Subgroups — C₁₅₁×#22995 #50327920

Order 38656.

1170 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#459×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₁₅₁	C₂	1	2	yes	maximal, complemented
3	#2366×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₄⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1957×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1947×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1934×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#1879×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1862×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₅₁	C₂²	1	2	yes	—
13	C₂×#127×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₅₁	—	2	1	no	—
15	C₂×C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₅₁	—	2	1	no	—
19	#459×C₁₅₁	C₄	1	8	yes	complemented
20	C₄×D₈×C₁₅₁	—	2	8	no	—
21	C₂×#107×C₁₅₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₅₁	C₂²	1	1	yes	characteristic
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×#102×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₅₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
30	#390×C₁₅₁	—	2	1	no	—
31	#390×C₁₅₁	C₂²	1	2	yes	—
32	#389×C₁₅₁	C₂²	1	2	yes	—
33	#386×C₁₅₁	—	2	2	no	—
34	#385×C₁₅₁	—	2	2	no	—
35	#384×C₁₅₁	C₂²	1	1	yes	characteristic
36	#380×C₁₅₁	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
39	#340×C₁₅₁	C₂²	1	1	yes	characteristic
40	#340×C₁₅₁	C₂²	1	2	yes	—
41	#340×C₁₅₁	C₂²	1	1	yes	characteristic
42	#336×C₁₅₁	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₅₁	—	2	1	no	—
44	C₂²×D₄×C₁₅₁	—	2	1	no	—
45	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₅₁	—	2	1	no	—
48	C₂³×C₄×C₁₅₁	—	2	2	no	—
49	C₂³×C₄×C₁₅₁	—	2	2	no	—
50	C₂×D₈×C₁₅₁	—	2	4	no	—
51	C₂×D₈×C₁₅₁	—	2	4	no	—
52	C₂×D₈×C₁₅₁	C₂×C₄	1	8	yes	complemented
53	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
56	#127×C₁₅₁	—	2	2	no	—
57	#127×C₁₅₁	C₂×C₄	1	4	yes	complemented
58	C₄×D₄×C₁₅₁	—	2	4	no	—
59	C₄×D₄×C₁₅₁	—	2	4	no	—
60	C₄×D₄×C₁₅₁	—	2	2	no	—
61	C₄×D₄×C₁₅₁	—	4	2	no	—
62	C₄×D₄×C₁₅₁	—	4	2	no	—
63	C₄×D₄×C₁₅₁	—	4	4	no	—
64	C₄×D₄×C₁₅₁	C₂×C₄	1	4	yes	complemented
65	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₅₁	—	4	4	no	—
69	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
80	C₂×C₄²×C₁₅₁	—	2	1	no	—
81	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
83	#107×C₁₅₁	—	2	4	no	—
84	C₄⋊C₈×C₁₅₁	C₂×C₄	1	4	yes	complemented
85	#102×C₁₅₁	—	2	2	no	—
86	#102×C₁₅₁	—	2	4	no	—
87	#102×C₁₅₁	—	4	2	no	—
88	#102×C₁₅₁	C₂×C₄	1	8	yes	complemented
89	#102×C₁₅₁	D₄	1	4	yes	complemented
90	C₄×C₈×C₁₅₁	—	2	4	no	—
91	C₄×C₈×C₁₅₁	—	2	2	no	—
92	#95×C₁₅₁	—	2	1	no	—
93	#95×C₁₅₁	—	2	2	no	—
94	#95×C₁₅₁	D₄	1	2	yes	—
95	C₂⁴×C₁₅₁	—	2	1	no	—
96	C₂⁴×C₁₅₁	—	2	2	no	—
97	C₂×D₄×C₁₅₁	—	2	4	no	—
98	C₂×D₄×C₁₅₁	—	2	4	no	—
99	C₂×D₄×C₁₅₁	—	2	2	no	—
100	C₂×D₄×C₁₅₁	—	2	1	no	—
101	C₂×D₄×C₁₅₁	—	2	2	no	—
102	C₂×D₄×C₁₅₁	—	2	2	no	—
103	C₂×D₄×C₁₅₁	—	2	1	no	—
104	C₂×D₄×C₁₅₁	—	2	2	no	—
105	C₂×D₄×C₁₅₁	—	2	1	no	—
