Finite Group Databasebeta

← C2×C3×C5×C13×D13⋊C3 #44478147

Subgroups — C2×C3×C5×C13×D13⋊C3 #44478147

Order 30420.

256 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C13×C13⋊C3C211yesmaximal, characteristic, complemented
2C3×C5×C13×D13⋊C3C211yesmaximal, characteristic, direct product factor
3C3×C5×C13×D13⋊C3C211yesmaximal, characteristic, direct product factor
4C2×C3×C5×C13×D13C311yesmaximal, characteristic, complemented
5C2×C5×C13×D13⋊C3C313yesmaximal, direct product factor
6C3×C5×C13×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×C3×C13×D13⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C3×C5×C13×D13C2×C311yescharacteristic, complemented
9C3×C5×C13×D13C2×C311yescharacteristic, complemented
10C2×C5×C13×C13⋊C3C2×C313yescomplemented
11C5×C13×D13⋊C3C2×C313yesdirect product factor
12C5×C13×D13⋊C3C2×C313yesdirect product factor
13C2×C3×C5×C132C2×C311yescharacteristic, complemented
14C2×C5×C13×D13C3211yescharacteristic, complemented, Hall
15C2×C3×C13×C13⋊C3C2×C511yescharacteristic, complemented
16C3×C13×D13⋊C3C2×C511yescharacteristic, direct product factor
17C3×C13×D13⋊C3C2×C511yescharacteristic, direct product factor
18C5×C13×C13⋊C3C22×C313yescomplemented
19C3×C5×C132C22×C311yescharacteristic, complemented
20C2×C3×C5×D13⋊C3C1311yesmaximal, characteristic, direct product factor
21C22×C32×C5×C13—131nomaximal
22C2×C3×C13×D13C3×C511yescharacteristic, complemented
23C2×C13×D13⋊C3C3×C513yesdirect product factor
24C2×C5×C132C2×C3211yescharacteristic, complemented
25C5×C13×D13C2×C3211yescharacteristic, complemented
26C5×C13×D13C2×C3211yescharacteristic, complemented
27C3×C13×C13⋊C3C22×C511yescharacteristic, complemented, Hall
28C2×C32×C5×C13—131no—
29C2×C32×C5×C13—131no—
30C2×C32×C5×C13—131no—
31C2×C3×C5×C13⋊C3C2×C1311yescharacteristic, complemented
32C3×C5×D13⋊C3C2×C1311yescharacteristic, direct product factor
33C3×C5×D13⋊C3C2×C1311yescharacteristic, direct product factor
34C2×C3×C132C2×C3×C511yescharacteristic, complemented
35C3×C13×D13C2×C3×C511yescharacteristic, complemented
36C3×C13×D13C2×C3×C511yescharacteristic, complemented
37C2×C13×C13⋊C3C2×C3×C513yescomplemented
38C13×D13⋊C3C2×C3×C513yesdirect product factor
39C13×D13⋊C3C2×C3×C513yesdirect product factor
40C5×C132C22×C3211yescharacteristic, complemented, Hall
41C22×C3×C5×C13—133no—
42C22×C3×C5×C13—391no—
43C2×C3×C5×D13C3×C1311yescharacteristic, complemented
44C2×C5×D13⋊C3C3×C1313yesdirect product factor
45C2×C13×D13C32×C511yescharacteristic, complemented, Hall
46C32×C5×C13—131no—
47C3×C5×C13⋊C3C22×C1311yescharacteristic, complemented
48C3×C132C22×C3×C511yescharacteristic, complemented
