	no	—
794	C₂×C₄×C₅₃	—	2	4	no	—
795	C₂×C₄×C₅₃	—	2	1	no	—
796	C₂×C₄×C₅₃	—	2	1	no	—
797	C₂×C₄×C₅₃	—	2	1	no	—
798	C₂×C₄×C₅₃	—	2	1	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	—	4	1	no	—
820	C₂×C₄×C₅₃	—	4	1	no	—
821	C₂×C₄×C₅₃	—	4	1	no	—
822	C₂×C₄×C₅₃	—	4	2	no	—
823	C₂×C₄×C₅₃	—	4	2	no	—
824	C₂×C₄×C₅₃	—	4	2	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	—	8	1	no	—
833	C₂×C₄×C₅₃	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
840	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
841	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
842	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
843	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
849	C₈×C₅₃	—	2	1	no	—
850	C₈×C₅₃	—	2	1	no	—
851	C₈×C₅₃	—	2	1	no	—
852	C₈×C₅₃	—	2	1	no	—
853	C₈×C₅₃	—	2	1	no	—
854	C₈×C₅₃	—	2	1	no	—
855	C₈×C₅₃	—	2	1	no	—
856	C₈×C₅₃	—	2	1	no	—
857	#61612	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
858	C₂²×C₅₃	—	2	1	no	—
859	C₂²×C₅₃	—	2	1	no	—
860	C₂²×C₅₃	—	2	1	no	—
861	C₂²×C₅₃	—	2	1	no	—
862	C₂²×C₅₃	—	2	1	no	—
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	1	no	—
871	C₂²×C₅₃	—	2	1	no	—
872	C₂²×C₅₃	—	4	4	no	—
873	C₂²×C₅₃	—	4	1	no	—
874	C₂²×C₅₃	—	4	1	no	—
875	C₂²×C₅₃	—	4	1	no	—
876	C₂²×C₅₃	—	4	1	no	—
877	C₂²×C₅₃	—	4	1	no	—
878	C₂²×C₅₃	—	4	1	no	—
879	C₂²×C₅₃	#578	1	2	yes	—
880	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
881	C₄×C₅₃	—	2	1	no	—
882	C₄×C₅₃	—	2	1	no	—
883	C₄×C₅₃	—	2	2	no	—
884	C₄×C₅₃	—	2	2	no	—
885	C₄×C₅₃	—	2	1	no	—
886	C₄×C₅₃	—	2	1	no	—
887	C₄×C₅₃	—	2	1	no	—
888	C₄×C₅₃	—	2	1	no	—
889	C₄×C₅₃	—	2	1	no	—
890	C₄×C₅₃	—	2	1	no	—
891	C₄×C₅₃	—	2	1	no	—
892	C₄×C₅₃	—	4	1	no	—
893	C₄×C₅₃	—	4	1	no	—
894	C₄×C₅₃	—	4	1	no	—
895	C₄×C₅₃	—	4	1	no	—
896	C₄×C₅₃	—	4	1	no	—
897	C₄×C₅₃	—	4	1	no	—
898	C₄×C₅₃	—	4	1	no	—
899	C₄×C₅₃	—	4	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	C₂×H(5,𝔽₂)	1	1	yes	characteristic
905	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
906	#3541	C₂×C₅₃	1	1	yes	characteristic, complemented
907	#3486	C₂×C₅₃	1	1	yes	characteristic, complemented
908	#3328	C₂×C₅₃	1	1	yes	characteristic, complemented
909	#3327	C₂×C₅₃	1	1	yes	characteristic, complemented
910	#3320	C₂×C₅₃	1	1	yes	characteristic, complemented
911	#3316	C₂×C₅₃	1	1	yes	characteristic, complemented
912	#3313	C₂×C₅₃	1	1	yes	characteristic, complemented
913	#3312	C₂×C₅₃	1	1	yes	characteristic, complemented
914	#3301	C₂×C₅₃	1	1	yes	characteristic, complemented
915	#3299	C₂×C₅₃	1	1	yes	characteristic, complemented
916	D₄×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
917	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
918	#3277	C₂×C₅₃	1	1	yes	characteristic, complemented
919	#3276	C₂×C₅₃	1	1	yes	characteristic, complemented
920	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
921	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
922	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
923	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
924	#3225	C₂×C₅₃	1	1	yes	characteristic, complemented
925	#3223	C₂×C₅₃	1	1	yes	characteristic, complemented
926	#3202	C₂×C₅₃	1	1	yes	characteristic, complemented
927	#3201	C₂×C₅₃	1	1	yes	characteristic, complemented
928	#3196	C₂×C₅₃	1	1	yes	characteristic, complemented
929	#3191	C₂×C₅₃	1	1	yes	characteristic, complemented
930	#3127	C₂×C₅₃	1	1	yes	characteristic, complemented
931	#3121	C₂×C₅₃	1	1	yes	characteristic, complemented
932	#3013	C₂×C₅₃	1	1	yes	characteristic, complemented
933	#3011	C₂×C₅₃	1	1	yes	characteristic, complemented
934	#3004	C₂×C₅₃	1	1	yes	characteristic, complemented
935	C₂×#451	C₂×C₅₃	1	1	yes	characteristic, complemented
936	#2976	C₂×C₅₃	1	1	yes	characteristic, complemented
937	C₂×C₅₃	—	2	2	no	—
938	C₂×C₅₃	—	4	1	no	—
939	C₂×C₅₃	—	4	1	no	—
940	C₂×C₅₃	—	4	1	no	—
941	C₂×C₅₃	—	4	1	no	—
942	C₂×C₅₃	—	8	1	no	—
943	C₂×C₅₃	—	8	1	no	—
944	C₂×C₅₃	#3484	1	1	yes	characteristic
945	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
946	C₂×C₅₃	#3586	1	1	yes	characteristic