106	C₂×D₄×C₁₅₁	—	2	2	no	—
107	C₂×D₄×C₁₅₁	—	4	2	no	—
108	C₂×D₄×C₁₅₁	—	4	2	no	—
109	C₂×D₄×C₁₅₁	—	8	1	no	—
110	C₂×D₄×C₁₅₁	—	8	1	no	—
111	C₂×D₄×C₁₅₁	C₂²×C₄	1	4	yes	—
112	C₂×D₄×C₁₅₁	C₂²×C₄	1	2	yes	—
113	C₂×D₄×C₁₅₁	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₁₅₁	#41	1	2	yes	—
115	C₂²×C₄×C₁₅₁	—	2	1	no	—
116	C₂²×C₄×C₁₅₁	—	2	1	no	—
117	C₂²×C₄×C₁₅₁	—	2	4	no	—
118	C₂²×C₄×C₁₅₁	—	2	1	no	—
119	C₂²×C₄×C₁₅₁	—	2	2	no	—
120	C₂²×C₄×C₁₅₁	—	4	4	no	—
121	C₂²×C₄×C₁₅₁	—	4	4	no	—
122	C₂²×C₄×C₁₅₁	—	4	2	no	—
123	C₂²×C₄×C₁₅₁	—	4	2	no	—
124	C₂²×C₄×C₁₅₁	—	4	4	no	—
125	C₂²×C₄×C₁₅₁	—	4	4	no	—
126	C₂²×C₄×C₁₅₁	—	8	2	no	—
127	C₂²×C₄×C₁₅₁	—	8	2	no	—
128	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
133	D₈×C₁₅₁	—	2	16	no	—
134	C₂×C₈×C₁₅₁	—	2	2	no	—
135	C₂×C₈×C₁₅₁	—	2	1	no	—
136	C₂×C₈×C₁₅₁	—	2	2	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	1	no	—
141	C₂×C₈×C₁₅₁	C₂²×C₄	1	4	yes	—
142	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₁₅₁	—	2	2	no	—
144	C₄⋊C₄×C₁₅₁	—	2	1	no	—
145	C₄⋊C₄×C₁₅₁	—	2	1	no	—
146	C₄⋊C₄×C₁₅₁	—	2	2	no	—
147	C₄⋊C₄×C₁₅₁	—	2	1	no	—
148	C₄⋊C₄×C₁₅₁	—	2	2	no	—
149	C₄⋊C₄×C₁₅₁	—	2	1	no	—
150	C₄⋊C₄×C₁₅₁	—	4	4	no	—
151	C₄⋊C₄×C₁₅₁	—	4	2	no	—
152	C₄⋊C₄×C₁₅₁	—	8	1	no	—
153	C₄⋊C₄×C₁₅₁	D₈	1	4	yes	complemented
154	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
155	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
157	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
158	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
159	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
160	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
161	C₄²×C₁₅₁	—	2	2	no	—
162	C₄²×C₁₅₁	—	2	2	no	—
163	C₄²×C₁₅₁	—	4	2	no	—
164	C₄²×C₁₅₁	C₂²×C₄	1	2	yes	—
165	C₄²×C₁₅₁	#41	1	2	yes	—
166	C₂³×C₁₅₁	—	2	2	no	—
167	C₂³×C₁₅₁	—	2	2	no	—
168	C₂³×C₁₅₁	—	2	2	no	—
169	C₂³×C₁₅₁	—	2	4	no	—
170	C₂³×C₁₅₁	—	4	1	no	—
171	C₂³×C₁₅₁	—	4	1	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	—	4	2	no	—
177	C₂³×C₁₅₁	—	4	2	no	—
178	C₂³×C₁₅₁	—	4	2	no	—
179	C₂³×C₁₅₁	—	4	2	no	—
180	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
181	D₄×C₁₅₁	—	2	4	no	—
182	D₄×C₁₅₁	—	2	2	no	—
183	D₄×C₁₅₁	—	2	4	no	—
184	D₄×C₁₅₁	—	2	2	no	—
185	D₄×C₁₅₁	—	2	2	no	—
186	D₄×C₁₅₁	—	4	2	no	—
187	D₄×C₁₅₁	—	4	2	no	—
188	D₄×C₁₅₁	—	4	8	no	—
189	D₄×C₁₅₁	—	8	4	no	—
190	D₄×C₁₅₁	C₄×D₄	1	4	yes	complemented
191	C₂×C₄×C₁₅₁	—	2	2	no	—
192	C₂×C₄×C₁₅₁	—	2	1	no	—
193	C₂×C₄×C₁₅₁	—	2	2	no	—
194	C₂×C₄×C₁₅₁	—	2	1	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	—	4	1	no	—
201	C₂×C₄×C₁₅₁	—	4	1	no	—
202	C₂×C₄×C₁₅₁	—	4	1	no	—
203	C₂×C₄×C₁₅₁	—	4	1	no	—
204	C₂×C₄×C₁₅₁	—	4	8	no	—
205	C₂×C₄×C₁₅₁	—	4	2	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	2	no	—
210	C₂×C₄×C₁₅₁	—	4	1	no	—
211	C₂×C₄×C₁₅₁	—	8	8	no	—
212	C₂×C₄×C₁₅₁	—	8	8	no	—
213	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₁₅₁	C₂×D₈	1	4	yes	—
216	C₂×C₄×C₁₅₁	C₂×D₈	1	2	yes	—
217	C₂×C₄×C₁₅₁	#135	1	2	yes	—
