Subgroups — C₄²×AGL(1,𝔽₅) #65685

Order 320.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×AGL(1,𝔽₅)	C₂	1	6	yes	maximal
2	C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×AGL(1,𝔽₅)	C₂²	1	4	yes	—
4	C₂×C₄×D₅	C₂²	1	3	yes	—
5	C₄×AGL(1,𝔽₅)	C₄	1	24	yes	direct product factor
6	C₄²×C₅	C₄	1	1	yes	characteristic, complemented
7	C₄×Dic₅	C₄	1	3	yes	complemented
8	C₄³	—	5	1	no	maximal, Sylow
9	C₂²×D₅	C₂³	1	1	yes	characteristic
10	C₂×AGL(1,𝔽₅)	C₂×C₄	1	24	yes	—
11	C₂×C₄×C₅	C₂×C₄	1	3	yes	—
12	C₂×Dic₅	C₂×C₄	1	3	yes	—
13	C₄×D₅	C₂×C₄	1	12	yes	—
14	C₂×C₄²	—	5	6	no	—
15	C₂×C₄²	—	5	1	no	—
16	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
17	C₂×D₅	C₂²×C₄	1	6	yes	—
18	AGL(1,𝔽₅)	C₄²	1	16	yes	direct product factor
19	C₄×C₅	C₄²	1	6	yes	complemented
20	Dic₅	C₄²	1	6	yes	complemented
21	C₂²×C₄	—	5	4	no	—
22	C₂²×C₄	—	5	3	no	—
23	C₄²	—	5	24	no	—
24	C₄²	—	5	3	no	—
25	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
26	C₂×C₅	C₂×C₄²	1	3	yes	—
27	D₅	C₂×C₄²	1	4	yes	—
28	C₂³	—	5	1	no	—
29	C₂×C₄	—	5	24	no	—
30	C₂×C₄	—	5	3	no	—
31	C₂×C₄	—	5	12	no	—
32	C₂×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
33	C₅	C₄³	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	5	6	no	—
35	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₄	—	5	16	no	—
37	C₄	—	5	6	no	—
38	C₄	C₄×AGL(1,𝔽₅)	1	6	yes	direct product factor
39	C₂	—	5	4	no	—
40	C₂	C₂×C₄×AGL(1,𝔽₅)	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.