Subgroups — #64667

Order 320.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#3926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₅	C₄	1	1	yes	characteristic
5	C₅×C₁₆	C₂²	1	1	yes	characteristic
6	#672	C₄	1	1	yes	characteristic
7	M₆₄	—	5	1	no	maximal, Sylow
8	C₄×D₅	C₈	1	1	yes	characteristic
9	C₅×C₈	C₂×C₄	1	1	yes	characteristic
10	#168	C₈	1	1	yes	characteristic
11	C₂×C₁₆	—	5	1	no	—
12	C₃₂	—	5	1	no	—
13	C₃₂	D₅	1	1	yes	characteristic, complemented
14	C₂×D₅	C₁₆	1	1	yes	characteristic
15	C₄×C₅	C₂×C₈	1	1	yes	characteristic
16	Dic₅	C₁₆	1	1	yes	characteristic
17	C₂×C₈	—	5	1	no	—
18	C₁₆	—	5	1	no	—
19	C₁₆	C₂×D₅	1	1	yes	characteristic
20	C₂×C₅	C₂×C₁₆	1	1	yes	characteristic
21	D₅	—	2	1	no	—
22	C₂×C₄	—	5	1	no	—
23	C₈	—	5	1	no	—
24	C₈	C₄×D₅	1	1	yes	characteristic
25	C₅	M₆₄	1	1	yes	characteristic, complemented, Sylow
26	C₂²	—	5	1	no	—
27	C₄	—	5	1	no	—
28	C₄	C₈×D₅	1	1	yes	characteristic
29	C₂	—	10	1	no	—
30	C₂	D₅×C₁₆	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.