Subgroups — C₁₅₁×#23826 #50328751

Order 38656.

746 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#125×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#124×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	#2101×C₁₅₁	C₂	1	2	yes	maximal, complemented
4	#2074×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2073×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	#2042×C₁₅₁	C₂	1	2	yes	maximal
7	#2026×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2025×C₁₅₁	C₂	1	1	yes	maximal, characteristic
9	#1763×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#1762×C₁₅₁	C₂	1	2	yes	maximal
11	#1745×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
17	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
18	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
19	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
20	C₂×#97×C₁₅₁	C₂²	1	2	yes	—
21	#391×C₁₅₁	C₂²	1	1	yes	characteristic
22	#390×C₁₅₁	C₂²	1	1	yes	characteristic
23	#389×C₁₅₁	C₂²	1	2	yes	—
24	#388×C₁₅₁	—	2	2	no	—
25	#387×C₁₅₁	—	2	2	no	—
26	#382×C₁₅₁	C₂²	1	1	yes	characteristic
27	#382×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₅₁	—	2	2	no	—
29	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
31	C₄³×C₁₅₁	C₂²	1	1	yes	characteristic
32	#340×C₁₅₁	C₂²	1	2	yes	—
33	#340×C₁₅₁	C₂²	1	2	yes	—
34	#340×C₁₅₁	C₂²	1	2	yes	—
35	#340×C₁₅₁	C₂²	1	2	yes	—
36	#336×C₁₅₁	C₂²	1	2	yes	—
37	#336×C₁₅₁	C₂²	1	1	yes	characteristic
38	#336×C₁₅₁	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₅₁	—	2	1	no	—
42	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
44	#125×C₁₅₁	—	2	4	no	—
45	#124×C₁₅₁	—	2	2	no	—
46	#124×C₁₅₁	—	2	2	no	—
47	C₄×Q₈×C₁₅₁	—	2	4	no	—
48	C₄×D₄×C₁₅₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
59	C₂×C₄²×C₁₅₁	—	2	1	no	—
60	C₂×C₄²×C₁₅₁	—	2	2	no	—
61	C₂×C₄²×C₁₅₁	D₄	1	2	yes	—
62	C₂×C₄²×C₁₅₁	D₄	1	2	yes	—
63	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
66	#103×C₁₅₁	—	2	4	no	—
67	#103×C₁₅₁	—	2	4	no	—
68	#102×C₁₅₁	—	2	4	no	—
69	#102×C₁₅₁	—	2	4	no	—
70	#97×C₁₅₁	—	2	4	no	—
71	#95×C₁₅₁	—	2	2	no	—
72	#95×C₁₅₁	—	2	2	no	—
73	#95×C₁₅₁	—	2	2	no	—
74	#95×C₁₅₁	—	2	2	no	—
75	#95×C₁₅₁	—	2	2	no	—
76	C₂⁴×C₁₅₁	—	2	1	no	—
77	C₂×Q₈×C₁₅₁	—	2	1	no	—
78	C₂×Q₈×C₁₅₁	—	2	2	no	—
79	C₂×Q₈×C₁₅₁	—	2	2	no	—
80	C₂×Q₈×C₁₅₁	#41	1	2	yes	—
81	C₂×D₄×C₁₅₁	—	2	2	no	—
82	C₂×D₄×C₁₅₁	—	2	2	no	—
83	C₂×D₄×C₁₅₁	—	2	1	no	—
84	C₂×D₄×C₁₅₁	#41	1	2	yes	—
85	C₂²×C₄×C₁₅₁	—	2	1	no	—
86	C₂²×C₄×C₁₅₁	—	2	2	no	—
