Subgroups — C₁₅₁×#24201 #50329126

Order 38656.

1068 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#462×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#440×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#2581×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2042×C₁₅₁	C₂	1	2	yes	maximal
6	#2015×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	#1878×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#1863×C₁₅₁	C₂	1	2	yes	maximal, complemented
11	#1804×C₁₅₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₅₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
14	#556×C₁₅₁	—	2	4	no	—
15	#556×C₁₅₁	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂×#126×C₁₅₁	—	2	2	no	—
18	C₂×#124×C₁₅₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊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	C₂×#117×C₁₅₁	—	2	1	no	—
25	#462×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×#102×C₁₅₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
35	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
36	#400×C₁₅₁	—	2	1	no	—
37	#395×C₁₅₁	—	2	1	no	—
38	#391×C₁₅₁	C₂²	1	2	yes	—
39	#389×C₁₅₁	C₂²	1	2	yes	—
40	#387×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×Q₁₆×C₁₅₁	—	2	4	no	—
51	C₂×Q₁₆×C₁₅₁	—	2	4	no	—
52	C₂×Q₁₆×C₁₅₁	—	4	2	no	—
53	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
54	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
55	C₂×SD₁₆×C₁₅₁	—	2	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	D₄	1	4	yes	—
61	#126×C₁₅₁	—	2	16	no	—
62	#124×C₁₅₁	—	2	4	no	—
63	#124×C₁₅₁	—	2	4	no	—
64	C₂²⋊Q₈×C₁₅₁	—	2	8	no	—
65	C₄×Q₈×C₁₅₁	—	2	4	no	—
66	C₄×Q₈×C₁₅₁	—	2	2	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×D₄×C₁₅₁	—	2	2	no	—
72	C₄×D₄×C₁₅₁	D₄	1	4	yes	—
73	#117×C₁₅₁	—	2	8	no	—
74	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₅₁	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₅₁	D₄	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×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
87	C₂×C₄²×C₁₅₁	—	2	2	no	—
88	C₂×C₄²×C₁₅₁	—	2	1	no	—
89	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
91	#107×C₁₅₁	—	2	2	no	—
92	C₄⋊C₈×C₁₅₁	—	2	2	no	—
93	#103×C₁₅₁	—	2	4	no	—
94	#103×C₁₅₁	—	2	2	no	—
95	#103×C₁₅₁	—	2	4	no	—
96	#103×C₁₅₁	—	4	2	no	—
97	#102×C₁₅₁	—	2	2	no	—
98	#102×C₁₅₁	—	4	2	no	—
99	#97×C₁₅₁	—	2	2	no	—
100	#95×C₁₅₁	—	2	1	no	—
101	#95×C₁₅₁	—	2	1	no	—
102	#95×C₁₅₁	—	2	2	no	—
103	#95×C₁₅₁	—	2	2	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	2	no	—
108	C₂×Q₈×C₁₅₁	—	2	1	no	—
109	C₂×Q₈×C₁₅₁	—	2	1	no	—
110	C₂×Q₈×C₁₅₁	—	2	1	no	—
111	C₂×Q₈×C₁₅₁	—	2	2	no	—
112	C₂×Q₈×C₁₅₁	—	2	1	no	—
113	C₂×Q₈×C₁₅₁	—	2	2	no	—
114	C₂×Q₈×C₁₅₁	—	2	2	no	—
115	C₂×Q₈×C₁₅₁	—	2	1	no	—
116	C₂×Q₈×C₁₅₁	—	2	2	no	—
117	C₂×Q₈×C₁₅₁	—	4	2	no	—
118	C₂×Q₈×C₁₅₁	C₂×D₄	1	4	yes	—
