Subgroups — C₁₅₁×#24340 #50329265

Order 38656.

1036 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#440×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#2580×C₁₅₁	C₂	1	1	yes	maximal, characteristic
5	#2059×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#2025×C₁₅₁	C₂	1	2	yes	maximal
7	#1993×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1985×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1880×C₁₅₁	C₂	1	2	yes	maximal
10	#1865×C₁₅₁	C₂	1	2	yes	maximal, complemented
11	#1805×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
13	#557×C₁₅₁	—	2	4	no	—
14	#557×C₁₅₁	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₁₅₁	—	2	1	no	—
16	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₁₅₁	—	2	2	no	—
18	C₂×#125×C₁₅₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₅₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₅₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
24	#476×C₁₅₁	—	2	4	no	—
25	#440×C₁₅₁	—	2	4	no	—
26	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
27	C₂×#106×C₁₅₁	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₁₅₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
31	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
32	C₂×#102×C₁₅₁	C₂²	1	1	yes	characteristic
33	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
34	#399×C₁₅₁	—	2	1	no	—
35	#393×C₁₅₁	—	2	1	no	—
36	#390×C₁₅₁	C₂²	1	2	yes	—
37	#389×C₁₅₁	C₂²	1	2	yes	—
38	#385×C₁₅₁	—	2	2	no	—
39	#382×C₁₅₁	C₂²	1	1	yes	characteristic
40	#340×C₁₅₁	C₂²	1	2	yes	—
41	#340×C₁₅₁	C₂²	1	2	yes	—
42	#340×C₁₅₁	C₂²	1	2	yes	—
43	#336×C₁₅₁	C₂²	1	2	yes	—
44	#336×C₁₅₁	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₅₁	—	2	1	no	—
46	C₂²×Q₈×C₁₅₁	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₅₁	—	2	1	no	—
50	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
51	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
52	C₂×SD₁₆×C₁₅₁	Q₈	1	4	yes	complemented
53	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₁₅₁	—	2	8	no	—
57	C₄⋊Q₈×C₁₅₁	—	2	2	no	—
58	C₄⋊Q₈×C₁₅₁	D₄	1	4	yes	—
59	#125×C₁₅₁	—	2	16	no	—
60	#125×C₁₅₁	—	2	4	no	—
61	#125×C₁₅₁	—	2	4	no	—
62	C₄×Q₈×C₁₅₁	—	2	8	no	—
63	C₄×Q₈×C₁₅₁	—	2	4	no	—
64	C₄×Q₈×C₁₅₁	—	2	2	no	—
65	C₄×Q₈×C₁₅₁	—	2	2	no	—
66	C₄×Q₈×C₁₅₁	—	2	2	no	—
67	C₄×Q₈×C₁₅₁	—	2	4	no	—
68	C₄×Q₈×C₁₅₁	D₄	1	4	yes	—
69	C₄×D₄×C₁₅₁	—	2	2	no	—
70	C₄×D₄×C₁₅₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₅₁	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
86	C₂×C₄²×C₁₅₁	—	2	2	no	—
87	C₂×C₄²×C₁₅₁	—	2	1	no	—
88	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
90	#107×C₁₅₁	—	2	2	no	—
91	#106×C₁₅₁	—	2	4	no	—
92	C₄⋊C₈×C₁₅₁	—	2	2	no	—
93	#103×C₁₅₁	—	2	2	no	—
94	#103×C₁₅₁	—	2	4	no	—
95	#102×C₁₅₁	—	2	2	no	—
96	#102×C₁₅₁	—	2	4	no	—
97	#97×C₁₅₁	—	2	2	no	—
98	#95×C₁₅₁	—	2	1	no	—
99	#95×C₁₅₁	—	2	1	no	—
100	#95×C₁₅₁	—	2	2	no	—
101	C₂⁴×C₁₅₁	—	2	1	no	—
102	C₂×Q₈×C₁₅₁	—	2	2	no	—
103	C₂×Q₈×C₁₅₁	—	2	4	no	—
104	C₂×Q₈×C₁₅₁	—	2	1	no	—
105	C₂×Q₈×C₁₅₁	—	2	1	no	—
106	C₂×Q₈×C₁₅₁	—	2	1	no	—
107	C₂×Q₈×C₁₅₁	—	4	2	no	—
108	C₂×Q₈×C₁₅₁	—	4	4	no	—
