Subgroups — #64972

Order 320.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4016	C₂	1	2	yes	maximal
2	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	#3950	C₂	1	2	yes	maximal
4	#3949	C₂	1	2	yes	maximal
5	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₅	C₂²	1	4	yes	—
9	#683	—	2	4	no	—
10	#499	—	5	1	no	maximal, Sylow
11	C₂×C₄×C₅	D₄	1	2	yes	—
12	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
13	C₂×Dic₅	—	2	4	no	—
14	C₅×C₈	Q₈	1	2	yes	—
15	C₅×C₈	Q₈	1	2	yes	—
16	#125	—	5	2	no	—
17	#107	—	5	2	no	—
18	#106	—	5	2	no	—
19	C₄×C₈	D₅	1	1	yes	characteristic
20	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
21	C₄×C₅	—	2	2	no	—
22	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
24	Dic₅	—	4	4	no	—
25	C₂×C₈	C₂×D₅	1	1	yes	characteristic
26	C₂×C₈	C₂×D₅	1	1	yes	characteristic
27	C₄⋊C₄	—	5	4	no	—
28	C₄⋊C₄	—	10	4	no	—
29	C₄²	C₂×D₅	1	1	yes	characteristic
30	C₂×C₅	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₅	#135	1	2	yes	—
32	C₂×C₄	—	10	4	no	—
33	C₂×C₄	D₂₀	1	2	yes	—
34	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
35	C₈	Dic₁₀	1	2	yes	—
36	C₈	Dic₁₀	1	2	yes	—
37	C₅	#499	1	1	yes	characteristic, complemented, Sylow
38	C₂²	C₂×D₂₀	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	20	4	no	—
41	C₄	C₂×Dic₁₀	1	1	yes	characteristic
42	C₄	C₂×Dic₁₀	1	1	yes	characteristic
43	C₂	#4015	1	1	yes	characteristic
44	C₂	#4050	1	2	yes	—

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

N	H ≅ G/N	type
37. C₅	#499	semidirect

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