Subgroups — C₃₁×#367 #14520548

Order 1984.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#107	C₂	1	2	yes	maximal
3	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
4	C₄⋊C₄×C₃₁	—	2	2	no	—
5	C₁₆×C₃₁	C₄	1	2	yes	complemented
6	C₂×C₄×C₃₁	—	4	2	no	—
7	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
8	C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₃₁	Q₈	1	1	yes	characteristic
10	C₂²×C₃₁	D₈	1	1	yes	characteristic
11	C₄×C₃₁	—	8	2	no	—
12	C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
13	C₄×C₃₁	Q₁₆	1	1	yes	characteristic
14	#367	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃₁	#107	1	1	yes	characteristic
16	C₂×C₃₁	SD₃₂	1	2	yes	—
17	C₂×C₁₆	C₂×C₃₁	1	1	yes	characteristic
18	#107	C₂×C₃₁	1	2	yes	—
19	C₃₁	#367	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
21	C₄⋊C₄	—	2	2	no	—
22	C₁₆	C₄×C₃₁	1	2	yes	complemented
23	C₂×C₄	—	4	2	no	—
24	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
25	C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
26	C₈	Q₈×C₃₁	1	1	yes	characteristic
27	C₂²	D₈×C₃₁	1	1	yes	characteristic
28	C₄	—	8	2	no	—
29	C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
30	C₄	Q₁₆×C₃₁	1	1	yes	characteristic
31	C₂	C₃₁×#107	1	1	yes	characteristic
32	C₂	C₃₁×SD₃₂	1	2	yes	—

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.