Subgroups — C₃×#6029 #10597068

Order 600.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	#6029	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₃×#168	—	5	6	no	maximal
5	C₄×C₅²	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₅	D₅	1	6	yes	—
8	C₂×C₅²	C₃×C₄	1	1	yes	characteristic
9	#168	—	5	6	no	—
10	C₂×C₃×C₅	Dic₅	1	6	yes	—
11	C₅²	C₃×C₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₈	—	25	1	no	Hall
13	C₄×C₅	C₃×D₅	1	6	yes	—
14	C₃×C₅	#168	1	6	yes	complemented
15	C₃×C₄	C₅⋊D₅	1	1	yes	characteristic
16	C₂×C₅	C₃×Dic₅	1	6	yes	—
17	C₈	—	25	1	no	Sylow
18	C₂×C₃	#1039	1	1	yes	characteristic
19	C₅	C₃×#168	1	6	yes	complemented
20	C₄	C₃×C₅⋊D₅	1	1	yes	characteristic
21	C₃	#6029	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×#1039	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.