Subgroups — #28293228

Order 13568.

7370 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288612	C₂	1	4	yes	maximal, complemented
2	#20288611	C₂	1	4	yes	maximal, complemented
3	#20288591	C₂	1	4	yes	maximal, complemented
4	#20288586	C₂	1	4	yes	maximal, complemented
5	#20288560	C₂	1	8	yes	maximal, complemented
6	#20288451	C₂	1	8	yes	maximal, complemented
7	#20288450	C₂	1	8	yes	maximal, complemented
8	#20288400	C₂	1	8	yes	maximal, complemented
9	#20288131	C₂	1	8	yes	maximal, complemented
10	#20288120	C₂	1	1	yes	maximal, characteristic, complemented
11	#20288044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16811192	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16811187	C₂	1	1	yes	maximal, characteristic, complemented
14	#20287916	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811097	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11719945	C₂²	1	1	yes	characteristic
18	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
19	#16811358	C₂²	1	16	yes	complemented
20	#16811356	C₂²	1	16	yes	complemented
21	#16811345	C₂²	1	16	yes	complemented
22	#16811336	C₂²	1	16	yes	complemented
23	#16811321	C₂²	1	16	yes	complemented
24	#16811317	C₂²	1	16	yes	complemented
25	#16811302	C₂²	1	32	yes	complemented
26	#16811297	C₂²	1	32	yes	complemented
27	#16811294	C₂²	1	16	yes	complemented
28	#16811274	C₂²	1	16	yes	complemented
29	#16811269	C₂²	1	32	yes	complemented
30	#16811263	C₂²	1	32	yes	complemented
31	#16811254	C₂²	1	4	yes	complemented
32	#16811251	C₂²	1	4	yes	complemented
33	#16811251	C₂²	1	4	yes	complemented
34	#16811249	C₂²	1	4	yes	—
35	#16811245	C₂²	1	16	yes	complemented
36	#16811244	C₂²	1	16	yes	complemented
37	#16811228	C₂²	1	16	yes	complemented
38	#16811224	C₂²	1	16	yes	complemented
39	#16811206	C₂²	1	32	yes	complemented
40	#16811201	C₂²	1	4	yes	complemented
41	#16811197	C₂²	1	2	yes	complemented
42	#16811194	C₂²	1	2	yes	complemented
43	#16811192	C₂²	1	4	yes	—
44	#16811192	C₂²	1	4	yes	—
45	#16811192	C₂²	1	4	yes	complemented
46	#16811192	C₂²	1	4	yes	complemented
47	#16811190	C₂²	1	2	yes	complemented
48	#16811187	C₂²	1	4	yes	—
49	#16811187	C₂²	1	4	yes	—
50	#16811187	C₂²	1	4	yes	complemented
51	#16811187	C₂²	1	4	yes	complemented
52	#16811187	C₂²	1	2	yes	complemented
53	#16811182	C₂²	1	4	yes	—
54	#16811180	C₂²	1	4	yes	complemented
55	#16811176	C₂²	1	4	yes	complemented
56	#16811176	C₂²	1	4	yes	complemented
57	#16811173	C₂²	1	16	yes	complemented
58	#16811170	C₂²	1	16	yes	complemented
59	#16811169	C₂²	1	4	yes	complemented
60	C₂×#13133214	C₂²	1	2	yes	complemented
61	C₂×#13133213	C₂²	1	2	yes	complemented
62	#16811160	C₂²	1	16	yes	complemented
63	#16811157	C₂²	1	16	yes	complemented
64	C₂×#13133206	C₂²	1	2	yes	complemented
65	C₂×#13133205	C₂²	1	2	yes	complemented
66	#16811134	C₂²	1	4	yes	complemented
67	#16811132	C₂²	1	32	yes	complemented
68	#16811130	C₂²	1	4	yes	complemented
69	C₂×#13133192	C₂²	1	4	yes	complemented
70	C₂×#13133191	C₂²	1	4	yes	complemented
71	C₂×#13133187	C₂²	1	4	yes	—
72	C₂×#13133185	C₂²	1	4	yes	—
73	#16811104	C₂²	1	4	yes	complemented
74	#16811103	C₂²	1	4	yes	complemented
75	#16811100	C₂²	1	2	yes	complemented
76	#16811097	C₂²	1	4	yes	complemented
77	#16811097	C₂²	1	4	yes	complemented
78	#16811097	C₂²	1	4	yes	complemented
79	#16811097	C₂²	1	4	yes	complemented
80	#16811097	C₂²	1	2	yes	complemented
81	#16811096	C₂²	1	4	yes	—
82	C₄×#11719945	C₂²	1	4	yes	complemented
83	#16811091	C₂²	1	4	yes	complemented
84	C₂×C₄×D₂₁₂	C₂²	1	4	yes	complemented
85	C₂×#13133179	C₂²	1	4	yes	complemented
86	C₂×#13133176	C₂²	1	1	yes	characteristic
87	C₂×#13133176	C₂²	1	1	yes	characteristic
88	#117×D₅₃	C₂²	1	4	yes	complemented
89	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
90	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
91	C₅₃×#520	C₂²	1	4	yes	complemented
92	C₅₃×#520	C₂²	1	4	yes	complemented
93	C₅₃×#519	C₂²	1	2	yes	complemented
94	C₅₃×#518	C₂²	1	4	yes	—
95	C₅₃×#518	C₂²	1	2	yes	complemented
96	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
97	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
98	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
99	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
100	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
101	C₂⁴×D₅₃	C₂³	1	2	yes	—
102	C₂×#11719945	—	2	8	no	—
103	C₂×#11719945	C₂³	1	2	yes	—
