Subgroups — C₁₅₁×#24199 #50329124

Order 38656.

1084 conjugacy classes of subgroups.

The subgroup lattice has 510 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×#461×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	#2043×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#2013×C₁₅₁	C₂	1	2	yes	maximal
7	#1985×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1960×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1880×C₁₅₁	C₂	1	2	yes	maximal
10	#1863×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	C₂²×SD₁₆×C₁₅₁	C₂²	1	2	yes	—
14	#557×C₁₅₁	—	2	4	no	—
15	#557×C₁₅₁	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
18	C₂×#125×C₁₅₁	—	2	2	no	—
19	C₂×#125×C₁₅₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₅₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₅₁	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
25	#461×C₁₅₁	—	2	4	no	—
26	#440×C₁₅₁	—	2	4	no	—
27	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
30	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
31	C₂×#103×C₁₅₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
33	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
34	C₂×#102×C₁₅₁	C₂²	1	1	yes	characteristic
35	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
36	#399×C₁₅₁	—	2	1	no	—
37	#393×C₁₅₁	—	2	1	no	—
38	#390×C₁₅₁	C₂²	1	2	yes	—
39	#389×C₁₅₁	C₂²	1	2	yes	—
40	#385×C₁₅₁	—	2	2	no	—
41	#382×C₁₅₁	C₂²	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₅₁	C₂³	1	2	yes	—
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	4	no	—
52	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
53	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
54	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
55	C₂×SD₁₆×C₁₅₁	—	4	2	no	—
56	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₅₁	—	2	2	no	—
60	C₄⋊Q₈×C₁₅₁	—	2	4	no	—
61	C₄⋊Q₈×C₁₅₁	—	2	4	no	—
62	C₄⋊Q₈×C₁₅₁	D₄	1	4	yes	—
63	#125×C₁₅₁	—	2	16	no	—
64	#125×C₁₅₁	—	2	8	no	—
65	C₄×Q₈×C₁₅₁	—	2	8	no	—
66	C₄×Q₈×C₁₅₁	—	2	4	no	—
67	C₄×Q₈×C₁₅₁	—	2	2	no	—
68	C₄×Q₈×C₁₅₁	—	2	2	no	—
69	C₄×Q₈×C₁₅₁	—	2	2	no	—
70	C₄×Q₈×C₁₅₁	—	2	4	no	—
71	C₄×Q₈×C₁₅₁	D₄	1	4	yes	—
72	C₄×D₄×C₁₅₁	—	2	2	no	—
73	C₄×D₄×C₁₅₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₅₁	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
89	C₂×C₄²×C₁₅₁	—	2	2	no	—
90	C₂×C₄²×C₁₅₁	—	2	1	no	—
91	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
93	#107×C₁₅₁	—	2	2	no	—
94	C₄⋊C₈×C₁₅₁	—	2	2	no	—
95	#103×C₁₅₁	—	2	4	no	—
96	#103×C₁₅₁	—	2	2	no	—
97	#103×C₁₅₁	—	2	4	no	—
98	#103×C₁₅₁	—	4	2	no	—
99	#103×C₁₅₁	—	4	2	no	—
100	#102×C₁₅₁	—	2	2	no	—
101	#97×C₁₅₁	—	2	2	no	—
102	#95×C₁₅₁	—	2	1	no	—
103	#95×C₁₅₁	—	2	1	no	—
104	#95×C₁₅₁	—	2	2	no	—
105	C₂⁴×C₁₅₁	—	2	1	no	—
106	C₂×Q₈×C₁₅₁	—	2	2	no	—
107	C₂×Q₈×C₁₅₁	—	2	4	no	—
108	C₂×Q₈×C₁₅₁	—	2	2	no	—
109	C₂×Q₈×C₁₅₁	—	2	1	no	—
110	C₂×Q₈×C₁₅₁	—	2	2	no	—
111	C₂×Q₈×C₁₅₁	—	2	1	no	—
112	C₂×Q₈×C₁₅₁	—	2	2	no	—
113	C₂×Q₈×C₁₅₁	—	2	1	no	—
114	C₂×Q₈×C₁₅₁	—	2	1	no	—
115	C₂×Q₈×C₁₅₁	—	2	2	no	—
116	C₂×Q₈×C₁₅₁	—	2	1	no	—
117	C₂×Q₈×C₁₅₁	—	2	2	no	—
118	C₂×Q₈×C₁₅₁	C₂×D₄	1	4	yes	—
