Subgroups — C₂×C₃²×D₁₃₁⋊C₅ #37556091

Order 23580.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₁₃₁⋊C₅
commutator, cosocle, hypocenter	C₁₃₁	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃₁	C₂×C₅
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₁₃₁⋊C₅	C₂	semidirect
2. C₃²×D₁₃₁⋊C₅	C₂	direct (N × H)
3. C₂×C₃×D₁₃₁⋊C₅	C₃	direct (N × H)
4. C₃²×C₁₃₁⋊C₅	C₂²	semidirect
5. C₂×C₃²×D₁₃₁	C₅	semidirect
6. C₃×D₁₃₁⋊C₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₁₃₁⋊C₅	C₂×C₃	semidirect
8. C₂×D₁₃₁⋊C₅	C₃²	direct (N × H)
9. C₃²×D₁₃₁	C₂×C₅	semidirect
10. C₂×C₃²×C₁₃₁	C₂×C₅	semidirect
11. C₃×C₁₃₁⋊C₅	C₂²×C₃	semidirect
12. C₂×C₃×D₁₃₁	C₃×C₅	semidirect
13. C₂×C₁₃₁⋊C₅	C₂×C₃²	semidirect
14. D₁₃₁⋊C₅	C₂×C₃²	direct (N × H)
15. C₃²×C₁₃₁	C₂²×C₅	semidirect
16. C₂×C₃×C₁₃₁	C₂×C₃×C₅	semidirect
17. C₃×D₁₃₁	C₂×C₃×C₅	semidirect
18. C₁₃₁⋊C₅	C₂²×C₃²	semidirect
19. C₂×D₁₃₁	C₃²×C₅	semidirect
20. C₃×C₁₃₁	C₂²×C₃×C₅	semidirect
21. C₂×C₁₃₁	C₂×C₃²×C₅	semidirect
22. D₁₃₁	C₂×C₃²×C₅	semidirect
24. C₁₃₁	C₂²×C₃²×C₅	semidirect
34. C₂×C₃²	D₁₃₁⋊C₅	direct (N × H)
39. C₃²	C₂×D₁₃₁⋊C₅	direct (N × H)
41. C₂×C₃	C₃×D₁₃₁⋊C₅	direct (N × H)
44. C₃	C₂×C₃×D₁₃₁⋊C₅	direct (N × H)
46. C₂	C₃²×D₁₃₁⋊C₅	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×C₃²×C₁₃₁⋊C₅	2
C₃²×D₁₃₁⋊C₅	2
C₂×C₃×D₁₃₁⋊C₅	3
C₂×C₃²×D₁₃₁	5
C₂²×C₃²×C₅	131

Subgroups — C2×C32×D131⋊C5 #37556091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₁₃₁⋊C₅ #37556091