Subgroups — #28292627

Order 13568.

11534 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#11719949	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288392	C₂	1	8	yes	maximal, complemented
4	#20288381	C₂	1	8	yes	maximal, complemented
5	#20288374	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288370	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288366	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288358	C₂	1	6	yes	maximal, complemented
9	#20288348	C₂	1	6	yes	maximal, complemented
10	D₄×#11719949	C₂	1	8	yes	maximal, complemented
11	#20288204	C₂	1	8	yes	maximal, complemented
12	#20288047	C₂	1	6	yes	maximal, complemented
13	#525×D₅₃	C₂	1	6	yes	maximal, complemented
14	#20287917	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811460	—	2	16	no	—
17	C₂×#13133265	C₂²	1	1	yes	characteristic, complemented
18	C₂×#13133265	C₂²	1	4	yes	complemented
19	C₂×#13133263	C₂²	1	6	yes	complemented
20	C₂×#13133263	C₂²	1	4	yes	complemented
21	C₂²×#11719949	—	2	16	no	—
22	C₂²×#11719949	C₂²	1	1	yes	characteristic
23	C₂²×#11719949	C₂²	1	3	yes	complemented
24	C₂²×#11719949	C₂²	1	3	yes	complemented
25	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#11719949	C₂²	1	8	yes	complemented
27	C₂²×#11719949	C₂²	1	8	yes	complemented
28	C₂²×#11719949	C₂²	1	4	yes	complemented
29	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
30	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
31	C₂³×D₂₁₂	C₂²	1	3	yes	complemented
32	C₂³×C₄×D₅₃	C₂²	1	3	yes	complemented
33	#16811295	C₂²	1	8	yes	complemented
34	#16811292	C₂²	1	8	yes	complemented
35	Q₈×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
36	#16811285	C₂²	1	8	yes	complemented
37	#16811284	C₂²	1	8	yes	complemented
38	#16811284	C₂²	1	8	yes	complemented
39	#16811276	C₂²	1	24	yes	complemented
40	#16811275	C₂²	1	24	yes	complemented
41	#16811269	C₂²	1	24	yes	complemented
42	#16811266	C₂²	1	24	yes	complemented
43	#16811264	C₂²	1	24	yes	complemented
44	#16811264	C₂²	1	24	yes	complemented
45	D₄×D₂₁₂	C₂²	1	24	yes	complemented
46	#16811257	C₂²	1	24	yes	complemented
47	#16811203	C₂²	1	24	yes	complemented
48	#16811198	C₂²	1	12	yes	complemented
49	#16811197	C₂²	1	6	yes	complemented
50	#16811192	C₂²	1	6	yes	complemented
51	#16811191	C₂²	1	12	yes	complemented
52	#16811187	C₂²	1	6	yes	complemented
53	#16811184	C₂²	1	24	yes	complemented
54	#16811174	C₂²	1	12	yes	complemented
55	#16811172	C₂²	1	12	yes	complemented
56	#16811136	C₂²	1	12	yes	complemented
57	#16811136	C₂²	1	24	yes	complemented
58	#16811135	C₂²	1	6	yes	complemented
59	#16811134	C₂²	1	6	yes	complemented
60	#16811133	C₂²	1	12	yes	complemented
61	#16811132	C₂²	1	24	yes	complemented
62	#16811131	C₂²	1	12	yes	complemented
63	#16811130	C₂²	1	6	yes	complemented
64	#16811129	C₂²	1	4	yes	complemented
65	#123×D₅₃	C₂²	1	12	yes	complemented
66	C₂²⋊Q₈×D₅₃	C₂²	1	12	yes	complemented
67	#121×D₅₃	C₂²	1	12	yes	complemented
68	#120×D₅₃	C₂²	1	12	yes	complemented
69	#16811105	C₂²	1	8	yes	complemented
70	#16811101	C₂²	1	1	yes	characteristic, complemented
71	#16811097	C₂²	1	6	yes	complemented
72	C₄×#11719949	C₂²	1	8	yes	complemented
73	C₄×D₄×D₅₃	C₂²	1	24	yes	complemented
74	#117×D₅₃	C₂²	1	6	yes	complemented
75	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
77	D₄×Q₈×C₅₃	C₂²	1	8	yes	complemented
78	C₅₃×#548	C₂²	1	8	yes	complemented
79	C₅₃×#536	C₂²	1	6	yes	complemented
80	C₅₃×#525	C₂²	1	6	yes	complemented
81	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
82	C₂⁴×D₅₃	C₂³	1	3	yes	—
83	#13133265	—	2	8	no	—
84	#13133265	—	2	32	no	—
85	#13133263	—	2	32	no	—
86	#13133263	—	2	48	no	—
87	C₂×#11719949	—	2	8	no	—
88	C₂×#11719949	—	2	64	no	—
89	C₂×#11719949	—	2	64	no	—
90	C₂×#11719949	—	2	32	no	—
91	C₂×#11719949	—	2	24	no	—
92	C₂×#11719949	—	2	24	no	—
93	C₂×#11719949	D₄	1	16	yes	complemented
94	C₂×#11719949	C₂³	1	24	yes	—
95	C₂×#11719949	C₂³	1	8	yes	—
