Subgroups — #28318349

Order 13568.

1018 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#430	C₂	1	1	yes	maximal, characteristic
2	#20291368	C₂	1	1	yes	maximal, characteristic
3	C₂×#16811586	C₂	1	2	yes	maximal
4	#20290521	C₂	1	4	yes	maximal, complemented
5	#20290517	C₂	1	4	yes	maximal, complemented
6	#20290396	C₂	1	2	yes	maximal
7	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂×#13133296	C₂²	1	2	yes	—
10	#16811638	C₄	1	8	yes	complemented
11	D₅₃⋊#108	C₂²	1	4	yes	—
12	#16811634	C₄	1	8	yes	complemented
13	#16811633	C₂²	1	4	yes	—
14	#16811586	—	2	2	no	—
15	#16811586	—	2	2	no	—
16	#16811586	C₂²	1	4	yes	—
17	#16811586	C₂²	1	4	yes	—
18	C₂×#13133271	—	2	2	no	—
19	C₂×C₈×#6157	—	2	2	no	—
20	#16811494	C₂²	1	8	yes	—
21	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
22	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
23	#117×D₅₃	C₂²	1	1	yes	characteristic
24	#16810581	C₄	1	1	yes	characteristic, complemented
25	#16810580	C₄	1	2	yes	complemented
26	#16810579	C₄	1	1	yes	characteristic, complemented
27	#16810578	C₄	1	1	yes	characteristic, complemented
28	#16810577	C₄	1	2	yes	complemented
29	#97×D₅₃	C₂²	1	2	yes	—
30	C₄×C₈×D₅₃	C₂²	1	2	yes	—
31	C₅₃×#405	C₄	1	1	yes	characteristic, complemented
32	C₂×#11719936	C₂×C₄	1	4	yes	—
33	D₅₃⋊M₁₆	—	2	2	no	—
34	D₅₃⋊M₁₆	—	2	2	no	—
35	D₅₃⋊M₁₆	C₂×C₄	1	4	yes	—
36	D₅₃⋊M₁₆	C₂³	1	4	yes	—
37	C₂×#11719940	—	2	2	no	—
38	C₂×D₅₃⋊C₈	—	2	2	no	—
39	#13133296	—	2	2	no	—
40	#13133296	—	2	2	no	—
41	#13133296	C₂×C₄	1	4	yes	—
42	#13133296	C₂³	1	4	yes	—
43	C₂×C₄⋊#6157	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊#6157	—	2	2	no	—
45	C₂×C₄×#6157	—	2	2	no	—
46	#13133288	C₂×C₄	1	8	yes	complemented
47	#13133287	C₂×C₄	1	8	yes	complemented
48	#13133286	C₂×C₄	1	8	yes	—
49	#13133285	C₂×C₄	1	8	yes	—
50	#13133271	—	2	4	no	—
51	#13133271	—	2	4	no	—
52	C₈×#6157	—	2	4	no	—
53	C₈×#6157	—	2	4	no	—
54	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
55	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
56	C₂×#11719912	C₂×C₄	1	2	yes	—
57	M₁₆×D₅₃	C₂×C₄	1	4	yes	—
58	M₁₆×D₅₃	C₂×C₄	1	4	yes	—
59	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	D₄	1	2	yes	—
63	C₂×C₈×D₅₃	D₄	1	2	yes	—
64	C₂×C₈×D₅₃	Q₈	1	2	yes	—
65	C₂×C₈×D₅₃	Q₈	1	2	yes	—
66	C₂×C₈×D₅₃	C₂³	1	2	yes	—
67	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
69	#13133176	C₂×C₄	1	1	yes	characteristic
70	#13133175	—	2	1	no	—
71	#13133174	C₂×C₄	1	2	yes	—
72	#13133173	—	2	1	no	—
73	C₄⋊C₄×D₅₃	—	2	1	no	—
74	C₂²⋊C₄×D₅₃	—	2	1	no	—
75	C₄²×D₅₃	C₂³	1	2	yes	—
76	#13133128	C₂×C₄	1	2	yes	complemented
77	#13133127	C₂×C₄	1	2	yes	complemented
78	#13133127	C₂×C₄	1	2	yes	complemented
79	C₄×#88322	C₂×C₄	1	2	yes	complemented
80	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
81	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
