Subgroups — C₁₅₁×#24202 #50329127

Order 38656.

1132 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#460×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#441×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2581×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2042×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#2015×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	#1985×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1961×C₁₅₁	C₂	1	1	yes	maximal, characteristic
9	#1877×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#1864×C₁₅₁	C₂	1	2	yes	maximal, complemented
11	#1805×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₅₁	C₂²	1	2	yes	—
14	#559×C₁₅₁	—	2	4	no	—
15	#559×C₁₅₁	—	2	4	no	—
16	C₂×#127×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₅₁	—	2	1	no	—
18	C₂×#124×C₁₅₁	C₂²	1	2	yes	—
19	C₂×#123×C₁₅₁	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
24	C₂×C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
25	#460×C₁₅₁	—	2	4	no	—
26	#441×C₁₅₁	—	2	4	no	—
27	C₂×#106×C₁₅₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
31	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
32	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
33	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
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	1	yes	characteristic
47	C₂²×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₅₁	—	2	1	no	—
49	C₂²×D₄×C₁₅₁	—	2	1	no	—
50	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₅₁	—	2	2	no	—
52	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
53	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
54	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
55	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
56	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
57	C₂×SD₁₆×C₁₅₁	—	4	2	no	—
58	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
61	#127×C₁₅₁	—	2	2	no	—
62	#127×C₁₅₁	D₄	1	4	yes	—
63	#124×C₁₅₁	—	2	8	no	—
64	#124×C₁₅₁	—	2	4	no	—
65	#124×C₁₅₁	—	2	4	no	—
66	#123×C₁₅₁	—	2	16	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	2	no	—
71	C₄×Q₈×C₁₅₁	—	2	2	no	—
72	C₄×Q₈×C₁₅₁	D₄	1	4	yes	—
73	C₄×D₄×C₁₅₁	—	2	8	no	—
74	C₄×D₄×C₁₅₁	—	2	4	no	—
75	C₄×D₄×C₁₅₁	—	2	4	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	2	no	—
86	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
87	C₂×C₄²×C₁₅₁	—	2	1	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	#106×C₁₅₁	—	2	2	no	—
92	C₄⋊C₈×C₁₅₁	—	2	2	no	—
93	#103×C₁₅₁	—	2	2	no	—
94	#103×C₁₅₁	—	2	2	no	—
95	#103×C₁₅₁	—	4	2	no	—
96	#102×C₁₅₁	—	2	4	no	—
97	#102×C₁₅₁	—	2	4	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	2	no	—
106	C₂×Q₈×C₁₅₁	—	2	2	no	—
107	C₂×Q₈×C₁₅₁	—	2	1	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	1	no	—
112	C₂×Q₈×C₁₅₁	—	2	1	no	—
113	C₂×Q₈×C₁₅₁	—	2	1	no	—
114	C₂×Q₈×C₁₅₁	—	2	1	no	—
115	C₂×Q₈×C₁₅₁	—	2	1	no	—
116	C₂×Q₈×C₁₅₁	—	2	1	no	—
117	C₂×Q₈×C₁₅₁	—	4	2	no	—
118	C₂×Q₈×C₁₅₁	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₁₅₁	#41	1	2	yes	—
120	C₂×D₄×C₁₅₁	—	2	4	no	—
121	C₂×D₄×C₁₅₁	—	2	4	no	—
122	C₂×D₄×C₁₅₁	—	2	2	no	—
123	C₂×D₄×C₁₅₁	—	2	2	no	—