119	C₂×Q₈×C₁₅₁	#41	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	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₅₁	—	2	1	no	—
127	C₂²×C₄×C₁₅₁	—	2	1	no	—
128	C₂²×C₄×C₁₅₁	—	2	2	no	—
129	C₂²×C₄×C₁₅₁	—	2	4	no	—
130	C₂²×C₄×C₁₅₁	—	2	2	no	—
131	C₂²×C₄×C₁₅₁	—	2	1	no	—
132	C₂²×C₄×C₁₅₁	—	4	4	no	—
133	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
138	Q₁₆×C₁₅₁	—	4	8	no	—
139	SD₁₆×C₁₅₁	—	2	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	2	no	—
146	C₂×C₈×C₁₅₁	—	2	1	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	4	no	—
151	C₄⋊C₄×C₁₅₁	—	2	4	no	—
152	C₄⋊C₄×C₁₅₁	—	2	2	no	—
153	C₄⋊C₄×C₁₅₁	—	2	4	no	—
154	C₄⋊C₄×C₁₅₁	—	2	1	no	—
155	C₄⋊C₄×C₁₅₁	—	2	1	no	—
156	C₄⋊C₄×C₁₅₁	—	2	1	no	—
157	C₄⋊C₄×C₁₅₁	—	2	2	no	—
158	C₄⋊C₄×C₁₅₁	—	2	2	no	—
159	C₄⋊C₄×C₁₅₁	—	4	4	no	—
160	C₄⋊C₄×C₁₅₁	—	4	2	no	—
161	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
163	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
164	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
165	C₄²×C₁₅₁	—	2	8	no	—
166	C₄²×C₁₅₁	—	2	2	no	—
167	C₄²×C₁₅₁	—	2	2	no	—
168	C₄²×C₁₅₁	—	4	2	no	—
169	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
170	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
171	C₂³×C₁₅₁	—	2	2	no	—
172	C₂³×C₁₅₁	—	4	1	no	—
173	C₂³×C₁₅₁	—	4	1	no	—
174	C₂³×C₁₅₁	—	4	2	no	—
175	C₂³×C₁₅₁	—	4	2	no	—
176	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₁₅₁	—	2	2	no	—
178	Q₈×C₁₅₁	—	2	4	no	—
179	Q₈×C₁₅₁	—	2	2	no	—
180	Q₈×C₁₅₁	—	2	4	no	—
181	Q₈×C₁₅₁	—	4	4	no	—
182	Q₈×C₁₅₁	—	4	2	no	—
183	Q₈×C₁₅₁	—	4	2	no	—
184	Q₈×C₁₅₁	—	4	1	no	—
185	Q₈×C₁₅₁	—	4	1	no	—
186	D₄×C₁₅₁	—	2	2	no	—
187	D₄×C₁₅₁	—	2	2	no	—
188	D₄×C₁₅₁	—	4	1	no	—
189	D₄×C₁₅₁	—	4	1	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	4	no	—
194	C₂×C₄×C₁₅₁	—	2	2	no	—
195	C₂×C₄×C₁₅₁	—	2	2	no	—
196	C₂×C₄×C₁₅₁	—	2	2	no	—
197	C₂×C₄×C₁₅₁	—	2	2	no	—
198	C₂×C₄×C₁₅₁	—	2	2	no	—
199	C₂×C₄×C₁₅₁	—	2	4	no	—
200	C₂×C₄×C₁₅₁	—	4	8	no	—
201	C₂×C₄×C₁₅₁	—	4	1	no	—
202	C₂×C₄×C₁₅₁	—	4	2	no	—
203	C₂×C₄×C₁₅₁	—	4	2	no	—
204	C₂×C₄×C₁₅₁	—	4	1	no	—
205	C₂×C₄×C₁₅₁	—	4	2	no	—
206	C₂×C₄×C₁₅₁	—	4	1	no	—
207	C₂×C₄×C₁₅₁	—	4	2	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	#120	1	2	yes	—
212	C₂×C₄×C₁₅₁	#120	1	2	yes	—
213	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₁₅₁	—	2	2	no	—
220	C₈×C₁₅₁	—	4	1	no	—
221	C₈×C₁₅₁	—	4	2	no	—
222	C₂²×C₁₅₁	—	4	2	no	—
223	C₂²×C₁₅₁	—	4	2	no	—
224	C₂²×C₁₅₁	—	4	2	no	—
225	C₂²×C₁₅₁	—	8	2	no	—
226	C₂²×C₁₅₁	—	8	2	no	—
227	C₂²×C₁₅₁	C₂×#120	1	1	yes	characteristic
228	C₂²×C₁₅₁	#548	1	1	yes	characteristic
229	C₂²×C₁₅₁	#550	1	1	yes	characteristic
230	C₂²×C₁₅₁	#575	1	2	yes	—
231	C₂²×C₁₅₁	#578	1	2	yes	—
232	C₄×C₁₅₁	—	2	2	no	—
233	C₄×C₁₅₁	—	2	2	no	—
234	C₄×C₁₅₁	—	4	4	no	—
235	C₄×C₁₅₁	—	4	2	no	—
236	C₄×C₁₅₁	—	4	2	no	—
237	C₄×C₁₅₁	—	4	2	no	—
238	C₄×C₁₅₁	—	4	2	no	—
239	C₄×C₁₅₁	—	8	2	no	—
240	C₄×C₁₅₁	—	8	1	no	—
