Subgroups — C₁₅₁×#23027 #50327952

Order 38656.

1050 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×#466×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#427×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2363×C₁₅₁	C₂	1	2	yes	maximal, complemented
5	#1970×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1942×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1926×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#1875×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1864×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	C₄×#107×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂×#121×C₁₅₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
16	C₂×#117×C₁₅₁	C₂²	1	2	yes	—
17	#466×C₁₅₁	C₄	1	8	yes	complemented
18	C₄×D₈×C₁₅₁	—	2	4	no	—
19	#427×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×#106×C₁₅₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
26	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
30	#390×C₁₅₁	—	2	2	no	—
31	#390×C₁₅₁	C₂²	1	2	yes	—
32	#389×C₁₅₁	C₂²	1	2	yes	—
33	#388×C₁₅₁	—	2	2	no	—
34	#386×C₁₅₁	—	2	2	no	—
35	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
37	C₄×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
38	#340×C₁₅₁	C₂²	1	2	yes	—
39	#340×C₁₅₁	C₂²	1	2	yes	—
40	#336×C₁₅₁	C₂²	1	1	yes	characteristic
41	#336×C₁₅₁	C₂²	1	1	yes	characteristic
42	C₂²×D₄×C₁₅₁	—	2	2	no	—
43	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₅₁	—	2	2	no	—
45	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₁₅₁	—	2	2	no	—
47	C₂×D₈×C₁₅₁	—	2	2	no	—
48	C₂×D₈×C₁₅₁	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₅₁	—	2	2	no	—
50	C₂²×C₈×C₁₅₁	—	2	2	no	—
51	C₂²×C₈×C₁₅₁	C₂×C₄	1	4	yes	complemented
52	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
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	#121×C₁₅₁	—	2	4	no	—
57	#121×C₁₅₁	C₂×C₄	1	8	yes	complemented
58	C₄×D₄×C₁₅₁	—	2	4	no	—
59	C₄×D₄×C₁₅₁	—	4	2	no	—
60	#117×C₁₅₁	—	2	4	no	—
61	#117×C₁₅₁	—	4	2	no	—
62	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₅₁	—	2	2	no	—
74	C₂×C₄²×C₁₅₁	—	2	2	no	—
75	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
77	#107×C₁₅₁	—	2	2	no	—
78	#107×C₁₅₁	C₂×C₄	1	4	yes	complemented
79	#107×C₁₅₁	D₄	1	4	yes	complemented
80	#106×C₁₅₁	—	2	4	no	—
81	#102×C₁₅₁	—	2	4	no	—
82	#102×C₁₅₁	—	4	2	no	—
83	#102×C₁₅₁	C₂×C₄	1	8	yes	complemented
84	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
85	C₄×C₈×C₁₅₁	—	2	2	no	—
86	C₄×C₈×C₁₅₁	—	2	2	no	—
87	#95×C₁₅₁	—	2	2	no	—
88	#95×C₁₅₁	—	2	2	no	—
89	#95×C₁₅₁	D₄	1	1	yes	characteristic
90	#95×C₁₅₁	D₄	1	1	yes	characteristic
91	C₂⁴×C₁₅₁	—	2	2	no	—
92	C₂⁴×C₁₅₁	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₁₅₁	—	2	8	no	—
94	C₂×D₄×C₁₅₁	—	2	2	no	—
95	C₂×D₄×C₁₅₁	—	2	2	no	—
96	C₂×D₄×C₁₅₁	—	2	2	no	—
97	C₂×D₄×C₁₅₁	—	2	2	no	—
98	C₂×D₄×C₁₅₁	—	2	2	no	—
99	C₂×D₄×C₁₅₁	—	8	2	no	—
100	C₂×D₄×C₁₅₁	—	8	2	no	—
101	C₂×D₄×C₁₅₁	C₂²×C₄	1	4	yes	—
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	1	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	—	4	4	no	—
110	C₂²×C₄×C₁₅₁	—	4	4	no	—
111	C₂²×C₄×C₁₅₁	—	8	2	no	—
112	C₂²×C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₅₁	#41	1	2	yes	—
119	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
120	D₈×C₁₅₁	—	2	8	no	—
121	C₂×C₈×C₁₅₁	—	2	1	no	—
122	C₂×C₈×C₁₅₁	—	2	1	no	—
