Subgroups — C₂×C₂₉×D₃₁₅ #49141309

Order 36540.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₃₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×D₁₀₅	—	3	1	no	maximal
4	C₅×C₇×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₉×D₆₃	—	5	1	no	maximal, Hall
6	C₂₉×D₁₀₅	—	3	2	no	—
7	C₂×C₃×C₅×C₇×C₂₉	D₃	1	1	yes	characteristic
8	C₂×C₂₉×D₄₅	—	7	1	no	maximal, Hall
9	C₂×C₂₉×D₃₅	—	9	1	no	Hall
10	C₂₉×D₆₃	—	5	2	no	—
11	C₂×C₇×C₉×C₂₉	D₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic
13	C₂₉×D₄₅	—	7	2	no	—
14	C₂×C₅×C₉×C₂₉	D₇	1	1	yes	characteristic, complemented
15	C₂×C₂₉×D₂₁	—	15	1	no	—
16	C₂₉×D₃₅	—	9	2	no	—
17	C₂×C₅×C₇×C₂₉	D₉	1	1	yes	characteristic, complemented
18	C₇×C₉×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₂₉×D₁₅	—	21	1	no	—
20	C₅×C₉×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃₁₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₃×C₇×C₂₉	D₁₅	1	1	yes	characteristic
23	C₂₉×D₂₁	—	15	2	no	—
24	C₂×D₉×C₂₉	—	35	1	no	Hall
25	C₅×C₇×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₂₉	D₂₁	1	1	yes	characteristic
27	C₂₉×D₁₅	—	21	2	no	—
28	C₂×D₇×C₂₉	—	45	1	no	Hall
29	C₂×C₅×C₇×C₉	C₂×C₂₉	1	1	yes	characteristic, complemented
30	D₃₁₅	C₂×C₂₉	1	2	yes	direct product factor
31	C₃×C₇×C₂₉	C₂×D₁₅	1	1	yes	characteristic
32	C₂×D₅×C₂₉	—	63	1	no	Hall
33	C₂×C₉×C₂₉	D₃₅	1	1	yes	characteristic, complemented
34	D₉×C₂₉	—	35	2	no	—
35	C₃×C₅×C₂₉	C₂×D₂₁	1	1	yes	characteristic
36	C₂×D₁₀₅	—	3	1	no	—
37	C₂×C₇×C₂₉	D₄₅	1	1	yes	characteristic, complemented
38	D₇×C₂₉	—	45	2	no	—
39	C₂×D₃×C₂₉	—	105	1	no	—
40	C₅×C₇×C₉	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₂₉	D₆₃	1	1	yes	characteristic, complemented
42	D₅×C₂₉	—	63	2	no	—
43	C₉×C₂₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
44	C₂×D₆₃	—	5	1	no	Hall
45	C₂×C₃×C₅×C₇	D₃×C₂₉	1	1	yes	characteristic
46	D₁₀₅	—	3	2	no	—
47	C₇×C₂₉	C₂×D₄₅	1	1	yes	characteristic, complemented, Hall
48	C₂×D₄₅	—	7	1	no	Hall
49	C₂×C₃×C₂₉	D₁₀₅	1	1	yes	characteristic
50	D₃×C₂₉	—	105	2	no	—
51	C₅×C₂₉	C₂×D₆₃	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃₅	—	9	1	no	Hall
53	C₂×C₇×C₉	D₅×C₂₉	1	1	yes	characteristic, complemented
54	D₆₃	—	5	2	no	—
55	C₂²×C₂₉	—	315	1	no	Hall
56	C₃×C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic
57	C₂×C₅×C₉	D₇×C₂₉	1	1	yes	characteristic, complemented
58	D₄₅	—	7	2	no	—
59	C₃×C₂₉	C₂×D₁₀₅	1	1	yes	characteristic
60	C₂×D₂₁	—	15	1	no	—
61	C₂×C₅×C₇	D₉×C₂₉	1	1	yes	characteristic, complemented
62	D₃₅	—	9	2	no	—
63	C₇×C₉	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
64	C₂×D₁₅	—	21	1	no	—
65	C₂×C₂₉	—	315	2	no	—
