Subgroups — C₅₉×(C₁₃⋊C₃)⋊D₇ #44567287

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃⋊C₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₉×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₅₉×D₁₃⋊C₃	—	7	1	no	maximal, Hall
5	C₃×D₇×C₅₉	—	13	1	no	maximal, Hall
6	C₁₃⋊C₃×C₅₉	D₇	1	1	yes	characteristic, complemented, Hall
7	D₁₃×C₅₉	—	7	1	no	Hall
8	C₃×C₇×C₅₉	—	13	1	no	Hall
9	D₇×C₅₉	—	13	1	no	Hall
10	C₁₃×C₅₉	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	(C₁₃⋊C₃)⋊D₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₅₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅₉	—	91	1	no	Hall
14	C₇×C₁₃⋊C₃	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
15	D₉₁	C₃×C₅₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅₉	—	13	1	no	Hall
17	C₂×C₅₉	—	91	1	no	Hall
18	C₇×C₁₃	C₂×C₃×C₅₉	1	1	yes	characteristic, complemented, Hall
19	D₁₃⋊C₃	—	7	1	no	Hall
20	C₅₉	(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×D₇	—	13	1	no	Hall
22	C₁₃⋊C₃	D₇×C₅₉	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	7	1	no	Hall
24	C₃×C₇	—	13	1	no	Hall
25	D₇	—	13	1	no	Hall
26	C₁₃	C₃×D₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₅₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	—	13	1	no	Sylow
30	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₉	(C₁₃⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₅₉	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₅₉

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.