Subgroups — C₂⁴×C₄×C₅ #66290

Order 320.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₅	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₅	C₄	1	16	yes	direct product factor
4	C₂⁴×C₅	C₂²	1	15	yes	—
5	C₂²×C₄×C₅	C₂²	1	140	yes	direct product factor
6	C₂⁴×C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂³×C₅	C₂×C₄	1	120	yes	direct product factor
8	C₂³×C₅	C₂³	1	35	yes	—
9	C₂×C₄×C₅	C₂³	1	120	yes	direct product factor
10	C₂⁵	C₂×C₅	1	1	yes	characteristic
11	C₂³×C₄	C₂×C₅	1	30	yes	direct product factor
12	C₂²×C₅	C₂²×C₄	1	140	yes	direct product factor
13	C₂²×C₅	C₂⁴	1	15	yes	—
14	C₄×C₅	C₂⁴	1	16	yes	direct product factor
15	C₂⁴	C₄×C₅	1	16	yes	direct product factor
16	C₂⁴	C₂²×C₅	1	15	yes	—
17	C₂²×C₄	C₂²×C₅	1	140	yes	direct product factor
18	C₂×C₅	C₂³×C₄	1	30	yes	direct product factor
19	C₂×C₅	C₂⁵	1	1	yes	characteristic
20	C₂³	C₂×C₄×C₅	1	120	yes	direct product factor
21	C₂³	C₂³×C₅	1	35	yes	—
22	C₂×C₄	C₂³×C₅	1	120	yes	direct product factor
23	C₅	C₂⁴×C₄	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²	C₂²×C₄×C₅	1	140	yes	direct product factor
25	C₂²	C₂⁴×C₅	1	15	yes	—
26	C₄	C₂⁴×C₅	1	16	yes	direct product factor
27	C₂	C₂³×C₄×C₅	1	30	yes	direct product factor
28	C₂	C₂⁵×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.