Subgroups — C₃×D₅×D₂₁₉ #27190299

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×D₂₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₅×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₂₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₅×D₇₃	—	3	1	no	maximal
6	C₃²×C₅×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×D₂₁₉	—	5	1	no	maximal, Hall
8	D₁₀₉₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₂₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₃₆₅	—	3	1	no	—
11	C₃×D₅×C₇₃	—	2	1	no	—
12	C₃×D₅×C₇₃	D₃	1	1	yes	characteristic, complemented
13	C₃×D₅×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₅×D₇₃	—	3	1	no	—
15	D₅×D₇₃	—	3	1	no	Hall
16	C₂×C₃²×C₇₃	—	5	1	no	—
17	C₃×D₂₁₉	—	5	1	no	—
18	C₃×D₂₁₉	D₅	1	1	yes	characteristic, direct product factor
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×D₂₁₉	—	5	1	no	—
23	C₂×C₃×D₇₃	—	15	1	no	—
24	D₃₆₅	—	3	1	no	—
25	C₅×D₇₃	—	3	1	no	—
26	D₅×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented
27	C₃²×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₇₃	—	5	1	no	—
29	C₂×C₃×C₇₃	—	5	1	no	—
30	C₂×C₃×C₇₃	—	10	1	no	—
31	D₂₁₉	—	5	1	no	—
32	D₂₁₉	C₃×D₅	1	1	yes	characteristic, direct product factor
33	C₃×D₇₃	—	3	1	no	—
34	C₃×D₇₃	—	15	1	no	—
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	—	5	1	no	—
42	D₇₃	—	3	1	no	—
43	D₇₃	—	15	1	no	—
44	C₃×D₁₅	—	73	1	no	—
45	C₃×C₅×D₃	—	73	1	no	—
46	C₃²×D₅	D₇₃	1	1	yes	characteristic, complemented
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	—	219	1	no	—
53	D₁₅	—	73	1	no	—
54	C₃×D₅	—	2	1	no	—
55	C₃×D₅	—	219	1	no	—
56	C₃×D₅	C₃×D₇₃	1	1	yes	characteristic, complemented
57	C₃×D₅	D₂₁₉	1	1	yes	characteristic, direct product factor
58	C₅×D₃	—	73	1	no	—
59	C₂×D₅	—	219	1	no	Hall
60	C₂×C₃²	—	5	1	no	—
61	C₃×D₃	—	73	1	no	—
62	C₃×D₃	—	365	1	no	—
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	C₂×C₃×D₇₃	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×D₂₁₉	1	1	yes	characteristic, complemented
66	C₂²×C₃	—	1095	1	no	—
67	C₂×D₃	—	365	1	no	—
68	C₂×C₅	—	219	1	no	—
69	D₅	—	219	1	no	—
70	D₅	C₃×D₂₁₉	1	1	yes	characteristic, direct product factor
71	C₃²	D₅×D₇₃	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	5	1	no	—
73	C₂×C₃	—	5	1	no	—
74	C₂×C₃	—	10	1	no	—
75	C₂×C₃	—	1095	1	no	—
76	C₂×C₃	—	219	1	no	—
77	D₃	—	73	1	no	—
78	D₃	—	365	1	no	—
79	C₅	C₂×C₃×D₂₁₉	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	1095	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₅×D₇₃	1	1	yes	characteristic, complemented
83	C₃	D₅×D₂₁₉	1	1	yes	characteristic, direct product factor
84	C₂	—	5	1	no	—
85	C₂	—	1095	1	no	—
86	C₂	—	219	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₂₁₉
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×D₂₁₉	C₂	semidirect
3. C₃²×D₅×C₇₃	C₂	semidirect
4. D₅×D₂₁₉	C₃	direct (N × H)
6. C₃²×C₅×C₇₃	C₂²	semidirect
8. D₁₀₉₅	C₂×C₃	semidirect
9. C₅×D₂₁₉	C₂×C₃	semidirect
12. C₃×D₅×C₇₃	D₃	semidirect
13. C₃×D₅×C₇₃	C₂×C₃	semidirect
18. C₃×D₂₁₉	D₅	direct (N × H)
20. C₃×C₅×C₇₃	C₂×D₃	semidirect
21. C₃×C₅×C₇₃	C₂²×C₃	semidirect
26. D₅×C₇₃	C₃×D₃	semidirect
27. C₃²×C₇₃	C₂×D₅	semidirect
32. D₂₁₉	C₃×D₅	direct (N × H)
35. C₅×C₇₃	C₂×C₃×D₃	semidirect
38. C₃×C₇₃	D₃×D₅	semidirect
39. C₃×C₇₃	C₂×C₃×D₅	semidirect
46. C₃²×D₅	D₇₃	semidirect
47. C₇₃	C₃×D₃×D₅	semidirect
50. C₃²×C₅	C₂×D₇₃	semidirect
56. C₃×D₅	C₃×D₇₃	semidirect
57. C₃×D₅	D₂₁₉	direct (N × H)
64. C₃×C₅	C₂×C₃×D₇₃	semidirect
65. C₃×C₅	C₂×D₂₁₉	semidirect
70. D₅	C₃×D₂₁₉	direct (N × H)
71. C₃²	D₅×D₇₃	semidirect
79. C₅	C₂×C₃×D₂₁₉	semidirect
82. C₃	C₃×D₅×D₇₃	semidirect
83. C₃	D₅×D₂₁₉	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×D₁₀₉₅	2
C₃×C₅×D₂₁₉	2
C₃²×D₅×C₇₃	2
D₅×D₂₁₉	3
C₃×D₅×D₇₃	3
C₂×C₃×D₂₁₉	5
C₃×D₃×D₅	73

Subgroups — C3×D5×D219 #27190299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₂₁₉ #27190299