Subgroups — #23778837

Order 10144.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14579268	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₃₁₇	C₂	1	1	yes	maximal, characteristic
3	#14579268	—	2	2	no	—
4	C₂²×D₃₁₇	C₄	1	1	yes	characteristic
5	C₂×Dic₃₁₇	C₂²	1	1	yes	characteristic
6	C₄×D₃₁₇	—	2	2	no	—
7	C₂×C₄×C₃₁₇	C₄	1	1	yes	characteristic
8	C₂²×C₃₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂×D₃₁₇	—	2	1	no	—
10	C₂×D₃₁₇	—	2	1	no	—
11	C₂×D₃₁₇	C₈	1	2	yes	complemented
12	C₄×C₃₁₇	—	2	1	no	—
13	Dic₃₁₇	D₄	1	2	yes	—
14	C₂×C₃₁₇	C₂²⋊C₄	1	1	yes	characteristic
15	C₂×C₃₁₇	C₂×C₈	1	1	yes	characteristic
16	C₂×C₃₁₇	M₁₆	1	1	yes	characteristic
17	D₃₁₇	—	2	2	no	—
18	C₃₁₇	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	317	1	no	maximal, Sylow
20	C₂²×C₄	—	317	1	no	—
21	C₂×C₈	—	317	2	no	—
22	C₂³	—	317	1	no	—
23	C₂×C₄	—	317	1	no	—
24	C₂×C₄	—	634	2	no	—
25	C₂×C₄	#11929639	1	1	yes	characteristic
26	C₈	—	634	2	no	—
27	C₂²	—	317	2	no	—
28	C₂²	—	634	1	no	—
29	C₂²	—	634	1	no	—
30	C₂²	C₂×#11929639	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	—	317	2	no	—
33	C₂	—	634	2	no	—
34	C₂	C₂²⋊#11929639	1	1	yes	characteristic
35	C₂	D₃₁₇⋊C₈	1	1	yes	characteristic
36	C₂	#19099584	1	1	yes	characteristic

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