Subgroups — #10597081

Order 600.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#64470	C₂	1	2	yes	maximal
3	C₅×Dic₁₀	—	3	1	no	maximal, Hall
4	C₂×C₅²⋊C₃	C₂²	1	1	yes	characteristic
5	C₄×C₅²	D₃	1	1	yes	characteristic
6	C₅×Dic₅	—	3	2	no	—
7	C₅²⋊C₃	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
9	C₅×Q₈	—	15	1	no	—
10	Dic₁₀	—	3	1	no	—
11	C₅²	Dic₆	1	1	yes	characteristic, complemented, Sylow
12	Dic₆	—	25	1	no	maximal, Hall
13	C₄×C₅	—	3	1	no	—
14	C₄×C₅	—	6	1	no	—
15	C₄×C₅	—	15	2	no	—
16	Dic₅	—	3	2	no	—
17	C₃×C₄	—	50	1	no	—
18	Dic₃	—	25	2	no	—
19	C₂×C₅	—	3	1	no	—
20	C₂×C₅	—	6	1	no	—
21	Q₈	—	15	1	no	Sylow
22	C₂×C₃	—	50	1	no	—
23	C₅	—	3	1	no	—
24	C₅	—	6	1	no	—
25	C₄	—	15	2	no	—
26	C₄	#3874	1	1	yes	characteristic
27	C₃	—	50	1	no	Sylow
28	C₂	C₂×#3874	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×#3874
commutator, prime radical, cosocle	C₂×C₅²⋊C₃	C₂²
Fitting	C₄×C₅²	D₃
socle	C₂×C₅²	C₂×D₃
hypercenter	C₄	#3874
hypocenter	C₅²⋊C₃	Q₈
LCS	G ▷ C₂×C₅²⋊C₃ ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂ ◁ C₄

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

N	H ≅ G/N	type
7. C₅²⋊C₃	Q₈	semidirect
11. C₅²	Dic₆	semidirect

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