241	C₄×C₁₅₁	#525	1	1	yes	characteristic
242	C₄×C₁₅₁	#537	1	1	yes	characteristic
243	C₄×C₁₅₁	#546	1	1	yes	characteristic
244	C₄×C₁₅₁	#547	1	1	yes	characteristic
245	C₂×C₁₅₁	—	8	2	no	—
246	C₂×C₁₅₁	#2407	1	1	yes	characteristic
247	C₂×C₁₅₁	#3005	1	1	yes	characteristic
248	C₂×C₁₅₁	#3011	1	1	yes	characteristic
249	C₂×C₁₅₁	#3377	1	2	yes	—
250	C₂×C₁₅₁	#3402	1	2	yes	—
251	#24201	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₁₅₁	#24201	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×#556	C₂×C₁₅₁	1	1	yes	characteristic
254	C₂×#462	C₂×C₁₅₁	1	1	yes	characteristic, complemented
255	C₂×#440	C₂×C₁₅₁	1	1	yes	characteristic
256	#2581	C₂×C₁₅₁	1	1	yes	characteristic, complemented
257	#2042	C₂×C₁₅₁	1	2	yes	—
258	#2015	C₂×C₁₅₁	1	2	yes	—
259	#1985	C₂×C₁₅₁	1	1	yes	characteristic, complemented
260	#1960	C₂×C₁₅₁	1	1	yes	characteristic, complemented
261	#1878	C₂×C₁₅₁	1	2	yes	complemented
262	#1863	C₂×C₁₅₁	1	2	yes	complemented
263	#1804	C₂×C₁₅₁	1	1	yes	characteristic
264	C₂²×Q₁₆	C₂²×C₁₅₁	1	2	yes	—
265	C₂²×SD₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
266	#556	—	2	4	no	—
267	#556	—	2	4	no	—
268	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
269	C₂×#126	—	2	2	no	—
270	C₂×#124	C₂²×C₁₅₁	1	2	yes	—
271	C₂×C₂²⋊Q₈	—	2	1	no	—
272	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₁₅₁	1	2	yes	—
274	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
276	C₂×#117	—	2	1	no	—
277	#462	—	2	4	no	—
278	#440	—	2	4	no	—
279	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
281	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
282	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
283	C₂×#103	C₂²×C₁₅₁	1	1	yes	characteristic
284	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
285	C₂×#102	C₂²×C₁₅₁	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
287	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
288	#400	—	2	1	no	—
289	#395	—	2	1	no	—
290	#391	C₂²×C₁₅₁	1	2	yes	—
291	#389	C₂²×C₁₅₁	1	2	yes	—
292	#387	—	2	2	no	—
293	#382	C₂²×C₁₅₁	1	1	yes	characteristic
294	#340	C₂²×C₁₅₁	1	2	yes	—
295	#336	C₂²×C₁₅₁	1	2	yes	—
296	#336	C₂²×C₁₅₁	1	2	yes	—
297	C₂²×Q₈	D₄×C₁₅₁	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
299	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
300	C₂²×D₄	C₂³×C₁₅₁	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂×Q₁₆	—	2	4	no	—
303	C₂×Q₁₆	—	2	4	no	—
304	C₂×Q₁₆	—	4	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
309	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	D₄×C₁₅₁	1	4	yes	—
313	#126	—	2	16	no	—
314	#124	—	2	4	no	—
315	#124	—	2	4	no	—
316	C₂²⋊Q₈	—	2	8	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	D₄×C₁₅₁	1	4	yes	—
325	#117	—	2	8	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
332	C₂×C₄⋊C₄	D₄×C₁₅₁	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
