Subgroups — #1363×C₂₅₁ #44545950

Order 32128.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#499×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#334×C₂₅₁	C₂	1	1	yes	maximal, characteristic
4	#125×C₂₅₁	—	2	1	no	—
5	C₂×C₁₆×C₂₅₁	—	2	1	no	—
6	#107×C₂₅₁	C₄	1	1	yes	characteristic
7	#107×C₂₅₁	C₄	1	1	yes	characteristic
8	#106×C₂₅₁	—	2	1	no	—
9	C₄⋊C₈×C₂₅₁	—	2	1	no	—
10	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₂₅₁	—	4	1	no	—
12	C₂×C₈×C₂₅₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₅₁	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₂₅₁	—	2	1	no	—
15	C₄⋊C₄×C₂₅₁	—	2	1	no	—
16	C₄⋊C₄×C₂₅₁	—	4	1	no	—
17	C₄⋊C₄×C₂₅₁	—	4	1	no	—
18	C₄²×C₂₅₁	D₄	1	1	yes	characteristic
19	C₁₆×C₂₅₁	—	4	1	no	—
20	C₂×C₄×C₂₅₁	—	4	1	no	—
21	C₂×C₄×C₂₅₁	—	4	1	no	—
22	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₅₁	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₅₁	SD₁₆	1	1	yes	characteristic
25	C₈×C₂₅₁	—	2	1	no	—
26	C₈×C₂₅₁	—	8	1	no	—
27	C₈×C₂₅₁	SD₁₆	1	1	yes	characteristic
28	C₈×C₂₅₁	Q₁₆	1	1	yes	characteristic
29	C₂²×C₂₅₁	#102	1	1	yes	characteristic
30	C₄×C₂₅₁	—	2	1	no	—
31	C₄×C₂₅₁	—	2	1	no	—
32	C₄×C₂₅₁	—	8	1	no	—
33	C₄×C₂₅₁	—	8	1	no	—
34	C₄×C₂₅₁	#101	1	1	yes	characteristic
35	C₄×C₂₅₁	#103	1	1	yes	characteristic
36	C₂×C₂₅₁	#332	1	1	yes	characteristic
37	C₂×C₂₅₁	#359	1	1	yes	characteristic
38	C₂×C₂₅₁	#360	1	1	yes	characteristic
39	C₂₅₁	#1363	1	1	yes	characteristic, direct product factor, Sylow
40	#1363	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	#499	C₂×C₂₅₁	1	1	yes	characteristic
42	C₄⋊C₁₆	C₂×C₂₅₁	1	1	yes	characteristic
43	#334	C₂×C₂₅₁	1	1	yes	characteristic
44	#125	—	2	1	no	—
45	C₂×C₁₆	—	2	1	no	—
46	#107	C₄×C₂₅₁	1	1	yes	characteristic
47	#107	C₄×C₂₅₁	1	1	yes	characteristic
48	#106	—	2	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
51	C₂×C₈	—	4	1	no	—
52	C₂×C₈	C₂×C₄×C₂₅₁	1	1	yes	characteristic
53	C₂×C₈	D₄×C₂₅₁	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	4	1	no	—
57	C₄⋊C₄	—	4	1	no	—
58	C₄²	D₄×C₂₅₁	1	1	yes	characteristic
59	C₁₆	—	4	1	no	—
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	4	1	no	—
62	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	1	yes	characteristic
63	C₂×C₄	D₈×C₂₅₁	1	1	yes	characteristic
64	C₂×C₄	SD₁₆×C₂₅₁	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	8	1	no	—
67	C₈	SD₁₆×C₂₅₁	1	1	yes	characteristic
68	C₈	Q₁₆×C₂₅₁	1	1	yes	characteristic
69	C₂²	#102×C₂₅₁	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2	1	no	—
72	C₄	—	8	1	no	—
73	C₄	—	8	1	no	—
74	C₄	#101×C₂₅₁	1	1	yes	characteristic
75	C₄	#103×C₂₅₁	1	1	yes	characteristic
76	C₂	#332×C₂₅₁	1	1	yes	characteristic
77	C₂	#359×C₂₅₁	1	1	yes	characteristic
78	C₂	#360×C₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₅₁	#102
commutator	C₂×C₈	C₂×C₄×C₂₅₁
Frattini, cosocle	C₄×C₈	C₂²×C₂₅₁
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ C₄²×C₂₅₁ ◁ C₄×C₈×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
39. C₂₅₁	#1363	direct (N × H)
40. #1363	C₂₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
#499×C₂₅₁	2
C₄⋊C₁₆×C₂₅₁	2
#334×C₂₅₁	2
#1363	251

Subgroups — #1363×C251 #44545950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1363×C₂₅₁ #44545950