Subgroups — D₄×D₅ #710

Order 80.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅	C₂	1	2	yes	maximal, complemented
2	C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
4	D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅	C₂²	1	2	yes	complemented
7	C₂×D₅	—	2	4	no	—
8	C₂×D₅	C₂²	1	1	yes	characteristic
9	C₂×D₅	C₂²	1	2	yes	complemented
10	C₄×C₅	C₂²	1	1	yes	characteristic, complemented
11	Dic₅	C₂²	1	1	yes	characteristic, complemented
12	C₂×D₄	—	5	1	no	maximal, Sylow
13	C₂×C₅	—	2	2	no	—
14	C₂×C₅	C₂³	1	1	yes	characteristic
15	D₅	—	2	2	no	—
16	D₅	D₄	1	2	yes	direct product factor
17	C₂³	—	5	2	no	—
18	D₄	—	5	2	no	—
19	D₄	—	5	1	no	—
20	D₄	D₅	1	1	yes	characteristic, direct product factor
21	C₂×C₄	—	5	1	no	—
22	C₅	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
23	C₂²	—	5	1	no	—
24	C₂²	—	5	2	no	—
25	C₂²	—	10	4	no	—
26	C₂²	C₂×D₅	1	2	yes	complemented
27	C₄	—	5	1	no	—
28	C₄	C₂×D₅	1	1	yes	characteristic, complemented
29	C₂	—	2	2	no	—
30	C₂	—	5	2	no	—
31	C₂	—	10	2	no	—
32	C₂	C₂²×D₅	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.