Subgroups — #64683

Order 320.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	#3944	C₂	1	2	yes	maximal
3	C₂×C₅×C₈	C₄	1	1	yes	characteristic
4	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₄²×C₅	C₄	1	1	yes	characteristic
6	#672	—	2	2	no	—
7	#364	—	5	1	no	maximal, Sylow
8	C₂×C₄×C₅	—	2	1	no	—
9	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₅×C₈	C₈	1	2	yes	—
11	C₅×C₈	D₄	1	1	yes	characteristic
12	C₅×C₈	Q₈	1	1	yes	characteristic
13	M₃₂	—	5	2	no	—
14	C₄×C₈	D₅	1	1	yes	characteristic
15	C₂²×C₅	M₁₆	1	1	yes	characteristic
16	C₄×C₅	—	2	2	no	—
17	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
18	C₄×C₅	C₂×C₈	1	1	yes	characteristic
19	C₂×C₈	Dic₅	1	1	yes	characteristic
20	C₂×C₈	C₂×D₅	1	1	yes	characteristic
21	C₄²	Dic₅	1	1	yes	characteristic
22	C₁₆	—	10	2	no	—
23	C₂×C₅	—	2	1	no	—
24	C₂×C₅	C₄⋊C₈	1	1	yes	characteristic
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×Dic₅	1	1	yes	characteristic
27	C₈	#168	1	2	yes	—
28	C₈	Dic₁₀	1	1	yes	characteristic
29	C₈	D₂₀	1	1	yes	characteristic
30	C₅	#364	1	1	yes	characteristic, complemented, Sylow
31	C₂²	#681	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₂×#168	1	1	yes	characteristic
34	C₄	C₄⋊Dic₅	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊#168	1	1	yes	characteristic

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

N	H ≅ G/N	type
30. C₅	#364	semidirect

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