Subgroups — C₂×D₁₅×C₁₅₇⋊C₃ #43246346

Order 28260.

88 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, complemented
2	D₁₅×C₁₅₇⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₁₅×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₁₅₇⋊C₃	—	3	1	no	maximal
5	C₃×C₅×C₁₅₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₁₅₇⋊C₃	—	5	1	no	maximal, Hall
7	D₅×C₁₅₇⋊C₃	—	3	2	no	—
8	D₁₅×C₁₅₇	C₂×C₃	1	2	yes	complemented
9	C₂×C₅×C₁₅₇⋊C₃	—	2	1	no	—
10	C₂×C₅×C₁₅₇⋊C₃	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×D₅×C₁₅₇	—	3	1	no	Hall
13	C₂×C₃×C₁₅₇⋊C₃	D₅	1	1	yes	characteristic, complemented
14	D₃×C₁₅₇⋊C₃	—	5	2	no	—
15	C₃×C₅×C₁₅₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₅×C₁₅₇⋊C₃	—	2	1	no	—
17	C₅×C₁₅₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×D₃×C₁₅₇	—	5	1	no	—
19	C₂²×C₁₅₇⋊C₃	—	15	1	no	—
20	C₂×C₅×C₁₅₇	C₃×D₃	1	1	yes	characteristic, complemented
21	D₅×C₁₅₇	—	3	2	no	—
22	C₃×C₁₅₇⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₁₅₇	C₃×D₅	1	1	yes	characteristic, complemented
24	D₃×C₁₅₇	—	5	2	no	—
25	C₂×C₁₅₇⋊C₃	—	2	1	no	—
26	C₂×C₁₅₇⋊C₃	—	15	2	no	—
27	C₂×C₁₅₇⋊C₃	D₁₅	1	1	yes	characteristic, direct product factor
28	C₅×C₁₅₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₁₅₇	—	15	1	no	Hall
30	C₃×C₁₅₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
31	C₁₅₇⋊C₃	—	2	1	no	—
32	C₁₅₇⋊C₃	C₂×D₁₅	1	1	yes	characteristic, direct product factor
33	C₂×C₁₅₇	—	15	2	no	—
34	C₂×C₁₅₇	C₃×D₁₅	1	1	yes	characteristic, complemented
35	C₂×C₃×D₁₅	—	157	1	no	maximal, Hall
36	C₁₅₇	C₂×C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²×C₅	—	157	1	no	—
38	C₃×D₁₅	—	157	2	no	—
39	C₂×D₁₅	C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×D₅	—	471	1	no	—
41	C₃²×C₅	—	157	1	no	Hall
42	C₂×C₃×D₃	—	785	1	no	Hall
43	C₂×C₃×C₅	—	314	1	no	—
44	C₂×C₃×C₅	—	157	1	no	—
45	C₂×C₃×C₅	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
46	D₁₅	C₂×C₁₅₇⋊C₃	1	2	yes	direct product factor
47	C₃×D₅	—	471	2	no	—
48	C₂×D₅	—	3	1	no	Hall
49	C₂×C₃²	—	157	1	no	—
50	C₃×D₃	—	785	2	no	—
51	C₃×C₅	—	314	1	no	—
52	C₃×C₅	—	157	1	no	—
53	C₃×C₅	C₂²×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	2355	1	no	—
55	C₂×D₃	—	5	1	no	—
56	C₂×C₅	D₃×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
57	D₅	—	3	2	no	—
58	C₃²	—	157	1	no	Sylow
59	C₂×C₃	—	2355	2	no	—
60	C₂×C₃	—	314	1	no	—
61	C₂×C₃	—	157	1	no	—
62	C₂×C₃	D₅×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
63	D₃	—	5	2	no	—
64	C₅	C₂×D₃×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	15	1	no	Sylow
66	C₃	—	314	1	no	—
67	C₃	—	157	1	no	—
68	C₃	C₂×D₅×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
69	C₂	—	15	2	no	—
70	C₂	D₁₅×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₅×C₁₅₇⋊C₃
commutator, cosocle, hypocenter	C₃×C₅×C₁₅₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₅₇	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₅₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₁₅₇⋊C₃	C₂	semidirect
2. D₁₅×C₁₅₇⋊C₃	C₂	direct (N × H)
3. C₂×D₁₅×C₁₅₇	C₃	semidirect
5. C₃×C₅×C₁₅₇⋊C₃	C₂²	semidirect
8. D₁₅×C₁₅₇	C₂×C₃	semidirect
10. C₂×C₅×C₁₅₇⋊C₃	D₃	semidirect
11. C₂×C₃×C₅×C₁₅₇	C₂×C₃	semidirect
13. C₂×C₃×C₁₅₇⋊C₃	D₅	semidirect
15. C₃×C₅×C₁₅₇	C₂²×C₃	semidirect
17. C₅×C₁₅₇⋊C₃	C₂×D₃	semidirect
20. C₂×C₅×C₁₅₇	C₃×D₃	semidirect
22. C₃×C₁₅₇⋊C₃	C₂×D₅	semidirect
23. C₂×C₃×C₁₅₇	C₃×D₅	semidirect
27. C₂×C₁₅₇⋊C₃	D₁₅	direct (N × H)
28. C₅×C₁₅₇	C₂×C₃×D₃	semidirect
30. C₃×C₁₅₇	C₂×C₃×D₅	semidirect
32. C₁₅₇⋊C₃	C₂×D₁₅	direct (N × H)
34. C₂×C₁₅₇	C₃×D₁₅	semidirect
36. C₁₅₇	C₂×C₃×D₁₅	semidirect
39. C₂×D₁₅	C₁₅₇⋊C₃	direct (N × H)
45. C₂×C₃×C₅	C₂×C₁₅₇⋊C₃	semidirect
46. D₁₅	C₂×C₁₅₇⋊C₃	direct (N × H)
53. C₃×C₅	C₂²×C₁₅₇⋊C₃	semidirect
56. C₂×C₅	D₃×C₁₅₇⋊C₃	semidirect
62. C₂×C₃	D₅×C₁₅₇⋊C₃	semidirect
64. C₅	C₂×D₃×C₁₅₇⋊C₃	semidirect
68. C₃	C₂×D₅×C₁₅₇⋊C₃	semidirect
70. C₂	D₁₅×C₁₅₇⋊C₃	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×C₃×C₅×C₁₅₇⋊C₃	2
D₁₅×C₁₅₇⋊C₃	2
C₂×D₁₅×C₁₅₇	3
C₂×D₅×C₁₅₇⋊C₃	3
C₂×D₃×C₁₅₇⋊C₃	5
C₂×C₃×D₁₅	157

Subgroups — C2×D15×C157⋊C3 #43246346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₅×C₁₅₇⋊C₃ #43246346