Subgroups — ΓL(1,𝔽₁₆)×C₅₆₉ #46802480

Order 34140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₅₆₉	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₅)×C₅₆₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₅₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₃×C₅₆₉	—	5	1	no	maximal, Hall
5	D₅×C₅₆₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅₆₉	—	5	1	no	—
7	C₅×C₅₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₄×C₅₆₉	—	15	1	no	Hall
9	C₃×C₅₆₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅₆₉	—	5	1	no	—
11	C₅₆₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
12	ΓL(1,𝔽₁₆)	C₅₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅	C₂×C₅₆₉	1	1	yes	characteristic
14	AGL(1,𝔽₅)	—	3	1	no	Hall
15	C₃×C₅	C₄×C₅₆₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	5	1	no	Hall
17	D₅	D₃×C₅₆₉	1	1	yes	characteristic
18	C₂×C₃	—	5	1	no	—
19	C₅	Dic₃×C₅₆₉	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	15	1	no	Sylow
21	C₃	AGL(1,𝔽₅)×C₅₆₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5	1	no	—

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.