Subgroups — C₁₅₁×#21529 #50326454

Order 38656.

1066 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#466×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#442×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#405×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2324×C₁₅₁	C₂	1	2	yes	maximal, complemented
5	#1972×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1943×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1934×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#1895×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1807×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1776×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₁₅₁	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₁₅₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
17	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
18	#466×C₁₅₁	C₄	1	8	yes	complemented
19	#442×C₁₅₁	—	2	4	no	—
20	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
21	C₂×#106×C₁₅₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
26	#405×C₁₅₁	—	2	4	no	—
27	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
31	#390×C₁₅₁	—	2	2	no	—
32	#390×C₁₅₁	C₂²	1	2	yes	—
33	#389×C₁₅₁	C₂²	1	2	yes	—
34	#388×C₁₅₁	—	2	2	no	—
35	#386×C₁₅₁	—	2	2	no	—
36	#385×C₁₅₁	—	2	2	no	—
37	#380×C₁₅₁	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
39	#340×C₁₅₁	C₂²	1	2	yes	—
40	#340×C₁₅₁	C₂²	1	2	yes	—
41	#340×C₁₅₁	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₅₁	—	2	2	no	—
43	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₅₁	—	2	2	no	—
45	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₁₅₁	—	2	2	no	—
47	C₂×D₈×C₁₅₁	—	2	2	no	—
48	C₂×D₈×C₁₅₁	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₁₅₁	—	2	2	no	—
50	C₂×M₁₆×C₁₅₁	—	2	2	no	—
51	C₂×M₁₆×C₁₅₁	—	2	2	no	—
52	C₂²×C₈×C₁₅₁	—	2	2	no	—
53	C₂²×C₈×C₁₅₁	—	2	2	no	—
54	C₂²×C₈×C₁₅₁	C₂×C₄	1	4	yes	complemented
55	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
59	#121×C₁₅₁	—	2	4	no	—
60	#121×C₁₅₁	C₂×C₄	1	8	yes	complemented
61	C₄×D₄×C₁₅₁	—	2	4	no	—
62	C₄×D₄×C₁₅₁	—	2	4	no	—
63	#117×C₁₅₁	—	2	2	no	—
64	#117×C₁₅₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₅₁	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	2	yes	—
76	C₂×C₄²×C₁₅₁	—	2	2	no	—
77	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
79	#107×C₁₅₁	C₂×C₄	1	4	yes	complemented
80	#106×C₁₅₁	—	2	2	no	—
81	#106×C₁₅₁	—	2	2	no	—
82	#102×C₁₅₁	—	2	4	no	—
83	#102×C₁₅₁	—	2	4	no	—
84	#102×C₁₅₁	C₂×C₄	1	8	yes	complemented
85	#97×C₁₅₁	—	2	2	no	—
86	#97×C₁₅₁	D₄	1	4	yes	complemented
87	C₄×C₈×C₁₅₁	—	2	2	no	—
88	C₄×C₈×C₁₅₁	—	2	2	no	—
89	#95×C₁₅₁	—	2	2	no	—
90	#95×C₁₅₁	—	2	2	no	—
91	#95×C₁₅₁	—	2	2	no	—
92	C₂⁴×C₁₅₁	—	2	2	no	—
93	C₂⁴×C₁₅₁	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₁₅₁	—	2	8	no	—
95	C₂×D₄×C₁₅₁	—	2	2	no	—
96	C₂×D₄×C₁₅₁	—	2	2	no	—
97	C₂×D₄×C₁₅₁	—	2	2	no	—
98	C₂×D₄×C₁₅₁	—	2	2	no	—
99	C₂×D₄×C₁₅₁	—	2	2	no	—
100	C₂×D₄×C₁₅₁	—	8	2	no	—
101	C₂×D₄×C₁₅₁	—	8	2	no	—
102	C₂×D₄×C₁₅₁	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₅₁	—	2	1	no	—
104	C₂²×C₄×C₁₅₁	—	2	1	no	—
105	C₂²×C₄×C₁₅₁	—	2	1	no	—
106	C₂²×C₄×C₁₅₁	—	2	1	no	—
107	C₂²×C₄×C₁₅₁	—	2	2	no	—
108	C₂²×C₄×C₁₅₁	—	2	2	no	—
