Subgroups — C₂×C₃⁵×C₁₁ #72184663

Order 5346.

10656 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₁₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃⁴×C₁₁	C₃	1	121	yes	maximal, direct product factor
3	C₃⁴×C₁₁	C₂×C₃	1	121	yes	direct product factor
4	C₂×C₃³×C₁₁	C₃²	1	1210	yes	direct product factor
5	C₂×C₃⁵	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃³×C₁₁	C₂×C₃²	1	1210	yes	direct product factor
7	C₃⁵	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₃²×C₁₁	C₃³	1	1210	yes	direct product factor
9	C₂×C₃⁴	C₃×C₁₁	1	121	yes	direct product factor
10	C₃²×C₁₁	C₂×C₃³	1	1210	yes	direct product factor
11	C₃⁴	C₂×C₃×C₁₁	1	121	yes	direct product factor
12	C₂×C₃×C₁₁	C₃⁴	1	121	yes	direct product factor
13	C₂×C₃³	C₃²×C₁₁	1	1210	yes	direct product factor
14	C₃×C₁₁	C₂×C₃⁴	1	121	yes	direct product factor
15	C₃³	C₂×C₃²×C₁₁	1	1210	yes	direct product factor
16	C₂×C₁₁	C₃⁵	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²	C₃³×C₁₁	1	1210	yes	direct product factor
18	C₁₁	C₂×C₃⁵	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₂×C₃³×C₁₁	1	1210	yes	direct product factor
20	C₂×C₃	C₃⁴×C₁₁	1	121	yes	direct product factor
21	C₃	C₂×C₃⁴×C₁₁	1	121	yes	direct product factor
22	C₂	C₃⁵×C₁₁	1	1	yes	characteristic, direct product factor, 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.