96	C₂×#11719949	C₂³	1	12	yes	—
97	C₂×#11719949	C₂³	1	12	yes	—
98	C₂×#11719949	C₂³	1	4	yes	—
99	C₂×#11719949	C₂³	1	4	yes	—
100	C₂×#11719949	C₂³	1	12	yes	complemented
101	C₂×#11719949	C₂³	1	4	yes	complemented
102	C₂×#11719949	C₂³	1	6	yes	complemented
103	C₂×#11719945	C₂³	1	6	yes	—
104	C₂×#11719945	C₂³	1	12	yes	complemented
105	C₂×#11719945	C₂³	1	12	yes	complemented
106	C₂×#11719947	C₂³	1	4	yes	—
107	C₂×#11719947	C₂³	1	6	yes	complemented
108	#41×D₅₃	—	2	32	no	—
109	#41×D₅₃	—	2	48	no	—
110	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
111	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
112	C₂²×D₂₁₂	—	2	24	no	—
113	C₂²×D₂₁₂	C₂³	1	24	yes	—
114	C₂²×D₂₁₂	C₂³	1	6	yes	—
115	C₂²×D₂₁₂	C₂³	1	3	yes	—
116	C₂²×D₂₁₂	C₂³	1	3	yes	—
117	C₂²×D₂₁₂	C₂³	1	12	yes	complemented
118	C₂×D₄×D₅₃	C₂³	1	12	yes	—
119	C₂×D₄×D₅₃	C₂³	1	24	yes	—
120	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
121	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
122	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
123	C₂²×C₄×D₅₃	—	2	24	no	—
124	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
125	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
126	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
127	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
128	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
129	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
130	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
131	#13133215	C₂³	1	12	yes	complemented
132	#13133214	C₂³	1	12	yes	complemented
133	#13133213	C₂³	1	12	yes	complemented
134	#13133206	C₂³	1	12	yes	complemented
135	#13133206	C₂³	1	12	yes	complemented
136	#13133205	C₂³	1	12	yes	complemented
137	#13133202	C₂³	1	24	yes	complemented
138	#13133202	C₂³	1	48	yes	complemented
139	#13133201	C₂³	1	4	yes	—
140	#13133200	C₂³	1	12	yes	—
141	#13133199	C₂³	1	24	yes	complemented
142	#13133198	C₂³	1	4	yes	—
143	#13133197	C₂³	1	12	yes	complemented
144	#13133196	C₂³	1	12	yes	—
145	#13133195	C₂³	1	24	yes	complemented
146	#13133194	C₂³	1	8	yes	—
147	#13133193	C₂³	1	24	yes	complemented
148	#13133193	C₂³	1	12	yes	complemented
149	#13133192	C₂³	1	48	yes	complemented
150	#13133192	C₂³	1	12	yes	complemented
151	#13133192	C₂³	1	24	yes	complemented
152	#13133191	C₂³	1	12	yes	—
153	#13133191	C₂³	1	24	yes	complemented
154	#13133190	C₂³	1	48	yes	complemented
155	#13133190	C₂³	1	24	yes	complemented
156	#13133189	C₂³	1	8	yes	—
157	#13133188	C₂³	1	12	yes	complemented
158	#13133187	C₂³	1	24	yes	—
159	#13133187	C₂³	1	12	yes	—
160	#13133187	C₂³	1	48	yes	complemented
161	#13133186	C₂³	1	4	yes	—
162	#13133185	C₂³	1	24	yes	—
163	#13133185	C₂³	1	12	yes	—
164	Q₈×Dic₅₃	C₂³	1	8	yes	complemented
165	C₄×D₂₁₂	C₂³	1	24	yes	complemented
166	C₄×D₂₁₂	C₂³	1	24	yes	complemented
167	D₄×Dic₅₃	C₂³	1	8	yes	—
168	#13133179	C₂³	1	24	yes	complemented
169	#13133179	C₂³	1	24	yes	complemented
170	C₄×C₂²⋊D₅₃	C₂³	1	24	yes	—
171	C₄×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
172	#13133177	C₂³	1	8	yes	—
173	#13133177	C₂³	1	24	yes	complemented
174	#13133176	C₂³	1	6	yes	—
175	#13133175	C₂³	1	12	yes	complemented
176	#13133174	C₂³	1	12	yes	complemented
177	#13133173	C₂³	1	4	yes	—
178	C₄⋊C₄×D₅₃	C₂³	1	24	yes	complemented
179	C₄⋊C₄×D₅₃	C₂³	1	12	yes	complemented
180	C₂²⋊C₄×D₅₃	C₂³	1	24	yes	—
181	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
182	C₂²⋊C₄×D₅₃	C₂³	1	24	yes	complemented
183	C₄²×D₅₃	C₂³	1	12	yes	complemented
184	2₋¹⁺⁴×C₅₃	—	2	8	no	—
185	C₂×#41×C₅₃	C₂³	1	6	yes	—
186	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
187	C₂²×Q₈×C₅₃	—	2	8	no	—
188	C₂²×Q₈×C₅₃	C₂³	1	8	yes	—
189	C₂²×Q₈×C₅₃	C₂³	1	3	yes	—
190	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×Q₈×C₅₃	C₂³	1	4	yes	complemented
192	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
193	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	complemented
