Subgroups — C₂×#19099584 #23778866

Order 10144.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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