Subgroups — #10604774

Order 640.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#65429	C₂	1	1	yes	maximal, characteristic
2	#64877	C₂	1	3	yes	maximal, complemented
3	C₂×#3928	C₂	1	3	yes	maximal, complemented
4	C₅×#131	C₄	1	1	yes	characteristic
5	#3944	C₄	1	3	yes	—
6	C₂×#672	C₂²	1	3	yes	—
7	#3928	C₂²	1	1	yes	characteristic
8	#3928	C₂²	1	3	yes	—
9	#2258	—	5	1	no	maximal, Sylow
10	C₅×#41	C₈	1	1	yes	characteristic
11	C₅×M₁₆	C₈	1	3	yes	—
12	C₂×C₅×C₈	C₂×C₄	1	3	yes	—
13	#672	C₂×C₄	1	3	yes	—
14	#672	C₂³	1	1	yes	characteristic
15	#504	—	5	1	no	—
16	M₆₄	—	5	3	no	—
17	C₂×C₃₂	—	5	3	no	—
18	C₅×Q₈	C₁₆	1	1	yes	characteristic
19	C₅×D₄	C₁₆	1	3	yes	—
20	C₂×C₄×C₅	C₂×C₈	1	3	yes	—
21	C₅×C₈	C₂×C₈	1	3	yes	—
22	C₅×C₈	C₂²×C₄	1	1	yes	characteristic
23	#131	AGL(1,𝔽₅)	1	1	yes	characteristic
24	M₃₂	—	5	3	no	—
25	C₂×C₁₆	—	5	3	no	—
26	C₃₂	—	5	1	no	—
27	C₃₂	—	5	3	no	—
28	C₂²×C₅	C₂×C₁₆	1	3	yes	—
29	C₄×C₅	C₂×C₁₆	1	3	yes	—
30	C₄×C₅	C₂²×C₈	1	1	yes	characteristic
31	#41	#170	1	1	yes	characteristic
32	M₁₆	#170	1	3	yes	—
33	C₂×C₈	C₂×AGL(1,𝔽₅)	1	3	yes	—
34	C₁₆	—	5	1	no	—
35	C₁₆	—	5	3	no	—
36	C₂×C₅	—	2	3	no	—
37	C₂×C₅	C₂²×C₁₆	1	1	yes	characteristic
38	Q₈	#674	1	1	yes	characteristic
39	D₄	#674	1	3	yes	—
40	C₂×C₄	C₂×#170	1	3	yes	—
41	C₈	C₂×#170	1	3	yes	—
42	C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
43	C₅	#2258	1	1	yes	characteristic, complemented, Sylow
44	C₂²	C₂×#674	1	3	yes	—
45	C₄	C₂×#674	1	3	yes	—
46	C₄	C₂²×#170	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#674	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.