Subgroups — C₂×C₃²×D₇₁₅ #38788307

Order 25740.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₇₁₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₁₄₃	—	5	1	no	maximal, Hall
6	C₃×D₇₁₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₁₁×C₁₃	C₂×C₃	1	4	yes	complemented
8	C₂×D₇₁₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×D₁₄₃	—	5	2	no	—
10	C₂×C₃²×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃²×D₆₅	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁×C₁₃	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃²×D₅₅	—	13	1	no	maximal, Hall
14	C₂×C₃×D₁₄₃	—	5	4	no	—
15	C₂×C₅×C₁₁×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
16	D₇₁₅	C₂×C₃²	1	2	yes	direct product factor
17	C₃²×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₃	D₁₁	1	1	yes	characteristic, complemented
19	C₃²×D₆₅	—	11	2	no	—
20	C₂×C₃²×C₅×C₁₁	D₁₃	1	1	yes	characteristic, complemented
21	C₃²×D₅₅	—	13	2	no	—
22	C₂×C₃×C₁₁×C₁₃	C₃×D₅	1	4	yes	complemented
23	C₃×D₁₄₃	—	5	8	no	—
24	C₂×C₃×D₆₅	—	11	4	no	—
25	C₅×C₁₁×C₁₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₅₅	—	13	4	no	—
27	C₃²×C₅×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₄₃	—	5	1	no	Hall
29	C₃²×C₅×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃²×D₁₃	—	55	1	no	Hall
31	C₃×C₁₁×C₁₃	C₂×C₃×D₅	1	4	yes	complemented
32	C₂×C₃²×D₁₁	—	65	1	no	Hall
33	C₂×C₃×C₅×C₁₃	C₃×D₁₁	1	4	yes	complemented
34	C₃×D₆₅	—	11	8	no	—
35	C₂×C₃×C₅×C₁₁	C₃×D₁₃	1	4	yes	complemented
36	C₃×D₅₅	—	13	8	no	—
37	C₂×C₁₁×C₁₃	C₃²×D₅	1	1	yes	characteristic, complemented
38	D₁₄₃	—	5	2	no	—
39	C₂×D₆₅	—	11	1	no	Hall
40	C₂×C₃²×C₁₃	D₅₅	1	1	yes	characteristic, complemented
41	C₃²×D₁₃	—	55	2	no	—
42	C₂×D₅₅	—	13	1	no	Hall
43	C₂×C₃²×C₁₁	D₆₅	1	1	yes	characteristic, complemented
44	C₃²×D₁₁	—	65	2	no	—
45	C₃×C₅×C₁₃	C₂×C₃×D₁₁	1	4	yes	complemented
46	C₂×C₃²×D₅	—	143	1	no	Hall
47	C₃×C₅×C₁₁	C₂×C₃×D₁₃	1	4	yes	complemented
48	C₂×C₃×D₁₃	—	55	4	no	—
49	C₁₁×C₁₃	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×D₁₁	—	65	4	no	—
51	C₂×C₅×C₁₃	C₃²×D₁₁	1	1	yes	characteristic, complemented
52	D₆₅	—	11	2	no	—
53	C₃²×C₁₃	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
54	C₂×C₅×C₁₁	C₃²×D₁₃	1	1	yes	characteristic, complemented
55	D₅₅	—	13	2	no	—
56	C₃²×C₁₁	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃²×C₅	D₁₄₃	1	1	yes	characteristic, complemented
58	C₃²×D₅	—	143	2	no	—
59	C₂×C₃×C₁₃	C₃×D₅₅	1	4	yes	complemented
60	C₃×D₁₃	—	55	8	no	—
61	C₂×C₃×C₁₁	C₃×D₆₅	1	4	yes	complemented
62	C₃×D₁₁	—	65	8	no	—
63	C₅×C₁₃	C₂×C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×D₅	—	143	4	no	—
65	C₅×C₁₁	C₂×C₃²×D₁₃	1	1	yes	characteristic, complemented, Hall
66	C₂×D₁₃	—	55	1	no	Hall
67	C₃²×C₅	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
68	C₂×D₁₁	—	65	1	no	Hall
69	C₃×C₁₃	C₂×C₃×D₅₅	1	4	yes	complemented
70	C₂²×C₃²	—	715	1	no	Hall
71	C₃×C₁₁	C₂×C₃×D₆₅	1	4	yes	complemented
72	C₂×C₃×C₅	C₃×D₁₄₃	1	4	yes	complemented
73	C₃×D₅	—	143	8	no	—
74	C₂×C₁₃	C₃²×D₅₅	1	1	yes	characteristic, complemented
