Subgroups — #1364×C₂₅₁ #44545951

Order 32128.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#335×C₂₅₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₂₅₁	—	2	1	no	—
5	C₂×C₁₆×C₂₅₁	—	2	1	no	—
6	#107×C₂₅₁	—	2	1	no	—
7	#107×C₂₅₁	C₄	1	2	yes	—
8	C₄⋊C₈×C₂₅₁	—	2	1	no	—
9	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₂₅₁	—	4	1	no	—
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	2	no	—
15	C₄⋊C₄×C₂₅₁	—	4	1	no	—
16	C₄²×C₂₅₁	D₄	1	1	yes	characteristic
17	C₁₆×C₂₅₁	—	4	1	no	—
18	Q₈×C₂₅₁	—	8	1	no	—
19	Q₈×C₂₅₁	—	8	1	no	—
20	C₂×C₄×C₂₅₁	—	4	2	no	—
21	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₅₁	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₅₁	SD₁₆	1	1	yes	characteristic
24	C₈×C₂₅₁	—	2	1	no	—
25	C₈×C₂₅₁	—	8	1	no	—
26	C₈×C₂₅₁	SD₁₆	1	1	yes	characteristic
27	C₈×C₂₅₁	Q₁₆	1	1	yes	characteristic
28	C₂²×C₂₅₁	#102	1	1	yes	characteristic
29	C₄×C₂₅₁	—	2	1	no	—
30	C₄×C₂₅₁	—	8	2	no	—
31	C₄×C₂₅₁	#101	1	1	yes	characteristic
32	C₄×C₂₅₁	#103	1	1	yes	characteristic
33	C₄×C₂₅₁	D₁₆	1	1	yes	characteristic
34	C₄×C₂₅₁	SD₃₂	1	1	yes	characteristic
35	C₂×C₂₅₁	#332	1	1	yes	characteristic
36	C₂×C₂₅₁	#357	1	1	yes	characteristic
37	C₂×C₂₅₁	#362	1	1	yes	characteristic
38	C₂₅₁	#1364	1	1	yes	characteristic, direct product factor, Sylow
39	#1364	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	#500	C₂×C₂₅₁	1	1	yes	characteristic
41	C₄⋊C₁₆	C₂×C₂₅₁	1	1	yes	characteristic
42	#335	C₂×C₂₅₁	1	1	yes	characteristic
43	C₄⋊Q₈	—	2	1	no	—
44	C₂×C₁₆	—	2	1	no	—
45	#107	—	2	1	no	—
46	#107	C₄×C₂₅₁	1	2	yes	—
47	C₄⋊C₈	—	2	1	no	—
48	C₄×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
49	C₂×Q₈	—	4	1	no	—
50	C₂×C₈	—	4	1	no	—
51	C₂×C₈	C₂×C₄×C₂₅₁	1	1	yes	characteristic
52	C₂×C₈	D₄×C₂₅₁	1	1	yes	characteristic
53	C₄⋊C₄	—	2	2	no	—
54	C₄⋊C₄	—	4	1	no	—
55	C₄²	D₄×C₂₅₁	1	1	yes	characteristic
56	C₁₆	—	4	1	no	—
57	Q₈	—	8	1	no	—
58	Q₈	—	8	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	1	yes	characteristic
61	C₂×C₄	D₈×C₂₅₁	1	1	yes	characteristic
62	C₂×C₄	SD₁₆×C₂₅₁	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	8	1	no	—
65	C₈	SD₁₆×C₂₅₁	1	1	yes	characteristic
66	C₈	Q₁₆×C₂₅₁	1	1	yes	characteristic
67	C₂²	#102×C₂₅₁	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	8	2	no	—
70	C₄	#101×C₂₅₁	1	1	yes	characteristic
71	C₄	#103×C₂₅₁	1	1	yes	characteristic
72	C₄	D₁₆×C₂₅₁	1	1	yes	characteristic
73	C₄	SD₃₂×C₂₅₁	1	1	yes	characteristic
74	C₂	#332×C₂₅₁	1	1	yes	characteristic
75	C₂	#357×C₂₅₁	1	1	yes	characteristic
76	C₂	#362×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
38. C₂₅₁	#1364	direct (N × H)
39. #1364	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
#500×C₂₅₁	2
C₄⋊C₁₆×C₂₅₁	2
#335×C₂₅₁	2
#1364	251

Subgroups — #1364×C251 #44545951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1364×C₂₅₁ #44545951