Subgroups — #3999

Order 160.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
3	C₂²×D₅	C₄	1	1	yes	characteristic, complemented
4	C₂²×D₅	C₂²	1	1	yes	characteristic
5	C₂×AGL(1,𝔽₅)	—	2	2	no	—
6	C₂×C₄×C₅	C₄	1	1	yes	characteristic, complemented
7	D₂₀	—	2	2	no	—
8	#99	—	5	1	no	maximal, Sylow
9	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
10	C₂×D₅	—	2	1	no	—
11	C₂×D₅	—	4	1	no	—
12	C₂×D₅	—	4	1	no	—
13	C₂×D₅	D₄	1	2	yes	—
14	AGL(1,𝔽₅)	—	4	2	no	—
15	C₄×C₅	—	2	1	no	—
16	C₂×D₄	—	5	1	no	—
17	C₂²⋊C₄	—	5	2	no	—
18	C₂×C₅	—	2	1	no	—
19	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
20	D₅	—	2	2	no	—
21	D₅	—	4	1	no	—
22	C₂³	—	5	1	no	—
23	C₂³	—	5	1	no	—
24	D₄	—	10	2	no	—
25	C₂×C₄	—	10	2	no	—
26	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
27	C₅	#99	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	5	2	no	—
29	C₂²	—	10	1	no	—
30	C₂²	—	20	1	no	—
31	C₂²	—	20	1	no	—
32	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	20	2	no	—
35	C₂	—	2	1	no	—
36	C₂	—	10	2	no	—
37	C₂	—	20	1	no	—
38	C₂	C₂²⋊AGL(1,𝔽₅)	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.