Finite Group Databasebeta

← C3×D5×D13×C13⋊C3 #44477976

Subgroups — C3×D5×D13×C13⋊C3 #44477976

Order 30420.

256 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C3×C13⋊C3×D65C211yesmaximal, characteristic, complemented
2C3×D5×C13×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×C5×D13×C13⋊C3C211yesmaximal, characteristic, complemented
4C3×D5×C13×D13C311yesmaximal, characteristic, complemented
5D5×D13×C13⋊C3C313yesmaximal, direct product factor
6C3×C5×C13×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×C3×D13×C13⋊C3—51nomaximal, Hall
8C3×C13×D65C2×C311yescharacteristic, complemented
9C3×D5×C132C2×C311yescharacteristic, complemented
10C3×C5×C13×D13C2×C311yescharacteristic, complemented
11C13⋊C3×D65C2×C313yescomplemented
12D5×C13×C13⋊C3C2×C313yescomplemented
13C5×D13×C13⋊C3C2×C313yescomplemented
14D5×C13×D13C3211yescharacteristic, complemented, Hall
15C2×C3×C13×C13⋊C3—51no—
16C3×D13×C13⋊C3—51no—
17C3×D13×C13⋊C3D511yescharacteristic, direct product factor
18C5×C13×C13⋊C3C22×C313yescomplemented
19C3×C5×C132C22×C311yescharacteristic, complemented
20C32×D5×D13—131nomaximal
21C2×C3×D5×C13⋊C3—131nomaximal
22C2×C3×C13×D13—51no—
23C2×D13×C13⋊C3—53no—
24C13×D65C2×C3211yescharacteristic, complemented
25D5×C132C2×C3211yescharacteristic, complemented
26C5×C13×D13C2×C3211yescharacteristic, complemented
27C3×C13×C13⋊C3C2×D511yescharacteristic, complemented, Hall
28C32×D65—131no—
29C32×D5×C13—131no—
30C32×C5×D13—131no—
31C2×C3×C5×C13⋊C3—131no—
32C3×D5×C13⋊C3—131no—
33C3×D5×C13⋊C3D1311yescharacteristic, direct product factor
34C2×C3×C132—51no—
35C3×C13×D13—51no—
36C3×C13×D13C3×D511yescharacteristic, complemented
37C2×C13×C13⋊C3—53no—
38D13×C13⋊C3—53no—
39D13×C13⋊C3C3×D513yesdirect product factor
40C5×C132C22×C3211yescharacteristic, complemented, Hall
41C2×C3×D5×C13—131no—
42C3×D5×D13—133no—
43C3×D5×D13C13⋊C311yescharacteristic, direct product factor
44C2×D5×C13⋊C3—133no—
45C2×C13×D13—51noHall
46C32×C5×C13—131no—
47C3×C5×C13⋊C3C2×D1311yescharacteristic, complemented
48C3×C132C2×C3×D511yescharacteristic, complemented
49C13×C13⋊C3C2×C3×D513yescomplemented
50C2×C32×D13—651no—
51C22×C3×C13⋊C3—651no—
52C2×C3×C5×C13—131no—
53C3×D65—133no—
54C3×D65C2×C13⋊C311yescharacteristic, complemented
55C3×D5×C13—62no—
56C3×D5×C13—131no—
57C3×D5×C13—133no—
58C3×D5×C13C2×C13⋊C311yescharacteristic, complemented
59C3×D5×C13C3×D1311yescharacteristic, complemented
60C3×C5×D13—133no—
61C3×C5×D13C2×C13⋊C311yescharacteristic, complemented
62C2×C5×C13⋊C3—133no—
63D5×C13⋊C3—133no—