49C13×C13⋊C3C22×C3×C513yescomplemented
50C22×C32×C13—131no—
51C2×C3×D13⋊C3C5×C1311yescharacteristic, direct product factor
52C2×C3×C5×C13—62no—
53C2×C3×C5×C13—133no—
54C2×C3×C5×C13—133no—
55C2×C3×C5×C13—133no—
56C2×C3×C5×C13—391no—
57C2×C3×C5×C13—391no—
58C2×C3×C5×C13D13⋊C311yescharacteristic, direct product factor
59C2×C3×C5×C13C2×C3×C1311yescharacteristic, complemented
60C3×C5×D13C2×C3×C1311yescharacteristic, complemented
61C3×C5×D13C2×C3×C1311yescharacteristic, complemented
62C2×C5×C13⋊C3C2×C3×C1313yescomplemented
63C5×D13⋊C3C2×C3×C1313yesdirect product factor
64C5×D13⋊C3C2×C3×C1313yesdirect product factor
65C2×C132C2×C32×C511yescharacteristic, complemented
66C13×D13C2×C32×C511yescharacteristic, complemented
67C13×D13C2×C32×C511yescharacteristic, complemented
68C22×C5×C13—391no—
69C2×C5×D13C32×C1311yescharacteristic, complemented
70C2×C32×C13—131no—
71C2×C32×C13—131no—
72C2×C32×C13—131no—
73C2×C3×C13⋊C3C2×C5×C1311yescharacteristic, complemented
74C3×D13⋊C3C2×C5×C1311yescharacteristic, direct product factor
75C3×D13⋊C3C2×C5×C1311yescharacteristic, direct product factor
76C3×C5×C13—62no—
77C3×C5×C13—133no—
78C3×C5×C13C2×D13⋊C311yescharacteristic, direct product factor
79C3×C5×C13C22×C3×C1311yescharacteristic, complemented
80C5×C13⋊C3C22×C3×C1313yescomplemented
81C22×C32×C5—131noHall
82C132C22×C32×C511yescharacteristic, complemented, Sylow
83C22×C3×C13—133no—
84C22×C3×C13—131no—
85C2×C3×D13C3×C5×C1311yescharacteristic, complemented
86C2×D13⋊C3C3×C5×C1313yesdirect product factor
87C2×C5×C13—62no—
88C2×C5×C13—391no—
89C2×C5×C13—391no—
90C2×C5×C13C3×D13⋊C311yescharacteristic, direct product factor
91C2×C5×C13C2×C32×C1311yescharacteristic, complemented
92C5×D13C2×C32×C1311yescharacteristic, complemented
93C5×D13C2×C32×C1311yescharacteristic, complemented
94C32×C13—131no—
95C3×C13⋊C3C22×C5×C1311yescharacteristic, complemented
96C2×C32×C5—131no—
97C2×C32×C5—131no—
98C2×C32×C5—131no—
99C2×C3×C13—62no—
100C2×C3×C13—133no—
101C2×C3×C13—133no—
102C2×C3×C13—133no—
103C2×C3×C13—391no—
104C2×C3×C13—391no—
105C2×C3×C13C5×D13⋊C311yescharacteristic, direct product factor
106C2×C3×C13C2×C3×C5×C1311yescharacteristic, complemented
107C3×D13C2×C3×C5×C1311yescharacteristic, complemented
108C3×D13C2×C3×C5×C1311yescharacteristic, complemented
109C2×C13⋊C3C2×C3×C5×C1313yescomplemented
110D13⋊C3C2×C3×C5×C1313yesdirect product factor
111D13⋊C3C2×C3×C5×C1313yesdirect product factor
112C5×C13—62no—
113C5×C13C2×C3×D13⋊C311yescharacteristic, direct product factor
114C5×C13C22×C32×C1311yescharacteristic, complemented
115C22×C3×C5—133no—
116C22×C3×C5—391no—
117C22×C13—131no—
