Finite Group Databasebeta

← C₅×D₃₆₇₉ #49145481

Subgroups — C₅×D₃₆₇₉ #49145481

Order 36790.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₆₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₂₈₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₂₈₃	—	13	1	no	maximal, Hall
5	C₅×C₂₈₃	D₁₃	1	1	yes	characteristic, complemented, Hall
6	D₂₈₃	—	13	1	no	Hall
7	C₂₈₃	C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
8	C₅×D₁₃	—	283	1	no	maximal, Hall
9	C₅×C₁₃	D₂₈₃	1	1	yes	characteristic, complemented, Hall
10	D₁₃	—	283	1	no	Hall
11	C₁₃	C₅×D₂₈₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	3679	1	no	Hall
13	C₅	D₃₆₇₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	3679	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₆₇₉
commutator, cosocle, hypocenter	C₁₃×C₂₈₃	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₂₈₃	C₂
LCS	G ▷ C₁₃×C₂₈₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₂₈₃	C₂	semidirect
2. D₃₆₇₉	C₅	direct (N × H)
3. C₁₃×C₂₈₃	C₂×C₅	semidirect
5. C₅×C₂₈₃	D₁₃	semidirect
7. C₂₈₃	C₅×D₁₃	semidirect
9. C₅×C₁₃	D₂₈₃	semidirect
11. C₁₃	C₅×D₂₈₃	semidirect
13. C₅	D₃₆₇₉	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×C₁₃×C₂₈₃	2
D₃₆₇₉	5
C₅×D₂₈₃	13
C₅×D₁₃	283