Subgroups — C₂×C₅²×D₄ #87908

Order 400.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅²	C₂	1	2	yes	maximal, complemented
2	C₅²×D₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅²	—	2	4	no	—
5	C₂²×C₅²	C₂²	1	1	yes	characteristic
6	C₂²×C₅²	C₂²	1	4	yes	complemented
7	C₄×C₅²	C₂²	1	2	yes	complemented
8	C₂×C₅×D₄	C₅	1	6	yes	maximal, direct product factor
9	C₂×C₅²	—	2	4	no	—
10	C₂×C₅²	D₄	1	2	yes	direct product factor
11	C₂×C₅²	C₂³	1	1	yes	characteristic
12	C₂³×C₅	C₂×C₅	1	12	yes	complemented
13	C₅×D₄	C₂×C₅	1	24	yes	direct product factor
14	C₂×C₄×C₅	C₂×C₅	1	6	yes	complemented
15	C₅²	C₂×D₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₅	—	2	24	no	—
17	C₂²×C₅	C₂²×C₅	1	6	yes	—
18	C₂²×C₅	C₂²×C₅	1	24	yes	complemented
19	C₄×C₅	C₂²×C₅	1	12	yes	complemented
20	C₂×D₄	C₅²	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₅	—	2	24	no	—
22	C₂×C₅	C₅×D₄	1	12	yes	direct product factor
23	C₂×C₅	C₂³×C₅	1	6	yes	—
24	C₂³	C₂×C₅²	1	2	yes	complemented
25	D₄	C₂×C₅²	1	4	yes	direct product factor
26	C₂×C₄	C₂×C₅²	1	1	yes	characteristic, complemented
27	C₅	C₂×C₅×D₄	1	6	yes	direct product factor
28	C₂²	—	2	4	no	—
29	C₂²	C₂²×C₅²	1	1	yes	characteristic
30	C₂²	C₂²×C₅²	1	4	yes	complemented
31	C₄	C₂²×C₅²	1	2	yes	complemented
32	C₂	—	2	4	no	—
33	C₂	C₅²×D₄	1	2	yes	direct product factor
34	C₂	C₂³×C₅²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅²	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₅²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅² ◁ 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.