Subgroups — #64921

Order 320.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4082	C₂	1	1	yes	maximal, characteristic
2	#4002	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₄	C₄	1	1	yes	characteristic
4	C₂×Dic₁₀	C₄	1	1	yes	characteristic
5	C₂×#170	—	2	2	no	—
6	C₂²⋊Dic₅	—	2	2	no	—
7	C₄×Dic₅	C₂²	1	1	yes	characteristic
8	#329	—	5	1	no	maximal, Sylow
9	C₂³×C₅	—	2	1	no	—
10	C₅×D₄	—	4	1	no	—
11	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₅	—	2	1	no	—
13	C₂×Dic₅	D₄	1	2	yes	—
14	Dic₁₀	—	4	1	no	—
15	#170	—	2	4	no	—
16	#124	—	5	1	no	—
17	#97	—	5	2	no	—
18	C₂²×C₅	—	4	1	no	—
19	C₂²×C₅	—	4	2	no	—
20	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₅	—	2	1	no	—
22	Dic₅	—	2	2	no	—
23	Dic₅	—	4	1	no	—
24	C₂×Q₈	—	5	1	no	—
25	C₂×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
26	C₂×C₈	—	10	2	no	—
27	C₂²⋊C₄	—	10	2	no	—
28	C₄²	—	5	1	no	—
29	C₂×C₅	—	8	1	no	—
30	C₂×C₅	#100	1	1	yes	characteristic
31	C₂×C₅	#104	1	2	yes	—
32	C₂³	—	2	1	no	—
33	Q₈	—	20	1	no	—
34	D₄	—	4	1	no	—
35	C₂×C₄	—	5	2	no	—
36	C₂×C₄	—	10	1	no	—
37	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
38	C₈	—	10	4	no	—
39	C₅	#329	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	4	2	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	10	2	no	—
45	C₄	—	20	1	no	—
46	C₂	—	8	1	no	—
47	C₂	#4008	1	2	yes	—
48	C₂	#4013	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #4002	C₂	semidirect
39. C₅	#329	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.