Subgroups — C₉×#15688382 #41001227

Order 26820.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₇₄₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#15688382	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×#10597010	—	5	1	no	maximal, Hall
5	C₃×D₇₄₅	C₂×C₃	1	1	yes	characteristic
6	#15688382	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×D₁₄₉	—	5	1	no	—
8	C₃×C₅×C₁₄₉	C₃×C₄	1	1	yes	characteristic
9	C₃×#10597010	—	5	1	no	—
10	D₇₄₅	C₂×C₉	1	1	yes	characteristic
11	C₉×C₁₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₄₉	—	5	1	no	—
13	C₅×C₁₄₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	#10597010	—	5	1	no	Hall
15	C₃×C₁₄₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
16	D₁₄₉	—	5	1	no	—
17	C₉×AGL(1,𝔽₅)	—	149	1	no	maximal, Hall
18	C₁₄₉	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	C₉×D₅	—	149	1	no	—
20	C₃×AGL(1,𝔽₅)	—	149	1	no	—
21	C₅×C₉	#10597010	1	1	yes	characteristic, complemented, Hall
22	C₄×C₉	—	745	1	no	Hall
23	C₃×D₅	—	149	1	no	—
24	AGL(1,𝔽₅)	—	149	1	no	Hall
25	C₂×C₉	—	745	1	no	—
26	C₃×C₅	C₃×#10597010	1	1	yes	characteristic
27	C₃×C₄	—	745	1	no	—
28	D₅	—	149	1	no	—
29	C₉	#15688382	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	745	1	no	—
31	C₅	C₉×#10597010	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	745	1	no	Sylow
33	C₃	C₃×#15688382	1	1	yes	characteristic
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.