Subgroups — C₂×C₁₃×C₂₃×C₁₃⋊C₃ #37552239

Order 23322.

48 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, direct product factor, Hall
2	C₂×C₁₃²×C₂₃	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	C₂×C₂₃×C₁₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₁₃×C₁₃⋊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, direct product factor
9	C₂×C₁₃×C₂₃	—	3	4	no	—
10	C₂×C₁₃×C₂₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
11	C₂×C₁₃×C₂₃	C₃×C₁₃	1	1	yes	characteristic, complemented
12	C₁₃×C₁₃⋊C₃	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₃²	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×C₂₃	—	3	4	no	—
15	C₁₃×C₂₃	C₂×C₁₃⋊C₃	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	C₂×C₁₃⋊C₃	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor
21	C₃×C₂₃	—	13	1	no	Hall
22	C₂×C₂₃	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₁₃	—	13	1	no	—
24	C₁₃⋊C₃	C₂×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor
25	C₂×C₁₃	—	3	4	no	—
26	C₂×C₁₃	C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
27	C₂×C₁₃	C₃×C₁₃×C₂₃	1	1	yes	characteristic, complemented
28	C₂₃	C₂×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₁₃	—	3	4	no	—
30	C₁₃	C₂×C₂₃×C₁₃⋊C₃	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	—	13	1	no	Sylow
34	C₂	C₁₃×C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂₃×C₁₃⋊C₃	C₂	direct (N × H)
2. C₂×C₁₃²×C₂₃	C₃	semidirect
3. C₁₃²×C₂₃	C₂×C₃	semidirect
5. C₂×C₂₃×C₁₃⋊C₃	C₁₃	direct (N × H)
6. C₂×C₁₃×C₁₃⋊C₃	C₂₃	direct (N × H)
8. C₂₃×C₁₃⋊C₃	C₂×C₁₃	direct (N × H)
10. C₂×C₁₃×C₂₃	C₁₃⋊C₃	direct (N × H)
11. C₂×C₁₃×C₂₃	C₃×C₁₃	semidirect
12. C₁₃×C₁₃⋊C₃	C₂×C₂₃	direct (N × H)
13. C₂×C₁₃²	C₃×C₂₃	semidirect
15. C₁₃×C₂₃	C₂×C₁₃⋊C₃	direct (N × H)
16. C₁₃×C₂₃	C₂×C₃×C₁₃	semidirect
17. C₁₃²	C₂×C₃×C₂₃	semidirect
20. C₂×C₁₃⋊C₃	C₁₃×C₂₃	direct (N × H)
22. C₂×C₂₃	C₁₃×C₁₃⋊C₃	direct (N × H)
24. C₁₃⋊C₃	C₂×C₁₃×C₂₃	direct (N × H)
26. C₂×C₁₃	C₂₃×C₁₃⋊C₃	direct (N × H)
27. C₂×C₁₃	C₃×C₁₃×C₂₃	semidirect
28. C₂₃	C₂×C₁₃×C₁₃⋊C₃	direct (N × H)
30. C₁₃	C₂×C₂₃×C₁₃⋊C₃	direct (N × H)
31. C₁₃	C₂×C₃×C₁₃×C₂₃	semidirect
34. C₂	C₁₃×C₂₃×C₁₃⋊C₃	direct (N × H)

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
C₂×C₁₃²×C₂₃	3
C₂×C₃×C₁₃×C₂₃	13
C₂×C₂₃×C₁₃⋊C₃	13
C₂×C₁₃×C₁₃⋊C₃	23

Subgroups — C2×C13×C23×C13⋊C3 #37552239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₂₃×C₁₃⋊C₃ #37552239