109	C₂×Q₈×C₁₅₁	C₂×D₄	1	2	yes	—
110	C₂×Q₈×C₁₅₁	C₂×Q₈	1	2	yes	—
111	C₂×Q₈×C₁₅₁	#41	1	2	yes	—
112	C₂×D₄×C₁₅₁	—	2	1	no	—
113	C₂×D₄×C₁₅₁	—	2	1	no	—
114	C₂×D₄×C₁₅₁	—	2	1	no	—
115	C₂×D₄×C₁₅₁	—	2	1	no	—
116	C₂×D₄×C₁₅₁	—	2	1	no	—
117	C₂×D₄×C₁₅₁	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₅₁	—	2	1	no	—
119	C₂²×C₄×C₁₅₁	—	2	1	no	—
120	C₂²×C₄×C₁₅₁	—	2	2	no	—
121	C₂²×C₄×C₁₅₁	—	2	2	no	—
122	C₂²×C₄×C₁₅₁	—	2	1	no	—
123	C₂²×C₄×C₁₅₁	—	4	2	no	—
124	C₂²×C₄×C₁₅₁	—	8	2	no	—
125	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
130	SD₁₆×C₁₅₁	—	2	8	no	—
131	C₂×C₈×C₁₅₁	—	2	1	no	—
132	C₂×C₈×C₁₅₁	—	2	1	no	—
133	C₂×C₈×C₁₅₁	—	2	1	no	—
134	C₂×C₈×C₁₅₁	—	2	2	no	—
135	C₂×C₈×C₁₅₁	—	2	2	no	—
136	C₂×C₈×C₁₅₁	—	2	1	no	—
137	C₂×C₈×C₁₅₁	—	2	1	no	—
138	C₂×C₈×C₁₅₁	—	2	2	no	—
139	C₂×C₈×C₁₅₁	C₂×Q₈	1	2	yes	—
140	C₄⋊C₄×C₁₅₁	—	2	8	no	—
141	C₄⋊C₄×C₁₅₁	—	2	8	no	—
142	C₄⋊C₄×C₁₅₁	—	2	8	no	—
143	C₄⋊C₄×C₁₅₁	—	2	4	no	—
144	C₄⋊C₄×C₁₅₁	—	2	4	no	—
145	C₄⋊C₄×C₁₅₁	—	2	2	no	—
146	C₄⋊C₄×C₁₅₁	—	2	4	no	—
147	C₄⋊C₄×C₁₅₁	—	2	1	no	—
148	C₄⋊C₄×C₁₅₁	—	2	2	no	—
149	C₄⋊C₄×C₁₅₁	—	2	1	no	—
150	C₄⋊C₄×C₁₅₁	—	2	1	no	—
151	C₄⋊C₄×C₁₅₁	—	2	2	no	—
152	C₄⋊C₄×C₁₅₁	—	2	2	no	—
153	C₄⋊C₄×C₁₅₁	—	8	2	no	—
154	C₄⋊C₄×C₁₅₁	C₂×D₄	1	4	yes	—
155	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
157	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
158	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
159	C₄²×C₁₅₁	—	2	8	no	—
160	C₄²×C₁₅₁	—	2	4	no	—
161	C₄²×C₁₅₁	—	2	2	no	—
162	C₄²×C₁₅₁	—	2	2	no	—
163	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
164	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
165	C₂³×C₁₅₁	—	2	2	no	—
166	C₂³×C₁₅₁	—	4	1	no	—
167	C₂³×C₁₅₁	—	4	1	no	—
168	C₂³×C₁₅₁	—	4	2	no	—
169	C₂³×C₁₅₁	—	4	2	no	—
170	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₅₁	—	2	2	no	—
172	Q₈×C₁₅₁	—	2	2	no	—
173	Q₈×C₁₅₁	—	2	2	no	—
174	Q₈×C₁₅₁	—	4	4	no	—
175	Q₈×C₁₅₁	—	4	8	no	—
176	Q₈×C₁₅₁	C₂²⋊Q₈	1	4	yes	—
177	D₄×C₁₅₁	—	2	2	no	—
178	D₄×C₁₅₁	—	2	2	no	—
179	D₄×C₁₅₁	—	4	1	no	—
180	D₄×C₁₅₁	—	4	1	no	—
181	C₂×C₄×C₁₅₁	—	2	2	no	—
182	C₂×C₄×C₁₅₁	—	2	2	no	—
183	C₂×C₄×C₁₅₁	—	2	2	no	—
184	C₂×C₄×C₁₅₁	—	2	2	no	—
185	C₂×C₄×C₁₅₁	—	2	2	no	—
186	C₂×C₄×C₁₅₁	—	2	2	no	—
187	C₂×C₄×C₁₅₁	—	2	4	no	—
188	C₂×C₄×C₁₅₁	—	2	2	no	—
189	C₂×C₄×C₁₅₁	—	2	2	no	—
190	C₂×C₄×C₁₅₁	—	2	2	no	—
191	C₂×C₄×C₁₅₁	—	2	2	no	—
192	C₂×C₄×C₁₅₁	—	2	2	no	—
193	C₂×C₄×C₁₅₁	—	2	2	no	—
194	C₂×C₄×C₁₅₁	—	4	4	no	—
195	C₂×C₄×C₁₅₁	—	4	2	no	—
196	C₂×C₄×C₁₅₁	—	4	1	no	—
197	C₂×C₄×C₁₅₁	—	4	2	no	—
198	C₂×C₄×C₁₅₁	—	4	2	no	—
199	C₂×C₄×C₁₅₁	—	4	2	no	—
200	C₂×C₄×C₁₅₁	—	4	2	no	—
201	C₂×C₄×C₁₅₁	—	8	4	no	—
202	C₂×C₄×C₁₅₁	#120	1	2	yes	—
203	C₂×C₄×C₁₅₁	#120	1	2	yes	—
204	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₅₁	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
209	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₁₅₁	—	2	2	no	—
211	C₈×C₁₅₁	—	4	1	no	—
212	C₈×C₁₅₁	—	4	2	no	—
213	C₂²×C₁₅₁	—	4	4	no	—
214	C₂²×C₁₅₁	—	4	2	no	—
215	C₂²×C₁₅₁	—	8	2	no	—
216	C₂²×C₁₅₁	—	8	1	no	—
217	C₂²×C₁₅₁	—	8	1	no	—
218	C₂²×C₁₅₁	C₂×#120	1	1	yes	characteristic
219	C₂²×C₁₅₁	#548	1	1	yes	characteristic