342	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
343	#107	—	2	2	no	—
344	C₄⋊C₈	—	2	2	no	—
345	#103	—	2	4	no	—
346	#103	—	2	4	no	—
347	#103	—	2	2	no	—
348	#103	—	4	2	no	—
349	#102	—	2	2	no	—
350	#102	—	4	2	no	—
351	#97	—	2	2	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	#95	—	2	2	no	—
357	C₂⁴	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	C₂×D₄×C₁₅₁	1	4	yes	—
371	C₂×Q₈	#41×C₁₅₁	1	2	yes	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂×D₄×C₁₅₁	1	2	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
390	Q₁₆	—	4	8	no	—
391	SD₁₆	—	2	8	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	#41×C₁₅₁	1	2	yes	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₄²	—	2	8	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	4	2	no	—
421	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
422	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	2	4	no	—
432	Q₈	—	2	4	no	—
433	Q₈	—	4	4	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	1	no	—
437	Q₈	—	4	1	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	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	4	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	#120×C₁₅₁	1	2	yes	—
464	C₂×C₄	#120×C₁₅₁	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
467	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
469	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
470	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×#120×C₁₅₁	1	1	yes	characteristic
480	C₂²	#548×C₁₅₁	1	1	yes	characteristic
481	C₂²	#550×C₁₅₁	1	1	yes	characteristic
482	C₂²	#575×C₁₅₁	1	2	yes	—
483	C₂²	#578×C₁₅₁	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	1	no	—
493	C₄	#525×C₁₅₁	1	1	yes	characteristic
494	C₄	#537×C₁₅₁	1	1	yes	characteristic
495	C₄	#546×C₁₅₁	1	1	yes	characteristic
496	C₄	#547×C₁₅₁	1	1	yes	characteristic
497	C₂	—	8	2	no	—
498	C₂	#2407×C₁₅₁	1	1	yes	characteristic
499	C₂	#3005×C₁₅₁	1	1	yes	characteristic
500	C₂	#3011×C₁₅₁	1	1	yes	characteristic
501	C₂	#3377×C₁₅₁	1	2	yes	—
502	C₂	#3402×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
2. C₂×#462×C₁₅₁	C₂	semidirect
4. #2581×C₁₅₁	C₂	semidirect
7. #1985×C₁₅₁	C₂	semidirect
8. #1960×C₁₅₁	C₂	semidirect
9. #1878×C₁₅₁	C₂	semidirect
10. #1863×C₁₅₁	C₂	semidirect
251. #24201	C₁₅₁	direct (N × H)
252. C₁₅₁	#24201	direct (N × H)
254. C₂×#462	C₂×C₁₅₁	semidirect
256. #2581	C₂×C₁₅₁	semidirect
259. #1985	C₂×C₁₅₁	semidirect
260. #1960	C₂×C₁₅₁	semidirect
261. #1878	C₂×C₁₅₁	semidirect
262. #1863	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×#556×C₁₅₁	2
C₂×#462×C₁₅₁	2
C₂×#440×C₁₅₁	2
#2581×C₁₅₁	2
#2042×C₁₅₁	2
#2015×C₁₅₁	2
#1985×C₁₅₁	2
#1960×C₁₅₁	2
#1878×C₁₅₁	2
#1863×C₁₅₁	2
#1804×C₁₅₁	2
#24201	151

Subgroups — C151×#24201 #50329126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#24201 #50329126