Subgroups — #34108859

Order 20096.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097777	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#23757782	C₂	1	1	yes	maximal, characteristic
4	#23757351	C₂	1	1	yes	maximal, characteristic, complemented
5	#23757349	C₂	1	1	yes	maximal, characteristic, complemented
6	#23757347	C₂	1	1	yes	maximal, characteristic, complemented
7	#23757347	C₂	1	1	yes	maximal, characteristic, complemented
8	#23757346	C₂	1	1	yes	maximal, characteristic, complemented
9	#23757338	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊D₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#23757298	C₂	1	1	yes	maximal, characteristic, complemented
12	#23757238	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×D₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#23757230	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14578954	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
18	#19097777	—	2	4	no	—
19	C₂×#14578938	C₂²	1	1	yes	characteristic
20	C₂×#14578938	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14578937	C₂²	1	1	yes	characteristic
22	C₂×#14578937	C₂²	1	1	yes	characteristic
23	C₂×#14578937	C₂²	1	1	yes	characteristic, complemented
24	M₁₆×D₁₅₇	—	2	4	no	—
25	C₂×C₈×D₁₅₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×D₁₅₇	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₁₅₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₅₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₅₇	C₂²	1	1	yes	characteristic, complemented
30	#19097756	C₄	1	1	yes	characteristic
31	#19097753	C₄	1	1	yes	characteristic
32	#19097749	C₄	1	1	yes	characteristic
33	#19097748	C₄	1	1	yes	characteristic
34	#19097744	C₄	1	1	yes	characteristic
35	#19097743	C₄	1	1	yes	characteristic
36	#19097741	C₄	1	1	yes	characteristic
37	#19097739	C₄	1	1	yes	characteristic
38	C₄×D₆₂₈	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₅₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₅₇	C₂²	1	1	yes	characteristic
41	#19097728	C₂²	1	1	yes	characteristic
42	C₄⋊#11929434	C₂²	1	1	yes	characteristic, complemented
43	#19097700	C₂²	1	1	yes	characteristic, complemented
44	#19097700	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊#11929434	C₂²	1	1	yes	characteristic
46	C₂²⋊#11929434	C₂²	1	1	yes	characteristic, complemented
47	#19097683	C₂²	1	1	yes	characteristic
48	#19097683	C₂²	1	1	yes	characteristic
49	#19097683	C₂²	1	1	yes	characteristic, complemented
50	#19097683	C₂²	1	1	yes	characteristic, complemented
51	#19097681	C₂²	1	1	yes	characteristic, complemented
52	C₄×#11929434	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₁₅₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₁₅₇	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₁₅₇	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₁₅₇	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₁₅₇	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₁₅₇	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₁₅₇	C₂²	1	1	yes	characteristic, complemented
