Subgroups — Dic₁₅×C₁₅₇⋊C₃ #43246306

Order 28260.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₅×C₁₅₇⋊C₃	—	3	1	no	maximal
3	Dic₁₅×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×C₁₅₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	Dic₃×C₁₅₇⋊C₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₅₇⋊C₃	—	2	1	no	—
7	C₂×C₅×C₁₅₇⋊C₃	D₃	1	1	yes	characteristic
8	C₂×C₃×C₅×C₁₅₇	C₂×C₃	1	1	yes	characteristic
9	Dic₅×C₁₅₇	—	3	1	no	Hall
10	C₂×C₃×C₁₅₇⋊C₃	D₅	1	1	yes	characteristic
11	C₃×C₅×C₁₅₇	C₃×C₄	1	1	yes	characteristic, complemented
12	C₅×C₁₅₇⋊C₃	—	2	1	no	—
13	C₅×C₁₅₇⋊C₃	Dic₃	1	1	yes	characteristic, complemented
14	Dic₃×C₁₅₇	—	5	1	no	—
15	C₄×C₁₅₇⋊C₃	—	15	1	no	—
16	C₂×C₅×C₁₅₇	C₃×D₃	1	1	yes	characteristic
17	C₃×C₁₅₇⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₅₇	C₃×D₅	1	1	yes	characteristic
19	C₂×C₁₅₇⋊C₃	—	2	1	no	—
20	C₂×C₁₅₇⋊C₃	D₁₅	1	1	yes	characteristic
21	C₅×C₁₅₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	C₄×C₁₅₇	—	15	1	no	Hall
23	C₃×C₁₅₇	C₃×Dic₅	1	1	yes	characteristic, complemented
24	C₁₅₇⋊C₃	—	2	1	no	—
25	C₁₅₇⋊C₃	Dic₁₅	1	1	yes	characteristic, direct product factor
26	C₂×C₁₅₇	C₃×D₁₅	1	1	yes	characteristic
27	C₃×Dic₁₅	—	157	1	no	maximal, Hall
28	C₁₅₇	C₃×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²×C₅	—	157	1	no	—
30	Dic₁₅	C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃×Dic₅	—	471	1	no	—
32	C₃²×C₅	—	157	1	no	Hall
33	C₃×Dic₃	—	785	1	no	Hall
34	C₂×C₃×C₅	—	314	1	no	—
35	C₂×C₃×C₅	—	157	1	no	—
36	C₂×C₃×C₅	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic
37	Dic₅	—	3	1	no	Hall
38	C₂×C₃²	—	157	1	no	—
39	C₃×C₅	—	314	1	no	—
40	C₃×C₅	—	157	1	no	—
41	C₃×C₅	C₄×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
42	C₃×C₄	—	2355	1	no	—
43	Dic₃	—	5	1	no	—
44	C₂×C₅	D₃×C₁₅₇⋊C₃	1	1	yes	characteristic
45	C₃²	—	157	1	no	Sylow
46	C₂×C₃	—	314	1	no	—
47	C₂×C₃	—	157	1	no	—
48	C₂×C₃	D₅×C₁₅₇⋊C₃	1	1	yes	characteristic
49	C₅	Dic₃×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	15	1	no	Sylow
51	C₃	—	314	1	no	—
52	C₃	—	157	1	no	—
53	C₃	Dic₅×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂	D₁₅×C₁₅₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₅×C₁₅₇⋊C₃
commutator, hypocenter	C₃×C₅×C₁₅₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₅×C₁₅₇	C₂×C₃
prime radical	C₂×C₃×C₅×C₁₅₇⋊C₃	C₂
LCS	G ▷ C₃×C₅×C₁₅₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. Dic₁₅×C₁₅₇	C₃	semidirect
4. C₃×C₅×C₁₅₇⋊C₃	C₄	semidirect
11. C₃×C₅×C₁₅₇	C₃×C₄	semidirect
13. C₅×C₁₅₇⋊C₃	Dic₃	semidirect
17. C₃×C₁₅₇⋊C₃	Dic₅	semidirect
21. C₅×C₁₅₇	C₃×Dic₃	semidirect
23. C₃×C₁₅₇	C₃×Dic₅	semidirect
25. C₁₅₇⋊C₃	Dic₁₅	direct (N × H)
28. C₁₅₇	C₃×Dic₁₅	semidirect
30. Dic₁₅	C₁₅₇⋊C₃	direct (N × H)
41. C₃×C₅	C₄×C₁₅₇⋊C₃	semidirect
49. C₅	Dic₃×C₁₅₇⋊C₃	semidirect
53. C₃	Dic₅×C₁₅₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₅₇⋊C₃	2
Dic₅×C₁₅₇⋊C₃	3
Dic₁₅×C₁₅₇	3
Dic₃×C₁₅₇⋊C₃	5
C₃×Dic₁₅	157

Subgroups — Dic15×C157⋊C3 #43246306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₅×C₁₅₇⋊C₃ #43246306