194	#124×C₅₃	C₂³	1	12	yes	complemented
195	#123×C₅₃	C₂³	1	12	yes	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
197	C₂²⋊Q₈×C₅₃	C₂³	1	24	yes	complemented
198	#121×C₅₃	C₂³	1	12	yes	—
199	#120×C₅₃	C₂³	1	4	yes	—
200	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
201	C₄×D₄×C₅₃	C₂³	1	24	yes	—
202	#117×C₅₃	C₂³	1	6	yes	—
203	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
204	C₂³×D₅₃	—	2	12	no	—
205	C₂³×D₅₃	—	4	12	no	—
206	C₂³×D₅₃	C₂⁴	1	12	yes	—
207	C₂³×D₅₃	C₂⁴	1	12	yes	—
208	C₂³×D₅₃	C₂⁴	1	3	yes	—
209	C₂³×D₅₃	C₂⁴	1	3	yes	—
210	#41×C₅₃	—	2	16	no	—
211	#41×C₅₃	—	2	24	no	—
212	C₂×Q₈×C₅₃	—	2	32	no	—
213	C₂×Q₈×C₅₃	—	2	16	no	—
214	C₂×Q₈×C₅₃	—	2	12	no	—
215	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	complemented
216	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
217	C₂×Q₈×C₅₃	C₂⁴	1	12	yes	—
218	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
219	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
220	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
221	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
222	C₂²×C₄×C₅₃	—	2	12	no	—
223	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
225	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
226	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
227	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
228	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
229	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
230	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
231	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
232	C₂²×Dic₅₃	—	2	4	no	—
233	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
234	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
235	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
236	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
237	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
238	#11719949	—	2	32	no	—
239	#11719949	—	2	16	no	—
240	#11719949	—	2	96	no	—
241	#11719949	—	2	48	no	—
242	#11719949	—	2	24	no	—
243	#11719949	—	2	48	no	—
244	#11719949	—	2	48	no	—
245	#11719949	C₂×D₄	1	32	yes	complemented
246	#11719949	C₂×D₄	1	32	yes	complemented
247	Q₈×D₅₃	—	2	16	no	—
248	Q₈×D₅₃	—	2	24	no	—
249	#11719947	—	2	16	no	—
250	#11719947	—	2	24	no	—
251	D₄×D₅₃	—	2	48	no	—
252	D₄×D₅₃	—	2	48	no	—
253	D₄×D₅₃	—	2	24	no	—
254	D₄×D₅₃	—	4	48	no	—
255	#11719945	—	2	24	no	—
256	#11719945	—	2	48	no	—
257	#11719945	—	2	48	no	—
258	C₂×D₂₁₂	—	2	24	no	—
259	C₂×D₂₁₂	—	2	12	no	—
260	C₂×D₂₁₂	—	2	96	no	—
261	C₂×D₂₁₂	—	2	48	no	—
262	C₂×D₂₁₂	C₂×D₄	1	24	yes	complemented
263	C₂×D₂₁₂	C₂⁴	1	12	yes	—
264	C₂×D₂₁₂	C₂⁴	1	24	yes	—
265	C₂×D₂₁₂	C₂⁴	1	6	yes	—
266	C₂×D₂₁₂	C₂⁴	1	12	yes	—
267	C₂×D₂₁₂	C₂⁴	1	24	yes	—
268	C₂×D₂₁₂	C₂⁴	1	12	yes	—
269	C₂×C₄×D₅₃	—	2	12	no	—
270	C₂×C₄×D₅₃	—	2	12	no	—
271	C₂×C₄×D₅₃	—	2	12	no	—
272	C₂×C₄×D₅₃	—	2	48	no	—
273	C₂×C₄×D₅₃	—	2	48	no	—
274	C₂×C₄×D₅₃	—	2	48	no	—
275	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	complemented
276	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
277	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
278	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
279	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
280	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
281	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
282	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
283	C₂×C₄×D₅₃	C₂⁴	1	24	yes	—
284	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
285	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
286	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
287	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
288	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
289	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
290	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
291	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
