Subgroups — C₅×C₇×C₂₃×C₁₃⋊C₃ #44536031

Order 31395.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₂₃×C₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₂₃×C₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₂₃	—	13	1	no	maximal, Hall
5	C₇×C₁₃×C₂₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×C₁₃×C₂₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₁₃⋊C₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×C₁₃⋊C₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₇×C₂₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₇×C₂₃	—	13	1	no	Hall
11	C₅×C₇×C₁₃	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₂₃	—	13	1	no	Hall
13	C₁₃×C₂₃	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₃⋊C₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₁₃⋊C₃	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₂₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₅×C₂₃	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×C₇	—	13	1	no	Hall
19	C₇×C₁₃	C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₂₃	—	13	1	no	Hall
21	C₅×C₁₃	C₃×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
22	C₁₃⋊C₃	C₅×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
23	C₅×C₇	C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂₃	C₅×C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₇	—	13	1	no	Hall
26	C₃×C₅	—	13	1	no	Hall
27	C₁₃	C₃×C₅×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₅×C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₇×C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇×C₂₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₅×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₂₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₃×C₂₃	C₃	semidirect
2. C₇×C₂₃×C₁₃⋊C₃	C₅	direct (N × H)
3. C₅×C₂₃×C₁₃⋊C₃	C₇	direct (N × H)
5. C₇×C₁₃×C₂₃	C₃×C₅	semidirect
6. C₅×C₁₃×C₂₃	C₃×C₇	semidirect
7. C₅×C₇×C₁₃⋊C₃	C₂₃	direct (N × H)
8. C₂₃×C₁₃⋊C₃	C₅×C₇	direct (N × H)
9. C₅×C₇×C₂₃	C₁₃⋊C₃	direct (N × H)
11. C₅×C₇×C₁₃	C₃×C₂₃	semidirect
13. C₁₃×C₂₃	C₃×C₅×C₇	semidirect
14. C₇×C₁₃⋊C₃	C₅×C₂₃	direct (N × H)
15. C₅×C₁₃⋊C₃	C₇×C₂₃	direct (N × H)
16. C₇×C₂₃	C₅×C₁₃⋊C₃	direct (N × H)
17. C₅×C₂₃	C₇×C₁₃⋊C₃	direct (N × H)
19. C₇×C₁₃	C₃×C₅×C₂₃	semidirect
21. C₅×C₁₃	C₃×C₇×C₂₃	semidirect
22. C₁₃⋊C₃	C₅×C₇×C₂₃	direct (N × H)
23. C₅×C₇	C₂₃×C₁₃⋊C₃	direct (N × H)
24. C₂₃	C₅×C₇×C₁₃⋊C₃	direct (N × H)
27. C₁₃	C₃×C₅×C₇×C₂₃	semidirect
28. C₇	C₅×C₂₃×C₁₃⋊C₃	direct (N × H)
29. C₅	C₇×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
C₅×C₇×C₁₃×C₂₃	3
C₇×C₂₃×C₁₃⋊C₃	5
C₅×C₂₃×C₁₃⋊C₃	7
C₃×C₅×C₇×C₂₃	13
C₅×C₇×C₁₃⋊C₃	23

Subgroups — C5×C7×C23×C13⋊C3 #44536031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₂₃×C₁₃⋊C₃ #44536031