Subgroups — C₁₅₁×#23735 #50328660

Order 38656.

1210 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#427×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₁₅₁	C₂	1	1	yes	maximal, characteristic
5	#2317×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2309×C₁₅₁	C₂	1	1	yes	maximal, characteristic
7	#2094×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#2093×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#2092×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#2092×C₁₅₁	C₂	1	2	yes	maximal, complemented
11	#1729×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×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×#117×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
19	#428×C₁₅₁	—	2	4	no	—
20	#427×C₁₅₁	—	2	4	no	—
21	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×#107×C₁₅₁	C₂²	1	2	yes	complemented
23	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×#106×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×#106×C₁₅₁	C₂²	1	2	yes	complemented
26	C₂×#106×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
27	#418×C₁₅₁	—	2	4	no	—
28	C₂×#102×C₁₅₁	—	2	4	no	—
29	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
30	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
31	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
32	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
33	#390×C₁₅₁	—	2	2	no	—
34	#390×C₁₅₁	C₂²	1	2	yes	—
35	#390×C₁₅₁	C₂²	1	2	yes	—
36	#389×C₁₅₁	—	2	2	no	—
37	#385×C₁₅₁	—	2	2	no	—
38	#384×C₁₅₁	C₂²	1	2	yes	complemented
39	#382×C₁₅₁	C₂²	1	2	yes	complemented
40	#379×C₁₅₁	—	2	2	no	—
41	#336×C₁₅₁	C₂²	1	2	yes	complemented
42	#336×C₁₅₁	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₅₁	—	2	1	no	—
44	C₂²×D₄×C₁₅₁	—	2	1	no	—
45	C₂²×D₄×C₁₅₁	—	2	2	no	—
46	C₂²×D₄×C₁₅₁	—	2	2	no	—
47	C₂²×D₄×C₁₅₁	—	2	2	no	—
48	C₂²×D₄×C₁₅₁	—	2	2	no	—
49	C₂²×D₄×C₁₅₁	—	2	2	no	—
50	C₂²×D₄×C₁₅₁	Q₈	1	4	yes	—
51	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₅₁	—	2	1	no	—
53	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₁₅₁	—	2	2	no	—
55	C₂×M₁₆×C₁₅₁	—	2	2	no	—
56	C₂×M₁₆×C₁₅₁	D₄	1	4	yes	—
57	C₂²×C₈×C₁₅₁	—	2	2	no	—
58	C₂²×C₈×C₁₅₁	—	2	2	no	—
59	C₂²×C₈×C₁₅₁	D₄	1	4	yes	—
60	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
63	#117×C₁₅₁	—	2	2	no	—
64	#117×C₁₅₁	—	2	2	no	—
65	#117×C₁₅₁	—	2	2	no	—
66	#117×C₁₅₁	—	2	2	no	—
67	#117×C₁₅₁	—	2	2	no	—
68	#117×C₁₅₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₅₁	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₅₁	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₅₁	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₁₅₁	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	2	yes	—
84	C₂×C₄²×C₁₅₁	—	2	1	no	—
85	C₂×C₄²×C₁₅₁	—	2	1	no	—
86	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
87	#107×C₁₅₁	—	2	2	no	—
88	#107×C₁₅₁	—	2	2	no	—
89	#107×C₁₅₁	—	2	4	no	—