119	C₂×Q₈×C₁₅₁	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₅₁	—	2	1	no	—
121	C₂×D₄×C₁₅₁	—	2	1	no	—
122	C₂×D₄×C₁₅₁	—	2	1	no	—
123	C₂×D₄×C₁₅₁	—	2	1	no	—
124	C₂×D₄×C₁₅₁	—	2	1	no	—
125	C₂×D₄×C₁₅₁	#41	1	2	yes	—
126	C₂²×C₄×C₁₅₁	—	2	1	no	—
127	C₂²×C₄×C₁₅₁	—	2	2	no	—
128	C₂²×C₄×C₁₅₁	—	2	1	no	—
129	C₂²×C₄×C₁₅₁	—	2	2	no	—
130	C₂²×C₄×C₁₅₁	—	2	1	no	—
131	C₂²×C₄×C₁₅₁	—	4	2	no	—
132	C₂²×C₄×C₁₅₁	—	8	2	no	—
133	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
138	SD₁₆×C₁₅₁	—	2	8	no	—
139	SD₁₆×C₁₅₁	—	4	8	no	—
140	C₂×C₈×C₁₅₁	—	2	1	no	—
141	C₂×C₈×C₁₅₁	—	2	1	no	—
142	C₂×C₈×C₁₅₁	—	2	1	no	—
143	C₂×C₈×C₁₅₁	—	2	2	no	—
144	C₂×C₈×C₁₅₁	—	2	2	no	—
145	C₂×C₈×C₁₅₁	—	2	1	no	—
146	C₂×C₈×C₁₅₁	—	2	2	no	—
147	C₂×C₈×C₁₅₁	—	2	1	no	—
148	C₂×C₈×C₁₅₁	#41	1	2	yes	—
149	C₄⋊C₄×C₁₅₁	—	2	8	no	—
150	C₄⋊C₄×C₁₅₁	—	2	8	no	—
151	C₄⋊C₄×C₁₅₁	—	2	8	no	—
152	C₄⋊C₄×C₁₅₁	—	2	4	no	—
153	C₄⋊C₄×C₁₅₁	—	2	4	no	—
154	C₄⋊C₄×C₁₅₁	—	2	4	no	—
155	C₄⋊C₄×C₁₅₁	—	2	4	no	—
156	C₄⋊C₄×C₁₅₁	—	2	2	no	—
157	C₄⋊C₄×C₁₅₁	—	2	1	no	—
158	C₄⋊C₄×C₁₅₁	—	2	1	no	—
159	C₄⋊C₄×C₁₅₁	—	2	1	no	—
160	C₄⋊C₄×C₁₅₁	—	2	2	no	—
161	C₄⋊C₄×C₁₅₁	—	2	2	no	—
162	C₄⋊C₄×C₁₅₁	—	8	2	no	—
163	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
165	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
166	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
167	C₄²×C₁₅₁	—	2	8	no	—
168	C₄²×C₁₅₁	—	2	4	no	—
169	C₄²×C₁₅₁	—	2	2	no	—
170	C₄²×C₁₅₁	—	2	2	no	—
171	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
172	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
173	C₂³×C₁₅₁	—	2	2	no	—
174	C₂³×C₁₅₁	—	4	1	no	—
175	C₂³×C₁₅₁	—	4	1	no	—
176	C₂³×C₁₅₁	—	4	2	no	—
177	C₂³×C₁₅₁	—	4	2	no	—
178	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₁₅₁	—	2	8	no	—
180	Q₈×C₁₅₁	—	2	2	no	—
181	Q₈×C₁₅₁	—	2	2	no	—
182	Q₈×C₁₅₁	—	2	4	no	—
183	Q₈×C₁₅₁	—	2	4	no	—
184	Q₈×C₁₅₁	—	4	2	no	—
185	Q₈×C₁₅₁	—	4	2	no	—
186	Q₈×C₁₅₁	—	4	1	no	—
187	Q₈×C₁₅₁	—	4	1	no	—
188	D₄×C₁₅₁	—	2	2	no	—
189	D₄×C₁₅₁	—	2	2	no	—
190	D₄×C₁₅₁	—	4	1	no	—
191	D₄×C₁₅₁	—	4	1	no	—
192	C₂×C₄×C₁₅₁	—	2	2	no	—
193	C₂×C₄×C₁₅₁	—	2	2	no	—
194	C₂×C₄×C₁₅₁	—	2	2	no	—
195	C₂×C₄×C₁₅₁	—	2	2	no	—
196	C₂×C₄×C₁₅₁	—	2	4	no	—
197	C₂×C₄×C₁₅₁	—	2	2	no	—
198	C₂×C₄×C₁₅₁	—	2	2	no	—
199	C₂×C₄×C₁₅₁	—	2	2	no	—
200	C₂×C₄×C₁₅₁	—	2	2	no	—
201	C₂×C₄×C₁₅₁	—	2	2	no	—
202	C₂×C₄×C₁₅₁	—	4	1	no	—
203	C₂×C₄×C₁₅₁	—	4	2	no	—
204	C₂×C₄×C₁₅₁	—	4	2	no	—
205	C₂×C₄×C₁₅₁	—	4	1	no	—
206	C₂×C₄×C₁₅₁	—	4	2	no	—
207	C₂×C₄×C₁₅₁	—	4	1	no	—
208	C₂×C₄×C₁₅₁	—	4	2	no	—
209	C₂×C₄×C₁₅₁	—	4	2	no	—
210	C₂×C₄×C₁₅₁	—	4	2	no	—
211	C₂×C₄×C₁₅₁	—	4	2	no	—
212	C₂×C₄×C₁₅₁	—	8	4	no	—
213	C₂×C₄×C₁₅₁	#120	1	2	yes	—
214	C₂×C₄×C₁₅₁	#120	1	2	yes	—
215	C₂×C₄×C₁₅₁	#137	1	4	yes	—
216	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
222	C₈×C₁₅₁	—	2	2	no	—
223	C₈×C₁₅₁	—	4	1	no	—
224	C₈×C₁₅₁	—	4	2	no	—
225	C₂²×C₁₅₁	—	4	4	no	—
226	C₂²×C₁₅₁	—	4	2	no	—
227	C₂²×C₁₅₁	—	8	2	no	—
228	C₂²×C₁₅₁	—	8	1	no	—
229	C₂²×C₁₅₁	—	8	1	no	—
230	C₂²×C₁₅₁	C₂×#120	1	1	yes	characteristic
231	C₂²×C₁₅₁	#548	1	1	yes	characteristic
232	C₂²×C₁₅₁	#550	1	1	yes	characteristic
