Subgroups — #4088

Order 160.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#709	C₂	1	1	yes	maximal, characteristic
3	#689	C₂	1	2	yes	maximal, complemented
4	#688	C₂	1	2	yes	maximal, complemented
5	#681	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Q₈	—	2	1	no	—
7	C₅×Q₈	C₂²	1	2	yes	—
8	C₂×C₄×C₅	—	2	1	no	—
9	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²⋊D₅	—	2	1	no	—
11	D₂₀	C₂²	1	1	yes	characteristic
12	C₄×D₅	—	2	1	no	—
13	Dic₁₀	C₂²	1	1	yes	characteristic
14	#168	C₂²	1	2	yes	—
15	#137	—	5	1	no	maximal, Sylow
16	C₂²×C₅	D₄	1	1	yes	characteristic
17	C₂×D₅	—	2	1	no	—
18	C₄×C₅	—	2	2	no	—
19	C₄×C₅	D₄	1	1	yes	characteristic
20	C₄×C₅	C₂³	1	1	yes	characteristic
21	Dic₅	—	2	1	no	—
22	#41	—	5	1	no	—
23	C₂×Q₈	D₅	1	1	yes	characteristic, complemented
24	Q₁₆	—	5	2	no	—
25	SD₁₆	—	5	2	no	—
26	M₁₆	—	5	1	no	—
27	C₂×C₅	—	2	1	no	—
28	C₂×C₅	C₂×D₄	1	1	yes	characteristic
29	D₅	—	4	1	no	—
30	Q₈	—	2	1	no	—
31	Q₈	—	5	1	no	—
32	Q₈	C₂×D₅	1	2	yes	—
33	D₄	—	5	1	no	—
34	D₄	—	10	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	—	10	1	no	—
37	C₂×C₄	C₂×D₅	1	1	yes	characteristic
38	C₈	—	5	2	no	—
39	C₅	#137	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	10	1	no	—
41	C₂²	C₂²⋊D₅	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	10	1	no	—
44	C₄	C₂²⋊D₅	1	1	yes	characteristic
45	C₄	C₂²×D₅	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	20	1	no	—
48	C₂	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.