Subgroups — D₅×C₅⋊D₅ #92565

Order 500.

128 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	C₅×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅³	C₂²	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₅⋊D₅	—	5	1	no	maximal
6	D₅²	—	5	6	no	maximal
7	C₂×C₅²	—	5	1	no	—
8	C₅⋊D₅	—	5	1	no	—
9	C₅⋊D₅	—	5	6	no	—
10	C₅⋊D₅	—	10	12	no	—
11	C₅⋊D₅	D₅	1	1	yes	characteristic, direct product factor
12	C₅×D₅	—	5	6	no	—
13	C₅×D₅	D₅	1	6	yes	complemented
14	C₅²	—	2	12	no	—
15	C₅²	C₂×D₅	1	6	yes	complemented
16	C₅²	C₂×D₅	1	1	yes	characteristic, complemented
17	C₂×D₅	—	25	6	no	—
18	C₂×D₅	—	25	1	no	—
19	C₂×C₅	—	5	6	no	—
20	C₂×C₅	—	25	1	no	—
21	D₅	—	5	6	no	—
22	D₅	—	25	6	no	—
23	D₅	—	25	1	no	—
24	D₅	—	50	12	no	—
25	D₅	C₅⋊D₅	1	1	yes	characteristic, direct product factor
26	C₅	—	2	12	no	—
27	C₅	D₅²	1	6	yes	complemented
28	C₅	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented
29	C₂²	—	125	1	no	Sylow
30	C₂	—	5	1	no	—
31	C₂	—	25	1	no	—
32	C₂	—	125	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅³	C₂²
LCS	G ▷ C₅³
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.