Subgroups — #13050384

Order 1320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×Dic₁₁	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×D₁₅	C₄	1	2	yes	complemented
7	D₃×Dic₁₁	—	5	1	no	maximal, Hall
8	C₂×D₅×C₁₁	—	3	1	no	—
9	Dic₅₅	D₃	1	1	yes	characteristic, complemented
10	C₅×Dic₁₁	—	3	1	no	—
11	C₃×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×D₃×C₁₁	—	5	1	no	—
13	Dic₃₃	D₅	1	1	yes	characteristic, complemented
14	C₃×Dic₁₁	—	5	1	no	—
15	#1200	—	11	1	no	maximal, Hall
16	C₂×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic
17	D₅×C₁₁	—	3	2	no	—
18	C₂×Dic₁₁	—	15	1	no	Hall
19	C₂×C₃×C₁₁	C₂×D₅	1	1	yes	characteristic
20	D₃×C₁₁	—	5	2	no	—
21	C₂×D₁₅	D₁₁	1	1	yes	characteristic
22	C₃×Dic₅	—	11	1	no	—
23	C₅×Dic₃	—	11	1	no	—
24	C₅×C₁₁	C₄×D₃	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₁₁	—	15	1	no	—
26	Dic₁₁	—	3	1	no	—
27	Dic₁₁	—	5	1	no	—
28	C₄×D₅	—	33	1	no	Hall
29	C₃×C₁₁	C₄×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅	C₂×D₁₁	1	1	yes	characteristic
31	D₁₅	Dic₁₁	1	2	yes	complemented
32	C₄×D₃	—	55	1	no	Hall
33	C₂×C₁₁	—	15	2	no	—
34	C₂×C₁₁	D₃×D₅	1	1	yes	characteristic
35	C₂×D₅	—	3	1	no	—
36	C₄×C₅	—	33	1	no	—
37	Dic₅	—	11	1	no	—
38	C₃×C₅	C₂×Dic₁₁	1	1	yes	characteristic, complemented, Hall
39	C₂×D₃	—	5	1	no	—
40	C₃×C₄	—	55	1	no	—
41	Dic₃	—	11	1	no	—
42	C₁₁	#1200	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₅	D₃×D₁₁	1	1	yes	characteristic
44	D₅	—	3	2	no	—
45	C₂×C₄	—	165	1	no	Sylow
46	C₂×C₃	D₅×D₁₁	1	1	yes	characteristic
47	D₃	—	5	2	no	—
48	C₅	D₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	15	1	no	—
50	C₄	—	33	1	no	—
51	C₄	—	55	1	no	—
52	C₃	D₅×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	15	2	no	—
54	C₂	D₁₅⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₅⋊D₁₁
commutator, hypocenter	C₃×C₅×C₁₁	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₅×C₁₁	C₂²
prime radical	C₂×C₁₁×D₁₅	C₂
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₃₃	C₂	semidirect
3. C₃×Dic₅₅	C₂	semidirect
6. C₁₁×D₁₅	C₄	semidirect
9. Dic₅₅	D₃	semidirect
11. C₃×C₅×C₁₁	C₂×C₄	semidirect
13. Dic₃₃	D₅	semidirect
24. C₅×C₁₁	C₄×D₃	semidirect
29. C₃×C₁₁	C₄×D₅	semidirect
31. D₁₅	Dic₁₁	semidirect
38. C₃×C₅	C₂×Dic₁₁	semidirect
42. C₁₁	#1200	semidirect
48. C₅	D₃×Dic₁₁	semidirect
52. C₃	D₅×Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×D₁₅	2
C₅×Dic₃₃	2
C₃×Dic₅₅	2
D₅×Dic₁₁	3
D₃×Dic₁₁	5
#1200	11