Subgroups — C₉×Dic₁₃₁⋊C₅ #37556035

Order 23580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×Dic₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₁₃₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	Dic₁₃₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₃₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₁₃₁⋊C₅	C₃×C₄	1	1	yes	characteristic
9	C₃×Dic₁₃₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₁₃₁⋊C₅	C₂×C₉	1	1	yes	characteristic
11	C₉×C₁₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₃₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₁₃₁⋊C₅	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	Dic₁₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₃₁	C₃×C₄×C₅	1	1	yes	characteristic
16	C₂×C₁₃₁	C₂×C₅×C₉	1	1	yes	characteristic
17	C₄×C₅×C₉	—	131	1	no	maximal, Hall
18	C₁₃₁	C₄×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×C₉	—	131	1	no	—
20	C₃×C₄×C₅	—	131	1	no	—
21	C₅×C₉	—	131	1	no	Hall
22	C₄×C₉	—	131	1	no	Hall
23	C₂×C₃×C₅	—	131	1	no	—
24	C₄×C₅	—	131	1	no	Hall
25	C₂×C₉	D₁₃₁⋊C₅	1	1	yes	characteristic
26	C₃×C₅	—	131	1	no	—
27	C₃×C₄	—	131	1	no	—
28	C₂×C₅	—	131	1	no	—
29	C₉	Dic₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₃×D₁₃₁⋊C₅	1	1	yes	characteristic
31	C₅	—	131	1	no	Sylow
32	C₄	—	131	1	no	Sylow
33	C₃	C₃×Dic₁₃₁⋊C₅	1	1	yes	characteristic
34	C₂	C₉×D₁₃₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₃₁⋊C₅
commutator, hypocenter	C₁₃₁	C₄×C₅×C₉
Frattini	C₂×C₃	C₃×D₁₃₁⋊C₅
Fitting	C₂×C₉×C₁₃₁	C₂×C₅
socle, cosocle	C₂×C₃×C₁₃₁	C₂×C₃×C₅
prime radical	C₂×C₃×C₁₃₁⋊C₅	C₂×C₃
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃₁⋊C₅	C₄	semidirect
4. C₉×Dic₁₃₁	C₅	semidirect
6. Dic₁₃₁⋊C₅	C₉	direct (N × H)
11. C₉×C₁₃₁	C₄×C₅	semidirect
13. C₁₃₁⋊C₅	C₄×C₉	semidirect
14. Dic₁₃₁	C₅×C₉	semidirect
18. C₁₃₁	C₄×C₅×C₉	semidirect
29. C₉	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×C₉×C₁₃₁⋊C₅	2
C₃×Dic₁₃₁⋊C₅	3
C₉×Dic₁₃₁	5
C₄×C₅×C₉	131

Subgroups — C9×Dic131⋊C5 #37556035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₁₃₁⋊C₅ #37556035