104	C₂×#11719945	C₂³	1	2	yes	—
105	C₂×#11719945	C₂³	1	2	yes	—
106	C₂×#11719945	C₂³	1	2	yes	—
107	C₂×#11719945	C₂³	1	32	yes	complemented
108	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
109	C₂²×D₂₁₂	—	2	8	no	—
110	C₂²×D₂₁₂	C₂³	1	2	yes	—
111	C₂²×D₂₁₂	C₂³	1	2	yes	—
112	C₂²×D₂₁₂	C₂³	1	2	yes	—
113	C₂²×D₂₁₂	C₂³	1	2	yes	—
114	C₂²×D₂₁₂	C₂³	1	2	yes	—
115	C₂²×D₂₁₂	C₂³	1	2	yes	—
116	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
117	C₂²×D₂₁₂	C₂³	1	8	yes	—
118	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
119	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
120	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
121	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
122	#13133217	C₂³	1	8	yes	complemented
123	#13133216	C₂³	1	8	yes	complemented
124	#13133216	C₂³	1	8	yes	complemented
125	#13133215	C₂³	1	4	yes	complemented
126	#13133214	C₂³	1	8	yes	—
127	#13133214	C₂³	1	8	yes	—
128	#13133213	C₂³	1	8	yes	—
129	#13133213	C₂³	1	8	yes	—
130	#13133213	C₂³	1	4	yes	complemented
131	#13133212	C₂³	1	32	yes	complemented
132	#13133211	C₂³	1	32	yes	complemented
133	#13133209	C₂³	1	8	yes	complemented
134	#13133208	C₂³	1	8	yes	complemented
135	#13133208	C₂³	1	8	yes	complemented
136	#13133206	C₂³	1	8	yes	—
137	#13133206	C₂³	1	8	yes	—
138	#13133206	C₂³	1	4	yes	complemented
139	#13133205	C₂³	1	8	yes	—
140	#13133205	C₂³	1	8	yes	—
141	#13133205	C₂³	1	32	yes	complemented
142	#13133204	C₂³	1	4	yes	complemented
143	#13133203	C₂³	1	32	yes	complemented
144	#13133202	C₂³	1	32	yes	complemented
145	#13133202	C₂³	1	32	yes	complemented
146	#13133200	C₂³	1	8	yes	—
147	#13133200	C₂³	1	32	yes	complemented
148	#13133199	C₂³	1	32	yes	complemented
149	#13133198	C₂³	1	8	yes	—
150	#13133196	C₂³	1	16	yes	—
151	#13133196	C₂³	1	8	yes	complemented
152	#13133195	C₂³	1	32	yes	complemented
153	#13133194	C₂³	1	16	yes	—
154	#13133194	C₂³	1	16	yes	—
155	#13133193	C₂³	1	8	yes	complemented
156	#13133192	C₂³	1	16	yes	—
157	#13133192	C₂³	1	16	yes	—
158	#13133191	C₂³	1	16	yes	—
159	#13133191	C₂³	1	16	yes	—
160	#13133191	C₂³	1	32	yes	complemented
161	#13133191	C₂³	1	8	yes	complemented
162	#13133190	C₂³	1	32	yes	complemented
163	#13133190	C₂³	1	32	yes	complemented
164	#13133189	C₂³	1	16	yes	—
165	#13133188	C₂³	1	8	yes	complemented
166	#13133187	C₂³	1	16	yes	—
167	#13133187	C₂³	1	16	yes	—
168	#13133186	C₂³	1	8	yes	—
169	#13133185	C₂³	1	8	yes	—
170	#13133185	C₂³	1	16	yes	—
171	#13133185	C₂³	1	16	yes	—
172	C₄×Dic₁₀₆	C₂³	1	16	yes	complemented
173	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
174	#13133182	C₂³	1	8	yes	complemented
175	C₄×D₂₁₂	C₂³	1	16	yes	—
176	C₄×D₂₁₂	C₂³	1	16	yes	—
177	C₄×D₂₁₂	C₂³	1	32	yes	complemented
178	C₄×D₂₁₂	C₂³	1	8	yes	complemented
179	#13133179	C₂³	1	16	yes	—
180	#13133179	C₂³	1	16	yes	—
181	#13133179	C₂³	1	8	yes	complemented
182	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
183	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
184	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
185	#13133177	C₂³	1	16	yes	—
186	#13133176	C₂³	1	2	yes	—
187	#13133176	C₂³	1	2	yes	—
188	#13133176	C₂³	1	2	yes	—
189	#13133176	C₂³	1	2	yes	—
190	#13133176	C₂³	1	2	yes	—
191	#13133176	C₂³	1	2	yes	—
192	#13133176	C₂³	1	2	yes	—
193	#13133176	C₂³	1	2	yes	—
194	#13133175	C₂³	1	8	yes	complemented
195	#13133174	C₂³	1	32	yes	complemented
196	#13133174	C₂³	1	8	yes	complemented
197	#13133173	C₂³	1	8	yes	—
198	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
199	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
200	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
201	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
203	C₂×#11719921	C₂³	1	8	yes	—
204	C₂×#11719921	C₂³	1	8	yes	—
205	C₂×#11719921	C₂³	1	8	yes	—
206	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
207	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
208	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
209	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
210	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
211	C₄²×D₅₃	C₂³	1	8	yes	complemented
212	C₂×#41×C₅₃	—	2	8	no	—
213	C₂×#41×C₅₃	C₂³	1	2	yes	—
214	C₂×#41×C₅₃	C₂³	1	2	yes	—
215	C₂×#41×C₅₃	C₂³	1	2	yes	—
216	C₂×#41×C₅₃	C₂³	1	2	yes	—
217	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
