Subgroups — C₁₅₁×#21525 #50326450

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#467×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#405×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#2323×C₁₅₁	C₂	1	2	yes	maximal
5	#1969×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1942×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1935×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#1894×C₁₅₁	C₂	1	2	yes	maximal
9	#1808×C₁₅₁	C₂	1	1	yes	maximal, characteristic
10	C₄×#107×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1763×C₁₅₁	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×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×C₂²⋊Q₈×C₁₅₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₅₁	C₂²	1	2	yes	—
17	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
18	#467×C₁₅₁	C₄	1	8	yes	complemented
19	C₄×Q₁₆×C₁₅₁	—	2	4	no	—
20	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
22	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
24	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
25	C₂×#103×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	#391×C₁₅₁	C₂²	1	2	yes	—
32	#389×C₁₅₁	—	2	2	no	—
33	#389×C₁₅₁	C₂²	1	2	yes	—
34	#388×C₁₅₁	—	2	2	no	—
35	#388×C₁₅₁	—	2	2	no	—
36	#387×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×Q₈×C₁₅₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
45	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
46	C₂×Q₁₆×C₁₅₁	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₁₅₁	—	2	2	no	—
48	C₂×M₁₆×C₁₅₁	—	2	2	no	—
49	C₂×M₁₆×C₁₅₁	—	2	2	no	—
50	C₂²×C₈×C₁₅₁	—	2	2	no	—
51	C₂²×C₈×C₁₅₁	—	2	2	no	—
52	C₂²×C₈×C₁₅₁	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
57	C₂²⋊Q₈×C₁₅₁	—	2	4	no	—
58	C₂²⋊Q₈×C₁₅₁	C₂×C₄	1	8	yes	—
59	C₄×Q₈×C₁₅₁	—	2	4	no	—
60	C₄×Q₈×C₁₅₁	—	2	4	no	—
61	#117×C₁₅₁	—	2	2	no	—
62	#117×C₁₅₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₅₁	—	2	2	no	—
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	—	2	2	no	—
80	#107×C₁₅₁	—	2	2	no	—
81	#107×C₁₅₁	C₂×C₄	1	4	yes	—
82	#103×C₁₅₁	—	2	4	no	—
83	#103×C₁₅₁	—	2	4	no	—
84	#103×C₁₅₁	C₂×C₄	1	8	yes	—
85	#97×C₁₅₁	—	2	2	no	—
86	#97×C₁₅₁	—	2	2	no	—
87	C₄×C₈×C₁₅₁	—	2	2	no	—
88	C₄×C₈×C₁₅₁	D₄	1	4	yes	—
89	#95×C₁₅₁	—	2	2	no	—
90	#95×C₁₅₁	—	2	2	no	—
91	#95×C₁₅₁	—	2	2	no	—
92	#95×C₁₅₁	—	2	2	no	—
93	#95×C₁₅₁	—	2	2	no	—
94	C₂⁴×C₁₅₁	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₅₁	—	2	2	no	—
96	C₂×Q₈×C₁₅₁	—	2	2	no	—
97	C₂×Q₈×C₁₅₁	—	2	2	no	—
98	C₂×Q₈×C₁₅₁	—	2	2	no	—
99	C₂×Q₈×C₁₅₁	—	2	2	no	—
100	C₂×Q₈×C₁₅₁	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₅₁	—	2	1	no	—
102	C₂²×C₄×C₁₅₁	—	2	1	no	—
103	C₂²×C₄×C₁₅₁	—	2	1	no	—
104	C₂²×C₄×C₁₅₁	—	2	1	no	—
105	C₂²×C₄×C₁₅₁	—	2	2	no	—
106	C₂²×C₄×C₁₅₁	—	2	2	no	—
107	C₂²×C₄×C₁₅₁	—	2	2	no	—
108	C₂²×C₄×C₁₅₁	—	2	2	no	—
109	C₂²×C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₅₁	#41	1	2	yes	—