123	C₂×C₈×C₁₅₁	—	2	8	no	—
124	C₂×C₈×C₁₅₁	—	2	1	no	—
125	C₂×C₈×C₁₅₁	—	2	1	no	—
126	C₂×C₈×C₁₅₁	—	2	1	no	—
127	C₂×C₈×C₁₅₁	—	2	1	no	—
128	C₂×C₈×C₁₅₁	—	2	1	no	—
129	C₂×C₈×C₁₅₁	—	2	1	no	—
130	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₅₁	#41	1	2	yes	—
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	—	8	2	no	—
139	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	4	yes	—
140	C₄⋊C₄×C₁₅₁	C₂×D₄	1	4	yes	—
141	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
142	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
143	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
144	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
145	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
146	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
147	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
148	C₄²×C₁₅₁	—	2	1	no	—
149	C₄²×C₁₅₁	—	2	1	no	—
150	C₄²×C₁₅₁	—	2	1	no	—
151	C₄²×C₁₅₁	—	2	1	no	—
152	C₄²×C₁₅₁	—	4	4	no	—
153	C₄²×C₁₅₁	—	8	2	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	—	2	1	no	—
160	C₂³×C₁₅₁	—	2	4	no	—
161	C₂³×C₁₅₁	—	4	2	no	—
162	C₂³×C₁₅₁	—	4	2	no	—
163	C₂³×C₁₅₁	—	4	2	no	—
164	C₂³×C₁₅₁	—	4	2	no	—
165	C₂³×C₁₅₁	—	4	2	no	—
166	C₂³×C₁₅₁	—	4	2	no	—
167	C₂³×C₁₅₁	C₄×D₄	1	2	yes	—
168	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₁₅₁	—	2	4	no	—
170	D₄×C₁₅₁	—	2	4	no	—
171	D₄×C₁₅₁	—	4	2	no	—
172	D₄×C₁₅₁	—	4	2	no	—
173	D₄×C₁₅₁	—	8	8	no	—
174	C₂×C₄×C₁₅₁	—	2	1	no	—
175	C₂×C₄×C₁₅₁	—	2	1	no	—
176	C₂×C₄×C₁₅₁	—	2	1	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	2	no	—
181	C₂×C₄×C₁₅₁	—	2	2	no	—
182	C₂×C₄×C₁₅₁	—	2	2	no	—
183	C₂×C₄×C₁₅₁	—	2	2	no	—
184	C₂×C₄×C₁₅₁	—	2	4	no	—
185	C₂×C₄×C₁₅₁	—	2	1	no	—
186	C₂×C₄×C₁₅₁	—	2	4	no	—
187	C₂×C₄×C₁₅₁	—	2	1	no	—
188	C₂×C₄×C₁₅₁	—	2	1	no	—
189	C₂×C₄×C₁₅₁	—	2	1	no	—
190	C₂×C₄×C₁₅₁	—	2	1	no	—
191	C₂×C₄×C₁₅₁	—	2	1	no	—
192	C₂×C₄×C₁₅₁	—	4	2	no	—
193	C₂×C₄×C₁₅₁	—	4	2	no	—
194	C₂×C₄×C₁₅₁	—	4	2	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	2	no	—
199	C₂×C₄×C₁₅₁	—	8	8	no	—
200	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₅₁	#135	1	2	yes	—
202	C₂×C₄×C₁₅₁	#135	1	2	yes	—
203	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₁₅₁	—	2	2	no	—
210	C₈×C₁₅₁	—	4	1	no	—
211	C₈×C₁₅₁	—	4	1	no	—
212	C₈×C₁₅₁	C₄×D₄	1	4	yes	—
213	C₂²×C₁₅₁	—	2	2	no	—
214	C₂²×C₁₅₁	—	2	2	no	—
215	C₂²×C₁₅₁	—	2	2	no	—
216	C₂²×C₁₅₁	—	4	1	no	—
217	C₂²×C₁₅₁	—	4	1	no	—
218	C₂²×C₁₅₁	—	4	1	no	—
219	C₂²×C₁₅₁	—	4	1	no	—
220	C₂²×C₁₅₁	—	4	4	no	—
221	C₂²×C₁₅₁	—	4	4	no	—
222	C₂²×C₁₅₁	—	4	4	no	—
223	C₂²×C₁₅₁	—	8	2	no	—
224	C₂²×C₁₅₁	—	8	2	no	—
225	C₂²×C₁₅₁	—	8	2	no	—
226	C₂²×C₁₅₁	—	8	2	no	—
227	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₁₅₁	D₄²	1	1	yes	characteristic
229	C₂²×C₁₅₁	#547	1	1	yes	characteristic
230	C₂²×C₁₅₁	C₂×#135	1	1	yes	characteristic
231	C₂²×C₁₅₁	C₂×#135	1	1	yes	characteristic
232	C₂²×C₁₅₁	#576	1	1	yes	characteristic
233	C₂²×C₁₅₁	#576	1	1	yes	characteristic
234	C₄×C₁₅₁	—	2	2	no	—
235	C₄×C₁₅₁	—	2	2	no	—
236	C₄×C₁₅₁	—	2	2	no	—
237	C₄×C₁₅₁	—	4	1	no	—
238	C₄×C₁₅₁	—	4	4	no	—
239	C₄×C₁₅₁	—	4	4	no	—
240	C₄×C₁₅₁	—	4	1	no	—
241	C₄×C₁₅₁	—	8	2	no	—
242	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₁₅₁	#520	1	1	yes	characteristic
244	C₄×C₁₅₁	#548	1	1	yes	characteristic
245	C₄×C₁₅₁	#553	1	1	yes	characteristic
246	C₂×C₁₅₁	—	4	2	no	—