124	C₂×D₄×C₁₅₁	—	2	2	no	—
125	C₂×D₄×C₁₅₁	—	2	2	no	—
126	C₂×D₄×C₁₅₁	—	2	2	no	—
127	C₂×D₄×C₁₅₁	—	4	4	no	—
128	C₂×D₄×C₁₅₁	—	8	2	no	—
129	C₂×D₄×C₁₅₁	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₅₁	—	2	1	no	—
131	C₂²×C₄×C₁₅₁	—	2	1	no	—
132	C₂²×C₄×C₁₅₁	—	2	1	no	—
133	C₂²×C₄×C₁₅₁	—	2	8	no	—
134	C₂²×C₄×C₁₅₁	—	2	2	no	—
135	C₂²×C₄×C₁₅₁	—	2	1	no	—
136	C₂²×C₄×C₁₅₁	—	8	4	no	—
137	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
142	Q₁₆×C₁₅₁	—	2	8	no	—
143	SD₁₆×C₁₅₁	—	4	8	no	—
144	C₂×C₈×C₁₅₁	—	2	1	no	—
145	C₂×C₈×C₁₅₁	—	2	1	no	—
146	C₂×C₈×C₁₅₁	—	2	1	no	—
147	C₂×C₈×C₁₅₁	—	2	2	no	—
148	C₂×C₈×C₁₅₁	—	2	2	no	—
149	C₂×C₈×C₁₅₁	—	2	1	no	—
150	C₂×C₈×C₁₅₁	—	2	2	no	—
151	C₂×C₈×C₁₅₁	—	2	1	no	—
152	C₂×C₈×C₁₅₁	#41	1	2	yes	—
153	C₄⋊C₄×C₁₅₁	—	2	4	no	—
154	C₄⋊C₄×C₁₅₁	—	2	2	no	—
155	C₄⋊C₄×C₁₅₁	—	2	4	no	—
156	C₄⋊C₄×C₁₅₁	—	2	1	no	—
157	C₄⋊C₄×C₁₅₁	—	2	1	no	—
158	C₄⋊C₄×C₁₅₁	—	2	1	no	—
159	C₄⋊C₄×C₁₅₁	—	2	2	no	—
160	C₄⋊C₄×C₁₅₁	—	2	2	no	—
161	C₄⋊C₄×C₁₅₁	—	4	4	no	—
162	C₄⋊C₄×C₁₅₁	—	4	2	no	—
163	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
165	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
166	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
167	C₄²×C₁₅₁	—	2	4	no	—
168	C₄²×C₁₅₁	—	2	2	no	—
169	C₄²×C₁₅₁	—	2	2	no	—
170	C₄²×C₁₅₁	—	4	2	no	—
171	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
172	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
173	C₂³×C₁₅₁	—	2	4	no	—
174	C₂³×C₁₅₁	—	4	2	no	—
175	C₂³×C₁₅₁	—	4	2	no	—
176	C₂³×C₁₅₁	—	4	4	no	—
177	C₂³×C₁₅₁	—	4	4	no	—
178	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₁₅₁	—	2	2	no	—
180	Q₈×C₁₅₁	—	2	2	no	—
181	Q₈×C₁₅₁	—	2	2	no	—
182	Q₈×C₁₅₁	—	2	2	no	—
183	Q₈×C₁₅₁	—	4	4	no	—
184	Q₈×C₁₅₁	—	4	1	no	—
185	Q₈×C₁₅₁	—	4	1	no	—
186	Q₈×C₁₅₁	—	4	1	no	—
187	Q₈×C₁₅₁	—	4	1	no	—
188	D₄×C₁₅₁	—	2	4	no	—
189	D₄×C₁₅₁	—	2	4	no	—
190	D₄×C₁₅₁	—	4	8	no	—
191	D₄×C₁₅₁	—	4	2	no	—
192	D₄×C₁₅₁	—	4	2	no	—
193	D₄×C₁₅₁	—	8	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	2	no	—
200	C₂×C₄×C₁₅₁	—	2	2	no	—
201	C₂×C₄×C₁₅₁	—	2	2	no	—
202	C₂×C₄×C₁₅₁	—	2	2	no	—
203	C₂×C₄×C₁₅₁	—	2	4	no	—
204	C₂×C₄×C₁₅₁	—	4	1	no	—
205	C₂×C₄×C₁₅₁	—	4	1	no	—
206	C₂×C₄×C₁₅₁	—	4	1	no	—
207	C₂×C₄×C₁₅₁	—	4	1	no	—
208	C₂×C₄×C₁₅₁	—	4	2	no	—
209	C₂×C₄×C₁₅₁	—	4	1	no	—
210	C₂×C₄×C₁₅₁	—	4	2	no	—
211	C₂×C₄×C₁₅₁	—	4	2	no	—
212	C₂×C₄×C₁₅₁	—	4	2	no	—
213	C₂×C₄×C₁₅₁	—	4	2	no	—
214	C₂×C₄×C₁₅₁	—	8	8	no	—
215	C₂×C₄×C₁₅₁	#120	1	2	yes	—
216	C₂×C₄×C₁₅₁	#120	1	2	yes	—
217	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
223	C₈×C₁₅₁	—	2	2	no	—
224	C₈×C₁₅₁	—	4	1	no	—
225	C₈×C₁₅₁	—	4	2	no	—
226	C₂²×C₁₅₁	—	4	4	no	—
227	C₂²×C₁₅₁	—	4	4	no	—
228	C₂²×C₁₅₁	—	4	4	no	—
229	C₂²×C₁₅₁	—	8	4	no	—
230	C₂²×C₁₅₁	—	8	4	no	—
231	C₂²×C₁₅₁	C₂×#120	1	1	yes	characteristic
232	C₂²×C₁₅₁	#548	1	1	yes	characteristic
233	C₂²×C₁₅₁	#550	1	1	yes	characteristic
234	C₂²×C₁₅₁	#575	1	2	yes	—
235	C₂²×C₁₅₁	#577	1	2	yes	—
236	C₄×C₁₅₁	—	2	2	no	—
237	C₄×C₁₅₁	—	2	2	no	—
238	C₄×C₁₅₁	—	4	2	no	—
239	C₄×C₁₅₁	—	4	2	no	—
240	C₄×C₁₅₁	—	4	2	no	—
241	C₄×C₁₅₁	—	4	2	no	—
242	C₄×C₁₅₁	—	4	2	no	—
243	C₄×C₁₅₁	—	8	2	no	—
244	C₄×C₁₅₁	—	8	1	no	—
245	C₄×C₁₅₁	#525	1	1	yes	characteristic
246	C₄×C₁₅₁	#537	1	1	yes	characteristic