109	C₂²×C₄×C₁₅₁	—	2	2	no	—
110	C₂²×C₄×C₁₅₁	—	4	4	no	—
111	C₂²×C₄×C₁₅₁	—	8	2	no	—
112	C₂²×C₄×C₁₅₁	—	8	2	no	—
113	C₂²×C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₅₁	#41	1	2	yes	—
118	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
119	D₈×C₁₅₁	—	2	8	no	—
120	M₁₆×C₁₅₁	—	2	8	no	—
121	C₂×C₈×C₁₅₁	—	2	1	no	—
122	C₂×C₈×C₁₅₁	—	2	1	no	—
123	C₂×C₈×C₁₅₁	—	2	1	no	—
124	C₂×C₈×C₁₅₁	—	2	1	no	—
125	C₂×C₈×C₁₅₁	—	2	1	no	—
126	C₂×C₈×C₁₅₁	—	2	1	no	—
127	C₂×C₈×C₁₅₁	—	2	8	no	—
128	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₅₁	#41	1	2	yes	—
133	C₂×C₈×C₁₅₁	#41	1	2	yes	—
134	C₄⋊C₄×C₁₅₁	—	2	4	no	—
135	C₄⋊C₄×C₁₅₁	—	2	2	no	—
136	C₄⋊C₄×C₁₅₁	—	2	2	no	—
137	C₄⋊C₄×C₁₅₁	—	2	2	no	—
138	C₄⋊C₄×C₁₅₁	—	2	2	no	—
139	C₄⋊C₄×C₁₅₁	—	2	2	no	—
140	C₄⋊C₄×C₁₅₁	—	8	2	no	—
141	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	4	yes	—
142	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
143	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
144	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
145	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
146	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
147	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
148	C₄²×C₁₅₁	—	2	1	no	—
149	C₄²×C₁₅₁	—	2	1	no	—
150	C₄²×C₁₅₁	—	8	2	no	—
151	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
152	C₄²×C₁₅₁	#41	1	2	yes	—
153	C₂³×C₁₅₁	—	2	1	no	—
154	C₂³×C₁₅₁	—	2	1	no	—
155	C₂³×C₁₅₁	—	2	2	no	—
156	C₂³×C₁₅₁	—	2	2	no	—
157	C₂³×C₁₅₁	—	2	4	no	—
158	C₂³×C₁₅₁	—	4	2	no	—
159	C₂³×C₁₅₁	—	4	2	no	—
160	C₂³×C₁₅₁	—	4	2	no	—
161	C₂³×C₁₅₁	—	4	2	no	—
162	C₂³×C₁₅₁	—	4	2	no	—
163	C₂³×C₁₅₁	—	4	2	no	—
164	C₂³×C₁₅₁	C₄×D₄	1	2	yes	—
165	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
166	D₄×C₁₅₁	—	2	4	no	—
167	D₄×C₁₅₁	—	2	4	no	—
168	D₄×C₁₅₁	—	4	2	no	—
169	D₄×C₁₅₁	—	4	2	no	—
170	D₄×C₁₅₁	—	8	8	no	—
171	C₂×C₄×C₁₅₁	—	2	1	no	—
172	C₂×C₄×C₁₅₁	—	2	1	no	—
173	C₂×C₄×C₁₅₁	—	2	2	no	—
174	C₂×C₄×C₁₅₁	—	2	2	no	—
175	C₂×C₄×C₁₅₁	—	2	2	no	—
176	C₂×C₄×C₁₅₁	—	2	2	no	—
177	C₂×C₄×C₁₅₁	—	2	2	no	—
178	C₂×C₄×C₁₅₁	—	2	2	no	—
179	C₂×C₄×C₁₅₁	—	2	4	no	—
180	C₂×C₄×C₁₅₁	—	2	2	no	—
181	C₂×C₄×C₁₅₁	—	2	2	no	—
182	C₂×C₄×C₁₅₁	—	2	2	no	—
183	C₂×C₄×C₁₅₁	—	4	2	no	—
184	C₂×C₄×C₁₅₁	—	4	2	no	—
185	C₂×C₄×C₁₅₁	—	4	2	no	—
186	C₂×C₄×C₁₅₁	—	4	2	no	—
187	C₂×C₄×C₁₅₁	—	4	2	no	—
188	C₂×C₄×C₁₅₁	—	4	2	no	—
189	C₂×C₄×C₁₅₁	—	4	2	no	—
190	C₂×C₄×C₁₅₁	—	4	2	no	—
191	C₂×C₄×C₁₅₁	—	8	8	no	—
192	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₁₅₁	#121	1	4	yes	—
194	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
200	C₈×C₁₅₁	—	2	2	no	—
201	C₈×C₁₅₁	—	2	2	no	—
202	C₈×C₁₅₁	—	2	2	no	—
203	C₈×C₁₅₁	C₄×D₄	1	4	yes	—
204	C₂²×C₁₅₁	—	2	2	no	—
205	C₂²×C₁₅₁	—	2	2	no	—
206	C₂²×C₁₅₁	—	2	2	no	—
207	C₂²×C₁₅₁	—	4	2	no	—
208	C₂²×C₁₅₁	—	4	2	no	—
209	C₂²×C₁₅₁	—	4	4	no	—
210	C₂²×C₁₅₁	—	4	4	no	—
211	C₂²×C₁₅₁	—	4	4	no	—
212	C₂²×C₁₅₁	—	8	2	no	—
213	C₂²×C₁₅₁	—	8	2	no	—
214	C₂²×C₁₅₁	—	8	2	no	—
215	C₂²×C₁₅₁	—	8	2	no	—
216	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
218	C₂²×C₁₅₁	#532	1	1	yes	characteristic
219	C₂²×C₁₅₁	#576	1	2	yes	—
220	C₂²×C₁₅₁	#577	1	2	yes	—
221	C₄×C₁₅₁	—	2	4	no	—
222	C₄×C₁₅₁	—	2	2	no	—
223	C₄×C₁₅₁	—	4	4	no	—
224	C₄×C₁₅₁	—	4	2	no	—
225	C₄×C₁₅₁	—	8	2	no	—