116	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₁₅₁	—	2	8	no	—
118	M₁₆×C₁₅₁	—	2	8	no	—
119	C₂×C₈×C₁₅₁	—	2	1	no	—
120	C₂×C₈×C₁₅₁	—	2	1	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	8	no	—
126	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₅₁	#41	1	2	yes	—
131	C₂×C₈×C₁₅₁	#41	1	2	yes	—
132	C₄⋊C₄×C₁₅₁	—	2	8	no	—
133	C₄⋊C₄×C₁₅₁	—	2	2	no	—
134	C₄⋊C₄×C₁₅₁	—	2	2	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	—	4	4	no	—
141	C₄⋊C₄×C₁₅₁	—	8	2	no	—
142	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	4	yes	—
143	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
144	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
145	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
146	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
147	C₄²×C₁₅₁	—	2	1	no	—
148	C₄²×C₁₅₁	—	2	1	no	—
149	C₄²×C₁₅₁	—	4	4	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	1	no	—
156	C₂³×C₁₅₁	—	2	1	no	—
157	C₂³×C₁₅₁	—	2	1	no	—
158	C₂³×C₁₅₁	—	2	1	no	—
159	C₂³×C₁₅₁	C₄×D₄	1	2	yes	—
160	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₁₅₁	—	2	4	no	—
162	Q₈×C₁₅₁	—	2	4	no	—
163	Q₈×C₁₅₁	—	4	2	no	—
164	Q₈×C₁₅₁	—	4	2	no	—
165	C₂×C₄×C₁₅₁	—	2	1	no	—
166	C₂×C₄×C₁₅₁	—	2	1	no	—
167	C₂×C₄×C₁₅₁	—	2	1	no	—
168	C₂×C₄×C₁₅₁	—	2	1	no	—
169	C₂×C₄×C₁₅₁	—	2	1	no	—
170	C₂×C₄×C₁₅₁	—	2	1	no	—
171	C₂×C₄×C₁₅₁	—	2	2	no	—
172	C₂×C₄×C₁₅₁	—	2	2	no	—
173	C₂×C₄×C₁₅₁	—	2	2	no	—
174	C₂×C₄×C₁₅₁	—	2	2	no	—
175	C₂×C₄×C₁₅₁	—	2	4	no	—
176	C₂×C₄×C₁₅₁	—	2	4	no	—
177	C₂×C₄×C₁₅₁	—	2	1	no	—
178	C₂×C₄×C₁₅₁	—	2	1	no	—
179	C₂×C₄×C₁₅₁	—	2	1	no	—
180	C₂×C₄×C₁₅₁	—	2	1	no	—
181	C₂×C₄×C₁₅₁	—	2	1	no	—
182	C₂×C₄×C₁₅₁	—	2	1	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	—	4	2	no	—
192	C₂×C₄×C₁₅₁	—	4	2	no	—
193	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₅₁	#121	1	2	yes	—
195	C₂×C₄×C₁₅₁	#121	1	2	yes	—
196	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₅₁	C₂²×D₄	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	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
202	C₈×C₁₅₁	—	2	2	no	—
203	C₈×C₁₅₁	—	2	2	no	—
204	C₈×C₁₅₁	—	2	2	no	—
205	C₈×C₁₅₁	C₄×D₄	1	4	yes	—
206	C₂²×C₁₅₁	—	2	2	no	—
207	C₂²×C₁₅₁	—	2	2	no	—
208	C₂²×C₁₅₁	—	2	2	no	—
209	C₂²×C₁₅₁	—	4	1	no	—
210	C₂²×C₁₅₁	—	4	1	no	—
211	C₂²×C₁₅₁	—	4	1	no	—
212	C₂²×C₁₅₁	—	4	1	no	—
213	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
215	C₂²×C₁₅₁	#532	1	1	yes	characteristic
216	C₂²×C₁₅₁	#576	1	1	yes	characteristic
217	C₂²×C₁₅₁	#578	1	1	yes	characteristic
218	C₂²×C₁₅₁	#578	1	1	yes	characteristic
219	C₂²×C₁₅₁	#578	1	1	yes	characteristic
220	C₄×C₁₅₁	—	2	2	no	—
221	C₄×C₁₅₁	—	2	2	no	—
222	C₄×C₁₅₁	—	2	2	no	—
223	C₄×C₁₅₁	—	4	4	no	—
224	C₄×C₁₅₁	—	4	1	no	—
225	C₄×C₁₅₁	—	4	1	no	—
226	C₄×C₁₅₁	—	4	4	no	—
227	C₄×C₁₅₁	—	8	2	no	—
228	C₄×C₁₅₁	—	8	2	no	—
229	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₁₅₁	C₄×#41	1	1	yes	characteristic
231	C₄×C₁₅₁	#525	1	1	yes	characteristic
