Subgroups — C₃²×#15688381 #41001276

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	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×#10597010	—	5	1	no	maximal, Hall
5	C₃×D₇₄₅	C₂×C₃	1	4	yes	—
6	#15688381	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×D₁₄₉	—	5	1	no	—
8	C₃×C₅×C₁₄₉	C₃×C₄	1	4	yes	complemented
9	C₃×#10597010	—	5	4	no	—
10	D₇₄₅	C₂×C₃²	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	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	#10597010	—	5	1	no	Hall
15	C₃×C₁₄₉	C₃×AGL(1,𝔽₅)	1	4	yes	complemented
16	D₁₄₉	—	5	1	no	—
17	C₃²×AGL(1,𝔽₅)	—	149	1	no	maximal, Hall
18	C₁₄₉	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	C₃²×D₅	—	149	1	no	—
20	C₃×AGL(1,𝔽₅)	—	149	4	no	—
21	C₃²×C₅	#10597010	1	1	yes	characteristic, complemented, Hall
22	C₃²×C₄	—	745	1	no	Hall
23	C₃×D₅	—	149	4	no	—
24	AGL(1,𝔽₅)	—	149	1	no	Hall
25	C₂×C₃²	—	745	1	no	—
26	C₃×C₅	C₃×#10597010	1	4	yes	complemented
27	C₃×C₄	—	745	4	no	—
28	D₅	—	149	1	no	—
29	C₃²	#15688381	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	745	4	no	—
31	C₅	C₃²×#10597010	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	745	1	no	Sylow
33	C₃	C₃×#15688381	1	4	yes	direct product factor
34	C₂	—	745	1	no	—

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.