Subgroups — #4022

Order 160.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	#685	C₂	1	3	yes	maximal
3	#683	C₂	1	3	yes	maximal, complemented
4	C₂²×D₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅	C₂²	1	3	yes	—
6	C₂×Dic₅	C₂²	1	3	yes	—
7	#126	—	5	1	no	maximal, Sylow
8	C₂²×C₅	C₂³	1	1	yes	characteristic
9	C₂×D₅	—	2	3	no	—
10	C₄×C₅	—	2	3	no	—
11	Dic₅	—	2	3	no	—
12	C₄⋊C₄	—	5	3	no	—
13	C₂²⋊C₄	—	5	3	no	—
14	C₄²	D₅	1	1	yes	characteristic, complemented
15	C₂×C₅	#41	1	3	yes	—
16	D₅	—	4	1	no	—
17	C₂³	—	5	1	no	—
18	C₂×C₄	—	5	3	no	—
19	C₂×C₄	C₂×D₅	1	3	yes	—
20	C₅	#126	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	10	3	no	—
22	C₂²	C₂²×D₅	1	1	yes	characteristic
23	C₄	—	2	3	no	—
24	C₄	—	10	3	no	—
25	C₂	—	20	1	no	—
26	C₂	#709	1	3	yes	—

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.