Subgroups — #2416×C₁₅₁ #34065748

Order 19328.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#121×C₁₅₁	C₂	1	2	yes	maximal, complemented
2	C₂×#121×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#121×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#396×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	#394×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#390×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#389×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#386×C₁₅₁	C₂	1	2	yes	maximal, complemented
11	#380×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₁₅₁	C₂²	1	2	yes	—
13	C₂²×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₁₅₁	C₂²	1	2	yes	—
15	C₂²×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₅₁	C₂²	1	2	yes	—
18	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
19	#121×C₁₅₁	—	2	8	no	—
20	#121×C₁₅₁	—	2	4	no	—
21	#121×C₁₅₁	—	2	4	no	—
22	C₄×D₄×C₁₅₁	—	2	4	no	—
23	C₂×C₄⋊C₄×C₁₅₁	—	2	4	no	—
24	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
27	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
28	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
37	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
38	#95×C₁₅₁	C₂²	1	2	yes	—
39	#95×C₁₅₁	C₂²	1	2	yes	—
40	C₂⁴×C₁₅₁	C₂³	1	2	yes	—
41	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
42	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
43	C₂×D₄×C₁₅₁	—	2	2	no	—
44	C₂×D₄×C₁₅₁	—	2	2	no	—
45	C₂×D₄×C₁₅₁	—	2	4	no	—
46	C₂×D₄×C₁₅₁	—	2	4	no	—
47	C₂×D₄×C₁₅₁	—	2	4	no	—
48	C₂×D₄×C₁₅₁	—	2	4	no	—
49	C₂×D₄×C₁₅₁	—	2	4	no	—
50	C₂×D₄×C₁₅₁	—	2	2	no	—
51	C₂×D₄×C₁₅₁	—	2	2	no	—
52	C₂×D₄×C₁₅₁	—	2	2	no	—
53	C₂×D₄×C₁₅₁	—	4	2	no	—
54	C₂×D₄×C₁₅₁	D₄	1	4	yes	complemented
55	C₂²×C₄×C₁₅₁	—	2	2	no	—
56	C₂²×C₄×C₁₅₁	—	2	2	no	—
57	C₂²×C₄×C₁₅₁	—	2	4	no	—
58	C₂²×C₄×C₁₅₁	—	2	4	no	—
59	C₂²×C₄×C₁₅₁	—	2	2	no	—
60	C₂²×C₄×C₁₅₁	—	2	2	no	—
61	C₂²×C₄×C₁₅₁	—	2	2	no	—
62	C₂²×C₄×C₁₅₁	—	4	2	no	—
63	C₂²×C₄×C₁₅₁	D₄	1	4	yes	complemented
64	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
67	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
68	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
69	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
72	C₄⋊C₄×C₁₅₁	—	2	4	no	—
73	C₄⋊C₄×C₁₅₁	—	2	2	no	—
74	C₄⋊C₄×C₁₅₁	—	2	2	no	—
75	C₄⋊C₄×C₁₅₁	—	2	4	no	—
76	C₄⋊C₄×C₁₅₁	—	2	2	no	—
77	C₄⋊C₄×C₁₅₁	D₄	1	4	yes	complemented
78	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
79	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
80	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
81	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
82	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
83	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
84	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
85	C₄²×C₁₅₁	—	2	2	no	—
86	C₂³×C₁₅₁	—	2	1	no	—
87	C₂³×C₁₅₁	—	2	1	no	—
88	C₂³×C₁₅₁	—	2	1	no	—
