Subgroups — D₃₉×D₂₁₉ #46802990

Order 34164.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₂₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₈₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₂₁₉	—	3	1	no	maximal
5	D₃₉×D₇₃	—	3	1	no	maximal
6	C₃²×C₁₃×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₈₄₇	—	3	1	no	—
8	D₂₈₄₇	—	3	1	no	—
9	D₂₈₄₇	—	6	1	no	—
10	C₇₃×D₃₉	D₃	1	1	yes	characteristic, complemented
11	C₁₃×D₂₁₉	D₃	1	1	yes	characteristic, complemented
12	C₃×D₁₃×C₇₃	—	3	1	no	—
13	C₃×C₁₃×D₇₃	—	3	1	no	—
14	D₁₃×D₇₃	—	9	1	no	Hall
15	C₃×C₁₃×C₇₃	—	2	1	no	—
16	C₃×C₁₃×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₂₁₉	—	13	1	no	maximal, Hall
19	D₉₄₉	—	9	1	no	—
20	C₁₃×D₇₃	—	3	1	no	—
21	D₁₃×C₇₃	—	3	1	no	—
22	C₃⋊D₂₁₉	—	13	1	no	—
23	C₃×D₂₁₉	D₁₃	1	1	yes	characteristic, complemented
24	C₃×D₃×C₇₃	—	13	1	no	—
25	C₁₃×C₇₃	D₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×D₂₁₉	—	39	1	no	—
27	D₃×D₇₃	—	39	1	no	—
28	C₃²×C₇₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₃×D₃₉	—	73	1	no	maximal, Hall
30	C₂×C₃×C₇₃	—	39	1	no	—
31	D₂₁₉	—	39	1	no	—
32	D₂₁₉	—	39	1	no	—
33	D₂₁₉	—	78	1	no	—
34	D₂₁₉	D₃₉	1	1	yes	characteristic, direct product factor
35	C₃×D₇₃	—	3	1	no	—
36	D₃×C₇₃	—	13	1	no	—
37	C₂×D₇₃	—	117	1	no	Hall
38	C₃⋊D₃₉	—	73	1	no	—
39	C₃×D₃₉	D₇₃	1	1	yes	characteristic, complemented
40	C₃×D₃×C₁₃	—	73	1	no	—
41	C₃×C₇₃	—	2	1	no	—
42	C₃×C₇₃	D₃×D₁₃	1	1	yes	characteristic, complemented
43	C₃×C₇₃	C₂×D₃₉	1	1	yes	characteristic, complemented
44	C₂×D₃₉	—	219	1	no	—
45	D₃×D₁₃	—	219	1	no	—
46	C₂×C₇₃	—	39	1	no	—
47	D₇₃	—	3	1	no	—
48	D₇₃	—	117	1	no	—
49	C₃²×C₁₃	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₁₃	—	219	1	no	—
51	D₃₉	—	438	1	no	—
52	D₃₉	—	219	1	no	—
53	D₃₉	—	219	1	no	—
54	D₃₉	D₂₁₉	1	1	yes	characteristic, direct product factor
55	C₃×D₁₃	—	3	1	no	—
56	D₃×C₁₃	—	73	1	no	—
57	C₇₃	D₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₃	—	657	1	no	Hall
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	D₃×D₇₃	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₂×D₂₁₉	1	1	yes	characteristic, complemented
62	D₃²	—	949	1	no	Hall
63	C₂×C₁₃	—	219	1	no	—
64	D₁₃	—	3	1	no	—
65	D₁₃	—	657	1	no	—
66	C₃⋊D₃	—	949	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	—	73	1	no	—
69	C₁₃	D₃×D₂₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	2847	1	no	—
71	C₂×D₃	—	2847	1	no	—
72	C₃²	D₁₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	39	1	no	—
74	C₂×C₃	—	219	1	no	—
75	D₃	—	13	1	no	—
76	D₃	—	2847	1	no	—
77	D₃	—	2847	1	no	—
78	D₃	—	5694	1	no	—
79	D₃	—	73	1	no	—
80	C₂²	—	8541	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃₉×D₇₃	1	1	yes	characteristic, complemented
83	C₃	D₁₃×D₂₁₉	1	1	yes	characteristic, complemented
84	C₂	—	39	1	no	—
85	C₂	—	8541	1	no	—
86	C₂	—	219	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃×C₇₃	C₂²
LCS	G ▷ C₃²×C₁₃×C₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×D₂₁₉	C₂	semidirect
2. C₃×C₇₃×D₃₉	C₂	semidirect
3. C₃⋊D₂₈₄₇	C₂	semidirect
6. C₃²×C₁₃×C₇₃	C₂²	semidirect
10. C₇₃×D₃₉	D₃	semidirect
11. C₁₃×D₂₁₉	D₃	semidirect
16. C₃×C₁₃×C₇₃	C₂×D₃	semidirect
17. C₃×C₁₃×C₇₃	C₂×D₃	semidirect
23. C₃×D₂₁₉	D₁₃	semidirect
25. C₁₃×C₇₃	D₃²	semidirect
28. C₃²×C₇₃	C₂×D₁₃	semidirect
34. D₂₁₉	D₃₉	direct (N × H)
39. C₃×D₃₉	D₇₃	semidirect
42. C₃×C₇₃	D₃×D₁₃	semidirect
43. C₃×C₇₃	C₂×D₃₉	semidirect
49. C₃²×C₁₃	C₂×D₇₃	semidirect
54. D₃₉	D₂₁₉	direct (N × H)
57. C₇₃	D₃×D₃₉	semidirect
60. C₃×C₁₃	D₃×D₇₃	semidirect
61. C₃×C₁₃	C₂×D₂₁₉	semidirect
69. C₁₃	D₃×D₂₁₉	semidirect
72. C₃²	D₁₃×D₇₃	semidirect
82. C₃	D₃₉×D₇₃	semidirect
83. C₃	D₁₃×D₂₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×D₂₁₉	2
C₃×C₇₃×D₃₉	2
C₃⋊D₂₈₄₇	2
D₁₃×D₂₁₉	3
D₃₉×D₇₃	3
D₃×D₂₁₉	13
D₃×D₃₉	73

Subgroups — D39×D219 #46802990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₉×D₂₁₉ #46802990