292	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
293	C₄²×C₅₃	C₂⁴	1	12	yes	—
294	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
295	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
296	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
297	#11719921	C₂⁴	1	24	yes	—
298	#11719921	C₂⁴	1	24	yes	—
299	#11719921	C₂⁴	1	24	yes	—
300	#11719921	C₂⁴	1	8	yes	—
301	#11719921	C₂⁴	1	24	yes	—
302	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
303	C₄⋊Dic₅₃	C₂⁴	1	12	yes	—
304	#11719919	C₂⁴	1	8	yes	—
305	#11719919	C₂⁴	1	8	yes	—
306	#11719919	C₂⁴	1	24	yes	—
307	C₄×Dic₅₃	C₂⁴	1	8	yes	—
308	C₄×Dic₅₃	C₂⁴	1	12	yes	—
309	C₂³×C₅₃	—	2	2	no	—
310	C₂³×C₅₃	—	2	4	no	—
311	C₂³×C₅₃	C₂⁵	1	4	yes	—
312	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
313	C₂³×C₅₃	C₂⁵	1	2	yes	—
314	C₂²×D₅₃	—	2	6	no	—
315	C₂²×D₅₃	—	2	24	no	—
316	C₂²×D₅₃	—	2	24	no	—
317	C₂²×D₅₃	—	2	24	no	—
318	C₂²×D₅₃	—	4	6	no	—
319	C₂²×D₅₃	—	4	12	no	—
320	C₂²×D₅₃	—	4	6	no	—
321	C₂²×D₅₃	—	4	24	no	—
322	C₂²×D₅₃	—	4	48	no	—
323	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
324	C₂²×D₅₃	C₂⁵	1	6	yes	—
325	C₂²×D₅₃	C₂⁵	1	4	yes	—
326	C₂²×D₅₃	C₂⁵	1	6	yes	—
327	Q₈×C₅₃	—	2	12	no	—
328	Q₈×C₅₃	—	2	24	no	—
329	Q₈×C₅₃	C₂²×D₄	1	16	yes	—
330	D₄×C₅₃	—	2	8	no	—
331	D₄×C₅₃	—	2	16	no	—
332	D₄×C₅₃	—	2	12	no	—
333	C₂×C₄×C₅₃	—	2	6	no	—
334	C₂×C₄×C₅₃	—	2	24	no	—
335	C₂×C₄×C₅₃	—	2	24	no	—
336	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
337	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
338	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
339	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
340	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
341	C₂²⋊D₅₃	—	2	8	no	—
342	C₂²⋊D₅₃	—	2	16	no	—
343	C₂²⋊D₅₃	—	2	24	no	—
344	C₂²⋊D₅₃	—	2	8	no	—
345	C₂²⋊D₅₃	—	4	24	no	—
346	C₂×Dic₅₃	—	2	2	no	—
347	C₂×Dic₅₃	—	2	4	no	—
348	C₂×Dic₅₃	—	2	4	no	—
349	C₂×Dic₅₃	—	2	8	no	—
350	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
351	C₂×Dic₅₃	C₂⁵	1	4	yes	—
352	C₂×Dic₅₃	C₂⁵	1	2	yes	—
353	C₂×Dic₅₃	C₂⁵	1	8	yes	—
354	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
355	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
356	D₂₁₂	—	2	48	no	—
357	D₂₁₂	—	2	24	no	—
358	D₂₁₂	—	2	24	no	—
359	D₂₁₂	—	2	12	no	—
360	D₂₁₂	—	4	24	no	—
361	D₂₁₂	C₂²×D₄	1	48	yes	—
362	C₄×D₅₃	—	2	24	no	—
363	C₄×D₅₃	—	2	24	no	—
364	C₄×D₅₃	—	2	24	no	—
365	C₄×D₅₃	—	2	24	no	—
366	C₄×D₅₃	—	2	8	no	—
367	C₄×D₅₃	—	2	12	no	—
368	C₄×D₅₃	—	2	12	no	—
369	C₄×D₅₃	—	4	24	no	—
370	C₄×D₅₃	C₂²×D₄	1	24	yes	—
371	C₄×D₅₃	C₂²×D₄	1	24	yes	—
372	Dic₁₀₆	—	2	12	no	—
373	Dic₁₀₆	—	2	8	no	—
374	#62811	—	53	1	no	maximal, Sylow
375	C₂²×C₅₃	—	2	8	no	—
376	C₂²×C₅₃	—	2	2	no	—
377	C₂²×C₅₃	—	2	2	no	—
378	C₂²×C₅₃	—	2	2	no	—
379	C₂²×C₅₃	—	2	4	no	—
380	C₂²×C₅₃	—	2	8	no	—
381	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
382	C₂²×C₅₃	#585	1	4	yes	complemented
383	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
384	C₂×D₅₃	—	2	12	no	—
385	C₂×D₅₃	—	2	6	no	—
386	C₂×D₅₃	—	2	4	no	—
387	C₂×D₅₃	—	2	8	no	—
388	C₂×D₅₃	—	2	12	no	—
389	C₂×D₅₃	—	4	12	no	—
390	C₂×D₅₃	—	4	48	no	—
391	C₂×D₅₃	—	4	12	no	—
392	C₂×D₅₃	—	8	24	no	—
393	C₂×D₅₃	C₂³×D₄	1	12	yes	—
394	C₄×C₅₃	—	2	4	no	—
395	C₄×C₅₃	—	2	6	no	—
396	C₄×C₅₃	—	2	8	no	—
397	C₄×C₅₃	C₂³×D₄	1	12	yes	—
398	Dic₅₃	—	2	4	no	—
399	Dic₅₃	—	2	2	no	—
400	Dic₅₃	—	2	8	no	—
401	Dic₅₃	C₂³×D₄	1	2	yes	—
402	Dic₅₃	C₂³×D₄	1	2	yes	—
403	C₂×#585	—	53	1	no	—
404	C₂³×#41	—	53	1	no	—
405	#3489	—	53	8	no	—
406	#3488	—	53	8	no	—
407	#3487	—	53	1	no	—
408	#3487	—	53	1	no	—
409	#3486	—	53	1	no	—
410	#3486	D₅₃	1	1	yes	characteristic, complemented
411	#3485	—	53	6	no	—
412	#3484	—	53	6	no	—
413	D₄×#41	—	53	8	no	—
414	D₄×#41	—	53	8	no	—
415	#3449	—	53	6	no	—
416	C₂×#525	—	53	6	no	—
417	#3428	—	53	1	no	—
418	C₂×C₅₃	—	2	2	no	—
419	C₂×C₅₃	—	2	4	no	—
420	C₂×C₅₃	—	4	4	no	—
421	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
