Subgroups — C₃⋊C₈×C₂₅ #10597020

Order 600.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂₅	—	3	1	no	maximal, Hall
3	C₂×C₃×C₂₅	C₄	1	1	yes	characteristic
4	C₅×C₃⋊C₈	C₅	1	1	yes	maximal, characteristic
5	C₄×C₂₅	D₃	1	1	yes	characteristic
6	C₃×C₂₅	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
8	C₂×C₂₅	Dic₃	1	1	yes	characteristic
9	C₅×C₈	—	3	1	no	—
10	C₂×C₃×C₅	C₄×C₅	1	1	yes	characteristic
11	C₂₅	C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
12	C₃⋊C₈	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₅	C₅×D₃	1	1	yes	characteristic
14	C₃×C₅	C₅×C₈	1	1	yes	characteristic
15	C₃×C₄	C₂×C₂₅	1	1	yes	characteristic
16	C₂×C₅	C₅×Dic₃	1	1	yes	characteristic
17	C₈	—	3	1	no	Sylow
18	C₂×C₃	C₄×C₂₅	1	1	yes	characteristic
19	C₅	C₅×C₃⋊C₈	1	1	yes	characteristic
20	C₄	D₃×C₂₅	1	1	yes	characteristic
21	C₃	C₈×C₂₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	Dic₃×C₂₅	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.