Subgroups — C₂⁵×C₁₁×C₈₁ #72205486

Order 28512.

3740 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₁×C₈₁	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₁₁×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₁₁×C₈₁	C₂²	1	155	yes	direct product factor
4	C₂⁴×C₁₁×C₂₇	C₂×C₃	1	31	yes	—
5	C₂²×C₁₁×C₈₁	C₂³	1	155	yes	direct product factor
6	C₂⁵×C₉×C₁₁	C₉	1	1	yes	characteristic
7	C₂⁵×C₈₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₁₁×C₂₇	C₂²×C₃	1	155	yes	—
9	C₂×C₁₁×C₈₁	C₂⁴	1	31	yes	direct product factor
10	C₂⁴×C₉×C₁₁	C₂×C₉	1	31	yes	—
11	C₂⁴×C₈₁	C₂×C₁₁	1	31	yes	direct product factor
12	C₂²×C₁₁×C₂₇	C₂³×C₃	1	155	yes	—
13	C₂⁵×C₃×C₁₁	C₂₇	1	1	yes	characteristic
14	C₁₁×C₈₁	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
15	C₂⁵×C₂₇	C₃×C₁₁	1	1	yes	characteristic
16	C₂³×C₉×C₁₁	C₂²×C₉	1	155	yes	—
17	C₂³×C₈₁	C₂²×C₁₁	1	155	yes	direct product factor
18	C₂×C₁₁×C₂₇	C₂⁴×C₃	1	31	yes	—
19	C₂⁴×C₃×C₁₁	C₂×C₂₇	1	31	yes	—
20	C₂⁴×C₂₇	C₂×C₃×C₁₁	1	31	yes	—
21	C₂²×C₉×C₁₁	C₂³×C₉	1	155	yes	—
22	C₂⁵×C₁₁	C₈₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₈₁	C₂³×C₁₁	1	155	yes	direct product factor
24	C₁₁×C₂₇	C₂⁵×C₃	1	1	yes	characteristic
25	C₂⁵×C₉	C₉×C₁₁	1	1	yes	characteristic
26	C₂³×C₃×C₁₁	C₂²×C₂₇	1	155	yes	—
27	C₂³×C₂₇	C₂²×C₃×C₁₁	1	155	yes	—
28	C₂×C₉×C₁₁	C₂⁴×C₉	1	31	yes	—
29	C₂⁴×C₁₁	C₂×C₈₁	1	31	yes	direct product factor
30	C₂×C₈₁	C₂⁴×C₁₁	1	31	yes	direct product factor
31	C₂⁴×C₉	C₂×C₉×C₁₁	1	31	yes	—
32	C₂²×C₃×C₁₁	C₂³×C₂₇	1	155	yes	—
33	C₂²×C₂₇	C₂³×C₃×C₁₁	1	155	yes	—
34	C₉×C₁₁	C₂⁵×C₉	1	1	yes	characteristic
35	C₂⁵×C₃	C₁₁×C₂₇	1	1	yes	characteristic
36	C₂³×C₁₁	C₂²×C₈₁	1	155	yes	direct product factor
37	C₈₁	C₂⁵×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
38	C₂³×C₉	C₂²×C₉×C₁₁	1	155	yes	—
39	C₂×C₃×C₁₁	C₂⁴×C₂₇	1	31	yes	—
40	C₂×C₂₇	C₂⁴×C₃×C₁₁	1	31	yes	—
41	C₂⁴×C₃	C₂×C₁₁×C₂₇	1	31	yes	—
42	C₂²×C₁₁	C₂³×C₈₁	1	155	yes	direct product factor
43	C₂²×C₉	C₂³×C₉×C₁₁	1	155	yes	—
44	C₃×C₁₁	C₂⁵×C₂₇	1	1	yes	characteristic
45	C₂⁵	C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂₇	C₂⁵×C₃×C₁₁	1	1	yes	characteristic
47	C₂³×C₃	C₂²×C₁₁×C₂₇	1	155	yes	—
48	C₂×C₁₁	C₂⁴×C₈₁	1	31	yes	direct product factor
49	C₂×C₉	C₂⁴×C₉×C₁₁	1	31	yes	—
50	C₂⁴	C₂×C₁₁×C₈₁	1	31	yes	direct product factor
51	C₂²×C₃	C₂³×C₁₁×C₂₇	1	155	yes	—
52	C₁₁	C₂⁵×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
53	C₉	C₂⁵×C₉×C₁₁	1	1	yes	characteristic
54	C₂³	C₂²×C₁₁×C₈₁	1	155	yes	direct product factor
55	C₂×C₃	C₂⁴×C₁₁×C₂₇	1	31	yes	—
56	C₂²	C₂³×C₁₁×C₈₁	1	155	yes	direct product factor
57	C₃	C₂⁵×C₁₁×C₂₇	1	1	yes	characteristic
58	C₂	C₂⁴×C₁₁×C₈₁	1	31	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₂⁵×C₃×C₁₁
socle, prime radical	C₂⁵×C₃×C₁₁	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₁₁×C₈₁	C₂	direct (N × H)
3. C₂³×C₁₁×C₈₁	C₂²	direct (N × H)
5. C₂²×C₁₁×C₈₁	C₂³	direct (N × H)
7. C₂⁵×C₈₁	C₁₁	direct (N × H)
9. C₂×C₁₁×C₈₁	C₂⁴	direct (N × H)
11. C₂⁴×C₈₁	C₂×C₁₁	direct (N × H)
14. C₁₁×C₈₁	C₂⁵	direct (N × H)
17. C₂³×C₈₁	C₂²×C₁₁	direct (N × H)
22. C₂⁵×C₁₁	C₈₁	direct (N × H)
23. C₂²×C₈₁	C₂³×C₁₁	direct (N × H)
29. C₂⁴×C₁₁	C₂×C₈₁	direct (N × H)
30. C₂×C₈₁	C₂⁴×C₁₁	direct (N × H)
36. C₂³×C₁₁	C₂²×C₈₁	direct (N × H)
37. C₈₁	C₂⁵×C₁₁	direct (N × H)
42. C₂²×C₁₁	C₂³×C₈₁	direct (N × H)
45. C₂⁵	C₁₁×C₈₁	direct (N × H)
48. C₂×C₁₁	C₂⁴×C₈₁	direct (N × H)
50. C₂⁴	C₂×C₁₁×C₈₁	direct (N × H)
52. C₁₁	C₂⁵×C₈₁	direct (N × H)
54. C₂³	C₂²×C₁₁×C₈₁	direct (N × H)
56. C₂²	C₂³×C₁₁×C₈₁	direct (N × H)
58. C₂	C₂⁴×C₁₁×C₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₁₁×C₈₁	2
C₂⁵×C₁₁×C₂₇	3
C₂⁵×C₈₁	11

Subgroups — C25×C11×C81 #72205486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₁₁×C₈₁ #72205486