Subgroups — C₅×SL(2,ℤ/4) #6743

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	C₅×C₂²⋊C₄	—	3	1	no	maximal, Hall
3	C₅×A₄	C₄	1	1	yes	characteristic, complemented
4	C₅×Dic₃	—	4	1	no	maximal
5	SL(2,ℤ/4)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₅	D₃	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	Dic₃	1	1	yes	characteristic, complemented
14	C₄×C₅	—	6	1	no	—
15	C₄×C₅	—	6	1	no	—
16	C₂²⋊C₄	—	3	1	no	Sylow
17	C₃×C₅	—	4	1	no	Hall
18	A₄	C₄×C₅	1	1	yes	characteristic, complemented
19	Dic₃	—	4	1	no	—
20	C₂×C₅	—	3	1	no	—
21	C₂×C₅	—	3	1	no	—
22	C₂×C₅	S₄	1	1	yes	characteristic
23	C₂³	C₅×D₃	1	1	yes	characteristic
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₂×C₃	—	4	1	no	—
27	C₅	SL(2,ℤ/4)	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	C₅×Dic₃	1	1	yes	characteristic, complemented
31	C₄	—	6	1	no	—
32	C₄	—	6	1	no	—
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	3	1	no	—
36	C₂	C₅×S₄	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.