Subgroups — C₅×C₂₃×D₁₄₁ #44569864

Order 32430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₂₃×D₄₇	—	3	1	no	maximal, Hall
3	C₂₃×D₁₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₃×C₄₇	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₃×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₄₇	—	3	1	no	Hall
7	C₅×D₁₄₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×C₄₇	C₅×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₅×D₃×C₂₃	—	47	1	no	maximal, Hall
11	C₅×D₄₇	—	3	1	no	Hall
12	C₃×C₅×C₂₃	D₄₇	1	1	yes	characteristic, complemented, Hall
13	D₁₄₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, 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	D₁₄₁	1	1	yes	characteristic, direct product factor, Hall
19	D₄₇	—	3	1	no	Hall
20	C₃×C₂₃	C₅×D₄₇	1	1	yes	characteristic, complemented, Hall
21	C₄₇	C₅×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₂₃	—	141	1	no	Hall
23	C₅×D₃	—	47	1	no	Hall
24	C₂₃	C₅×D₁₄₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂₃×D₄₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅	—	141	1	no	Hall
27	D₃	—	47	1	no	Hall
28	C₅	C₂₃×D₁₄₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₂₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	141	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	D₁₄₁
commutator, cosocle, hypocenter	C₃×C₄₇	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₃×C₄₇	C₂
LCS	G ▷ C₃×C₄₇
UCS	C₁ ◁ C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×C₄₇	C₂	semidirect
3. C₂₃×D₁₄₁	C₅	direct (N × H)
4. C₅×C₂₃×C₄₇	D₃	semidirect
5. C₃×C₂₃×C₄₇	C₂×C₅	semidirect
7. C₅×D₁₄₁	C₂₃	direct (N × H)
8. C₂₃×C₄₇	C₅×D₃	semidirect
9. C₃×C₅×C₄₇	C₂×C₂₃	semidirect
12. C₃×C₅×C₂₃	D₄₇	semidirect
13. D₁₄₁	C₅×C₂₃	direct (N × H)
14. C₅×C₄₇	D₃×C₂₃	semidirect
16. C₃×C₄₇	C₂×C₅×C₂₃	semidirect
18. C₅×C₂₃	D₁₄₁	direct (N × H)
20. C₃×C₂₃	C₅×D₄₇	semidirect
21. C₄₇	C₅×D₃×C₂₃	semidirect
24. C₂₃	C₅×D₁₄₁	direct (N × H)
25. C₃×C₅	C₂₃×D₄₇	semidirect
28. C₅	C₂₃×D₁₄₁	direct (N × H)
29. C₃	C₅×C₂₃×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₂₃×C₄₇	2
C₅×C₂₃×D₄₇	3
C₂₃×D₁₄₁	5
C₅×D₁₄₁	23
C₅×D₃×C₂₃	47

Subgroups — C5×C23×D141 #44569864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₃×D₁₄₁ #44569864