233	C₂²×C₁₅₁	C₂×#137	1	2	yes	—
234	C₂²×C₁₅₁	#577	1	2	yes	—
235	C₄×C₁₅₁	—	2	2	no	—
236	C₄×C₁₅₁	—	2	4	no	—
237	C₄×C₁₅₁	—	2	2	no	—
238	C₄×C₁₅₁	—	4	2	no	—
239	C₄×C₁₅₁	—	4	4	no	—
240	C₄×C₁₅₁	—	4	2	no	—
241	C₄×C₁₅₁	—	4	2	no	—
242	C₄×C₁₅₁	—	8	2	no	—
243	C₄×C₁₅₁	—	8	1	no	—
244	C₄×C₁₅₁	#525	1	1	yes	characteristic
245	C₄×C₁₅₁	#537	1	1	yes	characteristic
246	C₄×C₁₅₁	#546	1	1	yes	characteristic
247	C₄×C₁₅₁	#547	1	1	yes	characteristic
248	C₂×C₁₅₁	—	8	2	no	—
249	C₂×C₁₅₁	#2407	1	1	yes	characteristic
250	C₂×C₁₅₁	#3004	1	1	yes	characteristic
251	C₂×C₁₅₁	#3010	1	1	yes	characteristic
252	C₂×C₁₅₁	#3372	1	2	yes	—
253	C₂×C₁₅₁	#3400	1	2	yes	—
254	#24199	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₁₅₁	#24199	1	1	yes	characteristic, direct product factor, Sylow
256	C₂×#557	C₂×C₁₅₁	1	1	yes	characteristic, complemented
257	C₂×#461	C₂×C₁₅₁	1	1	yes	characteristic
258	C₂×#440	C₂×C₁₅₁	1	1	yes	characteristic
259	#2580	C₂×C₁₅₁	1	1	yes	characteristic
260	#2043	C₂×C₁₅₁	1	2	yes	complemented
261	#2013	C₂×C₁₅₁	1	2	yes	—
262	#1985	C₂×C₁₅₁	1	1	yes	characteristic, complemented
263	#1960	C₂×C₁₅₁	1	1	yes	characteristic, complemented
264	#1880	C₂×C₁₅₁	1	2	yes	—
265	#1863	C₂×C₁₅₁	1	2	yes	complemented
266	#1805	C₂×C₁₅₁	1	1	yes	characteristic, complemented
267	C₂²×SD₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
268	C₂²×SD₁₆	C₂²×C₁₅₁	1	2	yes	—
269	#557	—	2	4	no	—
270	#557	—	2	4	no	—
271	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	2	yes	—
272	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
273	C₂×#125	—	2	2	no	—
274	C₂×#125	—	2	1	no	—
275	C₂×C₄×Q₈	—	2	1	no	—
276	C₂×C₄×Q₈	C₂²×C₁₅₁	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
278	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
280	#461	—	2	4	no	—
281	#440	—	2	4	no	—
282	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
284	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
285	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
286	C₂×#103	C₂²×C₁₅₁	1	1	yes	characteristic
287	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
288	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
289	C₂×#102	C₂²×C₁₅₁	1	1	yes	characteristic
290	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
291	#399	—	2	1	no	—
292	#393	—	2	1	no	—
293	#390	C₂²×C₁₅₁	1	2	yes	—
294	#389	C₂²×C₁₅₁	1	2	yes	—
295	#385	—	2	2	no	—
296	#382	C₂²×C₁₅₁	1	1	yes	characteristic
297	#340	C₂²×C₁₅₁	1	2	yes	—
298	#336	C₂²×C₁₅₁	1	2	yes	—
299	#336	C₂²×C₁₅₁	1	2	yes	—
300	C₂²×Q₈	D₄×C₁₅₁	1	1	yes	characteristic
301	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
302	C₂²×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₁₅₁	1	1	yes	characteristic
304	C₂³×C₄	—	2	1	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	4	no	—
308	C₂×SD₁₆	—	2	4	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×SD₁₆	—	4	2	no	—
311	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
314	C₄⋊Q₈	—	2	4	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	D₄×C₁₅₁	1	4	yes	—
318	#125	—	2	16	no	—
319	#125	—	2	8	no	—
320	C₄×Q₈	—	2	8	no	—