218	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₁₅₁	—	2	4	no	—
225	C₈×C₁₅₁	—	2	2	no	—
226	C₈×C₁₅₁	—	4	1	no	—
227	C₂²×C₁₅₁	—	2	4	no	—
228	C₂²×C₁₅₁	—	4	2	no	—
229	C₂²×C₁₅₁	—	4	2	no	—
230	C₂²×C₁₅₁	—	4	2	no	—
231	C₂²×C₁₅₁	—	4	2	no	—
232	C₂²×C₁₅₁	—	4	2	no	—
233	C₂²×C₁₅₁	—	4	2	no	—
234	C₂²×C₁₅₁	—	4	4	no	—
235	C₂²×C₁₅₁	—	4	4	no	—
236	C₂²×C₁₅₁	—	4	4	no	—
237	C₂²×C₁₅₁	—	8	2	no	—
238	C₂²×C₁₅₁	—	8	2	no	—
239	C₂²×C₁₅₁	—	8	2	no	—
240	C₂²×C₁₅₁	—	8	2	no	—
241	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂²×C₁₅₁	D₄²	1	1	yes	characteristic
243	C₂²×C₁₅₁	#548	1	1	yes	characteristic
244	C₂²×C₁₅₁	C₂²×D₈	1	1	yes	characteristic
245	C₂²×C₁₅₁	C₂×#135	1	1	yes	characteristic
246	C₂²×C₁₅₁	#576	1	1	yes	characteristic
247	C₂²×C₁₅₁	#577	1	1	yes	characteristic
248	C₄×C₁₅₁	—	2	2	no	—
249	C₄×C₁₅₁	—	2	4	no	—
250	C₄×C₁₅₁	—	4	2	no	—
251	C₄×C₁₅₁	—	4	2	no	—
252	C₄×C₁₅₁	—	4	2	no	—
253	C₄×C₁₅₁	—	8	1	no	—
254	C₄×C₁₅₁	—	8	2	no	—
255	C₄×C₁₅₁	C₄×D₈	1	4	yes	complemented
256	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₁₅₁	#520	1	1	yes	characteristic
258	C₄×C₁₅₁	#547	1	1	yes	characteristic
259	C₄×C₁₅₁	#553	1	1	yes	characteristic
260	C₂×C₁₅₁	—	4	4	no	—
261	C₂×C₁₅₁	—	8	4	no	—
262	C₂×C₁₅₁	#2361	1	1	yes	characteristic
263	C₂×C₁₅₁	C₂×C₄×D₈	1	1	yes	characteristic
264	C₂×C₁₅₁	#2946	1	1	yes	characteristic
265	C₂×C₁₅₁	D₄×D₈	1	1	yes	characteristic
266	C₂×C₁₅₁	#3284	1	1	yes	characteristic
267	C₂×C₁₅₁	#3358	1	1	yes	characteristic
268	C₂×C₁₅₁	#3361	1	1	yes	characteristic
269	#22995	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₁₅₁	#22995	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×#459	C₂×C₁₅₁	1	1	yes	characteristic
272	C₂×C₄×D₈	C₂×C₁₅₁	1	2	yes	complemented
273	#2366	C₂×C₁₅₁	1	1	yes	characteristic, complemented
274	D₄×C₄⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
275	#1957	C₂×C₁₅₁	1	1	yes	characteristic, complemented
276	#1947	C₂×C₁₅₁	1	1	yes	characteristic, complemented
277	#1934	C₂×C₁₅₁	1	2	yes	complemented
278	#1879	C₂×C₁₅₁	1	2	yes	complemented
279	#1862	C₂×C₁₅₁	1	2	yes	complemented
280	C₈×C₄⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
281	C₄×#102	C₂×C₁₅₁	1	1	yes	characteristic, complemented
282	C₂²×D₈	C₂²×C₁₅₁	1	2	yes	—
283	C₂×#127	C₂²×C₁₅₁	1	1	yes	characteristic
284	C₂×C₄×D₄	—	2	1	no	—
285	C₂×C₄×D₄	C₂²×C₁₅₁	1	2	yes	—
286	C₂×C₄×D₄	C₂²×C₁₅₁	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	—	2	1	no	—
289	#459	C₄×C₁₅₁	1	8	yes	complemented
290	C₄×D₈	—	2	8	no	—
291	C₂×#107	C₂²×C₁₅₁	1	2	yes	—
292	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
293	C₂×#102	C₂²×C₁₅₁	1	1	yes	characteristic
294	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
295	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
296	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
297	C₂×#102	C₂²×C₁₅₁	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂²×C₁₅₁	1	2	yes	—
299	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
300	#390	—	2	1	no	—
301	#390	C₂²×C₁₅₁	1	2	yes	—
