Subgroups — #13100255

Order 1600.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#87756	C₂	1	1	yes	maximal, characteristic
2	#11716580	C₂	1	2	yes	maximal, complemented
3	C₂×C₅²×C₈	C₄	1	1	yes	characteristic
4	#87756	C₄	1	1	yes	characteristic
5	#87756	C₂²	1	1	yes	characteristic
6	#64877	—	5	6	no	maximal
7	C₂×C₄×C₅²	C₈	1	1	yes	characteristic
8	C₅²×C₈	C₈	1	1	yes	characteristic
9	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
10	C₂×#672	—	5	6	no	—
11	#3928	—	5	12	no	—
12	C₂²×C₅²	C₁₆	1	1	yes	characteristic
13	C₄×C₅²	C₁₆	1	1	yes	characteristic
14	C₄×C₅²	C₂×C₈	1	1	yes	characteristic
15	C₂×C₅×C₈	AGL(1,𝔽₅)	1	6	yes	—
16	#672	—	5	6	no	—
17	#672	—	5	6	no	—
18	M₆₄	—	25	1	no	Sylow
19	C₂×C₅²	—	2	1	no	—
20	C₂×C₅²	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₅	#170	1	6	yes	—
22	C₅×C₈	#170	1	6	yes	—
23	C₅×C₈	C₂×AGL(1,𝔽₅)	1	6	yes	—
24	C₂×C₁₆	—	25	1	no	—
25	C₃₂	—	25	2	no	—
26	C₅²	M₆₄	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₅	#674	1	6	yes	—
28	C₄×C₅	#674	1	6	yes	—
29	C₄×C₅	C₂×#170	1	6	yes	—
30	C₂×C₈	#1043	1	1	yes	characteristic
31	C₁₆	—	25	1	no	—
32	C₁₆	—	25	1	no	—
33	C₂×C₅	—	2	6	no	—
34	C₂×C₅	C₂×#674	1	6	yes	—
35	C₂×C₄	#6033	1	1	yes	characteristic
36	C₈	#6033	1	1	yes	characteristic
37	C₈	C₂×#1043	1	1	yes	characteristic
38	C₅	#64877	1	6	yes	complemented
39	C₂²	#87764	1	1	yes	characteristic
40	C₄	#87764	1	1	yes	characteristic
41	C₄	C₂×#6033	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	C₂×#87764	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.