219	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
221	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
223	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
224	C₄×D₄×C₅₃	C₂³	1	16	yes	—
225	C₄×D₄×C₅₃	C₂³	1	16	yes	—
226	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
227	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
228	#117×C₅₃	C₂³	1	2	yes	—
229	#117×C₅₃	C₂³	1	2	yes	—
230	#117×C₅₃	C₂³	1	2	yes	—
231	#117×C₅₃	C₂³	1	2	yes	—
232	#117×C₅₃	C₂³	1	2	yes	—
233	#117×C₅₃	C₂³	1	2	yes	—
234	#117×C₅₃	C₂³	1	2	yes	—
235	#117×C₅₃	C₂³	1	2	yes	—
236	#117×C₅₃	C₂³	1	8	yes	—
237	#117×C₅₃	C₂³	1	8	yes	complemented
238	#117×C₅₃	C₂³	1	8	yes	complemented
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
242	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
243	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
244	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
245	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
246	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
247	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
248	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
249	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂³×D₅₃	—	2	8	no	—
251	C₂³×D₅₃	—	8	4	no	—
252	C₂³×D₅₃	C₂⁴	1	4	yes	—
253	C₂³×D₅₃	C₂⁴	1	4	yes	—
254	C₂³×D₅₃	C₂⁴	1	2	yes	—
255	C₂³×D₅₃	C₂⁴	1	4	yes	—
256	#41×C₅₃	—	2	8	no	—
257	#41×C₅₃	—	2	8	no	—
258	#41×C₅₃	—	2	8	no	—
259	#41×C₅₃	—	2	8	no	—
260	C₂×Q₈×C₅₃	—	2	4	no	—
261	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₅₃	—	2	8	no	—
264	C₂×D₄×C₅₃	—	2	4	no	—
265	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
266	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
267	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
268	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₅₃	—	2	8	no	—
270	C₂²×C₄×C₅₃	#41	1	8	yes	complemented
271	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
276	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₂×C₂²⋊D₅₃	—	2	8	no	—
284	C₂×C₂²⋊D₅₃	—	8	8	no	—
285	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
286	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
287	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
288	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
289	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
290	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
291	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
292	#11719945	—	2	8	no	—
293	#11719945	—	2	8	no	—
294	#11719945	—	2	8	no	—
295	#11719945	—	2	8	no	—
296	#11719945	—	8	32	no	—
297	C₂×D₂₁₂	—	2	8	no	—
298	C₂×D₂₁₂	—	2	8	no	—
299	C₂×D₂₁₂	—	2	8	no	—
300	C₂×D₂₁₂	—	2	8	no	—
301	C₂×D₂₁₂	—	2	8	no	—
302	C₂×D₂₁₂	—	2	8	no	—
303	C₂×D₂₁₂	—	2	4	no	—
304	C₂×D₂₁₂	—	8	8	no	—
305	C₂×D₂₁₂	C₂⁴	1	4	yes	—
306	C₂×D₂₁₂	C₂⁴	1	4	yes	—
307	C₂×D₂₁₂	C₂⁴	1	2	yes	—
308	C₂×D₂₁₂	C₂⁴	1	4	yes	—
309	C₂×D₂₁₂	C₂⁴	1	4	yes	—
310	C₂×D₂₁₂	C₂⁴	1	2	yes	—
311	C₂×D₂₁₂	C₂⁴	1	32	yes	—
312	C₂×C₄×D₅₃	—	2	8	no	—
313	C₂×C₄×D₅₃	—	8	8	no	—
314	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
315	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
316	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
317	C₂×C₄×D₅₃	C₂⁴	1	32	yes	—
318	C₂×Dic₁₀₆	—	2	4	no	—
319	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
320	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
321	C₂×Dic₁₀₆	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
324	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
325	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
328	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
329	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
330	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
331	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
332	C₄²×C₅₃	C₂⁴	1	4	yes	—
333	C₄²×C₅₃	C₂⁴	1	4	yes	—
334	C₄²×C₅₃	C₂⁴	1	4	yes	—
335	C₄²×C₅₃	C₂⁴	1	4	yes	—
336	C₄²×C₅₃	C₂⁴	1	16	yes	—
337	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
338	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
339	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
340	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
341	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
342	#11719921	C₂⁴	1	32	yes	—
343	#11719921	C₂⁴	1	16	yes	—
344	#11719921	C₂⁴	1	32	yes	—
345	#11719921	C₂⁴	1	32	yes	—
346	#11719921	C₂⁴	1	16	yes	—