302	#389	C₂²×C₁₅₁	1	2	yes	—
303	#386	—	2	2	no	—
304	#385	—	2	2	no	—
305	#384	C₂²×C₁₅₁	1	1	yes	characteristic
306	#380	—	2	1	no	—
307	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
309	#340	C₂²×C₁₅₁	1	1	yes	characteristic
310	#340	C₂²×C₁₅₁	1	2	yes	—
311	#340	C₂²×C₁₅₁	1	1	yes	characteristic
312	#336	C₂²×C₁₅₁	1	2	yes	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
316	C₂²×D₄	C₂³×C₁₅₁	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	—	2	2	no	—
319	C₂³×C₄	—	2	2	no	—
320	C₂×D₈	—	2	4	no	—
321	C₂×D₈	—	2	4	no	—
322	C₂×D₈	C₂×C₄×C₁₅₁	1	8	yes	complemented
323	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
325	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
326	#127	—	2	2	no	—
327	#127	C₂×C₄×C₁₅₁	1	4	yes	complemented
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	4	2	no	—
332	C₄×D₄	—	4	2	no	—
333	C₄×D₄	—	4	4	no	—
334	C₄×D₄	C₂×C₄×C₁₅₁	1	4	yes	complemented
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	4	4	no	—
339	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
340	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
352	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
353	#107	—	2	4	no	—
354	C₄⋊C₈	C₂×C₄×C₁₅₁	1	4	yes	complemented
355	#102	—	2	2	no	—
356	#102	—	2	4	no	—
357	#102	—	4	2	no	—
358	#102	C₂×C₄×C₁₅₁	1	8	yes	complemented
359	#102	D₄×C₁₅₁	1	4	yes	complemented
360	C₄×C₈	—	2	4	no	—
361	C₄×C₈	—	2	2	no	—
362	#95	—	2	1	no	—
363	#95	—	2	2	no	—
364	#95	D₄×C₁₅₁	1	2	yes	—
365	C₂⁴	—	2	1	no	—
366	C₂⁴	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	8	1	no	—
380	C₂×D₄	—	8	1	no	—
381	C₂×D₄	C₂²×C₄×C₁₅₁	1	4	yes	—
382	C₂×D₄	C₂²×C₄×C₁₅₁	1	2	yes	—
383	C₂×D₄	C₂×D₄×C₁₅₁	1	2	yes	—
384	C₂×D₄	#41×C₁₅₁	1	2	yes	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	8	2	no	—
397	C₂²×C₄	—	8	2	no	—
398	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
403	D₈	—	2	16	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	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	C₂²×C₄×C₁₅₁	1	4	yes	—
412	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	4	4	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	8	1	no	—
423	C₄⋊C₄	D₈×C₁₅₁	1	4	yes	complemented
424	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
425	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	8	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	4	2	no	—
434	C₄²	C₂²×C₄×C₁₅₁	1	2	yes	—
435	C₄²	#41×C₁₅₁	1	2	yes	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
451	D₄	—	2	4	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	4	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	4	8	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	8	4	no	—
460	D₄	C₄×D₄×C₁₅₁	1	4	yes	complemented
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	8	8	no	—
482	C₂×C₄	—	8	8	no	—
483	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
484	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
485	C₂×C₄	C₂×D₈×C₁₅₁	1	4	yes	—
486	C₂×C₄	C₂×D₈×C₁₅₁	1	2	yes	—
