Subgroups — C₃×#27130989 #49137731

Order 36300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₁×C₅⋊D₅₅	C₂	1	2	yes	maximal, complemented
3	#27130989	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₅₅⋊D₁₁	—	5	6	no	maximal
6	C₁₁×C₅⋊D₅₅	C₂×C₃	1	2	yes	complemented
7	C₅²×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₁₁×D₅₅	—	5	12	no	—
9	C₃×C₅×C₁₁⋊D₁₁	D₅	1	6	yes	complemented
10	C₃×D₁₁×C₅⋊D₅	—	11	2	no	maximal
11	C₅²×C₁₁²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	D₅₅⋊D₁₁	—	5	6	no	—
13	C₃×C₅×C₁₁²	C₂×D₅	1	6	yes	complemented
14	C₃×C₅⋊D₅₅	D₁₁	1	2	yes	complemented
15	C₃×C₁₁×C₅⋊D₅	—	11	2	no	—
16	C₃×C₅²×D₁₁	—	11	2	no	—
17	C₃×C₅²×D₁₁	—	22	5	no	—
18	C₃×D₁₁²	—	25	1	no	Hall
19	C₁₁×D₅₅	—	5	12	no	—
20	C₅×C₁₁⋊D₁₁	C₃×D₅	1	6	yes	complemented
21	D₁₁×C₅⋊D₅	—	11	2	no	—
22	C₃×C₅²×C₁₁	—	2	5	no	—
23	C₃×C₅²×C₁₁	C₂×D₁₁	1	2	yes	complemented
24	C₃×C₁₁⋊D₁₁	C₅⋊D₅	1	1	yes	characteristic, complemented
25	C₃×C₁₁×D₁₁	—	25	2	no	—
26	C₃×D₅×D₁₁	—	55	12	no	—
27	C₅×C₁₁²	C₂×C₃×D₅	1	6	yes	complemented
28	C₅⋊D₅₅	C₃×D₁₁	1	2	yes	complemented
29	C₁₁×C₅⋊D₅	—	11	2	no	—
30	C₅²×D₁₁	—	11	2	no	—
31	C₅²×D₁₁	—	22	5	no	—
32	D₁₁²	—	25	1	no	Hall
33	C₃×C₁₁²	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
34	C₃×D₅₅	—	5	12	no	—
35	C₃×D₅×C₁₁	—	55	12	no	—
36	C₃×C₅×D₁₁	—	11	12	no	—
37	C₃×C₅×D₁₁	—	22	30	no	—
38	C₂×C₃×C₅⋊D₅	—	121	1	no	Hall
39	C₅²×C₁₁	—	2	5	no	—
40	C₅²×C₁₁	C₂×C₃×D₁₁	1	2	yes	complemented
41	C₁₁⋊D₁₁	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
42	C₁₁×D₁₁	—	25	2	no	—
43	D₅×D₁₁	—	55	12	no	—
44	C₃×C₅×C₁₁	—	2	30	no	—
45	C₃×C₅×C₁₁	D₅×D₁₁	1	12	yes	complemented
46	C₂×C₃×C₅²	—	121	1	no	—
47	C₃×C₅⋊D₅	—	11	2	no	—
48	C₂×C₃×D₁₁	—	275	2	no	—
49	C₁₁²	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
50	D₅₅	—	5	12	no	—
51	C₅×D₁₁	—	11	12	no	—
52	C₅×D₁₁	—	22	30	no	—
53	D₅×C₁₁	—	55	12	no	—
54	C₂×C₅⋊D₅	—	121	1	no	Hall
55	C₃×C₅²	D₁₁²	1	1	yes	characteristic, complemented, Hall
56	C₂×C₃×C₁₁	—	275	2	no	—
57	C₃×D₁₁	—	11	2	no	—
58	C₃×D₁₁	—	22	5	no	—
59	C₃×D₁₁	—	25	2	no	—
60	C₂×C₃×D₅	—	605	6	no	—
61	C₅×C₁₁	—	2	30	no	—