347	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
348	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
349	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
350	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
351	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
352	#11719919	C₂⁴	1	16	yes	—
353	#11719919	C₂⁴	1	16	yes	—
354	#11719919	C₂⁴	1	16	yes	—
355	#11719919	C₂⁴	1	16	yes	—
356	C₄×Dic₅₃	C₂⁴	1	4	yes	—
357	C₄×Dic₅₃	C₂⁴	1	16	yes	—
358	C₄×Dic₅₃	C₂⁴	1	4	yes	—
359	C₄×Dic₅₃	C₂⁴	1	4	yes	—
360	C₄×Dic₅₃	C₂⁴	1	4	yes	—
361	C₂³×C₅₃	—	2	4	no	—
362	C₂³×C₅₃	—	4	2	no	—
363	C₂³×C₅₃	—	4	4	no	—
364	C₂³×C₅₃	C₂×#41	1	4	yes	—
365	C₂³×C₅₃	C₂⁵	1	4	yes	—
366	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
367	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
368	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
369	C₂²×D₅₃	—	2	8	no	—
370	C₂²×D₅₃	—	2	4	no	—
371	C₂²×D₅₃	—	2	8	no	—
372	C₂²×D₅₃	—	2	8	no	—
373	C₂²×D₅₃	—	4	8	no	—
374	C₂²×D₅₃	—	4	4	no	—
375	C₂²×D₅₃	—	4	8	no	—
376	C₂²×D₅₃	—	4	8	no	—
377	C₂²×D₅₃	—	8	16	no	—
378	C₂²×D₅₃	C₂⁵	1	4	yes	—
379	C₂²×D₅₃	C₂⁵	1	8	yes	—
380	Q₈×C₅₃	—	2	4	no	—
381	Q₈×C₅₃	—	2	4	no	—
382	D₄×C₅₃	—	2	8	no	—
383	D₄×C₅₃	—	2	8	no	—
384	D₄×C₅₃	—	2	4	no	—
385	D₄×C₅₃	—	2	4	no	—
386	C₂×C₄×C₅₃	—	2	4	no	—
387	C₂×C₄×C₅₃	—	2	8	no	—
388	C₂×C₄×C₅₃	—	2	8	no	—
389	C₂×C₄×C₅₃	—	4	4	no	—
390	C₂×C₄×C₅₃	—	4	4	no	—
391	C₂×C₄×C₅₃	—	4	16	no	—
392	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
393	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
394	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
395	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
396	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
397	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
398	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
399	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
400	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
401	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
403	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
404	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
405	C₂²⋊D₅₃	—	2	8	no	—
406	C₂²⋊D₅₃	—	2	8	no	—
407	C₂²⋊D₅₃	—	4	16	no	—
408	C₂²⋊D₅₃	—	4	32	no	—
409	C₂×Dic₅₃	—	2	4	no	—
410	C₂×Dic₅₃	—	4	4	no	—
411	C₂×Dic₅₃	—	4	4	no	—
412	C₂×Dic₅₃	C₂⁵	1	8	yes	—
413	C₂×Dic₅₃	C₂⁵	1	8	yes	—
414	C₂×Dic₅₃	C₂⁵	1	4	yes	—
415	D₂₁₂	—	2	8	no	—
416	D₂₁₂	—	2	8	no	—
417	D₂₁₂	—	2	8	no	—
418	D₂₁₂	—	2	8	no	—
419	D₂₁₂	—	2	4	no	—
420	D₂₁₂	—	2	4	no	—
421	D₂₁₂	—	4	32	no	—
422	C₄×D₅₃	—	2	8	no	—
423	C₄×D₅₃	—	2	8	no	—
424	C₄×D₅₃	—	4	32	no	—
425	C₄×D₅₃	—	4	16	no	—
426	Dic₁₀₆	—	2	4	no	—
427	Dic₁₀₆	—	2	4	no	—
428	Dic₁₀₆	—	4	16	no	—
429	#62855	—	53	1	no	maximal, Sylow
430	C₂²×C₅₃	—	2	2	no	—
431	C₂²×C₅₃	—	2	2	no	—
432	C₂²×C₅₃	—	2	2	no	—
433	C₂²×C₅₃	—	2	4	no	—
434	C₂²×C₅₃	—	2	8	no	—
435	C₂²×C₅₃	—	4	4	no	—
436	C₂²×C₅₃	—	8	4	no	—
437	C₂²×C₅₃	C₂²×#41	1	2	yes	—
438	C₂²×C₅₃	C₂²×#41	1	2	yes	—
439	C₂²×C₅₃	C₂²×#41	1	2	yes	—
440	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
441	C₂×D₅₃	—	2	4	no	—
442	C₂×D₅₃	—	2	8	no	—
443	C₂×D₅₃	—	2	8	no	—
444	C₂×D₅₃	—	2	16	no	—
445	C₂×D₅₃	—	4	16	no	—
446	C₂×D₅₃	—	8	4	no	—
447	C₂×D₅₃	—	8	8	no	—
448	C₂×D₅₃	—	8	8	no	—
449	C₄×C₅₃	—	2	4	no	—
450	C₄×C₅₃	—	2	8	no	—
451	C₄×C₅₃	—	2	8	no	—
452	C₄×C₅₃	C₂²×#41	1	2	yes	—
453	C₄×C₅₃	C₂²×#41	1	2	yes	—
454	C₄×C₅₃	C₂²×#41	1	2	yes	—
455	C₄×C₅₃	C₂²×#41	1	2	yes	—
456	Dic₅₃	—	2	4	no	—
457	Dic₅₃	—	2	8	no	—
458	Dic₅₃	—	2	8	no	—
459	#3510	—	53	4	no	—
460	#3510	—	53	4	no	—
461	#3508	—	53	4	no	—
462	#3508	—	53	4	no	—
463	#3506	—	53	8	no	—
464	#3494	—	53	8	no	—
465	#3494	—	53	8	no	—
466	#3490	—	53	8	no	—
467	#3460	—	53	8	no	—
468	#3458	—	53	1	no	—
469	#3449	—	53	1	no	—
470	C₂×#535	—	53	1	no	—
471	C₂×#535	—	53	1	no	—
472	#3428	—	53	1	no	—
473	#3428	D₅₃	1	1	yes	characteristic, complemented
474	C₂×#518	—	53	1	no	—
475	C₂×C₅₃	—	2	2	no	—
476	C₂×C₅₃	—	2	2	no	—
477	C₂×C₅₃	—	2	2	no	—
478	C₂×C₅₃	—	4	4	no	—
479	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
480	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
481	D₅₃	—	4	8	no	—
482	D₅₃	—	4	4	no	—
483	C₂²×#41	—	53	1	no	—
484	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic
485	C₂³×D₄	—	53	1	no	—
486	#559	—	53	16	no	—
487	#559	—	53	16	no	—
488	#556	—	53	16	no	—
489	#555	—	53	16	no	—