422	C₂×C₅₃	C₂×#585	1	2	yes	—
423	D₅₃	—	2	12	no	—
424	D₅₃	—	4	6	no	—
425	D₅₃	—	4	4	no	—
426	#585	—	106	16	no	—
427	C₂×2₋¹⁺⁴	—	53	1	no	—
428	C₂×2₋¹⁺⁴	—	53	4	no	—
429	C₂×2₋¹⁺⁴	C₂×D₅₃	1	1	yes	characteristic, complemented
430	C₂×H(5,𝔽₂)	—	53	6	no	—
431	C₂×H(5,𝔽₂)	—	53	4	no	—
432	C₂²×#41	—	53	6	no	—
433	C₂²×#41	—	53	4	no	—
434	C₂²×#41	—	53	1	no	—
435	C₂²×#41	—	53	3	no	—
436	C₂²×#41	—	53	8	no	—
437	C₂²×#41	—	53	3	no	—
438	C₂²×#41	—	53	1	no	—
439	C₂²×#41	—	53	8	no	—
440	C₂²×#41	—	53	4	no	—
441	C₂²×#41	—	106	16	no	—
442	C₂³×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
443	C₂³×D₄	—	53	3	no	—
444	C₂⁴×C₄	—	53	3	no	—
445	#550	—	53	8	no	—
446	#550	—	53	8	no	—
447	D₄×Q₈	—	53	8	no	—
448	D₄×Q₈	C₂×D₅₃	1	8	yes	complemented
449	#548	—	53	8	no	—
450	#548	—	53	8	no	—
451	#548	—	53	8	no	—
452	#548	C₂×D₅₃	1	8	yes	complemented
453	#547	—	53	24	no	—
454	#547	—	53	24	no	—
455	#546	—	53	24	no	—
456	#546	—	53	24	no	—
457	#546	—	53	24	no	—
458	#546	—	53	24	no	—
459	D₄²	—	53	24	no	—
460	D₄²	—	53	24	no	—
461	#537	—	53	24	no	—
462	#536	—	53	6	no	—
463	#536	—	53	12	no	—
464	#536	C₂×D₅₃	1	6	yes	complemented
465	#535	—	53	6	no	—
466	#535	—	53	12	no	—
467	#535	—	53	6	no	—
468	#534	—	53	24	no	—
469	#532	—	53	12	no	—
470	#532	—	53	12	no	—
471	#525	—	53	6	no	—
472	#525	—	53	6	no	—
473	#525	—	53	12	no	—
474	#525	—	53	12	no	—
475	#525	—	53	24	no	—
476	#525	—	53	12	no	—
477	#525	—	53	4	no	—
478	#525	—	53	24	no	—
479	#525	—	53	6	no	—
480	#525	C₂×D₅₃	1	6	yes	complemented
481	C₂×#123	—	53	12	no	—
482	C₂×C₂²⋊Q₈	—	53	12	no	—
483	C₂×#121	—	53	12	no	—
484	C₂×#120	—	53	12	no	—
485	#520	—	53	8	no	—
486	#519	—	53	1	no	—
487	#519	C₂×D₅₃	1	1	yes	characteristic, complemented
488	#518	—	53	6	no	—
489	C₄×#41	—	53	8	no	—
490	C₂×C₄×D₄	—	53	24	no	—
491	C₂×#117	—	53	6	no	—
492	C₅₃	#62811	1	1	yes	characteristic, complemented, Sylow
493	C₂⁵	—	53	3	no	—
494	2₋¹⁺⁴	—	2	8	no	—
495	2₋¹⁺⁴	—	106	32	no	—
496	2₋¹⁺⁴	—	106	8	no	—
497	H(5,𝔽₂)	—	106	48	no	—
498	H(5,𝔽₂)	—	106	32	no	—
499	C₂×#41	—	53	16	no	—
500	C₂×#41	—	53	4	no	—
501	C₂×#41	—	53	4	no	—
502	C₂×#41	—	53	12	no	—
503	C₂×#41	—	53	6	no	—
504	C₂×#41	—	53	12	no	—
505	C₂×#41	—	53	24	no	—
506	C₂×#41	—	53	12	no	—
507	C₂×#41	—	53	8	no	—
508	C₂×#41	—	53	4	no	—
509	C₂×#41	—	53	4	no	—
510	C₂×#41	—	53	6	no	—
511	C₂×#41	—	53	6	no	—
512	C₂×#41	—	53	12	no	—
513	C₂×#41	—	53	12	no	—
514	C₂×#41	—	106	24	no	—
515	C₂×#41	—	106	48	no	—
516	C₂×#41	—	106	24	no	—
517	C₂×#41	—	106	64	no	—
518	C₂×#41	—	106	64	no	—
519	C₂×#41	—	106	32	no	—
520	C₂×#41	—	106	32	no	—
521	C₂×#41	—	106	8	no	—
522	C₂×#41	C₂²×D₅₃	1	6	yes	—
523	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
524	C₂²×Q₈	—	2	8	no	—
525	C₂²×Q₈	—	53	6	no	—
526	C₂²×Q₈	—	53	4	no	—
527	C₂²×Q₈	C₂²×D₅₃	1	3	yes	—
528	C₂²×Q₈	C₂²×D₅₃	1	8	yes	—
529	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
530	C₂²×Q₈	C₂²×D₅₃	1	4	yes	complemented
531	C₂²×D₄	—	53	12	no	—
532	C₂²×D₄	—	53	6	no	—
533	C₂²×D₄	—	53	12	no	—
534	C₂²×D₄	—	53	24	no	—
535	C₂²×D₄	—	53	3	no	—
536	C₂²×D₄	—	53	6	no	—
537	C₂²×D₄	—	53	3	no	—
538	C₂²×D₄	—	53	24	no	—
539	C₂²×D₄	—	53	12	no	—
540	C₂²×D₄	—	106	24	no	—
541	C₂³×C₄	—	53	3	no	—
542	C₂³×C₄	—	53	1	no	—
543	C₂³×C₄	—	53	12	no	—
544	C₂³×C₄	—	53	12	no	—
545	C₂³×C₄	—	53	12	no	—
546	C₂³×C₄	—	53	3	no	—
547	C₂³×C₄	—	53	3	no	—
548	C₂³×C₄	—	53	3	no	—
549	C₂³×C₄	—	106	24	no	—
550	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
551	C₄⋊Q₈	—	53	12	no	—
552	C₄⋊Q₈	C₂²×D₅₃	1	12	yes	complemented
553	#127	—	53	12	no	—
554	#127	—	53	12	no	—
555	#124	—	53	12	no	—
556	#124	—	53	12	no	—
557	#124	—	53	12	no	—
558	#124	C₂²×D₅₃	1	12	yes	complemented
559	#123	—	53	4	no	—
560	#123	—	53	12	no	—
561	#123	—	53	24	no	—
562	#123	—	53	48	no	—
563	#123	—	53	4	no	—
564	#123	—	53	24	no	—
565	#123	C₂²×D₅₃	1	12	yes	—
566	C₂²⋊Q₈	—	53	12	no	—
567	C₂²⋊Q₈	—	53	24	no	—
568	C₂²⋊Q₈	—	53	12	no	—
569	C₂²⋊Q₈	—	53	24	no	—