60	#97×C₁₅₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₅₇	C₂×C₄	1	1	yes	characteristic
62	#14578954	—	2	2	no	—
63	#14578954	—	2	2	no	—
64	C₂×Dic₃₁₄	C₂×C₄	1	1	yes	characteristic
65	C₂×D₆₂₈	C₂×C₄	1	1	yes	characteristic
66	C₂×D₆₂₈	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₅₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₁₅₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₅₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₅₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₅₇	—	2	2	no	—
73	C₂×C₄×D₁₅₇	—	2	2	no	—
74	C₂×C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₅₇	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₁₅₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₅₇	C₂³	1	1	yes	characteristic
79	#14578938	—	2	2	no	—
80	#14578938	—	2	2	no	—
81	#14578937	—	2	2	no	—
82	#14578937	—	2	2	no	—
83	#14578937	D₄	1	4	yes	complemented
84	C₂×#11929434	C₂³	1	1	yes	characteristic
85	C₂×#11929434	C₂³	1	1	yes	characteristic
86	C₂×#11929434	C₂³	1	1	yes	characteristic
87	C₂×#11929434	C₂³	1	1	yes	characteristic
88	C₈×D₁₅₇	—	2	2	no	—
89	C₈×D₁₅₇	—	2	2	no	—
90	C₈×D₁₅₇	—	2	2	no	—
91	C₈×D₁₅₇	—	2	2	no	—
92	C₈×D₁₅₇	—	2	2	no	—
93	C₄⋊Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
94	#14578933	C₂×C₄	1	1	yes	characteristic
95	#14578933	C₂×C₄	1	1	yes	characteristic
96	#14578933	C₂×C₄	1	1	yes	characteristic
97	#14578933	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
100	#14578931	C₂×C₄	1	1	yes	characteristic
101	#14578931	C₂×C₄	1	1	yes	characteristic
102	#14578931	C₂×C₄	1	1	yes	characteristic
103	#14578931	C₂×C₄	1	1	yes	characteristic
104	#14578931	C₂×C₄	1	1	yes	characteristic
105	#14578931	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₅₇	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
110	M₁₆×C₁₅₇	—	2	2	no	—
111	C₂×C₈×C₁₅₇	—	2	2	no	—
112	C₂×C₈×C₁₅₇	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₅₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₅₇	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₅₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₁₅₇	C₂³	1	1	yes	characteristic
120	C₂²×D₁₅₇	—	2	2	no	—
121	C₂²×D₁₅₇	—	2	2	no	—
122	C₂²×D₁₅₇	—	4	1	no	—
123	C₂²×D₁₅₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₁₅₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₁₅₇	C₂²×C₄	1	1	yes	characteristic
126	Dic₃₁₄	—	2	2	no	—
127	D₆₂₈	—	2	2	no	—
128	D₆₂₈	—	2	2	no	—
129	C₂²⋊D₁₅₇	—	2	2	no	—
130	C₂²⋊D₁₅₇	—	2	2	no	—
131	C₂²⋊D₁₅₇	—	2	2	no	—
132	C₂²⋊D₁₅₇	—	4	1	no	—
133	C₂×Dic₁₅₇	—	2	2	no	—
134	C₂×Dic₁₅₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₁₅₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×Dic₁₅₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₁₅₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₅₇	C₂²×C₄	1	1	yes	characteristic
