Subgroups — C₂⁴×Dic₃₁ #14521868

Order 1984.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₃₁	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₃₁	C₄	1	16	yes	complemented
4	C₂⁴×C₃₁	C₂²	1	15	yes	—
5	C₂²×Dic₃₁	C₂²	1	140	yes	direct product factor
6	C₂³×C₃₁	C₂×C₄	1	120	yes	complemented
7	C₂³×C₃₁	C₂³	1	35	yes	—
8	C₂×Dic₃₁	C₂³	1	120	yes	direct product factor
9	C₂²×C₃₁	C₂²×C₄	1	140	yes	complemented
10	C₂²×C₃₁	C₂⁴	1	15	yes	—
11	Dic₃₁	C₂⁴	1	16	yes	direct product factor
12	C₂⁴×C₄	—	31	1	no	maximal, Sylow
13	C₂×C₃₁	C₂³×C₄	1	30	yes	complemented
14	C₂×C₃₁	C₂⁵	1	1	yes	characteristic
15	C₂⁵	D₃₁	1	1	yes	characteristic
16	C₂³×C₄	—	31	30	no	—
17	C₃₁	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂⁴	Dic₃₁	1	16	yes	direct product factor
19	C₂⁴	C₂×D₃₁	1	15	yes	—
20	C₂²×C₄	—	31	140	no	—
21	C₂³	C₂×Dic₃₁	1	120	yes	direct product factor
22	C₂³	C₂²×D₃₁	1	35	yes	—
23	C₂×C₄	—	31	120	no	—
24	C₂²	C₂²×Dic₃₁	1	140	yes	direct product factor
25	C₂²	C₂³×D₃₁	1	15	yes	—
26	C₄	—	31	16	no	—
27	C₂	C₂³×Dic₃₁	1	30	yes	direct product factor
28	C₂	C₂⁴×D₃₁	1	1	yes	characteristic

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.