226	C₄×C₁₅₁	—	8	2	no	—
227	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₁₅₁	C₄×#41	1	1	yes	characteristic
229	C₄×C₁₅₁	#525	1	1	yes	characteristic
230	C₄×C₁₅₁	#529	1	1	yes	characteristic
231	C₂×C₁₅₁	—	4	2	no	—
232	C₂×C₁₅₁	—	8	4	no	—
233	C₂×C₁₅₁	C₄×#121	1	1	yes	characteristic
234	C₂×C₁₅₁	#2948	1	1	yes	characteristic
235	C₂×C₁₅₁	#2952	1	1	yes	characteristic
236	C₂×C₁₅₁	#3062	1	2	yes	—
237	C₂×C₁₅₁	#3179	1	2	yes	—
238	#21529	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₅₁	#21529	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×#466	C₂×C₁₅₁	1	1	yes	characteristic
241	C₂×#442	C₂×C₁₅₁	1	1	yes	characteristic, complemented
242	C₂×#405	C₂×C₁₅₁	1	1	yes	characteristic, complemented
243	#2324	C₂×C₁₅₁	1	2	yes	complemented
244	#1972	C₂×C₁₅₁	1	1	yes	characteristic, complemented
245	#1943	C₂×C₁₅₁	1	1	yes	characteristic, complemented
246	#1934	C₂×C₁₅₁	1	2	yes	complemented
247	#1895	C₂×C₁₅₁	1	2	yes	complemented
248	#1807	C₂×C₁₅₁	1	1	yes	characteristic, complemented
249	#1776	C₂×C₁₅₁	1	1	yes	characteristic, complemented
250	C₄×#102	C₂×C₁₅₁	1	2	yes	complemented
251	C₂²×D₈	C₂²×C₁₅₁	1	1	yes	characteristic
252	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
254	C₂×#121	C₂²×C₁₅₁	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₅₁	1	2	yes	—
256	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
257	#466	C₄×C₁₅₁	1	8	yes	complemented
258	#442	—	2	4	no	—
259	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
260	C₂×#106	C₂²×C₁₅₁	1	1	yes	characteristic
261	C₂×#106	C₂²×C₁₅₁	1	1	yes	characteristic
262	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
263	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
264	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
265	#405	—	2	4	no	—
266	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
267	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
269	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
270	#390	—	2	2	no	—
271	#390	C₂²×C₁₅₁	1	2	yes	—
272	#389	C₂²×C₁₅₁	1	2	yes	—
273	#388	—	2	2	no	—
274	#386	—	2	2	no	—
275	#385	—	2	2	no	—
276	#380	C₂²×C₁₅₁	1	2	yes	—
277	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
278	#340	C₂²×C₁₅₁	1	2	yes	—
279	#340	C₂²×C₁₅₁	1	2	yes	—
280	#340	C₂²×C₁₅₁	1	2	yes	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	C₂×C₄×C₁₅₁	1	4	yes	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	C₂×C₄×C₁₅₁	1	4	yes	complemented
294	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
298	#121	—	2	4	no	—
299	#121	C₂×C₄×C₁₅₁	1	8	yes	complemented
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	D₄×C₁₅₁	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	2	yes	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
318	#107	C₂×C₄×C₁₅₁	1	4	yes	complemented
319	#106	—	2	2	no	—
320	#106	—	2	2	no	—
321	#102	—	2	4	no	—
322	#102	—	2	4	no	—
323	#102	C₂×C₄×C₁₅₁	1	8	yes	complemented
324	#97	—	2	2	no	—
325	#97	D₄×C₁₅₁	1	4	yes	complemented
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×D₄×C₁₅₁	1	1	yes	characteristic
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	C₂²×C₄×C₁₅₁	1	4	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	—	8	2	no	—
