Subgroups — D₃₉×D₁₃₃ #35209161

Order 20748.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₁₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₉×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₃₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇₂₉	—	3	1	no	—
7	C₁₃×D₁₃₃	D₃	1	1	yes	characteristic, complemented
8	C₇×C₁₉×D₁₃	—	3	1	no	—
9	D₁₉×D₃₉	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×D₁₃₃	—	13	1	no	maximal, Hall
12	D₇₄₁	—	7	1	no	—
13	C₁₉×D₃₉	D₇	1	1	yes	characteristic, complemented
14	C₃×C₁₃×D₁₉	—	7	1	no	—
15	D₇×D₃₉	—	19	1	no	maximal, Hall
16	D₁₃×D₁₉	—	21	1	no	Hall
17	D₃₉₉	—	13	1	no	—
18	D₃×C₇×C₁₉	—	13	1	no	—
19	C₃×D₁₃₃	D₁₃	1	1	yes	characteristic, complemented
20	C₃×C₁₃×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	D₂₇₃	—	19	1	no	—
22	C₇×D₃₉	D₁₉	1	1	yes	characteristic, complemented
23	C₃×C₁₃×D₇	—	19	1	no	—
24	C₂×D₁₃₃	—	39	1	no	Hall
25	D₂₄₇	—	21	1	no	—
26	C₁₃×D₁₉	—	7	1	no	—
27	C₁₉×D₁₃	—	3	1	no	—
28	C₃×C₇×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₇×D₁₃	—	57	1	no	Hall
30	C₃×C₇×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×C₁₉	—	39	1	no	—
32	D₁₃₃	—	39	1	no	—
33	D₁₃₃	D₃₉	1	1	yes	characteristic, direct product factor
34	C₁₃×C₁₉	D₃×D₇	1	1	yes	characteristic, complemented, Hall
35	D₃×D₁₉	—	91	1	no	Hall
36	D₉₁	—	57	1	no	—
37	C₇×D₁₃	—	3	1	no	—
38	C₁₃×D₇	—	19	1	no	—
39	C₂×D₃₉	—	133	1	no	Hall
40	C₇×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
41	D₅₇	—	91	1	no	—
42	C₃×D₁₉	—	7	1	no	—
43	D₃×C₁₉	—	13	1	no	—
44	C₇×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	—	247	1	no	Hall
46	C₂×C₃×C₁₃	—	133	1	no	—
47	D₃₉	—	133	1	no	—
48	D₃₉	D₁₃₃	1	1	yes	characteristic, direct product factor
49	C₂×D₁₉	—	273	1	no	Hall
50	C₃×C₁₉	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	399	1	no	Hall
52	D₂₁	—	247	1	no	—
53	C₃×D₇	—	19	1	no	—
54	D₃×C₇	—	13	1	no	—
55	C₃×C₁₃	C₂×D₁₃₃	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	39	1	no	—
57	D₁₉	—	7	1	no	—
58	D₁₉	—	273	1	no	—
59	C₂×D₇	—	741	1	no	Hall
60	C₂×C₁₃	—	133	1	no	—
61	D₁₃	—	3	1	no	—
62	D₁₃	—	399	1	no	—
63	C₃×C₇	D₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
64	C₁₉	D₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₇	—	39	1	no	—
66	D₇	—	19	1	no	—
67	D₇	—	741	1	no	—
68	C₁₃	D₃×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	1729	1	no	Hall
70	C₇	D₁₉×D₃₉	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	133	1	no	—
72	D₃	—	13	1	no	—
73	D₃	—	1729	1	no	—
74	C₂²	—	5187	1	no	Sylow
75	C₃	D₁₃×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	39	1	no	—
77	C₂	—	5187	1	no	—
78	C₂	—	133	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₁₈₇	C₂	semidirect
2. C₇×C₁₉×D₃₉	C₂	semidirect
3. C₃×C₁₃×D₁₃₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂²	semidirect
7. C₁₃×D₁₃₃	D₃	semidirect
10. C₇×C₁₃×C₁₉	C₂×D₃	semidirect
13. C₁₉×D₃₉	D₇	semidirect
19. C₃×D₁₃₃	D₁₃	semidirect
20. C₃×C₁₃×C₁₉	C₂×D₇	semidirect
22. C₇×D₃₉	D₁₉	semidirect
28. C₃×C₇×C₁₉	C₂×D₁₃	semidirect
30. C₃×C₇×C₁₃	C₂×D₁₉	semidirect
33. D₁₃₃	D₃₉	direct (N × H)
34. C₁₃×C₁₉	D₃×D₇	semidirect
40. C₇×C₁₉	C₂×D₃₉	semidirect
44. C₇×C₁₃	D₃×D₁₉	semidirect
48. D₃₉	D₁₃₃	direct (N × H)
50. C₃×C₁₉	D₇×D₁₃	semidirect
55. C₃×C₁₃	C₂×D₁₃₃	semidirect
63. C₃×C₇	D₁₃×D₁₉	semidirect
64. C₁₉	D₇×D₃₉	semidirect
68. C₁₃	D₃×D₁₃₃	semidirect
70. C₇	D₁₉×D₃₉	semidirect
75. C₃	D₁₃×D₁₃₃	semidirect

Maximal subgroups

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

subgroup	index
D₅₁₈₇	2
C₇×C₁₉×D₃₉	2
C₃×C₁₃×D₁₃₃	2
D₁₃×D₁₃₃	3
D₁₉×D₃₉	7
D₃×D₁₃₃	13
D₇×D₃₉	19

Subgroups — D39×D133 #35209161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₉×D₁₃₃ #35209161