Subgroups — C₅×Dic₂₀ #87786

Order 400.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₁₀	C₂	1	2	yes	maximal
2	C₅²×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅²	C₂²	1	1	yes	characteristic
4	C₅×Dic₅	—	2	2	no	—
5	C₅×Q₁₆	—	5	1	no	maximal
6	Dic₂₀	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅²	D₄	1	1	yes	characteristic
8	C₅×Q₈	—	5	2	no	—
9	Dic₁₀	C₂×C₅	1	2	yes	—
10	C₅×C₈	—	2	2	no	—
11	C₅×C₈	D₅	1	1	yes	characteristic
12	C₅×C₈	C₂×C₅	1	1	yes	characteristic
13	C₅²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₄×C₅	—	2	2	no	—
15	C₄×C₅	—	10	2	no	—
16	C₄×C₅	C₂×D₅	1	1	yes	characteristic
17	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
18	Dic₅	—	2	2	no	—
19	Q₁₆	—	5	1	no	Sylow
20	C₂×C₅	—	2	2	no	—
21	C₂×C₅	D₂₀	1	1	yes	characteristic
22	C₂×C₅	C₅×D₄	1	1	yes	characteristic
23	Q₈	—	5	2	no	—
24	C₈	C₅×D₅	1	1	yes	characteristic
25	C₅	—	2	2	no	—
26	C₅	Dic₂₀	1	1	yes	characteristic, direct product factor
27	C₅	C₅×Q₁₆	1	1	yes	characteristic, complemented
28	C₄	—	10	2	no	—
29	C₄	C₂×C₅×D₅	1	1	yes	characteristic
30	C₂	C₅×D₂₀	1	1	yes	characteristic

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.