Subgroups — C₅×D₄₀ #87785

Order 400.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₀	C₂	1	2	yes	maximal, complemented
2	C₅²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅	—	2	2	no	—
4	C₄×C₅²	C₂²	1	1	yes	characteristic
5	C₅×D₈	—	5	1	no	maximal
6	D₄₀	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅²	D₄	1	1	yes	characteristic
8	C₅×D₅	—	4	2	no	—
9	C₅×D₄	—	5	2	no	—
10	D₂₀	C₂×C₅	1	2	yes	complemented
11	C₅×C₈	—	2	2	no	—
12	C₅×C₈	D₅	1	1	yes	characteristic, complemented
13	C₅×C₈	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅²	D₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅	—	10	2	no	—
16	C₂×D₅	—	2	2	no	—
17	C₄×C₅	—	2	2	no	—
18	C₄×C₅	C₂×D₅	1	1	yes	characteristic
19	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
20	D₈	—	5	1	no	Sylow
21	C₂×C₅	—	2	2	no	—
22	C₂×C₅	—	20	2	no	—
23	C₂×C₅	D₂₀	1	1	yes	characteristic
24	C₂×C₅	C₅×D₄	1	1	yes	characteristic
25	D₅	—	4	2	no	—
26	D₄	—	5	2	no	—
27	C₈	C₅×D₅	1	1	yes	characteristic, complemented
28	C₅	—	2	2	no	—
29	C₅	D₄₀	1	1	yes	characteristic, direct product factor
30	C₅	C₅×D₈	1	1	yes	characteristic, complemented
31	C₂²	—	10	2	no	—
32	C₄	C₂×C₅×D₅	1	1	yes	characteristic
33	C₂	—	20	2	no	—
34	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.