247	C₄×C₁₅₁	#546	1	1	yes	characteristic
248	C₄×C₁₅₁	#547	1	1	yes	characteristic
249	C₂×C₁₅₁	—	8	4	no	—
250	C₂×C₁₅₁	#2407	1	1	yes	characteristic
251	C₂×C₁₅₁	#3005	1	1	yes	characteristic
252	C₂×C₁₅₁	#3009	1	1	yes	characteristic
253	C₂×C₁₅₁	#3371	1	2	yes	—
254	C₂×C₁₅₁	#3401	1	2	yes	—
255	#24202	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₁₅₁	#24202	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#559	C₂×C₁₅₁	1	1	yes	characteristic
258	C₂×#460	C₂×C₁₅₁	1	1	yes	characteristic
259	C₂×#441	C₂×C₁₅₁	1	1	yes	characteristic, complemented
260	#2581	C₂×C₁₅₁	1	1	yes	characteristic, complemented
261	#2042	C₂×C₁₅₁	1	2	yes	complemented
262	#2015	C₂×C₁₅₁	1	2	yes	complemented
263	#1985	C₂×C₁₅₁	1	1	yes	characteristic, complemented
264	#1961	C₂×C₁₅₁	1	1	yes	characteristic
265	#1877	C₂×C₁₅₁	1	2	yes	complemented
266	#1864	C₂×C₁₅₁	1	2	yes	complemented
267	#1805	C₂×C₁₅₁	1	1	yes	characteristic, complemented
268	C₂²×Q₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
269	C₂²×SD₁₆	C₂²×C₁₅₁	1	2	yes	—
270	#559	—	2	4	no	—
271	#559	—	2	4	no	—
272	C₂×#127	C₂²×C₁₅₁	1	1	yes	characteristic
273	C₂×#124	—	2	1	no	—
274	C₂×#124	C₂²×C₁₅₁	1	2	yes	—
275	C₂×#123	—	2	2	no	—
276	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
277	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
278	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
279	C₂×C₄×D₄	—	2	1	no	—
280	C₂×C₄×D₄	C₂²×C₁₅₁	1	2	yes	—
281	#460	—	2	4	no	—
282	#441	—	2	4	no	—
283	C₂×#106	C₂²×C₁₅₁	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
285	C₂×#103	C₂²×C₁₅₁	1	1	yes	characteristic
286	C₂×#103	C₂²×C₁₅₁	1	1	yes	characteristic
287	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
288	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
289	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
290	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
291	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
292	#400	—	2	1	no	—
293	#395	—	2	1	no	—
294	#391	C₂²×C₁₅₁	1	2	yes	—
295	#389	C₂²×C₁₅₁	1	2	yes	—
296	#387	—	2	2	no	—
297	#382	C₂²×C₁₅₁	1	1	yes	characteristic
298	#340	C₂²×C₁₅₁	1	2	yes	—
299	#336	C₂²×C₁₅₁	1	2	yes	—
300	#336	C₂²×C₁₅₁	1	2	yes	—
301	C₂²×Q₈	D₄×C₁₅₁	1	1	yes	characteristic
302	C₂²×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
307	C₂³×C₄	—	2	2	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×Q₁₆	—	2	2	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×SD₁₆	—	2	4	no	—
312	C₂×SD₁₆	—	2	4	no	—
313	C₂×SD₁₆	—	4	2	no	—
314	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
315	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
317	#127	—	2	2	no	—
318	#127	D₄×C₁₅₁	1	4	yes	—
319	#124	—	2	8	no	—
320	#124	—	2	4	no	—
321	#124	—	2	4	no	—
322	#123	—	2	16	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	D₄×C₁₅₁	1	4	yes	—
329	C₄×D₄	—	2	8	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
336	C₂×C₄⋊C₄	D₄×C₁₅₁	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
346	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
347	#106	—	2	2	no	—
348	C₄⋊C₈	—	2	2	no	—
349	#103	—	2	2	no	—
350	#103	—	2	2	no	—
351	#103	—	4	2	no	—
352	#102	—	2	4	no	—
353	#102	—	2	4	no	—
