Subgroups — C₄×C₅×A₄ #6791

Order 240.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×A₄	C₄	1	1	yes	characteristic, direct product factor
4	C₃×C₄×C₅	—	4	1	no	maximal
5	C₄×A₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₅	C₂×C₃	1	1	yes	characteristic
7	C₂×C₄×C₅	—	3	1	no	—
8	C₂×C₄×C₅	—	3	1	no	—
9	C₂×C₃×C₅	—	4	1	no	—
10	C₂×A₄	C₂×C₅	1	1	yes	characteristic
11	C₂²×C₅	—	3	1	no	—
12	C₂²×C₅	—	3	1	no	—
13	C₂²×C₅	C₃×C₄	1	1	yes	characteristic, complemented
14	C₄×C₅	—	3	1	no	—
15	C₄×C₅	A₄	1	1	yes	characteristic, direct product factor
16	C₂²×C₄	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅	—	4	1	no	Hall
18	A₄	C₄×C₅	1	1	yes	characteristic, direct product factor
19	C₃×C₄	—	4	1	no	—
20	C₂×C₅	—	3	1	no	—
21	C₂×C₅	—	3	1	no	—
22	C₂×C₅	C₂×A₄	1	1	yes	characteristic
23	C₂³	C₂×C₃×C₅	1	1	yes	characteristic
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₂×C₃	—	4	1	no	—
27	C₅	C₄×A₄	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	C₃×C₄×C₅	1	1	yes	characteristic, complemented
31	C₄	—	3	1	no	—
32	C₄	C₅×A₄	1	1	yes	characteristic, direct product factor
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	3	1	no	—
36	C₂	C₂×C₅×A₄	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.