75	D₁₃	—	55	2	no	—
76	C₂×C₁₁	C₃²×D₆₅	1	1	yes	characteristic, complemented
77	D₁₁	—	65	2	no	—
78	C₂×D₅	—	143	1	no	Hall
79	C₂×C₃²	—	715	2	no	—
80	C₂×C₃²	D₇₁₅	1	1	yes	characteristic, direct product factor
81	C₃×C₅	C₂×C₃×D₁₄₃	1	4	yes	complemented
82	C₁₃	C₂×C₃²×D₅₅	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₃	—	715	4	no	—
84	C₁₁	C₂×C₃²×D₆₅	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	C₃²×D₁₄₃	1	1	yes	characteristic, complemented
86	D₅	—	143	2	no	—
87	C₃²	C₂×D₇₁₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	715	8	no	—
89	C₂×C₃	C₃×D₇₁₅	1	4	yes	direct product factor
90	C₅	C₂×C₃²×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	715	1	no	Sylow
92	C₃	C₂×C₃×D₇₁₅	1	4	yes	direct product factor
93	C₂	—	715	2	no	—
94	C₂	C₃²×D₇₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₇₁₅
commutator, cosocle, hypocenter	C₅×C₁₁×C₁₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₅×C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₇₁₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₁×C₁₃	C₂	semidirect
3. C₂×C₃×D₇₁₅	C₃	direct (N × H)
4. C₃²×C₅×C₁₁×C₁₃	C₂²	semidirect
6. C₃×D₇₁₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₁₁×C₁₃	C₂×C₃	semidirect
8. C₂×D₇₁₅	C₃²	direct (N × H)
10. C₂×C₃²×C₁₁×C₁₃	D₅	semidirect
12. C₃×C₅×C₁₁×C₁₃	C₂²×C₃	semidirect
15. C₂×C₅×C₁₁×C₁₃	C₂×C₃²	semidirect
16. D₇₁₅	C₂×C₃²	direct (N × H)
17. C₃²×C₁₁×C₁₃	C₂×D₅	semidirect
18. C₂×C₃²×C₅×C₁₃	D₁₁	semidirect
20. C₂×C₃²×C₅×C₁₁	D₁₃	semidirect
22. C₂×C₃×C₁₁×C₁₃	C₃×D₅	semidirect
25. C₅×C₁₁×C₁₃	C₂²×C₃²	semidirect
27. C₃²×C₅×C₁₃	C₂×D₁₁	semidirect
29. C₃²×C₅×C₁₁	C₂×D₁₃	semidirect
31. C₃×C₁₁×C₁₃	C₂×C₃×D₅	semidirect
33. C₂×C₃×C₅×C₁₃	C₃×D₁₁	semidirect
35. C₂×C₃×C₅×C₁₁	C₃×D₁₃	semidirect
37. C₂×C₁₁×C₁₃	C₃²×D₅	semidirect
40. C₂×C₃²×C₁₃	D₅₅	semidirect
43. C₂×C₃²×C₁₁	D₆₅	semidirect
45. C₃×C₅×C₁₃	C₂×C₃×D₁₁	semidirect
47. C₃×C₅×C₁₁	C₂×C₃×D₁₃	semidirect
49. C₁₁×C₁₃	C₂×C₃²×D₅	semidirect
51. C₂×C₅×C₁₃	C₃²×D₁₁	semidirect
53. C₃²×C₁₃	C₂×D₅₅	semidirect
54. C₂×C₅×C₁₁	C₃²×D₁₃	semidirect
56. C₃²×C₁₁	C₂×D₆₅	semidirect
57. C₂×C₃²×C₅	D₁₄₃	semidirect
59. C₂×C₃×C₁₃	C₃×D₅₅	semidirect
61. C₂×C₃×C₁₁	C₃×D₆₅	semidirect
63. C₅×C₁₃	C₂×C₃²×D₁₁	semidirect
65. C₅×C₁₁	C₂×C₃²×D₁₃	semidirect
67. C₃²×C₅	C₂×D₁₄₃	semidirect
69. C₃×C₁₃	C₂×C₃×D₅₅	semidirect
71. C₃×C₁₁	C₂×C₃×D₆₅	semidirect
72. C₂×C₃×C₅	C₃×D₁₄₃	semidirect
74. C₂×C₁₃	C₃²×D₅₅	semidirect
76. C₂×C₁₁	C₃²×D₆₅	semidirect
80. C₂×C₃²	D₇₁₅	direct (N × H)
81. C₃×C₅	C₂×C₃×D₁₄₃	semidirect
82. C₁₃	C₂×C₃²×D₅₅	semidirect
84. C₁₁	C₂×C₃²×D₆₅	semidirect
85. C₂×C₅	C₃²×D₁₄₃	semidirect
87. C₃²	C₂×D₇₁₅	direct (N × H)
89. C₂×C₃	C₃×D₇₁₅	direct (N × H)
90. C₅	C₂×C₃²×D₁₄₃	semidirect
92. C₃	C₂×C₃×D₇₁₅	direct (N × H)
94. C₂	C₃²×D₇₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₇₁₅	2
C₂×C₃²×C₅×C₁₁×C₁₃	2
C₂×C₃×D₇₁₅	3
C₂×C₃²×D₁₄₃	5
C₂×C₃²×D₆₅	11
C₂×C₃²×D₅₅	13

Subgroups — C2×C32×D715 #38788307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₇₁₅ #38788307