Subgroups — C₂×C₅×#13108656⋊C₂ #45656367

Order 32580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#13108656⋊C₂	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#13108656	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₁₈₁	C₃	1	1	yes	maximal, characteristic
4	C₅×#13108656	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#13108656⋊C₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×D₁₈₁	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₈₁	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×D₁₈₁	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×#13108656	C₂×C₅	1	1	yes	characteristic, complemented
10	#13108656⋊C₂	C₂×C₅	1	2	yes	direct product factor
11	C₃×C₅×C₁₈₁	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×D₁₈₁	C₃×C₅	1	1	yes	characteristic
13	C₂×C₅×C₁₈₁	C₂×C₉	1	1	yes	characteristic, complemented
14	C₅×D₁₈₁	C₂×C₉	1	2	yes	complemented
15	#13108656	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₈₁	C₂×C₃×C₅	1	1	yes	characteristic
17	C₃×D₁₈₁	C₂×C₃×C₅	1	2	yes	—
18	C₅×C₁₈₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₈₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₈₁	C₂²×C₃×C₅	1	1	yes	characteristic
21	C₂×C₁₈₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented
22	D₁₈₁	C₂×C₅×C₉	1	2	yes	complemented
23	C₁₈₁	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₅×C₉	—	181	1	no	maximal, Hall
25	C₂×C₅×C₉	—	181	2	no	—
26	C₂×C₅×C₉	—	181	1	no	—
27	C₂²×C₃×C₅	—	181	1	no	—
28	C₅×C₉	—	181	1	no	Hall
29	C₂²×C₉	—	181	1	no	Hall
30	C₂×C₃×C₅	—	181	2	no	—
31	C₂×C₃×C₅	D₁₈₁⋊C₃	1	1	yes	characteristic
32	C₂²×C₅	—	181	1	no	Hall
33	C₂×C₉	—	181	2	no	—
34	C₂×C₉	—	181	1	no	—
35	C₃×C₅	C₂×D₁₈₁⋊C₃	1	1	yes	characteristic
36	C₂²×C₃	—	181	1	no	—
37	C₂×C₅	—	181	2	no	—
38	C₂×C₅	#13108656⋊C₂	1	1	yes	characteristic, direct product factor
39	C₉	—	181	1	no	Sylow
40	C₂×C₃	—	181	2	no	—
41	C₂×C₃	C₅×D₁₈₁⋊C₃	1	1	yes	characteristic
42	C₅	C₂×#13108656⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	181	1	no	Sylow
44	C₃	C₂×C₅×D₁₈₁⋊C₃	1	1	yes	characteristic
45	C₂	—	181	2	no	—
46	C₂	C₅×#13108656⋊C₂	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₁₈₁⋊C₃
commutator, hypocenter	C₁₈₁	C₂²×C₅×C₉
Frattini	C₃	C₂×C₅×D₁₈₁⋊C₃
Fitting, socle	C₂×C₃×C₅×C₁₈₁	C₂×C₃
prime radical	C₂×C₃×C₅×D₁₈₁	C₃
cosocle	C₃×C₁₈₁	C₂²×C₃×C₅
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#13108656⋊C₂	C₂	direct (N × H)
2. C₂×C₅×#13108656	C₂	semidirect
4. C₅×#13108656	C₂²	semidirect
5. C₂×#13108656⋊C₂	C₅	direct (N × H)
8. C₂×C₅×D₁₈₁	C₉	semidirect
9. C₂×#13108656	C₂×C₅	semidirect
10. #13108656⋊C₂	C₂×C₅	direct (N × H)
13. C₂×C₅×C₁₈₁	C₂×C₉	semidirect
14. C₅×D₁₈₁	C₂×C₉	semidirect
15. #13108656	C₂²×C₅	semidirect
18. C₅×C₁₈₁	C₂²×C₉	semidirect
19. C₂×D₁₈₁	C₅×C₉	semidirect
21. C₂×C₁₈₁	C₂×C₅×C₉	semidirect
22. D₁₈₁	C₂×C₅×C₉	semidirect
23. C₁₈₁	C₂²×C₅×C₉	semidirect
38. C₂×C₅	#13108656⋊C₂	direct (N × H)
42. C₅	C₂×#13108656⋊C₂	direct (N × H)
46. C₂	C₅×#13108656⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#13108656⋊C₂	2
C₂×C₅×#13108656	2
C₂×C₃×C₅×D₁₈₁	3
C₂×#13108656⋊C₂	5
C₂²×C₅×C₉	181

Subgroups — C2×C5×#13108656⋊C2 #45656367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#13108656⋊C₂ #45656367