Subgroups — C₂×#689 #4089

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
2	C₂×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	#689	C₂	1	4	yes	maximal, direct product factor
4	C₂×#168	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈	—	2	1	no	—
6	C₅×Q₈	C₂²	1	2	yes	—
7	C₂×C₄×C₅	—	2	1	no	—
8	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₅	—	2	1	no	—
10	Dic₁₀	—	2	1	no	—
11	Dic₁₀	C₂²	1	2	yes	—
12	#168	C₂²	1	2	yes	—
13	C₂×Q₁₆	—	5	1	no	maximal, Sylow
14	C₂²×C₅	D₄	1	1	yes	characteristic
15	C₄×C₅	—	2	2	no	—
16	C₄×C₅	D₄	1	1	yes	characteristic
17	C₄×C₅	C₂³	1	1	yes	characteristic
18	Dic₅	—	2	2	no	—
19	C₂×Q₈	—	5	1	no	—
20	C₂×Q₈	D₅	1	1	yes	characteristic
21	Q₁₆	—	5	4	no	—
22	C₂×C₈	—	5	1	no	—
23	C₂×C₅	Q₁₆	1	2	yes	complemented
24	C₂×C₅	C₂×D₄	1	1	yes	characteristic
25	Q₈	—	2	1	no	—
26	Q₈	—	5	2	no	—
27	Q₈	—	10	1	no	—
28	Q₈	C₂×D₅	1	2	yes	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	—	10	1	no	—
31	C₂×C₄	C₂×D₅	1	1	yes	characteristic
32	C₈	—	5	2	no	—
33	C₅	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂²	C₂²⋊D₅	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	10	2	no	—
37	C₄	C₂²⋊D₅	1	1	yes	characteristic
38	C₄	C₂²×D₅	1	1	yes	characteristic
39	C₂	#689	1	2	yes	direct product factor
40	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.