Subgroups — #64726

Order 320.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#3951	C₂	1	2	yes	maximal
3	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
4	#681	—	2	2	no	—
5	C₅×C₁₆	C₄	1	2	yes	—
6	#368	—	5	1	no	maximal, Sylow
7	C₂×C₄×C₅	D₄	1	1	yes	characteristic
8	C₅×C₈	C₂×C₄	1	1	yes	characteristic
9	C₅×C₈	Q₈	1	1	yes	characteristic
10	#168	—	4	2	no	—
11	C₂×C₁₆	D₅	1	1	yes	characteristic
12	#108	—	5	2	no	—
13	C₂²×C₅	Q₁₆	1	1	yes	characteristic
14	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₅	D₈	1	1	yes	characteristic
16	M₁₆	—	10	2	no	—
17	C₂×C₈	C₂×D₅	1	1	yes	characteristic
18	C₁₆	Dic₅	1	2	yes	—
19	C₂×C₅	—	2	1	no	—
20	C₂×C₅	#107	1	1	yes	characteristic
21	C₂×C₄	D₂₀	1	1	yes	characteristic
22	C₈	—	20	2	no	—
23	C₈	Dic₁₀	1	1	yes	characteristic
24	C₈	C₂×Dic₅	1	1	yes	characteristic
25	C₅	#368	1	1	yes	characteristic, complemented, Sylow
26	C₂²	Dic₂₀	1	1	yes	characteristic
27	C₄	D₄₀	1	1	yes	characteristic
28	C₄	C₄⋊Dic₅	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	#3950	1	1	yes	characteristic

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

N	H ≅ G/N	type
25. C₅	#368	semidirect

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