232	C₄×C₁₅₁	#529	1	1	yes	characteristic
233	C₂×C₁₅₁	—	4	2	no	—
234	C₂×C₁₅₁	C₄×#121	1	1	yes	characteristic
235	C₂×C₁₅₁	#2950	1	1	yes	characteristic
236	C₂×C₁₅₁	#2951	1	1	yes	characteristic
237	C₂×C₁₅₁	#3059	1	1	yes	characteristic
238	C₂×C₁₅₁	#3061	1	1	yes	characteristic
239	C₂×C₁₅₁	#3175	1	1	yes	characteristic
240	C₂×C₁₅₁	#3177	1	1	yes	characteristic
241	#21525	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₁₅₁	#21525	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×#467	C₂×C₁₅₁	1	1	yes	characteristic
244	C₂×C₄×Q₁₆	C₂×C₁₅₁	1	1	yes	characteristic, complemented
245	C₂×#405	C₂×C₁₅₁	1	1	yes	characteristic
246	#2323	C₂×C₁₅₁	1	2	yes	—
247	#1969	C₂×C₁₅₁	1	1	yes	characteristic, complemented
248	#1942	C₂×C₁₅₁	1	1	yes	characteristic, complemented
249	#1935	C₂×C₁₅₁	1	2	yes	complemented
250	#1894	C₂×C₁₅₁	1	2	yes	—
251	#1808	C₂×C₁₅₁	1	1	yes	characteristic
252	C₄×#107	C₂×C₁₅₁	1	1	yes	characteristic, complemented
253	#1763	C₂×C₁₅₁	1	2	yes	complemented
254	C₂²×Q₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
256	C₂³×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₁₅₁	1	2	yes	—
258	C₂×C₄×Q₈	C₂²×C₁₅₁	1	2	yes	—
259	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
260	#467	C₄×C₁₅₁	1	8	yes	complemented
261	C₄×Q₁₆	—	2	4	no	—
262	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
263	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
264	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
265	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
266	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
267	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
268	#405	—	2	4	no	—
269	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
270	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
271	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
273	#391	C₂²×C₁₅₁	1	2	yes	—
274	#389	—	2	2	no	—
275	#389	C₂²×C₁₅₁	1	2	yes	—
276	#388	—	2	2	no	—
277	#388	—	2	2	no	—
278	#387	—	2	2	no	—
279	#380	C₂²×C₁₅₁	1	2	yes	—
280	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
281	#340	C₂²×C₁₅₁	1	2	yes	—
282	#340	C₂²×C₁₅₁	1	2	yes	—
283	#340	C₂²×C₁₅₁	1	2	yes	—
284	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	C₂×C₄×C₁₅₁	1	4	yes	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	C₂×C₄×C₁₅₁	1	4	yes	—
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	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	C₂×C₄×C₁₅₁	1	8	yes	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	2	4	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	#107	—	2	2	no	—
323	#107	C₂×C₄×C₁₅₁	1	4	yes	—
324	#103	—	2	4	no	—
325	#103	—	2	4	no	—
326	#103	C₂×C₄×C₁₅₁	1	8	yes	—
327	#97	—	2	2	no	—
328	#97	—	2	2	no	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	D₄×C₁₅₁	1	4	yes	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	C₂⁴	C₂×D₄×C₁₅₁	1	1	yes	characteristic