82	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
84	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
85	#97×C₅₃	C₂×C₄	1	2	yes	complemented
86	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
87	C₂³×D₅₃	#41	1	1	yes	characteristic
88	C₂²×#6157	—	2	4	no	—
89	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₅₃	#41	1	1	yes	characteristic
91	C₂×C₄×D₅₃	—	2	2	no	—
92	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
95	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
96	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
97	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
98	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
100	C₂²⋊#6157	—	2	4	no	—
101	C₂²⋊#6157	—	2	4	no	—
102	#11719940	—	2	4	no	—
103	#11719940	—	2	4	no	—
104	C₂×#88324	—	2	4	no	—
105	C₄⋊#6157	—	2	4	no	—
106	C₄⋊#6157	C₂²×C₄	1	8	yes	—
107	C₄×#6157	—	2	4	no	—
108	C₄×#6157	—	2	4	no	—
109	#11719936	—	2	4	no	—
110	#11719936	C₂²×C₄	1	8	yes	—
111	D₅₃⋊C₈	—	2	4	no	—
112	D₅₃⋊C₈	—	2	4	no	—
113	M₁₆×C₅₃	C₄²	1	4	yes	—
114	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
115	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
116	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₄⋊C₄×C₅₃	—	2	1	no	—
120	C₂²⋊C₄×C₅₃	—	2	1	no	—
121	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
122	C₂²⋊Dic₅₃	—	2	1	no	—
123	#11719921	—	2	2	no	—
124	C₄⋊Dic₅₃	—	2	1	no	—
125	#11719919	—	2	2	no	—
126	C₄×Dic₅₃	—	2	2	no	—
127	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
128	#11719917	C₄²	1	4	yes	—
129	C₂×#88322	C₄⋊C₄	1	2	yes	—
130	C₂×#88322	C₄⋊C₄	1	2	yes	—
131	C₂×#88322	C₂²×C₄	1	2	yes	—
132	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
133	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
134	#11719912	C₄²	1	8	yes	—
135	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
136	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
137	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
138	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
139	C₈×D₅₃	C₂²×C₄	1	4	yes	—
140	C₈×D₅₃	C₂²×C₄	1	4	yes	—
141	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
142	C₈×D₅₃	C₂×D₄	1	2	yes	—
143	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
144	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
145	C₈×D₅₃	C₂×Q₈	1	2	yes	—
146	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
147	C₂³×C₅₃	#117	1	1	yes	characteristic
148	C₂²×D₅₃	—	4	2	no	—
149	C₂²×D₅₃	#117	1	1	yes	characteristic
150	C₂²×D₅₃	C₄×D₄	1	2	yes	—
151	C₂²×D₅₃	C₄×Q₈	1	2	yes	—
152	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
153	C₂×#6157	—	2	8	no	—
154	C₂×#6157	—	4	8	no	—
155	C₂×C₄×C₅₃	—	2	2	no	—
156	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₅₃	—	2	2	no	—
