Finite Group Databasebeta

← #13108559

Subgroups — #13108559

Order 1620.

448 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 61 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×C3⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
2C3×C5×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×C3⋊D15C211yesmaximal, characteristic, complemented
4C5⋊#1113—34nomaximal
5D15⋊(C3⋊D3)—31nomaximal
6C3⋊D3×D15—31nomaximal
7C34×C5C2211yescharacteristic, complemented, Hall
8C3⋊#1113—51nomaximal, Hall
9C3⋊(C3⋊D15)D311yescharacteristic, complemented
10C5×C3⋊(C3⋊D3)D311yescharacteristic, complemented
11C3×C3⋊D15—31no—
12C3×C3⋊D15—34no—
13C3×C3⋊D15—64no—
14C3×C3⋊D15D314yescomplemented
15C3×C5×C3⋊D3—31no—
16C3×C5×C3⋊D3—34no—
17C3×C5×C3⋊D3—64no—
18C32×D15—31no—
19C32×D15—31no—
20C32×D15—61no—
21(C3⋊D3)⋊D5—94no—
22D3×D15—94no—
23D3×D15—91no—
24D5×C3⋊D3—91no—
25C3×C3⋊(C3⋊D3)—51no—
26C3×C3⋊(C3⋊D3)D511yescharacteristic, complemented
27C32×C3⋊D3—51no—
28C33×C5—21no—
29C33×C5—24no—
30C33×C5—24no—
31C33×C5—44no—
32C33×C5C2×D311yescharacteristic, complemented
33C33×C5C2×D314yescomplemented
34C33×C5C2×D311yescharacteristic, complemented
35#1113—154no—
36D3×C3⋊D3—151no—
37D3×C3⋊D3—151no—
38C3⋊D15—31no—
39C3⋊D15—34no—
40C3⋊D15—64no—
41C3⋊D15C3⋊D311yescharacteristic, complemented
42C5×C3⋊D3—31no—
43C5×C3⋊D3—34no—
44C5×C3⋊D3—64no—
45C3×D15—34no—
46C3×D15—34no—
47C3×D15—64no—
48C3×D15—94no—
49C3×D15—91no—
50C3×D15—184no—
51C3×C5×D3—94no—
52C3×C5×D3—91no—
53C3×C5×D3—184no—
54C32×D5—91no—
55C34C2×D511yescharacteristic, complemented, Sylow
56C2×D15—271no—
57D3×D5—274no—
58D3×D5—271no—
59C3⋊(C3⋊D3)—51no—
60C3⋊(C3⋊D3)D1511yescharacteristic, complemented
61C3×C3⋊D3—31no—
62C3×C3⋊D3—34no—
63C3×C3⋊D3—54no—
64C3×C3⋊D3—64no—
65C3×C3⋊D3—151no—
66C3×C3⋊D3—154no—
67C3×C3⋊D3—304no—
68C32×D3—151no—
69C32×D3—151no—
70C32×D3—301no—
71C32×C5—24no—
72C32×C5—24no—
73C32×C5—24no—
74C32×C5—24no—
75C32×C5—24no—
76C32×C5—44no—
77C32×C5—412no—
78C32×C5—44no—
79C32×C5D3214yescomplemented
80C32×C5D3211yescharacteristic, complemented
81C32×C5D3214yescomplemented
82C32×C5C2×C3⋊D311yescharacteristic, complemented
83C2×C3⋊D3—451no—
84D32—454no—
85D32—451no—
86D32—454no—
87C2×C3×C5—271no—
88D15—31no—
89D15—31no—
90D15—61no—
91D15—91no—
92D15—94no—
93D15—184no—
94C3×D5—94no—
95C3×D5—271no—
96C5×D3—91no—
97C5×D3—94no—
98C5×D3—184no—
99C33—21no—
100C33—24no—
101C33—24no—
102C33—44no—
103C33D3×D511yescharacteristic, complemented
104C33D3×D514yescomplemented