139	C₄×D₁₅₇	—	2	2	no	—
140	C₄×D₁₅₇	—	2	1	no	—
141	C₄×D₁₅₇	—	2	1	no	—
142	C₄×D₁₅₇	—	2	1	no	—
143	C₄×D₁₅₇	—	2	1	no	—
144	C₄×D₁₅₇	—	2	2	no	—
145	C₄×D₁₅₇	C₂×D₄	1	2	yes	—
146	C₄×D₁₅₇	#41	1	2	yes	—
147	#11929434	—	2	1	no	—
148	#11929434	—	2	1	no	—
149	#11929434	—	2	1	no	—
150	#11929434	C₂×D₄	1	2	yes	—
151	C₂³×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
152	C₂³×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
153	D₄×C₁₅₇	—	4	1	no	—
154	C₂×C₄×C₁₅₇	—	2	1	no	—
155	C₂×C₄×C₁₅₇	—	2	1	no	—
156	C₂×C₄×C₁₅₇	—	2	1	no	—
157	C₂×C₄×C₁₅₇	—	2	1	no	—
158	C₂×C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₅₇	C₂⁴	1	1	yes	characteristic
163	C₈×C₁₅₇	—	2	1	no	—
164	C₈×C₁₅₇	—	2	1	no	—
165	C₈×C₁₅₇	—	2	1	no	—
166	C₈×C₁₅₇	C₂×D₄	1	2	yes	—
167	C₂²×C₁₅₇	—	2	1	no	—
168	C₂²×C₁₅₇	—	2	1	no	—
169	C₂²×C₁₅₇	—	2	1	no	—
170	C₂²×C₁₅₇	—	2	1	no	—
171	C₂²×C₁₅₇	—	2	1	no	—
172	C₂²×C₁₅₇	—	2	1	no	—
173	C₂²×C₁₅₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₁₅₇	—	2	1	no	—
175	C₂×D₁₅₇	—	2	1	no	—
176	C₂×D₁₅₇	—	2	1	no	—
177	C₂×D₁₅₇	—	2	1	no	—
178	C₂×D₁₅₇	—	2	1	no	—
179	C₂×D₁₅₇	—	2	1	no	—
180	C₂×D₁₅₇	—	2	1	no	—
181	C₂×D₁₅₇	—	4	4	no	—
182	C₂×D₁₅₇	C₄×D₄	1	2	yes	—
183	C₂×D₁₅₇	#131	1	2	yes	complemented
184	C₄×C₁₅₇	—	2	1	no	—
185	C₄×C₁₅₇	—	2	1	no	—
186	C₄×C₁₅₇	—	2	1	no	—
187	C₄×C₁₅₇	—	2	1	no	—
188	C₄×C₁₅₇	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₁₅₇	C₂×#41	1	1	yes	characteristic
190	Dic₁₅₇	—	2	1	no	—
191	Dic₁₅₇	—	2	1	no	—
192	Dic₁₅₇	—	2	1	no	—
193	Dic₁₅₇	—	2	1	no	—
194	Dic₁₅₇	C₄×D₄	1	2	yes	—
195	C₂×C₁₅₇	—	4	1	no	—
196	C₂×C₁₅₇	—	4	1	no	—
197	C₂×C₁₅₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×C₁₅₇	C₂×#131	1	1	yes	characteristic
199	C₂×C₁₅₇	#568	1	1	yes	characteristic
200	D₁₅₇	—	2	2	no	—
201	D₁₅₇	—	2	2	no	—
202	D₁₅₇	—	4	1	no	—
203	C₁₅₇	#2933	1	1	yes	characteristic, complemented, Sylow
204	#2933	—	157	1	no	maximal, Sylow
205	C₂×#131	—	157	1	no	—
206	C₂²×M₁₆	—	157	1	no	—
207	#525	—	157	1	no	—
208	#436	—	157	1	no	—
209	#436	—	157	1	no	—
210	#435	—	157	1	no	—
211	#435	—	157	1	no	—
212	#435	—	157	1	no	—
213	#435	D₁₅₇	1	1	yes	characteristic, complemented
214	C₈×D₄	—	157	1	no	—
215	C₈×D₄	—	157	1	no	—
216	#424	—	157	1	no	—
217	#408	—	157	1	no	—
218	C₂×C₂²⋊C₈	—	157	1	no	—
219	#405	—	157	1	no	—
220	C₂×#41	—	157	1	no	—
221	C₂³×C₄	—	157	1	no	—
222	#131	—	314	4	no	—
223	C₂×M₁₆	—	314	4	no	—
224	C₂×M₁₆	—	157	1	no	—
225	C₂×M₁₆	—	157	1	no	—
226	C₂×M₁₆	—	157	1	no	—
227	C₂×M₁₆	—	157	1	no	—
228	C₂×M₁₆	—	157	1	no	—
229	C₂×M₁₆	C₂×D₁₅₇	1	1	yes	characteristic
230	C₂²×C₈	—	157	1	no	—
231	C₂²×C₈	—	157	1	no	—
232	C₂²×C₈	—	157	1	no	—
233	C₂²×C₈	—	157	1	no	—
234	C₂²×C₈	—	157	1	no	—
235	C₂²×C₈	C₂×D₁₅₇	1	1	yes	characteristic, complemented
236	#123	—	157	1	no	—
