Subgroups — C₄×Dic₂₅ #87717

Order 400.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₅	C₂	1	2	yes	maximal
3	C₂²×C₂₅	C₂²	1	1	yes	characteristic
4	C₄×C₂₅	C₄	1	2	yes	complemented
5	Dic₂₅	C₄	1	4	yes	direct product factor
6	C₄×Dic₅	—	5	1	no	maximal
7	C₂×C₂₅	C₂×C₄	1	2	yes	—
8	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅	D₅	1	1	yes	characteristic
10	C₂×Dic₅	—	5	2	no	—
11	C₂₅	C₄²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
13	C₄×C₅	Dic₅	1	2	yes	—
14	Dic₅	—	5	4	no	—
15	C₄²	—	25	1	no	Sylow
16	C₂×C₅	C₄×D₅	1	2	yes	—
17	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
18	C₂×C₄	—	25	2	no	—
19	C₂×C₄	D₂₅	1	1	yes	characteristic
20	C₅	C₄×Dic₅	1	1	yes	characteristic
21	C₂²	C₂×D₂₅	1	1	yes	characteristic
22	C₄	—	25	4	no	—
23	C₄	Dic₂₅	1	2	yes	direct product factor
24	C₂	C₄×D₂₅	1	2	yes	—
25	C₂	C₂×Dic₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₂₅
commutator, hypocenter	C₂₅	C₄²
Frattini, socle, prime radical	C₂²×C₅	C₂×D₅
Fitting	C₂×C₄×C₂₅	C₂
cosocle	C₂²×C₂₅	C₂²
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₄

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.