89	C₂³×C₁₅₁	—	2	1	no	—
90	C₂³×C₁₅₁	—	2	1	no	—
91	C₂³×C₁₅₁	—	2	1	no	—
92	C₂³×C₁₅₁	—	2	1	no	—
93	C₂³×C₁₅₁	—	2	1	no	—
94	C₂³×C₁₅₁	—	2	1	no	—
95	C₂³×C₁₅₁	—	2	1	no	—
96	C₂³×C₁₅₁	—	2	2	no	—
97	C₂³×C₁₅₁	—	2	2	no	—
98	C₂³×C₁₅₁	—	2	2	no	—
99	C₂³×C₁₅₁	—	2	2	no	—
100	C₂³×C₁₅₁	—	2	2	no	—
101	C₂³×C₁₅₁	—	2	2	no	—
102	C₂³×C₁₅₁	—	2	2	no	—
103	C₂³×C₁₅₁	C₂×D₄	1	2	yes	—
104	C₂³×C₁₅₁	C₂×D₄	1	2	yes	—
105	C₂³×C₁₅₁	C₂×D₄	1	2	yes	—
106	C₂³×C₁₅₁	#41	1	2	yes	—
107	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
108	D₄×C₁₅₁	—	2	8	no	—
109	D₄×C₁₅₁	—	4	8	no	—
110	D₄×C₁₅₁	—	4	8	no	—
111	D₄×C₁₅₁	—	4	4	no	—
112	C₂×C₄×C₁₅₁	—	2	1	no	—
113	C₂×C₄×C₁₅₁	—	2	1	no	—
114	C₂×C₄×C₁₅₁	—	2	2	no	—
115	C₂×C₄×C₁₅₁	—	2	1	no	—
116	C₂×C₄×C₁₅₁	—	2	1	no	—
117	C₂×C₄×C₁₅₁	—	2	2	no	—
118	C₂×C₄×C₁₅₁	—	2	8	no	—
119	C₂×C₄×C₁₅₁	—	2	1	no	—
120	C₂×C₄×C₁₅₁	—	2	1	no	—
121	C₂×C₄×C₁₅₁	—	2	2	no	—
122	C₂×C₄×C₁₅₁	—	2	1	no	—
123	C₂×C₄×C₁₅₁	—	2	2	no	—
124	C₂×C₄×C₁₅₁	—	2	2	no	—
125	C₂×C₄×C₁₅₁	—	2	2	no	—
126	C₂×C₄×C₁₅₁	—	2	1	no	—
127	C₂×C₄×C₁₅₁	—	2	2	no	—
128	C₂×C₄×C₁₅₁	—	2	1	no	—
129	C₂×C₄×C₁₅₁	—	2	2	no	—
130	C₂×C₄×C₁₅₁	—	2	1	no	—
131	C₂×C₄×C₁₅₁	—	4	8	no	—
132	C₂×C₄×C₁₅₁	—	4	4	no	—
133	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
135	C₂×C₄×C₁₅₁	C₂×D₄	1	4	yes	—
136	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
137	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₁₅₁	#41	1	2	yes	—
139	C₂²×C₁₅₁	—	2	2	no	—
140	C₂²×C₁₅₁	—	2	2	no	—
141	C₂²×C₁₅₁	—	2	2	no	—
142	C₂²×C₁₅₁	—	2	2	no	—
143	C₂²×C₁₅₁	—	2	2	no	—
144	C₂²×C₁₅₁	—	2	2	no	—
145	C₂²×C₁₅₁	—	2	2	no	—
146	C₂²×C₁₅₁	—	2	2	no	—
147	C₂²×C₁₅₁	—	2	2	no	—
148	C₂²×C₁₅₁	—	4	1	no	—
149	C₂²×C₁₅₁	—	4	1	no	—
150	C₂²×C₁₅₁	—	4	1	no	—
151	C₂²×C₁₅₁	—	4	1	no	—
152	C₂²×C₁₅₁	—	4	2	no	—
153	C₂²×C₁₅₁	—	4	2	no	—
154	C₂²×C₁₅₁	—	4	2	no	—
155	C₂²×C₁₅₁	—	4	2	no	—
156	C₂²×C₁₅₁	—	4	2	no	—
157	C₂²×C₁₅₁	—	4	2	no	—
158	C₂²×C₁₅₁	—	4	2	no	—
159	C₂²×C₁₅₁	#121	1	4	yes	complemented
160	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
161	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
163	C₂²×C₁₅₁	C₂×#41	1	1	yes	characteristic
164	C₂²×C₁₅₁	C₂×#41	1	1	yes	characteristic
165	C₂²×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂²×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
167	C₄×C₁₅₁	—	2	2	no	—
168	C₄×C₁₅₁	—	2	2	no	—
169	C₄×C₁₅₁	—	2	4	no	—
170	C₄×C₁₅₁	—	4	1	no	—
171	C₄×C₁₅₁	—	4	2	no	—
172	C₄×C₁₅₁	—	4	1	no	—
173	C₄×C₁₅₁	—	4	2	no	—
174	C₄×C₁₅₁	#121	1	4	yes	complemented
175	C₂×C₁₅₁	—	2	4	no	—
176	C₂×C₁₅₁	—	4	2	no	—
177	C₂×C₁₅₁	—	8	2	no	—
178	C₂×C₁₅₁	C₂×#121	1	1	yes	characteristic
179	C₂×C₁₅₁	C₂×#121	1	1	yes	characteristic
180	C₂×C₁₅₁	#537	1	1	yes	characteristic
181	C₂×C₁₅₁	D₄²	1	1	yes	characteristic
182	C₂×C₁₅₁	#547	1	1	yes	characteristic
183	C₂×C₁₅₁	#548	1	1	yes	characteristic
184	C₂×C₁₅₁	#553	1	1	yes	characteristic
185	C₁₅₁	#2416	1	1	yes	characteristic, direct product factor, Sylow