947	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
948	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
949	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
950	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
951	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
955	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
956	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#563	—	2	1	no	—
958	#562	—	2	1	no	—
959	#556	C₂²×C₅₃	1	1	yes	characteristic
960	#554	—	2	1	no	—
961	#554	C₂²×C₅₃	1	1	yes	characteristic
962	#553	—	2	1	no	—
963	#553	C₂²×C₅₃	1	1	yes	characteristic
964	#552	C₂²×C₅₃	1	1	yes	characteristic
965	D₄×Q₈	—	2	1	no	—
966	D₄×Q₈	—	2	1	no	—
967	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
968	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
969	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
970	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
971	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
972	#548	—	2	1	no	—
973	#548	—	2	1	no	—
974	#548	C₂²×C₅₃	1	1	yes	characteristic
975	#548	C₂²×C₅₃	1	1	yes	characteristic
976	#548	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	#547	C₂²×C₅₃	1	1	yes	characteristic
981	#542	—	2	1	no	—
982	#542	C₂²×C₅₃	1	1	yes	characteristic
983	#541	C₂²×C₅₃	1	1	yes	characteristic
984	#539	—	2	1	no	—
985	#538	—	2	1	no	—
986	#538	—	2	1	no	—
987	#537	C₂²×C₅₃	1	1	yes	characteristic
988	#536	—	2	1	no	—
989	#536	—	2	1	no	—
990	#536	C₂²×C₅₃	1	1	yes	characteristic
991	#536	C₂²×C₅₃	1	1	yes	characteristic
992	#536	C₂²×C₅₃	1	1	yes	characteristic
993	#525	—	2	1	no	—
994	#525	—	2	1	no	—
995	#525	C₂²×C₅₃	1	1	yes	characteristic
996	#525	C₂²×C₅₃	1	1	yes	characteristic
997	#525	C₂²×C₅₃	1	1	yes	characteristic
998	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
999	#519	C₂²×C₅₃	1	1	yes	characteristic
1000	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#485	C₂²×C₅₃	1	1	yes	characteristic
1009	#485	C₂²×C₅₃	1	1	yes	characteristic
1010	#485	C₂²×C₅₃	1	1	yes	characteristic
1011	#485	C₂²×C₅₃	1	1	yes	characteristic
1012	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#484	C₂²×C₅₃	1	1	yes	characteristic
1015	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#482	C₂²×C₅₃	1	1	yes	characteristic
1018	#482	C₂²×C₅₃	1	1	yes	characteristic
1019	#481	C₂²×C₅₃	1	1	yes	characteristic
1020	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#470	C₂²×C₅₃	1	1	yes	characteristic
1025	#470	C₂²×C₅₃	1	1	yes	characteristic
1026	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#468	C₂²×C₅₃	1	1	yes	characteristic
1030	#468	C₂²×C₅₃	1	1	yes	characteristic
1031	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#467	C₂²×C₅₃	1	1	yes	characteristic
1033	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#466	C₂²×C₅₃	1	1	yes	characteristic
1037	#465	C₂²×C₅₃	1	1	yes	characteristic
1038	#465	C₂²×C₅₃	1	1	yes	characteristic
1039	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#452	C₂²×C₅₃	1	1	yes	characteristic
1053	#452	C₂²×C₅₃	1	1	yes	characteristic
1054	#452	C₂²×C₅₃	1	1	yes	characteristic
1055	#452	C₂²×C₅₃	1	1	yes	characteristic
1056	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#451	C₂²×C₅₃	1	1	yes	characteristic
1062	#451	C₂²×C₅₃	1	1	yes	characteristic
1063	#451	C₂²×C₅₃	1	1	yes	characteristic
1064	#451	C₂²×C₅₃	1	1	yes	characteristic
1065	#451	C₂²×C₅₃	1	1	yes	characteristic
1066	#451	C₂²×C₅₃	1	1	yes	characteristic
1067	#451	C₂²×C₅₃	1	1	yes	characteristic
1068	#451	C₂²×C₅₃	1	1	yes	characteristic
1069	#451	C₂²×C₅₃	1	1	yes	characteristic
1070	#451	C₂²×C₅₃	1	1	yes	characteristic
1071	#451	C₂²×C₅₃	1	1	yes	characteristic
1072	#451	C₂²×C₅₃	1	1	yes	characteristic
1073	#451	C₂²×C₅₃	1	1	yes	characteristic
1074	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#449	C₂²×C₅₃	1	1	yes	characteristic
1080	#449	C₂²×C₅₃	1	1	yes	characteristic
1081	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#448	C₂²×C₅₃	1	1	yes	characteristic
1083	#448	C₂²×C₅₃	1	1	yes	characteristic
1084	#448	C₂²×C₅₃	1	1	yes	characteristic
