Subgroups — C₂⁴×Dic₂₈₁ #31824282

Order 17984.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₂₈₁	C₂	1	30	yes	maximal, direct product factor
2	C₂⁵×C₂₈₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₂₈₁	C₂²	1	140	yes	direct product factor
4	C₂⁴×C₂₈₁	C₄	1	16	yes	complemented
5	C₂⁴×C₂₈₁	C₂²	1	15	yes	—
6	C₂×Dic₂₈₁	C₂³	1	120	yes	direct product factor
7	C₂³×C₂₈₁	C₂×C₄	1	120	yes	complemented
8	C₂³×C₂₈₁	C₂³	1	35	yes	—
9	C₂²×C₂₈₁	C₂²×C₄	1	140	yes	complemented
10	C₂²×C₂₈₁	C₂⁴	1	15	yes	—
11	Dic₂₈₁	C₂⁴	1	16	yes	direct product factor
12	C₂×C₂₈₁	C₂³×C₄	1	30	yes	complemented
13	C₂×C₂₈₁	C₂⁵	1	1	yes	characteristic
14	C₂₈₁	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂⁴×C₄	—	281	1	no	maximal, Sylow
16	C₂⁵	D₂₈₁	1	1	yes	characteristic
17	C₂³×C₄	—	281	30	no	—
18	C₂⁴	Dic₂₈₁	1	16	yes	direct product factor
19	C₂⁴	C₂×D₂₈₁	1	15	yes	—
20	C₂²×C₄	—	281	140	no	—
21	C₂³	C₂×Dic₂₈₁	1	120	yes	direct product factor
22	C₂³	C₂²×D₂₈₁	1	35	yes	—
23	C₂×C₄	—	281	120	no	—
24	C₂²	C₂²×Dic₂₈₁	1	140	yes	direct product factor
25	C₂²	C₂³×D₂₈₁	1	15	yes	—
26	C₄	—	281	16	no	—
27	C₂	C₂³×Dic₂₈₁	1	30	yes	direct product factor
28	C₂	C₂⁴×D₂₈₁	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.