Subgroups — C₄⋊Dic₂₅ #87719

Order 400.

39 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	—	2	2	no	—
6	C₄⋊Dic₅	—	5	1	no	maximal
7	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
8	C₂×C₂₅	D₄	1	1	yes	characteristic
9	C₂×C₂₅	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₅	D₅	1	1	yes	characteristic
11	C₂×Dic₅	—	5	2	no	—
12	C₂₅	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
14	C₄×C₅	Dic₅	1	2	yes	—
15	Dic₅	—	10	2	no	—
16	C₄⋊C₄	—	25	1	no	Sylow
17	C₂×C₅	Dic₁₀	1	1	yes	characteristic
18	C₂×C₅	D₂₀	1	1	yes	characteristic
19	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
20	C₂×C₄	—	25	2	no	—
21	C₂×C₄	D₂₅	1	1	yes	characteristic
22	C₅	C₄⋊Dic₅	1	1	yes	characteristic
23	C₂²	C₂×D₂₅	1	1	yes	characteristic
24	C₄	—	50	2	no	—
25	C₄	Dic₂₅	1	2	yes	complemented
26	C₂	Dic₅₀	1	1	yes	characteristic
27	C₂	D₁₀₀	1	1	yes	characteristic
28	C₂	C₂×Dic₂₅	1	1	yes	characteristic

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