Subgroups — C₅×C₃⋊D₃×D₁₃₁ #37556124

Order 23580.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊D₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊D₃₉₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×D₁₃₁	—	3	4	no	maximal
5	C₃²×C₅×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×D₁₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₃₉₃	—	3	4	no	—
8	C₅×D₃×C₁₃₁	—	3	4	no	—
9	C₃×C₅×D₁₃₁	D₃	1	4	yes	complemented
10	C₂×C₅×D₁₃₁	—	9	1	no	Hall
11	C₃⋊D₃₉₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃⋊D₃×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃²×D₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₁₃₁	C₂×D₃	1	4	yes	complemented
15	D₃×D₁₃₁	—	3	4	no	—
16	C₂×C₅×C₁₃₁	—	9	1	no	—
17	C₅×D₁₃₁	—	9	1	no	—
18	C₅×D₁₃₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	C₃²×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	D₃₉₃	—	3	4	no	—
21	C₃×D₁₃₁	C₅×D₃	1	4	yes	complemented
22	D₃×C₁₃₁	—	3	4	no	—
23	C₅×C₁₃₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₃₁	—	9	1	no	Hall
25	C₃×C₁₃₁	C₂×C₅×D₃	1	4	yes	complemented
26	C₂×C₁₃₁	—	9	1	no	—
27	D₁₃₁	—	9	1	no	—
28	D₁₃₁	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
29	C₂×C₅×C₃⋊D₃	—	131	1	no	maximal, Hall
30	C₁₃₁	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃²×C₅	—	131	1	no	—
32	C₅×C₃⋊D₃	—	131	1	no	—
33	C₅×C₃⋊D₃	D₁₃₁	1	1	yes	characteristic, direct product factor
34	C₂×C₅×D₃	—	393	4	no	—
35	C₃²×C₅	C₂×D₁₃₁	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃⋊D₃	—	131	1	no	Hall
37	C₂×C₃×C₅	—	131	4	no	—
38	C₅×D₃	—	3	4	no	—
39	C₅×D₃	—	393	4	no	—
40	C₂²×C₅	—	1179	1	no	Hall
41	C₂×C₃²	—	131	1	no	—
42	C₃⋊D₃	—	131	1	no	—
43	C₃⋊D₃	C₅×D₁₃₁	1	1	yes	characteristic, direct product factor
44	C₃×C₅	D₃×D₁₃₁	1	4	yes	complemented
45	C₂×D₃	—	393	4	no	—
46	C₂×C₅	—	9	1	no	—
47	C₂×C₅	—	131	1	no	—
48	C₂×C₅	—	1179	1	no	—
49	C₃²	C₂×C₅×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	131	4	no	—
51	D₃	—	3	4	no	—
52	D₃	—	393	4	no	—
53	C₅	C₃⋊D₃×D₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	1179	1	no	Sylow
55	C₃	C₅×D₃×D₁₃₁	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	131	1	no	—
58	C₂	—	1179	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₃×D₁₃₁
commutator, cosocle, hypocenter	C₃²×C₁₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃₁	C₂²
LCS	G ▷ C₃²×C₁₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×D₁₃₁	C₂	semidirect
2. C₅×C₃⋊D₃×C₁₃₁	C₂	semidirect
3. C₅×C₃⋊D₃₉₃	C₂	semidirect
5. C₃²×C₅×C₁₃₁	C₂²	semidirect
6. C₃⋊D₃×D₁₃₁	C₅	direct (N × H)
9. C₃×C₅×D₁₃₁	D₃	semidirect
11. C₃⋊D₃₉₃	C₂×C₅	semidirect
12. C₃⋊D₃×C₁₃₁	C₂×C₅	semidirect
13. C₃²×D₁₃₁	C₂×C₅	semidirect
14. C₃×C₅×C₁₃₁	C₂×D₃	semidirect
18. C₅×D₁₃₁	C₃⋊D₃	direct (N × H)
19. C₃²×C₁₃₁	C₂²×C₅	semidirect
21. C₃×D₁₃₁	C₅×D₃	semidirect
23. C₅×C₁₃₁	C₂×C₃⋊D₃	semidirect
25. C₃×C₁₃₁	C₂×C₅×D₃	semidirect
28. D₁₃₁	C₅×C₃⋊D₃	direct (N × H)
30. C₁₃₁	C₂×C₅×C₃⋊D₃	semidirect
33. C₅×C₃⋊D₃	D₁₃₁	direct (N × H)
35. C₃²×C₅	C₂×D₁₃₁	semidirect
43. C₃⋊D₃	C₅×D₁₃₁	direct (N × H)
44. C₃×C₅	D₃×D₁₃₁	semidirect
49. C₃²	C₂×C₅×D₁₃₁	semidirect
53. C₅	C₃⋊D₃×D₁₃₁	direct (N × H)
55. C₃	C₅×D₃×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₁₃₁	2
C₅×C₃⋊D₃×C₁₃₁	2
C₅×C₃⋊D₃₉₃	2
C₅×D₃×D₁₃₁	3
C₃⋊D₃×D₁₃₁	5
C₂×C₅×C₃⋊D₃	131

Subgroups — C5×C3⋊D3×D131 #37556124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₃×D₁₃₁ #37556124