Subgroups — #23778769

Order 10144.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂₆₈	C₂	1	1	yes	maximal, characteristic
2	#19099551	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×C₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₃₁₇	C₂²	1	2	yes	—
6	D₁₂₆₈	—	2	2	no	—
7	C₂×Dic₃₁₇	C₂²	1	2	yes	—
8	Q₈×C₃₁₇	—	2	2	no	—
9	C₂×C₄×C₃₁₇	C₂²	1	2	yes	—
10	C₂×C₄×C₃₁₇	C₂²	1	1	yes	characteristic
11	C₂²×C₃₁₇	C₂³	1	1	yes	characteristic
12	C₂×D₃₁₇	—	2	2	no	—
13	C₂×D₃₁₇	—	2	4	no	—
14	C₄×C₃₁₇	—	2	2	no	—
15	C₄×C₃₁₇	D₄	1	2	yes	—
16	Dic₃₁₇	—	2	2	no	—
17	C₂×C₃₁₇	C₂×D₄	1	1	yes	characteristic
18	C₂×C₃₁₇	#41	1	2	yes	—
19	D₃₁₇	—	4	2	no	—
20	C₃₁₇	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	317	1	no	maximal, Sylow
22	C₂×Q₈	D₃₁₇	1	1	yes	characteristic, complemented
23	C₂×D₄	—	317	1	no	—
24	C₂²⋊C₄	—	317	4	no	—
25	C₄²	—	317	1	no	—
26	C₂³	—	317	2	no	—
27	Q₈	—	2	2	no	—
28	D₄	—	634	2	no	—
29	C₂×C₄	—	317	2	no	—
30	C₂×C₄	C₂×D₃₁₇	1	2	yes	—
31	C₂×C₄	C₂×D₃₁₇	1	1	yes	characteristic
32	C₂²	—	634	2	no	—
33	C₂²	—	634	4	no	—
34	C₂²	C₂²×D₃₁₇	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	634	2	no	—
37	C₄	C₂²⋊D₃₁₇	1	2	yes	—
38	C₂	—	1268	2	no	—
39	C₂	C₂×C₂²⋊D₃₁₇	1	1	yes	characteristic
40	C₂	#19099575	1	2	yes	—

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