Subgroups — C₂×C₅×D₁₂₈₇ #38787927

Order 25740.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₂₈₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄₂₉	—	3	1	no	maximal
4	C₅×C₉×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₂₈₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₄₂₉	—	3	2	no	—
7	C₂×C₃×C₅×C₁₁×C₁₃	D₃	1	1	yes	characteristic
8	C₂×C₅×D₁₄₃	—	9	1	no	Hall
9	D₁₂₈₇	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₉×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×D₁₁₇	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic
13	C₂×C₅×D₉₉	—	13	1	no	maximal, Hall
14	C₂×D₄₂₉	—	3	1	no	—
15	C₂×C₅×C₁₁×C₁₃	D₉	1	1	yes	characteristic, complemented
16	C₅×D₁₄₃	—	9	2	no	—
17	C₉×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₉×C₁₃	D₁₁	1	1	yes	characteristic, complemented
19	C₅×D₁₁₇	—	11	2	no	—
20	C₂×C₅×C₉×C₁₁	D₁₃	1	1	yes	characteristic, complemented
21	C₅×D₉₉	—	13	2	no	—
22	C₂×C₃×C₁₁×C₁₃	C₅×D₃	1	1	yes	characteristic
23	D₄₂₉	—	3	2	no	—
24	C₂×C₅×D₃₉	—	33	1	no	—
25	C₅×C₁₁×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×D₃₃	—	39	1	no	—
27	C₅×C₉×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₄₃	—	9	1	no	Hall
29	C₅×C₉×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×D₁₁₇	—	11	1	no	Hall
31	C₃×C₁₁×C₁₃	C₂×C₅×D₃	1	1	yes	characteristic
32	C₂×D₉₉	—	13	1	no	Hall
33	C₂×C₃×C₅×C₁₃	D₃₃	1	1	yes	characteristic
34	C₅×D₃₉	—	33	2	no	—
35	C₂×C₃×C₅×C₁₁	D₃₉	1	1	yes	characteristic
36	C₅×D₃₃	—	39	2	no	—
37	C₂×C₁₁×C₁₃	C₅×D₉	1	1	yes	characteristic, complemented
38	D₁₄₃	—	9	2	no	—
39	C₂×C₅×D₁₃	—	99	1	no	Hall
40	C₂×C₉×C₁₃	C₅×D₁₁	1	1	yes	characteristic, complemented
41	D₁₁₇	—	11	2	no	—
42	C₂×C₅×D₁₁	—	117	1	no	Hall
43	C₂×C₉×C₁₁	C₅×D₁₃	1	1	yes	characteristic, complemented
44	D₉₉	—	13	2	no	—
45	C₃×C₅×C₁₃	C₂×D₃₃	1	1	yes	characteristic
46	C₂×C₅×D₉	—	143	1	no	Hall
47	C₃×C₅×C₁₁	C₂×D₃₉	1	1	yes	characteristic
48	C₂×D₃₉	—	33	1	no	—
49	C₁₁×C₁₃	C₂×C₅×D₉	1	1	yes	characteristic, complemented, Hall
50	C₂×D₃₃	—	39	1	no	—
51	C₂×C₅×C₁₃	D₉₉	1	1	yes	characteristic, complemented
52	C₅×D₁₃	—	99	2	no	—
53	C₉×C₁₃	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
54	C₂×C₅×C₁₁	D₁₁₇	1	1	yes	characteristic, complemented
55	C₅×D₁₁	—	117	2	no	—
56	C₉×C₁₁	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₅×C₉	D₁₄₃	1	1	yes	characteristic, complemented
58	C₅×D₉	—	143	2	no	—
59	C₂×C₃×C₁₃	C₅×D₃₃	1	1	yes	characteristic
60	D₃₉	—	33	2	no	—
61	C₂×C₃×C₁₁	C₅×D₃₉	1	1	yes	characteristic
62	D₃₃	—	39	2	no	—
63	C₅×C₁₃	C₂×D₉₉	1	1	yes	characteristic, complemented, Hall
64	C₂×C₅×D₃	—	429	1	no	—
65	C₅×C₁₁	C₂×D₁₁₇	1	1	yes	characteristic, complemented, Hall
66	C₂×D₁₃	—	99	1	no	Hall
