Subgroups — C₅₃×#61195 #27268707

Order 13568.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3304	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#556	—	2	1	no	—
32	C₅₃×#556	C₂²	1	2	yes	complemented
33	C₅₃×#555	—	2	1	no	—
34	C₅₃×#555	C₂²	1	2	yes	complemented
35	C₅₃×#553	—	2	1	no	—
36	C₅₃×#553	C₂²	1	2	yes	complemented
37	C₅₃×#552	—	2	1	no	—
38	C₅₃×#552	C₂²	1	2	yes	complemented
39	C₅₃×#550	C₂²	1	2	yes	—
40	C₅₃×#548	C₂²	1	2	yes	—
41	C₅₃×#546	—	2	2	no	—
42	C₅₃×#546	C₂²	1	2	yes	—
43	D₄²×C₅₃	—	2	2	no	—
44	D₄²×C₅₃	C₂²	1	2	yes	—
45	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#538	—	2	2	no	—
47	C₅₃×#537	—	2	1	no	—
48	C₅₃×#537	C₂²	1	1	yes	characteristic
49	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#535	—	2	1	no	—
51	C₅₃×#535	C₂²	1	1	yes	characteristic
52	C₅₃×#529	—	2	2	no	—
53	C₅₃×#525	—	2	1	no	—
54	C₅₃×#525	C₂²	1	1	yes	characteristic
55	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
56	C₂×#121×C₅₃	—	2	1	no	—
57	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
58	C₅₃×#520	C₂²	1	1	yes	characteristic
59	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#490	C₂²	1	2	yes	complemented
63	C₅₃×#489	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#486	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#484	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#479	C₂²	1	2	yes	complemented
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#476	C₂²	1	2	yes	complemented
77	C₅₃×#475	C₂²	1	2	yes	complemented
78	C₅₃×#470	C₂²	1	2	yes	complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#466	C₂²	1	2	yes	complemented
83	C₅₃×#465	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#460	C₂²	1	2	yes	complemented
89	C₅₃×#459	C₂²	1	2	yes	complemented
90	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#452	C₂²	1	2	yes	complemented
93	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#450	C₂²	1	2	yes	complemented
96	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#447	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
106	C₅₃×#436	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
110	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#419	C₂²	1	2	yes	complemented
115	C₅₃×#418	C₂²	1	2	yes	complemented
116	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#418	C₂²	1	2	yes	complemented
118	C₅₃×#417	C₂²	1	1	yes	characteristic
119	C₅₃×#417	C₂²	1	1	yes	characteristic
120	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#417	C₂²	1	2	yes	complemented
123	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	1	yes	characteristic
125	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#416	C₂²	1	2	yes	complemented
127	C₅₃×#416	C₂²	1	2	yes	complemented
128	C₅₃×#416	C₂²	1	2	yes	complemented
129	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
131	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₅₃	—	2	4	no	—
136	H(5,𝔽₂)×C₅₃	—	4	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	4	no	—
141	C₂×#41×C₅₃	—	4	2	no	—
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₅₃	C₂³	1	2	yes	—
146	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₅₃	—	2	1	no	—
151	C₂²×D₄×C₅₃	—	2	1	no	—
152	C₂²×D₄×C₅₃	—	2	1	no	—
153	C₂²×D₄×C₅₃	—	2	2	no	—
154	C₂²×D₄×C₅₃	—	2	2	no	—
155	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
158	C₂³×C₄×C₅₃	—	2	1	no	—
159	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
160	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
161	#135×C₅₃	—	2	4	no	—
162	#135×C₅₃	—	4	2	no	—
163	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
168	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
170	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×D₈×C₅₃	C₂³	1	2	yes	—
173	#131×C₅₃	—	4	2	no	—
174	C₂×M₁₆×C₅₃	—	4	2	no	—
175	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
179	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
182	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
183	C₄⋊Q₈×C₅₃	—	2	1	no	—
184	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
185	#127×C₅₃	—	2	2	no	—
186	#127×C₅₃	C₂³	1	2	yes	—
187	#126×C₅₃	—	2	2	no	—
188	#126×C₅₃	—	2	2	no	—
189	#126×C₅₃	—	2	2	no	—
190	#126×C₅₃	—	2	2	no	—
191	#125×C₅₃	—	2	2	no	—
192	#125×C₅₃	—	2	1	no	—
193	#125×C₅₃	C₂³	1	2	yes	—
194	#124×C₅₃	—	2	2	no	—
195	#124×C₅₃	—	2	2	no	—
196	#124×C₅₃	—	2	2	no	—
197	#124×C₅₃	—	2	2	no	—
198	#124×C₅₃	C₂³	1	2	yes	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	1	no	—
203	#123×C₅₃	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	D₄	1	1	yes	characteristic
230	#121×C₅₃	D₄	1	1	yes	characteristic
231	#121×C₅₃	C₂³	1	2	yes	—
232	#121×C₅₃	C₂³	1	2	yes	—
