Subgroups — C₃×D₃×D₃₆₅ #27190300

Order 13140.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₀₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₃₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₃₆₅	—	3	1	no	maximal
5	D₃×D₃₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₅×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃×D₇₃	—	5	1	no	maximal, Hall
8	D₁₀₉₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₃×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₃₆₅	—	2	1	no	—
11	C₃×D₃₆₅	—	3	1	no	—
12	C₃×D₃₆₅	D₃	1	1	yes	characteristic, direct product factor
13	C₃×D₃₆₅	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×C₇₃	—	3	1	no	—
15	C₂×D₃₆₅	—	3	1	no	Hall
16	C₃×D₂₁₉	—	5	1	no	—
17	C₃×D₃×C₇₃	D₅	1	1	yes	characteristic, complemented
18	C₃²×D₇₃	—	5	1	no	—
19	C₃×C₅×C₇₃	—	2	1	no	—
20	C₃×C₅×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×D₇₃	—	15	1	no	—
23	D₃×D₇₃	—	5	1	no	—
24	C₂×C₅×C₇₃	—	3	1	no	—
25	D₃₆₅	—	3	1	no	—
26	D₃₆₅	C₃×D₃	1	1	yes	characteristic, direct product factor
27	C₃²×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₇₃	—	3	1	no	—
29	D₂₁₉	—	5	1	no	—
30	C₃×D₇₃	—	5	1	no	—
31	C₃×D₇₃	—	5	1	no	—
32	C₃×D₇₃	—	10	1	no	—
33	C₃×D₇₃	—	15	1	no	—
34	D₃×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented
35	C₅×C₇₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
36	C₂×D₇₃	—	15	1	no	Hall
37	C₃×C₇₃	—	2	1	no	—
38	C₃×C₇₃	D₃×D₅	1	1	yes	characteristic, complemented
39	C₃×C₇₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
40	C₃×D₃×D₅	—	73	1	no	maximal, Hall
41	C₂×C₇₃	—	3	1	no	—
42	D₇₃	—	5	1	no	—
43	D₇₃	—	15	1	no	—
44	C₃×D₁₅	—	73	1	no	—
45	C₃×C₅×D₃	D₇₃	1	1	yes	characteristic, complemented
46	C₃²×D₅	—	73	1	no	—
47	C₇₃	C₃×D₃×D₅	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×D₅	—	219	1	no	—
49	D₃×D₅	—	73	1	no	—
50	C₃²×C₅	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×D₃	—	365	1	no	Hall
52	C₂×C₃×C₅	—	3	1	no	—
53	D₁₅	—	73	1	no	—
54	C₃×D₅	—	73	1	no	—
55	C₃×D₅	—	73	1	no	—
56	C₃×D₅	—	146	1	no	—
57	C₃×D₅	—	219	1	no	—
58	C₅×D₃	C₃×D₇₃	1	1	yes	characteristic, complemented
59	C₂×D₅	—	219	1	no	Hall
60	C₂×C₃²	—	365	1	no	—
61	C₃×D₃	—	365	1	no	—
62	C₃×D₃	D₃₆₅	1	1	yes	characteristic, direct product factor
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₇₃	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×C₃×D₇₃	1	1	yes	characteristic, complemented
66	C₂²×C₃	—	1095	1	no	—
67	C₂×D₃	—	365	1	no	—
68	C₂×C₅	—	3	1	no	—
69	D₅	—	73	1	no	—
70	D₅	—	219	1	no	—
71	C₃²	C₂×D₃₆₅	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	1095	1	no	—
74	C₂×C₃	—	365	1	no	—
75	C₂×C₃	—	365	1	no	—
76	C₂×C₃	—	730	1	no	—
77	D₃	—	365	1	no	—
78	D₃	C₃×D₃₆₅	1	1	yes	characteristic, direct product factor
79	C₅	C₃×D₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	1095	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₃₆₅	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×D₃₆₅	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	1095	1	no	—
86	C₂	—	365	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×D₃₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₃	C₂²
LCS	G ▷ C₃×C₅×C₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₀₉₅	C₂	semidirect
2. C₃×C₅×D₃×C₇₃	C₂	semidirect
3. C₃²×D₃₆₅	C₂	semidirect
5. D₃×D₃₆₅	C₃	direct (N × H)
6. C₃²×C₅×C₇₃	C₂²	semidirect
8. D₁₀₉₅	C₂×C₃	semidirect
9. C₅×D₃×C₇₃	C₂×C₃	semidirect
12. C₃×D₃₆₅	D₃	direct (N × H)
13. C₃×D₃₆₅	C₂×C₃	semidirect
17. C₃×D₃×C₇₃	D₅	semidirect
20. C₃×C₅×C₇₃	C₂×D₃	semidirect
21. C₃×C₅×C₇₃	C₂²×C₃	semidirect
26. D₃₆₅	C₃×D₃	direct (N × H)
27. C₃²×C₇₃	C₂×D₅	semidirect
34. D₃×C₇₃	C₃×D₅	semidirect
35. C₅×C₇₃	C₂×C₃×D₃	semidirect
38. C₃×C₇₃	D₃×D₅	semidirect
39. C₃×C₇₃	C₂×C₃×D₅	semidirect
45. C₃×C₅×D₃	D₇₃	semidirect
47. C₇₃	C₃×D₃×D₅	semidirect
50. C₃²×C₅	C₂×D₇₃	semidirect
58. C₅×D₃	C₃×D₇₃	semidirect
62. C₃×D₃	D₃₆₅	direct (N × H)
64. C₃×C₅	D₃×D₇₃	semidirect
65. C₃×C₅	C₂×C₃×D₇₃	semidirect
71. C₃²	C₂×D₃₆₅	semidirect
78. D₃	C₃×D₃₆₅	direct (N × H)
79. C₅	C₃×D₃×D₇₃	semidirect
82. C₃	D₃×D₃₆₅	direct (N × H)
83. C₃	C₂×C₃×D₃₆₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₁₀₉₅	2
C₃×C₅×D₃×C₇₃	2
C₃²×D₃₆₅	2
C₂×C₃×D₃₆₅	3
D₃×D₃₆₅	3
C₃×D₃×D₇₃	5
C₃×D₃×D₅	73

Subgroups — C3×D3×D365 #27190300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₃₆₅ #27190300