Subgroups — C₃×C₅×D₃×C₂₃ #14523398

Order 2070.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃×C₅×C₂₃	—	3	1	no	maximal
3	C₅×D₃×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×D₃×C₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₂₃	—	2	1	no	—
6	C₃×C₅×C₂₃	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₅×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅×C₂₃	—	3	1	no	Hall
9	C₃²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₂₃	—	3	1	no	—
11	D₃×C₂₃	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₅×C₂₃	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×D₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₂₃	—	2	1	no	—
15	C₃×C₂₃	C₅×D₃	1	1	yes	characteristic, direct product factor
16	C₃×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
17	C₂×C₂₃	—	3	1	no	Hall
18	C₃²×C₅	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅	—	3	1	no	—
20	C₅×D₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor
21	C₂₃	C₃×C₅×D₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×D₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅	—	2	1	no	—
24	C₃×C₅	D₃×C₂₃	1	1	yes	characteristic, direct product factor
25	C₃×C₅	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
26	C₂×C₅	—	3	1	no	Hall
27	C₃²	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3	1	no	—
29	D₃	C₃×C₅×C₂₃	1	1	yes	characteristic, direct product factor
30	C₅	C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₃	—	2	1	no	—
32	C₃	C₅×D₃×C₂₃	1	1	yes	characteristic, direct product factor
33	C₃	C₂×C₃×C₅×C₂₃	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₂₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₂₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₂₃	C₂	semidirect
3. C₅×D₃×C₂₃	C₃	direct (N × H)
4. C₃×D₃×C₂₃	C₅	direct (N × H)
6. C₃×C₅×C₂₃	D₃	direct (N × H)
7. C₃×C₅×C₂₃	C₂×C₃	semidirect
9. C₃²×C₂₃	C₂×C₅	semidirect
11. D₃×C₂₃	C₃×C₅	direct (N × H)
12. C₅×C₂₃	C₃×D₃	direct (N × H)
13. C₃×C₅×D₃	C₂₃	direct (N × H)
15. C₃×C₂₃	C₅×D₃	direct (N × H)
16. C₃×C₂₃	C₂×C₃×C₅	semidirect
18. C₃²×C₅	C₂×C₂₃	semidirect
20. C₅×D₃	C₃×C₂₃	direct (N × H)
21. C₂₃	C₃×C₅×D₃	direct (N × H)
22. C₃×D₃	C₅×C₂₃	direct (N × H)
24. C₃×C₅	D₃×C₂₃	direct (N × H)
25. C₃×C₅	C₂×C₃×C₂₃	semidirect
27. C₃²	C₂×C₅×C₂₃	semidirect
29. D₃	C₃×C₅×C₂₃	direct (N × H)
30. C₅	C₃×D₃×C₂₃	direct (N × H)
32. C₃	C₅×D₃×C₂₃	direct (N × H)
33. C₃	C₂×C₃×C₅×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₂₃	2
C₂×C₃×C₅×C₂₃	3
C₅×D₃×C₂₃	3
C₃×D₃×C₂₃	5
C₃×C₅×D₃	23

Subgroups — C3×C5×D3×C23 #14523398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₃×C₂₃ #14523398