352	C₂²×C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
356	C₂²×C₄	#41×C₁₅₁	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
358	D₈	—	2	8	no	—
359	M₁₆	—	2	8	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
368	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
371	C₂×C₈	#41×C₁₅₁	1	2	yes	—
372	C₂×C₈	#41×C₁₅₁	1	2	yes	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	8	2	no	—
380	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	4	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	8	2	no	—
385	C₂²⋊C₄	—	8	2	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	8	2	no	—
390	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
391	C₄²	#41×C₁₅₁	1	2	yes	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	C₄×D₄×C₁₅₁	1	2	yes	—
404	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	8	8	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	8	no	—
431	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
432	C₂×C₄	#121×C₁₅₁	1	4	yes	—
433	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	C₄×D₄×C₁₅₁	1	4	yes	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
456	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
457	C₂²	#532×C₁₅₁	1	1	yes	characteristic
458	C₂²	#576×C₁₅₁	1	2	yes	—
459	C₂²	#577×C₁₅₁	1	2	yes	—
460	C₄	—	2	4	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
467	C₄	C₄×#41×C₁₅₁	1	1	yes	characteristic
468	C₄	#525×C₁₅₁	1	1	yes	characteristic
469	C₄	#529×C₁₅₁	1	1	yes	characteristic
470	C₂	—	4	2	no	—
471	C₂	—	8	4	no	—
472	C₂	C₄×#121×C₁₅₁	1	1	yes	characteristic
473	C₂	#2948×C₁₅₁	1	1	yes	characteristic
474	C₂	#2952×C₁₅₁	1	1	yes	characteristic
475	C₂	#3062×C₁₅₁	1	2	yes	—
476	C₂	#3179×C₁₅₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂×#466×C₁₅₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₂×#117×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#442×C₁₅₁	C₂	semidirect
3. C₂×#405×C₁₅₁	C₂	semidirect
4. #2324×C₁₅₁	C₂	semidirect
5. #1972×C₁₅₁	C₂	semidirect
6. #1943×C₁₅₁	C₂	semidirect
7. #1934×C₁₅₁	C₂	semidirect
8. #1895×C₁₅₁	C₂	semidirect
9. #1807×C₁₅₁	C₂	semidirect
10. #1776×C₁₅₁	C₂	semidirect
11. C₄×#102×C₁₅₁	C₂	semidirect
18. #466×C₁₅₁	C₄	semidirect
54. C₂²×C₈×C₁₅₁	C₂×C₄	semidirect
60. #121×C₁₅₁	C₂×C₄	semidirect
79. #107×C₁₅₁	C₂×C₄	semidirect
84. #102×C₁₅₁	C₂×C₄	semidirect
86. #97×C₁₅₁	D₄	semidirect
238. #21529	C₁₅₁	direct (N × H)
239. C₁₅₁	#21529	direct (N × H)
241. C₂×#442	C₂×C₁₅₁	semidirect
242. C₂×#405	C₂×C₁₅₁	semidirect
243. #2324	C₂×C₁₅₁	semidirect
244. #1972	C₂×C₁₅₁	semidirect
245. #1943	C₂×C₁₅₁	semidirect
246. #1934	C₂×C₁₅₁	semidirect
247. #1895	C₂×C₁₅₁	semidirect
248. #1807	C₂×C₁₅₁	semidirect
249. #1776	C₂×C₁₅₁	semidirect
250. C₄×#102	C₂×C₁₅₁	semidirect
257. #466	C₄×C₁₅₁	semidirect
293. C₂²×C₈	C₂×C₄×C₁₅₁	semidirect
299. #121	C₂×C₄×C₁₅₁	semidirect
318. #107	C₂×C₄×C₁₅₁	semidirect
323. #102	C₂×C₄×C₁₅₁	semidirect
325. #97	D₄×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#466×C₁₅₁	2
C₂×#442×C₁₅₁	2
C₂×#405×C₁₅₁	2
#2324×C₁₅₁	2
#1972×C₁₅₁	2
#1943×C₁₅₁	2
#1934×C₁₅₁	2
#1895×C₁₅₁	2
#1807×C₁₅₁	2
#1776×C₁₅₁	2
C₄×#102×C₁₅₁	2
#21529	151

Subgroups — C151×#21529 #50326454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#21529 #50326454