161	C₂×Dic₅₃	#117	1	1	yes	characteristic
162	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
163	C₂×Dic₅₃	C₄×Q₈	1	2	yes	—
164	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
165	C₄×D₅₃	—	4	4	no	—
166	C₄×D₅₃	C₂×C₄²	1	2	yes	—
167	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₄×D₅₃	C₄×D₄	1	2	yes	—
169	C₄×D₅₃	C₄×D₄	1	2	yes	—
170	C₄×D₅₃	C₄×Q₈	1	2	yes	—
171	C₄×D₅₃	C₄×Q₈	1	2	yes	—
172	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
173	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
174	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
175	C₄×D₅₃	C₂²×Q₈	1	1	yes	characteristic
176	#88324	—	2	8	no	—
177	C₈×C₅₃	C₂×C₄²	1	4	yes	—
178	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	#88322	C₂×C₄²	1	4	yes	—
182	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
183	#88322	C₂×C₄⋊C₄	1	2	yes	—
184	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
185	#20444	—	53	1	no	maximal, Sylow
186	C₂²×C₅₃	—	4	1	no	—
187	C₂²×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
188	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
189	C₂×D₅₃	—	2	2	no	—
190	C₂×D₅₃	—	2	4	no	—
191	C₂×D₅₃	—	4	1	no	—
192	C₂×D₅₃	—	4	2	no	—
193	C₂×D₅₃	C₄×C₄⋊C₄	1	2	yes	—
194	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×D₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
196	#6157	—	4	8	no	—
197	C₄×C₅₃	—	4	2	no	—
198	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
199	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
200	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
201	Dic₅₃	—	4	2	no	—
202	Dic₅₃	C₄×C₄⋊C₄	1	2	yes	—
203	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
204	Dic₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
205	C₂×#430	—	53	1	no	—
206	#2911	—	53	1	no	—
207	C₂×#405	—	53	1	no	—
208	C₂×#405	—	53	2	no	—
209	#1773	—	53	4	no	—
210	#1772	—	53	4	no	—
211	#1733	—	53	2	no	—
212	C₂×C₅₃	—	2	1	no	—
213	C₂×C₅₃	—	2	2	no	—
214	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
215	D₅₃	—	2	1	no	—
216	D₅₃	—	2	2	no	—
217	D₅₃	#2955	1	2	yes	—
218	C₂²×M₁₆	—	53	1	no	—
219	C₂²×M₁₆	—	53	2	no	—
220	C₂³×C₈	—	53	1	no	—
221	C₂×#117	—	53	1	no	—
222	C₂×#117	—	53	2	no	—
223	#430	—	53	8	no	—
224	C₂×#108	—	53	4	no	—
225	#428	—	53	8	no	—
226	#427	—	53	4	no	—
227	#405	—	53	1	no	—
228	#405	—	53	1	no	—
229	#405	—	53	1	no	—
230	#405	—	53	2	no	—
231	#405	—	53	2	no	—
232	#405	—	53	4	no	—
233	#405	—	53	4	no	—
234	#405	—	106	2	no	—
235	#405	—	106	2	no	—
236	#405	#6157	1	1	yes	characteristic, complemented
237	C₂×#97	—	53	2	no	—
238	C₂×#97	—	106	2	no	—
239	C₂×C₄×C₈	—	53	2	no	—
240	C₂×C₄×C₈	—	106	2	no	—
241	#339	—	53	8	no	—
242	C₅₃	#20444	1	1	yes	characteristic, complemented, Sylow
243	C₂³×C₄	—	53	1	no	—
244	C₂×M₁₆	—	53	1	no	—
245	C₂×M₁₆	—	53	4	no	—
246	C₂×M₁₆	—	53	4	no	—