233	#121×C₅₃	C₂³	1	1	yes	characteristic
234	#121×C₅₃	C₂³	1	1	yes	characteristic
235	#121×C₅₃	C₂³	1	2	yes	—
236	#121×C₅₃	C₂³	1	2	yes	—
237	#120×C₅₃	—	2	2	no	—
238	#120×C₅₃	—	2	2	no	—
239	#120×C₅₃	—	2	2	no	—
240	#120×C₅₃	—	2	1	no	—
241	#120×C₅₃	—	2	2	no	—
242	#120×C₅₃	D₄	1	2	yes	—
243	C₄×Q₈×C₅₃	—	2	2	no	—
244	C₄×Q₈×C₅₃	—	2	1	no	—
245	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	—	2	2	no	—
249	C₄×D₄×C₅₃	—	2	2	no	—
250	C₄×D₄×C₅₃	—	2	2	no	—
251	C₄×D₄×C₅₃	—	2	2	no	—
252	C₄×D₄×C₅₃	—	2	2	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	C₂³	1	2	yes	—
257	C₄×D₄×C₅₃	C₂³	1	2	yes	—
258	C₄×D₄×C₅₃	C₂³	1	2	yes	—
259	C₄×D₄×C₅₃	C₂³	1	2	yes	—
260	#117×C₅₃	—	2	1	no	—
261	#117×C₅₃	—	2	1	no	—
262	#117×C₅₃	—	2	2	no	—
263	#117×C₅₃	—	2	2	no	—
264	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	—	2	1	no	—
266	#117×C₅₃	C₂³	1	2	yes	—
267	#117×C₅₃	C₂³	1	2	yes	—
268	#117×C₅₃	C₂³	1	2	yes	—
269	#117×C₅₃	C₂³	1	1	yes	characteristic
270	#117×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
272	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
277	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
278	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
279	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
280	C₂×C₄²×C₅₃	—	2	1	no	—
281	#107×C₅₃	C₂³	1	2	yes	—
282	#107×C₅₃	C₂³	1	2	yes	—
283	#107×C₅₃	C₂³	1	2	yes	—
284	#106×C₅₃	C₂³	1	2	yes	—
285	#106×C₅₃	C₂³	1	2	yes	—
286	#106×C₅₃	C₂³	1	2	yes	—
287	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
288	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	1	yes	characteristic
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	#102×C₅₃	C₂³	1	1	yes	characteristic
310	#102×C₅₃	C₂³	1	2	yes	—
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	#97×C₅₃	C₂³	1	2	yes	—
320	C₄×C₈×C₅₃	C₂³	1	2	yes	—
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	2	no	—
323	C₂⁴×C₅₃	—	2	1	no	—
324	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	2	no	—
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	2	4	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	2	no	—
334	#41×C₅₃	—	2	2	no	—
335	#41×C₅₃	—	4	4	no	—
336	#41×C₅₃	—	4	1	no	—
337	#41×C₅₃	—	4	1	no	—
338	#41×C₅₃	—	4	2	no	—
339	#41×C₅₃	—	4	4	no	—
340	#41×C₅₃	—	4	4	no	—
341	#41×C₅₃	#41	1	4	yes	—
342	C₂×Q₈×C₅₃	—	2	1	no	—
343	C₂×Q₈×C₅₃	—	2	2	no	—
344	C₂×Q₈×C₅₃	—	2	2	no	—
345	C₂×Q₈×C₅₃	—	4	1	no	—
346	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₅₃	—	2	1	no	—
351	C₂×D₄×C₅₃	—	2	2	no	—
352	C₂×D₄×C₅₃	—	2	4	no	—
353	C₂×D₄×C₅₃	—	2	1	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	1	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	1	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	2	2	no	—
363	C₂×D₄×C₅₃	—	2	2	no	—
364	C₂×D₄×C₅₃	—	2	1	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	2	2	no	—
369	C₂×D₄×C₅₃	—	2	2	no	—
370	C₂×D₄×C₅₃	—	2	2	no	—
371	C₂×D₄×C₅₃	—	4	1	no	—
372	C₂×D₄×C₅₃	—	4	2	no	—
373	C₂×D₄×C₅₃	—	4	4	no	—
374	C₂×D₄×C₅₃	—	4	8	no	—
375	C₂×D₄×C₅₃	—	4	4	no	—
376	C₂×D₄×C₅₃	—	8	4	no	—
377	C₂×D₄×C₅₃	—	8	2	no	—
378	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
381	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
383	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	1	no	—
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	1	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	1	no	—
397	C₂²×C₄×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	—	2	1	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	—	2	2	no	—
401	C₂²×C₄×C₅₃	—	4	4	no	—
402	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	Q₁₆×C₅₃	—	2	2	no	—
410	Q₁₆×C₅₃	—	4	1	no	—
411	SD₁₆×C₅₃	—	2	2	no	—
412	SD₁₆×C₅₃	—	2	2	no	—
413	SD₁₆×C₅₃	—	4	1	no	—
414	SD₁₆×C₅₃	—	4	1	no	—
415	SD₁₆×C₅₃	—	4	2	no	—
416	D₈×C₅₃	—	2	2	no	—
417	D₈×C₅₃	—	4	1	no	—
418	D₈×C₅₃	—	4	2	no	—
419	M₁₆×C₅₃	—	2	2	no	—
420	M₁₆×C₅₃	—	2	2	no	—
421	M₁₆×C₅₃	—	4	2	no	—
422	M₁₆×C₅₃	—	4	2	no	—
423	C₂×C₈×C₅₃	—	2	2	no	—
424	C₂×C₈×C₅₃	—	2	2	no	—
425	C₂×C₈×C₅₃	—	4	2	no	—
426	C₂×C₈×C₅₃	—	4	2	no	—
427	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
429	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	1	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	—	2	1	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	1	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	1	no	—
443	C₄⋊C₄×C₅₃	—	2	2	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	2	no	—
446	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
449	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
450	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	1	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	1	no	—
