Subgroups — D₅×D₂₅ #92540

Order 500.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂₅	C₂²	1	1	yes	characteristic, complemented, Sylow
5	D₅²	—	5	1	no	maximal
6	C₂×D₂₅	—	5	1	no	maximal
7	C₅⋊D₅	—	5	1	no	—
8	C₅×D₅	—	5	1	no	—
9	C₅×D₅	D₅	1	1	yes	characteristic
10	C₂×C₂₅	—	5	1	no	—
11	D₂₅	—	5	1	no	—
12	D₂₅	—	10	2	no	—
13	D₂₅	D₅	1	1	yes	characteristic, direct product factor
14	C₅²	C₂×D₅	1	1	yes	characteristic
15	C₂₅	—	2	2	no	—
16	C₂₅	C₂×D₅	1	1	yes	characteristic, complemented
17	C₂×D₅	—	25	1	no	—
18	C₂×D₅	—	25	1	no	—
19	C₂×C₅	—	5	1	no	—
20	C₂×C₅	—	25	1	no	—
21	D₅	—	5	1	no	—
22	D₅	—	25	1	no	—
23	D₅	—	25	1	no	—
24	D₅	—	50	2	no	—
25	D₅	D₂₅	1	1	yes	characteristic, direct product factor
26	C₅	—	2	2	no	—
27	C₅	C₂×D₂₅	1	1	yes	characteristic, complemented
28	C₅	D₅²	1	1	yes	characteristic
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, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₂₅	C₂²
Frattini	C₅	D₅²
socle	C₅²	C₂×D₅
LCS	G ▷ C₅×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.