354	#102	—	4	2	no	—
355	#97	—	2	2	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	2	no	—
359	#95	—	2	2	no	—
360	#95	—	2	2	no	—
361	C₂⁴	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	4	2	no	—
374	C₂×Q₈	C₂×D₄×C₁₅₁	1	2	yes	—
375	C₂×Q₈	#41×C₁₅₁	1	2	yes	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	8	2	no	—
385	C₂×D₄	C₂×D₄×C₁₅₁	1	4	yes	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	8	4	no	—
393	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
398	Q₁₆	—	2	8	no	—
399	SD₁₆	—	4	8	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	#41×C₁₅₁	1	2	yes	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	4	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	—	4	4	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	4	2	no	—
427	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
428	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
429	C₂³	—	2	4	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	4	4	no	—
434	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	4	no	—
440	Q₈	—	4	1	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	Q₈	—	4	1	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	8	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	8	no	—
471	C₂×C₄	#120×C₁₅₁	1	2	yes	—
472	C₂×C₄	#120×C₁₅₁	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
477	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
478	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	4	1	no	—
481	C₈	—	4	2	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	8	4	no	—
486	C₂²	—	8	4	no	—
487	C₂²	C₂×#120×C₁₅₁	1	1	yes	characteristic
488	C₂²	#548×C₁₅₁	1	1	yes	characteristic
489	C₂²	#550×C₁₅₁	1	1	yes	characteristic
490	C₂²	#575×C₁₅₁	1	2	yes	—
491	C₂²	#577×C₁₅₁	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	2	no	—
500	C₄	—	8	1	no	—
501	C₄	#525×C₁₅₁	1	1	yes	characteristic
502	C₄	#537×C₁₅₁	1	1	yes	characteristic
503	C₄	#546×C₁₅₁	1	1	yes	characteristic
504	C₄	#547×C₁₅₁	1	1	yes	characteristic
505	C₂	—	8	4	no	—
506	C₂	#2407×C₁₅₁	1	1	yes	characteristic
507	C₂	#3005×C₁₅₁	1	1	yes	characteristic
508	C₂	#3009×C₁₅₁	1	1	yes	characteristic
509	C₂	#3371×C₁₅₁	1	2	yes	—
510	C₂	#3401×C₁₅₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂×#127×C₁₅₁	C₂²
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
3. C₂×#441×C₁₅₁	C₂	semidirect
4. #2581×C₁₅₁	C₂	semidirect
5. #2042×C₁₅₁	C₂	semidirect
6. #2015×C₁₅₁	C₂	semidirect
7. #1985×C₁₅₁	C₂	semidirect
9. #1877×C₁₅₁	C₂	semidirect
10. #1864×C₁₅₁	C₂	semidirect
11. #1805×C₁₅₁	C₂	semidirect
255. #24202	C₁₅₁	direct (N × H)
256. C₁₅₁	#24202	direct (N × H)
259. C₂×#441	C₂×C₁₅₁	semidirect
260. #2581	C₂×C₁₅₁	semidirect
261. #2042	C₂×C₁₅₁	semidirect
262. #2015	C₂×C₁₅₁	semidirect
263. #1985	C₂×C₁₅₁	semidirect
265. #1877	C₂×C₁₅₁	semidirect
266. #1864	C₂×C₁₅₁	semidirect
267. #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×#559×C₁₅₁	2
C₂×#460×C₁₅₁	2
C₂×#441×C₁₅₁	2
#2581×C₁₅₁	2
#2042×C₁₅₁	2
#2015×C₁₅₁	2
#1985×C₁₅₁	2
#1961×C₁₅₁	2
#1877×C₁₅₁	2
#1864×C₁₅₁	2
#1805×C₁₅₁	2
#24202	151

Subgroups — C151×#24202 #50329127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#24202 #50329127