87	C₂²×C₄×C₁₅₁	—	2	2	no	—
88	C₂²×C₄×C₁₅₁	—	2	1	no	—
89	C₂²×C₄×C₁₅₁	—	2	1	no	—
90	C₂²×C₄×C₁₅₁	—	4	4	no	—
91	C₂²×C₄×C₁₅₁	—	4	2	no	—
92	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₁₅₁	—	2	2	no	—
98	C₂×C₈×C₁₅₁	—	2	2	no	—
99	C₂×C₈×C₁₅₁	—	2	2	no	—
100	C₂×C₈×C₁₅₁	—	2	2	no	—
101	C₂×C₈×C₁₅₁	—	2	2	no	—
102	C₂×C₈×C₁₅₁	—	2	2	no	—
103	C₄⋊C₄×C₁₅₁	—	2	8	no	—
104	C₄⋊C₄×C₁₅₁	—	2	2	no	—
105	C₄⋊C₄×C₁₅₁	—	2	2	no	—
106	C₄⋊C₄×C₁₅₁	—	2	2	no	—
107	C₄⋊C₄×C₁₅₁	—	2	2	no	—
108	C₄⋊C₄×C₁₅₁	—	2	2	no	—
109	C₄⋊C₄×C₁₅₁	—	4	4	no	—
110	C₄⋊C₄×C₁₅₁	—	4	2	no	—
111	C₄⋊C₄×C₁₅₁	#41	1	4	yes	—
112	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
113	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
114	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
115	C₄²×C₁₅₁	—	2	1	no	—
116	C₄²×C₁₅₁	—	2	1	no	—
117	C₄²×C₁₅₁	—	2	2	no	—
118	C₄²×C₁₅₁	—	4	2	no	—
119	C₄²×C₁₅₁	—	4	2	no	—
120	C₄²×C₁₅₁	—	4	4	no	—
121	C₄²×C₁₅₁	—	4	2	no	—
122	C₄²×C₁₅₁	#41	1	4	yes	—
123	C₂³×C₁₅₁	—	2	2	no	—
124	C₂³×C₁₅₁	—	4	1	no	—
125	C₂³×C₁₅₁	—	4	1	no	—
126	C₂³×C₁₅₁	—	4	2	no	—
127	C₂³×C₁₅₁	—	4	2	no	—
128	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₅₁	—	2	4	no	—
130	Q₈×C₁₅₁	—	4	2	no	—
131	D₄×C₁₅₁	—	2	4	no	—
132	D₄×C₁₅₁	—	4	2	no	—
133	C₂×C₄×C₁₅₁	—	2	2	no	—
134	C₂×C₄×C₁₅₁	—	2	2	no	—
135	C₂×C₄×C₁₅₁	—	2	2	no	—
136	C₂×C₄×C₁₅₁	—	2	2	no	—
137	C₂×C₄×C₁₅₁	—	2	2	no	—
138	C₂×C₄×C₁₅₁	—	2	4	no	—
139	C₂×C₄×C₁₅₁	—	2	2	no	—
140	C₂×C₄×C₁₅₁	—	2	2	no	—
141	C₂×C₄×C₁₅₁	—	2	2	no	—
142	C₂×C₄×C₁₅₁	—	2	2	no	—
143	C₂×C₄×C₁₅₁	—	4	1	no	—
144	C₂×C₄×C₁₅₁	—	4	1	no	—
145	C₂×C₄×C₁₅₁	—	4	2	no	—
146	C₂×C₄×C₁₅₁	—	4	2	no	—
147	C₂×C₄×C₁₅₁	—	4	2	no	—
148	C₂×C₄×C₁₅₁	—	4	1	no	—
149	C₂×C₄×C₁₅₁	—	4	1	no	—
150	C₂×C₄×C₁₅₁	—	4	2	no	—
151	C₂×C₄×C₁₅₁	—	4	2	no	—
152	C₂×C₄×C₁₅₁	—	4	2	no	—
153	C₂×C₄×C₁₅₁	—	4	2	no	—
154	C₂×C₄×C₁₅₁	—	8	4	no	—
155	C₂×C₄×C₁₅₁	#124	1	2	yes	—
156	C₂×C₄×C₁₅₁	#124	1	2	yes	—
157	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₅₁	C₂×#41	1	2	yes	—
159	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₁₅₁	C₂×#41	1	2	yes	—
161	C₈×C₁₅₁	—	4	2	no	—
162	C₈×C₁₅₁	—	4	2	no	—
163	C₂²×C₁₅₁	—	4	4	no	—
164	C₂²×C₁₅₁	—	4	2	no	—
165	C₂²×C₁₅₁	—	8	2	no	—
166	C₂²×C₁₅₁	—	8	1	no	—
167	C₂²×C₁₅₁	—	8	1	no	—
168	C₂²×C₁₅₁	#525	1	1	yes	characteristic
169	C₂²×C₁₅₁	#525	1	1	yes	characteristic
170	C₂²×C₁₅₁	C₂×#124	1	1	yes	characteristic
171	C₂²×C₁₅₁	#575	1	2	yes	—
172	C₂²×C₁₅₁	#575	1	2	yes	—
173	C₄×C₁₅₁	—	2	2	no	—
174	C₄×C₁₅₁	—	2	2	no	—
175	C₄×C₁₅₁	—	4	2	no	—
