Subgroups — #65690

Order 320.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	(C₂×AGL(1,𝔽₅))⋊C₄	C₂	1	6	yes	maximal
3	C₂²×AGL(1,𝔽₅)	C₂²	1	4	yes	—
4	C₂×C₄×D₅	C₂²	1	3	yes	—
5	C₄²×C₅	C₄	1	1	yes	characteristic, complemented
6	C₄×Dic₅	C₄	1	3	yes	complemented
7	#383	—	5	1	no	maximal, Sylow
8	C₂²×D₅	C₂³	1	1	yes	characteristic
9	C₂×AGL(1,𝔽₅)	—	2	12	no	—
10	C₂×C₄×C₅	C₂×C₄	1	3	yes	—
11	C₂×Dic₅	C₂×C₄	1	3	yes	—
12	C₄×D₅	—	2	6	no	—
13	C₂×C₄²	—	5	1	no	—
14	#95	—	5	6	no	—
15	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
16	C₂×D₅	#41	1	6	yes	—
17	AGL(1,𝔽₅)	—	4	4	no	—
18	C₄×C₅	—	2	3	no	—
19	Dic₅	—	2	3	no	—
20	C₂²×C₄	—	5	3	no	—
21	C₂²×C₄	—	5	4	no	—
22	C₄²	—	5	3	no	—
23	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
24	C₂×C₅	#117	1	3	yes	—
25	D₅	#126	1	4	yes	—
26	C₂³	—	5	1	no	—
27	C₂×C₄	—	5	3	no	—
28	C₂×C₄	—	10	6	no	—
29	C₂×C₄	—	10	12	no	—
30	C₂×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
31	C₅	#383	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	5	6	no	—
33	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₄	—	2	3	no	—
35	C₄	—	10	3	no	—
36	C₄	—	20	4	no	—
37	C₂	—	5	4	no	—
38	C₂	#4130	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.