Subgroups — #64931

Order 320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4090	C₂	1	1	yes	maximal, characteristic
2	#4004	C₂	1	2	yes	maximal
3	C₂×C₅×Q₈	C₄	1	1	yes	characteristic
4	C₂×Dic₁₀	C₄	1	1	yes	characteristic
5	C₂×#170	—	2	2	no	—
6	#683	—	2	2	no	—
7	C₄×Dic₅	C₂²	1	1	yes	characteristic
8	#333	—	5	1	no	maximal, Sylow
9	C₅×Q₈	—	4	1	no	—
10	C₂×C₄×C₅	—	2	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	—	4	2	no	—
16	C₄⋊Q₈	—	5	1	no	—
17	C₄⋊C₈	—	5	2	no	—
18	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₅	—	2	1	no	—
20	C₄×C₅	—	4	1	no	—
21	Dic₅	—	4	1	no	—
22	Dic₅	SD₁₆	1	2	yes	—
23	Dic₅	Q₁₆	1	2	yes	—
24	C₂×Q₈	—	5	1	no	—
25	C₂×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
26	C₂×C₈	—	10	2	no	—
27	C₄⋊C₄	—	10	2	no	—
28	C₄²	—	5	1	no	—
29	C₂×C₅	#100	1	1	yes	characteristic
30	C₂×C₅	#103	1	2	yes	—
31	Q₈	—	4	1	no	—
32	Q₈	—	20	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	5	2	no	—
35	C₂×C₄	—	10	1	no	—
36	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₈	—	20	2	no	—
38	C₅	#333	1	1	yes	characteristic, complemented, Sylow
39	C₂²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	5	2	no	—
43	C₄	—	5	2	no	—
44	C₄	—	20	1	no	—
45	C₂	#4009	1	2	yes	—
46	C₂	#4013	1	1	yes	characteristic

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

N	H ≅ G/N	type
38. C₅	#333	semidirect

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