Subgroups — C₄×C₂⁴⋊C₅ #66246

Order 320.

147 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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