Subgroups — C₅₉⋊#10587722 #44567293

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#63270	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₃₆₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₁₃⋊C₃)⋊D₅₉	—	7	1	no	maximal, Hall
5	ΓL(1,𝔽₈)⋊D₅₉	—	13	1	no	maximal, Hall
6	C₁₃⋊C₃×C₅₉	—	7	1	no	Hall
7	D₇₆₇	—	7	1	no	Hall
8	ΓL(1,𝔽₈)×C₅₉	—	13	1	no	Hall
9	D₄₁₃	—	13	1	no	Hall
10	C₁₃×C₅₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
11	#10587722	—	59	1	no	maximal, Hall
12	C₇×C₅₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅₉	—	91	1	no	Hall
14	#63270	D₅₉	1	1	yes	characteristic, complemented, Hall
15	D₉₁	—	59	1	no	Hall
16	C₃×C₅₉	—	91	1	no	Hall
17	D₅₉	—	91	1	no	Hall
18	C₇×C₁₃	C₃×D₅₉	1	1	yes	characteristic, complemented, Hall
19	D₁₃⋊C₃	—	413	1	no	Hall
20	C₅₉	#10587722	1	1	yes	characteristic, complemented, Sylow
21	AGL(1,𝔽₇)	—	767	1	no	Hall
22	C₁₃⋊C₃	—	7	1	no	Hall
23	D₁₃	—	413	1	no	Hall
24	ΓL(1,𝔽₈)	—	13	1	no	Hall
25	D₇	—	767	1	no	Hall
26	C₁₃	ΓL(1,𝔽₈)⋊D₅₉	1	1	yes	characteristic, complemented, Sylow
27	C₇	(C₁₃⋊C₃)⋊D₅₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	5369	1	no	Hall
29	C₃	—	91	1	no	Sylow
30	C₂	—	5369	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₅₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₅₉
UCS	C₁

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.