Subgroups — C₅×D₃×C₄₇⋊C₂₃ #44569874

Order 32430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄₇⋊C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×C₄₇⋊C₂₃	—	3	1	no	maximal, Hall
3	D₃×C₄₇⋊C₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₄₇⋊C₂₃	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₄₇⋊C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₄₇⋊C₂₃	—	3	1	no	Hall
7	C₅×D₃×C₄₇	C₂₃	1	1	yes	maximal, characteristic, complemented, Hall
8	C₄₇⋊C₂₃	C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₅×D₃×C₂₃	—	47	1	no	maximal, Hall
11	C₂×C₅×C₄₇	—	3	1	no	Hall
12	C₃×C₅×C₂₃	—	47	1	no	Hall
13	D₃×C₄₇	C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
14	C₅×C₄₇	D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₂₃	—	141	1	no	Hall
16	C₃×C₄₇	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
17	D₃×C₂₃	—	47	1	no	Hall
18	C₅×C₂₃	—	47	1	no	Hall
19	C₂×C₄₇	—	3	1	no	Hall
20	C₃×C₂₃	—	47	1	no	Hall
21	C₄₇	C₅×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₂₃	—	141	1	no	Hall
23	C₅×D₃	C₄₇⋊C₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂₃	—	47	1	no	Sylow
25	C₃×C₅	C₂×C₄₇⋊C₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅	—	3	1	no	Hall
27	D₃	C₅×C₄₇⋊C₂₃	1	1	yes	characteristic, direct product factor, Hall
28	C₅	D₃×C₄₇⋊C₂₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₂×C₅×C₄₇⋊C₂₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃×C₄₇⋊C₂₃
commutator, cosocle, hypocenter	C₃×C₄₇	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₄₇	C₂×C₂₃
LCS	G ▷ C₃×C₄₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₄₇⋊C₂₃	C₂	semidirect
3. D₃×C₄₇⋊C₂₃	C₅	direct (N × H)
4. C₅×C₄₇⋊C₂₃	D₃	direct (N × H)
5. C₃×C₄₇⋊C₂₃	C₂×C₅	semidirect
7. C₅×D₃×C₄₇	C₂₃	semidirect
8. C₄₇⋊C₂₃	C₅×D₃	direct (N × H)
9. C₃×C₅×C₄₇	C₂×C₂₃	semidirect
13. D₃×C₄₇	C₅×C₂₃	semidirect
14. C₅×C₄₇	D₃×C₂₃	semidirect
16. C₃×C₄₇	C₂×C₅×C₂₃	semidirect
21. C₄₇	C₅×D₃×C₂₃	semidirect
23. C₅×D₃	C₄₇⋊C₂₃	direct (N × H)
25. C₃×C₅	C₂×C₄₇⋊C₂₃	semidirect
27. D₃	C₅×C₄₇⋊C₂₃	direct (N × H)
28. C₅	D₃×C₄₇⋊C₂₃	direct (N × H)
29. C₃	C₂×C₅×C₄₇⋊C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₄₇⋊C₂₃	2
C₂×C₅×C₄₇⋊C₂₃	3
D₃×C₄₇⋊C₂₃	5
C₅×D₃×C₄₇	23
C₅×D₃×C₂₃	47

Subgroups — C5×D3×C47⋊C23 #44569874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₄₇⋊C₂₃ #44569874