186	#2416	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×#121	C₂×C₁₅₁	1	2	yes	complemented
188	C₂×#121	C₂×C₁₅₁	1	1	yes	characteristic, complemented
189	C₂×#121	C₂×C₁₅₁	1	1	yes	characteristic, complemented
190	C₂×C₄×D₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
191	C₂²×C₄⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
192	#396	C₂×C₁₅₁	1	2	yes	complemented
193	#394	C₂×C₁₅₁	1	2	yes	complemented
194	#390	C₂×C₁₅₁	1	1	yes	characteristic, complemented
195	#389	C₂×C₁₅₁	1	1	yes	characteristic, complemented
196	#386	C₂×C₁₅₁	1	2	yes	complemented
197	#380	C₂×C₁₅₁	1	1	yes	characteristic, complemented
198	C₂²×D₄	C₂²×C₁₅₁	1	2	yes	—
199	C₂²×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
200	C₂²×D₄	C₂²×C₁₅₁	1	2	yes	—
201	C₂²×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
202	C₂³×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
203	C₂³×C₄	C₂²×C₁₅₁	1	2	yes	—
204	C₂³×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
205	#121	—	2	8	no	—
206	#121	—	2	4	no	—
207	#121	—	2	4	no	—
208	C₄×D₄	—	2	4	no	—
209	C₂×C₄⋊C₄	—	2	4	no	—
210	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
212	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
215	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
217	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
221	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
223	C₂×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
224	#95	C₂²×C₁₅₁	1	2	yes	—
225	#95	C₂²×C₁₅₁	1	2	yes	—
226	C₂⁴	C₂³×C₁₅₁	1	2	yes	—
227	C₂⁴	C₂³×C₁₅₁	1	1	yes	characteristic
228	C₂⁴	C₂³×C₁₅₁	1	1	yes	characteristic
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	2	4	no	—
232	C₂×D₄	—	2	4	no	—
233	C₂×D₄	—	2	4	no	—
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	—	2	2	no	—
236	C₂×D₄	—	2	4	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	2	2	no	—
239	C₂×D₄	—	4	2	no	—
240	C₂×D₄	D₄×C₁₅₁	1	4	yes	complemented
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	4	2	no	—
249	C₂²×C₄	D₄×C₁₅₁	1	4	yes	complemented
250	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
251	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
252	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
253	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
254	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
255	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
257	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	D₄×C₁₅₁	1	4	yes	complemented
264	C₂²⋊C₄	—	2	2	no	—
265	C₂²⋊C₄	—	2	4	no	—
266	C₂²⋊C₄	—	2	2	no	—
267	C₂²⋊C₄	—	2	4	no	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₂²⋊C₄	—	2	4	no	—
270	C₂²⋊C₄	—	4	2	no	—
271	C₄²	—	2	2	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	—	2	1	no	—
276	C₂³	—	2	1	no	—
277	C₂³	—	2	1	no	—
278	C₂³	—	2	1	no	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	1	no	—
