Subgroups — D₅×A₅ #10597165

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×A₄	—	5	1	no	maximal
3	C₂×A₅	—	5	1	no	maximal
4	D₅²	—	6	1	no	maximal
5	C₅×A₄	—	5	1	no	—
6	D₃×D₅	—	10	1	no	maximal
7	A₅	D₅	1	1	yes	characteristic, direct product factor
8	C₅⋊D₅	—	6	1	no	—
9	C₅×D₅	—	6	1	no	—
10	C₅×D₅	—	6	1	no	—
11	C₂²×D₅	—	5	1	no	—
12	D₁₅	—	10	1	no	—
13	C₃×D₅	—	10	1	no	—
14	C₅×D₃	—	10	1	no	—
15	C₅²	—	6	1	no	Sylow
16	C₂×A₄	—	25	1	no	Hall
17	C₂²×C₅	—	5	1	no	—
18	C₂×D₅	—	15	1	no	—
19	C₂×D₅	—	15	1	no	—
20	C₂×D₅	—	30	1	no	—
21	C₃×C₅	—	10	1	no	—
22	C₂×D₃	—	50	1	no	—
23	A₄	—	5	1	no	—
24	C₂×C₅	—	15	1	no	—
25	C₂×C₅	—	30	1	no	—
26	D₅	—	6	1	no	—
27	D₅	—	15	1	no	—
28	D₅	—	30	1	no	—
29	D₅	—	60	2	no	—
30	D₅	A₅	1	1	yes	maximal normal, characteristic, direct product factor
31	C₂³	—	25	1	no	Sylow
32	C₂×C₃	—	50	1	no	—
33	D₃	—	10	1	no	—
34	D₃	—	50	1	no	—
35	C₅	—	6	1	no	—
36	C₅	—	12	2	no	—
37	C₅	C₂×A₅	1	1	yes	characteristic, complemented
38	C₂²	—	5	1	no	—
39	C₂²	—	75	1	no	—
40	C₂²	—	75	1	no	—
41	C₃	—	10	1	no	Sylow
42	C₂	—	5	1	no	—
43	C₂	—	15	1	no	—
44	C₂	—	75	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₅×A₅	C₂
Fitting, cosocle	C₅	C₂×A₅
LCS	G ▷ C₅×A₅
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.