1085	#448	C₂²×C₅₃	1	1	yes	characteristic
1086	#448	C₂²×C₅₃	1	1	yes	characteristic
1087	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#436	C₂²×C₅₃	1	1	yes	characteristic
1097	#436	C₂²×C₅₃	1	1	yes	characteristic
1098	#435	C₂²×C₅₃	1	1	yes	characteristic
1099	#435	C₂²×C₅₃	1	1	yes	characteristic
1100	#435	C₂²×C₅₃	1	1	yes	characteristic
1101	#435	C₂²×C₅₃	1	1	yes	characteristic
1102	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1103	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1104	#433	C₂²×C₅₃	1	1	yes	characteristic
1105	#433	C₂²×C₅₃	1	1	yes	characteristic
1106	#419	C₂²×C₅₃	1	1	yes	characteristic
1107	#419	C₂²×C₅₃	1	1	yes	characteristic
1108	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1111	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
1112	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
1113	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#408	C₂²×C₅₃	1	1	yes	characteristic
1115	#408	C₂²×C₅₃	1	1	yes	characteristic
1116	#407	C₂²×C₅₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
1118	C₅₃	#61612	1	1	yes	characteristic, direct product factor, Sylow
1119	2₋¹⁺⁴	—	4	2	no	—
1120	2₋¹⁺⁴	—	4	2	no	—
1121	C₂×#41	—	2	1	no	—
1122	C₂×#41	—	2	1	no	—
1123	C₂×#41	—	2	1	no	—
1124	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂²×Q₈	—	2	1	no	—
1131	C₂²×Q₈	—	2	1	no	—
1132	C₂²×Q₈	—	2	1	no	—
1133	C₂²×Q₈	—	2	1	no	—
1134	C₂²×Q₈	—	4	2	no	—
1135	C₂²×Q₈	—	4	2	no	—
1136	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂³×C₄	—	2	1	no	—
1147	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1148	#137	—	4	2	no	—
1149	#137	—	4	2	no	—
1150	#137	—	4	2	no	—
1151	#137	—	4	2	no	—
1152	#135	—	4	2	no	—
1153	C₂×Q₁₆	—	4	2	no	—
1154	C₂×Q₁₆	—	4	2	no	—
1155	C₂×Q₁₆	—	4	2	no	—
1156	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1157	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1158	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1159	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1160	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1161	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1162	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1163	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
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×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1177	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1186	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1187	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1188	C₄⋊Q₈	—	2	1	no	—
1189	C₄⋊Q₈	—	2	1	no	—
1190	C₄⋊Q₈	—	2	1	no	—
1191	C₄⋊Q₈	—	2	1	no	—
1192	C₄⋊Q₈	—	2	1	no	—
1193	C₄⋊Q₈	—	2	1	no	—
1194	C₄⋊Q₈	—	2	1	no	—
1195	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1196	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1197	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1198	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1199	#126	—	2	1	no	—
1200	#126	—	2	1	no	—
1201	#126	—	2	1	no	—
1202	#126	—	2	1	no	—
1203	#126	—	2	1	no	—
1204	#126	—	2	1	no	—
1205	#126	—	2	1	no	—
1206	#125	—	2	1	no	—
1207	#125	—	2	1	no	—
1208	#125	—	2	1	no	—
1209	#125	—	2	1	no	—
1210	#125	C₂³×C₅₃	1	1	yes	characteristic
1211	#124	—	2	1	no	—
1212	#124	—	2	1	no	—
1213	#124	—	2	1	no	—
1214	#124	—	2	1	no	—
1215	#124	—	2	1	no	—
1216	#124	—	2	1	no	—
1217	#124	—	2	1	no	—
1218	#124	—	2	1	no	—
1219	#124	—	2	1	no	—
1220	#124	—	2	1	no	—
1221	#124	C₂³×C₅₃	1	1	yes	characteristic
1222	#124	C₂³×C₅₃	1	1	yes	characteristic
1223	#124	C₂³×C₅₃	1	1	yes	characteristic
1224	#123	—	2	1	no	—
1225	#123	—	2	1	no	—
1226	#123	—	2	1	no	—
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	D₄×C₅₃	1	1	yes	characteristic
1238	#123	D₄×C₅₃	1	1	yes	characteristic
1239	C₂²⋊Q₈	—	2	1	no	—
1240	C₂²⋊Q₈	—	2	1	no	—
1241	C₂²⋊Q₈	—	2	1	no	—
1242	C₂²⋊Q₈	—	2	1	no	—
1243	C₂²⋊Q₈	—	2	1	no	—
1244	C₂²⋊Q₈	—	2	1	no	—
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	D₄×C₅₃	1	1	yes	characteristic
