Subgroups — C₂²×C₅×Q₈×C₁₁ #13183457

Order 1760.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	12	yes	maximal, direct product factor
2	C₂²×C₄×C₅×C₁₁	C₂	1	3	yes	maximal
3	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
4	C₅×Q₈×C₁₁	C₂²	1	16	yes	direct product factor
5	C₂×C₄×C₅×C₁₁	C₂²	1	18	yes	—
6	C₂²×Q₈×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₁₁	Q₈	1	4	yes	direct product factor
8	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
9	C₄×C₅×C₁₁	C₂³	1	12	yes	—
10	C₂×Q₈×C₁₁	C₂×C₅	1	12	yes	direct product factor
11	C₂²×C₄×C₁₁	C₂×C₅	1	3	yes	—
12	C₂²×C₅×Q₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₁₁	C₂×Q₈	1	6	yes	direct product factor
14	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
15	C₂³×C₁₁	C₂²×C₅	1	1	yes	characteristic
16	Q₈×C₁₁	C₂²×C₅	1	16	yes	direct product factor
17	C₂×C₄×C₁₁	C₂²×C₅	1	18	yes	—
18	C₂×C₅×Q₈	C₂×C₁₁	1	12	yes	direct product factor
19	C₂²×C₄×C₅	C₂×C₁₁	1	3	yes	—
20	C₅×C₁₁	C₂²×Q₈	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₁₁	C₅×Q₈	1	4	yes	direct product factor
22	C₂²×C₁₁	C₂³×C₅	1	3	yes	—
23	C₄×C₁₁	C₂³×C₅	1	12	yes	—
24	C₂³×C₅	C₂²×C₁₁	1	1	yes	characteristic
25	C₅×Q₈	C₂²×C₁₁	1	16	yes	direct product factor
26	C₂×C₄×C₅	C₂²×C₁₁	1	18	yes	—
27	C₂²×Q₈	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₁₁	C₂×C₅×Q₈	1	6	yes	direct product factor
29	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
30	C₂²×C₅	Q₈×C₁₁	1	4	yes	direct product factor
31	C₂²×C₅	C₂³×C₁₁	1	3	yes	—
32	C₄×C₅	C₂³×C₁₁	1	12	yes	—
33	C₂×Q₈	C₂×C₅×C₁₁	1	12	yes	direct product factor
34	C₂²×C₄	C₂×C₅×C₁₁	1	3	yes	—
35	C₁₁	C₂²×C₅×Q₈	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₅	C₂×Q₈×C₁₁	1	6	yes	direct product factor
37	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
38	C₂³	C₂²×C₅×C₁₁	1	1	yes	characteristic
39	Q₈	C₂²×C₅×C₁₁	1	16	yes	direct product factor
40	C₂×C₄	C₂²×C₅×C₁₁	1	18	yes	—
41	C₅	C₂²×Q₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	C₅×Q₈×C₁₁	1	4	yes	direct product factor
43	C₂²	C₂³×C₅×C₁₁	1	3	yes	—
44	C₄	C₂³×C₅×C₁₁	1	12	yes	—
45	C₂	C₂×C₅×Q₈×C₁₁	1	6	yes	direct product factor
46	C₂	C₂⁴×C₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅×C₁₁	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₅×C₁₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×C₁₁	C₂	direct (N × H)
4. C₅×Q₈×C₁₁	C₂²	direct (N × H)
6. C₂²×Q₈×C₁₁	C₅	direct (N × H)
7. C₂²×C₅×C₁₁	Q₈	direct (N × H)
10. C₂×Q₈×C₁₁	C₂×C₅	direct (N × H)
12. C₂²×C₅×Q₈	C₁₁	direct (N × H)
13. C₂×C₅×C₁₁	C₂×Q₈	direct (N × H)
16. Q₈×C₁₁	C₂²×C₅	direct (N × H)
18. C₂×C₅×Q₈	C₂×C₁₁	direct (N × H)
20. C₅×C₁₁	C₂²×Q₈	direct (N × H)
21. C₂²×C₁₁	C₅×Q₈	direct (N × H)
25. C₅×Q₈	C₂²×C₁₁	direct (N × H)
27. C₂²×Q₈	C₅×C₁₁	direct (N × H)
28. C₂×C₁₁	C₂×C₅×Q₈	direct (N × H)
30. C₂²×C₅	Q₈×C₁₁	direct (N × H)
33. C₂×Q₈	C₂×C₅×C₁₁	direct (N × H)
35. C₁₁	C₂²×C₅×Q₈	direct (N × H)
36. C₂×C₅	C₂×Q₈×C₁₁	direct (N × H)
39. Q₈	C₂²×C₅×C₁₁	direct (N × H)
41. C₅	C₂²×Q₈×C₁₁	direct (N × H)
42. C₂²	C₅×Q₈×C₁₁	direct (N × H)
45. C₂	C₂×C₅×Q₈×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
C₂×C₅×Q₈×C₁₁	2
C₂²×C₄×C₅×C₁₁	2
C₂²×Q₈×C₁₁	5
C₂²×C₅×Q₈	11

Subgroups — C22×C5×Q8×C11 #13183457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×Q₈×C₁₁ #13183457