570	C₂²⋊Q₈	—	53	12	no	—
571	C₂²⋊Q₈	—	53	8	no	—
572	C₂²⋊Q₈	C₂²×D₅₃	1	12	yes	—
573	C₂²⋊Q₈	C₂²×D₅₃	1	24	yes	complemented
574	#121	—	53	8	no	—
575	#121	—	53	12	no	—
576	#121	—	53	12	no	—
577	#121	—	53	24	no	—
578	#121	—	53	12	no	—
579	#121	—	53	24	no	—
580	#121	—	53	48	no	—
581	#121	—	53	24	no	—
582	#121	—	53	48	no	—
583	#121	C₂²×D₅₃	1	12	yes	—
584	#120	—	53	4	no	—
585	#120	—	53	12	no	—
586	#120	—	53	24	no	—
587	#120	—	53	12	no	—
588	#120	—	53	24	no	—
589	#120	—	53	48	no	—
590	#120	C₂²×D₅₃	1	4	yes	—
591	C₄×Q₈	—	53	8	no	—
592	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
593	C₄×D₄	—	53	8	no	—
594	C₄×D₄	—	53	24	no	—
595	C₄×D₄	—	53	24	no	—
596	C₄×D₄	—	53	24	no	—
597	C₄×D₄	—	53	24	no	—
598	C₄×D₄	—	53	8	no	—
599	C₄×D₄	—	53	24	no	—
600	C₄×D₄	—	53	24	no	—
601	C₄×D₄	—	53	24	no	—
602	C₄×D₄	C₂²×D₅₃	1	24	yes	—
603	#117	—	53	6	no	—
604	#117	—	53	12	no	—
605	#117	—	53	4	no	—
606	#117	—	53	12	no	—
607	#117	C₂²×D₅₃	1	6	yes	—
608	C₂×C₄⋊C₄	—	53	12	no	—
609	C₂×C₄⋊C₄	—	53	24	no	—
610	C₂×C₂²⋊C₄	—	53	12	no	—
611	C₂×C₂²⋊C₄	—	53	24	no	—
612	C₂×C₂²⋊C₄	—	53	24	no	—
613	C₂×C₄²	—	53	12	no	—
614	C₂⁴	—	53	3	no	—
615	C₂⁴	—	53	12	no	—
616	C₂⁴	—	53	12	no	—
617	C₂⁴	—	53	3	no	—
618	C₂⁴	—	106	12	no	—
619	C₂⁴	—	212	12	no	—
620	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
621	#41	—	2	16	no	—
622	#41	—	2	24	no	—
623	#41	—	53	32	no	—
624	#41	—	53	32	no	—
625	#41	—	106	48	no	—
626	#41	—	106	48	no	—
627	#41	—	106	16	no	—
628	#41	—	106	24	no	—
629	#41	—	106	48	no	—
630	#41	—	106	24	no	—
631	#41	—	106	48	no	—
632	#41	—	106	96	no	—
633	#41	—	106	48	no	—
634	#41	—	106	32	no	—
635	#41	—	106	16	no	—
636	#41	—	106	24	no	—
637	C₂×Q₈	—	2	32	no	—
638	C₂×Q₈	—	2	16	no	—
639	C₂×Q₈	—	2	12	no	—
640	C₂×Q₈	—	53	4	no	—
641	C₂×Q₈	—	53	6	no	—
642	C₂×Q₈	—	106	24	no	—
643	C₂×Q₈	—	106	16	no	—
644	C₂×Q₈	D₄×D₅₃	1	8	yes	complemented
645	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
646	C₂×Q₈	C₂³×D₅₃	1	12	yes	—
647	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
648	C₂×D₄	—	53	8	no	—
649	C₂×D₄	—	53	4	no	—
650	C₂×D₄	—	53	12	no	—
651	C₂×D₄	—	53	4	no	—
652	C₂×D₄	—	53	24	no	—
653	C₂×D₄	—	53	24	no	—
654	C₂×D₄	—	53	12	no	—
655	C₂×D₄	—	53	12	no	—
656	C₂×D₄	—	53	24	no	—
657	C₂×D₄	—	53	6	no	—
658	C₂×D₄	—	53	12	no	—
659	C₂×D₄	—	53	24	no	—
660	C₂×D₄	—	106	96	no	—
661	C₂×D₄	—	106	48	no	—
662	C₂×D₄	—	106	24	no	—
663	C₂×D₄	—	106	24	no	—
664	C₂×D₄	—	106	48	no	—
665	C₂×D₄	—	106	48	no	—
666	C₂×D₄	—	106	12	no	—
667	C₂×D₄	—	212	48	no	—
668	C₂×D₄	C₂³×D₅₃	1	8	yes	—
669	C₂×D₄	C₂³×D₅₃	1	4	yes	—
670	C₂×D₄	C₂³×D₅₃	1	6	yes	—
671	C₂²×C₄	—	2	12	no	—
672	C₂²×C₄	—	53	1	no	—
673	C₂²×C₄	—	53	24	no	—
674	C₂²×C₄	—	53	6	no	—
675	C₂²×C₄	—	53	6	no	—
676	C₂²×C₄	—	53	2	no	—
677	C₂²×C₄	—	53	4	no	—
678	C₂²×C₄	—	53	2	no	—
679	C₂²×C₄	—	53	1	no	—
680	C₂²×C₄	—	53	12	no	—
681	C₂²×C₄	—	53	12	no	—
682	C₂²×C₄	—	53	4	no	—
683	C₂²×C₄	—	53	6	no	—
684	C₂²×C₄	—	53	12	no	—
685	C₂²×C₄	—	53	12	no	—
686	C₂²×C₄	—	53	6	no	—
687	C₂²×C₄	—	53	24	no	—
688	C₂²×C₄	—	106	12	no	—
689	C₂²×C₄	—	106	48	no	—
690	C₂²×C₄	—	106	48	no	—
691	C₂²×C₄	—	106	48	no	—
692	C₂²×C₄	—	106	12	no	—
693	C₂²×C₄	—	106	4	no	—
694	C₂²×C₄	—	106	12	no	—
695	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
696	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
697	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
698	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
699	C₄⋊C₄	—	53	8	no	—
700	C₄⋊C₄	—	53	8	no	—
701	C₄⋊C₄	—	53	8	no	—
702	C₄⋊C₄	—	53	12	no	—
703	C₄⋊C₄	—	53	24	no	—
704	C₄⋊C₄	C₂³×D₅₃	1	12	yes	—
705	C₄⋊C₄	C₂³×D₅₃	1	24	yes	—
706	C₂²⋊C₄	—	53	4	no	—
707	C₂²⋊C₄	—	53	8	no	—
708	C₂²⋊C₄	—	53	8	no	—
709	C₂²⋊C₄	—	53	8	no	—
710	C₂²⋊C₄	—	53	24	no	—
711	C₂²⋊C₄	—	53	24	no	—
712	C₂²⋊C₄	—	53	24	no	—
713	C₂²⋊C₄	—	53	24	no	—
714	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
715	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
