Subgroups — #685

Order 80.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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