Subgroups — C₄⋊C₄×C₂₅ #87728

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	2	yes	maximal
2	C₂×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₅	C₂²	1	1	yes	characteristic
4	C₄×C₂₅	—	2	2	no	—
5	C₄×C₂₅	C₄	1	2	yes	complemented
6	C₅×C₄⋊C₄	C₅	1	1	yes	maximal, characteristic
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	C₂×C₅	1	2	yes	—
11	C₂×C₄×C₅	C₂×C₅	1	1	yes	characteristic
12	C₂₅	C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
14	C₄×C₅	—	2	2	no	—
15	C₄×C₅	C₄×C₅	1	2	yes	—
16	C₄⋊C₄	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₅	C₂×C₄×C₅	1	1	yes	characteristic
18	C₂×C₅	C₅×D₄	1	1	yes	characteristic
19	C₂×C₅	C₅×Q₈	1	1	yes	characteristic
20	C₂×C₄	C₂×C₂₅	1	2	yes	—
21	C₂×C₄	C₂×C₂₅	1	1	yes	characteristic
22	C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
23	C₂²	C₂²×C₂₅	1	1	yes	characteristic
24	C₄	—	2	2	no	—
25	C₄	C₄×C₂₅	1	2	yes	complemented
26	C₂	C₂×C₄×C₂₅	1	1	yes	characteristic
27	C₂	D₄×C₂₅	1	1	yes	characteristic
28	C₂	Q₈×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₂₅	C₂²
commutator	C₂	C₂×C₄×C₂₅
Frattini, socle, prime radical, cosocle	C₂²×C₅	C₂²×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅ ◁ G

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.

subgroup	index
C₂×C₄×C₂₅	2
C₅×C₄⋊C₄	5