716	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
717	C₄²	—	53	8	no	—
718	C₄²	—	53	12	no	—
719	C₄²	C₂³×D₅₃	1	12	yes	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	53	6	no	—
723	C₂³	—	53	12	no	—
724	C₂³	—	53	4	no	—
725	C₂³	—	53	6	no	—
726	C₂³	—	106	24	no	—
727	C₂³	—	106	24	no	—
728	C₂³	—	106	6	no	—
729	C₂³	—	106	24	no	—
730	C₂³	—	212	24	no	—
731	C₂³	—	212	6	no	—
732	C₂³	—	212	12	no	—
733	C₂³	—	212	6	no	—
734	C₂³	—	212	48	no	—
735	C₂³	C₂⁴×D₅₃	1	4	yes	—
736	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
737	C₂³	C₂⁴×D₅₃	1	2	yes	—
738	Q₈	—	2	24	no	—
739	Q₈	—	2	12	no	—
740	Q₈	—	106	8	no	—
741	Q₈	—	106	12	no	—
742	Q₈	C₂×D₄×D₅₃	1	16	yes	—
743	D₄	—	2	8	no	—
744	D₄	—	2	16	no	—
745	D₄	—	2	12	no	—
746	D₄	—	53	48	no	—
747	D₄	—	106	24	no	—
748	D₄	—	106	48	no	—
749	D₄	—	106	8	no	—
750	D₄	—	106	24	no	—
751	D₄	—	106	8	no	—
752	D₄	—	106	16	no	—
753	D₄	—	106	24	no	—
754	D₄	—	106	12	no	—
755	D₄	—	212	24	no	—
756	D₄	—	212	24	no	—
757	C₂×C₄	—	2	6	no	—
758	C₂×C₄	—	2	24	no	—
759	C₂×C₄	—	2	24	no	—
760	C₂×C₄	—	53	4	no	—
761	C₂×C₄	—	53	1	no	—
762	C₂×C₄	—	53	1	no	—
763	C₂×C₄	—	53	24	no	—
764	C₂×C₄	—	53	24	no	—
765	C₂×C₄	—	53	8	no	—
766	C₂×C₄	—	53	2	no	—
767	C₂×C₄	—	53	4	no	—
768	C₂×C₄	—	106	8	no	—
769	C₂×C₄	—	106	12	no	—
770	C₂×C₄	—	106	12	no	—
771	C₂×C₄	—	106	24	no	—
772	C₂×C₄	—	106	24	no	—
773	C₂×C₄	—	106	4	no	—
774	C₂×C₄	—	106	4	no	—
775	C₂×C₄	—	106	8	no	—
776	C₂×C₄	—	106	2	no	—
777	C₂×C₄	—	106	24	no	—
778	C₂×C₄	—	106	24	no	—
779	C₂×C₄	—	212	24	no	—
780	C₂×C₄	C₂×D₄×D₅₃	1	12	yes	—
781	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
782	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
783	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
784	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
785	C₂²	—	2	8	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	8	no	—
791	C₂²	—	53	12	no	—
792	C₂²	—	106	12	no	—
793	C₂²	—	106	4	no	—
794	C₂²	—	106	6	no	—
795	C₂²	—	106	8	no	—
796	C₂²	—	106	12	no	—
797	C₂²	—	424	24	no	—
798	C₂²	—	212	12	no	—
799	C₂²	—	212	48	no	—
800	C₂²	—	212	12	no	—
801	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
802	C₂²	#16811460	1	4	yes	complemented
803	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	2	6	no	—
806	C₄	—	2	8	no	—
807	C₄	—	53	2	no	—
808	C₄	—	53	2	no	—
809	C₄	—	106	2	no	—
810	C₄	—	106	4	no	—
811	C₄	—	106	8	no	—
812	C₄	C₂²×D₄×D₅₃	1	12	yes	—
813	C₂	—	2	2	no	—
814	C₂	—	2	4	no	—
815	C₂	—	4	4	no	—
816	C₂	—	106	12	no	—
817	C₂	—	212	4	no	—
818	C₂	—	212	6	no	—
819	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
820	C₂	C₂×#16811460	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3486	C₂
hypercenter	#3486	D₅₃
hypocenter	C₅₃	#62811
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3486

Complements

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

N	H ≅ G/N	type
1. C₂×#16811460	C₂	semidirect
2. C₂³×#11719949	C₂	semidirect
3. #20288392	C₂	semidirect
4. #20288381	C₂	semidirect
5. #20288374	C₂	semidirect
6. #20288370	C₂	semidirect
7. #20288366	C₂	semidirect
8. #20288358	C₂	semidirect
9. #20288348	C₂	semidirect
10. D₄×#11719949	C₂	semidirect
11. #20288204	C₂	semidirect
12. #20288047	C₂	semidirect
13. #525×D₅₃	C₂	semidirect
14. #20287917	C₂	semidirect
15. C₅₃×#3486	C₂	semidirect
17. C₂×#13133265	C₂²	semidirect
18. C₂×#13133265	C₂²	semidirect
19. C₂×#13133263	C₂²	semidirect
20. C₂×#13133263	C₂²	semidirect
23. C₂²×#11719949	C₂²	semidirect
24. C₂²×#11719949	C₂²	semidirect
25. C₂²×#11719949	C₂²	semidirect
26. C₂²×#11719949	C₂²	semidirect
27. C₂²×#11719949	C₂²	semidirect
28. C₂²×#11719949	C₂²	semidirect
29. C₂×#41×D₅₃	C₂²	semidirect
30. C₂×#41×D₅₃	C₂²	semidirect
31. C₂³×D₂₁₂	C₂²	semidirect
32. C₂³×C₄×D₅₃	C₂²	semidirect
33. #16811295	C₂²	semidirect
34. #16811292	C₂²	semidirect
35. Q₈×C₂²⋊D₅₃	C₂²	semidirect
36. #16811285	C₂²	semidirect
37. #16811284	C₂²	semidirect
38. #16811284	C₂²	semidirect
