Subgroups — C₇×D₂₄₀₅ #46797608

Order 33670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₈₁	—	5	1	no	maximal, Hall
3	D₂₄₀₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₃×C₃₇	D₅	1	1	yes	characteristic, complemented, Hall
5	C₇×D₁₈₅	—	13	1	no	maximal, Hall
6	C₅×C₁₃×C₃₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₃₇	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₄₈₁	—	5	1	no	Hall
9	C₇×D₆₅	—	37	1	no	maximal, Hall
10	C₇×D₃₇	—	65	1	no	Hall
11	C₁₃×C₃₇	C₇×D₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₇×C₁₃	D₃₇	1	1	yes	characteristic, complemented, Hall
13	D₁₈₅	—	13	1	no	Hall
14	C₇×C₃₇	D₆₅	1	1	yes	characteristic, complemented, Hall
15	C₅×C₃₇	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₇×D₁₃	—	185	1	no	Hall
17	D₆₅	—	37	1	no	Hall
18	C₇×C₁₃	D₁₈₅	1	1	yes	characteristic, complemented, Hall
19	D₃₇	—	65	1	no	Hall
20	C₇×D₅	—	481	1	no	Hall
21	C₅×C₁₃	C₇×D₃₇	1	1	yes	characteristic, complemented, Hall
22	C₃₇	C₇×D₆₅	1	1	yes	characteristic, complemented, Sylow
23	C₅×C₇	D₄₈₁	1	1	yes	characteristic, complemented, Hall
24	D₁₃	—	185	1	no	Hall
25	C₂×C₇	—	2405	1	no	Hall
26	C₁₃	C₇×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
27	D₅	—	481	1	no	Hall
28	C₇	D₂₄₀₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₇×D₄₈₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	2405	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₄₀₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₃₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₃₇	C₂
LCS	G ▷ C₅×C₁₃×C₃₇
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.