462	C₂²⋊C₄×C₅₃	—	2	1	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	—	2	2	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	1	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
474	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
477	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
478	C₄²×C₅₃	—	2	2	no	—
479	C₄²×C₅₃	—	2	2	no	—
480	C₄²×C₅₃	—	2	2	no	—
481	C₄²×C₅₃	—	2	2	no	—
482	C₄²×C₅₃	—	2	2	no	—
483	C₄²×C₅₃	—	2	1	no	—
484	C₄²×C₅₃	C₂⁴	1	2	yes	—
485	C₂³×C₅₃	—	2	1	no	—
486	C₂³×C₅₃	—	2	2	no	—
487	C₂³×C₅₃	—	2	1	no	—
488	C₂³×C₅₃	—	2	1	no	—
489	C₂³×C₅₃	—	2	2	no	—
490	C₂³×C₅₃	—	4	1	no	—
491	C₂³×C₅₃	—	4	1	no	—
492	C₂³×C₅₃	—	4	2	no	—
493	C₂³×C₅₃	—	4	4	no	—
494	C₂³×C₅₃	—	4	2	no	—
495	C₂³×C₅₃	—	4	2	no	—
496	C₂³×C₅₃	—	8	1	no	—
497	C₂³×C₅₃	—	8	1	no	—
498	C₂³×C₅₃	—	8	2	no	—
499	C₂³×C₅₃	—	8	1	no	—
500	C₂³×C₅₃	—	8	2	no	—
501	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
502	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
503	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	Q₈×C₅₃	—	2	2	no	—
506	Q₈×C₅₃	—	2	1	no	—
507	Q₈×C₅₃	—	2	1	no	—
508	Q₈×C₅₃	—	2	1	no	—
509	Q₈×C₅₃	—	2	1	no	—
510	Q₈×C₅₃	—	2	1	no	—
511	Q₈×C₅₃	—	4	2	no	—
512	Q₈×C₅₃	—	8	2	no	—
513	Q₈×C₅₃	C₂×#41	1	2	yes	—
514	D₄×C₅₃	—	2	4	no	—
515	D₄×C₅₃	—	2	4	no	—
516	D₄×C₅₃	—	2	2	no	—
517	D₄×C₅₃	—	2	2	no	—
518	D₄×C₅₃	—	2	1	no	—
519	D₄×C₅₃	—	2	1	no	—
520	D₄×C₅₃	—	2	1	no	—
521	D₄×C₅₃	—	2	2	no	—
522	D₄×C₅₃	—	2	1	no	—
523	D₄×C₅₃	—	2	1	no	—
524	D₄×C₅₃	—	4	2	no	—
525	D₄×C₅₃	—	4	2	no	—
526	D₄×C₅₃	—	4	4	no	—
527	D₄×C₅₃	—	4	2	no	—
528	D₄×C₅₃	—	4	4	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	4	2	no	—
531	D₄×C₅₃	—	4	4	no	—
532	D₄×C₅₃	—	4	2	no	—
533	D₄×C₅₃	—	4	2	no	—
534	D₄×C₅₃	—	4	2	no	—
535	D₄×C₅₃	—	8	2	no	—
536	D₄×C₅₃	—	8	2	no	—
537	D₄×C₅₃	—	8	2	no	—
538	D₄×C₅₃	—	8	1	no	—
539	D₄×C₅₃	—	8	1	no	—
540	D₄×C₅₃	—	8	2	no	—
541	D₄×C₅₃	—	8	2	no	—
542	D₄×C₅₃	C₂×#41	1	2	yes	—
543	C₂×C₄×C₅₃	—	2	2	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	2	no	—
546	C₂×C₄×C₅₃	—	2	2	no	—
547	C₂×C₄×C₅₃	—	2	4	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	2	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	2	no	—
556	C₂×C₄×C₅₃	—	2	2	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	2	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	4	2	no	—
562	C₂×C₄×C₅₃	—	4	4	no	—
563	C₂×C₄×C₅₃	—	4	2	no	—
564	C₂×C₄×C₅₃	—	4	2	no	—
565	C₂×C₄×C₅₃	—	4	2	no	—
566	C₂×C₄×C₅₃	—	4	2	no	—
567	C₂×C₄×C₅₃	—	8	2	no	—
568	C₂×C₄×C₅₃	—	8	2	no	—
569	C₂×C₄×C₅₃	—	8	1	no	—
570	C₂×C₄×C₅₃	—	8	1	no	—
571	C₂×C₄×C₅₃	—	8	2	no	—
572	C₂×C₄×C₅₃	—	8	1	no	—
573	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
575	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
576	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
578	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
580	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
581	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
582	C₈×C₅₃	—	2	1	no	—
583	C₈×C₅₃	—	2	1	no	—
584	C₈×C₅₃	—	2	1	no	—
585	C₈×C₅₃	—	2	1	no	—
586	C₈×C₅₃	—	2	2	no	—
587	C₈×C₅₃	—	2	2	no	—
588	#61195	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
589	C₂²×C₅₃	—	2	1	no	—
590	C₂²×C₅₃	—	2	1	no	—
591	C₂²×C₅₃	—	2	1	no	—
592	C₂²×C₅₃	—	2	2	no	—
593	C₂²×C₅₃	—	2	1	no	—
594	C₂²×C₅₃	—	2	2	no	—
595	C₂²×C₅₃	—	2	1	no	—
596	C₂²×C₅₃	—	2	1	no	—
597	C₂²×C₅₃	—	2	1	no	—
598	C₂²×C₅₃	—	2	1	no	—
599	C₂²×C₅₃	—	2	2	no	—
600	C₂²×C₅₃	—	2	2	no	—
601	C₂²×C₅₃	—	4	1	no	—
602	C₂²×C₅₃	—	4	1	no	—
603	C₂²×C₅₃	—	4	1	no	—
604	C₂²×C₅₃	—	4	1	no	—
605	C₂²×C₅₃	—	4	2	no	—
606	C₂²×C₅₃	—	4	1	no	—
607	C₂²×C₅₃	—	4	2	no	—
608	C₂²×C₅₃	—	4	1	no	—
609	C₂²×C₅₃	—	4	1	no	—
610	C₂²×C₅₃	—	4	2	no	—
611	C₂²×C₅₃	—	4	1	no	—
612	C₂²×C₅₃	—	8	2	no	—
613	C₂²×C₅₃	—	8	4	no	—
614	C₂²×C₅₃	—	16	2	no	—
615	C₂²×C₅₃	—	16	4	no	—
616	C₂²×C₅₃	#546	1	2	yes	—
617	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₅₃	—	2	2	no	—
619	C₄×C₅₃	—	2	2	no	—
620	C₄×C₅₃	—	2	1	no	—
621	C₄×C₅₃	—	2	1	no	—
622	C₄×C₅₃	—	2	2	no	—
623	C₄×C₅₃	—	2	2	no	—
624	C₄×C₅₃	—	4	2	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	2	no	—
627	C₄×C₅₃	—	4	2	no	—
628	C₄×C₅₃	—	4	1	no	—
629	C₄×C₅₃	—	4	1	no	—
630	C₄×C₅₃	—	4	1	no	—
631	C₄×C₅₃	#546	1	2	yes	—
632	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
633	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
634	#3493	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3488	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3327	C₂×C₅₃	1	2	yes	complemented
637	#3325	C₂×C₅₃	1	2	yes	complemented
638	#3321	C₂×C₅₃	1	2	yes	complemented
639	#3311	C₂×C₅₃	1	2	yes	complemented
640	#3310	C₂×C₅₃	1	2	yes	complemented
