Subgroups — C₅×(C₁₁⋊D₁₁)⋊C₉ #24926113

Order 10890.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₁⋊D₁₁	C₃	1	1	yes	maximal, characteristic
3	(C₁₁⋊D₁₁)⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁²	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₁⋊D₁₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₁²⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₁⋊D₁₁	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₁²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic
10	C₃×C₅×D₁₁	—	33	4	no	—
11	C₁₁⋊D₁₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₁₁	—	3	4	no	—
13	C₁₁²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
14	C₅×D₁₁	—	33	4	no	—
15	C₂×C₅×C₉	—	121	1	no	maximal, Hall
16	C₃×D₁₁	—	33	4	no	—
17	C₅×C₁₁	—	3	4	no	—
18	C₅×C₉	—	121	1	no	Hall
19	C₃×C₁₁	—	3	4	no	—
20	C₂×C₃×C₅	—	121	1	no	—
21	D₁₁	—	33	4	no	—
22	C₂×C₉	—	121	1	no	Hall
23	C₃×C₅	(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
24	C₁₁	—	3	4	no	—
25	C₂×C₅	—	121	1	no	Hall
26	C₉	—	121	1	no	Sylow
27	C₂×C₃	—	121	1	no	—
28	C₅	(C₁₁⋊D₁₁)⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
30	C₂	—	121	1	no	Sylow

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.