Subgroups — C₇×D₂₃₀₁ #44567262

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₆₇	—	3	1	no	maximal, Hall
3	C₇×C₁₃×C₅₉	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₃₀₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₇₇	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₇₆₇	—	3	1	no	Hall
8	C₃×C₇×C₅₉	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₇×D₅₉	—	39	1	no	Hall
10	C₁₃×C₅₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₉	—	59	1	no	maximal, Hall
12	C₇×C₅₉	D₃₉	1	1	yes	characteristic, complemented, Hall
13	D₁₇₇	—	13	1	no	Hall
14	C₃×C₇×C₁₃	D₅₉	1	1	yes	characteristic, complemented, Hall
15	C₇×D₁₃	—	177	1	no	Hall
16	C₃×C₅₉	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
17	D₅₉	—	39	1	no	Hall
18	C₇×C₁₃	D₁₇₇	1	1	yes	characteristic, complemented, Hall
19	D₃₉	—	59	1	no	Hall
20	C₅₉	C₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
21	D₃×C₇	—	767	1	no	Hall
22	C₃×C₁₃	C₇×D₅₉	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	177	1	no	Hall
24	C₃×C₇	D₇₆₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇	—	2301	1	no	Hall
26	C₁₃	C₇×D₁₇₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	D₂₃₀₁	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	767	1	no	Hall
29	C₃	C₇×D₇₆₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	2301	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₃₀₁
commutator, cosocle, hypocenter	C₃×C₁₃×C₅₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₅₉	C₂
LCS	G ▷ C₃×C₁₃×C₅₉
UCS	C₁ ◁ C₇

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.