90	#106×C₁₅₁	—	2	2	no	—
91	#106×C₁₅₁	—	2	2	no	—
92	#106×C₁₅₁	—	2	4	no	—
93	#102×C₁₅₁	—	2	4	no	—
94	#102×C₁₅₁	—	2	4	no	—
95	#102×C₁₅₁	—	2	4	no	—
96	#102×C₁₅₁	—	2	4	no	—
97	#95×C₁₅₁	—	2	4	no	—
98	C₂⁴×C₁₅₁	—	2	2	no	—
99	C₂⁴×C₁₅₁	—	2	4	no	—
100	C₂⁴×C₁₅₁	—	4	2	no	—
101	C₂⁴×C₁₅₁	—	4	2	no	—
102	C₂⁴×C₁₅₁	—	8	2	no	—
103	C₂⁴×C₁₅₁	—	8	2	no	—
104	C₂⁴×C₁₅₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₁₅₁	—	2	8	no	—
106	C₂×D₄×C₁₅₁	—	2	8	no	—
107	C₂×D₄×C₁₅₁	—	2	4	no	—
108	C₂×D₄×C₁₅₁	—	2	2	no	—
109	C₂×D₄×C₁₅₁	—	2	2	no	—
110	C₂×D₄×C₁₅₁	—	2	2	no	—
111	C₂×D₄×C₁₅₁	—	2	2	no	—
112	C₂×D₄×C₁₅₁	—	2	2	no	—
113	C₂×D₄×C₁₅₁	—	4	4	no	—
114	C₂×D₄×C₁₅₁	—	4	4	no	—
115	C₂×D₄×C₁₅₁	—	4	2	no	—
116	C₂×D₄×C₁₅₁	—	4	2	no	—
117	C₂×D₄×C₁₅₁	C₂×Q₈	1	4	yes	—
118	C₂²×C₄×C₁₅₁	—	2	1	no	—
119	C₂²×C₄×C₁₅₁	—	2	2	no	—
120	C₂²×C₄×C₁₅₁	—	2	1	no	—
121	C₂²×C₄×C₁₅₁	—	2	1	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	4	yes	—
126	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₅₁	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₁₅₁	#41	1	2	yes	—
131	C₂²×C₄×C₁₅₁	#41	1	2	yes	—
132	C₂²×C₄×C₁₅₁	#41	1	2	yes	—
133	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₁₅₁	—	2	8	no	—
135	C₂×C₈×C₁₅₁	—	2	8	no	—
136	C₂×C₈×C₁₅₁	—	2	1	no	—
137	C₂×C₈×C₁₅₁	—	2	1	no	—
138	C₂×C₈×C₁₅₁	—	2	1	no	—
139	C₂×C₈×C₁₅₁	—	2	1	no	—
140	C₂×C₈×C₁₅₁	—	2	2	no	—
141	C₂×C₈×C₁₅₁	—	2	2	no	—
142	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₅₁	C₂×D₄	1	4	yes	—
144	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₁₅₁	—	2	4	no	—
146	C₄⋊C₄×C₁₅₁	—	2	2	no	—
147	C₄⋊C₄×C₁₅₁	—	2	1	no	—
148	C₄⋊C₄×C₁₅₁	—	2	1	no	—
149	C₄⋊C₄×C₁₅₁	—	2	1	no	—
150	C₄⋊C₄×C₁₅₁	—	2	2	no	—
151	C₄⋊C₄×C₁₅₁	—	2	1	no	—
152	C₄⋊C₄×C₁₅₁	—	2	1	no	—
153	C₄⋊C₄×C₁₅₁	—	2	1	no	—
154	C₄⋊C₄×C₁₅₁	—	2	1	no	—
155	C₄⋊C₄×C₁₅₁	—	2	1	no	—
156	C₄⋊C₄×C₁₅₁	—	4	2	no	—
157	C₄⋊C₄×C₁₅₁	—	8	4	no	—
158	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
159	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
160	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
161	C₂²⋊C₄×C₁₅₁	—	8	4	no	—
162	C₂²⋊C₄×C₁₅₁	—	8	4	no	—
163	C₄²×C₁₅₁	—	2	2	no	—
164	C₄²×C₁₅₁	—	2	2	no	—
165	C₄²×C₁₅₁	—	4	2	no	—
166	C₄²×C₁₅₁	—	4	2	no	—
167	C₂³×C₁₅₁	—	2	2	no	—
168	C₂³×C₁₅₁	—	2	2	no	—
169	C₂³×C₁₅₁	—	2	4	no	—
170	C₂³×C₁₅₁	—	4	2	no	—
171	C₂³×C₁₅₁	—	4	2	no	—
172	C₂³×C₁₅₁	—	4	4	no	—
173	C₂³×C₁₅₁	—	4	4	no	—
174	C₂³×C₁₅₁	—	4	8	no	—
175	C₂³×C₁₅₁	—	8	8	no	—
176	C₂³×C₁₅₁	—	8	8	no	—
177	C₂³×C₁₅₁	—	8	4	no	—
178	C₂³×C₁₅₁	—	8	4	no	—
179	C₂³×C₁₅₁	C₂²⋊Q₈	1	2	yes	—
180	C₂³×C₁₅₁	#123	1	2	yes	—
181	C₂³×C₁₅₁	#127	1	2	yes	—
182	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
183	D₄×C₁₅₁	—	2	4	no	—
184	D₄×C₁₅₁	—	2	4	no	—
185	D₄×C₁₅₁	—	4	2	no	—
186	D₄×C₁₅₁	—	4	2	no	—
187	D₄×C₁₅₁	—	4	8	no	—
188	C₂×C₄×C₁₅₁	—	2	4	no	—
189	C₂×C₄×C₁₅₁	—	2	4	no	—
190	C₂×C₄×C₁₅₁	—	2	4	no	—
191	C₂×C₄×C₁₅₁	—	4	1	no	—
192	C₂×C₄×C₁₅₁	—	4	1	no	—
193	C₂×C₄×C₁₅₁	—	4	1	no	—