1264	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1265	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1266	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1267	C₂²⋊Q₈	C₂³×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	#121	—	2	1	no	—
1281	#121	—	2	1	no	—
1282	#121	—	2	1	no	—
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	D₄×C₅₃	1	1	yes	characteristic
1292	#121	D₄×C₅₃	1	1	yes	characteristic
1293	#121	C₂³×C₅₃	1	1	yes	characteristic
1294	#121	C₂³×C₅₃	1	1	yes	characteristic
1295	#121	C₂³×C₅₃	1	1	yes	characteristic
1296	#121	C₂³×C₅₃	1	1	yes	characteristic
1297	#121	C₂³×C₅₃	1	1	yes	characteristic
1298	#120	—	2	1	no	—
1299	#120	—	2	1	no	—
1300	#120	D₄×C₅₃	1	1	yes	characteristic
1301	#120	D₄×C₅₃	1	1	yes	characteristic
1302	C₄×Q₈	—	2	1	no	—
1303	C₄×Q₈	—	2	1	no	—
1304	C₄×Q₈	—	2	1	no	—
1305	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1306	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1307	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1308	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1309	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1310	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1311	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1312	C₄×D₄	—	2	1	no	—
1313	C₄×D₄	—	2	1	no	—
1314	C₄×D₄	—	2	1	no	—
1315	C₄×D₄	—	2	1	no	—
1316	C₄×D₄	—	2	1	no	—
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	C₂³×C₅₃	1	1	yes	characteristic
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	#117	—	2	1	no	—
1335	#117	—	2	1	no	—
1336	#117	—	2	1	no	—
1337	#117	C₂³×C₅₃	1	1	yes	characteristic
1338	#117	C₂³×C₅₃	1	1	yes	characteristic
1339	#117	C₂³×C₅₃	1	1	yes	characteristic
1340	#117	C₂³×C₅₃	1	1	yes	characteristic
1341	C₂×C₄⋊C₄	—	2	1	no	—
1342	C₂×C₄⋊C₄	—	2	1	no	—
1343	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1344	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1345	C₂×C₂²⋊C₄	—	2	1	no	—
1346	#107	C₂³×C₅₃	1	1	yes	characteristic
1347	#107	C₂³×C₅₃	1	1	yes	characteristic
1348	#107	C₂³×C₅₃	1	1	yes	characteristic
1349	#107	C₂³×C₅₃	1	1	yes	characteristic
1350	#106	C₂³×C₅₃	1	1	yes	characteristic
1351	#106	C₂³×C₅₃	1	1	yes	characteristic
1352	#106	C₂³×C₅₃	1	1	yes	characteristic
1353	#106	C₂³×C₅₃	1	1	yes	characteristic
1354	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1355	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1356	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1357	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1358	#103	C₂³×C₅₃	1	1	yes	characteristic
1359	#103	C₂³×C₅₃	1	1	yes	characteristic
1360	#103	C₂³×C₅₃	1	1	yes	characteristic
1361	#103	C₂³×C₅₃	1	1	yes	characteristic
1362	#103	C₂³×C₅₃	1	1	yes	characteristic
1363	#103	C₂³×C₅₃	1	1	yes	characteristic
1364	#103	C₂³×C₅₃	1	1	yes	characteristic
1365	#103	C₂³×C₅₃	1	1	yes	characteristic
1366	#103	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	#102	C₂³×C₅₃	1	1	yes	characteristic
1385	#102	C₂³×C₅₃	1	1	yes	characteristic
1386	#102	C₂³×C₅₃	1	1	yes	characteristic
1387	#102	C₂³×C₅₃	1	1	yes	characteristic
1388	#102	C₂³×C₅₃	1	1	yes	characteristic
1389	#102	C₂³×C₅₃	1	1	yes	characteristic
1390	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1391	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1392	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1393	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1394	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1395	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1396	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1397	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1398	C₂²⋊C₈	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	#97	C₂³×C₅₃	1	1	yes	characteristic
1403	#97	C₂³×C₅₃	1	1	yes	characteristic
1404	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1405	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1406	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1407	#41	—	2	2	no	—
1408	#41	—	2	2	no	—
1409	#41	—	4	1	no	—
1410	#41	—	4	1	no	—
1411	#41	—	4	1	no	—
1412	#41	—	4	1	no	—