641	#3309	C₂×C₅₃	1	2	yes	complemented
642	#3304	C₂×C₅₃	1	2	yes	complemented
643	#3297	C₂×C₅₃	1	2	yes	complemented
644	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
645	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
646	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#3060	C₂×C₅₃	1	1	yes	characteristic, complemented
649	#3055	C₂×C₅₃	1	1	yes	characteristic, complemented
650	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
653	#2951	C₂×C₅₃	1	1	yes	characteristic, complemented
654	#2933	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
656	#2896	C₂×C₅₃	1	1	yes	characteristic, complemented
657	C₂×C₅₃	—	2	2	no	—
658	C₂×C₅₃	—	4	1	no	—
659	C₂×C₅₃	—	4	1	no	—
660	C₂×C₅₃	—	4	2	no	—
661	C₂×C₅₃	—	4	2	no	—
662	C₂×C₅₃	—	8	1	no	—
663	C₂×C₅₃	—	8	1	no	—
664	C₂×C₅₃	—	8	2	no	—
665	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
666	C₂×C₅₃	#3584	1	1	yes	characteristic
667	C₂×C₅₃	#3585	1	1	yes	characteristic
668	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
669	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
670	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
672	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	#556	—	2	1	no	—
676	#556	C₂²×C₅₃	1	2	yes	complemented
677	#555	—	2	1	no	—
678	#555	C₂²×C₅₃	1	2	yes	complemented
679	#553	—	2	1	no	—
680	#553	C₂²×C₅₃	1	2	yes	complemented
681	#552	—	2	1	no	—
682	#552	C₂²×C₅₃	1	2	yes	complemented
683	#550	C₂²×C₅₃	1	2	yes	—
684	#548	C₂²×C₅₃	1	2	yes	—
685	#546	—	2	2	no	—
686	#546	C₂²×C₅₃	1	2	yes	—
687	D₄²	—	2	2	no	—
688	D₄²	C₂²×C₅₃	1	2	yes	—
689	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#538	—	2	2	no	—
691	#537	—	2	1	no	—
692	#537	C₂²×C₅₃	1	1	yes	characteristic
693	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#535	—	2	1	no	—
695	#535	C₂²×C₅₃	1	1	yes	characteristic
696	#529	—	2	2	no	—
697	#525	—	2	1	no	—
698	#525	C₂²×C₅₃	1	1	yes	characteristic
699	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	C₂×#121	—	2	1	no	—
701	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
702	#520	C₂²×C₅₃	1	1	yes	characteristic
703	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#490	C₂²×C₅₃	1	2	yes	complemented
707	#489	C₂²×C₅₃	1	2	yes	complemented
708	#488	C₂²×C₅₃	1	2	yes	complemented
709	#486	C₂²×C₅₃	1	2	yes	complemented
710	#485	C₂²×C₅₃	1	2	yes	complemented
711	#484	C₂²×C₅₃	1	2	yes	complemented
712	#482	C₂²×C₅₃	1	2	yes	complemented
713	#482	C₂²×C₅₃	1	2	yes	complemented
714	#482	C₂²×C₅₃	1	2	yes	complemented
715	#482	C₂²×C₅₃	1	2	yes	complemented
716	#482	C₂²×C₅₃	1	2	yes	complemented
717	#480	C₂²×C₅₃	1	2	yes	complemented
718	#479	C₂²×C₅₃	1	2	yes	complemented
719	#478	C₂²×C₅₃	1	2	yes	complemented
720	#476	C₂²×C₅₃	1	2	yes	complemented
721	#475	C₂²×C₅₃	1	2	yes	complemented
722	#470	C₂²×C₅₃	1	2	yes	complemented
723	#469	C₂²×C₅₃	1	2	yes	complemented
724	#469	C₂²×C₅₃	1	2	yes	complemented
725	#468	C₂²×C₅₃	1	2	yes	complemented
726	#466	C₂²×C₅₃	1	2	yes	complemented
727	#465	C₂²×C₅₃	1	2	yes	complemented
728	#465	C₂²×C₅₃	1	2	yes	complemented
729	#465	C₂²×C₅₃	1	2	yes	complemented
730	#464	C₂²×C₅₃	1	2	yes	complemented
731	#463	C₂²×C₅₃	1	2	yes	complemented
732	#460	C₂²×C₅₃	1	2	yes	complemented
733	#459	C₂²×C₅₃	1	2	yes	complemented
734	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	#452	C₂²×C₅₃	1	2	yes	complemented
737	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#450	C₂²×C₅₃	1	2	yes	complemented
740	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#449	C₂²×C₅₃	1	2	yes	complemented
743	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	#447	C₂²×C₅₃	1	2	yes	complemented
746	#440	C₂²×C₅₃	1	2	yes	complemented
747	#440	C₂²×C₅₃	1	2	yes	complemented
748	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
749	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
750	#436	C₂²×C₅₃	1	2	yes	complemented
751	#435	C₂²×C₅₃	1	2	yes	complemented
752	#435	C₂²×C₅₃	1	2	yes	complemented
753	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
754	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
755	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	#419	C₂²×C₅₃	1	2	yes	complemented
759	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	#418	C₂²×C₅₃	1	2	yes	complemented
761	#418	C₂²×C₅₃	1	2	yes	complemented
762	#417	C₂²×C₅₃	1	1	yes	characteristic
763	#417	C₂²×C₅₃	1	1	yes	characteristic
764	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	#417	C₂²×C₅₃	1	2	yes	complemented
767	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#416	C₂²×C₅₃	1	1	yes	characteristic
769	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
