Subgroups — #4072

Order 160.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊Dic₅	C₂	1	2	yes	maximal
3	C₄⋊Dic₅	C₂	1	2	yes	maximal, complemented
4	C₄×Dic₅	C₂	1	2	yes	maximal, complemented
5	C₂³×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅	C₄	1	4	yes	complemented
7	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₅	C₂²	1	4	yes	—
10	#117	—	5	1	no	maximal, Sylow
11	C₂²×C₅	—	2	2	no	—
12	C₂²×C₅	C₂×C₄	1	2	yes	—
13	C₂²×C₅	C₂³	1	1	yes	characteristic
14	C₄×C₅	C₂×C₄	1	2	yes	—
15	C₄×C₅	C₂×C₄	1	2	yes	—
16	Dic₅	—	2	4	no	—
17	C₂²×C₄	D₅	1	1	yes	characteristic
18	C₄⋊C₄	—	5	2	no	—
19	C₂²⋊C₄	—	5	2	no	—
20	C₄²	—	5	2	no	—
21	C₂×C₅	—	2	2	no	—
22	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₅	#41	1	2	yes	—
24	C₂³	C₂×D₅	1	1	yes	characteristic
25	C₂×C₄	—	5	4	no	—
26	C₂×C₄	Dic₅	1	4	yes	complemented
27	C₂×C₄	C₂×D₅	1	1	yes	characteristic
28	C₂×C₄	C₂×D₅	1	1	yes	characteristic
29	C₅	#117	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₅	1	2	yes	—
32	C₂²	C₂²×D₅	1	1	yes	characteristic
33	C₄	—	10	4	no	—
34	C₄	C₂×Dic₅	1	2	yes	—
35	C₄	C₂×Dic₅	1	2	yes	—
36	C₂	—	2	2	no	—
37	C₂	#709	1	2	yes	—
38	C₂	C₂²×Dic₅	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.