1413	#41	—	4	1	no	—
1414	#41	—	4	1	no	—
1415	#41	—	4	4	no	—
1416	#41	—	4	4	no	—
1417	#41	—	4	1	no	—
1418	#41	—	4	1	no	—
1419	#41	—	4	1	no	—
1420	#41	—	4	1	no	—
1421	#41	—	4	4	no	—
1422	C₂×Q₈	—	2	2	no	—
1423	C₂×Q₈	—	2	2	no	—
1424	C₂×Q₈	—	2	1	no	—
1425	C₂×Q₈	—	2	1	no	—
1426	C₂×Q₈	—	2	1	no	—
1427	C₂×Q₈	—	2	1	no	—
1428	C₂×Q₈	—	2	1	no	—
1429	C₂×Q₈	—	2	1	no	—
1430	C₂×Q₈	—	2	1	no	—
1431	C₂×Q₈	—	2	1	no	—
1432	C₂×Q₈	—	2	1	no	—
1433	C₂×Q₈	—	2	1	no	—
1434	C₂×Q₈	—	2	1	no	—
1435	C₂×Q₈	—	2	2	no	—
1436	C₂×Q₈	—	2	2	no	—
1437	C₂×Q₈	—	2	2	no	—
1438	C₂×Q₈	—	2	2	no	—
1439	C₂×Q₈	—	2	2	no	—
1440	C₂×Q₈	—	2	2	no	—
1441	C₂×Q₈	—	4	1	no	—
1442	C₂×Q₈	—	4	1	no	—
1443	C₂×Q₈	—	4	1	no	—
1444	C₂×Q₈	—	4	1	no	—
1445	C₂×Q₈	—	4	1	no	—
1446	C₂×Q₈	—	4	1	no	—
1447	C₂×Q₈	—	4	1	no	—
1448	C₂×Q₈	—	4	1	no	—
1449	C₂×Q₈	—	4	4	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	4	no	—
1455	C₂×Q₈	—	4	4	no	—
1456	C₂×Q₈	—	4	4	no	—
1457	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1458	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1459	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1460	C₂×Q₈	C₂⁴×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×D₄	—	2	1	no	—
1467	C₂×D₄	—	2	1	no	—
1468	C₂×D₄	—	2	1	no	—
1469	C₂×D₄	—	2	1	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	C₂×D₄×C₅₃	1	1	yes	characteristic
1477	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1478	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1479	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1480	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1481	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1482	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1483	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1484	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₂²×C₄	—	2	1	no	—
1486	C₂²×C₄	—	2	1	no	—
1487	C₂²×C₄	—	2	1	no	—
1488	C₂²×C₄	—	2	1	no	—
1489	C₂²×C₄	—	2	1	no	—
1490	C₂²×C₄	—	2	1	no	—
1491	C₂²×C₄	—	2	1	no	—
1492	C₂²×C₄	—	2	1	no	—
1493	C₂²×C₄	—	2	1	no	—
1494	C₂²×C₄	—	2	1	no	—
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	—	4	1	no	—
1504	C₂²×C₄	—	4	1	no	—
1505	C₂²×C₄	—	4	4	no	—
1506	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1507	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1508	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1509	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1510	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1511	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1512	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1513	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1514	Q₁₆	—	2	2	no	—
1515	Q₁₆	—	2	2	no	—
1516	Q₁₆	—	2	2	no	—
1517	Q₁₆	—	2	2	no	—
1518	Q₁₆	—	2	2	no	—
1519	Q₁₆	—	2	2	no	—
1520	Q₁₆	—	4	1	no	—
1521	Q₁₆	—	4	1	no	—
1522	Q₁₆	—	4	1	no	—
1523	Q₁₆	—	4	1	no	—
1524	Q₁₆	—	4	1	no	—
1525	Q₁₆	—	4	1	no	—
1526	Q₁₆	—	4	1	no	—
1527	Q₁₆	—	4	1	no	—
1528	Q₁₆	—	4	1	no	—
1529	SD₁₆	—	2	2	no	—
1530	SD₁₆	—	2	2	no	—
1531	SD₁₆	—	4	1	no	—
1532	SD₁₆	—	4	1	no	—
1533	SD₁₆	—	4	1	no	—
1534	SD₁₆	—	4	1	no	—
1535	SD₁₆	—	4	1	no	—
1536	SD₁₆	—	4	1	no	—
1537	D₈	—	4	1	no	—
1538	M₁₆	—	4	1	no	—
1539	M₁₆	—	4	1	no	—
1540	M₁₆	—	4	1	no	—
1541	M₁₆	—	4	1	no	—
1542	C₂×C₈	—	4	1	no	—
1543	C₂×C₈	—	4	1	no	—
1544	C₂×C₈	—	4	1	no	—
1545	C₂×C₈	—	4	1	no	—
1546	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1547	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1548	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1549	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1550	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1551	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1552	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1553	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1554	C₄⋊C₄	—	2	1	no	—
1555	C₄⋊C₄	—	2	1	no	—
1556	C₄⋊C₄	—	2	1	no	—
1557	C₄⋊C₄	—	2	1	no	—
1558	C₄⋊C₄	—	2	1	no	—
1559	C₄⋊C₄	—	2	1	no	—
1560	C₄⋊C₄	—	2	1	no	—
1561	C₄⋊C₄	—	2	1	no	—
1562	C₄⋊C₄	—	2	1	no	—
1563	C₄⋊C₄	—	2	1	no	—
1564	C₄⋊C₄	—	2	1	no	—