770	#416	C₂²×C₅₃	1	2	yes	complemented
771	#416	C₂²×C₅₃	1	2	yes	complemented
772	#416	C₂²×C₅₃	1	2	yes	complemented
773	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
774	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
775	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
776	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
777	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
778	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
779	C₅₃	#61195	1	1	yes	characteristic, direct product factor, Sylow
780	H(5,𝔽₂)	—	2	4	no	—
781	H(5,𝔽₂)	—	4	2	no	—
782	C₂×#41	—	2	1	no	—
783	C₂×#41	—	2	1	no	—
784	C₂×#41	—	2	1	no	—
785	C₂×#41	—	2	4	no	—
786	C₂×#41	—	4	2	no	—
787	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
789	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
790	C₂×#41	C₂³×C₅₃	1	2	yes	—
791	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
792	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
793	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
794	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
795	C₂²×D₄	—	2	1	no	—
796	C₂²×D₄	—	2	1	no	—
797	C₂²×D₄	—	2	1	no	—
798	C₂²×D₄	—	2	2	no	—
799	C₂²×D₄	—	2	2	no	—
800	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
802	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
803	C₂³×C₄	—	2	1	no	—
804	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
805	AGL(1,ℤ/8)	—	4	2	no	—
806	#135	—	2	4	no	—
807	#135	—	4	2	no	—
808	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
809	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
810	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
811	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
812	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
813	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
815	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₂×D₈	C₂³×C₅₃	1	2	yes	—
818	#131	—	4	2	no	—
819	C₂×M₁₆	—	4	2	no	—
820	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
821	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
822	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
823	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
824	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
825	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
826	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
827	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
828	C₄⋊Q₈	—	2	1	no	—
829	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
830	#127	—	2	2	no	—
831	#127	C₂³×C₅₃	1	2	yes	—
832	#126	—	2	2	no	—
833	#126	—	2	2	no	—
834	#126	—	2	2	no	—
835	#126	—	2	2	no	—
836	#125	—	2	2	no	—
837	#125	—	2	1	no	—
838	#125	C₂³×C₅₃	1	2	yes	—
839	#124	—	2	2	no	—
840	#124	—	2	2	no	—
841	#124	—	2	2	no	—
842	#124	—	2	2	no	—
843	#124	C₂³×C₅₃	1	2	yes	—
844	#123	—	2	2	no	—
845	#123	—	2	1	no	—
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	D₄×C₅₃	1	2	yes	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	2	no	—
852	C₂²⋊Q₈	—	2	2	no	—
853	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
854	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
858	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
859	#121	—	2	1	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	1	no	—
864	#121	—	2	2	no	—
865	#121	—	2	2	no	—
866	#121	—	2	1	no	—
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	2	no	—
871	#121	—	2	2	no	—
872	#121	—	2	2	no	—
873	#121	—	2	2	no	—
874	#121	D₄×C₅₃	1	1	yes	characteristic
875	#121	D₄×C₅₃	1	1	yes	characteristic
876	#121	C₂³×C₅₃	1	2	yes	—
877	#121	C₂³×C₅₃	1	2	yes	—
878	#121	C₂³×C₅₃	1	1	yes	characteristic
879	#121	C₂³×C₅₃	1	1	yes	characteristic
880	#121	C₂³×C₅₃	1	2	yes	—
881	#121	C₂³×C₅₃	1	2	yes	—
882	#120	—	2	1	no	—
883	#120	—	2	2	no	—
884	#120	—	2	2	no	—
885	#120	—	2	2	no	—
886	#120	—	2	2	no	—
887	#120	D₄×C₅₃	1	2	yes	—
888	C₄×Q₈	—	2	1	no	—
889	C₄×Q₈	—	2	2	no	—
890	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
891	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
892	C₄×D₄	—	2	2	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	2	no	—
897	C₄×D₄	—	2	2	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	—	2	2	no	—
901	C₄×D₄	C₂³×C₅₃	1	2	yes	—
902	C₄×D₄	C₂³×C₅₃	1	2	yes	—
903	C₄×D₄	C₂³×C₅₃	1	2	yes	—
904	C₄×D₄	C₂³×C₅₃	1	2	yes	—
905	#117	—	2	1	no	—
906	#117	—	2	1	no	—
907	#117	—	2	1	no	—
908	#117	—	2	1	no	—
909	#117	—	2	2	no	—
910	#117	—	2	2	no	—
911	#117	C₂³×C₅₃	1	2	yes	—
912	#117	C₂³×C₅₃	1	2	yes	—
913	#117	C₂³×C₅₃	1	1	yes	characteristic
914	#117	C₂³×C₅₃	1	2	yes	—
915	#117	C₂³×C₅₃	1	1	yes	characteristic
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	—	2	1	no	—