490	#553	—	53	16	no	—
491	#553	—	53	16	no	—
492	#551	—	53	32	no	—
493	#551	—	53	32	no	—
494	#550	—	53	16	no	—
495	#547	—	53	16	no	—
496	#546	—	53	32	no	—
497	#546	—	53	32	no	—
498	#544	—	53	4	no	—
499	#544	—	53	4	no	—
500	#544	—	53	4	no	—
501	#543	—	53	4	no	—
502	#542	—	53	16	no	—
503	#542	—	53	16	no	—
504	#540	—	53	16	no	—
505	#540	—	53	16	no	—
506	#538	—	53	32	no	—
507	#537	—	53	4	no	—
508	#536	—	53	2	no	—
509	#536	—	53	2	no	—
510	#535	—	53	4	no	—
511	#535	—	53	4	no	—
512	#535	—	53	4	no	—
513	#535	—	53	4	no	—
514	#535	—	53	2	no	—
515	#535	—	53	2	no	—
516	#535	—	53	4	no	—
517	#535	—	53	4	no	—
518	#535	—	53	4	no	—
519	#535	—	53	4	no	—
520	#534	—	53	4	no	—
521	#533	—	53	4	no	—
522	#533	—	53	4	no	—
523	#533	—	53	4	no	—
524	#532	—	53	4	no	—
525	#532	—	53	16	no	—
526	#532	—	53	16	no	—
527	C₂×#127	—	53	2	no	—
528	C₂×#127	—	53	2	no	—
529	#529	—	53	16	no	—
530	#529	—	53	16	no	—
531	C₂×#124	—	53	2	no	—
532	C₂×#124	—	53	2	no	—
533	#525	—	53	4	no	—
534	#525	—	53	4	no	—
535	#525	—	53	32	no	—
536	C₂×#121	—	53	4	no	—
537	C₂×#121	—	53	4	no	—
538	C₂×#120	—	53	4	no	—
539	C₂×#120	—	53	4	no	—
540	#520	—	53	4	no	—
541	#520	—	53	4	no	—
542	#520	C₂×D₅₃	1	4	yes	complemented
543	#520	C₂×D₅₃	1	4	yes	complemented
544	#519	—	53	2	no	—
545	#519	C₂×D₅₃	1	2	yes	complemented
546	#518	—	53	4	no	—
547	#518	—	53	4	no	—
548	#518	—	53	4	no	—
549	#518	—	53	4	no	—
550	#518	—	53	2	no	—
551	#518	—	53	4	no	—
552	#518	C₂×D₅₃	1	4	yes	—
553	#518	C₂×D₅₃	1	2	yes	complemented
554	C₄×#41	—	53	4	no	—
555	C₄×#41	—	53	4	no	—
556	C₄×#41	C₂×D₅₃	1	4	yes	complemented
557	C₄×#41	C₂×D₅₃	1	4	yes	complemented
558	C₂×C₄×D₄	—	53	4	no	—
559	C₂×C₄×D₄	—	53	4	no	—
560	C₂×#117	—	53	1	no	—
561	C₂×#117	—	53	1	no	—
562	C₂×#117	—	53	4	no	—
563	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
564	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
565	C₂×#117	C₂×D₅₃	1	4	yes	complemented
566	C₂²×C₂²⋊C₄	—	53	4	no	—
567	C₅₃	#62855	1	1	yes	characteristic, complemented, Sylow
568	C₂⁵	—	53	2	no	—
569	C₂×#41	—	2	8	no	—
570	C₂×#41	—	53	2	no	—
571	C₂×#41	—	53	2	no	—
572	C₂×#41	—	53	2	no	—
573	C₂×#41	—	53	2	no	—
574	C₂×#41	—	53	32	no	—
575	C₂×#41	—	106	8	no	—
576	C₂×#41	C₂²×D₅₃	1	2	yes	—
577	C₂×#41	C₂²×D₅₃	1	2	yes	—
578	C₂×#41	C₂²×D₅₃	1	2	yes	—
579	C₂×#41	C₂²×D₅₃	1	2	yes	—
580	C₂²×Q₈	—	53	1	no	—
581	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
582	C₂²×D₄	—	53	2	no	—
583	C₂²×D₄	—	53	8	no	—
584	C₂²×D₄	—	53	2	no	—
585	C₂²×D₄	—	53	2	no	—
586	C₂²×D₄	—	53	2	no	—
587	C₂²×D₄	—	53	2	no	—
588	C₂²×D₄	—	53	2	no	—
589	C₂²×D₄	—	53	2	no	—
590	C₂²×D₄	—	53	1	no	—
591	C₂²×D₄	—	53	8	no	—
592	C₂²×D₄	—	106	8	no	—
593	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
594	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
595	C₂³×C₄	—	53	2	no	—
596	C₂³×C₄	—	53	8	no	—
597	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
598	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
599	C₄⋊Q₈	—	53	4	no	—
600	C₄⋊Q₈	—	53	8	no	—
601	C₄⋊Q₈	—	53	8	no	—
602	C₄⋊Q₈	—	53	8	no	—
603	#127	—	53	8	no	—
604	#127	—	53	8	no	—
605	#127	—	53	4	no	—
606	#127	—	53	8	no	—
607	#127	—	53	8	no	—
608	#126	—	53	32	no	—
609	#126	—	53	32	no	—
610	#125	—	53	8	no	—
611	#125	—	53	8	no	—
612	#125	—	53	8	no	—
613	#124	—	53	8	no	—
614	#124	—	53	8	no	—
615	#124	—	53	4	no	—
616	#124	—	53	4	no	—
617	#124	—	53	32	no	—
618	#124	—	53	8	no	—
619	#124	—	53	8	no	—
620	#124	—	53	32	no	—
621	#123	—	53	8	no	—
622	#123	—	53	8	no	—
623	#123	—	53	32	no	—
624	#123	—	53	32	no	—
625	#123	—	53	32	no	—
626	#123	—	53	32	no	—
627	C₂²⋊Q₈	—	53	8	no	—
628	C₂²⋊Q₈	—	53	8	no	—
629	C₂²⋊Q₈	—	53	16	no	—
630	C₂²⋊Q₈	—	53	32	no	—
631	C₂²⋊Q₈	—	53	16	no	—
632	C₂²⋊Q₈	—	53	16	no	—
633	#121	—	53	16	no	—
634	#121	—	53	8	no	—
635	#121	—	53	16	no	—
636	#121	—	53	16	no	—
637	#121	—	53	8	no	—
638	#121	—	53	32	no	—
639	#121	—	53	16	no	—
640	#121	—	53	16	no	—
641	#121	—	53	32	no	—
642	#121	—	53	32	no	—
643	#120	—	53	8	no	—
644	#120	—	53	16	no	—
645	#120	—	53	16	no	—
646	#120	—	53	8	no	—
647	#120	—	53	16	no	—
648	#120	—	53	16	no	—
649	C₄×Q₈	—	53	8	no	—
650	C₄×Q₈	—	53	8	no	—
651	C₄×Q₈	—	53	16	no	—
652	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
653	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
654	C₄×D₄	—	53	16	no	—
655	C₄×D₄	—	53	16	no	—
656	C₄×D₄	—	53	32	no	—
657	C₄×D₄	—	53	16	no	—
658	C₄×D₄	—	53	16	no	—