118C2×D13C32×C5×C1311yescharacteristic, complemented
119C32×C5—131noHall
120C3×C13—62no—
121C3×C13—133no—
122C3×C13C2×C5×D13⋊C311yescharacteristic, direct product factor
123C3×C13C22×C3×C5×C1311yescharacteristic, complemented
124C13⋊C3C22×C3×C5×C1313yescomplemented
125C22×C32—131noHall
126C2×C3×C5—133no—
127C2×C3×C5—133no—
128C2×C3×C5—133no—
129C2×C3×C5—391no—
130C2×C3×C5—391no—
131C2×C3×C5C13×D13⋊C311yescharacteristic, direct product factor
132C2×C13—62no—
133C2×C13—391no—
134C2×C13—391no—
135C2×C13C3×C5×D13⋊C311yescharacteristic, direct product factor
136C2×C13C2×C32×C5×C1311yescharacteristic, complemented
137D13C2×C32×C5×C1311yescharacteristic, complemented
138D13C2×C32×C5×C1311yescharacteristic, complemented
139C22×C5—391noHall
140C2×C32—131no—
141C2×C32—131no—
142C2×C32—131no—
143C3×C5—133no—
144C3×C5C2×C13×D13⋊C311yescharacteristic, direct product factor
145C13—62no—
146C13C22×C32×C5×C1311yescharacteristic, complemented
147C13C2×C3×C5×D13⋊C311yescharacteristic, direct product factor
148C22×C3—133no—
149C22×C3—391no—
150C2×C5—391no—
151C2×C5—391no—
152C2×C5C3×C13×D13⋊C311yescharacteristic, direct product factor
153C32—131noSylow
154C2×C3—133no—
155C2×C3—131no—
156C2×C3—133no—
157C2×C3—133no—
158C2×C3—391no—
159C2×C3C5×C13×D13⋊C311yescharacteristic, direct product factor
160C5C2×C3×C13×D13⋊C311yescharacteristic, direct product factor, Sylow
161C22—391noSylow
162C3—133no—
163C3C2×C5×C13×D13⋊C311yescharacteristic, direct product factor
164C2—131no—
165C2—391no—
166C2C3×C5×C13×D13⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C13D13⋊C3
commutator, cosocle, hypocenterC13C22×C32×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C132C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C13

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C13×C13⋊C3C2semidirect
2. C3×C5×C13×D13⋊C3C2direct (N × H)
3. C3×C5×C13×D13⋊C3C2direct (N × H)
4. C2×C3×C5×C13×D13C3semidirect
5. C2×C5×C13×D13⋊C3C3direct (N × H)
6. C3×C5×C13×C13⋊C3C22semidirect
7. C2×C3×C13×D13⋊C3C5direct (N × H)
8. C3×C5×C13×D13C2×C3semidirect
9. C3×C5×C13×D13C2×C3semidirect
10. C2×C5×C13×C13⋊C3C2×C3semidirect
11. C5×C13×D13⋊C3C2×C3direct (N × H)
12. C5×C13×D13⋊C3C2×C3direct (N × H)
13. C2×C3×C5×C132C2×C3semidirect
14. C2×C5×C13×D13C32semidirect
15. C2×C3×C13×C13⋊C3C2×C5semidirect
16. C3×C13×D13⋊C3C2×C5direct (N × H)
17. C3×C13×D13⋊C3C2×C5direct (N × H)
18. C5×C13×C13⋊C3C22×C3semidirect
19. C3×C5×C132C22×C3semidirect
20. C2×C3×C5×D13⋊C3C13direct (N × H)
22. C2×C3×C13×D13C3×C5semidirect
23. C2×C13×D13⋊C3C3×C5direct (N × H)
24. C2×C5×C132C2×C32semidirect
25. C5×C13×D13C2×C32semidirect