918	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
921	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
922	C₂×C₂²⋊C₄	—	2	1	no	—
923	C₂×C₂²⋊C₄	—	2	1	no	—
924	C₂×C₂²⋊C₄	—	2	2	no	—
925	C₂×C₄²	—	2	1	no	—
926	#107	C₂³×C₅₃	1	2	yes	—
927	#107	C₂³×C₅₃	1	2	yes	—
928	#107	C₂³×C₅₃	1	2	yes	—
929	#106	C₂³×C₅₃	1	2	yes	—
930	#106	C₂³×C₅₃	1	2	yes	—
931	#106	C₂³×C₅₃	1	2	yes	—
932	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
933	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
934	#103	C₂³×C₅₃	1	1	yes	characteristic
935	#103	C₂³×C₅₃	1	1	yes	characteristic
936	#103	C₂³×C₅₃	1	2	yes	—
937	#103	C₂³×C₅₃	1	2	yes	—
938	#103	C₂³×C₅₃	1	2	yes	—
939	#103	C₂³×C₅₃	1	2	yes	—
940	#103	C₂³×C₅₃	1	1	yes	characteristic
941	#103	C₂³×C₅₃	1	1	yes	characteristic
942	#103	C₂³×C₅₃	1	2	yes	—
943	#102	C₂³×C₅₃	1	1	yes	characteristic
944	#102	C₂³×C₅₃	1	2	yes	—
945	#102	C₂³×C₅₃	1	2	yes	—
946	#102	C₂³×C₅₃	1	2	yes	—
947	#102	C₂³×C₅₃	1	2	yes	—
948	#102	C₂³×C₅₃	1	2	yes	—
949	#102	C₂³×C₅₃	1	2	yes	—
950	#102	C₂³×C₅₃	1	1	yes	characteristic
951	#102	C₂³×C₅₃	1	2	yes	—
952	#102	C₂³×C₅₃	1	2	yes	—
953	#102	C₂³×C₅₃	1	2	yes	—
954	#102	C₂³×C₅₃	1	2	yes	—
955	#102	C₂³×C₅₃	1	1	yes	characteristic
956	#102	C₂³×C₅₃	1	1	yes	characteristic
957	#102	C₂³×C₅₃	1	2	yes	—
958	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
959	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
964	#97	C₂³×C₅₃	1	2	yes	—
965	C₄×C₈	C₂³×C₅₃	1	2	yes	—
966	C₂⁴	—	2	1	no	—
967	C₂⁴	—	2	2	no	—
968	C₂⁴	—	2	1	no	—
969	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
970	#41	—	2	2	no	—
971	#41	—	2	2	no	—
972	#41	—	2	2	no	—
973	#41	—	2	2	no	—
974	#41	—	2	4	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	2	2	no	—
979	#41	—	2	2	no	—
980	#41	—	4	4	no	—
981	#41	—	4	1	no	—
982	#41	—	4	1	no	—
983	#41	—	4	2	no	—
984	#41	—	4	4	no	—
985	#41	—	4	4	no	—
986	#41	#41×C₅₃	1	4	yes	—
987	C₂×Q₈	—	2	1	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	2	2	no	—
990	C₂×Q₈	—	4	1	no	—
991	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
992	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
993	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
994	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	4	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	4	1	no	—
1017	C₂×D₄	—	4	2	no	—
1018	C₂×D₄	—	4	4	no	—
1019	C₂×D₄	—	4	8	no	—
1020	C₂×D₄	—	4	4	no	—
1021	C₂×D₄	—	8	4	no	—
1022	C₂×D₄	—	8	2	no	—
1023	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1024	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1025	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1027	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1028	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1029	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₂²×C₄	—	2	1	no	—
1032	C₂²×C₄	—	2	2	no	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	4	4	no	—
1047	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1048	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1049	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1051	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1054	Q₁₆	—	2	2	no	—
1055	Q₁₆	—	4	1	no	—
1056	SD₁₆	—	2	2	no	—
1057	SD₁₆	—	2	2	no	—
1058	SD₁₆	—	4	1	no	—
1059	SD₁₆	—	4	1	no	—
1060	SD₁₆	—	4	2	no	—
1061	D₈	—	2	2	no	—
1062	D₈	—	4	1	no	—
1063	D₈	—	4	2	no	—
1064	M₁₆	—	2	2	no	—
1065	M₁₆	—	2	2	no	—
1066	M₁₆	—	4	2	no	—
1067	M₁₆	—	4	2	no	—
1068	C₂×C₈	—	2	2	no	—
1069	C₂×C₈	—	2	2	no	—
1070	C₂×C₈	—	4	2	no	—
1071	C₂×C₈	—	4	2	no	—
1072	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1073	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1074	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1075	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1076	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1077	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1092	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1094	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1096	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1098	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1119	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1120	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1121	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1123	C₄²	—	2	2	no	—
1124	C₄²	—	2	2	no	—
1125	C₄²	—	2	2	no	—
1126	C₄²	—	2	2	no	—
1127	C₄²	—	2	2	no	—
1128	C₄²	—	2	1	no	—
1129	C₄²	C₂⁴×C₅₃	1	2	yes	—
1130	C₂³	—	2	1	no	—
1131	C₂³	—	2	2	no	—
1132	C₂³	—	2	1	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	4	1	no	—
1136	C₂³	—	4	1	no	—
1137	C₂³	—	4	2	no	—
1138	C₂³	—	4	4	no	—
