Subgroups — C₅²×C₃⋊C₈ #10597069

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	C₅²×C₈	—	3	1	no	maximal, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₅×C₃⋊C₈	C₅	1	6	yes	maximal, direct product factor
5	C₄×C₅²	D₃	1	1	yes	characteristic
6	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₅	C₂×C₅	1	6	yes	—
8	C₂×C₅²	Dic₃	1	1	yes	characteristic
9	C₅×C₈	—	3	6	no	—
10	C₂×C₃×C₅	C₄×C₅	1	6	yes	—
11	C₅²	C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
12	C₃⋊C₈	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₅	C₅×D₃	1	6	yes	—
14	C₃×C₅	C₅×C₈	1	6	yes	complemented
15	C₃×C₄	C₂×C₅²	1	1	yes	characteristic
16	C₂×C₅	C₅×Dic₃	1	6	yes	—
17	C₈	—	3	1	no	Sylow
18	C₂×C₃	C₄×C₅²	1	1	yes	characteristic
19	C₅	C₅×C₃⋊C₈	1	6	yes	direct product factor
20	C₄	C₅²×D₃	1	1	yes	characteristic
21	C₃	C₅²×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₅²×Dic₃	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.