176	C₄×C₁₅₁	—	4	2	no	—
177	C₄×C₁₅₁	—	4	4	no	—
178	C₄×C₁₅₁	—	4	2	no	—
179	C₄×C₁₅₁	—	8	2	no	—
180	C₄×C₁₅₁	—	8	1	no	—
181	C₄×C₁₅₁	—	8	1	no	—
182	C₄×C₁₅₁	#529	1	2	yes	—
183	C₄×C₁₅₁	#529	1	2	yes	—
184	C₂×C₁₅₁	—	8	2	no	—
185	C₂×C₁₅₁	#2398	1	1	yes	characteristic
186	C₂×C₁₅₁	#3111	1	2	yes	—
187	C₂×C₁₅₁	#3111	1	2	yes	—
188	C₂×C₁₅₁	#3140	1	1	yes	characteristic
189	C₂×C₁₅₁	#3142	1	1	yes	characteristic
190	#23826	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₅₁	#23826	1	1	yes	characteristic, direct product factor, Sylow
192	C₄×#125	C₂×C₁₅₁	1	1	yes	characteristic, complemented
193	C₄×#124	C₂×C₁₅₁	1	1	yes	characteristic
194	#2101	C₂×C₁₅₁	1	2	yes	complemented
195	#2074	C₂×C₁₅₁	1	1	yes	characteristic, complemented
196	#2073	C₂×C₁₅₁	1	1	yes	characteristic
197	#2042	C₂×C₁₅₁	1	2	yes	—
198	#2026	C₂×C₁₅₁	1	1	yes	characteristic, complemented
199	#2025	C₂×C₁₅₁	1	1	yes	characteristic
200	#1763	C₂×C₁₅₁	1	2	yes	complemented
201	#1762	C₂×C₁₅₁	1	2	yes	—
202	#1745	C₂×C₁₅₁	1	1	yes	characteristic, complemented
203	C₂×#125	C₂²×C₁₅₁	1	1	yes	characteristic
204	C₂×#124	C₂²×C₁₅₁	1	1	yes	characteristic
205	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
207	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
208	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
209	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
210	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
211	C₂×#97	C₂²×C₁₅₁	1	2	yes	—
212	#391	C₂²×C₁₅₁	1	1	yes	characteristic
213	#390	C₂²×C₁₅₁	1	1	yes	characteristic
214	#389	C₂²×C₁₅₁	1	2	yes	—
215	#388	—	2	2	no	—
216	#387	—	2	2	no	—
217	#382	C₂²×C₁₅₁	1	1	yes	characteristic
218	#382	C₂²×C₁₅₁	1	1	yes	characteristic
219	C₄×C₄⋊C₄	—	2	2	no	—
220	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
221	C₄×C₂²⋊C₄	—	2	2	no	—
222	C₄³	C₂²×C₁₅₁	1	1	yes	characteristic
223	#340	C₂²×C₁₅₁	1	2	yes	—
224	#340	C₂²×C₁₅₁	1	2	yes	—
225	#340	C₂²×C₁₅₁	1	2	yes	—
226	#340	C₂²×C₁₅₁	1	2	yes	—
227	#336	C₂²×C₁₅₁	1	1	yes	characteristic
228	#336	C₂²×C₁₅₁	1	1	yes	characteristic
229	#336	C₂²×C₁₅₁	1	2	yes	—
230	C₂²×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
231	C₂²×D₄	C₂³×C₁₅₁	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
235	#125	—	2	4	no	—
236	#124	—	2	2	no	—
237	#124	—	2	2	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×D₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	D₄×C₁₅₁	1	2	yes	—
253	C₂×C₄²	D₄×C₁₅₁	1	2	yes	—
254	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