1139	C₂³	—	4	2	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	8	1	no	—
1142	C₂³	—	8	1	no	—
1143	C₂³	—	8	2	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	2	no	—
1146	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1147	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1148	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1149	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1150	Q₈	—	2	2	no	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	1	no	—
1153	Q₈	—	2	1	no	—
1154	Q₈	—	2	1	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	4	2	no	—
1157	Q₈	—	8	2	no	—
1158	Q₈	C₂×#41×C₅₃	1	2	yes	—
1159	D₄	—	2	4	no	—
1160	D₄	—	2	4	no	—
1161	D₄	—	2	2	no	—
1162	D₄	—	2	1	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	1	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	4	2	no	—
1170	D₄	—	4	2	no	—
1171	D₄	—	4	4	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	4	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	8	2	no	—
1181	D₄	—	8	2	no	—
1182	D₄	—	8	2	no	—
1183	D₄	—	8	1	no	—
1184	D₄	—	8	1	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	C₂×#41×C₅₃	1	2	yes	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	4	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	4	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	8	2	no	—
1213	C₂×C₄	—	8	2	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	—	8	1	no	—
1216	C₂×C₄	—	8	2	no	—
1217	C₂×C₄	—	8	1	no	—
1218	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1219	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1222	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1223	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1224	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1225	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1226	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1227	C₈	—	2	1	no	—
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	1	no	—
1231	C₈	—	2	2	no	—
1232	C₈	—	2	2	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	2	2	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	2	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	8	2	no	—
1257	C₂²	—	8	4	no	—
1258	C₂²	—	16	2	no	—
1259	C₂²	—	16	4	no	—
1260	C₂²	C₅₃×#546	1	2	yes	—
1261	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	2	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	2	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	1	no	—
1275	C₄	C₅₃×#546	1	2	yes	—
1276	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1277	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1278	C₂	—	2	2	no	—
1279	C₂	—	4	1	no	—
1280	C₂	—	4	1	no	—
1281	C₂	—	4	2	no	—
1282	C₂	—	4	2	no	—
1283	C₂	—	8	1	no	—
1284	C₂	—	8	2	no	—
1285	C₂	—	8	1	no	—
1286	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1287	C₂	C₅₃×#3584	1	1	yes	characteristic
1288	C₂	C₅₃×#3585	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×#3493	C₂	semidirect
2. C₅₃×#3488	C₂	semidirect
3. C₅₃×#3327	C₂	semidirect
4. C₅₃×#3325	C₂	semidirect
5. C₅₃×#3321	C₂	semidirect
6. C₅₃×#3311	C₂	semidirect
7. C₅₃×#3310	C₂	semidirect
8. C₅₃×#3309	C₂	semidirect
9. C₅₃×#3304	C₂	semidirect
10. C₅₃×#3297	C₂	semidirect
11. C₅₃×#3136	C₂	semidirect
12. C₅₃×#3098	C₂	semidirect
13. C₂×C₅₃×#482	C₂	semidirect
14. C₅₃×#3084	C₂	semidirect
15. C₅₃×#3060	C₂	semidirect
16. C₅₃×#3055	C₂	semidirect
17. C₅₃×#3045	C₂	semidirect
18. C₅₃×#3012	C₂	semidirect
19. C₅₃×#3002	C₂	semidirect
20. C₅₃×#2951	C₂	semidirect
21. C₅₃×#2933	C₂	semidirect
22. C₅₃×#2897	C₂	semidirect
23. C₅₃×#2896	C₂	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂×#135×C₅₃	C₂²	semidirect
29. C₂×#131×C₅₃	C₂²	semidirect
30. C₂²×M₁₆×C₅₃	C₂²	semidirect
32. C₅₃×#556	C₂²	semidirect
34. C₅₃×#555	C₂²	semidirect
36. C₅₃×#553	C₂²	semidirect
38. C₅₃×#552	C₂²	semidirect
45. C₅₃×#544	C₂²	semidirect
49. C₅₃×#537	C₂²	semidirect
55. C₅₃×#525	C₂²	semidirect
59. C₅₃×#520	C₂²	semidirect
60. C₅₃×#520	C₂²	semidirect
61. C₂×#117×C₅₃	C₂²	semidirect
62. C₅₃×#490	C₂²	semidirect
63. C₅₃×#489	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#484	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#470	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#466	C₂²	semidirect
83. C₅₃×#465	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#460	C₂²	semidirect
89. C₅₃×#459	C₂²	semidirect
90. C₅₃×#452	C₂²	semidirect
91. C₅₃×#452	C₂²	semidirect
92. C₅₃×#452	C₂²	semidirect
93. C₅₃×#451	C₂²	semidirect
94. C₅₃×#450	C₂²	semidirect
95. C₅₃×#450	C₂²	semidirect
96. C₅₃×#449	C₂²	semidirect
97. C₅₃×#449	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
