Subgroups — #34115140

Order 20096.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758165	C₂	1	2	yes	maximal, complemented
2	#23757639	C₂	1	1	yes	maximal, characteristic
3	#19097845	—	2	2	no	—
4	#19097768	C₄	1	1	yes	characteristic
5	#19097691	—	2	2	no	—
6	#19097682	C₂²	1	1	yes	characteristic
7	#125×C₁₅₇	C₄	1	1	yes	characteristic
8	#14578957	—	2	4	no	—
9	C₂×D₆₂₈	—	2	1	no	—
10	C₂×D₆₂₈	—	4	1	no	—
11	C₂×#11929434	D₄	1	2	yes	—
12	C₄⋊C₄×C₁₅₇	—	2	1	no	—
13	C₄⋊C₄×C₁₅₇	—	4	1	no	—
14	C₄²×C₁₅₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×D₁₅₇	—	4	1	no	—
16	D₆₂₈	—	4	2	no	—
17	D₆₂₈	—	8	2	no	—
18	#11929434	—	2	2	no	—
19	C₂×C₄×C₁₅₇	—	2	1	no	—
20	C₂×C₄×C₁₅₇	—	4	1	no	—
21	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂²×C₁₅₇	#100	1	1	yes	characteristic
23	C₂×D₁₅₇	—	8	2	no	—
24	C₂×D₁₅₇	—	8	1	no	—
25	C₄×C₁₅₇	—	4	1	no	—
26	C₄×C₁₅₇	—	8	1	no	—
27	C₄×C₁₅₇	#104	1	2	yes	—
28	C₂×C₁₅₇	—	2	1	no	—
29	C₂×C₁₅₇	#329	1	1	yes	characteristic
30	D₁₅₇	—	16	1	no	—
31	C₁₅₇	#1355	1	1	yes	characteristic, complemented, Sylow
32	#1355	—	157	1	no	maximal, Sylow
33	#490	—	157	1	no	—
34	#347	—	157	2	no	—
35	#127	—	157	1	no	—
36	#125	#10597845	1	1	yes	characteristic
37	M₃₂	—	314	2	no	—
38	#102	—	314	2	no	—
39	#97	—	157	1	no	—
40	C₂×D₄	—	314	1	no	—
41	C₂×D₄	—	628	1	no	—
42	C₂×C₈	—	157	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×#10597845	1	1	yes	characteristic
46	C₁₆	—	314	4	no	—
47	C₂³	—	628	1	no	—
48	D₄	—	628	2	no	—
49	D₄	—	1256	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊#10597845	1	1	yes	characteristic
53	C₈	—	314	2	no	—
54	C₂²	—	1256	2	no	—
55	C₂²	—	1256	1	no	—
56	C₂²	#19097831	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#19097836	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	2512	1	no	—
62	C₂	#23758129	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23758129
commutator	C₄²×C₁₅₇	C₂×C₄
Frattini	C₄²	C₂×#10597845
Fitting	#125×C₁₅₇	C₄
socle	C₂×C₁₅₇	#329
prime radical	#19097768	C₄
cosocle	#19097682	C₂²
hypercenter	#125	#10597845
hypocenter	C₁₅₇	#1355
LCS	G ▷ C₄²×C₁₅₇ ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #23758165	C₂	semidirect
31. C₁₅₇	#1355	semidirect

Maximal subgroups

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

subgroup	index
#23758165	2
#23757639	2
#1355	157