220	C₂²×C₁₅₁	D₄×Q₈	1	1	yes	characteristic
221	C₂²×C₁₅₁	#575	1	2	yes	—
222	C₂²×C₁₅₁	#577	1	2	yes	—
223	C₄×C₁₅₁	—	2	4	no	—
224	C₄×C₁₅₁	—	2	2	no	—
225	C₄×C₁₅₁	—	2	2	no	—
226	C₄×C₁₅₁	—	4	2	no	—
227	C₄×C₁₅₁	—	4	4	no	—
228	C₄×C₁₅₁	—	4	2	no	—
229	C₄×C₁₅₁	—	4	2	no	—
230	C₄×C₁₅₁	—	8	2	no	—
231	C₄×C₁₅₁	—	8	1	no	—
232	C₄×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
233	C₄×C₁₅₁	#536	1	1	yes	characteristic
234	C₄×C₁₅₁	#548	1	1	yes	characteristic
235	C₄×C₁₅₁	D₄×Q₈	1	1	yes	characteristic
236	C₂×C₁₅₁	—	8	2	no	—
237	C₂×C₁₅₁	#2409	1	1	yes	characteristic
238	C₂×C₁₅₁	#3005	1	1	yes	characteristic
239	C₂×C₁₅₁	#3010	1	1	yes	characteristic
240	C₂×C₁₅₁	#3371	1	2	yes	—
241	C₂×C₁₅₁	#3388	1	2	yes	—
242	#24340	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₁₅₁	#24340	1	1	yes	characteristic, direct product factor, Sylow
244	C₂×#557	C₂×C₁₅₁	1	1	yes	characteristic, complemented
245	C₂×#476	C₂×C₁₅₁	1	1	yes	characteristic
246	C₂×#440	C₂×C₁₅₁	1	1	yes	characteristic
247	#2580	C₂×C₁₅₁	1	1	yes	characteristic
248	#2059	C₂×C₁₅₁	1	2	yes	complemented
249	#2025	C₂×C₁₅₁	1	2	yes	—
250	#1993	C₂×C₁₅₁	1	1	yes	characteristic, complemented
251	#1985	C₂×C₁₅₁	1	1	yes	characteristic, complemented
252	#1880	C₂×C₁₅₁	1	2	yes	—
253	#1865	C₂×C₁₅₁	1	2	yes	complemented
254	#1805	C₂×C₁₅₁	1	1	yes	characteristic, complemented
255	C₂²×SD₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
256	#557	—	2	4	no	—
257	#557	—	2	4	no	—
258	C₂×C₄⋊Q₈	—	2	1	no	—
259	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
260	C₂×#125	—	2	2	no	—
261	C₂×#125	C₂²×C₁₅₁	1	2	yes	—
262	C₂×C₄×Q₈	—	2	1	no	—
263	C₂×C₄×Q₈	C₂²×C₁₅₁	1	2	yes	—
264	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
267	#476	—	2	4	no	—
268	#440	—	2	4	no	—
269	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
270	C₂×#106	C₂²×C₁₅₁	1	2	yes	—
271	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
272	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
273	C₂×#103	C₂²×C₁₅₁	1	1	yes	characteristic
274	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
275	C₂×#102	C₂²×C₁₅₁	1	1	yes	characteristic
276	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
277	#399	—	2	1	no	—
278	#393	—	2	1	no	—
279	#390	C₂²×C₁₅₁	1	2	yes	—
280	#389	C₂²×C₁₅₁	1	2	yes	—
281	#385	—	2	2	no	—
282	#382	C₂²×C₁₅₁	1	1	yes	characteristic
283	#340	C₂²×C₁₅₁	1	2	yes	—
284	#340	C₂²×C₁₅₁	1	2	yes	—
285	#340	C₂²×C₁₅₁	1	2	yes	—
286	#336	C₂²×C₁₅₁	1	2	yes	—
287	#336	C₂²×C₁₅₁	1	2	yes	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	D₄×C₁₅₁	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
291	C₂²×D₄	C₂³×C₁₅₁	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂×SD₁₆	—	2	2	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×SD₁₆	Q₈×C₁₅₁	1	4	yes	complemented
296	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
298	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
299	C₄⋊Q₈	—	2	8	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	D₄×C₁₅₁	1	4	yes	—
302	#125	—	2	16	no	—
303	#125	—	2	4	no	—
304	#125	—	2	4	no	—
305	C₄×Q₈	—	2	8	no	—
