Subgroups — C₁₃₁×Dic₄₅ #37556033

Order 23580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	Dic₁₅×C₁₃₁	—	3	1	no	maximal
3	C₅×C₉×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₉×C₁₃₁	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₃₁	D₃	1	1	yes	characteristic
6	Dic₅×C₁₃₁	—	9	1	no	Hall
7	C₂×C₉×C₁₃₁	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₃₁	Dic₃	1	1	yes	characteristic
9	Dic₃×C₁₃₁	—	15	1	no	—
10	C₂×C₅×C₁₃₁	D₉	1	1	yes	characteristic
11	C₉×C₁₃₁	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₃₁	D₁₅	1	1	yes	characteristic
13	C₅×C₁₃₁	Dic₉	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₃₁	—	45	1	no	Hall
15	C₃×C₁₃₁	Dic₁₅	1	1	yes	characteristic
16	C₂×C₁₃₁	D₄₅	1	1	yes	characteristic
17	Dic₄₅	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₃₁	Dic₄₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅×C₉	C₂×C₁₃₁	1	1	yes	characteristic
20	Dic₁₅	—	3	1	no	—
21	C₅×C₉	C₄×C₁₃₁	1	1	yes	characteristic, complemented, Hall
22	Dic₉	—	5	1	no	Hall
23	C₂×C₃×C₅	D₃×C₁₃₁	1	1	yes	characteristic
24	Dic₅	—	9	1	no	Hall
25	C₂×C₉	D₅×C₁₃₁	1	1	yes	characteristic
26	C₃×C₅	Dic₃×C₁₃₁	1	1	yes	characteristic
27	Dic₃	—	15	1	no	—
28	C₂×C₅	D₉×C₁₃₁	1	1	yes	characteristic
29	C₉	Dic₅×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	D₁₅×C₁₃₁	1	1	yes	characteristic
31	C₅	Dic₉×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	45	1	no	Sylow
33	C₃	Dic₁₅×C₁₃₁	1	1	yes	characteristic
34	C₂	D₄₅×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃₁	D₄₅
commutator, hypocenter	C₅×C₉	C₄×C₁₃₁
Frattini	C₂×C₃	D₁₅×C₁₃₁
Fitting	C₂×C₅×C₉×C₁₃₁	C₂
socle, prime radical	C₂×C₃×C₅×C₁₃₁	D₃
cosocle	C₂×C₅×C₉	C₂×C₁₃₁
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₁₃₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃₁	C₄	semidirect
11. C₉×C₁₃₁	Dic₅	semidirect
13. C₅×C₁₃₁	Dic₉	semidirect
17. Dic₄₅	C₁₃₁	direct (N × H)
18. C₁₃₁	Dic₄₅	direct (N × H)
21. C₅×C₉	C₄×C₁₃₁	semidirect
29. C₉	Dic₅×C₁₃₁	semidirect
31. C₅	Dic₉×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉×C₁₃₁	2
Dic₁₅×C₁₃₁	3
Dic₉×C₁₃₁	5
Dic₄₅	131

Subgroups — C131×Dic45 #37556033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×Dic₄₅ #37556033