67	C₅×C₉	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
68	C₂×D₁₁	—	117	1	no	Hall
69	C₃×C₁₃	C₂×C₅×D₃₃	1	1	yes	characteristic
70	C₂×D₉	—	143	1	no	Hall
71	C₃×C₁₁	C₂×C₅×D₃₉	1	1	yes	characteristic
72	C₂×C₃×C₅	D₄₂₉	1	1	yes	characteristic
73	C₅×D₃	—	429	2	no	—
74	C₂×C₁₃	C₅×D₉₉	1	1	yes	characteristic, complemented
75	D₁₃	—	99	2	no	—
76	C₂×C₁₁	C₅×D₁₁₇	1	1	yes	characteristic, complemented
77	D₁₁	—	117	2	no	—
78	C₂²×C₅	—	1287	1	no	Hall
79	C₂×C₉	C₅×D₁₄₃	1	1	yes	characteristic, complemented
80	D₉	—	143	2	no	—
81	C₃×C₅	C₂×D₄₂₉	1	1	yes	characteristic
82	C₁₃	C₂×C₅×D₉₉	1	1	yes	characteristic, complemented, Sylow
83	C₂×D₃	—	429	1	no	—
84	C₁₁	C₂×C₅×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	1287	2	no	—
86	C₂×C₅	D₁₂₈₇	1	1	yes	characteristic, direct product factor
87	C₉	C₂×C₅×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₅×D₄₂₉	1	1	yes	characteristic
89	D₃	—	429	2	no	—
90	C₅	C₂×D₁₂₈₇	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	1287	1	no	Sylow
92	C₃	C₂×C₅×D₄₂₉	1	1	yes	characteristic
93	C₂	—	1287	2	no	—
94	C₂	C₅×D₁₂₈₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₂₈₇
commutator, cosocle, hypocenter	C₉×C₁₁×C₁₃	C₂²×C₅
Frattini	C₃	C₂×C₅×D₄₂₉
Fitting	C₂×C₅×C₉×C₁₁×C₁₃	C₂
socle	C₂×C₃×C₅×C₁₁×C₁₃	D₃
LCS	G ▷ C₉×C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₂₈₇	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₁×C₁₃	C₂	semidirect
4. C₅×C₉×C₁₁×C₁₃	C₂²	semidirect
5. C₂×D₁₂₈₇	C₅	direct (N × H)
9. D₁₂₈₇	C₂×C₅	direct (N × H)
10. C₂×C₉×C₁₁×C₁₃	C₂×C₅	semidirect
15. C₂×C₅×C₁₁×C₁₃	D₉	semidirect
17. C₉×C₁₁×C₁₃	C₂²×C₅	semidirect
18. C₂×C₅×C₉×C₁₃	D₁₁	semidirect
20. C₂×C₅×C₉×C₁₁	D₁₃	semidirect
25. C₅×C₁₁×C₁₃	C₂×D₉	semidirect
27. C₅×C₉×C₁₃	C₂×D₁₁	semidirect
29. C₅×C₉×C₁₁	C₂×D₁₃	semidirect
37. C₂×C₁₁×C₁₃	C₅×D₉	semidirect
40. C₂×C₉×C₁₃	C₅×D₁₁	semidirect
43. C₂×C₉×C₁₁	C₅×D₁₃	semidirect
49. C₁₁×C₁₃	C₂×C₅×D₉	semidirect
51. C₂×C₅×C₁₃	D₉₉	semidirect
53. C₉×C₁₃	C₂×C₅×D₁₁	semidirect
54. C₂×C₅×C₁₁	D₁₁₇	semidirect
56. C₉×C₁₁	C₂×C₅×D₁₃	semidirect
57. C₂×C₅×C₉	D₁₄₃	semidirect
63. C₅×C₁₃	C₂×D₉₉	semidirect
65. C₅×C₁₁	C₂×D₁₁₇	semidirect
67. C₅×C₉	C₂×D₁₄₃	semidirect
74. C₂×C₁₃	C₅×D₉₉	semidirect
76. C₂×C₁₁	C₅×D₁₁₇	semidirect
79. C₂×C₉	C₅×D₁₄₃	semidirect
82. C₁₃	C₂×C₅×D₉₉	semidirect
84. C₁₁	C₂×C₅×D₁₁₇	semidirect
86. C₂×C₅	D₁₂₈₇	direct (N × H)
87. C₉	C₂×C₅×D₁₄₃	semidirect
90. C₅	C₂×D₁₂₈₇	direct (N × H)
94. C₂	C₅×D₁₂₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₁₂₈₇	2
C₂×C₅×C₉×C₁₁×C₁₃	2
C₂×C₅×D₄₂₉	3
C₂×D₁₂₈₇	5
C₂×C₅×D₁₁₇	11
C₂×C₅×D₉₉	13

Subgroups — C2×C5×D1287 #38787927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₂₈₇ #38787927