39. #16811276	C₂²	semidirect
40. #16811275	C₂²	semidirect
41. #16811269	C₂²	semidirect
42. #16811266	C₂²	semidirect
43. #16811264	C₂²	semidirect
44. #16811264	C₂²	semidirect
45. D₄×D₂₁₂	C₂²	semidirect
46. #16811257	C₂²	semidirect
47. #16811203	C₂²	semidirect
48. #16811198	C₂²	semidirect
49. #16811197	C₂²	semidirect
50. #16811192	C₂²	semidirect
51. #16811191	C₂²	semidirect
52. #16811187	C₂²	semidirect
53. #16811184	C₂²	semidirect
54. #16811174	C₂²	semidirect
55. #16811172	C₂²	semidirect
56. #16811136	C₂²	semidirect
57. #16811136	C₂²	semidirect
58. #16811135	C₂²	semidirect
59. #16811134	C₂²	semidirect
60. #16811133	C₂²	semidirect
61. #16811132	C₂²	semidirect
62. #16811131	C₂²	semidirect
63. #16811130	C₂²	semidirect
64. #16811129	C₂²	semidirect
65. #123×D₅₃	C₂²	semidirect
66. C₂²⋊Q₈×D₅₃	C₂²	semidirect
67. #121×D₅₃	C₂²	semidirect
68. #120×D₅₃	C₂²	semidirect
69. #16811105	C₂²	semidirect
70. #16811101	C₂²	semidirect
71. #16811097	C₂²	semidirect
72. C₄×#11719949	C₂²	semidirect
73. C₄×D₄×D₅₃	C₂²	semidirect
74. #117×D₅₃	C₂²	semidirect
75. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
76. C₂³×Q₈×C₅₃	C₂²	semidirect
77. D₄×Q₈×C₅₃	C₂²	semidirect
78. C₅₃×#548	C₂²	semidirect
79. C₅₃×#536	C₂²	semidirect
80. C₅₃×#525	C₂²	semidirect
81. C₅₃×#519	C₂²	semidirect
93. C₂×#11719949	D₄	semidirect
100. C₂×#11719949	C₂³	semidirect
101. C₂×#11719949	C₂³	semidirect
102. C₂×#11719949	C₂³	semidirect
104. C₂×#11719945	C₂³	semidirect
105. C₂×#11719945	C₂³	semidirect
107. C₂×#11719947	C₂³	semidirect
110. C₂×Q₈×D₅₃	C₂³	semidirect
111. C₂×Q₈×D₅₃	C₂³	semidirect
117. C₂²×D₂₁₂	C₂³	semidirect
120. C₂×D₄×D₅₃	C₂³	semidirect
121. C₂×D₄×D₅₃	C₂³	semidirect
130. C₂²×C₄×D₅₃	C₂³	semidirect
131. #13133215	C₂³	semidirect
132. #13133214	C₂³	semidirect
133. #13133213	C₂³	semidirect
134. #13133206	C₂³	semidirect
135. #13133206	C₂³	semidirect
136. #13133205	C₂³	semidirect
137. #13133202	C₂³	semidirect
138. #13133202	C₂³	semidirect
141. #13133199	C₂³	semidirect
143. #13133197	C₂³	semidirect
145. #13133195	C₂³	semidirect
147. #13133193	C₂³	semidirect
148. #13133193	C₂³	semidirect
149. #13133192	C₂³	semidirect
150. #13133192	C₂³	semidirect
151. #13133192	C₂³	semidirect
153. #13133191	C₂³	semidirect
154. #13133190	C₂³	semidirect
155. #13133190	C₂³	semidirect
157. #13133188	C₂³	semidirect
160. #13133187	C₂³	semidirect
164. Q₈×Dic₅₃	C₂³	semidirect
165. C₄×D₂₁₂	C₂³	semidirect
166. C₄×D₂₁₂	C₂³	semidirect
168. #13133179	C₂³	semidirect
169. #13133179	C₂³	semidirect
171. C₄×C₂²⋊D₅₃	C₂³	semidirect
173. #13133177	C₂³	semidirect
175. #13133175	C₂³	semidirect
176. #13133174	C₂³	semidirect
178. C₄⋊C₄×D₅₃	C₂³	semidirect
179. C₄⋊C₄×D₅₃	C₂³	semidirect
182. C₂²⋊C₄×D₅₃	C₂³	semidirect
183. C₄²×D₅₃	C₂³	semidirect
186. C₂×#41×C₅₃	C₂³	semidirect
191. C₂²×Q₈×C₅₃	C₂³	semidirect
193. C₄⋊Q₈×C₅₃	C₂³	semidirect
194. #124×C₅₃	C₂³	semidirect
197. C₂²⋊Q₈×C₅₃	C₂³	semidirect
200. C₄×Q₈×C₅₃	C₂³	semidirect
215. C₂×Q₈×C₅₃	C₂×D₄	semidirect
245. #11719949	C₂×D₄	semidirect
246. #11719949	C₂×D₄	semidirect
262. C₂×D₂₁₂	C₂×D₄	semidirect
275. C₂×C₄×D₅₃	C₂×D₄	semidirect
382. C₂²×C₅₃	#585	semidirect
410. #3486	D₅₃	semidirect
429. C₂×2₋¹⁺⁴	C₂×D₅₃	semidirect
442. C₂³×Q₈	C₂×D₅₃	semidirect
448. D₄×Q₈	C₂×D₅₃	semidirect
452. #548	C₂×D₅₃	semidirect
464. #536	C₂×D₅₃	semidirect
480. #525	C₂×D₅₃	semidirect
487. #519	C₂×D₅₃	semidirect
492. C₅₃	#62811	semidirect
523. C₂×#41	C₂²×D₅₃	semidirect
530. C₂²×Q₈	C₂²×D₅₃	semidirect
552. C₄⋊Q₈	C₂²×D₅₃	semidirect
558. #124	C₂²×D₅₃	semidirect
573. C₂²⋊Q₈	C₂²×D₅₃	semidirect
592. C₄×Q₈	C₂²×D₅₃	semidirect
644. C₂×Q₈	D₄×D₅₃	semidirect
802. C₂²	#16811460	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811460	2
C₂³×#11719949	2
#20288392	2
#20288381	2
#20288374	2
#20288370	2
#20288366	2
#20288358	2
#20288348	2
D₄×#11719949	2
#20288204	2
#20288047	2
#525×D₅₃	2
#20287917	2
C₅₃×#3486	2
#62811	53