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	C₂²×C₄×C₁₅₁	1	4	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
357	C₂²×C₄	#41×C₁₅₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
359	Q₁₆	—	2	8	no	—
360	M₁₆	—	2	8	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	1	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
369	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
372	C₂×C₈	#41×C₁₅₁	1	2	yes	—
373	C₂×C₈	#41×C₁₅₁	1	2	yes	—
374	C₄⋊C₄	—	2	8	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	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	4	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	4	4	no	—
392	C₄²	—	8	2	no	—
393	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
394	C₄²	#41×C₁₅₁	1	2	yes	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	C₄×D₄×C₁₅₁	1	2	yes	—
402	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	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	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	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	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
436	C₂×C₄	#121×C₁₅₁	1	2	yes	—
437	C₂×C₄	#121×C₁₅₁	1	2	yes	—
438	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	C₄×D₄×C₁₅₁	1	4	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	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	1	yes	characteristic
459	C₂²	#578×C₁₅₁	1	1	yes	characteristic
460	C₂²	#578×C₁₅₁	1	1	yes	characteristic
461	C₂²	#578×C₁₅₁	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	2	no	—
471	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
472	C₄	C₄×#41×C₁₅₁	1	1	yes	characteristic
473	C₄	#525×C₁₅₁	1	1	yes	characteristic
474	C₄	#529×C₁₅₁	1	1	yes	characteristic
475	C₂	—	4	2	no	—
476	C₂	C₄×#121×C₁₅₁	1	1	yes	characteristic
477	C₂	#2950×C₁₅₁	1	1	yes	characteristic
478	C₂	#2951×C₁₅₁	1	1	yes	characteristic
479	C₂	#3059×C₁₅₁	1	1	yes	characteristic
480	C₂	#3061×C₁₅₁	1	1	yes	characteristic
481	C₂	#3175×C₁₅₁	1	1	yes	characteristic
482	C₂	#3177×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂⁴×C₁₅₁	C₂×D₄
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×C₄×Q₁₆×C₁₅₁	C₂	semidirect
5. #1969×C₁₅₁	C₂	semidirect
6. #1942×C₁₅₁	C₂	semidirect
7. #1935×C₁₅₁	C₂	semidirect
10. C₄×#107×C₁₅₁	C₂	semidirect
11. #1763×C₁₅₁	C₂	semidirect
18. #467×C₁₅₁	C₄	semidirect
241. #21525	C₁₅₁	direct (N × H)
242. C₁₅₁	#21525	direct (N × H)
244. C₂×C₄×Q₁₆	C₂×C₁₅₁	semidirect
247. #1969	C₂×C₁₅₁	semidirect
248. #1942	C₂×C₁₅₁	semidirect
249. #1935	C₂×C₁₅₁	semidirect
252. C₄×#107	C₂×C₁₅₁	semidirect
253. #1763	C₂×C₁₅₁	semidirect
260. #467	C₄×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#467×C₁₅₁	2
C₂×C₄×Q₁₆×C₁₅₁	2
C₂×#405×C₁₅₁	2
#2323×C₁₅₁	2
#1969×C₁₅₁	2
#1942×C₁₅₁	2
#1935×C₁₅₁	2
#1894×C₁₅₁	2
#1808×C₁₅₁	2
C₄×#107×C₁₅₁	2
#1763×C₁₅₁	2
#21525	151

Subgroups — C151×#21525 #50326450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#21525 #50326450