247	C₂×C₁₅₁	—	8	4	no	—
248	C₂×C₁₅₁	#2361	1	1	yes	characteristic
249	C₂×C₁₅₁	C₄×#135	1	1	yes	characteristic
250	C₂×C₁₅₁	#2948	1	1	yes	characteristic
251	C₂×C₁₅₁	#3280	1	1	yes	characteristic
252	C₂×C₁₅₁	#3287	1	1	yes	characteristic
253	C₂×C₁₅₁	#3339	1	1	yes	characteristic
254	C₂×C₁₅₁	#3341	1	1	yes	characteristic
255	#23027	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₁₅₁	#23027	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#466	C₂×C₁₅₁	1	1	yes	characteristic
258	C₂×C₄×D₈	C₂×C₁₅₁	1	1	yes	characteristic, complemented
259	C₂×#427	C₂×C₁₅₁	1	1	yes	characteristic, complemented
260	#2363	C₂×C₁₅₁	1	2	yes	complemented
261	#1970	C₂×C₁₅₁	1	1	yes	characteristic, complemented
262	#1942	C₂×C₁₅₁	1	1	yes	characteristic, complemented
263	#1926	C₂×C₁₅₁	1	2	yes	complemented
264	#1875	C₂×C₁₅₁	1	2	yes	complemented
265	#1864	C₂×C₁₅₁	1	2	yes	complemented
266	C₄×#107	C₂×C₁₅₁	1	1	yes	characteristic, complemented
267	C₈×C₂²⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
268	C₂²×D₈	C₂²×C₁₅₁	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
270	C₂×#121	C₂²×C₁₅₁	1	2	yes	—
271	C₂×C₄×D₄	C₂²×C₁₅₁	1	2	yes	—
272	C₂×#117	C₂²×C₁₅₁	1	2	yes	—
273	#466	C₄×C₁₅₁	1	8	yes	complemented
274	C₄×D₈	—	2	4	no	—
275	#427	—	2	4	no	—
276	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
277	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
278	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
279	C₂×#106	C₂²×C₁₅₁	1	2	yes	—
280	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
281	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
282	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
286	#390	—	2	2	no	—
287	#390	C₂²×C₁₅₁	1	2	yes	—
288	#389	C₂²×C₁₅₁	1	2	yes	—
289	#388	—	2	2	no	—
290	#386	—	2	2	no	—
291	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
292	C₄×C₂²⋊C₄	—	2	2	no	—
293	C₄×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
294	#340	C₂²×C₁₅₁	1	2	yes	—
295	#340	C₂²×C₁₅₁	1	2	yes	—
296	#336	C₂²×C₁₅₁	1	1	yes	characteristic
297	#336	C₂²×C₁₅₁	1	1	yes	characteristic
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	C₂×C₄×C₁₅₁	1	4	yes	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	C₂×C₄×C₁₅₁	1	4	yes	complemented
308	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
312	#121	—	2	4	no	—
313	#121	C₂×C₄×C₁₅₁	1	8	yes	complemented
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	4	2	no	—
316	#117	—	2	4	no	—
317	#117	—	4	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
333	#107	—	2	2	no	—
334	#107	C₂×C₄×C₁₅₁	1	4	yes	complemented
335	#107	D₄×C₁₅₁	1	4	yes	complemented
336	#106	—	2	4	no	—
337	#102	—	2	4	no	—
338	#102	—	4	2	no	—
339	#102	C₂×C₄×C₁₅₁	1	8	yes	complemented
340	C₂²⋊C₈	—	2	2	no	—
341	C₄×C₈	—	2	2	no	—
342	C₄×C₈	—	2	2	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	D₄×C₁₅₁	1	1	yes	characteristic
346	#95	D₄×C₁₅₁	1	1	yes	characteristic
347	C₂⁴	—	2	2	no	—
348	C₂⁴	C₂×D₄×C₁₅₁	1	1	yes	characteristic
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	—	8	2	no	—
357	C₂×D₄	C₂²×C₄×C₁₅₁	1	4	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
374	C₂²×C₄	#41×C₁₅₁	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
376	D₈	—	2	8	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	8	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
387	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
