Subgroups — Q₈×Dic₅₅ #13183241

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	C₄⋊Dic₅₅	C₂	1	3	yes	maximal
3	C₄×Dic₅₅	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×Dic₅₅	C₂²	1	3	yes	—
7	C₂×Dic₅₅	C₂²	1	1	yes	characteristic
8	Q₈×Dic₁₁	—	5	1	no	maximal, Hall
9	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
10	C₄×C₅×C₁₁	C₂×C₄	1	6	yes	—
11	Dic₅₅	—	2	3	no	—
12	Dic₅₅	Q₈	1	2	yes	direct product factor
13	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic
14	C₄⋊Dic₁₁	—	5	3	no	—
15	C₄×Dic₁₁	—	5	3	no	—
16	Q₈×Dic₅	—	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	Dic₅	1	4	yes	complemented
21	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
22	C₂×Dic₁₁	—	5	1	no	—
23	C₂×Dic₁₁	—	5	3	no	—
24	C₂×C₅×Q₈	D₁₁	1	1	yes	characteristic
25	C₄⋊Dic₅	—	11	3	no	—
26	C₄×Dic₅	—	11	3	no	—
27	C₅×C₁₁	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
29	C₄×C₁₁	C₂×Dic₅	1	6	yes	—
30	Dic₁₁	—	5	2	no	—
31	Dic₁₁	—	10	3	no	—
32	C₅×Q₈	Dic₁₁	1	4	yes	complemented
33	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
34	C₂×Dic₅	—	11	1	no	—
35	C₂×Dic₅	—	11	3	no	—
36	C₄×Q₈	—	55	1	no	Sylow
37	C₂×C₁₁	Q₈×D₅	1	1	yes	characteristic
38	C₂×C₁₁	#713	1	1	yes	characteristic
39	C₂×C₁₁	C₂²×Dic₅	1	1	yes	characteristic
40	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
41	C₄×C₅	C₂×Dic₁₁	1	6	yes	—
42	Dic₅	—	11	2	no	—
43	Dic₅	—	22	3	no	—
44	C₂×Q₈	D₅₅	1	1	yes	characteristic
45	C₄⋊C₄	—	55	3	no	—
46	C₄²	—	55	3	no	—
47	C₁₁	Q₈×Dic₅	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	Dic₅₅	1	4	yes	direct product factor
52	C₂×C₄	—	55	1	no	—
53	C₂×C₄	—	55	3	no	—
54	C₂×C₄	C₂×D₅₅	1	3	yes	—
55	C₅	Q₈×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
56	C₂²	C₂²×D₅₅	1	1	yes	characteristic
57	C₄	—	55	2	no	—
58	C₄	—	110	3	no	—
59	C₄	C₂×Dic₅₅	1	6	yes	—
60	C₂	Q₈×D₅₅	1	1	yes	characteristic
61	C₂	#11725035	1	1	yes	characteristic
62	C₂	C₂²×Dic₅₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₅
commutator	C₂×C₅×C₁₁	C₂²×C₄
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle, prime radical, cosocle	C₂²×C₅×C₁₁	C₂³
hypercenter	C₂×Q₈	D₅₅
hypocenter	C₅×C₁₁	C₄×Q₈
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
4. C₅×Q₈×C₁₁	C₄	semidirect
12. Dic₅₅	Q₈	direct (N × H)
20. Q₈×C₁₁	Dic₅	semidirect
27. C₅×C₁₁	C₄×Q₈	semidirect
32. C₅×Q₈	Dic₁₁	semidirect
47. C₁₁	Q₈×Dic₅	semidirect
51. Q₈	Dic₅₅	direct (N × H)
55. C₅	Q₈×Dic₁₁	semidirect

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
C₄⋊Dic₅₅	2
C₄×Dic₅₅	2
Q₈×Dic₁₁	5
Q₈×Dic₅	11

Subgroups — Q8×Dic55 #13183241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Dic₅₅ #13183241