Subgroups — C₂×C₄×D₅ #707

Order 80.

54 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	C₄×D₅	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅	C₂²	1	1	yes	characteristic
6	C₂×D₅	C₄	1	4	yes	direct product factor
7	C₂×D₅	C₂²	1	2	yes	—
8	C₄×C₅	C₂²	1	2	yes	complemented
9	Dic₅	C₂²	1	2	yes	complemented
10	C₂²×C₄	—	5	1	no	maximal, Sylow
11	C₂×C₅	C₂×C₄	1	2	yes	complemented
12	C₂×C₅	C₂³	1	1	yes	characteristic
13	D₅	C₂×C₄	1	4	yes	direct product factor
14	C₂³	—	5	1	no	—
15	C₂×C₄	—	5	1	no	—
16	C₂×C₄	—	5	4	no	—
17	C₂×C₄	D₅	1	1	yes	characteristic, direct product factor
18	C₅	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	5	4	no	—
20	C₂²	—	5	2	no	—
21	C₂²	C₂×D₅	1	1	yes	characteristic
22	C₄	—	5	2	no	—
23	C₄	C₂×D₅	1	2	yes	direct product factor
24	C₂	—	5	4	no	—
25	C₂	C₄×D₅	1	2	yes	direct product factor
26	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.