194	C₂×C₄×C₁₅₁	—	4	1	no	—
195	C₂×C₄×C₁₅₁	—	4	2	no	—
196	C₂×C₄×C₁₅₁	—	4	2	no	—
197	C₂×C₄×C₁₅₁	—	4	2	no	—
198	C₂×C₄×C₁₅₁	—	4	4	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	C₂²⋊Q₈	1	4	yes	—
203	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	4	yes	—
204	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	2	yes	—
205	C₂×C₄×C₁₅₁	#123	1	4	yes	—
206	C₂×C₄×C₁₅₁	#123	1	4	yes	—
207	C₂×C₄×C₁₅₁	#123	1	2	yes	—
208	C₂×C₄×C₁₅₁	#127	1	2	yes	—
209	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₅₁	C₂²×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
215	C₈×C₁₅₁	—	2	2	no	—
216	C₈×C₁₅₁	—	2	2	no	—
217	C₈×C₁₅₁	—	2	4	no	—
218	C₂²×C₁₅₁	—	2	4	no	—
219	C₂²×C₁₅₁	—	2	4	no	—
220	C₂²×C₁₅₁	—	2	2	no	—
221	C₂²×C₁₅₁	—	2	2	no	—
222	C₂²×C₁₅₁	—	4	8	no	—
223	C₂²×C₁₅₁	—	4	4	no	—
224	C₂²×C₁₅₁	—	8	16	no	—
225	C₂²×C₁₅₁	—	8	4	no	—
226	C₂²×C₁₅₁	—	8	2	no	—
227	C₂²×C₁₅₁	—	8	2	no	—
228	C₂²×C₁₅₁	#399	1	4	yes	—
229	C₂²×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
230	C₂²×C₁₅₁	C₂×#123	1	1	yes	characteristic
231	C₂²×C₁₅₁	C₂×#127	1	1	yes	characteristic
232	C₂²×C₁₅₁	#576	1	2	yes	—
233	C₂²×C₁₅₁	#577	1	2	yes	—
234	C₄×C₁₅₁	—	4	4	no	—
235	C₄×C₁₅₁	—	8	1	no	—
236	C₄×C₁₅₁	—	8	1	no	—
237	C₄×C₁₅₁	—	8	1	no	—
238	C₄×C₁₅₁	—	8	1	no	—
239	C₄×C₁₅₁	—	8	2	no	—
240	C₄×C₁₅₁	#399	1	4	yes	—
241	C₄×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₄×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₁₅₁	C₂×#123	1	1	yes	characteristic
244	C₄×C₁₅₁	C₂×#123	1	1	yes	characteristic
245	C₂×C₁₅₁	—	2	4	no	—
246	C₂×C₁₅₁	—	8	4	no	—
247	C₂×C₁₅₁	C₂×#399	1	1	yes	characteristic
248	C₂×C₁₅₁	#3081	1	2	yes	—
249	C₂×C₁₅₁	#3096	1	2	yes	—
250	C₂×C₁₅₁	#3154	1	1	yes	characteristic
251	C₂×C₁₅₁	#3155	1	1	yes	characteristic
252	#23735	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₁₅₁	#23735	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×#428	C₂×C₁₅₁	1	1	yes	characteristic, complemented
255	C₂×#427	C₂×C₁₅₁	1	1	yes	characteristic, complemented
256	C₂×#418	C₂×C₁₅₁	1	1	yes	characteristic
257	C₂²×#102	C₂×C₁₅₁	1	1	yes	characteristic
258	#2317	C₂×C₁₅₁	1	1	yes	characteristic, complemented
259	#2309	C₂×C₁₅₁	1	1	yes	characteristic
260	#2094	C₂×C₁₅₁	1	2	yes	complemented
261	#2093	C₂×C₁₅₁	1	2	yes	complemented
262	#2092	C₂×C₁₅₁	1	2	yes	complemented
263	#2092	C₂×C₁₅₁	1	2	yes	complemented
264	#1729	C₂×C₁₅₁	1	1	yes	characteristic, complemented
265	C₂³×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
266	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
267	C₂³×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
268	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
269	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
270	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
272	#428	—	2	4	no	—
273	#427	—	2	4	no	—
274	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic, complemented
