Subgroups — C₂×#686 #4077

Order 160.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#686	C₂	1	4	yes	maximal, direct product factor
4	C₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅	—	2	1	no	—
6	C₂²×D₅	—	2	1	no	—
7	C₅×D₄	—	2	1	no	—
8	C₅×D₄	C₂²	1	2	yes	complemented
9	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
10	D₂₀	—	2	1	no	—
11	D₂₀	C₂²	1	2	yes	complemented
12	#168	C₂²	1	2	yes	complemented
13	C₂×D₈	—	5	1	no	maximal, Sylow
14	C₂²×C₅	—	2	2	no	—
15	C₂²×C₅	—	4	2	no	—
16	C₂²×C₅	D₄	1	1	yes	characteristic
17	C₂×D₅	—	2	2	no	—
18	C₂×D₅	—	4	2	no	—
19	C₄×C₅	D₄	1	1	yes	characteristic
20	C₄×C₅	C₂³	1	1	yes	characteristic
21	C₂×D₄	—	5	1	no	—
22	C₂×D₄	D₅	1	1	yes	characteristic, complemented
23	D₈	—	5	4	no	—
24	C₂×C₈	—	5	1	no	—
25	C₂×C₅	—	4	2	no	—
26	C₂×C₅	D₈	1	2	yes	complemented
27	C₂×C₅	C₂×D₄	1	1	yes	characteristic
28	D₅	—	4	2	no	—
29	C₂³	—	2	1	no	—
30	C₂³	—	10	1	no	—
31	D₄	—	2	1	no	—
32	D₄	—	5	2	no	—
33	D₄	—	10	1	no	—
34	D₄	C₂×D₅	1	2	yes	complemented
35	C₂×C₄	C₂×D₅	1	1	yes	characteristic
36	C₈	—	5	2	no	—
37	C₅	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
38	C₂²	—	2	2	no	—
39	C₂²	—	4	2	no	—
40	C₂²	—	10	2	no	—
41	C₂²	—	20	2	no	—
42	C₂²	C₂²⋊D₅	1	1	yes	characteristic
43	C₄	C₂²⋊D₅	1	1	yes	characteristic
44	C₄	C₂²×D₅	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	—	20	2	no	—
47	C₂	#686	1	2	yes	direct product factor
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.