99. C₅₃×#448	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₄×Q₁₆×C₅₃	C₂²	semidirect
105. C₄×D₈×C₅₃	C₂²	semidirect
106. C₅₃×#436	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₈×D₄×C₅₃	C₂²	semidirect
110. C₅₃×#428	C₂²	semidirect
111. C₂×#107×C₅₃	C₂²	semidirect
112. C₂×#106×C₅₃	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
114. C₅₃×#419	C₂²	semidirect
115. C₅₃×#418	C₂²	semidirect
116. C₅₃×#418	C₂²	semidirect
117. C₅₃×#418	C₂²	semidirect
120. C₅₃×#417	C₂²	semidirect
121. C₅₃×#417	C₂²	semidirect
122. C₅₃×#417	C₂²	semidirect
123. C₅₃×#417	C₂²	semidirect
125. C₅₃×#416	C₂²	semidirect
126. C₅₃×#416	C₂²	semidirect
127. C₅₃×#416	C₂²	semidirect
128. C₅₃×#416	C₂²	semidirect
129. C₂×#102×C₅₃	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
131. C₂×#102×C₅₃	C₂²	semidirect
132. C₅₃×#408	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
588. #61195	C₅₃	direct (N × H)
634. #3493	C₂×C₅₃	semidirect
635. #3488	C₂×C₅₃	semidirect
636. #3327	C₂×C₅₃	semidirect
637. #3325	C₂×C₅₃	semidirect
638. #3321	C₂×C₅₃	semidirect
639. #3311	C₂×C₅₃	semidirect
640. #3310	C₂×C₅₃	semidirect
641. #3309	C₂×C₅₃	semidirect
642. #3304	C₂×C₅₃	semidirect
643. #3297	C₂×C₅₃	semidirect
644. #3136	C₂×C₅₃	semidirect
645. #3098	C₂×C₅₃	semidirect
646. C₂×#482	C₂×C₅₃	semidirect
647. #3084	C₂×C₅₃	semidirect
648. #3060	C₂×C₅₃	semidirect
649. #3055	C₂×C₅₃	semidirect
650. #3045	C₂×C₅₃	semidirect
651. #3012	C₂×C₅₃	semidirect
652. #3002	C₂×C₅₃	semidirect
653. #2951	C₂×C₅₃	semidirect
654. #2933	C₂×C₅₃	semidirect
655. #2897	C₂×C₅₃	semidirect
656. #2896	C₂×C₅₃	semidirect
670. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
672. C₂×#135	C₂²×C₅₃	semidirect
673. C₂×#131	C₂²×C₅₃	semidirect
674. C₂²×M₁₆	C₂²×C₅₃	semidirect
676. #556	C₂²×C₅₃	semidirect
678. #555	C₂²×C₅₃	semidirect
680. #553	C₂²×C₅₃	semidirect
682. #552	C₂²×C₅₃	semidirect
689. #544	C₂²×C₅₃	semidirect
693. #537	C₂²×C₅₃	semidirect
699. #525	C₂²×C₅₃	semidirect
703. #520	C₂²×C₅₃	semidirect
704. #520	C₂²×C₅₃	semidirect
705. C₂×#117	C₂²×C₅₃	semidirect
706. #490	C₂²×C₅₃	semidirect
707. #489	C₂²×C₅₃	semidirect
708. #488	C₂²×C₅₃	semidirect
709. #486	C₂²×C₅₃	semidirect
710. #485	C₂²×C₅₃	semidirect
711. #484	C₂²×C₅₃	semidirect
712. #482	C₂²×C₅₃	semidirect
713. #482	C₂²×C₅₃	semidirect
714. #482	C₂²×C₅₃	semidirect
715. #482	C₂²×C₅₃	semidirect
716. #482	C₂²×C₅₃	semidirect
717. #480	C₂²×C₅₃	semidirect
718. #479	C₂²×C₅₃	semidirect
719. #478	C₂²×C₅₃	semidirect
720. #476	C₂²×C₅₃	semidirect
721. #475	C₂²×C₅₃	semidirect
722. #470	C₂²×C₅₃	semidirect
723. #469	C₂²×C₅₃	semidirect
724. #469	C₂²×C₅₃	semidirect
725. #468	C₂²×C₅₃	semidirect
726. #466	C₂²×C₅₃	semidirect
727. #465	C₂²×C₅₃	semidirect
728. #465	C₂²×C₅₃	semidirect
729. #465	C₂²×C₅₃	semidirect
730. #464	C₂²×C₅₃	semidirect
731. #463	C₂²×C₅₃	semidirect
732. #460	C₂²×C₅₃	semidirect
733. #459	C₂²×C₅₃	semidirect
734. #452	C₂²×C₅₃	semidirect
735. #452	C₂²×C₅₃	semidirect
736. #452	C₂²×C₅₃	semidirect
737. #451	C₂²×C₅₃	semidirect
738. #450	C₂²×C₅₃	semidirect
739. #450	C₂²×C₅₃	semidirect
740. #449	C₂²×C₅₃	semidirect
741. #449	C₂²×C₅₃	semidirect
742. #449	C₂²×C₅₃	semidirect
743. #448	C₂²×C₅₃	semidirect
744. #447	C₂²×C₅₃	semidirect
745. #447	C₂²×C₅₃	semidirect
746. #440	C₂²×C₅₃	semidirect
747. #440	C₂²×C₅₃	semidirect
748. C₄×Q₁₆	C₂²×C₅₃	semidirect
749. C₄×D₈	C₂²×C₅₃	semidirect
750. #436	C₂²×C₅₃	semidirect
751. #435	C₂²×C₅₃	semidirect
752. #435	C₂²×C₅₃	semidirect
753. C₈×D₄	C₂²×C₅₃	semidirect
754. #428	C₂²×C₅₃	semidirect
755. C₂×#107	C₂²×C₅₃	semidirect
756. C₂×#106	C₂²×C₅₃	semidirect
757. #424	C₂²×C₅₃	semidirect
758. #419	C₂²×C₅₃	semidirect
759. #418	C₂²×C₅₃	semidirect
760. #418	C₂²×C₅₃	semidirect
761. #418	C₂²×C₅₃	semidirect
764. #417	C₂²×C₅₃	semidirect
765. #417	C₂²×C₅₃	semidirect
766. #417	C₂²×C₅₃	semidirect
767. #417	C₂²×C₅₃	semidirect
769. #416	C₂²×C₅₃	semidirect
770. #416	C₂²×C₅₃	semidirect
771. #416	C₂²×C₅₃	semidirect
772. #416	C₂²×C₅₃	semidirect
773. C₂×#102	C₂²×C₅₃	semidirect
774. C₂×#102	C₂²×C₅₃	semidirect
775. C₂×#102	C₂²×C₅₃	semidirect
776. #408	C₂²×C₅₃	semidirect
777. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
778. #405	C₂²×C₅₃	semidirect
779. C₅₃	#61195	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×#3493	2
C₅₃×#3488	2
C₅₃×#3327	2
C₅₃×#3325	2
C₅₃×#3321	2
C₅₃×#3311	2
C₅₃×#3310	2
C₅₃×#3309	2
C₅₃×#3304	2
C₅₃×#3297	2
C₅₃×#3136	2
C₅₃×#3098	2
C₂×C₅₃×#482	2
C₅₃×#3084	2
C₅₃×#3060	2
C₅₃×#3055	2
C₅₃×#3045	2
C₅₃×#3012	2
C₅₃×#3002	2
C₅₃×#2951	2
C₅₃×#2933	2
C₅₃×#2897	2
C₅₃×#2896	2
#61195	53

Subgroups — C53×#61195 #27268707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61195 #27268707