62	C₅×C₁₁	C₃×D₅×D₁₁	1	12	yes	complemented
63	C₂×C₅²	—	121	1	no	—
64	C₅⋊D₅	—	11	2	no	—
65	C₂×D₁₁	—	275	2	no	—
66	C₃×C₁₁	—	2	5	no	—
67	C₃×C₁₁	D₁₁×C₅⋊D₅	1	2	yes	complemented
68	C₂×C₃×C₅	—	121	6	no	—
69	C₃×D₅	—	55	12	no	—
70	C₅²	C₃×D₁₁²	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₁₁	—	275	2	no	—
72	D₁₁	—	11	2	no	—
73	D₁₁	—	22	5	no	—
74	D₁₁	—	25	2	no	—
75	C₂×D₅	—	605	6	no	—
76	C₃×C₅	D₅₅⋊D₁₁	1	6	yes	complemented
77	C₂²×C₃	—	3025	1	no	Hall
78	C₁₁	—	2	5	no	—
79	C₁₁	C₃×D₁₁×C₅⋊D₅	1	2	yes	complemented
80	C₂×C₅	—	121	6	no	—
81	D₅	—	55	12	no	—
82	C₂×C₃	—	275	2	no	—
83	C₂×C₃	—	121	1	no	—
84	C₅	C₃×D₅₅⋊D₁₁	1	6	yes	complemented
85	C₂²	—	3025	1	no	Sylow
86	C₃	#27130989	1	1	yes	characteristic, direct product factor, Sylow
87	C₂	—	275	2	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#27130989
commutator, cosocle, hypocenter	C₅²×C₁₁²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₂²
LCS	G ▷ C₅²×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁⋊D₁₁	C₂	semidirect
2. C₃×C₁₁×C₅⋊D₅₅	C₂	semidirect
3. #27130989	C₃	direct (N × H)
4. C₃×C₅²×C₁₁²	C₂²	semidirect
6. C₁₁×C₅⋊D₅₅	C₂×C₃	semidirect
7. C₅²×C₁₁⋊D₁₁	C₂×C₃	semidirect
9. C₃×C₅×C₁₁⋊D₁₁	D₅	semidirect
11. C₅²×C₁₁²	C₂²×C₃	semidirect
13. C₃×C₅×C₁₁²	C₂×D₅	semidirect
14. C₃×C₅⋊D₅₅	D₁₁	semidirect
20. C₅×C₁₁⋊D₁₁	C₃×D₅	semidirect
23. C₃×C₅²×C₁₁	C₂×D₁₁	semidirect
24. C₃×C₁₁⋊D₁₁	C₅⋊D₅	semidirect
27. C₅×C₁₁²	C₂×C₃×D₅	semidirect
28. C₅⋊D₅₅	C₃×D₁₁	semidirect
33. C₃×C₁₁²	C₂×C₅⋊D₅	semidirect
40. C₅²×C₁₁	C₂×C₃×D₁₁	semidirect
41. C₁₁⋊D₁₁	C₃×C₅⋊D₅	semidirect
45. C₃×C₅×C₁₁	D₅×D₁₁	semidirect
49. C₁₁²	C₂×C₃×C₅⋊D₅	semidirect
55. C₃×C₅²	D₁₁²	semidirect
62. C₅×C₁₁	C₃×D₅×D₁₁	semidirect
67. C₃×C₁₁	D₁₁×C₅⋊D₅	semidirect
70. C₅²	C₃×D₁₁²	semidirect
76. C₃×C₅	D₅₅⋊D₁₁	semidirect
79. C₁₁	C₃×D₁₁×C₅⋊D₅	semidirect
84. C₅	C₃×D₅₅⋊D₁₁	semidirect
86. C₃	#27130989	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁⋊D₁₁	2
C₃×C₁₁×C₅⋊D₅₅	2
#27130989	3
C₃×D₅₅⋊D₁₁	5
C₃×D₁₁×C₅⋊D₅	11

Subgroups — C3×#27130989 #49137731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#27130989 #49137731