Subgroups — C₂×#19097571 #23756583

Order 10016.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097571	C₂	1	4	yes	maximal, direct product factor
2	C₂×#14578816	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₃₁₃	C₂	1	1	yes	maximal, characteristic
4	#14578816	C₂²	1	4	yes	complemented
5	C₂²×D₃₁₃	C₄	1	1	yes	characteristic
6	C₂×Dic₃₁₃	C₂²	1	1	yes	characteristic
7	C₄×D₃₁₃	C₄	1	2	yes	—
8	C₄×D₃₁₃	C₂²	1	2	yes	—
9	C₂×C₄×C₃₁₃	C₄	1	1	yes	characteristic
10	C₂²×C₃₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂×D₃₁₃	—	2	2	no	—
12	C₂×D₃₁₃	C₂×C₄	1	2	yes	—
13	C₄×C₃₁₃	C₂×C₄	1	2	yes	—
14	Dic₃₁₃	C₂×C₄	1	1	yes	characteristic
15	Dic₃₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₃₁₃	M₁₆	1	2	yes	complemented
17	C₂×C₃₁₃	C₂²×C₄	1	1	yes	characteristic
18	D₃₁₃	—	2	2	no	—
19	C₃₁₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂×M₁₆	—	313	1	no	maximal, Sylow
21	C₂²×C₄	—	313	1	no	—
22	M₁₆	—	313	4	no	—
23	C₂×C₈	—	313	2	no	—
24	C₂³	—	313	1	no	—
25	C₂×C₄	—	313	1	no	—
26	C₂×C₄	—	313	2	no	—
27	C₂×C₄	—	313	2	no	—
28	C₂×C₄	#11929411	1	1	yes	characteristic
29	C₈	—	313	4	no	—
30	C₂²	—	313	2	no	—
31	C₂²	—	626	2	no	—
32	C₂²	C₂×#11929411	1	1	yes	characteristic
33	C₄	—	313	1	no	—
34	C₄	—	313	1	no	—
35	C₄	C₂×#11929411	1	2	yes	—
36	C₂	—	626	2	no	—
37	C₂	#19097571	1	2	yes	direct product factor
38	C₂	C₂²×#11929411	1	1	yes	characteristic

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