Subgroups — C₃×C₂₃×D₂₃₅ #44569860

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	C₂₃×D₂₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₃×D₄₇	—	5	1	no	maximal, Hall
4	C₅×C₂₃×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₃×C₄₇	D₅	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₄₇	—	5	1	no	Hall
7	C₃×D₂₃₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×C₄₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₅×C₂₃	—	47	1	no	maximal, Hall
11	D₂₃₅	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅×C₂₃	D₄₇	1	1	yes	characteristic, complemented, Hall
13	C₃×D₄₇	—	5	1	no	Hall
14	C₅×C₄₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
15	D₅×C₂₃	—	47	1	no	Hall
16	C₃×C₄₇	D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₂₃	—	235	1	no	Hall
18	C₅×C₂₃	C₃×D₄₇	1	1	yes	characteristic, complemented, Hall
19	D₄₇	—	5	1	no	Hall
20	C₃×C₂₃	D₂₃₅	1	1	yes	characteristic, direct product factor, Hall
21	C₄₇	C₃×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₂₃	—	235	1	no	Hall
23	C₃×D₅	—	47	1	no	Hall
24	C₂₃	C₃×D₂₃₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂₃×D₄₇	1	1	yes	characteristic, complemented, Hall
26	D₅	—	47	1	no	Hall
27	C₂×C₃	—	235	1	no	Hall
28	C₅	C₃×C₂₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₂₃×D₂₃₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	235	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₂₃₅
commutator, cosocle, hypocenter	C₅×C₄₇	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₃×C₄₇	C₂
LCS	G ▷ C₅×C₄₇
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×C₄₇	C₂	semidirect
2. C₂₃×D₂₃₅	C₃	direct (N × H)
4. C₅×C₂₃×C₄₇	C₂×C₃	semidirect
5. C₃×C₂₃×C₄₇	D₅	semidirect
7. C₃×D₂₃₅	C₂₃	direct (N × H)
8. C₂₃×C₄₇	C₃×D₅	semidirect
9. C₃×C₅×C₄₇	C₂×C₂₃	semidirect
11. D₂₃₅	C₃×C₂₃	direct (N × H)
12. C₃×C₅×C₂₃	D₄₇	semidirect
14. C₅×C₄₇	C₂×C₃×C₂₃	semidirect
16. C₃×C₄₇	D₅×C₂₃	semidirect
18. C₅×C₂₃	C₃×D₄₇	semidirect
20. C₃×C₂₃	D₂₃₅	direct (N × H)
21. C₄₇	C₃×D₅×C₂₃	semidirect
24. C₂₃	C₃×D₂₃₅	direct (N × H)
25. C₃×C₅	C₂₃×D₄₇	semidirect
28. C₅	C₃×C₂₃×D₄₇	semidirect
29. C₃	C₂₃×D₂₃₅	direct (N × H)

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
C₂₃×D₂₃₅	3
C₃×C₂₃×D₄₇	5
C₃×D₂₃₅	23
C₃×D₅×C₂₃	47

Subgroups — C3×C23×D235 #44569860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₃×D₂₃₅ #44569860