321	C₄×Q₈	—	2	4	no	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	D₄×C₁₅₁	1	4	yes	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	D₄×C₁₅₁	1	2	yes	—
337	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
347	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
348	#107	—	2	2	no	—
349	C₄⋊C₈	—	2	2	no	—
350	#103	—	2	2	no	—
351	#103	—	2	4	no	—
352	#103	—	2	4	no	—
353	#103	—	4	2	no	—
354	#103	—	4	2	no	—
355	#102	—	2	2	no	—
356	#97	—	2	2	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	2	no	—
360	C₂⁴	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	C₂×D₄×C₁₅₁	1	4	yes	—
374	C₂×Q₈	C₂×D₄×C₁₅₁	1	2	yes	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	#41×C₁₅₁	1	2	yes	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	8	2	no	—
388	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
393	SD₁₆	—	2	8	no	—
394	SD₁₆	—	4	8	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	#41×C₁₅₁	1	2	yes	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	8	2	no	—
418	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	8	2	no	—
422	C₄²	—	2	8	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
427	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
428	C₂³	—	2	2	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
434	Q₈	—	2	8	no	—
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	4	no	—
438	Q₈	—	2	4	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	8	4	no	—
468	C₂×C₄	#120×C₁₅₁	1	2	yes	—
469	C₂×C₄	#120×C₁₅₁	1	2	yes	—
470	C₂×C₄	#137×C₁₅₁	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
475	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
476	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	C₂×#120×C₁₅₁	1	1	yes	characteristic
486	C₂²	#548×C₁₅₁	1	1	yes	characteristic
487	C₂²	#550×C₁₅₁	1	1	yes	characteristic
488	C₂²	C₂×#137×C₁₅₁	1	2	yes	—
489	C₂²	#577×C₁₅₁	1	2	yes	—
490	C₄	—	2	2	no	—
491	C₄	—	2	4	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	1	no	—
499	C₄	#525×C₁₅₁	1	1	yes	characteristic
500	C₄	#537×C₁₅₁	1	1	yes	characteristic
501	C₄	#546×C₁₅₁	1	1	yes	characteristic
502	C₄	#547×C₁₅₁	1	1	yes	characteristic
503	C₂	—	8	2	no	—
504	C₂	#2407×C₁₅₁	1	1	yes	characteristic
505	C₂	#3004×C₁₅₁	1	1	yes	characteristic
506	C₂	#3010×C₁₅₁	1	1	yes	characteristic
507	C₂	#3372×C₁₅₁	1	2	yes	—
508	C₂	#3400×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. #2043×C₁₅₁	C₂	semidirect
7. #1985×C₁₅₁	C₂	semidirect
8. #1960×C₁₅₁	C₂	semidirect
10. #1863×C₁₅₁	C₂	semidirect
11. #1805×C₁₅₁	C₂	semidirect
254. #24199	C₁₅₁	direct (N × H)
255. C₁₅₁	#24199	direct (N × H)
256. C₂×#557	C₂×C₁₅₁	semidirect
260. #2043	C₂×C₁₅₁	semidirect
262. #1985	C₂×C₁₅₁	semidirect
263. #1960	C₂×C₁₅₁	semidirect
265. #1863	C₂×C₁₅₁	semidirect
266. #1805	C₂×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×#461×C₁₅₁	2
C₂×#440×C₁₅₁	2
#2580×C₁₅₁	2
#2043×C₁₅₁	2
#2013×C₁₅₁	2
#1985×C₁₅₁	2
#1960×C₁₅₁	2
#1880×C₁₅₁	2
#1863×C₁₅₁	2
#1805×C₁₅₁	2
#24199	151

Subgroups — C151×#24199 #50329124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#24199 #50329124