Subgroups — C₁₃×C₂₃×D₁₃⋊C₃ #37552223

Order 23322.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂₃×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×C₂₃×D₁₃	C₃	semidirect
3. C₁₃²×C₂₃	C₂×C₃	semidirect
5. C₂₃×D₁₃⋊C₃	C₁₃	direct (N × H)
6. C₁₃×D₁₃⋊C₃	C₂₃	direct (N × H)
8. C₂₃×C₁₃⋊C₃	C₂×C₁₃	semidirect
10. C₂₃×D₁₃	C₃×C₁₃	semidirect
11. C₁₃×C₁₃⋊C₃	C₂×C₂₃	semidirect
12. C₁₃×D₁₃	C₃×C₂₃	semidirect
14. C₁₃×C₂₃	D₁₃⋊C₃	direct (N × H)
15. C₁₃×C₂₃	C₂×C₃×C₁₃	semidirect
16. C₁₃²	C₂×C₃×C₂₃	semidirect
19. D₁₃⋊C₃	C₁₃×C₂₃	direct (N × H)
23. C₁₃⋊C₃	C₂×C₁₃×C₂₃	semidirect
25. D₁₃	C₃×C₁₃×C₂₃	semidirect
26. C₂₃	C₁₃×D₁₃⋊C₃	direct (N × H)
28. C₁₃	C₂₃×D₁₃⋊C₃	direct (N × H)
29. C₁₃	C₂×C₃×C₁₃×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₂₃×C₁₃⋊C₃	2
C₁₃×C₂₃×D₁₃	3
C₂×C₃×C₁₃×C₂₃	13
C₂₃×D₁₃⋊C₃	13
C₁₃×D₁₃⋊C₃	23

Subgroups — C13×C23×D13⋊C3 #37552223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₂₃×D₁₃⋊C₃ #37552223