64D5×C13⋊C3C3×D1313yesdirect product factor
65C2×C132—51no—
66C13×D13—51no—
67C13×D13C32×D511yescharacteristic, complemented
68C2×D5×C13—131no—
69D5×D13C3×C13⋊C311yescharacteristic, direct product factor
70C2×C32×C13—651no—
71C32×D13—131no—
72C32×D13—651no—
73C2×C3×C13⋊C3—51no—
74C2×C3×C13⋊C3—131no—
75C2×C3×C13⋊C3—651no—
76C3×C5×C13—62no—
77C3×C5×C13—133no—
78C3×C5×C13C22×C13⋊C311yescharacteristic, complemented
79C3×C5×C13C2×C3×D1311yescharacteristic, complemented
80C5×C13⋊C3C2×C3×D1313yescomplemented
81C2×C32×D5—1691noHall
82C132C2×C32×D511yescharacteristic, complemented, Sylow
83C22×C3×C13—651no—
84C2×C3×D13—51no—
85C2×C3×D13—653no—
86C22×C13⋊C3—653no—
87C2×C5×C13—131no—
88D65C2×C3×C13⋊C311yescharacteristic, complemented
89C5×D13C2×C3×C13⋊C311yescharacteristic, complemented
90D5×C13—62no—
91D5×C13—131no—
92D5×C13C2×C3×C13⋊C311yescharacteristic, complemented
93D5×C13C32×D1311yescharacteristic, complemented
94C32×C13—131no—
95C3×C13⋊C3D5×D1311yescharacteristic, direct product factor
96C2×C32×C5—1691no—
97C32×D5—131no—
98C32×D5—1691no—
99C2×C3×C13—51no—
100C2×C3×C13—51no—
101C2×C3×C13—131no—
102C2×C3×C13—302no—
103C2×C3×C13—653no—
104C2×C3×C13—651no—
105C3×D13—51no—
106C3×D13—133no—
107C3×D13—653no—
108C3×D13D5×C13⋊C311yescharacteristic, direct product factor
109C2×C13⋊C3—53no—
110C2×C13⋊C3—133no—
111C2×C13⋊C3—653no—
112C5×C13—62no—
113C5×C13C22×C3×C13⋊C311yescharacteristic, complemented
114C5×C13C2×C32×D1311yescharacteristic, complemented
115C2×C3×D5—131no—
116C2×C3×D5—1693no—
117C22×C13—651no—
118C2×D13—51no—
119C32×C5—131noHall
120C3×C13—62no—
121C3×C13—133no—
122C3×C13C2×D5×C13⋊C311yescharacteristic, complemented
123C3×C13C3×D5×D1311yescharacteristic, complemented
124C13⋊C3C3×D5×D1313yesdirect product factor
125C22×C32—8451noHall
126C2×C3×C5—131no—
127C2×C3×C5—1693no—
128C3×D5—131no—
129C3×D5—133no—
130C3×D5—1693no—
131C3×D5D13×C13⋊C311yescharacteristic, direct product factor
132C2×C13—51no—
133C2×C13—51no—
134C2×C13—131no—
135C2×C13—302no—
136C2×C13—651no—
137D13—51no—
138D13C3×D5×C13⋊C311yescharacteristic, direct product factor
139C2×D5—131noHall
140C2×C32—651no—
141C2×C32—8451no—
142C2×C32—1691no—
143C3×C5—133no—
144C3×C5C2×D13×C13⋊C311yescharacteristic, complemented
145C13—62no—
146C13C2×C3×D5×C13⋊C311yescharacteristic, complemented
147C13C32×D5×D1311yescharacteristic, complemented
148C22×C3—651no—
149C22×C3—8453no—
150C2×C5—131no—
151D5—131no—
152D5C3×D13×C13⋊C311yescharacteristic, direct product factor
153C32—131noSylow
154C2×C3—51no—
