Subgroups — S₄×C₂₅ #10597053

Order 600.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₂₅	—	3	1	no	maximal, Hall
3	D₃×C₂₅	—	4	1	no	maximal
4	C₅×S₄	C₅	1	1	yes	maximal, characteristic
5	C₂²×C₂₅	—	3	1	no	—
6	C₂²×C₂₅	D₃	1	1	yes	characteristic, complemented
7	C₄×C₂₅	—	3	1	no	—
8	C₃×C₂₅	—	4	1	no	Hall
9	C₅×A₄	C₂×C₅	1	1	yes	characteristic
10	C₂×C₂₅	—	3	1	no	—
11	C₂×C₂₅	—	6	1	no	—
12	C₅×D₄	—	3	1	no	—
13	C₅×D₃	—	4	1	no	—
14	C₂₅	S₄	1	1	yes	characteristic, direct product factor, Sylow
15	S₄	C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₅	—	3	1	no	—
17	C₂²×C₅	C₅×D₃	1	1	yes	characteristic
18	C₄×C₅	—	3	1	no	—
19	C₃×C₅	—	4	1	no	—
20	A₄	C₂×C₂₅	1	1	yes	characteristic, complemented
21	C₂×C₅	—	3	1	no	—
22	C₂×C₅	—	6	1	no	—
23	D₄	—	3	1	no	Sylow
24	D₃	—	4	1	no	—
25	C₅	C₅×S₄	1	1	yes	characteristic
26	C₂²	—	3	1	no	—
27	C₂²	D₃×C₂₅	1	1	yes	characteristic, complemented
28	C₄	—	3	1	no	—
29	C₃	—	4	1	no	Sylow
30	C₂	—	3	1	no	—
31	C₂	—	6	1	no	—

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.