1565	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1588	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1589	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1590	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1591	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1592	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1593	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1594	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1595	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1596	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1597	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1598	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1599	C₂²⋊C₄	—	2	1	no	—
1600	C₂²⋊C₄	—	2	1	no	—
1601	C₂²⋊C₄	—	2	1	no	—
1602	C₂²⋊C₄	—	2	1	no	—
1603	C₂²⋊C₄	—	2	1	no	—
1604	C₂²⋊C₄	—	2	1	no	—
1605	C₂²⋊C₄	—	2	1	no	—
1606	C₂²⋊C₄	—	2	1	no	—
1607	C₂²⋊C₄	—	2	1	no	—
1608	C₂²⋊C₄	—	2	1	no	—
1609	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1630	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1631	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1632	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1633	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1634	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1635	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1636	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1637	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1638	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1639	C₄²	—	2	1	no	—
1640	C₄²	—	2	1	no	—
1641	C₄²	—	2	1	no	—
1642	C₄²	—	2	1	no	—
1643	C₄²	—	2	1	no	—
1644	C₄²	—	2	1	no	—
1645	C₄²	—	2	1	no	—
1646	C₄²	—	2	1	no	—
1647	C₄²	—	2	1	no	—
1648	C₄²	—	2	1	no	—
1649	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1650	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1651	C₂³	—	2	2	no	—
1652	C₂³	—	2	1	no	—
1653	C₂³	—	2	1	no	—
1654	C₂³	—	4	1	no	—
1655	C₂³	—	4	1	no	—
1656	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1657	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1658	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1659	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1660	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1661	Q₈	—	2	4	no	—
1662	Q₈	—	2	1	no	—
1663	Q₈	—	2	1	no	—
1664	Q₈	—	2	1	no	—
1665	Q₈	—	2	1	no	—
1666	Q₈	—	2	1	no	—
1667	Q₈	—	2	1	no	—
1668	Q₈	—	2	1	no	—
1669	Q₈	—	2	1	no	—
1670	Q₈	—	2	1	no	—
1671	Q₈	—	2	1	no	—
1672	Q₈	—	2	1	no	—
1673	Q₈	—	2	1	no	—
1674	Q₈	—	2	1	no	—
1675	Q₈	—	2	1	no	—
1676	Q₈	—	4	1	no	—
1677	Q₈	—	4	2	no	—
1678	Q₈	—	4	2	no	—
1679	Q₈	—	4	2	no	—
1680	Q₈	—	4	2	no	—
1681	Q₈	—	4	2	no	—
1682	Q₈	—	4	2	no	—
1683	Q₈	—	4	2	no	—
1684	Q₈	—	8	1	no	—
1685	Q₈	—	8	1	no	—
1686	Q₈	—	8	1	no	—
1687	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1688	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1689	D₄	—	2	2	no	—
1690	D₄	—	2	2	no	—
1691	D₄	—	2	1	no	—
1692	D₄	—	2	1	no	—
1693	D₄	—	2	1	no	—
1694	D₄	—	2	1	no	—
1695	D₄	—	4	1	no	—
1696	D₄	—	4	1	no	—
1697	D₄	—	4	1	no	—
1698	D₄	—	4	1	no	—
1699	D₄	—	4	1	no	—
1700	D₄	—	4	2	no	—
1701	D₄	—	4	2	no	—
1702	D₄	—	4	2	no	—
1703	D₄	—	4	2	no	—
1704	D₄	—	4	2	no	—
1705	D₄	—	4	2	no	—
1706	D₄	—	8	1	no	—
1707	D₄	—	8	1	no	—
1708	D₄	—	8	1	no	—
1709	D₄	—	8	1	no	—
1710	C₂×C₄	—	2	4	no	—
1711	C₂×C₄	—	2	1	no	—
1712	C₂×C₄	—	2	1	no	—
1713	C₂×C₄	—	2	1	no	—
1714	C₂×C₄	—	2	1	no	—
1715	C₂×C₄	—	2	1	no	—
1716	C₂×C₄	—	2	1	no	—
1717	C₂×C₄	—	2	1	no	—
1718	C₂×C₄	—	2	1	no	—
1719	C₂×C₄	—	2	1	no	—
1720	C₂×C₄	—	2	1	no	—
1721	C₂×C₄	—	2	1	no	—
1722	C₂×C₄	—	2	1	no	—
1723	C₂×C₄	—	2	1	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	—	4	1	no	—
1736	C₂×C₄	—	4	1	no	—
1737	C₂×C₄	—	4	1	no	—
1738	C₂×C₄	—	4	2	no	—
1739	C₂×C₄	—	4	2	no	—
1740	C₂×C₄	—	4	2	no	—
1741	C₂×C₄	—	4	2	no	—
1742	C₂×C₄	—	4	2	no	—
1743	C₂×C₄	—	4	2	no	—
1744	C₂×C₄	—	4	2	no	—
1745	C₂×C₄	—	4	2	no	—
1746	C₂×C₄	—	4	2	no	—
1747	C₂×C₄	—	4	2	no	—
1748	C₂×C₄	—	8	1	no	—
1749	C₂×C₄	—	8	1	no	—
1750	C₂×C₄	—	8	1	no	—
1751	C₂×C₄	—	8	1	no	—
