Subgroups — C₅×C₂₃×D₁₂₃ #43246607

Order 28290.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₂₃×D₄₁	—	3	1	no	maximal, Hall
3	C₂₃×D₁₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₃×C₄₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₃×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₄₁	—	3	1	no	Hall
7	C₅×D₁₂₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×C₄₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
9	C₅×D₃×C₂₃	—	41	1	no	maximal, Hall
10	C₃×C₅×C₄₁	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₅×D₄₁	—	3	1	no	Hall
12	C₃×C₅×C₂₃	D₄₁	1	1	yes	characteristic, complemented, Hall
13	D₁₂₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₂₃	—	123	1	no	Hall
15	C₅×C₄₁	D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
16	D₃×C₂₃	—	41	1	no	Hall
17	C₃×C₄₁	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
18	C₅×C₂₃	D₁₂₃	1	1	yes	characteristic, direct product factor, Hall
19	D₄₁	—	3	1	no	Hall
20	C₃×C₂₃	C₅×D₄₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₃	—	123	1	no	Hall
22	C₄₁	C₅×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
23	C₅×D₃	—	41	1	no	Hall
24	C₂₃	C₅×D₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂₃×D₄₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅	—	123	1	no	Hall
27	D₃	—	41	1	no	Hall
28	C₅	C₂₃×D₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₂₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	123	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	D₁₂₃
commutator, cosocle, hypocenter	C₃×C₄₁	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₃×C₄₁	C₂
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×C₄₁	C₂	semidirect
3. C₂₃×D₁₂₃	C₅	direct (N × H)
4. C₅×C₂₃×C₄₁	D₃	semidirect
5. C₃×C₂₃×C₄₁	C₂×C₅	semidirect
7. C₅×D₁₂₃	C₂₃	direct (N × H)
8. C₂₃×C₄₁	C₅×D₃	semidirect
10. C₃×C₅×C₄₁	C₂×C₂₃	semidirect
12. C₃×C₅×C₂₃	D₄₁	semidirect
13. D₁₂₃	C₅×C₂₃	direct (N × H)
15. C₅×C₄₁	D₃×C₂₃	semidirect
17. C₃×C₄₁	C₂×C₅×C₂₃	semidirect
18. C₅×C₂₃	D₁₂₃	direct (N × H)
20. C₃×C₂₃	C₅×D₄₁	semidirect
22. C₄₁	C₅×D₃×C₂₃	semidirect
24. C₂₃	C₅×D₁₂₃	direct (N × H)
25. C₃×C₅	C₂₃×D₄₁	semidirect
28. C₅	C₂₃×D₁₂₃	direct (N × H)
29. C₃	C₅×C₂₃×D₄₁	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×C₄₁	2
C₅×C₂₃×D₄₁	3
C₂₃×D₁₂₃	5
C₅×D₁₂₃	23
C₅×D₃×C₂₃	41

Subgroups — C5×C23×D123 #43246607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₃×D₁₂₃ #43246607