Subgroups — A₄×D₂₅ #10597055

Order 600.

36 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	C₂²×D₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×D₂₅	—	4	1	no	maximal
4	D₅×A₄	—	5	1	no	maximal
5	C₂²×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×D₂₅	—	3	1	no	—
7	C₂×D₂₅	—	3	1	no	—
8	C₃×C₂₅	—	4	1	no	Hall
9	C₅×A₄	D₅	1	1	yes	characteristic
10	C₂×C₂₅	—	3	1	no	—
11	D₂₅	—	3	1	no	—
12	D₂₅	A₄	1	1	yes	characteristic, direct product factor
13	C₂²×D₅	—	5	1	no	—
14	C₃×D₅	—	20	1	no	—
15	C₂₅	C₂×A₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×A₄	—	25	1	no	Hall
17	C₂²×C₅	C₃×D₅	1	1	yes	characteristic
18	C₂×D₅	—	15	1	no	—
19	C₂×D₅	—	15	1	no	—
20	C₃×C₅	—	4	1	no	—
21	A₄	D₂₅	1	1	yes	characteristic, direct product factor
22	C₂×C₅	—	3	1	no	—
23	D₅	—	5	1	no	—
24	D₅	—	15	1	no	—
25	C₂³	—	25	1	no	Sylow
26	C₂×C₃	—	100	1	no	—
27	C₅	D₅×A₄	1	1	yes	characteristic
28	C₂²	—	75	1	no	—
29	C₂²	—	75	1	no	—
30	C₂²	C₃×D₂₅	1	1	yes	characteristic, complemented
31	C₃	—	4	1	no	Sylow
32	C₂	—	3	1	no	—
33	C₂	—	25	1	no	—
34	C₂	—	75	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂²×C₂₅	C₂×C₃
Frattini	C₅	D₅×A₄
socle	C₂²×C₅	C₃×D₅
LCS	G ▷ C₂²×C₂₅
UCS	C₁

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.