Subgroups — C₂×C₅²×D₅ #92567

Order 500.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₅³	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₅²

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.