237	#123	—	157	1	no	—
238	C₂²⋊Q₈	—	157	1	no	—
239	C₂²⋊Q₈	—	157	1	no	—
240	#121	—	157	1	no	—
241	#121	—	157	1	no	—
242	#120	—	157	1	no	—
243	#120	—	157	1	no	—
244	C₄×D₄	—	157	1	no	—
245	C₄×D₄	—	157	1	no	—
246	C₄×D₄	—	157	1	no	—
247	C₄×D₄	C₂×D₁₅₇	1	1	yes	characteristic
248	#117	—	157	1	no	—
249	C₄⋊C₈	—	157	1	no	—
250	C₄⋊C₈	—	157	1	no	—
251	C₄⋊C₈	—	157	1	no	—
252	C₄⋊C₈	C₂×D₁₅₇	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	—	157	1	no	—
254	C₂²⋊C₈	—	157	1	no	—
255	C₂²⋊C₈	—	157	1	no	—
256	C₂²⋊C₈	—	157	1	no	—
257	C₂²⋊C₈	—	157	1	no	—
258	C₂²⋊C₈	—	157	1	no	—
259	C₂²⋊C₈	C₂×D₁₅₇	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₁₅₇	1	1	yes	characteristic, complemented
261	#97	—	157	1	no	—
262	#97	C₂×D₁₅₇	1	1	yes	characteristic, complemented
263	C₄×C₈	—	157	1	no	—
264	C₄×C₈	—	157	1	no	—
265	C₂⁴	—	157	1	no	—
266	#41	—	314	2	no	—
267	#41	—	314	2	no	—
268	C₂×Q₈	—	157	1	no	—
269	C₂×D₄	—	157	1	no	—
270	C₂×D₄	—	157	1	no	—
271	C₂×D₄	—	157	1	no	—
272	C₂×D₄	—	157	1	no	—
273	C₂×D₄	—	157	1	no	—
274	C₂×D₄	—	157	1	no	—
275	C₂×D₄	C₄×D₁₅₇	1	1	yes	characteristic
276	C₂²×C₄	—	314	2	no	—
277	C₂²×C₄	—	314	2	no	—
278	C₂²×C₄	—	157	1	no	—
279	C₂²×C₄	—	157	1	no	—
280	C₂²×C₄	—	157	1	no	—
281	C₂²×C₄	—	157	1	no	—
282	C₂²×C₄	—	157	1	no	—
283	C₂²×C₄	—	157	1	no	—
284	C₂²×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	314	2	no	—
288	M₁₆	—	314	2	no	—
289	M₁₆	—	314	2	no	—
290	M₁₆	—	314	2	no	—
291	M₁₆	—	157	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	314	2	no	—
294	C₂×C₈	—	314	2	no	—
295	C₂×C₈	—	314	2	no	—
296	C₂×C₈	—	314	2	no	—
297	C₂×C₈	—	314	2	no	—
298	C₂×C₈	—	157	1	no	—
299	C₂×C₈	—	157	1	no	—
300	C₂×C₈	—	157	1	no	—
301	C₂×C₈	—	157	1	no	—
302	C₂×C₈	C₂²×D₁₅₇	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₁₅₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₁₅₇	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₁₅₇	1	1	yes	characteristic
306	C₄⋊C₄	—	157	1	no	—
307	C₄⋊C₄	—	157	1	no	—
308	C₄⋊C₄	—	157	1	no	—
309	C₄⋊C₄	—	157	1	no	—
310	C₄⋊C₄	—	157	1	no	—
311	C₄⋊C₄	C₄×D₁₅₇	1	1	yes	characteristic
312	C₂²⋊C₄	—	157	1	no	—
313	C₂²⋊C₄	—	157	1	no	—
314	C₂²⋊C₄	—	157	1	no	—
315	C₂²⋊C₄	—	157	1	no	—
316	C₂²⋊C₄	—	157	1	no	—
317	C₂²⋊C₄	—	157	1	no	—
318	C₂²⋊C₄	—	157	1	no	—
319	C₂²⋊C₄	—	157	1	no	—
320	C₂²⋊C₄	C₄×D₁₅₇	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₁₅₇	1	1	yes	characteristic
322	C₄²	—	157	1	no	—
323	C₄²	C₂²×D₁₅₇	1	1	yes	characteristic
324	C₂³	—	314	2	no	—
325	C₂³	—	314	2	no	—
326	C₂³	—	628	1	no	—
327	C₂³	—	157	1	no	—
328	C₂³	—	157	1	no	—
329	C₂³	—	157	1	no	—
330	C₂³	C₂×C₄×D₁₅₇	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₁₅₇	1	1	yes	characteristic
332	Q₈	—	314	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	314	2	no	—
335	D₄	—	314	2	no	—
336	D₄	—	314	2	no	—
337	D₄	—	314	2	no	—
338	D₄	—	314	2	no	—
339	D₄	—	628	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	314	2	no	—