275	C₂×#107	C₂²×C₁₅₁	1	2	yes	complemented
276	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic, complemented
277	C₂×#106	C₂²×C₁₅₁	1	1	yes	characteristic, complemented
278	C₂×#106	C₂²×C₁₅₁	1	2	yes	complemented
279	C₂×#106	C₂²×C₁₅₁	1	1	yes	characteristic, complemented
280	#418	—	2	4	no	—
281	C₂×#102	—	2	4	no	—
282	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
283	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
284	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
285	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
286	#390	—	2	2	no	—
287	#390	C₂²×C₁₅₁	1	2	yes	—
288	#390	C₂²×C₁₅₁	1	2	yes	—
289	#389	—	2	2	no	—
290	#385	—	2	2	no	—
291	#384	C₂²×C₁₅₁	1	2	yes	complemented
292	#382	C₂²×C₁₅₁	1	2	yes	complemented
293	#379	—	2	2	no	—
294	#336	C₂²×C₁₅₁	1	2	yes	complemented
295	#336	C₂²×C₁₅₁	1	2	yes	complemented
296	C₂⁵	—	2	1	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	Q₈×C₁₅₁	1	4	yes	—
304	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	D₄×C₁₅₁	1	4	yes	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	D₄×C₁₅₁	1	4	yes	—
313	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
316	#117	—	2	2	no	—
317	#117	—	2	2	no	—
318	#117	—	2	2	no	—
319	#117	—	2	2	no	—
320	#117	—	2	2	no	—
321	#117	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	D₄×C₁₅₁	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	4	no	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	2	yes	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
340	#107	—	2	2	no	—
341	#107	—	2	2	no	—
342	#107	—	2	4	no	—
343	#106	—	2	2	no	—
344	#106	—	2	2	no	—
345	#106	—	2	4	no	—
346	#102	—	2	4	no	—
347	#102	—	2	4	no	—
348	#102	—	2	4	no	—
349	#102	—	2	4	no	—
350	#95	—	2	4	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	4	2	no	—
354	C₂⁴	—	4	2	no	—
355	C₂⁴	—	8	2	no	—
356	C₂⁴	—	8	2	no	—
357	C₂⁴	C₂×D₄×C₁₅₁	1	1	yes	characteristic
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	C₂×Q₈×C₁₅₁	1	4	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	8	2	no	—
378	C₂²×C₄	C₂×D₄×C₁₅₁	1	4	yes	—
379	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
382	C₂²×C₄	C₂×Q₈×C₁₅₁	1	2	yes	—
383	C₂²×C₄	#41×C₁₅₁	1	2	yes	—
384	C₂²×C₄	#41×C₁₅₁	1	2	yes	—
385	C₂²×C₄	#41×C₁₅₁	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
387	M₁₆	—	2	8	no	—
388	C₂×C₈	—	2	8	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₁₅₁	1	4	yes	—
397	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	8	4	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	8	4	no	—
415	C₂²⋊C₄	—	8	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	4	2	no	—
419	C₄²	—	4	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	8	8	no	—
429	C₂³	—	8	4	no	—
430	C₂³	—	8	4	no	—
431	C₂³	—	8	8	no	—
432	C₂³	C₂²⋊Q₈×C₁₅₁	1	2	yes	—
433	C₂³	#123×C₁₅₁	1	2	yes	—
434	C₂³	#127×C₁₅₁	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	2	yes	—
