Subgroups — C₃⋊(C₃⋊#15688381) #41001306

Order 26820.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇₄₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15688381	—	3	4	no	maximal
3	C₃²×C₅×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#10597010)	—	5	1	no	maximal, Hall
5	C₃×D₇₄₅	D₃	1	4	yes	—
6	#15688381	—	9	1	no	Hall
7	C₃²×D₁₄₉	—	5	1	no	—
8	C₃×C₅×C₁₄₉	Dic₃	1	4	yes	complemented
9	C₃⋊#10597010	—	15	4	no	—
10	D₇₄₅	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₁₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₄₉	—	5	4	no	—
13	C₅×C₁₄₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	#10597010	—	45	1	no	Hall
15	C₃×C₁₄₉	ΓL(1,𝔽₁₆)	1	4	yes	complemented
16	D₁₄₉	—	5	1	no	—
17	C₃⋊ΓL(1,𝔽₁₆)	—	149	1	no	maximal, Hall
18	C₁₄₉	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
19	C₃²×D₅	—	149	1	no	—
20	ΓL(1,𝔽₁₆)	—	447	4	no	—
21	C₃²×C₅	#10597010	1	1	yes	characteristic, complemented, Hall
22	C₃⋊Dic₃	—	745	1	no	Hall
23	C₃×D₅	—	149	4	no	—
24	AGL(1,𝔽₅)	—	1341	1	no	Hall
25	C₂×C₃²	—	745	1	no	—
26	C₃×C₅	C₃⋊#10597010	1	4	yes	complemented
27	Dic₃	—	2235	4	no	—
28	D₅	—	149	1	no	—
29	C₃²	#15688381	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	745	4	no	—
31	C₅	C₃⋊(C₃⋊#10597010)	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	6705	1	no	Sylow
33	C₃	C₃⋊#15688381	1	4	yes	complemented
34	C₂	—	745	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₄₉	C₄
prime radical, cosocle	C₃²×D₇₄₅	C₂
LCS	G ▷ C₃²×C₅×C₁₄₉
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.