Subgroups — #4021

Order 160.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#685	C₂	1	4	yes	maximal, complemented
5	C₂²×D₅	C₂²	1	2	yes	—
6	C₂×C₄×C₅	C₂²	1	2	yes	—
7	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×Dic₅	C₂²	1	2	yes	—
9	D₂₀	—	2	2	no	—
10	Dic₁₀	—	2	2	no	—
11	#124	—	5	1	no	maximal, Sylow
12	C₂²×C₅	C₂³	1	1	yes	characteristic
13	C₂×D₅	—	2	2	no	—
14	C₂×D₅	—	2	4	no	—
15	C₄×C₅	—	2	2	no	—
16	C₄×C₅	D₄	1	2	yes	—
17	Dic₅	—	2	2	no	—
18	C₂×Q₈	—	5	1	no	—
19	C₂×D₄	—	5	1	no	—
20	C₂²⋊C₄	—	5	4	no	—
21	C₄²	D₅	1	1	yes	characteristic, complemented
22	C₂×C₅	C₂×D₄	1	1	yes	characteristic
23	C₂×C₅	#41	1	2	yes	—
24	D₅	—	4	2	no	—
25	C₂³	—	5	2	no	—
26	Q₈	—	10	2	no	—
27	D₄	—	10	2	no	—
28	C₂×C₄	—	5	2	no	—
29	C₂×C₄	C₂×D₅	1	2	yes	—
30	C₂×C₄	C₂×D₅	1	1	yes	characteristic
31	C₅	#124	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	10	2	no	—
33	C₂²	—	10	4	no	—
34	C₂²	C₂²×D₅	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	10	2	no	—
37	C₄	D₂₀	1	2	yes	—
38	C₂	—	20	2	no	—
39	C₂	C₂×D₂₀	1	1	yes	characteristic
40	C₂	#709	1	2	yes	—

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.