Subgroups — C₂³×Dic₁₀ #66270

Order 320.

850 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₅	C₂	1	2	yes	maximal
3	C₂²×Dic₁₀	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₅	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₅	C₂²	1	14	yes	—
6	C₂²×Dic₅	C₂²	1	28	yes	—
7	C₂×Dic₁₀	C₂²	1	112	yes	direct product factor
8	C₂³×Q₈	—	5	1	no	maximal, Sylow
9	C₂³×C₅	Q₈	1	8	yes	complemented
10	C₂³×C₅	C₂³	1	7	yes	—
11	C₂×C₄×C₅	C₂³	1	28	yes	—
12	C₂×Dic₅	C₂³	1	56	yes	—
13	Dic₁₀	C₂³	1	64	yes	direct product factor
14	C₂²×Q₈	—	5	28	no	—
15	C₂³×C₄	—	5	2	no	—
16	C₂³×C₄	D₅	1	1	yes	characteristic
17	C₂²×C₅	C₂×Q₈	1	28	yes	complemented
18	C₂²×C₅	C₂⁴	1	7	yes	—
19	C₄×C₅	C₂⁴	1	8	yes	—
20	Dic₅	C₂⁴	1	16	yes	—
21	C₂⁴	C₂×D₅	1	1	yes	characteristic
22	C₂×Q₈	—	5	112	no	—
23	C₂²×C₄	—	5	28	no	—
24	C₂²×C₄	C₂×D₅	1	14	yes	—
25	C₂×C₅	C₂²×Q₈	1	14	yes	complemented
26	C₂×C₅	C₂⁵	1	1	yes	characteristic
27	C₂³	Dic₁₀	1	8	yes	direct product factor
28	C₂³	C₂²×D₅	1	7	yes	—
29	Q₈	—	5	64	no	—
30	C₂×C₄	—	5	56	no	—
31	C₂×C₄	C₂²×D₅	1	28	yes	—
32	C₅	C₂³×Q₈	1	1	yes	characteristic, complemented, Sylow
33	C₂²	C₂×Dic₁₀	1	28	yes	direct product factor
34	C₂²	C₂³×D₅	1	7	yes	—
35	C₄	—	5	16	no	—
36	C₄	C₂³×D₅	1	8	yes	—
37	C₂	C₂²×Dic₁₀	1	14	yes	direct product factor
38	C₂	C₂⁴×D₅	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.