Subgroups — C₇×D₂₂₆₅ #44540254

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₅₅	—	3	1	no	maximal, Hall
3	C₇×D₄₅₃	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₅₁	D₃	1	1	yes	characteristic, complemented, Hall
5	D₂₂₆₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇×C₁₅₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₁₅₁	—	15	1	no	Hall
9	D₇₅₅	—	3	1	no	Hall
10	C₇×C₁₅₁	D₁₅	1	1	yes	characteristic, complemented, Hall
11	D₄₅₃	—	5	1	no	Hall
12	C₅×C₁₅₁	D₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₁	C₇×D₅	1	1	yes	characteristic, complemented, Hall
14	D₁₅₁	—	15	1	no	Hall
15	C₇×D₁₅	—	151	1	no	maximal, Hall
16	C₁₅₁	C₇×D₁₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₅₁	1	1	yes	characteristic, complemented, Hall
18	C₇×D₅	—	453	1	no	Hall
19	D₃×C₇	—	755	1	no	Hall
20	C₅×C₇	D₄₅₃	1	1	yes	characteristic, complemented, Hall
21	D₁₅	—	151	1	no	Hall
22	C₃×C₇	D₇₅₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	C₇×D₁₅₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇	—	2265	1	no	Hall
25	D₅	—	453	1	no	Hall
26	C₇	D₂₂₆₅	1	1	yes	characteristic, direct product factor, Sylow
27	D₃	—	755	1	no	Hall
28	C₅	C₇×D₄₅₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇×D₇₅₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	2265	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₂₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₅₁	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₃×C₅×C₁₅₁
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.