66	C₂×C₂₉	D₃₁₅	1	1	yes	characteristic, direct product factor
67	C₅×C₉	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×C₇	C₂₉×D₁₅	1	1	yes	characteristic
69	D₂₁	—	15	2	no	—
70	C₂×D₉	—	35	1	no	Hall
71	C₅×C₇	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	C₂₉×D₂₁	1	1	yes	characteristic
73	D₁₅	—	21	2	no	—
74	C₂₉	C₂×D₃₁₅	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×D₇	—	45	1	no	Hall
76	C₃×C₇	C₂×C₂₉×D₁₅	1	1	yes	characteristic
77	C₂×D₅	—	63	1	no	Hall
78	C₂×C₉	C₂₉×D₃₅	1	1	yes	characteristic, complemented
79	D₉	—	35	2	no	—
80	C₃×C₅	C₂×C₂₉×D₂₁	1	1	yes	characteristic
81	C₂×C₇	C₂₉×D₄₅	1	1	yes	characteristic, complemented
82	D₇	—	45	2	no	—
83	C₂×D₃	—	105	1	no	—
84	C₂×C₅	C₂₉×D₆₃	1	1	yes	characteristic, complemented
85	D₅	—	63	2	no	—
86	C₉	C₂×C₂₉×D₃₅	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₂₉×D₄₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₂₉×D₁₀₅	1	1	yes	characteristic
89	D₃	—	105	2	no	—
90	C₅	C₂×C₂₉×D₆₃	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	315	1	no	Sylow
92	C₃	C₂×C₂₉×D₁₀₅	1	1	yes	characteristic
93	C₂	—	315	2	no	—
94	C₂	C₂₉×D₃₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₃₁₅
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₂₉
Frattini	C₃	C₂×C₂₉×D₁₀₅
Fitting	C₂×C₅×C₇×C₉×C₂₉	C₂
socle	C₂×C₃×C₅×C₇×C₂₉	D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₃₁₅	C₂	direct (N × H)
2. C₂×C₅×C₇×C₉×C₂₉	C₂	semidirect
4. C₅×C₇×C₉×C₂₉	C₂²	semidirect
11. C₂×C₇×C₉×C₂₉	D₅	semidirect
14. C₂×C₅×C₉×C₂₉	D₇	semidirect
17. C₂×C₅×C₇×C₂₉	D₉	semidirect
18. C₇×C₉×C₂₉	C₂×D₅	semidirect
20. C₅×C₉×C₂₉	C₂×D₇	semidirect
21. C₂×D₃₁₅	C₂₉	direct (N × H)
25. C₅×C₇×C₂₉	C₂×D₉	semidirect
29. C₂×C₅×C₇×C₉	C₂×C₂₉	semidirect
30. D₃₁₅	C₂×C₂₉	direct (N × H)
33. C₂×C₉×C₂₉	D₃₅	semidirect
37. C₂×C₇×C₂₉	D₄₅	semidirect
40. C₅×C₇×C₉	C₂²×C₂₉	semidirect
41. C₂×C₅×C₂₉	D₆₃	semidirect
43. C₉×C₂₉	C₂×D₃₅	semidirect
47. C₇×C₂₉	C₂×D₄₅	semidirect
51. C₅×C₂₉	C₂×D₆₃	semidirect
53. C₂×C₇×C₉	D₅×C₂₉	semidirect
57. C₂×C₅×C₉	D₇×C₂₉	semidirect
61. C₂×C₅×C₇	D₉×C₂₉	semidirect
63. C₇×C₉	C₂×D₅×C₂₉	semidirect
66. C₂×C₂₉	D₃₁₅	direct (N × H)
67. C₅×C₉	C₂×D₇×C₂₉	semidirect
71. C₅×C₇	C₂×D₉×C₂₉	semidirect
74. C₂₉	C₂×D₃₁₅	direct (N × H)
78. C₂×C₉	C₂₉×D₃₅	semidirect
81. C₂×C₇	C₂₉×D₄₅	semidirect
84. C₂×C₅	C₂₉×D₆₃	semidirect
86. C₉	C₂×C₂₉×D₃₅	semidirect
87. C₇	C₂×C₂₉×D₄₅	semidirect
90. C₅	C₂×C₂₉×D₆₃	semidirect
94. C₂	C₂₉×D₃₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×D₃₁₅	2
C₂×C₅×C₇×C₉×C₂₉	2
C₂×C₂₉×D₁₀₅	3
C₂×C₂₉×D₆₃	5
C₂×C₂₉×D₄₅	7
C₂×D₃₁₅	29

Subgroups — C2×C29×D315 #49141309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×D₃₁₅ #49141309