Subgroups — C₅×D₅² #92564

Order 500.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₅	C₂	1	2	yes	maximal, complemented
3	C₅³	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅×D₅	—	5	2	no	maximal
5	D₅²	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅²	—	5	2	no	—
7	C₅⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅×D₅	—	2	4	no	—
9	C₅×D₅	—	5	2	no	—
10	C₅×D₅	—	10	2	no	—
11	C₅×D₅	D₅	1	2	yes	direct product factor
12	C₅×D₅	C₂×C₅	1	2	yes	complemented
13	C₅²	—	2	2	no	—
14	C₅²	—	2	4	no	—
15	C₅²	—	4	4	no	—
16	C₅²	C₂×D₅	1	2	yes	complemented
17	C₅²	C₂²×C₅	1	1	yes	characteristic, complemented
18	C₂²×C₅	—	25	1	no	—
19	C₂×D₅	—	5	2	no	—
20	C₂×C₅	—	5	2	no	—
21	C₂×C₅	—	5	2	no	—
22	C₂×C₅	—	10	4	no	—
23	C₂×C₅	—	25	1	no	—
24	D₅	—	5	2	no	—
25	D₅	—	10	2	no	—
26	D₅	C₅×D₅	1	2	yes	direct product factor
27	C₅	—	2	2	no	—
28	C₅	—	2	4	no	—
29	C₅	—	4	4	no	—
30	C₅	D₅²	1	1	yes	characteristic, direct product factor
31	C₅	C₂×C₅×D₅	1	2	yes	complemented
32	C₂²	—	25	1	no	Sylow
33	C₂	—	5	2	no	—
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₅²
commutator, cosocle, hypocenter	C₅²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅³	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₅

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.