Subgroups — #6045⋊C₃ #10597086

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	#1039⋊C₃	C₂	1	2	yes	maximal
3	#6045	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₅²⋊C₃	C₂²	1	1	yes	characteristic
5	C₄×C₅²	C₂×C₃	1	1	yes	characteristic
6	#1039	C₂×C₃	1	2	yes	—
7	C₅²⋊C₃	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅²	C₂²×C₃	1	1	yes	characteristic
9	Dic₁₀	—	15	2	no	—
10	C₅²	C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
11	C₃×Q₈	—	25	1	no	maximal, Hall
12	C₄×C₅	—	3	2	no	—
13	Dic₅	—	15	4	no	—
14	C₃×C₄	—	25	2	no	—
15	C₃×C₄	—	50	1	no	—
16	C₂×C₅	—	3	2	no	—
17	Q₈	—	25	1	no	Sylow
18	C₂×C₃	—	50	1	no	—
19	C₅	—	3	2	no	—
20	C₄	—	25	2	no	—
21	C₄	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
22	C₃	—	50	1	no	Sylow
23	C₂	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic

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

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