Subgroups — C₂⁵×C₃×C₅ #92137

Order 480.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₅	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂³×C₃×C₅	C₂²	1	155	yes	direct product factor
4	C₂⁵×C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁴×C₅	C₂×C₃	1	31	yes	direct product factor
6	C₂²×C₃×C₅	C₂³	1	155	yes	direct product factor
7	C₂⁴×C₃	C₂×C₅	1	31	yes	direct product factor
8	C₂³×C₅	C₂²×C₃	1	155	yes	direct product factor
9	C₂⁵	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃×C₅	C₂⁴	1	31	yes	direct product factor
11	C₂³×C₃	C₂²×C₅	1	155	yes	direct product factor
12	C₂²×C₅	C₂³×C₃	1	155	yes	direct product factor
13	C₂⁴	C₂×C₃×C₅	1	31	yes	direct product factor
14	C₃×C₅	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₃	C₂³×C₅	1	155	yes	direct product factor
16	C₂×C₅	C₂⁴×C₃	1	31	yes	direct product factor
17	C₂³	C₂²×C₃×C₅	1	155	yes	direct product factor
18	C₂×C₃	C₂⁴×C₅	1	31	yes	direct product factor
19	C₅	C₂⁵×C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	C₂³×C₃×C₅	1	155	yes	direct product factor
21	C₃	C₂⁵×C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂⁴×C₃×C₅	1	31	yes	direct product factor

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.