Subgroups — #44501969

Order 30699.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779524	C₃	1	1	yes	maximal, characteristic
2	#16811787	C₉	1	1	yes	characteristic
3	C₃×C₃₇₉	C₂₇	1	1	yes	characteristic
4	C₃₇₉	C₈₁	1	1	yes	characteristic, complemented, Sylow
5	C₈₁	—	379	1	no	maximal, Sylow
6	C₂₇	—	379	1	no	—
7	C₉	—	379	1	no	—
8	C₃	#23779526	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23779526
commutator, hypocenter	C₃₇₉	C₈₁
Fitting, socle, prime radical	C₃×C₃₇₉	C₂₇
cosocle	#23779524	C₃
LCS	G ▷ C₃₇₉
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
4. C₃₇₉	C₈₁	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23779524	3
C₈₁	379