247	C₂×M₁₆	—	53	2	no	—
248	C₂×M₁₆	—	53	4	no	—
249	C₂×M₁₆	—	53	4	no	—
250	C₂×M₁₆	—	53	4	no	—
251	C₂×M₁₆	—	106	2	no	—
252	C₂×M₁₆	—	106	2	no	—
253	C₂×M₁₆	—	106	2	no	—
254	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
255	C₂²×C₈	—	53	1	no	—
256	C₂²×C₈	—	53	2	no	—
257	C₂²×C₈	—	53	2	no	—
258	C₂²×C₈	—	53	2	no	—
259	C₂²×C₈	—	53	2	no	—
260	C₂²×C₈	—	53	1	no	—
261	C₂²×C₈	—	53	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	53	2	no	—
265	C₂²×C₈	—	106	2	no	—
266	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
267	#117	—	53	1	no	—
268	#117	—	53	2	no	—
269	#117	—	53	4	no	—
270	#117	—	53	4	no	—
271	#117	—	106	1	no	—
272	#117	—	106	1	no	—
273	#117	—	106	2	no	—
274	#117	—	106	2	no	—
275	#117	C₂×#6157	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	53	4	no	—
277	C₂×C₄⋊C₄	—	106	1	no	—
278	C₂×C₂²⋊C₄	—	106	1	no	—
279	C₂×C₂²⋊C₄	—	106	2	no	—
280	C₂×C₄²	—	53	2	no	—
281	C₂×C₄²	—	106	2	no	—
282	#108	—	53	8	no	—
283	#108	—	53	8	no	—
284	#107	—	53	8	no	—
285	#106	—	53	8	no	—
286	#97	—	53	2	no	—
287	#97	—	53	2	no	—
288	#97	—	53	2	no	—
289	#97	—	106	4	no	—
290	#97	—	106	4	no	—
291	#97	C₂×#6157	1	2	yes	complemented
292	C₄×C₈	—	53	2	no	—
293	C₄×C₈	—	53	2	no	—
294	C₄×C₈	—	53	2	no	—
295	C₄×C₈	—	106	4	no	—
296	C₄×C₈	—	106	4	no	—
297	C₄×C₈	C₂×#6157	1	2	yes	complemented
298	C₂⁴	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	2	no	—
301	C₂²×C₄	—	53	2	no	—
302	C₂²×C₄	—	53	2	no	—
303	C₂²×C₄	—	53	2	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	106	2	no	—
309	C₂²×C₄	—	106	4	no	—
310	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
311	M₁₆	—	53	4	no	—
312	M₁₆	—	53	8	no	—
313	M₁₆	—	53	8	no	—
314	M₁₆	—	106	4	no	—
315	M₁₆	—	106	4	no	—
316	M₁₆	—	106	4	no	—
317	M₁₆	C₄×#6157	1	4	yes	—
318	C₂×C₈	—	53	2	no	—
319	C₂×C₈	—	53	2	no	—
320	C₂×C₈	—	53	1	no	—
321	C₂×C₈	—	53	2	no	—
322	C₂×C₈	—	53	1	no	—
323	C₂×C₈	—	53	4	no	—
324	C₂×C₈	—	53	4	no	—
325	C₂×C₈	—	53	2	no	—
326	C₂×C₈	—	53	1	no	—
327	C₂×C₈	—	53	2	no	—
328	C₂×C₈	—	53	2	no	—
329	C₂×C₈	—	53	2	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	2	no	—
332	C₂×C₈	—	53	1	no	—
333	C₂×C₈	—	53	2	no	—
334	C₂×C₈	—	53	1	no	—
335	C₂×C₈	—	106	4	no	—
336	C₂×C₈	—	106	4	no	—
337	C₂×C₈	—	106	4	no	—
338	C₂×C₈	C₄⋊#6157	1	2	yes	—
339	C₂×C₈	C₄⋊#6157	1	2	yes	—
340	C₂×C₈	C₂²×#6157	1	2	yes	—
341	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
342	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	53	8	no	—
345	C₄⋊C₄	—	106	2	no	—
346	C₄⋊C₄	—	106	4	no	—
347	C₄⋊C₄	—	106	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	106	2	no	—
350	C₂²⋊C₄	—	106	4	no	—
351	C₂²⋊C₄	—	106	4	no	—
352	C₂²⋊C₄	—	106	1	no	—
353	C₄²	—	53	2	no	—
354	C₄²	—	106	2	no	—
355	C₄²	—	106	4	no	—
356	C₄²	—	106	4	no	—
357	C₄²	C₂²×#6157	1	2	yes	—
358	C₂³	—	53	2	no	—
