Subgroups — #64669

Order 320.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₀	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈₀	C₂	1	1	yes	maximal, characteristic
3	C₅×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₂₀	—	2	1	no	—
5	D₄₀	—	2	1	no	—
6	C₅×C₁₆	C₂²	1	1	yes	characteristic
7	SD₆₄	—	5	1	no	maximal, Sylow
8	D₂₀	—	4	1	no	—
9	Dic₁₀	—	4	1	no	—
10	C₅×C₈	D₄	1	1	yes	characteristic
11	Q₃₂	—	5	1	no	—
12	D₁₆	—	5	1	no	—
13	C₃₂	D₅	1	1	yes	characteristic, complemented
14	C₂×D₅	—	8	1	no	—
15	C₄×C₅	D₈	1	1	yes	characteristic
16	Dic₅	—	8	1	no	—
17	Q₁₆	—	10	1	no	—
18	D₈	—	10	1	no	—
19	C₁₆	C₂×D₅	1	1	yes	characteristic
20	C₂×C₅	D₁₆	1	1	yes	characteristic
21	D₅	—	16	1	no	—
22	Q₈	—	20	1	no	—
23	D₄	—	20	1	no	—
24	C₈	D₂₀	1	1	yes	characteristic
25	C₅	SD₆₄	1	1	yes	characteristic, complemented, Sylow
26	C₂²	—	40	1	no	—
27	C₄	—	40	1	no	—
28	C₄	D₄₀	1	1	yes	characteristic
29	C₂	—	80	1	no	—
30	C₂	D₈₀	1	1	yes	characteristic

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

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