Subgroups — C₅×C₂₃×#63270 #44536033

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	C₂₃×#63270	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₂₃×C₁₃⋊C₃	—	7	1	no	maximal, Hall
4	C₅×ΓL(1,𝔽₈)×C₂₃	—	13	1	no	maximal, Hall
5	C₇×C₁₃×C₂₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×C₁₃×C₂₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
7	C₅×#63270	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×C₁₃⋊C₃	—	7	1	no	Hall
9	C₅×C₇×C₂₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
10	ΓL(1,𝔽₈)×C₂₃	—	13	1	no	Hall
11	C₅×C₇×C₁₃	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₂₃	—	91	1	no	Hall
13	C₁₃×C₂₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
14	#63270	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₁₃⋊C₃	—	7	1	no	Hall
16	C₇×C₂₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₅×C₂₃	#63270	1	1	yes	characteristic, direct product factor, Hall
18	C₅×ΓL(1,𝔽₈)	—	13	1	no	Hall
19	C₇×C₁₃	C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₂₃	—	91	1	no	Hall
21	C₅×C₁₃	ΓL(1,𝔽₈)×C₂₃	1	1	yes	characteristic, complemented, Hall
22	C₁₃⋊C₃	—	7	1	no	Hall
23	C₅×C₇	C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₂₃	C₅×#63270	1	1	yes	characteristic, direct product factor, Sylow
25	ΓL(1,𝔽₈)	—	13	1	no	Hall
26	C₃×C₅	—	91	1	no	Hall
27	C₁₃	C₅×ΓL(1,𝔽₈)×C₂₃	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₅×C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₅	C₂₃×#63270	1	1	yes	characteristic, direct product factor, Sylow
30	C₃	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	#63270
commutator, cosocle, hypocenter	C₇×C₁₃	C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₂₃	C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₅×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. C₂₃×#63270	C₅	direct (N × H)
5. C₇×C₁₃×C₂₃	C₃×C₅	semidirect
6. C₅×C₁₃×C₂₃	ΓL(1,𝔽₈)	semidirect
7. C₅×#63270	C₂₃	direct (N × H)
9. C₅×C₇×C₂₃	C₁₃⋊C₃	semidirect
11. C₅×C₇×C₁₃	C₃×C₂₃	semidirect
13. C₁₃×C₂₃	C₅×ΓL(1,𝔽₈)	semidirect
14. #63270	C₅×C₂₃	direct (N × H)
16. C₇×C₂₃	C₅×C₁₃⋊C₃	semidirect
17. C₅×C₂₃	#63270	direct (N × H)
19. C₇×C₁₃	C₃×C₅×C₂₃	semidirect
21. C₅×C₁₃	ΓL(1,𝔽₈)×C₂₃	semidirect
23. C₅×C₇	C₂₃×C₁₃⋊C₃	semidirect
24. C₂₃	C₅×#63270	direct (N × H)
27. C₁₃	C₅×ΓL(1,𝔽₈)×C₂₃	semidirect
28. C₇	C₅×C₂₃×C₁₃⋊C₃	semidirect
29. C₅	C₂₃×#63270	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
C₂₃×#63270	5
C₅×C₂₃×C₁₃⋊C₃	7
C₅×ΓL(1,𝔽₈)×C₂₃	13
C₅×#63270	23

Subgroups — C5×C23×#63270 #44536033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₃×#63270 #44536033