Subgroups — C₅²×C₉²×C₁₁ #72199724

Order 22275.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₉×C₁₁	C₃	1	4	yes	maximal
2	C₅×C₉²×C₁₁	C₅	1	6	yes	maximal, direct product factor
3	C₅²×C₉²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃²×C₅²×C₁₁	C₃²	1	1	yes	characteristic
5	C₅²×C₉×C₁₁	C₉	1	12	yes	direct product factor
6	C₃×C₅×C₉×C₁₁	C₃×C₅	1	24	yes	—
7	C₉²×C₁₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅²×C₁₁	C₃×C₉	1	4	yes	—
9	C₃×C₅²×C₉	C₃×C₁₁	1	4	yes	—
10	C₃²×C₅×C₁₁	C₃²×C₅	1	6	yes	—
11	C₅×C₉×C₁₁	C₅×C₉	1	72	yes	direct product factor
12	C₅×C₉²	C₅×C₁₁	1	6	yes	direct product factor
13	C₃×C₉×C₁₁	C₃×C₅²	1	4	yes	—
14	C₅²×C₁₁	C₉²	1	1	yes	characteristic, direct product factor, Hall
15	C₃²×C₅²	C₃²×C₁₁	1	1	yes	characteristic
16	C₅²×C₉	C₉×C₁₁	1	12	yes	direct product factor
17	C₃×C₅×C₁₁	C₃×C₅×C₉	1	24	yes	—
18	C₃×C₅×C₉	C₃×C₅×C₁₁	1	24	yes	—
19	C₃²×C₁₁	C₃²×C₅²	1	1	yes	characteristic
20	C₉×C₁₁	C₅²×C₉	1	12	yes	direct product factor
21	C₉²	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₅²	C₃×C₉×C₁₁	1	4	yes	—
23	C₅×C₁₁	C₅×C₉²	1	6	yes	direct product factor
24	C₃²×C₅	C₃²×C₅×C₁₁	1	6	yes	—
25	C₅×C₉	C₅×C₉×C₁₁	1	72	yes	direct product factor
26	C₃×C₁₁	C₃×C₅²×C₉	1	4	yes	—
27	C₃×C₉	C₃×C₅²×C₁₁	1	4	yes	—
28	C₅²	C₉²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₅	C₃×C₅×C₉×C₁₁	1	24	yes	—
30	C₁₁	C₅²×C₉²	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²	C₃²×C₅²×C₁₁	1	1	yes	characteristic
32	C₉	C₅²×C₉×C₁₁	1	12	yes	direct product factor
33	C₅	C₅×C₉²×C₁₁	1	6	yes	direct product factor
34	C₃	C₃×C₅²×C₉×C₁₁	1	4	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²	C₃²×C₅²×C₁₁
socle, prime radical	C₃²×C₅²×C₁₁	C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×C₉²×C₁₁	C₅	direct (N × H)
3. C₅²×C₉²	C₁₁	direct (N × H)
5. C₅²×C₉×C₁₁	C₉	direct (N × H)
7. C₉²×C₁₁	C₅²	direct (N × H)
11. C₅×C₉×C₁₁	C₅×C₉	direct (N × H)
12. C₅×C₉²	C₅×C₁₁	direct (N × H)
14. C₅²×C₁₁	C₉²	direct (N × H)
16. C₅²×C₉	C₉×C₁₁	direct (N × H)
20. C₉×C₁₁	C₅²×C₉	direct (N × H)
21. C₉²	C₅²×C₁₁	direct (N × H)
23. C₅×C₁₁	C₅×C₉²	direct (N × H)
25. C₅×C₉	C₅×C₉×C₁₁	direct (N × H)
28. C₅²	C₉²×C₁₁	direct (N × H)
30. C₁₁	C₅²×C₉²	direct (N × H)
32. C₉	C₅²×C₉×C₁₁	direct (N × H)
33. C₅	C₅×C₉²×C₁₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅²×C₉×C₁₁	3
C₅×C₉²×C₁₁	5
C₅²×C₉²	11

Subgroups — C52×C92×C11 #72199724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₉²×C₁₁ #72199724