Subgroups — #10598656

Order 640.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64877	C₂	1	2	yes	maximal
2	#64722	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₁₆	C₄	1	1	yes	characteristic
4	C₈×Dic₅	C₄	1	1	yes	characteristic
5	C₂×#672	C₂²	1	1	yes	characteristic
6	#3928	C₄	1	4	yes	complemented
7	#1398	—	5	1	no	maximal, Sylow
8	C₂×C₅×C₈	C₂×C₄	1	1	yes	characteristic
9	C₄×Dic₅	C₈	1	1	yes	characteristic
10	C₂×#168	C₈	1	1	yes	characteristic
11	C₅×C₁₆	C₈	1	2	yes	—
12	#672	C₂×C₄	1	2	yes	—
13	M₆₄	—	5	2	no	—
14	#346	—	5	1	no	—
15	C₂×C₄×C₅	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₅	—	2	1	no	—
17	C₅×C₈	C₄²	1	1	yes	characteristic
18	C₅×C₈	C₂×C₈	1	1	yes	characteristic
19	#168	—	2	1	no	—
20	C₂×C₁₆	—	5	1	no	—
21	C₂×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
22	C₄×C₈	—	5	1	no	—
23	C₃₂	—	5	4	no	—
24	C₂²×C₅	M₃₂	1	1	yes	characteristic
25	C₄×C₅	C₄×C₈	1	1	yes	characteristic
26	C₄×C₅	M₃₂	1	1	yes	characteristic
27	Dic₅	—	4	1	no	—
28	C₂×C₈	—	5	1	no	—
29	C₂×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₄²	—	5	1	no	—
31	C₁₆	—	5	2	no	—
32	C₁₆	#170	1	2	yes	—
33	C₂×C₅	—	2	1	no	—
34	C₂×C₅	#346	1	1	yes	characteristic
35	C₂×C₄	—	10	1	no	—
36	C₂×C₄	D₅⋊C₈	1	1	yes	characteristic
37	C₈	—	10	1	no	—
38	C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₈	C₂×#170	1	1	yes	characteristic
40	C₅	#1398	1	1	yes	characteristic, complemented, Sylow
41	C₂²	#3990	1	1	yes	characteristic
42	C₄	—	20	1	no	—
43	C₄	#3990	1	1	yes	characteristic
44	C₄	C₄×#170	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#64886	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. #3928	C₄	semidirect
40. C₅	#1398	semidirect

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