1752	C₂×C₄	—	8	1	no	—
1753	C₂×C₄	—	8	1	no	—
1754	C₂×C₄	—	8	1	no	—
1755	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1756	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1757	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1758	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1759	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1760	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1761	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1762	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1763	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1764	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1765	C₈	—	2	1	no	—
1766	C₈	—	2	1	no	—
1767	C₈	—	2	1	no	—
1768	C₈	—	2	1	no	—
1769	C₈	—	2	1	no	—
1770	C₈	—	2	1	no	—
1771	C₈	—	2	1	no	—
1772	C₈	—	2	1	no	—
1773	C₂²	—	2	1	no	—
1774	C₂²	—	2	1	no	—
1775	C₂²	—	2	1	no	—
1776	C₂²	—	2	1	no	—
1777	C₂²	—	2	1	no	—
1778	C₂²	—	2	1	no	—
1779	C₂²	—	2	1	no	—
1780	C₂²	—	2	1	no	—
1781	C₂²	—	2	1	no	—
1782	C₂²	—	2	1	no	—
1783	C₂²	—	2	1	no	—
1784	C₂²	—	2	1	no	—
1785	C₂²	—	2	1	no	—
1786	C₂²	—	2	1	no	—
1787	C₂²	—	4	4	no	—
1788	C₂²	—	4	1	no	—
1789	C₂²	—	4	1	no	—
1790	C₂²	—	4	1	no	—
1791	C₂²	—	4	1	no	—
1792	C₂²	—	4	1	no	—
1793	C₂²	—	4	1	no	—
1794	C₂²	C₅₃×#578	1	2	yes	—
1795	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1796	C₄	—	2	2	no	—
1797	C₄	—	2	2	no	—
1798	C₄	—	2	1	no	—
1799	C₄	—	2	1	no	—
1800	C₄	—	2	1	no	—
1801	C₄	—	2	1	no	—
1802	C₄	—	2	1	no	—
1803	C₄	—	2	1	no	—
1804	C₄	—	2	1	no	—
1805	C₄	—	2	1	no	—
1806	C₄	—	2	1	no	—
1807	C₄	—	4	1	no	—
1808	C₄	—	4	1	no	—
1809	C₄	—	4	1	no	—
1810	C₄	—	4	1	no	—
1811	C₄	—	4	1	no	—
1812	C₄	—	4	1	no	—
1813	C₄	—	4	1	no	—
1814	C₄	—	4	1	no	—
1815	C₄	—	4	1	no	—
1816	C₄	—	4	1	no	—
1817	C₄	—	4	1	no	—
1818	C₄	—	4	1	no	—
1819	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1820	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1821	C₂	—	2	2	no	—
1822	C₂	—	4	1	no	—
1823	C₂	—	4	1	no	—
1824	C₂	—	4	1	no	—
1825	C₂	—	4	1	no	—
1826	C₂	—	8	1	no	—
1827	C₂	—	8	1	no	—
1828	C₂	C₅₃×#3484	1	1	yes	characteristic
1829	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
1830	C₂	C₅₃×#3586	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×#3486	C₂	semidirect
3. C₅₃×#3328	C₂	semidirect
4. C₅₃×#3327	C₂	semidirect
5. C₅₃×#3320	C₂	semidirect
6. C₅₃×#3316	C₂	semidirect
7. C₅₃×#3313	C₂	semidirect
8. C₅₃×#3312	C₂	semidirect
9. C₅₃×#3301	C₂	semidirect
10. C₅₃×#3299	C₂	semidirect
11. D₄×Q₁₆×C₅₃	C₂	semidirect
12. C₅₃×#3285	C₂	semidirect
13. C₅₃×#3277	C₂	semidirect
14. C₅₃×#3276	C₂	semidirect
15. C₅₃×#3270	C₂	semidirect
16. C₅₃×#3270	C₂	semidirect
17. C₅₃×#3270	C₂	semidirect
18. C₅₃×#3269	C₂	semidirect
19. C₅₃×#3225	C₂	semidirect
20. C₅₃×#3223	C₂	semidirect
21. C₅₃×#3202	C₂	semidirect
22. C₅₃×#3201	C₂	semidirect
23. C₅₃×#3196	C₂	semidirect
24. C₅₃×#3191	C₂	semidirect
25. C₅₃×#3127	C₂	semidirect
26. C₅₃×#3121	C₂	semidirect
27. C₅₃×#3013	C₂	semidirect
28. C₅₃×#3011	C₂	semidirect
29. C₅₃×#3004	C₂	semidirect
30. C₂×C₅₃×#451	C₂	semidirect
31. C₅₃×#2976	C₂	semidirect
36. C₂×#137×C₅₃	C₂²	semidirect
37. C₂×#137×C₅₃	C₂²	semidirect
38. C₂×#135×C₅₃	C₂²	semidirect
41. C₂²×Q₁₆×C₅₃	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
97. C₅₃×#485	C₂²	semidirect
98. C₅₃×#485	C₂²	semidirect
100. C₅₃×#484	C₂²	semidirect
101. C₅₃×#483	C₂²	semidirect
105. C₅₃×#479	C₂²	semidirect
106. C₅₃×#479	C₂²	semidirect
107. C₅₃×#477	C₂²	semidirect
108. C₅₃×#475	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
112. C₅₃×#470	C₂²	semidirect
113. C₅₃×#470	C₂²	semidirect
116. C₅₃×#468	C₂²	semidirect
118. C₅₃×#467	C₂²	semidirect
119. C₅₃×#467	C₂²	semidirect
120. C₅₃×#467	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×#464	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×#462	C₂²	semidirect
136. C₅₃×#461	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
142. C₅₃×#452	C₂²	semidirect
143. C₅₃×#452	C₂²	semidirect
144. C₅₃×#452	C₂²	semidirect
145. C₅₃×#452	C₂²	semidirect
159. C₅₃×#451	C₂²	semidirect
