Subgroups — (C₂×AGL(1,𝔽₅))⋊C₄ #4006

Order 160.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₂×C₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×D₅	C₂²	1	1	yes	characteristic
4	C₂×AGL(1,𝔽₅)	—	2	2	no	—
5	C₂×AGL(1,𝔽₅)	—	2	2	no	—
6	C₂×AGL(1,𝔽₅)	C₄	1	4	yes	complemented
7	C₂×C₄×C₅	C₄	1	1	yes	characteristic, complemented
8	C₂×Dic₅	C₄	1	1	yes	characteristic, complemented
9	C₄×D₅	—	2	2	no	—
10	#95	—	5	1	no	maximal, Sylow
11	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×D₅	C₂×C₄	1	2	yes	—
13	C₂×D₅	D₄	1	1	yes	characteristic
14	C₂×D₅	D₄	1	2	yes	—
15	C₂×D₅	Q₈	1	1	yes	characteristic
16	AGL(1,𝔽₅)	—	2	4	no	—
17	C₄×C₅	—	2	1	no	—
18	Dic₅	—	2	1	no	—
19	C₂²×C₄	—	5	2	no	—
20	C₂²×C₄	—	5	1	no	—
21	C₂×C₅	C₄²	1	1	yes	characteristic
22	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₅	C₄⋊C₄	1	1	yes	characteristic
24	D₅	C₂²⋊C₄	1	2	yes	—
25	D₅	C₄⋊C₄	1	2	yes	—
26	C₂³	—	5	1	no	—
27	C₂×C₄	—	5	4	no	—
28	C₂×C₄	—	5	1	no	—
29	C₂×C₄	—	10	2	no	—
30	C₂×C₄	—	10	2	no	—
31	C₂×C₄	—	10	2	no	—
32	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
33	C₅	#95	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	5	2	no	—
35	C₂²	—	5	1	no	—
36	C₂²	—	5	1	no	—
37	C₂²	—	5	2	no	—
38	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	10	4	no	—
41	C₄	—	10	1	no	—
42	C₂	—	5	2	no	—
43	C₂	—	5	2	no	—
44	C₂	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
45	C₂	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
46	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.