456	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	4	yes	—
457	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	4	yes	—
458	C₂×C₄	#123×C₁₅₁	1	2	yes	—
459	C₂×C₄	#123×C₁₅₁	1	4	yes	—
460	C₂×C₄	#123×C₁₅₁	1	4	yes	—
461	C₂×C₄	#127×C₁₅₁	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×Q₈×C₁₅₁	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
467	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	8	16	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	4	no	—
481	C₂²	#399×C₁₅₁	1	4	yes	—
482	C₂²	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
483	C₂²	C₂×#123×C₁₅₁	1	1	yes	characteristic
484	C₂²	C₂×#127×C₁₅₁	1	1	yes	characteristic
485	C₂²	#576×C₁₅₁	1	2	yes	—
486	C₂²	#577×C₁₅₁	1	2	yes	—
487	C₄	—	4	4	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	2	no	—
491	C₄	—	8	1	no	—
492	C₄	—	8	1	no	—
493	C₄	#399×C₁₅₁	1	4	yes	—
494	C₄	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
495	C₄	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
496	C₄	C₂×#123×C₁₅₁	1	1	yes	characteristic
497	C₄	C₂×#123×C₁₅₁	1	1	yes	characteristic
498	C₂	—	2	4	no	—
499	C₂	—	8	4	no	—
500	C₂	C₂×#399×C₁₅₁	1	1	yes	characteristic
501	C₂	#3081×C₁₅₁	1	2	yes	—
502	C₂	#3096×C₁₅₁	1	2	yes	—
503	C₂	#3154×C₁₅₁	1	1	yes	characteristic
504	C₂	#3155×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂³×D₄×C₁₅₁	C₂²
LCS	G ▷ C₂²×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
1. C₂×#428×C₁₅₁	C₂	semidirect
2. C₂×#427×C₁₅₁	C₂	semidirect
5. #2317×C₁₅₁	C₂	semidirect
7. #2094×C₁₅₁	C₂	semidirect
8. #2093×C₁₅₁	C₂	semidirect
9. #2092×C₁₅₁	C₂	semidirect
10. #2092×C₁₅₁	C₂	semidirect
11. #1729×C₁₅₁	C₂	semidirect
21. C₂×#107×C₁₅₁	C₂²	semidirect
22. C₂×#107×C₁₅₁	C₂²	semidirect
23. C₂×#107×C₁₅₁	C₂²	semidirect
24. C₂×#106×C₁₅₁	C₂²	semidirect
25. C₂×#106×C₁₅₁	C₂²	semidirect
26. C₂×#106×C₁₅₁	C₂²	semidirect
38. #384×C₁₅₁	C₂²	semidirect
39. #382×C₁₅₁	C₂²	semidirect
41. #336×C₁₅₁	C₂²	semidirect
42. #336×C₁₅₁	C₂²	semidirect
252. #23735	C₁₅₁	direct (N × H)
253. C₁₅₁	#23735	direct (N × H)
254. C₂×#428	C₂×C₁₅₁	semidirect
255. C₂×#427	C₂×C₁₅₁	semidirect
258. #2317	C₂×C₁₅₁	semidirect
260. #2094	C₂×C₁₅₁	semidirect
261. #2093	C₂×C₁₅₁	semidirect
262. #2092	C₂×C₁₅₁	semidirect
263. #2092	C₂×C₁₅₁	semidirect
264. #1729	C₂×C₁₅₁	semidirect
274. C₂×#107	C₂²×C₁₅₁	semidirect
275. C₂×#107	C₂²×C₁₅₁	semidirect
276. C₂×#107	C₂²×C₁₅₁	semidirect
277. C₂×#106	C₂²×C₁₅₁	semidirect
278. C₂×#106	C₂²×C₁₅₁	semidirect
279. C₂×#106	C₂²×C₁₅₁	semidirect
291. #384	C₂²×C₁₅₁	semidirect
292. #382	C₂²×C₁₅₁	semidirect
294. #336	C₂²×C₁₅₁	semidirect
295. #336	C₂²×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#428×C₁₅₁	2
C₂×#427×C₁₅₁	2
C₂×#418×C₁₅₁	2
C₂²×#102×C₁₅₁	2
#2317×C₁₅₁	2
#2309×C₁₅₁	2
#2094×C₁₅₁	2
#2093×C₁₅₁	2
#2092×C₁₅₁	2
#1729×C₁₅₁	2
#23735	151

Subgroups — C151×#23735 #50328660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#23735 #50328660