659	C₄×D₄	—	53	8	no	—
660	C₄×D₄	—	53	16	no	—
661	C₄×D₄	—	53	16	no	—
662	C₄×D₄	—	53	16	no	—
663	C₄×D₄	—	53	8	no	—
664	C₄×D₄	—	53	32	no	—
665	C₄×D₄	C₂²×D₅₃	1	16	yes	—
666	C₄×D₄	C₂²×D₅₃	1	16	yes	—
667	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
668	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
669	#117	—	53	2	no	—
670	#117	—	53	2	no	—
671	#117	—	53	2	no	—
672	#117	—	53	2	no	—
673	#117	—	53	2	no	—
674	#117	—	53	2	no	—
675	#117	—	53	2	no	—
676	#117	—	53	2	no	—
677	#117	—	53	8	no	—
678	#117	—	53	8	no	—
679	#117	—	53	8	no	—
680	#117	—	53	32	no	—
681	#117	C₂²×D₅₃	1	2	yes	—
682	#117	C₂²×D₅₃	1	2	yes	—
683	#117	C₂²×D₅₃	1	2	yes	—
684	#117	C₂²×D₅₃	1	2	yes	—
685	#117	C₂²×D₅₃	1	2	yes	—
686	#117	C₂²×D₅₃	1	2	yes	—
687	#117	C₂²×D₅₃	1	2	yes	—
688	#117	C₂²×D₅₃	1	2	yes	—
689	#117	C₂²×D₅₃	1	8	yes	—
690	#117	C₂²×D₅₃	1	8	yes	complemented
691	#117	C₂²×D₅₃	1	8	yes	complemented
692	C₂×C₄⋊C₄	—	53	2	no	—
693	C₂×C₄⋊C₄	—	53	2	no	—
694	C₂×C₄⋊C₄	—	53	8	no	—
695	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂²×D₅₃	1	8	yes	complemented
698	C₂×C₂²⋊C₄	—	53	2	no	—
699	C₂×C₂²⋊C₄	—	53	2	no	—
700	C₂×C₂²⋊C₄	—	53	8	no	—
701	C₂×C₂²⋊C₄	—	53	8	no	—
702	C₂×C₂²⋊C₄	—	53	8	no	—
703	C₂×C₂²⋊C₄	—	53	16	no	—
704	C₂×C₂²⋊C₄	—	53	16	no	—
705	C₂×C₂²⋊C₄	—	53	8	no	—
706	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
709	C₂×C₄²	—	53	2	no	—
710	C₂×C₄²	—	53	2	no	—
711	C₂×C₄²	—	53	8	no	—
712	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
713	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
714	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
715	C₂⁴	—	53	4	no	—
716	C₂⁴	—	53	4	no	—
717	C₂⁴	—	53	2	no	—
718	C₂⁴	—	53	4	no	—
719	C₂⁴	—	106	8	no	—
720	C₂⁴	—	424	4	no	—
721	C₂⁴	C₂³×D₅₃	1	2	yes	—
722	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
723	#41	—	2	8	no	—
724	#41	—	2	8	no	—
725	#41	—	2	8	no	—
726	#41	—	2	8	no	—
727	#41	—	106	8	no	—
728	#41	—	106	8	no	—
729	#41	—	106	8	no	—
730	#41	—	106	8	no	—
731	#41	—	424	32	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	53	2	no	—
734	C₂×Q₈	—	53	2	no	—
735	C₂×Q₈	—	53	16	no	—
736	C₂×Q₈	—	106	4	no	—
737	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
738	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
739	C₂×D₄	—	2	8	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	53	4	no	—
742	C₂×D₄	—	53	4	no	—
743	C₂×D₄	—	53	16	no	—
744	C₂×D₄	—	53	32	no	—
745	C₂×D₄	—	53	4	no	—
746	C₂×D₄	—	53	4	no	—
747	C₂×D₄	—	53	4	no	—
748	C₂×D₄	—	53	2	no	—
749	C₂×D₄	—	53	4	no	—
750	C₂×D₄	—	53	2	no	—
751	C₂×D₄	—	53	32	no	—
752	C₂×D₄	—	106	8	no	—
753	C₂×D₄	—	106	8	no	—
754	C₂×D₄	—	106	8	no	—
755	C₂×D₄	—	106	8	no	—
756	C₂×D₄	—	106	8	no	—
757	C₂×D₄	—	106	8	no	—
758	C₂×D₄	—	106	8	no	—
759	C₂×D₄	—	106	4	no	—
760	C₂×D₄	—	424	8	no	—
761	C₂×D₄	—	424	8	no	—
762	C₂×D₄	C₂³×D₅₃	1	4	yes	—
763	C₂×D₄	C₂³×D₅₃	1	4	yes	—
764	C₂×D₄	C₂³×D₅₃	1	2	yes	—
765	C₂×D₄	C₂³×D₅₃	1	2	yes	—
766	C₂²×C₄	—	2	8	no	—
767	C₂²×C₄	—	53	2	no	—
768	C₂²×C₄	—	53	4	no	—
769	C₂²×C₄	—	53	4	no	—
770	C₂²×C₄	—	53	4	no	—
771	C₂²×C₄	—	53	4	no	—
772	C₂²×C₄	—	53	16	no	—
773	C₂²×C₄	—	53	32	no	—
774	C₂²×C₄	—	106	8	no	—
775	C₂²×C₄	—	424	8	no	—
776	C₂²×C₄	#11719945	1	8	yes	complemented
777	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
778	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
779	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
780	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
781	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
782	C₂²×C₄	C₂³×D₅₃	1	16	yes	—
783	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
784	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
785	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
786	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
787	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
788	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
789	C₄⋊C₄	—	53	4	no	—
790	C₄⋊C₄	—	53	4	no	—
791	C₄⋊C₄	—	53	4	no	—
792	C₄⋊C₄	—	53	4	no	—
793	C₄⋊C₄	—	53	16	no	—
794	C₄⋊C₄	—	53	16	no	—
795	C₄⋊C₄	—	53	16	no	—
796	C₄⋊C₄	—	53	16	no	—
797	C₄⋊C₄	—	53	16	no	—
798	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
799	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
800	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
801	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