345	C₂×C₄	—	314	2	no	—
346	C₂×C₄	—	314	2	no	—
347	C₂×C₄	—	314	1	no	—
348	C₂×C₄	—	314	1	no	—
349	C₂×C₄	—	314	1	no	—
350	C₂×C₄	—	314	1	no	—
351	C₂×C₄	—	157	1	no	—
352	C₂×C₄	—	157	1	no	—
353	C₂×C₄	—	157	1	no	—
354	C₂×C₄	—	157	1	no	—
355	C₂×C₄	—	157	1	no	—
356	C₂×C₄	—	157	2	no	—
357	C₂×C₄	—	157	2	no	—
358	C₂×C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₁₅₇	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	314	1	no	—
367	C₈	—	314	1	no	—
368	C₈	—	314	1	no	—
369	C₈	—	157	2	no	—
370	C₈	D₄×D₁₅₇	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	314	1	no	—
378	C₂²	—	314	1	no	—
379	C₂²	—	314	1	no	—
380	C₂²	—	314	1	no	—
381	C₂²	—	314	1	no	—
382	C₂²	—	314	1	no	—
383	C₂²	—	314	1	no	—
384	C₂²	—	628	4	no	—
385	C₂²	—	157	2	no	—
386	C₂²	—	157	2	no	—
387	C₂²	C₂²×C₄×D₁₅₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	314	1	no	—
393	C₄	—	314	1	no	—
394	C₄	—	314	1	no	—
395	C₄	—	314	1	no	—
396	C₄	—	157	2	no	—
397	C₄	C₂×D₄×D₁₅₇	1	1	yes	characteristic
398	C₄	#41×D₁₅₇	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	314	2	no	—
402	C₂	—	314	2	no	—
403	C₂	—	628	1	no	—
404	C₂	C₄×D₄×D₁₅₇	1	1	yes	characteristic
405	C₂	#131×D₁₅₇	1	1	yes	characteristic
406	C₂	#23758039	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅₇
commutator, socle	C₂²×C₁₅₇	C₂³×C₄
Fitting	#435×C₁₅₇	C₂
prime radical	#23757782	C₂
cosocle	C₂×C₄×C₁₅₇	C₂⁴
hypercenter	#435	D₁₅₇
hypocenter	C₁₅₇	#2933
LCS	G ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#19097777	C₂	semidirect
2. C₂×M₁₆×D₁₅₇	C₂	semidirect
4. #23757351	C₂	semidirect
5. #23757349	C₂	semidirect
6. #23757347	C₂	semidirect
7. #23757347	C₂	semidirect
8. #23757346	C₂	semidirect
9. #23757338	C₂	semidirect
10. C₈×C₂²⋊D₁₅₇	C₂	semidirect
11. #23757298	C₂	semidirect
12. #23757238	C₂	semidirect
13. C₂²⋊C₈×D₁₅₇	C₂	semidirect
14. #23757230	C₂	semidirect
15. #435×C₁₅₇	C₂	semidirect
20. C₂×#14578938	C₂²	semidirect
23. C₂×#14578937	C₂²	semidirect
29. C₂×C₈×D₁₅₇	C₂²	semidirect
42. C₄⋊#11929434	C₂²	semidirect
43. #19097700	C₂²	semidirect
44. #19097700	C₂²	semidirect
46. C₂²⋊#11929434	C₂²	semidirect
49. #19097683	C₂²	semidirect
50. #19097683	C₂²	semidirect
51. #19097681	C₂²	semidirect
52. C₄×#11929434	C₂²	semidirect
53. C₈×Dic₁₅₇	C₂²	semidirect
55. C₂²×C₈×C₁₅₇	C₂²	semidirect
57. C₄⋊C₈×C₁₅₇	C₂²	semidirect
59. C₂²⋊C₈×C₁₅₇	C₂²	semidirect
60. #97×C₁₅₇	C₂²	semidirect
83. #14578937	D₄	semidirect
183. C₂×D₁₅₇	#131	semidirect
203. C₁₅₇	#2933	semidirect
213. #435	D₁₅₇	semidirect
235. C₂²×C₈	C₂×D₁₅₇	semidirect
252. C₄⋊C₈	C₂×D₁₅₇	semidirect
260. C₂²⋊C₈	C₂×D₁₅₇	semidirect
262. #97	C₂×D₁₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19097777	2
C₂×M₁₆×D₁₅₇	2
#23757782	2
#23757351	2
#23757349	2
#23757347	2
#23757346	2
#23757338	2
C₈×C₂²⋊D₁₅₇	2
#23757298	2
#23757238	2
C₂²⋊C₈×D₁₅₇	2
#23757230	2
#435×C₁₅₇	2
#2933	157