Subgroups — C₅×Q₈×Dic₁₁ #13183069

Order 1760.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊Dic₁₁	C₂	1	3	yes	maximal
3	C₄×C₅×Dic₁₁	C₂	1	3	yes	maximal
4	C₅×Q₈×C₁₁	C₄	1	4	yes	complemented
5	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
6	C₂×C₅×Dic₁₁	C₂²	1	3	yes	—
7	C₂×C₅×Dic₁₁	C₂²	1	1	yes	characteristic
8	Q₈×Dic₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
10	C₄×C₅×C₁₁	C₂×C₄	1	6	yes	—
11	C₅×Dic₁₁	—	2	3	no	—
12	C₅×Dic₁₁	Q₈	1	2	yes	direct product factor
13	C₂×Q₈×C₁₁	C₂×C₅	1	1	yes	characteristic
14	C₄⋊Dic₁₁	C₂×C₅	1	3	yes	—
15	C₄×Dic₁₁	C₂×C₅	1	3	yes	—
16	C₄×C₅×Q₈	—	11	1	no	maximal, Hall
17	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₅×C₁₁	C₂×Q₈	1	1	yes	characteristic
19	C₂×C₅×C₁₁	#41	1	1	yes	characteristic
20	Q₈×C₁₁	C₄×C₅	1	4	yes	complemented
21	C₂×C₄×C₁₁	C₂²×C₅	1	3	yes	—
22	C₂×Dic₁₁	C₂²×C₅	1	3	yes	—
23	C₂×Dic₁₁	C₂²×C₅	1	1	yes	characteristic
24	C₂×C₅×Q₈	D₁₁	1	1	yes	characteristic
25	C₅×C₄⋊C₄	—	11	3	no	—
26	C₄²×C₅	—	11	3	no	—
27	C₅×C₁₁	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
29	C₄×C₁₁	C₂×C₄×C₅	1	6	yes	—
30	Dic₁₁	—	2	3	no	—
31	Dic₁₁	C₅×Q₈	1	2	yes	direct product factor
32	C₅×Q₈	Dic₁₁	1	4	yes	direct product factor
33	C₂×C₄×C₅	—	11	1	no	—
34	C₂×C₄×C₅	—	11	3	no	—
35	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
36	C₄×Q₈	—	11	1	no	Sylow
37	C₂×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
38	C₂×C₁₁	C₂×C₅×Q₈	1	1	yes	characteristic
39	C₂×C₁₁	C₅×#41	1	1	yes	characteristic
40	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
41	C₄×C₅	—	11	2	no	—
42	C₄×C₅	—	22	3	no	—
43	C₄×C₅	C₂×Dic₁₁	1	6	yes	—
44	C₂×Q₈	C₅×D₁₁	1	1	yes	characteristic
45	C₄⋊C₄	—	11	3	no	—
46	C₄²	—	11	3	no	—
47	C₁₁	C₄×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₅	Q₈×D₁₁	1	1	yes	characteristic
49	C₂×C₅	#4343	1	1	yes	characteristic
50	C₂×C₅	C₂²×Dic₁₁	1	1	yes	characteristic
51	Q₈	C₅×Dic₁₁	1	4	yes	direct product factor
52	C₂×C₄	—	11	1	no	—
53	C₂×C₄	—	11	3	no	—
54	C₂×C₄	C₂×C₅×D₁₁	1	3	yes	—
55	C₅	Q₈×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²	C₂²×C₅×D₁₁	1	1	yes	characteristic
57	C₄	—	11	2	no	—
58	C₄	—	22	3	no	—
59	C₄	C₂×C₅×Dic₁₁	1	6	yes	—
60	C₂	C₅×Q₈×D₁₁	1	1	yes	characteristic
61	C₂	C₅×#4343	1	1	yes	characteristic
62	C₂	C₂²×C₅×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₅
Frattini	C₂²	C₂²×C₅×D₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	C₂³
cosocle	C₂²×C₁₁	C₂³×C₅
hypercenter	C₂×C₅×Q₈	D₁₁
hypocenter	C₁₁	C₄×C₅×Q₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×Q₈

Complements

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

N	H ≅ G/N	type
4. C₅×Q₈×C₁₁	C₄	semidirect
8. Q₈×Dic₁₁	C₅	direct (N × H)
12. C₅×Dic₁₁	Q₈	direct (N × H)
20. Q₈×C₁₁	C₄×C₅	semidirect
27. C₅×C₁₁	C₄×Q₈	semidirect
31. Dic₁₁	C₅×Q₈	direct (N × H)
32. C₅×Q₈	Dic₁₁	direct (N × H)
47. C₁₁	C₄×C₅×Q₈	semidirect
51. Q₈	C₅×Dic₁₁	direct (N × H)
55. C₅	Q₈×Dic₁₁	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
C₅×C₄⋊Dic₁₁	2
C₄×C₅×Dic₁₁	2
Q₈×Dic₁₁	5
C₄×C₅×Q₈	11

Subgroups — C5×Q8×Dic11 #13183069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Q₈×Dic₁₁ #13183069