802	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
803	C₂²⋊C₄	—	53	4	no	—
804	C₂²⋊C₄	—	53	4	no	—
805	C₂²⋊C₄	—	53	4	no	—
806	C₂²⋊C₄	—	53	4	no	—
807	C₂²⋊C₄	—	53	16	no	—
808	C₂²⋊C₄	—	53	32	no	—
809	C₂²⋊C₄	—	53	16	no	—
810	C₂²⋊C₄	—	53	32	no	—
811	C₂²⋊C₄	—	53	32	no	—
812	C₂²⋊C₄	—	53	16	no	—
813	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
814	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
815	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
816	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
817	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
818	C₄²	—	53	4	no	—
819	C₄²	—	53	16	no	—
820	C₄²	—	53	4	no	—
821	C₄²	—	53	4	no	—
822	C₄²	—	53	4	no	—
823	C₄²	C₂³×D₅₃	1	4	yes	—
824	C₄²	C₂³×D₅₃	1	4	yes	—
825	C₄²	C₂³×D₅₃	1	4	yes	—
826	C₄²	C₂³×D₅₃	1	4	yes	—
827	C₄²	C₂³×D₅₃	1	16	yes	—
828	C₂³	—	2	4	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	53	8	no	—
832	C₂³	—	53	4	no	—
833	C₂³	—	106	4	no	—
834	C₂³	—	106	8	no	—
835	C₂³	—	106	8	no	—
836	C₂³	—	106	8	no	—
837	C₂³	—	424	16	no	—
838	C₂³	—	212	4	no	—
839	C₂³	—	212	8	no	—
840	C₂³	—	212	8	no	—
841	C₂³	—	212	8	no	—
842	C₂³	C₂×#11719945	1	4	yes	—
843	C₂³	C₂⁴×D₅₃	1	4	yes	—
844	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
845	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
846	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
847	Q₈	—	2	4	no	—
848	Q₈	—	2	4	no	—
849	Q₈	—	106	4	no	—
850	Q₈	—	106	4	no	—
851	Q₈	—	212	16	no	—
852	D₄	—	2	8	no	—
853	D₄	—	2	8	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	4	no	—
856	D₄	—	106	8	no	—
857	D₄	—	106	8	no	—
858	D₄	—	106	8	no	—
859	D₄	—	106	8	no	—
860	D₄	—	106	8	no	—
861	D₄	—	106	8	no	—
862	D₄	—	106	4	no	—
863	D₄	—	106	4	no	—
864	D₄	—	212	32	no	—
865	D₄	—	212	32	no	—
866	D₄	—	212	16	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	8	no	—
869	C₂×C₄	—	2	8	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	16	no	—
873	C₂×C₄	—	53	4	no	—
874	C₂×C₄	—	53	8	no	—
875	C₂×C₄	—	53	8	no	—
876	C₂×C₄	—	106	4	no	—
877	C₂×C₄	—	106	8	no	—
878	C₂×C₄	—	106	8	no	—
879	C₂×C₄	—	212	32	no	—
880	C₂×C₄	—	212	16	no	—
881	C₂×C₄	—	212	4	no	—
882	C₂×C₄	—	212	4	no	—
883	C₂×C₄	C₂×#11719945	1	4	yes	—
884	C₂×C₄	C₂×#11719945	1	4	yes	—
885	C₂×C₄	C₂×#11719945	1	4	yes	—
886	C₂×C₄	C₂×#11719945	1	4	yes	—
887	C₂×C₄	C₂×#11719945	1	4	yes	—
888	C₂×C₄	C₂×#11719945	1	4	yes	—
889	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
890	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
891	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
892	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
893	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
894	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
895	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	2	8	no	—
901	C₂²	—	4	4	no	—
902	C₂²	—	8	4	no	—
903	C₂²	—	106	4	no	—
904	C₂²	—	106	8	no	—
905	C₂²	—	106	8	no	—
906	C₂²	—	106	16	no	—
907	C₂²	—	424	8	no	—
908	C₂²	—	424	8	no	—
909	C₂²	—	424	4	no	—
910	C₂²	—	212	16	no	—
911	C₂²	C₂²×#11719945	1	2	yes	—
912	C₂²	C₂²×#11719945	1	2	yes	—
913	C₂²	C₂²×#11719945	1	2	yes	—
914	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
915	C₄	—	2	4	no	—
916	C₄	—	2	8	no	—
917	C₄	—	2	8	no	—
918	C₄	—	106	4	no	—
919	C₄	—	106	8	no	—
920	C₄	—	106	8	no	—
921	C₄	C₂²×#11719945	1	2	yes	—
922	C₄	C₂²×#11719945	1	2	yes	—
923	C₄	C₂²×#11719945	1	2	yes	—
924	C₄	C₂²×#11719945	1	2	yes	—
925	C₂	—	2	2	no	—
926	C₂	—	2	2	no	—
927	C₂	—	2	2	no	—
928	C₂	—	4	4	no	—
929	C₂	—	212	8	no	—
930	C₂	—	212	4	no	—
931	C₂	C₂³×#11719945	1	1	yes	characteristic
932	C₂	#20289526	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3428	C₂
hypercenter	#3428	D₅₃
hypocenter	C₅₃	#62855
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3428

Complements

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

N	H ≅ G/N	type
1. #20288612	C₂	semidirect
2. #20288611	C₂	semidirect
3. #20288591	C₂	semidirect
4. #20288586	C₂	semidirect
5. #20288560	C₂	semidirect
6. #20288451	C₂	semidirect
7. #20288450	C₂	semidirect
8. #20288400	C₂	semidirect
9. #20288131	C₂	semidirect
10. #20288120	C₂	semidirect
11. #20288044	C₂	semidirect
12. C₂×#16811192	C₂	semidirect
13. C₂×#16811187	C₂	semidirect
14. #20287916	C₂	semidirect
15. C₂×#16811097	C₂	semidirect
16. C₅₃×#3428	C₂	semidirect
19. #16811358	C₂²	semidirect
20. #16811356	C₂²	semidirect
