Subgroups — D₂₁₉⋊D₃₅ #44501445

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×D₁₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₂₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₅₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₅×D₇₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁⋊D₇₃	—	5	1	no	maximal, Hall
7	D₂₅₅₅	D₃	1	1	yes	characteristic, complemented
8	D₃₅×C₇₃	—	3	1	no	—
9	C₅×C₇×D₇₃	—	3	1	no	—
10	D₁₅⋊D₇₃	—	7	1	no	maximal, Hall
11	D₂₁×C₇₃	—	5	1	no	—
12	C₇×D₂₁₉	D₅	1	1	yes	characteristic, complemented
13	C₃×D₅₁₁	—	5	1	no	—
14	C₅×C₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₅×C₇₃	—	7	1	no	—
16	C₅×D₂₁₉	D₇	1	1	yes	characteristic, complemented
17	C₃×D₃₆₅	—	7	1	no	—
18	D₇×D₇₃	—	15	1	no	Hall
19	C₃×C₇×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅×D₇₃	—	21	1	no	Hall
21	C₃×C₅×C₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₅₁₁	—	5	1	no	—
23	C₇×D₇₃	—	3	1	no	—
24	D₇×C₇₃	—	15	1	no	—
25	D₃×D₇₃	—	35	1	no	Hall
26	D₃₆₅	—	7	1	no	—
27	C₅×D₇₃	—	3	1	no	—
28	D₅×C₇₃	—	21	1	no	—
29	C₇×C₇₃	D₃×D₅	1	1	yes	characteristic, complemented, Hall
30	D₂₁₉	D₃₅	1	1	yes	characteristic, complemented
31	C₃×D₇₃	—	35	1	no	—
32	D₃×C₇₃	—	35	1	no	—
33	D₃×D₃₅	—	73	1	no	maximal, Hall
34	C₅×C₇₃	D₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₃	—	105	1	no	Hall
36	C₃×C₇₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
37	D₁₀₅	D₇₃	1	1	yes	characteristic, complemented
38	C₅×D₃×C₇	—	73	1	no	—
39	C₃×D₃₅	—	73	1	no	—
40	C₂×C₇₃	—	105	1	no	—
41	D₇₃	—	3	1	no	—
42	D₇₃	—	35	1	no	—
43	C₂×D₃₅	—	219	1	no	Hall
44	C₃×C₅×C₇	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	—	365	1	no	Hall
46	C₇₃	D₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅×C₇	—	219	1	no	—
48	D₃₅	—	3	1	no	—
49	D₃₅	—	73	1	no	—
50	D₃×D₅	—	511	1	no	Hall
51	D₂₁	—	5	1	no	—
52	C₃×D₇	—	365	1	no	—
53	D₃×C₇	—	73	1	no	—
54	C₅×C₇	D₃×D₇₃	1	1	yes	characteristic, complemented, Hall
55	D₁₅	—	7	1	no	—
56	C₃×D₅	—	511	1	no	—
57	C₅×D₃	—	73	1	no	—
58	C₂×D₇	—	1095	1	no	Hall
59	C₃×C₇	D₅×D₇₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	1533	1	no	Hall
61	C₃×C₅	D₇×D₇₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	219	1	no	—
63	D₇	—	15	1	no	—
64	D₇	—	365	1	no	—
65	C₂×D₃	—	2555	1	no	Hall
66	C₂×C₅	—	219	1	no	—
67	D₅	—	21	1	no	—
68	D₅	—	511	1	no	—
69	C₇	D₁₅⋊D₇₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	2555	1	no	—
71	D₃	—	35	1	no	—
72	D₃	—	73	1	no	—
73	C₅	D₂₁⋊D₇₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	7665	1	no	Sylow
75	C₃	D₃₅×D₇₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	105	1	no	—
77	C₂	—	219	1	no	—
78	C₂	—	2555	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇×C₇₃	C₂²
LCS	G ▷ C₃×C₅×C₇×C₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇₃×D₁₀₅	C₂	semidirect
2. C₅×C₇×D₂₁₉	C₂	semidirect
3. C₃×D₂₅₅₅	C₂	semidirect
5. C₃×C₅×C₇×C₇₃	C₂²	semidirect
7. D₂₅₅₅	D₃	semidirect
12. C₇×D₂₁₉	D₅	semidirect
14. C₅×C₇×C₇₃	C₂×D₃	semidirect
16. C₅×D₂₁₉	D₇	semidirect
19. C₃×C₇×C₇₃	C₂×D₅	semidirect
21. C₃×C₅×C₇₃	C₂×D₇	semidirect
29. C₇×C₇₃	D₃×D₅	semidirect
30. D₂₁₉	D₃₅	semidirect
34. C₅×C₇₃	D₃×D₇	semidirect
36. C₃×C₇₃	C₂×D₃₅	semidirect
37. D₁₀₅	D₇₃	semidirect
44. C₃×C₅×C₇	C₂×D₇₃	semidirect
46. C₇₃	D₃×D₃₅	semidirect
54. C₅×C₇	D₃×D₇₃	semidirect
59. C₃×C₇	D₅×D₇₃	semidirect
61. C₃×C₅	D₇×D₇₃	semidirect
69. C₇	D₁₅⋊D₇₃	semidirect
73. C₅	D₂₁⋊D₇₃	semidirect
75. C₃	D₃₅×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×D₁₀₅	2
C₅×C₇×D₂₁₉	2
C₃×D₂₅₅₅	2
D₃₅×D₇₃	3
D₂₁⋊D₇₃	5
D₁₅⋊D₇₃	7
D₃×D₃₅	73

Subgroups — D219⋊D35 #44501445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁₉⋊D₃₅ #44501445