Subgroups — C₃²×Dic₁₃₁⋊C₅ #37556065

Order 23580.

72 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
2	C₃×Dic₁₃₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₃₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×Dic₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₁₃₁⋊C₅	C₂×C₃	1	4	yes	—
6	Dic₁₃₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₁₃₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₁₃₁⋊C₅	C₃×C₄	1	4	yes	complemented
9	C₃×Dic₁₃₁	C₃×C₅	1	4	yes	complemented
10	C₂×C₁₃₁⋊C₅	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₁₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₃₁	C₂×C₃×C₅	1	4	yes	—
13	C₁₃₁⋊C₅	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	Dic₁₃₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₃₁	C₃×C₄×C₅	1	4	yes	complemented
16	C₂×C₁₃₁	C₂×C₃²×C₅	1	1	yes	characteristic
17	C₃²×C₄×C₅	—	131	1	no	maximal, Hall
18	C₁₃₁	C₃²×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₅	—	131	1	no	—
20	C₃×C₄×C₅	—	131	4	no	—
21	C₃²×C₅	—	131	1	no	Hall
22	C₃²×C₄	—	131	1	no	Hall
23	C₂×C₃×C₅	—	131	4	no	—
24	C₄×C₅	—	131	1	no	Hall
25	C₂×C₃²	D₁₃₁⋊C₅	1	1	yes	characteristic
26	C₃×C₅	—	131	4	no	—
27	C₃×C₄	—	131	4	no	—
28	C₂×C₅	—	131	1	no	—
29	C₃²	Dic₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₃×D₁₃₁⋊C₅	1	4	yes	—
31	C₅	—	131	1	no	Sylow
32	C₄	—	131	1	no	Sylow
33	C₃	C₃×Dic₁₃₁⋊C₅	1	4	yes	direct product factor
34	C₂	C₃²×D₁₃₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₁₃₁⋊C₅
commutator, hypocenter	C₁₃₁	C₃²×C₄×C₅
Frattini	C₂	C₃²×D₁₃₁⋊C₅
Fitting, socle	C₂×C₃²×C₁₃₁	C₂×C₅
prime radical	C₂×C₃²×C₁₃₁⋊C₅	C₂
cosocle	C₂×C₁₃₁	C₂×C₃²×C₅
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₁₃₁⋊C₅	C₃	direct (N × H)
3. C₃²×C₁₃₁⋊C₅	C₄	semidirect
4. C₃²×Dic₁₃₁	C₅	semidirect
6. Dic₁₃₁⋊C₅	C₃²	direct (N × H)
8. C₃×C₁₃₁⋊C₅	C₃×C₄	semidirect
9. C₃×Dic₁₃₁	C₃×C₅	semidirect
11. C₃²×C₁₃₁	C₄×C₅	semidirect
13. C₁₃₁⋊C₅	C₃²×C₄	semidirect
14. Dic₁₃₁	C₃²×C₅	semidirect
15. C₃×C₁₃₁	C₃×C₄×C₅	semidirect
18. C₁₃₁	C₃²×C₄×C₅	semidirect
29. C₃²	Dic₁₃₁⋊C₅	direct (N × H)
33. C₃	C₃×Dic₁₃₁⋊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
C₃×Dic₁₃₁⋊C₅	3
C₃²×Dic₁₃₁	5
C₃²×C₄×C₅	131

Subgroups — C32×Dic131⋊C5 #37556065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Dic₁₃₁⋊C₅ #37556065