Subgroups — C₃×C₁₃×C₂₃×D₁₃ #37552243

Order 23322.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₂₃×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃²×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₂₃	—	13	1	no	maximal
5	C₃×C₂₃×D₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃×C₁₃×D₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₃×C₂₃	—	2	6	no	—
8	C₃×C₁₃×C₂₃	D₁₃	1	1	yes	characteristic, direct product factor
9	C₃×C₁₃×C₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
10	C₂×C₁₃×C₂₃	—	13	1	no	—
11	C₂₃×D₁₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor
12	C₃×C₁₃²	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×D₁₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₁₃×C₂₃	—	2	6	no	—
15	C₁₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic, direct product factor
16	C₁₃×C₂₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
17	C₁₃²	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₂₃	—	13	1	no	Hall
19	C₂×C₃×C₁₃	—	13	1	no	—
20	C₃×D₁₃	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor
21	C₃×C₂₃	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₂₃	—	13	1	no	Hall
23	C₃×C₁₃	—	2	6	no	—
24	C₃×C₁₃	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
25	C₃×C₁₃	C₂×C₁₃×C₂₃	1	1	yes	characteristic, complemented
26	C₂×C₁₃	—	13	1	no	—
27	D₁₃	C₃×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor
28	C₂₃	C₃×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₁₃	—	2	6	no	—
30	C₁₃	C₃×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
31	C₁₃	C₂×C₃×C₁₃×C₂₃	1	1	yes	characteristic, complemented
32	C₂×C₃	—	13	1	no	Hall
33	C₃	C₁₃×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₂₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₁₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₂₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃²×C₂₃	C₂	semidirect
2. C₁₃×C₂₃×D₁₃	C₃	direct (N × H)
3. C₁₃²×C₂₃	C₂×C₃	semidirect
5. C₃×C₂₃×D₁₃	C₁₃	direct (N × H)
6. C₃×C₁₃×D₁₃	C₂₃	direct (N × H)
8. C₃×C₁₃×C₂₃	D₁₃	direct (N × H)
9. C₃×C₁₃×C₂₃	C₂×C₁₃	semidirect
11. C₂₃×D₁₃	C₃×C₁₃	direct (N × H)
12. C₃×C₁₃²	C₂×C₂₃	semidirect
13. C₁₃×D₁₃	C₃×C₂₃	direct (N × H)
15. C₁₃×C₂₃	C₃×D₁₃	direct (N × H)
16. C₁₃×C₂₃	C₂×C₃×C₁₃	semidirect
17. C₁₃²	C₂×C₃×C₂₃	semidirect
20. C₃×D₁₃	C₁₃×C₂₃	direct (N × H)
21. C₃×C₂₃	C₁₃×D₁₃	direct (N × H)
24. C₃×C₁₃	C₂₃×D₁₃	direct (N × H)
25. C₃×C₁₃	C₂×C₁₃×C₂₃	semidirect
27. D₁₃	C₃×C₁₃×C₂₃	direct (N × H)
28. C₂₃	C₃×C₁₃×D₁₃	direct (N × H)
30. C₁₃	C₃×C₂₃×D₁₃	direct (N × H)
31. C₁₃	C₂×C₃×C₁₃×C₂₃	semidirect
33. C₃	C₁₃×C₂₃×D₁₃	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×C₁₃²×C₂₃	2
C₁₃×C₂₃×D₁₃	3
C₂×C₃×C₁₃×C₂₃	13
C₃×C₂₃×D₁₃	13
C₃×C₁₃×D₁₃	23

Subgroups — C3×C13×C23×D13 #37552243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₂₃×D₁₃ #37552243