Subgroups — C₂×C₃×C₇×C₂₅×D₁₃ #41031332

Order 27300.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₂₅×D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₂₅×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₃×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₅×C₇×D₁₃	C₅	1	1	yes	maximal, characteristic
6	C₇×C₂₅×D₁₃	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₇×C₁₃×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₂₅×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₇×D₁₃	C₂×C₅	1	2	yes	—
10	C₂×C₃×C₅×C₇×C₁₃	C₂×C₅	1	1	yes	characteristic
11	C₇×C₁₃×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃×C₇×C₂₅	—	13	1	no	maximal, Hall
13	C₂×C₃×C₁₃×C₂₅	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×C₂₅×D₁₃	C₂×C₇	1	2	yes	direct product factor
15	C₂×C₅×C₇×D₁₃	C₃×C₅	1	1	yes	characteristic
16	C₃×C₅×C₇×C₁₃	C₂²×C₅	1	1	yes	characteristic
17	C₂×C₂₅×D₁₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₇×D₁₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₇×C₂₅	—	13	2	no	—
20	C₂×C₃×C₇×C₂₅	D₁₃	1	1	yes	characteristic, direct product factor
21	C₃×C₁₃×C₂₅	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₇×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
23	C₅×C₇×D₁₃	C₂×C₃×C₅	1	2	yes	—
24	C₂×C₃×C₅×D₁₃	C₅×C₇	1	1	yes	characteristic
25	C₂²×C₇×C₂₅	—	13	1	no	Hall
26	C₂×C₁₃×C₂₅	C₂×C₃×C₇	1	1	yes	characteristic, complemented
27	C₂₅×D₁₃	C₂×C₃×C₇	1	2	yes	direct product factor
28	C₂×C₃×C₇×C₁₃	C₂×C₂₅	1	1	yes	characteristic, complemented
29	C₃×C₇×D₁₃	C₂×C₂₅	1	2	yes	direct product factor
30	C₃×C₇×C₂₅	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₇×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic
32	C₂²×C₃×C₅×C₇	—	13	1	no	—
33	C₂×C₃×C₅×C₁₃	C₂×C₅×C₇	1	1	yes	characteristic
34	C₃×C₅×D₁₃	C₂×C₅×C₇	1	2	yes	—
35	C₂×C₇×D₁₃	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₇×C₂₅	—	13	2	no	—
37	C₂×C₇×C₂₅	C₃×D₁₃	1	1	yes	characteristic, direct product factor
38	C₁₃×C₂₅	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃×C₂₅	—	13	1	no	Hall
40	C₃×C₇×C₁₃	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×D₁₃	C₃×C₅×C₇	1	1	yes	characteristic
42	C₂×C₃×C₅×C₇	—	13	2	no	—
43	C₂×C₃×C₅×C₇	C₅×D₁₃	1	1	yes	characteristic
44	C₃×C₅×C₁₃	C₂²×C₅×C₇	1	1	yes	characteristic
45	C₂×C₇×C₁₃	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
46	C₇×D₁₃	C₂×C₃×C₂₅	1	2	yes	direct product factor
47	C₇×C₂₅	C₂×C₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₃×D₁₃	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₃×C₂₅	—	13	2	no	—
50	C₂×C₃×C₂₅	C₇×D₁₃	1	1	yes	characteristic, direct product factor
51	C₂²×C₅×C₇	—	13	1	no	—
52	C₂×C₅×C₁₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic
53	C₅×D₁₃	C₂×C₃×C₅×C₇	1	2	yes	—
54	C₃×C₅×C₇	C₂×C₅×D₁₃	1	1	yes	characteristic
55	C₂²×C₂₅	—	13	1	no	Hall
56	C₇×C₁₃	C₂²×C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
57	C₂²×C₃×C₇	—	13	1	no	Hall
58	C₂×C₃×C₁₃	C₂×C₇×C₂₅	1	1	yes	characteristic, complemented
59	C₃×D₁₃	C₂×C₇×C₂₅	1	2	yes	direct product factor
60	C₃×C₂₅	C₂×C₇×D₁₃	1	1	yes	characteristic, direct product factor, Hall
61	C₂×C₅×C₇	—	13	2	no	—
62	C₂×C₅×C₇	C₃×C₅×D₁₃	1	1	yes	characteristic
63	C₅×C₁₃	C₂²×C₃×C₅×C₇	1	1	yes	characteristic
64	C₂²×C₃×C₅	—	13	1	no	—
65	C₂×D₁₃	C₃×C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
66	C₂×C₂₅	—	13	2	no	—
67	C₂×C₂₅	C₃×C₇×D₁₃	1	1	yes	characteristic, direct product factor
68	C₂×C₃×C₇	—	13	2	no	—
