Subgroups — ΓL(1,𝔽₈)⋊D₅₅₉ #37553535

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×ΓL(1,𝔽₈)×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₅₅₉	—	7	1	no	maximal, Hall
5	ΓL(1,𝔽₈)⋊D₄₃	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₄₃	—	7	1	no	Hall
7	D₅₅₉	—	7	1	no	Hall
8	ΓL(1,𝔽₈)×C₄₃	D₁₃	1	1	yes	characteristic, complemented, Hall
9	D₃₀₁	—	13	1	no	Hall
10	C₁₃×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
11	ΓL(1,𝔽₈)⋊D₁₃	—	43	1	no	maximal, Hall
12	C₇×C₄₃	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×ΓL(1,𝔽₈)	D₄₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₄₃	—	91	1	no	Hall
15	D₉₁	—	43	1	no	Hall
16	C₃×C₄₃	—	7	1	no	Hall
17	C₇×C₁₃	C₃×D₄₃	1	1	yes	characteristic, complemented, Hall
18	D₄₃	—	91	1	no	Hall
19	C₃×D₁₃	—	301	1	no	Hall
20	C₄₃	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
21	AGL(1,𝔽₇)	—	559	1	no	Hall
22	C₃×C₁₃	—	7	1	no	Hall
23	D₁₃	—	301	1	no	Hall
24	ΓL(1,𝔽₈)	D₅₅₉	1	1	yes	characteristic, complemented, Hall
25	D₇	—	559	1	no	Hall
26	C₁₃	ΓL(1,𝔽₈)⋊D₄₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₅₅₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3913	1	no	Hall
29	C₃	—	7	1	no	Sylow
30	C₂	—	3913	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₄₃
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.