Subgroups — C₂×D₃×C₁₈₁⋊C₅ #24925821

Order 10860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₈₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₈₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₈₁⋊C₅	—	3	1	no	maximal, Hall
4	C₃×C₁₈₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₁₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₁₈₁⋊C₅	—	3	2	no	—
7	C₂×C₁₈₁⋊C₅	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₃×C₁₈₁	C₂×C₅	1	1	yes	characteristic, complemented
9	D₃×C₁₈₁	C₂×C₅	1	2	yes	complemented
10	C₁₈₁⋊C₅	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₁₈₁	—	3	1	no	Hall
12	C₃×C₁₈₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₈₁	—	3	2	no	—
14	C₂×C₁₈₁	C₅×D₃	1	1	yes	characteristic, complemented
15	C₁₈₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅×D₃	—	181	1	no	maximal, Hall
17	C₂×C₃×C₅	—	181	1	no	—
18	C₅×D₃	—	181	2	no	—
19	C₂²×C₅	—	543	1	no	Hall
20	C₃×C₅	—	181	1	no	Hall
21	C₂×D₃	C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅	—	543	2	no	—
23	C₂×C₅	—	181	1	no	—
24	C₂×C₃	C₂×C₁₈₁⋊C₅	1	1	yes	characteristic, complemented
25	D₃	C₂×C₁₈₁⋊C₅	1	2	yes	direct product factor
26	C₅	—	181	1	no	Sylow
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₁₈₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×C₁₈₁⋊C₅
commutator, cosocle, hypocenter	C₃×C₁₈₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₈₁	C₂×C₅
LCS	G ▷ C₃×C₁₈₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₈₁⋊C₅	C₂	direct (N × H)
2. C₂×C₃×C₁₈₁⋊C₅	C₂	semidirect
4. C₃×C₁₈₁⋊C₅	C₂²	semidirect
5. C₂×D₃×C₁₈₁	C₅	semidirect
7. C₂×C₁₈₁⋊C₅	D₃	direct (N × H)
8. C₂×C₃×C₁₈₁	C₂×C₅	semidirect
9. D₃×C₁₈₁	C₂×C₅	semidirect
10. C₁₈₁⋊C₅	C₂×D₃	direct (N × H)
12. C₃×C₁₈₁	C₂²×C₅	semidirect
14. C₂×C₁₈₁	C₅×D₃	semidirect
15. C₁₈₁	C₂×C₅×D₃	semidirect
21. C₂×D₃	C₁₈₁⋊C₅	direct (N × H)
24. C₂×C₃	C₂×C₁₈₁⋊C₅	semidirect
25. D₃	C₂×C₁₈₁⋊C₅	direct (N × H)
28. C₃	C₂²×C₁₈₁⋊C₅	semidirect
30. C₂	D₃×C₁₈₁⋊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
D₃×C₁₈₁⋊C₅	2
C₂×C₃×C₁₈₁⋊C₅	2
C₂²×C₁₈₁⋊C₅	3
C₂×D₃×C₁₈₁	5
C₂×C₅×D₃	181

Subgroups — C2×D3×C181⋊C5 #24925821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₁₈₁⋊C₅ #24925821