257	#103	—	2	4	no	—
258	#103	—	2	4	no	—
259	#102	—	2	4	no	—
260	#102	—	2	4	no	—
261	#97	—	2	4	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	C₂⁴	—	2	1	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	#41×C₁₅₁	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	#41×C₁₅₁	1	2	yes	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	#41×C₁₅₁	1	4	yes	—
303	C₂²⋊C₄	—	2	8	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	4	2	no	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	4	no	—
312	C₄²	—	4	2	no	—
313	C₄²	#41×C₁₅₁	1	4	yes	—
314	C₂³	—	2	2	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
320	Q₈	—	2	4	no	—
321	Q₈	—	4	2	no	—
322	D₄	—	2	4	no	—
323	D₄	—	4	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	4	no	—
346	C₂×C₄	#124×C₁₅₁	1	2	yes	—
347	C₂×C₄	#124×C₁₅₁	1	2	yes	—
348	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₁₅₁	1	2	yes	—
351	C₂×C₄	C₂×#41×C₁₅₁	1	2	yes	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	#525×C₁₅₁	1	1	yes	characteristic
360	C₂²	#525×C₁₅₁	1	1	yes	characteristic
361	C₂²	C₂×#124×C₁₅₁	1	1	yes	characteristic
362	C₂²	#575×C₁₅₁	1	2	yes	—
363	C₂²	#575×C₁₅₁	1	2	yes	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	4	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	1	no	—
372	C₄	—	8	1	no	—
373	C₄	#529×C₁₅₁	1	2	yes	—
374	C₄	#529×C₁₅₁	1	2	yes	—
375	C₂	—	8	2	no	—
376	C₂	#2398×C₁₅₁	1	1	yes	characteristic
377	C₂	#3111×C₁₅₁	1	2	yes	—
378	C₂	#3111×C₁₅₁	1	2	yes	—
379	C₂	#3140×C₁₅₁	1	1	yes	characteristic
380	C₂	#3142×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂²×D₄×C₁₅₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₄³×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×#125×C₁₅₁	C₂	semidirect
3. #2101×C₁₅₁	C₂	semidirect
4. #2074×C₁₅₁	C₂	semidirect
7. #2026×C₁₅₁	C₂	semidirect
9. #1763×C₁₅₁	C₂	semidirect
11. #1745×C₁₅₁	C₂	semidirect
190. #23826	C₁₅₁	direct (N × H)
191. C₁₅₁	#23826	direct (N × H)
192. C₄×#125	C₂×C₁₅₁	semidirect
194. #2101	C₂×C₁₅₁	semidirect
195. #2074	C₂×C₁₅₁	semidirect
198. #2026	C₂×C₁₅₁	semidirect
200. #1763	C₂×C₁₅₁	semidirect
202. #1745	C₂×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×#125×C₁₅₁	2
C₄×#124×C₁₅₁	2
#2101×C₁₅₁	2
#2074×C₁₅₁	2
#2073×C₁₅₁	2
#2042×C₁₅₁	2
#2026×C₁₅₁	2
#2025×C₁₅₁	2
#1763×C₁₅₁	2
#1762×C₁₅₁	2
#1745×C₁₅₁	2
#23826	151

Subgroups — C151×#23826 #50328751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#23826 #50328751