69	C₂×C₃×C₇	C₂₅×D₁₃	1	1	yes	characteristic, direct product factor
70	C₃×C₁₃	C₂²×C₇×C₂₅	1	1	yes	characteristic, complemented, Hall
71	C₅×C₇	C₂×C₃×C₅×D₁₃	1	1	yes	characteristic
72	C₂×C₃×C₅	—	13	2	no	—
73	C₂×C₃×C₅	C₅×C₇×D₁₃	1	1	yes	characteristic
74	C₂²×C₇	—	13	1	no	Hall
75	C₂×C₁₃	C₂×C₃×C₇×C₂₅	1	1	yes	characteristic, complemented
76	D₁₃	C₂×C₃×C₇×C₂₅	1	2	yes	direct product factor
77	C₂₅	C₂×C₃×C₇×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
78	C₃×C₇	C₂×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor, Hall
79	C₂²×C₅	—	13	1	no	—
80	C₃×C₅	C₂×C₅×C₇×D₁₃	1	1	yes	characteristic
81	C₂×C₇	—	13	2	no	—
82	C₂×C₇	C₃×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor
83	C₁₃	C₂²×C₃×C₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₃	—	13	1	no	Hall
85	C₂×C₅	—	13	2	no	—
86	C₂×C₅	C₃×C₅×C₇×D₁₃	1	1	yes	characteristic
87	C₇	C₂×C₃×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	13	2	no	—
89	C₂×C₃	C₇×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor
90	C₅	C₂×C₃×C₅×C₇×D₁₃	1	1	yes	characteristic
91	C₂²	—	13	1	no	Sylow
92	C₃	C₂×C₇×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	—	13	2	no	—
94	C₂	C₃×C₇×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₂₅	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₃×C₇×C₂₅
Frattini	C₅	C₂×C₃×C₅×C₇×D₁₃
Fitting	C₂×C₃×C₇×C₁₃×C₂₅	C₂
socle	C₂×C₃×C₅×C₇×C₁₃	C₂×C₅
prime radical	C₂×C₃×C₅×C₇×D₁₃	C₅
cosocle	C₅×C₁₃	C₂²×C₃×C₅×C₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₇×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₂₅×D₁₃	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₃×C₂₅	C₂	semidirect
3. C₂×C₇×C₂₅×D₁₃	C₃	direct (N × H)
4. C₃×C₇×C₁₃×C₂₅	C₂²	semidirect
6. C₇×C₂₅×D₁₃	C₂×C₃	direct (N × H)
7. C₂×C₇×C₁₃×C₂₅	C₂×C₃	semidirect
8. C₂×C₃×C₂₅×D₁₃	C₇	direct (N × H)
11. C₇×C₁₃×C₂₅	C₂²×C₃	semidirect
13. C₂×C₃×C₁₃×C₂₅	C₂×C₇	semidirect
14. C₃×C₂₅×D₁₃	C₂×C₇	direct (N × H)
17. C₂×C₂₅×D₁₃	C₃×C₇	direct (N × H)
18. C₂×C₃×C₇×D₁₃	C₂₅	direct (N × H)
20. C₂×C₃×C₇×C₂₅	D₁₃	direct (N × H)
21. C₃×C₁₃×C₂₅	C₂²×C₇	semidirect
26. C₂×C₁₃×C₂₅	C₂×C₃×C₇	semidirect
27. C₂₅×D₁₃	C₂×C₃×C₇	direct (N × H)
28. C₂×C₃×C₇×C₁₃	C₂×C₂₅	semidirect
29. C₃×C₇×D₁₃	C₂×C₂₅	direct (N × H)
30. C₃×C₇×C₂₅	C₂×D₁₃	direct (N × H)
35. C₂×C₇×D₁₃	C₃×C₂₅	direct (N × H)
37. C₂×C₇×C₂₅	C₃×D₁₃	direct (N × H)
38. C₁₃×C₂₅	C₂²×C₃×C₇	semidirect
40. C₃×C₇×C₁₃	C₂²×C₂₅	semidirect
45. C₂×C₇×C₁₃	C₂×C₃×C₂₅	semidirect
46. C₇×D₁₃	C₂×C₃×C₂₅	direct (N × H)
47. C₇×C₂₅	C₂×C₃×D₁₃	direct (N × H)
48. C₂×C₃×D₁₃	C₇×C₂₅	direct (N × H)
50. C₂×C₃×C₂₅	C₇×D₁₃	direct (N × H)
56. C₇×C₁₃	C₂²×C₃×C₂₅	semidirect
58. C₂×C₃×C₁₃	C₂×C₇×C₂₅	semidirect
59. C₃×D₁₃	C₂×C₇×C₂₅	direct (N × H)
60. C₃×C₂₅	C₂×C₇×D₁₃	direct (N × H)
65. C₂×D₁₃	C₃×C₇×C₂₅	direct (N × H)
67. C₂×C₂₅	C₃×C₇×D₁₃	direct (N × H)
69. C₂×C₃×C₇	C₂₅×D₁₃	direct (N × H)
70. C₃×C₁₃	C₂²×C₇×C₂₅	semidirect
75. C₂×C₁₃	C₂×C₃×C₇×C₂₅	semidirect
76. D₁₃	C₂×C₃×C₇×C₂₅	direct (N × H)
77. C₂₅	C₂×C₃×C₇×D₁₃	direct (N × H)
78. C₃×C₇	C₂×C₂₅×D₁₃	direct (N × H)
82. C₂×C₇	C₃×C₂₅×D₁₃	direct (N × H)
83. C₁₃	C₂²×C₃×C₇×C₂₅	semidirect
87. C₇	C₂×C₃×C₂₅×D₁₃	direct (N × H)
89. C₂×C₃	C₇×C₂₅×D₁₃	direct (N × H)
92. C₃	C₂×C₇×C₂₅×D₁₃	direct (N × H)
94. C₂	C₃×C₇×C₂₅×D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₂₅×D₁₃	2
C₂×C₃×C₇×C₁₃×C₂₅	2
C₂×C₇×C₂₅×D₁₃	3
C₂×C₃×C₅×C₇×D₁₃	5
C₂×C₃×C₂₅×D₁₃	7
C₂²×C₃×C₇×C₂₅	13

Subgroups — C2×C3×C7×C25×D13 #41031332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₂₅×D₁₃ #41031332