Subgroups — C₄×ΓL(1,𝔽₁₆) #6759

Order 240.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal
2	C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₄×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
4	C₂×C₃×D₅	C₂²	1	1	yes	characteristic
5	ΓL(1,𝔽₁₆)	C₄	1	4	yes	direct product factor
6	C₃×C₄×C₅	C₄	1	1	yes	characteristic, complemented
7	C₃×Dic₅	C₄	1	1	yes	characteristic, complemented
8	C₄×Dic₃	—	5	1	no	maximal, Hall
9	C₂×AGL(1,𝔽₅)	—	3	2	no	—
10	C₄×D₅	D₃	1	1	yes	characteristic
11	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×D₅	C₂×C₄	1	2	yes	—
13	C₂×C₃×C₄	—	5	1	no	—
14	C₂×Dic₃	—	5	2	no	—
15	C₂×D₅	C₂×D₃	1	1	yes	characteristic
16	AGL(1,𝔽₅)	—	3	4	no	—
17	C₄×C₅	Dic₃	1	1	yes	characteristic, complemented
18	Dic₅	Dic₃	1	1	yes	characteristic, complemented
19	C₄²	—	15	1	no	Sylow
20	C₃×C₅	C₄²	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃	—	5	1	no	—
22	C₃×C₄	—	5	1	no	—
23	C₃×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
24	Dic₃	—	5	4	no	—
25	C₂×C₅	C₂×Dic₃	1	1	yes	characteristic
26	D₅	C₄×D₃	1	2	yes	—
27	C₂×C₄	—	5	1	no	—
28	C₂×C₄	—	15	2	no	—
29	C₂×C₃	—	5	2	no	—
30	C₂×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₅	C₄×Dic₃	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	5	1	no	—
33	C₄	—	5	1	no	—
34	C₄	—	15	4	no	—
35	C₄	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor
36	C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	5	2	no	—
38	C₂	C₂×ΓL(1,𝔽₁₆)	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.