Subgroups — C₃×D₄₄₄₅ #40998680

Order 26670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₄₄₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₈₈₉	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₆₃₅	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₂₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₂₇	D₇	1	1	yes	characteristic, complemented, Hall
8	D₈₈₉	—	5	1	no	Hall
9	D₆₃₅	—	7	1	no	Hall
10	C₇×C₁₂₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₂₇	—	35	1	no	Hall
12	C₅×C₁₂₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₂₇	D₃₅	1	1	yes	characteristic, complemented, Hall
14	D₁₂₇	—	35	1	no	Hall
15	C₃×D₃₅	—	127	1	no	maximal, Hall
16	C₁₂₇	C₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₂₇	1	1	yes	characteristic, complemented, Hall
18	D₃₅	—	127	1	no	Hall
19	C₃×D₇	—	635	1	no	Hall
20	C₅×C₇	C₃×D₁₂₇	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	889	1	no	Hall
22	C₃×C₇	D₆₃₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₈₈₉	1	1	yes	characteristic, complemented, Hall
24	D₇	—	635	1	no	Hall
25	D₅	—	889	1	no	Hall
26	C₇	C₃×D₆₃₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	4445	1	no	Hall
28	C₅	C₃×D₈₈₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₄₄₄₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	4445	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₄₄₄₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₂₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₂₇	C₂
LCS	G ▷ C₅×C₇×C₁₂₇
UCS	C₁ ◁ C₃

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.