26. C5×C13×D13C2×C32semidirect
27. C3×C13×C13⋊C3C22×C5semidirect
31. C2×C3×C5×C13⋊C3C2×C13semidirect
32. C3×C5×D13⋊C3C2×C13direct (N × H)
33. C3×C5×D13⋊C3C2×C13direct (N × H)
34. C2×C3×C132C2×C3×C5semidirect
35. C3×C13×D13C2×C3×C5semidirect
36. C3×C13×D13C2×C3×C5semidirect
37. C2×C13×C13⋊C3C2×C3×C5semidirect
38. C13×D13⋊C3C2×C3×C5direct (N × H)
39. C13×D13⋊C3C2×C3×C5direct (N × H)
40. C5×C132C22×C32semidirect
43. C2×C3×C5×D13C3×C13semidirect
44. C2×C5×D13⋊C3C3×C13direct (N × H)
45. C2×C13×D13C32×C5semidirect
47. C3×C5×C13⋊C3C22×C13semidirect
48. C3×C132C22×C3×C5semidirect
49. C13×C13⋊C3C22×C3×C5semidirect
51. C2×C3×D13⋊C3C5×C13direct (N × H)
58. C2×C3×C5×C13D13⋊C3direct (N × H)
59. C2×C3×C5×C13C2×C3×C13semidirect
60. C3×C5×D13C2×C3×C13semidirect
61. C3×C5×D13C2×C3×C13semidirect
62. C2×C5×C13⋊C3C2×C3×C13semidirect
63. C5×D13⋊C3C2×C3×C13direct (N × H)
64. C5×D13⋊C3C2×C3×C13direct (N × H)
65. C2×C132C2×C32×C5semidirect
66. C13×D13C2×C32×C5semidirect
67. C13×D13C2×C32×C5semidirect
69. C2×C5×D13C32×C13semidirect
73. C2×C3×C13⋊C3C2×C5×C13semidirect
74. C3×D13⋊C3C2×C5×C13direct (N × H)
75. C3×D13⋊C3C2×C5×C13direct (N × H)
78. C3×C5×C13C2×D13⋊C3direct (N × H)
79. C3×C5×C13C22×C3×C13semidirect
80. C5×C13⋊C3C22×C3×C13semidirect
82. C132C22×C32×C5semidirect
85. C2×C3×D13C3×C5×C13semidirect
86. C2×D13⋊C3C3×C5×C13direct (N × H)
90. C2×C5×C13C3×D13⋊C3direct (N × H)
91. C2×C5×C13C2×C32×C13semidirect
92. C5×D13C2×C32×C13semidirect
93. C5×D13C2×C32×C13semidirect
95. C3×C13⋊C3C22×C5×C13semidirect
105. C2×C3×C13C5×D13⋊C3direct (N × H)
106. C2×C3×C13C2×C3×C5×C13semidirect
107. C3×D13C2×C3×C5×C13semidirect
108. C3×D13C2×C3×C5×C13semidirect
109. C2×C13⋊C3C2×C3×C5×C13semidirect
110. D13⋊C3C2×C3×C5×C13direct (N × H)
111. D13⋊C3C2×C3×C5×C13direct (N × H)
113. C5×C13C2×C3×D13⋊C3direct (N × H)
114. C5×C13C22×C32×C13semidirect
118. C2×D13C32×C5×C13semidirect
122. C3×C13C2×C5×D13⋊C3direct (N × H)
123. C3×C13C22×C3×C5×C13semidirect
124. C13⋊C3C22×C3×C5×C13semidirect
131. C2×C3×C5C13×D13⋊C3direct (N × H)
135. C2×C13C3×C5×D13⋊C3direct (N × H)
136. C2×C13C2×C32×C5×C13semidirect
137. D13C2×C32×C5×C13semidirect
138. D13C2×C32×C5×C13semidirect
144. C3×C5C2×C13×D13⋊C3direct (N × H)
146. C13C22×C32×C5×C13semidirect
147. C13C2×C3×C5×D13⋊C3direct (N × H)
152. C2×C5C3×C13×D13⋊C3direct (N × H)
159. C2×C3C5×C13×D13⋊C3direct (N × H)
160. C5C2×C3×C13×D13⋊C3direct (N × H)
163. C3C2×C5×C13×D13⋊C3direct (N × H)
166. C2C3×C5×C13×D13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C13×C13⋊C32
C3×C5×C13×D13⋊C32
C2×C3×C5×C13×D133
C2×C5×C13×D13⋊C33
C2×C3×C13×D13⋊C35
C2×C3×C5×D13⋊C313
C22×C32×C5×C1313