Subgroups — C₃⋊(C₃⋊#13091733) #27190306

Order 13140.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₃₆₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13091733	—	3	4	no	maximal
3	C₃²×C₅×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#64408)	—	5	1	no	maximal, Hall
5	C₃×D₃₆₅	D₃	1	4	yes	—
6	#13091733	—	9	1	no	Hall
7	C₃²×D₇₃	—	5	1	no	—
8	C₃×C₅×C₇₃	Dic₃	1	4	yes	complemented
9	C₃⋊#64408	—	15	4	no	—
10	D₃₆₅	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₇₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₇₃	—	5	4	no	—
13	C₅×C₇₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	#64408	—	45	1	no	Hall
15	C₃×C₇₃	ΓL(1,𝔽₁₆)	1	4	yes	complemented
16	C₃⋊ΓL(1,𝔽₁₆)	—	73	1	no	maximal, Hall
17	D₇₃	—	5	1	no	—
18	C₃²×D₅	—	73	1	no	—
19	C₇₃	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
20	ΓL(1,𝔽₁₆)	—	219	4	no	—
21	C₃²×C₅	#64408	1	1	yes	characteristic, complemented, Hall
22	C₃⋊Dic₃	—	365	1	no	Hall
23	C₃×D₅	—	73	4	no	—
24	AGL(1,𝔽₅)	—	657	1	no	Hall
25	C₂×C₃²	—	365	1	no	—
26	C₃×C₅	C₃⋊#64408	1	4	yes	complemented
27	Dic₃	—	1095	4	no	—
28	D₅	—	73	1	no	—
29	C₃²	#13091733	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	365	4	no	—
31	C₅	C₃⋊(C₃⋊#64408)	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	3285	1	no	Sylow
33	C₃	C₃⋊#13091733	1	4	yes	complemented
34	C₂	—	365	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₇₃	C₄
prime radical, cosocle	C₃²×D₃₆₅	C₂
LCS	G ▷ C₃²×C₅×C₇₃
UCS	C₁

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.