Subgroups — #65688

Order 320.

186 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)	—	2	12	no	—
6	C₄²×C₅	C₄	1	1	yes	characteristic, complemented
7	C₄×Dic₅	C₄	1	3	yes	complemented
8	#384	—	5	1	no	maximal, Sylow
9	C₂²×D₅	C₂³	1	1	yes	characteristic
10	C₂×AGL(1,𝔽₅)	—	2	12	no	—
11	C₂×C₄×C₅	C₂×C₄	1	3	yes	—
12	C₂×Dic₅	C₂×C₄	1	3	yes	—
13	C₄×D₅	D₄	1	6	yes	—
14	C₄×D₅	Q₈	1	6	yes	—
15	C₂×C₄⋊C₄	—	5	6	no	—
16	C₂×C₄²	—	5	1	no	—
17	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
18	C₂×D₅	C₂×D₄	1	3	yes	—
19	C₂×D₅	C₂×Q₈	1	3	yes	—
20	AGL(1,𝔽₅)	—	4	4	no	—
21	C₄×C₅	C₄⋊C₄	1	6	yes	complemented
22	Dic₅	C₄⋊C₄	1	6	yes	complemented
23	C₂²×C₄	—	5	3	no	—
24	C₂²×C₄	—	5	4	no	—
25	C₄⋊C₄	—	10	12	no	—
26	C₄²	—	5	3	no	—
27	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
28	C₂×C₅	C₂×C₄⋊C₄	1	3	yes	—
29	D₅	#127	1	1	yes	characteristic
30	D₅	C₄⋊Q₈	1	3	yes	—
31	C₂³	—	5	1	no	—
32	C₂×C₄	—	5	3	no	—
33	C₂×C₄	—	5	6	no	—
34	C₂×C₄	—	5	6	no	—
35	C₂×C₄	—	10	12	no	—
36	C₂×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
37	C₅	#384	1	1	yes	characteristic, complemented, Sylow
38	C₂²	—	5	3	no	—
39	C₂²	—	5	3	no	—
40	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
41	C₄	—	5	6	no	—
42	C₄	—	20	4	no	—
43	C₄	C₄⋊AGL(1,𝔽₅)	1	6	yes	complemented
44	C₂	—	5	1	no	—
45	C₂	—	5	3	no	—
46	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.