Finite Group Databasebeta

← C₇₉×C₁₃⋊C₉ #22604453

Subgroups — C₇₉×C₁₃⋊C₉ #22604453

Order 9243.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₇₉	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₇₉	C₉	1	1	yes	characteristic, complemented, Hall
3	C₉×C₇₉	—	13	1	no	maximal, Hall
4	C₃×C₇₉	C₁₃⋊C₃	1	1	yes	characteristic
5	C₁₃⋊C₉	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇₉	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₁₃	C₃×C₇₉	1	1	yes	characteristic
8	C₁₃	C₉×C₇₉	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	13	1	no	Sylow
10	C₃	C₁₃⋊C₃×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₇₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₇₉
Frattini	C₃	C₁₃⋊C₃×C₇₉
Fitting, socle	C₃×C₁₃×C₇₉	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇₉

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₇₉	C₉	semidirect
5. C₁₃⋊C₉	C₇₉	direct (N × H)
6. C₇₉	C₁₃⋊C₉	direct (N × H)
8. C₁₃	C₉×C₇₉	semidirect