Subgroups — C₄×SL(2,𝔽₅) #91146

Order 480.

55 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SL(2,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	SL(2,𝔽₅)	C₄	1	1	yes	characteristic, direct product factor
3	C₄×SL(2,𝔽₃)	—	5	1	no	maximal, Hall
4	C₄×Dic₅	—	6	1	no	maximal
5	C₂×SL(2,𝔽₃)	—	5	1	no	—
6	C₄×Dic₃	—	10	1	no	maximal
7	C₂×C₄×C₅	—	6	1	no	—
8	C₂×Dic₅	—	6	1	no	—
9	C₂×Dic₅	—	6	1	no	—
10	C₄×Q₈	—	5	1	no	Sylow
11	C₂×C₃×C₄	—	10	1	no	—
12	C₂×Dic₃	—	10	1	no	—
13	C₂×Dic₃	—	10	1	no	—
14	SL(2,𝔽₃)	—	5	1	no	—
15	C₂²×C₅	—	6	1	no	—
16	C₄×C₅	—	6	2	no	—
17	Dic₅	—	6	1	no	—
18	Dic₅	—	6	1	no	—
19	Dic₅	—	6	2	no	—
20	C₂×Q₈	—	5	1	no	—
21	C₄⋊C₄	—	15	1	no	—
22	C₄²	—	15	1	no	—
23	C₂²×C₃	—	10	1	no	—
24	C₃×C₄	—	10	2	no	—
25	Dic₃	—	10	1	no	—
26	Dic₃	—	10	1	no	—
27	Dic₃	—	10	2	no	—
28	C₂×C₅	—	6	1	no	—
29	C₂×C₅	—	6	1	no	—
30	C₂×C₅	—	6	1	no	—
31	Q₈	—	5	1	no	—
32	Q₈	—	15	1	no	—
33	C₂×C₄	—	15	1	no	—
34	C₂×C₄	—	15	1	no	—
35	C₂×C₄	A₅	1	1	yes	maximal normal, characteristic
36	C₂×C₃	—	10	1	no	—
37	C₂×C₃	—	10	1	no	—
38	C₂×C₃	—	10	1	no	—
39	C₅	—	6	1	no	Sylow
40	C₂²	C₂×A₅	1	1	yes	characteristic
41	C₄	—	15	1	no	—
42	C₄	—	15	1	no	—
43	C₄	—	30	1	no	—
44	C₄	SL(2,𝔽₅)	1	2	yes	direct product factor
45	C₃	—	10	1	no	Sylow
46	C₂	C₄×A₅	1	1	yes	characteristic
47	C₂	#6732	1	1	yes	characteristic
48	C₂	C₂×SL(2,𝔽₅)	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. SL(2,𝔽₅)	C₄	direct (N × H)
44. C₄	SL(2,𝔽₅)	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.