Subgroups — C₂×D₃₂×C₁₅₇ #34096617

Order 20096.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×C₁₅₇	C₂	1	2	yes	maximal, complemented
2	D₃₂×C₁₅₇	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₁₅₇	—	2	2	no	—
5	D₁₆×C₁₅₇	—	2	2	no	—
6	D₁₆×C₁₅₇	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₁₅₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₅₇	C₂²	1	2	yes	complemented
9	C₂×D₄×C₁₅₇	—	4	2	no	—
10	D₈×C₁₅₇	—	2	4	no	—
11	D₈×C₁₅₇	—	4	2	no	—
12	C₂×C₈×C₁₅₇	D₄	1	1	yes	characteristic
13	C₁₆×C₁₅₇	D₄	1	1	yes	characteristic
14	C₁₆×C₁₅₇	C₂³	1	1	yes	characteristic
15	C₂³×C₁₅₇	—	8	2	no	—
16	D₄×C₁₅₇	—	4	4	no	—
17	D₄×C₁₅₇	—	8	2	no	—
18	C₂×C₄×C₁₅₇	D₈	1	1	yes	characteristic
19	C₈×C₁₅₇	D₈	1	1	yes	characteristic
20	C₈×C₁₅₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₁₅₇	—	8	4	no	—
22	C₂²×C₁₅₇	—	16	4	no	—
23	C₂²×C₁₅₇	D₁₆	1	1	yes	characteristic
24	C₄×C₁₅₇	D₁₆	1	1	yes	characteristic
25	C₄×C₁₅₇	C₂×D₈	1	1	yes	characteristic
26	C₂×C₁₅₇	—	16	4	no	—
27	C₂×C₁₅₇	D₃₂	1	2	yes	direct product factor
28	C₂×C₁₅₇	C₂×D₁₆	1	1	yes	characteristic
29	C₁₅₇	C₂×D₃₂	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₃₂	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×D₁₆	C₂×C₁₅₇	1	2	yes	complemented
32	D₃₂	C₂×C₁₅₇	1	4	yes	direct product factor
33	C₂×C₃₂	C₂×C₁₅₇	1	1	yes	characteristic, complemented
34	C₂×D₈	—	2	2	no	—
35	D₁₆	—	2	2	no	—
36	D₁₆	C₂²×C₁₅₇	1	4	yes	complemented
37	C₂×C₁₆	C₂²×C₁₅₇	1	1	yes	characteristic
38	C₃₂	C₂²×C₁₅₇	1	2	yes	complemented
39	C₂×D₄	—	4	2	no	—
40	D₈	—	2	4	no	—
41	D₈	—	4	2	no	—
42	C₂×C₈	D₄×C₁₅₇	1	1	yes	characteristic
43	C₁₆	D₄×C₁₅₇	1	1	yes	characteristic
44	C₁₆	C₂³×C₁₅₇	1	1	yes	characteristic
45	C₂³	—	8	2	no	—
46	D₄	—	4	4	no	—
47	D₄	—	8	2	no	—
48	C₂×C₄	D₈×C₁₅₇	1	1	yes	characteristic
49	C₈	D₈×C₁₅₇	1	1	yes	characteristic
50	C₈	C₂×D₄×C₁₅₇	1	1	yes	characteristic
51	C₂²	—	8	4	no	—
52	C₂²	—	16	4	no	—
53	C₂²	D₁₆×C₁₅₇	1	1	yes	characteristic
54	C₄	D₁₆×C₁₅₇	1	1	yes	characteristic
55	C₄	C₂×D₈×C₁₅₇	1	1	yes	characteristic
56	C₂	—	16	4	no	—
57	C₂	D₃₂×C₁₅₇	1	2	yes	direct product factor
58	C₂	C₂×D₁₆×C₁₅₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₇	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₁₅₇
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₇ ◁ C₂×C₄×C₁₅₇ ◁ C₂×C₈×C₁₅₇ ◁ C₂×C₁₆×C₁₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₆×C₁₅₇	C₂	semidirect
2. D₃₂×C₁₅₇	C₂	direct (N × H)
3. C₂×C₃₂×C₁₅₇	C₂	semidirect
6. D₁₆×C₁₅₇	C₂²	semidirect
8. C₃₂×C₁₅₇	C₂²	semidirect
27. C₂×C₁₅₇	D₃₂	direct (N × H)
29. C₁₅₇	C₂×D₃₂	direct (N × H)
30. C₂×D₃₂	C₁₅₇	direct (N × H)
31. C₂×D₁₆	C₂×C₁₅₇	semidirect
32. D₃₂	C₂×C₁₅₇	direct (N × H)
33. C₂×C₃₂	C₂×C₁₅₇	semidirect
36. D₁₆	C₂²×C₁₅₇	semidirect
38. C₃₂	C₂²×C₁₅₇	semidirect
57. C₂	D₃₂×C₁₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₆×C₁₅₇	2
D₃₂×C₁₅₇	2
C₂×C₃₂×C₁₅₇	2
C₂×D₃₂	157

Subgroups — C2×D32×C157 #34096617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₂×C₁₅₇ #34096617