Subgroups — #3941

Order 160.

50 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	C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅	—	2	1	no	—
5	C₂×C₄×C₅	—	2	1	no	—
6	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
7	D₂₀	—	2	1	no	—
8	D₂₀	C₄	1	2	yes	complemented
9	#168	—	2	1	no	—
10	#102	—	5	1	no	maximal, Sylow
11	C₂²×C₅	D₄	1	1	yes	characteristic
12	C₂×D₅	—	2	2	no	—
13	C₂×D₅	—	4	1	no	—
14	C₂×D₅	—	4	1	no	—
15	C₄×C₅	—	4	1	no	—
16	C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₄×C₅	D₄	1	1	yes	characteristic
18	C₂×D₄	—	5	1	no	—
19	C₂×C₈	—	5	1	no	—
20	C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
21	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₅	D₈	1	1	yes	characteristic
23	C₂×C₅	SD₁₆	1	1	yes	characteristic
24	D₅	—	4	2	no	—
25	C₂³	—	10	1	no	—
26	D₄	—	5	2	no	—
27	D₄	—	10	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	C₂×D₅	1	1	yes	characteristic
30	C₈	—	10	1	no	—
31	C₅	#102	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	10	2	no	—
33	C₂²	—	20	1	no	—
34	C₂²	—	20	1	no	—
35	C₂²	C₂²⋊D₅	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₅	1	1	yes	characteristic
38	C₄	D₂₀	1	1	yes	characteristic
39	C₂	—	20	2	no	—
40	C₂	#685	1	1	yes	characteristic
41	C₂	#686	1	1	yes	characteristic
42	C₂	#688	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.