Subgroups — #64854

Order 320.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4021	C₂	1	1	yes	maximal, characteristic
2	#3999	C₂	1	2	yes	maximal
3	C₂×D₂₀	C₂²	1	1	yes	characteristic
4	C₂×Dic₁₀	C₄	1	1	yes	characteristic, complemented
5	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
6	C₄²×C₅	C₄	1	1	yes	characteristic, complemented
7	#685	—	2	2	no	—
8	#354	—	5	1	no	maximal, Sylow
9	C₂²×D₅	D₄	1	2	yes	—
10	C₂×AGL(1,𝔽₅)	—	4	2	no	—
11	C₂×C₄×C₅	—	2	1	no	—
12	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₅	—	2	1	no	—
14	D₂₀	—	4	1	no	—
15	Dic₁₀	—	4	1	no	—
16	#124	—	5	1	no	—
17	#99	—	5	2	no	—
18	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×D₅	—	2	2	no	—
20	C₂×D₅	—	4	2	no	—
21	AGL(1,𝔽₅)	—	8	2	no	—
22	C₄×C₅	—	2	1	no	—
23	C₄×C₅	—	4	1	no	—
24	Dic₅	—	4	1	no	—
25	C₂×Q₈	—	5	1	no	—
26	C₂×D₄	—	5	1	no	—
27	C₂²⋊C₄	—	10	2	no	—
28	C₂²⋊C₄	—	10	2	no	—
29	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
30	C₂×C₅	—	2	1	no	—
31	C₂×C₅	#99	1	1	yes	characteristic
32	D₅	—	4	2	no	—
33	C₂³	—	5	2	no	—
34	Q₈	—	20	1	no	—
35	D₄	—	20	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	10	1	no	—
38	C₂×C₄	—	20	2	no	—
39	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₅	#354	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	10	2	no	—
42	C₂²	—	20	2	no	—
43	C₂²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	20	1	no	—
47	C₄	—	40	2	no	—
48	C₂	—	2	1	no	—
49	C₂	—	20	2	no	—
50	C₂	#3999	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.