487	C₂×C₄	#135×C₁₅₁	1	2	yes	—
488	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
492	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
493	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
494	C₈	—	2	4	no	—
495	C₈	—	2	2	no	—
496	C₈	—	4	1	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
512	C₂²	D₄²×C₁₅₁	1	1	yes	characteristic
513	C₂²	#548×C₁₅₁	1	1	yes	characteristic
514	C₂²	C₂²×D₈×C₁₅₁	1	1	yes	characteristic
515	C₂²	C₂×#135×C₁₅₁	1	1	yes	characteristic
516	C₂²	#576×C₁₅₁	1	1	yes	characteristic
517	C₂²	#577×C₁₅₁	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	1	no	—
524	C₄	—	8	2	no	—
525	C₄	C₄×D₈×C₁₅₁	1	4	yes	complemented
526	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
527	C₄	#520×C₁₅₁	1	1	yes	characteristic
528	C₄	#547×C₁₅₁	1	1	yes	characteristic
529	C₄	#553×C₁₅₁	1	1	yes	characteristic
530	C₂	—	4	4	no	—
531	C₂	—	8	4	no	—
532	C₂	#2361×C₁₅₁	1	1	yes	characteristic
533	C₂	C₂×C₄×D₈×C₁₅₁	1	1	yes	characteristic
534	C₂	#2946×C₁₅₁	1	1	yes	characteristic
535	C₂	D₄×D₈×C₁₅₁	1	1	yes	characteristic
536	C₂	#3284×C₁₅₁	1	1	yes	characteristic
537	C₂	#3358×C₁₅₁	1	1	yes	characteristic
538	C₂	#3361×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×#459×C₁₅₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₄×C₄⋊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. #2366×C₁₅₁	C₂	semidirect
4. D₄×C₄⋊C₄×C₁₅₁	C₂	semidirect
5. #1957×C₁₅₁	C₂	semidirect
6. #1947×C₁₅₁	C₂	semidirect
7. #1934×C₁₅₁	C₂	semidirect
8. #1879×C₁₅₁	C₂	semidirect
9. #1862×C₁₅₁	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₅₁	C₂	semidirect
11. C₄×#102×C₁₅₁	C₂	semidirect
19. #459×C₁₅₁	C₄	semidirect
52. C₂×D₈×C₁₅₁	C₂×C₄	semidirect
57. #127×C₁₅₁	C₂×C₄	semidirect
64. C₄×D₄×C₁₅₁	C₂×C₄	semidirect
84. C₄⋊C₈×C₁₅₁	C₂×C₄	semidirect
88. #102×C₁₅₁	C₂×C₄	semidirect
89. #102×C₁₅₁	D₄	semidirect
153. C₄⋊C₄×C₁₅₁	D₈	semidirect
190. D₄×C₁₅₁	C₄×D₄	semidirect
255. C₄×C₁₅₁	C₄×D₈	semidirect
269. #22995	C₁₅₁	direct (N × H)
270. C₁₅₁	#22995	direct (N × H)
272. C₂×C₄×D₈	C₂×C₁₅₁	semidirect
273. #2366	C₂×C₁₅₁	semidirect
274. D₄×C₄⋊C₄	C₂×C₁₅₁	semidirect
275. #1957	C₂×C₁₅₁	semidirect
276. #1947	C₂×C₁₅₁	semidirect
277. #1934	C₂×C₁₅₁	semidirect
278. #1879	C₂×C₁₅₁	semidirect
279. #1862	C₂×C₁₅₁	semidirect
280. C₈×C₄⋊C₄	C₂×C₁₅₁	semidirect
281. C₄×#102	C₂×C₁₅₁	semidirect
289. #459	C₄×C₁₅₁	semidirect
322. C₂×D₈	C₂×C₄×C₁₅₁	semidirect
327. #127	C₂×C₄×C₁₅₁	semidirect
334. C₄×D₄	C₂×C₄×C₁₅₁	semidirect
354. C₄⋊C₈	C₂×C₄×C₁₅₁	semidirect
358. #102	C₂×C₄×C₁₅₁	semidirect
359. #102	D₄×C₁₅₁	semidirect
423. C₄⋊C₄	D₈×C₁₅₁	semidirect
460. D₄	C₄×D₄×C₁₅₁	semidirect
525. C₄	C₄×D₈×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#459×C₁₅₁	2
C₂×C₄×D₈×C₁₅₁	2
#2366×C₁₅₁	2
D₄×C₄⋊C₄×C₁₅₁	2
#1957×C₁₅₁	2
#1947×C₁₅₁	2
#1934×C₁₅₁	2
#1879×C₁₅₁	2
#1862×C₁₅₁	2
C₈×C₄⋊C₄×C₁₅₁	2
C₄×#102×C₁₅₁	2
#22995	151

Subgroups — C151×#22995 #50327920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#22995 #50327920