306	C₄×Q₈	—	2	4	no	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	D₄×C₁₅₁	1	4	yes	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
321	C₂×C₄⋊C₄	D₄×C₁₅₁	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
333	#107	—	2	2	no	—
334	#106	—	2	4	no	—
335	C₄⋊C₈	—	2	2	no	—
336	#103	—	2	4	no	—
337	#103	—	2	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	4	no	—
340	#97	—	2	2	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	2	no	—
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	C₂×D₄×C₁₅₁	1	2	yes	—
353	C₂×Q₈	C₂×Q₈×C₁₅₁	1	2	yes	—
354	C₂×Q₈	#41×C₁₅₁	1	2	yes	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂×Q₈×C₁₅₁	1	2	yes	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
373	SD₁₆	—	2	8	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×Q₈×C₁₅₁	1	2	yes	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	8	2	no	—
397	C₄⋊C₄	C₂×D₄×C₁₅₁	1	4	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	8	2	no	—
402	C₄²	—	2	8	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
407	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
408	C₂³	—	2	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	4	4	no	—
418	Q₈	—	4	8	no	—
419	Q₈	C₂²⋊Q₈×C₁₅₁	1	4	yes	—
420	D₄	—	2	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	8	4	no	—
445	C₂×C₄	#120×C₁₅₁	1	2	yes	—
446	C₂×C₄	#120×C₁₅₁	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
449	C₂×C₄	C₂²×Q₈×C₁₅₁	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
451	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
452	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	C₂×#120×C₁₅₁	1	1	yes	characteristic
462	C₂²	#548×C₁₅₁	1	1	yes	characteristic
463	C₂²	D₄×Q₈×C₁₅₁	1	1	yes	characteristic
464	C₂²	#575×C₁₅₁	1	2	yes	—
465	C₂²	#577×C₁₅₁	1	2	yes	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
476	C₄	#536×C₁₅₁	1	1	yes	characteristic
477	C₄	#548×C₁₅₁	1	1	yes	characteristic
478	C₄	D₄×Q₈×C₁₅₁	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	#2409×C₁₅₁	1	1	yes	characteristic
481	C₂	#3005×C₁₅₁	1	1	yes	characteristic
482	C₂	#3010×C₁₅₁	1	1	yes	characteristic
483	C₂	#3371×C₁₅₁	1	2	yes	—
484	C₂	#3388×C₁₅₁	1	2	yes	—

	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 ◁ C₂×C₄×Q₈×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#557×C₁₅₁	C₂	semidirect
5. #2059×C₁₅₁	C₂	semidirect
7. #1993×C₁₅₁	C₂	semidirect
8. #1985×C₁₅₁	C₂	semidirect
10. #1865×C₁₅₁	C₂	semidirect
11. #1805×C₁₅₁	C₂	semidirect
52. C₂×SD₁₆×C₁₅₁	Q₈	semidirect
242. #24340	C₁₅₁	direct (N × H)
243. C₁₅₁	#24340	direct (N × H)
244. C₂×#557	C₂×C₁₅₁	semidirect
248. #2059	C₂×C₁₅₁	semidirect
250. #1993	C₂×C₁₅₁	semidirect
251. #1985	C₂×C₁₅₁	semidirect
253. #1865	C₂×C₁₅₁	semidirect
254. #1805	C₂×C₁₅₁	semidirect
295. C₂×SD₁₆	Q₈×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₁₅₁	2
C₂×#476×C₁₅₁	2
C₂×#440×C₁₅₁	2
#2580×C₁₅₁	2
#2059×C₁₅₁	2
#2025×C₁₅₁	2
#1993×C₁₅₁	2
#1985×C₁₅₁	2
#1880×C₁₅₁	2
#1865×C₁₅₁	2
#1805×C₁₅₁	2
#24340	151

Subgroups — C151×#24340 #50329265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#24340 #50329265