281	C₂³	—	2	1	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	C₂×D₄×C₁₅₁	1	2	yes	—
290	C₂³	C₂×D₄×C₁₅₁	1	2	yes	—
291	C₂³	C₂×D₄×C₁₅₁	1	2	yes	—
292	C₂³	#41×C₁₅₁	1	2	yes	—
293	C₂³	C₂⁴×C₁₅₁	1	1	yes	characteristic
294	D₄	—	2	8	no	—
295	D₄	—	4	8	no	—
296	D₄	—	4	8	no	—
297	D₄	—	4	4	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
320	C₂×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
321	C₂×C₄	C₂×D₄×C₁₅₁	1	4	yes	—
322	C₂×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
323	C₂×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
324	C₂×C₄	#41×C₁₅₁	1	2	yes	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	#121×C₁₅₁	1	4	yes	complemented
346	C₂²	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
347	C₂²	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
348	C₂²	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
349	C₂²	C₂×#41×C₁₅₁	1	1	yes	characteristic
350	C₂²	C₂×#41×C₁₅₁	1	1	yes	characteristic
351	C₂²	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
352	C₂²	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	2	no	—
360	C₄	#121×C₁₅₁	1	4	yes	complemented
361	C₂	—	2	4	no	—
362	C₂	—	4	2	no	—
363	C₂	—	8	2	no	—
364	C₂	C₂×#121×C₁₅₁	1	1	yes	characteristic
365	C₂	C₂×#121×C₁₅₁	1	1	yes	characteristic
366	C₂	#537×C₁₅₁	1	1	yes	characteristic
367	C₂	D₄²×C₁₅₁	1	1	yes	characteristic
368	C₂	#547×C₁₅₁	1	1	yes	characteristic
369	C₂	#548×C₁₅₁	1	1	yes	characteristic
370	C₂	#553×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₅₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#121×C₁₅₁	C₂	semidirect
2. C₂×#121×C₁₅₁	C₂	semidirect
3. C₂×#121×C₁₅₁	C₂	semidirect
4. C₂×C₄×D₄×C₁₅₁	C₂	semidirect
5. C₂²×C₄⋊C₄×C₁₅₁	C₂	semidirect
6. #396×C₁₅₁	C₂	semidirect
7. #394×C₁₅₁	C₂	semidirect
8. #390×C₁₅₁	C₂	semidirect
9. #389×C₁₅₁	C₂	semidirect
10. #386×C₁₅₁	C₂	semidirect
11. #380×C₁₅₁	C₂	semidirect
54. C₂×D₄×C₁₅₁	D₄	semidirect
63. C₂²×C₄×C₁₅₁	D₄	semidirect
77. C₄⋊C₄×C₁₅₁	D₄	semidirect
159. C₂²×C₁₅₁	#121	semidirect
174. C₄×C₁₅₁	#121	semidirect
185. C₁₅₁	#2416	direct (N × H)
186. #2416	C₁₅₁	direct (N × H)
187. C₂×#121	C₂×C₁₅₁	semidirect
188. C₂×#121	C₂×C₁₅₁	semidirect
189. C₂×#121	C₂×C₁₅₁	semidirect
190. C₂×C₄×D₄	C₂×C₁₅₁	semidirect
191. C₂²×C₄⋊C₄	C₂×C₁₅₁	semidirect
192. #396	C₂×C₁₅₁	semidirect
193. #394	C₂×C₁₅₁	semidirect
194. #390	C₂×C₁₅₁	semidirect
195. #389	C₂×C₁₅₁	semidirect
196. #386	C₂×C₁₅₁	semidirect
197. #380	C₂×C₁₅₁	semidirect
240. C₂×D₄	D₄×C₁₅₁	semidirect
249. C₂²×C₄	D₄×C₁₅₁	semidirect
263. C₄⋊C₄	D₄×C₁₅₁	semidirect
345. C₂²	#121×C₁₅₁	semidirect
360. C₄	#121×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#121×C₁₅₁	2
C₂×C₄×D₄×C₁₅₁	2
C₂²×C₄⋊C₄×C₁₅₁	2
#396×C₁₅₁	2
#394×C₁₅₁	2
#390×C₁₅₁	2
#389×C₁₅₁	2
#386×C₁₅₁	2
#380×C₁₅₁	2
#2416	151

Subgroups — #2416×C151 #34065748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2416×C₁₅₁ #34065748