Subgroups — C₃²×C₁₇×C₄₁⋊C₅ #44535853

Order 31365.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₄₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₁₇×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₄₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₁₇×C₄₁	C₃×C₅	1	4	yes	complemented
5	C₃²×C₄₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₅×C₁₇	—	41	1	no	maximal, Hall
7	C₁₇×C₄₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₁⋊C₅	C₃×C₁₇	1	4	yes	direct product factor
9	C₃²×C₄₁	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₁₇	—	41	4	no	—
11	C₄₁⋊C₅	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₁₇	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₄₁	C₃×C₅×C₁₇	1	4	yes	complemented
14	C₅×C₁₇	—	41	1	no	Hall
15	C₃×C₁₇	C₃×C₄₁⋊C₅	1	4	yes	direct product factor
16	C₃²×C₅	—	41	1	no	Hall
17	C₄₁	C₃²×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
18	C₁₇	C₃²×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	—	41	4	no	—
20	C₃²	C₁₇×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	—	41	1	no	Sylow
22	C₃	C₃×C₁₇×C₄₁⋊C₅	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²×C₁₇	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₃²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₄₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃²×C₁₇

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.