Subgroups — #10597074

Order 600.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1039⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#6034	—	3	1	no	maximal, Hall
3	C₂×C₅²⋊C₃	C₄	1	1	yes	characteristic
4	#1039	D₃	1	1	yes	characteristic
5	C₅²⋊C₃	C₈	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅²	Dic₃	1	1	yes	characteristic
7	#170	—	15	1	no	—
8	#170	—	15	1	no	—
9	C₅²	C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
10	C₃⋊C₈	—	25	1	no	maximal, Hall
11	Dic₅	—	15	1	no	—
12	Dic₅	—	30	1	no	—
13	C₃×C₄	—	25	1	no	—
14	C₂×C₅	—	3	1	no	—
15	C₂×C₅	—	6	1	no	—
16	C₈	—	75	1	no	Sylow
17	C₂×C₃	—	100	1	no	—
18	C₅	—	3	1	no	—
19	C₅	—	6	1	no	—
20	C₄	—	25	1	no	—
21	C₃	—	100	1	no	Sylow
22	C₂	#64480	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#64480
commutator, hypocenter	C₅²⋊C₃	C₈
Fitting, socle	C₂×C₅²	Dic₃
prime radical	C₂×C₅²⋊C₃	C₄
cosocle	#1039⋊C₃	C₂
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
5. C₅²⋊C₃	C₈	semidirect
9. C₅²	C₃⋊C₈	semidirect

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