21. #16811345	C₂²	semidirect
22. #16811336	C₂²	semidirect
23. #16811321	C₂²	semidirect
24. #16811317	C₂²	semidirect
25. #16811302	C₂²	semidirect
26. #16811297	C₂²	semidirect
27. #16811294	C₂²	semidirect
28. #16811274	C₂²	semidirect
29. #16811269	C₂²	semidirect
30. #16811263	C₂²	semidirect
31. #16811254	C₂²	semidirect
32. #16811251	C₂²	semidirect
33. #16811251	C₂²	semidirect
35. #16811245	C₂²	semidirect
36. #16811244	C₂²	semidirect
37. #16811228	C₂²	semidirect
38. #16811224	C₂²	semidirect
39. #16811206	C₂²	semidirect
40. #16811201	C₂²	semidirect
41. #16811197	C₂²	semidirect
42. #16811194	C₂²	semidirect
45. #16811192	C₂²	semidirect
46. #16811192	C₂²	semidirect
47. #16811190	C₂²	semidirect
50. #16811187	C₂²	semidirect
51. #16811187	C₂²	semidirect
52. #16811187	C₂²	semidirect
54. #16811180	C₂²	semidirect
55. #16811176	C₂²	semidirect
56. #16811176	C₂²	semidirect
57. #16811173	C₂²	semidirect
58. #16811170	C₂²	semidirect
59. #16811169	C₂²	semidirect
60. C₂×#13133214	C₂²	semidirect
61. C₂×#13133213	C₂²	semidirect
62. #16811160	C₂²	semidirect
63. #16811157	C₂²	semidirect
64. C₂×#13133206	C₂²	semidirect
65. C₂×#13133205	C₂²	semidirect
66. #16811134	C₂²	semidirect
67. #16811132	C₂²	semidirect
68. #16811130	C₂²	semidirect
69. C₂×#13133192	C₂²	semidirect
70. C₂×#13133191	C₂²	semidirect
73. #16811104	C₂²	semidirect
74. #16811103	C₂²	semidirect
75. #16811100	C₂²	semidirect
76. #16811097	C₂²	semidirect
77. #16811097	C₂²	semidirect
78. #16811097	C₂²	semidirect
79. #16811097	C₂²	semidirect
80. #16811097	C₂²	semidirect
82. C₄×#11719945	C₂²	semidirect
83. #16811091	C₂²	semidirect
84. C₂×C₄×D₂₁₂	C₂²	semidirect
85. C₂×#13133179	C₂²	semidirect
88. #117×D₅₃	C₂²	semidirect
91. C₅₃×#520	C₂²	semidirect
92. C₅₃×#520	C₂²	semidirect
93. C₅₃×#519	C₂²	semidirect
95. C₅₃×#518	C₂²	semidirect
96. C₄×#41×C₅₃	C₂²	semidirect
97. C₄×#41×C₅₃	C₂²	semidirect
100. C₂×#117×C₅₃	C₂²	semidirect
107. C₂×#11719945	C₂³	semidirect
122. #13133217	C₂³	semidirect
123. #13133216	C₂³	semidirect
124. #13133216	C₂³	semidirect
125. #13133215	C₂³	semidirect
130. #13133213	C₂³	semidirect
131. #13133212	C₂³	semidirect
132. #13133211	C₂³	semidirect
133. #13133209	C₂³	semidirect
134. #13133208	C₂³	semidirect
135. #13133208	C₂³	semidirect
138. #13133206	C₂³	semidirect
141. #13133205	C₂³	semidirect
142. #13133204	C₂³	semidirect
143. #13133203	C₂³	semidirect
144. #13133202	C₂³	semidirect
145. #13133202	C₂³	semidirect
147. #13133200	C₂³	semidirect
148. #13133199	C₂³	semidirect
151. #13133196	C₂³	semidirect
152. #13133195	C₂³	semidirect
155. #13133193	C₂³	semidirect
160. #13133191	C₂³	semidirect
161. #13133191	C₂³	semidirect
162. #13133190	C₂³	semidirect
163. #13133190	C₂³	semidirect
165. #13133188	C₂³	semidirect
172. C₄×Dic₁₀₆	C₂³	semidirect
173. C₄×Dic₁₀₆	C₂³	semidirect
174. #13133182	C₂³	semidirect
177. C₄×D₂₁₂	C₂³	semidirect
178. C₄×D₂₁₂	C₂³	semidirect
181. #13133179	C₂³	semidirect
183. C₄×C₂²⋊D₅₃	C₂³	semidirect
184. C₄×C₂²⋊D₅₃	C₂³	semidirect
194. #13133175	C₂³	semidirect
195. #13133174	C₂³	semidirect
196. #13133174	C₂³	semidirect
200. C₄⋊C₄×D₅₃	C₂³	semidirect
211. C₄²×D₅₃	C₂³	semidirect
222. C₄×Q₈×C₅₃	C₂³	semidirect
223. C₄×Q₈×C₅₃	C₂³	semidirect
226. C₄×D₄×C₅₃	C₂³	semidirect
227. C₄×D₄×C₅₃	C₂³	semidirect
237. #117×C₅₃	C₂³	semidirect
238. #117×C₅₃	C₂³	semidirect
241. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
247. C₂×C₄²×C₅₃	C₂³	semidirect
270. C₂²×C₄×C₅₃	#41	semidirect
473. #3428	D₅₃	semidirect
542. #520	C₂×D₅₃	semidirect
543. #520	C₂×D₅₃	semidirect
545. #519	C₂×D₅₃	semidirect
553. #518	C₂×D₅₃	semidirect
556. C₄×#41	C₂×D₅₃	semidirect
557. C₄×#41	C₂×D₅₃	semidirect
565. C₂×#117	C₂×D₅₃	semidirect
567. C₅₃	#62855	semidirect
652. C₄×Q₈	C₂²×D₅₃	semidirect
653. C₄×Q₈	C₂²×D₅₃	semidirect
667. C₄×D₄	C₂²×D₅₃	semidirect
668. C₄×D₄	C₂²×D₅₃	semidirect
690. #117	C₂²×D₅₃	semidirect
691. #117	C₂²×D₅₃	semidirect
697. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
714. C₂×C₄²	C₂²×D₅₃	semidirect
776. C₂²×C₄	#11719945	semidirect

Maximal subgroups

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

subgroup	index
#20288612	2
#20288611	2
#20288591	2
#20288586	2
#20288560	2
#20288451	2
#20288450	2
#20288400	2
#20288131	2
#20288120	2
#20288044	2
C₂×#16811192	2
C₂×#16811187	2
#20287916	2
C₂×#16811097	2
C₅₃×#3428	2
#62855	53