155C2×C3—131no—
156C2×C3—653no—
157C2×C3—651no—
158C2×C3—8453no—
159C2×C3—1693no—
160C5C2×C3×D13×C13⋊C311yescharacteristic, complemented, Sylow
161C22—651noSylow
162C3—133no—
163C3D5×D13×C13⋊C311yescharacteristic, direct product factor
164C2—51no—
165C2—131no—
166C2—651no—
subgroupG/H
center, hypercenterC3D5×D13×C13⋊C3
commutator, cosocle, hypocenterC5×C132C22×C32
FrattiniC1G
Fitting, socleC3×C5×C132C22×C3
LCSG ▷ C5×C132
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C13⋊C3×D65C2semidirect
2. C3×D5×C13×C13⋊C3C2semidirect
3. C3×C5×D13×C13⋊C3C2semidirect
4. C3×D5×C13×D13C3semidirect
5. D5×D13×C13⋊C3C3direct (N × H)
6. C3×C5×C13×C13⋊C3C22semidirect
8. C3×C13×D65C2×C3semidirect
9. C3×D5×C132C2×C3semidirect
10. C3×C5×C13×D13C2×C3semidirect
11. C13⋊C3×D65C2×C3semidirect
12. D5×C13×C13⋊C3C2×C3semidirect
13. C5×D13×C13⋊C3C2×C3semidirect
14. D5×C13×D13C32semidirect
17. C3×D13×C13⋊C3D5direct (N × H)
18. C5×C13×C13⋊C3C22×C3semidirect
19. C3×C5×C132C22×C3semidirect
24. C13×D65C2×C32semidirect
25. D5×C132C2×C32semidirect
26. C5×C13×D13C2×C32semidirect
27. C3×C13×C13⋊C3C2×D5semidirect
33. C3×D5×C13⋊C3D13direct (N × H)
36. C3×C13×D13C3×D5semidirect
39. D13×C13⋊C3C3×D5direct (N × H)
40. C5×C132C22×C32semidirect
43. C3×D5×D13C13⋊C3direct (N × H)
47. C3×C5×C13⋊C3C2×D13semidirect
48. C3×C132C2×C3×D5semidirect
49. C13×C13⋊C3C2×C3×D5semidirect
54. C3×D65C2×C13⋊C3semidirect
58. C3×D5×C13C2×C13⋊C3semidirect
59. C3×D5×C13C3×D13semidirect
61. C3×C5×D13C2×C13⋊C3semidirect
64. D5×C13⋊C3C3×D13direct (N × H)
67. C13×D13C32×D5semidirect
69. D5×D13C3×C13⋊C3direct (N × H)
78. C3×C5×C13C22×C13⋊C3semidirect
79. C3×C5×C13C2×C3×D13semidirect
80. C5×C13⋊C3C2×C3×D13semidirect
82. C132C2×C32×D5semidirect
88. D65C2×C3×C13⋊C3semidirect
89. C5×D13C2×C3×C13⋊C3semidirect
92. D5×C13C2×C3×C13⋊C3semidirect
93. D5×C13C32×D13semidirect
95. C3×C13⋊C3D5×D13direct (N × H)
108. C3×D13D5×C13⋊C3direct (N × H)
113. C5×C13C22×C3×C13⋊C3semidirect
114. C5×C13C2×C32×D13semidirect
122. C3×C13C2×D5×C13⋊C3semidirect
123. C3×C13C3×D5×D13semidirect
124. C13⋊C3C3×D5×D13direct (N × H)
131. C3×D5D13×C13⋊C3direct (N × H)
138. D13C3×D5×C13⋊C3direct (N × H)
144. C3×C5C2×D13×C13⋊C3semidirect
146. C13C2×C3×D5×C13⋊C3semidirect
147. C13C32×D5×D13semidirect
152. D5C3×D13×C13⋊C3direct (N × H)
160. C5C2×C3×D13×C13⋊C3semidirect
163. C3D5×D13×C13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C13⋊C3×D652
C3×D5×C13×C13⋊C32
C3×C5×D13×C13⋊C32
C3×D5×C13×D133
D5×D13×C13⋊C33
C2×C3×D13×C13⋊C35
C32×D5×D1313
C2×C3×D5×C13⋊C313