Subgroups — C₅×(C₆₇⋊C₉)⋊C₁₁ #45684239

Order 33165.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₆₇⋊C₁₁	C₃	1	1	yes	maximal, characteristic
2	(C₆₇⋊C₉)⋊C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₆₇⋊C₁₁	C₉	1	1	yes	characteristic, complemented, Hall
4	C₅×C₆₇⋊C₉	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₆₇⋊C₁₁	C₃×C₅	1	1	yes	characteristic
6	C₃×C₅×C₆₇	C₃×C₁₁	1	1	yes	characteristic
7	C₆₇⋊C₁₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
8	C₆₇⋊C₉	C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₅×C₉×C₁₁	—	67	1	no	maximal, Hall
10	C₅×C₆₇	C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₆₇	C₃×C₅×C₁₁	1	1	yes	characteristic
12	C₃×C₅×C₁₁	—	67	1	no	—
13	C₉×C₁₁	—	67	1	no	Hall
14	C₆₇	C₅×C₉×C₁₁	1	1	yes	characteristic, complemented, Sylow
15	C₅×C₁₁	—	67	1	no	Hall
16	C₅×C₉	—	67	1	no	Hall
17	C₃×C₁₁	—	67	1	no	—
18	C₃×C₅	(C₆₇⋊C₃)⋊C₁₁	1	1	yes	characteristic
19	C₁₁	—	67	1	no	Sylow
20	C₉	—	67	1	no	Sylow
21	C₅	(C₆₇⋊C₉)⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₅×(C₆₇⋊C₃)⋊C₁₁	1	1	yes	characteristic

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.