Subgroups — C₂×#713 #4146

Order 160.

164 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	#713	C₂	1	8	yes	maximal, direct product factor
3	C₂×D₂₀	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×D₅	C₂	1	3	yes	maximal, complemented
5	C₂²×D₅	C₂²	1	3	yes	—
6	C₅×Q₈	C₂²	1	4	yes	complemented
7	C₂×C₄×C₅	C₂²	1	3	yes	—
8	C₂×Dic₅	C₂²	1	1	yes	characteristic
9	D₂₀	C₂²	1	12	yes	complemented
10	C₄×D₅	C₂²	1	12	yes	complemented
11	C₂×#41	—	5	1	no	maximal, Sylow
12	C₂²×C₅	C₂³	1	1	yes	characteristic
13	C₂×D₅	—	2	6	no	—
14	C₂×D₅	C₂³	1	6	yes	—
15	C₄×C₅	C₂³	1	6	yes	—
16	Dic₅	C₂³	1	2	yes	—
17	#41	—	5	8	no	—
18	C₂×Q₈	D₅	1	1	yes	characteristic, complemented
19	C₂×D₄	—	5	3	no	—
20	C₂²×C₄	—	5	3	no	—
21	C₂×C₅	#41	1	2	yes	complemented
22	C₂×C₅	C₂⁴	1	1	yes	characteristic
23	D₅	—	2	6	no	—
24	C₂³	—	5	3	no	—
25	Q₈	C₂×D₅	1	4	yes	complemented
26	D₄	—	5	12	no	—
27	C₂×C₄	—	5	1	no	—
28	C₂×C₄	—	5	12	no	—
29	C₂×C₄	C₂×D₅	1	3	yes	—
30	C₅	C₂×#41	1	1	yes	characteristic, complemented, Sylow
31	C₂²	—	5	6	no	—
32	C₂²	—	10	6	no	—
33	C₂²	C₂²×D₅	1	1	yes	characteristic
34	C₄	—	5	2	no	—
35	C₄	C₂²×D₅	1	6	yes	—
36	C₂	—	10	6	no	—
37	C₂	#713	1	2	yes	direct product factor
38	C₂	C₂³×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.