105C33C2×D1511yescharacteristic, complemented
106C2×D5—811noHall
107C2×C32—451no—
108C3⋊D3—31no—
109C3⋊D3—34no—
110C3⋊D3—51no—
111C3⋊D3—64no—
112C3⋊D3—151no—
113C3⋊D3—154no—
114C3⋊D3—304no—
115C3×D3—91no—
116C3×D3—94no—
117C3×D3—154no—
118C3×D3—154no—
119C3×D3—184no—
120C3×D3—304no—
121C3×D3—451no—
122C3×D3—454no—
123C3×D3—904no—
124C3×C5—24no—
125C3×C5—21no—
126C3×C5—24no—
127C3×C5—44no—
128C3×C5D3×C3⋊D311yescharacteristic, complemented
129C3×C5D3×C3⋊D311yescharacteristic, complemented
130C3×C5#111314yescomplemented
131C2×D3—1351no—
132C2×D3—1354no—
133C2×D3—1351no—
134C2×C5—271no—
135D5—91no—
136D5—271no—
137C32—24no—
138C32—24no—
139C32—24no—
140C32—24no—
141C32—24no—
142C32—44no—
143C32—412no—
144C32—44no—
145C32D5×C3⋊D311yescharacteristic, complemented
146C32D3×D1514yescomplemented
147C32D3×D1511yescharacteristic, complemented
148C32(C3⋊D3)⋊D514yescomplemented
149C2×C3—271no—
150C2×C3—454no—
151C2×C3—1351no—
152D3—91no—
153D3—94no—
154D3—151no—
155D3—151no—
156D3—184no—
157D3—301no—
158D3—451no—
159D3—454no—
160D3—904no—
161C5C3⋊#111311yescharacteristic, complemented, Sylow
162C22—4051noSylow
163C3—24no—
164C3—21no—
165C3—24no—
166C3—44no—
167C3C3⋊D3×D1511yescharacteristic, complemented
168C3D15⋊(C3⋊D3)11yescharacteristic, complemented
169C3C5⋊#111314yescomplemented
170C2—271no—
171C2—451no—
172C2—1351no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC34×C5C22
LCSG ▷ C34×C5
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊(C3⋊D15)C2semidirect
2. C3×C5×C3⋊(C3⋊D3)C2semidirect
3. C32×C3⋊D15C2semidirect
7. C34×C5C22semidirect
9. C3⋊(C3⋊D15)D3semidirect
10. C5×C3⋊(C3⋊D3)D3semidirect
14. C3×C3⋊D15D3semidirect
26. C3×C3⋊(C3⋊D3)D5semidirect
32. C33×C5C2×D3semidirect
33. C33×C5C2×D3semidirect
34. C33×C5C2×D3semidirect
41. C3⋊D15C3⋊D3semidirect
55. C34C2×D5semidirect
60. C3⋊(C3⋊D3)D15semidirect
79. C32×C5D32semidirect
80. C32×C5D32semidirect
81. C32×C5D32semidirect
82. C32×C5C2×C3⋊D3semidirect
103. C33D3×D5semidirect
104. C33D3×D5semidirect
105. C33C2×D15semidirect
128. C3×C5D3×C3⋊D3semidirect
129. C3×C5D3×C3⋊D3semidirect
130. C3×C5#1113semidirect
145. C32D5×C3⋊D3semidirect
146. C32D3×D15semidirect
147. C32D3×D15semidirect
148. C32(C3⋊D3)⋊D5semidirect
161. C5C3⋊#1113semidirect
167. C3C3⋊D3×D15semidirect
168. C3D15⋊(C3⋊D3)semidirect
169. C3C5⋊#1113semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊(C3⋊D15)2
C3×C5×C3⋊(C3⋊D3)2
C32×C3⋊D152
C5⋊#11133
D15⋊(C3⋊D3)3
C3⋊D3×D153
C3⋊#11135