Subgroups — #64877

Order 320.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#672	C₂	1	1	yes	maximal, characteristic
2	#3928	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×C₈	C₄	1	1	yes	characteristic
4	#672	C₄	1	1	yes	characteristic
5	#672	C₂²	1	1	yes	characteristic
6	M₆₄	—	5	1	no	maximal, Sylow
7	C₂×C₄×C₅	C₈	1	1	yes	characteristic
8	C₅×C₈	C₈	1	1	yes	characteristic
9	C₅×C₈	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆	—	5	1	no	—
11	C₃₂	—	5	2	no	—
12	C₂²×C₅	C₁₆	1	1	yes	characteristic
13	C₄×C₅	C₁₆	1	1	yes	characteristic
14	C₄×C₅	C₂×C₈	1	1	yes	characteristic
15	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
16	C₁₆	—	5	1	no	—
17	C₁₆	—	5	1	no	—
18	C₂×C₅	—	2	1	no	—
19	C₂×C₅	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₄	#170	1	1	yes	characteristic
21	C₈	#170	1	1	yes	characteristic
22	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
23	C₅	M₆₄	1	1	yes	characteristic, complemented, Sylow
24	C₂²	#674	1	1	yes	characteristic
25	C₄	#674	1	1	yes	characteristic
26	C₄	C₂×#170	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×#674	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #3928	C₂	semidirect
23. C₅	M₆₄	semidirect

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