Subgroups — #23756594

Order 10016.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097573	C₂	1	2	yes	maximal, complemented
2	#19097569	C₂	1	1	yes	maximal, characteristic
3	#14578816	C₄	1	1	yes	characteristic
4	#14578816	C₂²	1	1	yes	characteristic
5	C₄×D₃₁₃	C₄	1	1	yes	characteristic
6	C₂×D₃₁₃	C₈	1	1	yes	characteristic
7	C₄×C₃₁₃	C₈	1	1	yes	characteristic
8	Dic₃₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₃₁₃	C₂×C₈	1	1	yes	characteristic
10	D₃₁₃	—	2	1	no	—
11	C₃₁₃	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	313	1	no	maximal, Sylow
13	C₂×C₈	—	313	1	no	—
14	C₁₆	—	313	2	no	—
15	C₂×C₄	—	313	1	no	—
16	C₈	—	313	1	no	—
17	C₈	—	313	1	no	—
18	C₂²	—	313	1	no	—
19	C₄	—	313	1	no	—
20	C₄	#14578818	1	1	yes	characteristic
21	C₂	—	626	1	no	—
22	C₂	C₂×#14578818	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #19097573	C₂	semidirect
11. C₃₁₃	M₃₂	semidirect