Subgroups — #709

Order 80.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
3	D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₅	C₂	1	2	yes	maximal, complemented
5	Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅	C₂²	1	1	yes	characteristic
7	C₂×D₅	C₂²	1	2	yes	—
8	C₄×C₅	C₂²	1	1	yes	characteristic
9	C₄×C₅	C₂²	1	1	yes	characteristic
10	Dic₅	C₂²	1	2	yes	—
11	#41	—	5	1	no	maximal, Sylow
12	C₂×C₅	—	2	1	no	—
13	C₂×C₅	C₂³	1	1	yes	characteristic
14	D₅	—	2	2	no	—
15	Q₈	—	5	1	no	—
16	D₄	—	5	2	no	—
17	D₄	—	5	1	no	—
18	C₂×C₄	—	5	2	no	—
19	C₂×C₄	D₅	1	1	yes	characteristic, complemented
20	C₅	#41	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	5	2	no	—
22	C₂²	C₂×D₅	1	1	yes	characteristic
23	C₄	—	5	2	no	—
24	C₄	C₂×D₅	1	1	yes	characteristic
25	C₄	C₂×D₅	1	1	yes	characteristic
26	C₂	—	2	1	no	—
27	C₂	—	10	2	no	—
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.