160. C₅₃×#451	C₂²	semidirect
161. C₅₃×#451	C₂²	semidirect
162. C₅₃×#451	C₂²	semidirect
163. C₅₃×#451	C₂²	semidirect
166. C₅₃×#449	C₂²	semidirect
172. C₅₃×#448	C₂²	semidirect
173. C₅₃×#441	C₂²	semidirect
174. C₅₃×#441	C₂²	semidirect
175. C₅₃×#441	C₂²	semidirect
176. C₅₃×#440	C₂²	semidirect
177. C₄×Q₁₆×C₅₃	C₂²	semidirect
178. C₄×Q₁₆×C₅₃	C₂²	semidirect
179. C₄×Q₁₆×C₅₃	C₂²	semidirect
180. C₄×SD₁₆×C₅₃	C₂²	semidirect
193. C₅₃×#419	C₂²	semidirect
194. C₅₃×#417	C₂²	semidirect
195. C₅₃×#416	C₂²	semidirect
198. C₂×#103×C₅₃	C₂²	semidirect
857. #61612	C₅₃	direct (N × H)
906. #3541	C₂×C₅₃	semidirect
907. #3486	C₂×C₅₃	semidirect
908. #3328	C₂×C₅₃	semidirect
909. #3327	C₂×C₅₃	semidirect
910. #3320	C₂×C₅₃	semidirect
911. #3316	C₂×C₅₃	semidirect
912. #3313	C₂×C₅₃	semidirect
913. #3312	C₂×C₅₃	semidirect
914. #3301	C₂×C₅₃	semidirect
915. #3299	C₂×C₅₃	semidirect
916. D₄×Q₁₆	C₂×C₅₃	semidirect
917. #3285	C₂×C₅₃	semidirect
918. #3277	C₂×C₅₃	semidirect
919. #3276	C₂×C₅₃	semidirect
920. #3270	C₂×C₅₃	semidirect
921. #3270	C₂×C₅₃	semidirect
922. #3270	C₂×C₅₃	semidirect
923. #3269	C₂×C₅₃	semidirect
924. #3225	C₂×C₅₃	semidirect
925. #3223	C₂×C₅₃	semidirect
926. #3202	C₂×C₅₃	semidirect
927. #3201	C₂×C₅₃	semidirect
928. #3196	C₂×C₅₃	semidirect
929. #3191	C₂×C₅₃	semidirect
930. #3127	C₂×C₅₃	semidirect
931. #3121	C₂×C₅₃	semidirect
932. #3013	C₂×C₅₃	semidirect
933. #3011	C₂×C₅₃	semidirect
934. #3004	C₂×C₅₃	semidirect
935. C₂×#451	C₂×C₅₃	semidirect
936. #2976	C₂×C₅₃	semidirect
951. C₂×#137	C₂²×C₅₃	semidirect
952. C₂×#137	C₂²×C₅₃	semidirect
953. C₂×#135	C₂²×C₅₃	semidirect
956. C₂²×Q₁₆	C₂²×C₅₃	semidirect
1000. #497	C₂²×C₅₃	semidirect
1001. #497	C₂²×C₅₃	semidirect
1002. #495	C₂²×C₅₃	semidirect
1003. #494	C₂²×C₅₃	semidirect
1004. #491	C₂²×C₅₃	semidirect
1005. #489	C₂²×C₅₃	semidirect
1006. #488	C₂²×C₅₃	semidirect
1007. #487	C₂²×C₅₃	semidirect
1012. #485	C₂²×C₅₃	semidirect
1013. #485	C₂²×C₅₃	semidirect
1015. #484	C₂²×C₅₃	semidirect
1016. #483	C₂²×C₅₃	semidirect
1020. #479	C₂²×C₅₃	semidirect
1021. #479	C₂²×C₅₃	semidirect
1022. #477	C₂²×C₅₃	semidirect
1023. #475	C₂²×C₅₃	semidirect
1026. #470	C₂²×C₅₃	semidirect
1027. #470	C₂²×C₅₃	semidirect
1028. #470	C₂²×C₅₃	semidirect
1031. #468	C₂²×C₅₃	semidirect
1033. #467	C₂²×C₅₃	semidirect
1034. #467	C₂²×C₅₃	semidirect
1035. #467	C₂²×C₅₃	semidirect
1039. #465	C₂²×C₅₃	semidirect
1040. #464	C₂²×C₅₃	semidirect
1041. #464	C₂²×C₅₃	semidirect
1042. #464	C₂²×C₅₃	semidirect
1043. #464	C₂²×C₅₃	semidirect
1044. #464	C₂²×C₅₃	semidirect
1045. #463	C₂²×C₅₃	semidirect
1046. #462	C₂²×C₅₃	semidirect
1047. #462	C₂²×C₅₃	semidirect
1048. #462	C₂²×C₅₃	semidirect
1049. #462	C₂²×C₅₃	semidirect
1050. #462	C₂²×C₅₃	semidirect
1051. #461	C₂²×C₅₃	semidirect
1056. #452	C₂²×C₅₃	semidirect
1057. #452	C₂²×C₅₃	semidirect
1058. #452	C₂²×C₅₃	semidirect
1059. #452	C₂²×C₅₃	semidirect
1060. #452	C₂²×C₅₃	semidirect
1074. #451	C₂²×C₅₃	semidirect
1075. #451	C₂²×C₅₃	semidirect
1076. #451	C₂²×C₅₃	semidirect
1077. #451	C₂²×C₅₃	semidirect
1078. #451	C₂²×C₅₃	semidirect
1081. #449	C₂²×C₅₃	semidirect
1087. #448	C₂²×C₅₃	semidirect
1088. #441	C₂²×C₅₃	semidirect
1089. #441	C₂²×C₅₃	semidirect
1090. #441	C₂²×C₅₃	semidirect
1091. #440	C₂²×C₅₃	semidirect
1092. C₄×Q₁₆	C₂²×C₅₃	semidirect
1093. C₄×Q₁₆	C₂²×C₅₃	semidirect
1094. C₄×Q₁₆	C₂²×C₅₃	semidirect
1095. C₄×SD₁₆	C₂²×C₅₃	semidirect
1108. #419	C₂²×C₅₃	semidirect
1109. #417	C₂²×C₅₃	semidirect
1110. #416	C₂²×C₅₃	semidirect
1113. C₂×#103	C₂²×C₅₃	semidirect
1118. C₅₃	#61612	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×#3486	2
C₅₃×#3328	2
C₅₃×#3327	2
C₅₃×#3320	2
C₅₃×#3316	2
C₅₃×#3313	2
C₅₃×#3312	2
C₅₃×#3301	2
C₅₃×#3299	2
D₄×Q₁₆×C₅₃	2
C₅₃×#3285	2
C₅₃×#3277	2
C₅₃×#3276	2
C₅₃×#3270	2
C₅₃×#3269	2
C₅₃×#3225	2
C₅₃×#3223	2
C₅₃×#3202	2
C₅₃×#3201	2
C₅₃×#3196	2
C₅₃×#3191	2
C₅₃×#3127	2
C₅₃×#3121	2
C₅₃×#3013	2
C₅₃×#3011	2
C₅₃×#3004	2
C₂×C₅₃×#451	2
C₅₃×#2976	2
#61612	53

Subgroups — C53×#61612 #27269124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61612 #27269124