Subgroups — #64742

Order 320.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	Dic₄₀	C₂	1	1	yes	maximal, characteristic
3	#3926	C₂	1	1	yes	maximal, characteristic
4	C₅×Q₁₆	—	2	1	no	—
5	Dic₂₀	—	2	1	no	—
6	C₅×C₁₆	C₂²	1	1	yes	characteristic
7	Q₆₄	—	5	1	no	maximal, Sylow
8	C₅×Q₈	—	4	1	no	—
9	Dic₁₀	—	4	1	no	—
10	C₅×C₈	D₄	1	1	yes	characteristic
11	Q₃₂	—	5	1	no	—
12	Q₃₂	D₅	1	1	yes	characteristic
13	C₃₂	—	5	1	no	—
14	C₄×C₅	—	8	1	no	—
15	C₄×C₅	D₈	1	1	yes	characteristic
16	Dic₅	—	8	1	no	—
17	Q₁₆	—	2	1	no	—
18	Q₁₆	—	10	1	no	—
19	C₁₆	C₂×D₅	1	1	yes	characteristic
20	C₂×C₅	D₁₆	1	1	yes	characteristic
21	Q₈	—	4	1	no	—
22	Q₈	—	20	1	no	—
23	C₈	C₂²⋊D₅	1	1	yes	characteristic
24	C₅	Q₆₄	1	1	yes	characteristic, complemented, Sylow
25	C₄	—	8	1	no	—
26	C₄	—	40	1	no	—
27	C₄	#686	1	1	yes	characteristic
28	C₂	#3958	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₅	Q₆₄	semidirect

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