Subgroups — C₅×#20266783 #45656406

Order 32580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#13108658	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₈₁⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₅×#13108658	C₄	1	1	yes	characteristic, complemented, Hall
4	#20266783	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₈₁⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₅×Dic₁₈₁	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×#13108658	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₈₁⋊C₃	C₃×C₄	1	1	yes	characteristic
9	Dic₁₈₁⋊C₃	C₃×C₅	1	1	yes	characteristic
10	C₂×C₅×C₁₈₁	C₂×C₉	1	1	yes	characteristic
11	#13108658	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₈₁⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×C₁₈₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	Dic₁₈₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₁₈₁⋊C₃	C₃×C₄×C₅	1	1	yes	characteristic
16	C₂×C₁₈₁	C₂×C₅×C₉	1	1	yes	characteristic
17	C₁₈₁	C₄×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅×C₉	—	181	1	no	maximal, Hall
19	C₂×C₅×C₉	—	181	1	no	—
20	C₃×C₄×C₅	—	181	1	no	—
21	C₅×C₉	—	181	1	no	Hall
22	C₄×C₉	—	181	1	no	Hall
23	C₂×C₃×C₅	—	181	1	no	—
24	C₄×C₅	—	181	1	no	Hall
25	C₂×C₉	—	181	1	no	—
26	C₃×C₅	—	181	1	no	—
27	C₃×C₄	—	181	1	no	—
28	C₂×C₅	#13108658⋊C₂	1	1	yes	characteristic
29	C₉	—	181	1	no	Sylow
30	C₂×C₃	—	181	1	no	—
31	C₅	#20266783	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	—	181	1	no	Sylow
33	C₃	—	181	1	no	—
34	C₂	C₅×#13108658⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	#13108658⋊C₂
commutator, hypocenter	C₁₈₁	C₄×C₅×C₉
Frattini	C₂	C₅×#13108658⋊C₂
Fitting, socle	C₂×C₅×C₁₈₁	C₂×C₉
prime radical	C₂×C₅×C₁₈₁⋊C₃	C₂×C₃
cosocle	C₂×C₁₈₁⋊C₃	C₂×C₃×C₅
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×#13108658	C₄	semidirect
4. #20266783	C₅	direct (N × H)
6. C₅×Dic₁₈₁	C₉	semidirect
11. #13108658	C₄×C₅	semidirect
13. C₅×C₁₈₁	C₄×C₉	semidirect
14. Dic₁₈₁	C₅×C₉	semidirect
17. C₁₈₁	C₄×C₅×C₉	semidirect
31. C₅	#20266783	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×C₅×#13108658	2
C₅×Dic₁₈₁⋊C₃	3
#20266783	5
C₄×C₅×C₉	181

Subgroups — C5×#20266783 #45656406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20266783 #45656406