388	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
389	C₂×C₈	#41×C₁₅₁	1	2	yes	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	8	2	no	—
395	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	4	yes	—
396	C₄⋊C₄	C₂×D₄×C₁₅₁	1	4	yes	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	8	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	4	4	no	—
409	C₄²	—	8	2	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	C₄×D₄×C₁₅₁	1	2	yes	—
424	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	8	8	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	8	8	no	—
456	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
457	C₂×C₄	#135×C₁₅₁	1	2	yes	—
458	C₂×C₄	#135×C₁₅₁	1	2	yes	—
459	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
463	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
464	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	C₄×D₄×C₁₅₁	1	4	yes	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
484	C₂²	D₄²×C₁₅₁	1	1	yes	characteristic
485	C₂²	#547×C₁₅₁	1	1	yes	characteristic
486	C₂²	C₂×#135×C₁₅₁	1	1	yes	characteristic
487	C₂²	C₂×#135×C₁₅₁	1	1	yes	characteristic
488	C₂²	#576×C₁₅₁	1	1	yes	characteristic
489	C₂²	#576×C₁₅₁	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	2	no	—
498	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
499	C₄	#520×C₁₅₁	1	1	yes	characteristic
500	C₄	#548×C₁₅₁	1	1	yes	characteristic
501	C₄	#553×C₁₅₁	1	1	yes	characteristic
502	C₂	—	4	2	no	—
503	C₂	—	8	4	no	—
504	C₂	#2361×C₁₅₁	1	1	yes	characteristic
505	C₂	C₄×#135×C₁₅₁	1	1	yes	characteristic
506	C₂	#2948×C₁₅₁	1	1	yes	characteristic
507	C₂	#3280×C₁₅₁	1	1	yes	characteristic
508	C₂	#3287×C₁₅₁	1	1	yes	characteristic
509	C₂	#3339×C₁₅₁	1	1	yes	characteristic
510	C₂	#3341×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	C₂×#466×C₁₅₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₄×C₂²⋊C₄×C₁₅₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₁₅₁	C₂	semidirect
3. C₂×#427×C₁₅₁	C₂	semidirect
4. #2363×C₁₅₁	C₂	semidirect
5. #1970×C₁₅₁	C₂	semidirect
6. #1942×C₁₅₁	C₂	semidirect
7. #1926×C₁₅₁	C₂	semidirect
8. #1875×C₁₅₁	C₂	semidirect
9. #1864×C₁₅₁	C₂	semidirect
10. C₄×#107×C₁₅₁	C₂	semidirect
11. C₈×C₂²⋊C₄×C₁₅₁	C₂	semidirect
17. #466×C₁₅₁	C₄	semidirect
51. C₂²×C₈×C₁₅₁	C₂×C₄	semidirect
57. #121×C₁₅₁	C₂×C₄	semidirect
78. #107×C₁₅₁	C₂×C₄	semidirect
79. #107×C₁₅₁	D₄	semidirect
83. #102×C₁₅₁	C₂×C₄	semidirect
255. #23027	C₁₅₁	direct (N × H)
256. C₁₅₁	#23027	direct (N × H)
258. C₂×C₄×D₈	C₂×C₁₅₁	semidirect
259. C₂×#427	C₂×C₁₅₁	semidirect
260. #2363	C₂×C₁₅₁	semidirect
261. #1970	C₂×C₁₅₁	semidirect
262. #1942	C₂×C₁₅₁	semidirect
263. #1926	C₂×C₁₅₁	semidirect
264. #1875	C₂×C₁₅₁	semidirect
265. #1864	C₂×C₁₅₁	semidirect
266. C₄×#107	C₂×C₁₅₁	semidirect
267. C₈×C₂²⋊C₄	C₂×C₁₅₁	semidirect
273. #466	C₄×C₁₅₁	semidirect
307. C₂²×C₈	C₂×C₄×C₁₅₁	semidirect
313. #121	C₂×C₄×C₁₅₁	semidirect
334. #107	C₂×C₄×C₁₅₁	semidirect
335. #107	D₄×C₁₅₁	semidirect
339. #102	C₂×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×#466×C₁₅₁	2
C₂×C₄×D₈×C₁₅₁	2
C₂×#427×C₁₅₁	2
#2363×C₁₅₁	2
#1970×C₁₅₁	2
#1942×C₁₅₁	2
#1926×C₁₅₁	2
#1875×C₁₅₁	2
#1864×C₁₅₁	2
C₄×#107×C₁₅₁	2
C₈×C₂²⋊C₄×C₁₅₁	2
#23027	151

Subgroups — C151×#23027 #50327952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#23027 #50327952