359	C₂³	—	53	1	no	—
360	C₂³	—	53	2	no	—
361	C₂³	—	53	1	no	—
362	C₂³	—	212	2	no	—
363	C₂³	#13133296	1	1	yes	characteristic
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	53	2	no	—
366	C₂×C₄	—	53	2	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	53	2	no	—
370	C₂×C₄	—	53	2	no	—
371	C₂×C₄	—	53	2	no	—
372	C₂×C₄	—	53	2	no	—
373	C₂×C₄	—	53	2	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	1	no	—
376	C₂×C₄	—	53	2	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	106	8	no	—
380	C₂×C₄	—	106	2	no	—
381	C₂×C₄	—	212	4	no	—
382	C₂×C₄	—	212	8	no	—
383	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
384	C₂×C₄	C₂×C₄⋊#6157	1	2	yes	—
385	C₂×C₄	#13133296	1	1	yes	characteristic
386	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
387	C₈	—	53	4	no	—
388	C₈	—	53	1	no	—
389	C₈	—	53	1	no	—
390	C₈	—	53	2	no	—
391	C₈	—	106	8	no	—
392	C₈	C₂×C₄×#6157	1	4	yes	—
393	C₈	C₂×C₄⋊#6157	1	2	yes	—
394	C₈	C₂×C₄⋊#6157	1	1	yes	characteristic
395	C₈	C₂×C₄⋊#6157	1	1	yes	characteristic
396	C₂²	—	4	1	no	—
397	C₂²	—	53	1	no	—
398	C₂²	—	53	1	no	—
399	C₂²	—	53	2	no	—
400	C₂²	—	106	2	no	—
401	C₂²	—	106	4	no	—
402	C₂²	—	212	1	no	—
403	C₂²	—	212	2	no	—
404	C₂²	C₄×C₄⋊#6157	1	2	yes	—
405	C₂²	C₂×#13133296	1	1	yes	characteristic
406	C₄	—	4	2	no	—
407	C₄	—	53	1	no	—
408	C₄	—	53	1	no	—
409	C₄	—	53	2	no	—
410	C₄	—	212	2	no	—
411	C₄	—	212	8	no	—
412	C₄	C₄×C₄⋊#6157	1	2	yes	—
413	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
414	C₄	C₂²×C₄⋊#6157	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	2	no	—
417	C₂	—	53	2	no	—
418	C₂	—	106	1	no	—
419	C₂	—	106	2	no	—
420	C₂	C₂×C₄×C₄⋊#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×C₄⋊#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₅₃×#405	C₄
socle	C₂×C₅₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₅₃	#41
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	#20444
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #20290521	C₂	semidirect
5. #20290517	C₂	semidirect
10. #16811638	C₄	semidirect
12. #16811634	C₄	semidirect
24. #16810581	C₄	semidirect
25. #16810580	C₄	semidirect
26. #16810579	C₄	semidirect
27. #16810578	C₄	semidirect
28. #16810577	C₄	semidirect
31. C₅₃×#405	C₄	semidirect
46. #13133288	C₂×C₄	semidirect
47. #13133287	C₂×C₄	semidirect
76. #13133128	C₂×C₄	semidirect
77. #13133127	C₂×C₄	semidirect
78. #13133127	C₂×C₄	semidirect
79. C₄×#88322	C₂×C₄	semidirect
80. C₈×Dic₅₃	C₂×C₄	semidirect
81. C₈×Dic₅₃	C₂×C₄	semidirect
85. #97×C₅₃	C₂×C₄	semidirect
86. C₄×C₈×C₅₃	C₂×C₄	semidirect
236. #405	#6157	semidirect
242. C₅₃	#20444	semidirect
291. #97	C₂×#6157	semidirect
297. C₄×C₈	C₂×#6157	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#430	2
#20291368	2
C₂×#16811586	2
#20290521	2
#20290517	2
#20290396	2
#405×D₅₃	2
#20444	53