Subgroups — C₃²×C₇×C₄₁⋊C₅ #27166552

Order 12915.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₄₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₇×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃²×C₄₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₄₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₇×C₄₁	C₃×C₅	1	4	yes	complemented
6	C₃×C₄₁⋊C₅	C₃×C₇	1	4	yes	direct product factor
7	C₃²×C₄₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₇	—	41	1	no	maximal, Hall
9	C₇×C₄₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
10	C₄₁⋊C₅	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₄₁	C₃×C₅×C₇	1	4	yes	complemented
12	C₃×C₅×C₇	—	41	4	no	—
13	C₃²×C₇	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃²×C₅	—	41	1	no	Hall
15	C₄₁	C₃²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
16	C₅×C₇	—	41	1	no	Hall
17	C₃×C₇	C₃×C₄₁⋊C₅	1	4	yes	direct product factor
18	C₃×C₅	—	41	4	no	—
19	C₃²	C₇×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₃²×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	—	41	1	no	Sylow
22	C₃	C₃×C₇×C₄₁⋊C₅	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²×C₇	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₃²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₄₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃²×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.