Finite Group Databasebeta

← #14293722

Subgroups — #14293722

Order 1920.

440 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 115 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×C5×#498C211yesmaximal, characteristic, complemented
2#11751189C212yesmaximal, complemented
3#11751186C212yesmaximal, complemented
4#11750796C211yesmaximal, characteristic
5#11746276C211yesmaximal, characteristic, complemented
6#10602129—31nomaximal, Hall
7C3×C5×C4⋊Q8C2212yes—
8C2×#6717—24no—
9C2×D120—22no—
10#91763C2211yescharacteristic
11#91763C2211yescharacteristic
12C3×C5×#106—22no—
13C3×C4×C5×C8C2211yescharacteristic
14#91093—24no—
15C4×C3⋊#168C2212yes—
16#71336—51nomaximal, Hall
17C5×#498D311yescharacteristic, complemented
18#65377—32no—
19#65374—32no—
20#64984—31no—
21#64675—31no—
22C2×C3×C5×Q8—22no—
23C2×D60—21no—
24C2×D60—21no—
25C2×D60—22no—
26C2×D60—22no—
27C2×C3×C5×C8D412yes—
28C3×C5×C4⋊C4—22no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31#6717—48no—
32C2×C3⋊#168D414yes—
33D120—44no—
34C3×#498D511yescharacteristic, complemented
35#5088—52no—
36#5085—52no—
37#4695—51no—
38#4455—51no—
39C5×C4⋊Q8C2×D312yes—
40C2×#688—64no—
41C2×D40—62no—
42#4020—31no—
43#4020—31no—
44C5×#106—22no—
45C4×C5×C8C2×D311yescharacteristic
46#3941—64no—
47C4×#168—32no—
48#1715—151noSylow
49C22×D15—41no—
50C22×D15—41no—
51C3×C5×Q8—44no—
52C2×C3×C4×C5—42no—
53C2×C3×C4×C5C2×D411yescharacteristic
54C2×C3×C4×C5C2×D412yes—
55D60—42no—
56D60—42no—
57D60—44no—
58D60—44no—
59C3×C5×C8SD1614yescomplemented
60C3⋊#168—24no—
61C3×C4⋊Q8C2×D512yes—
62C2×#215—104no—
63C2×D24—102no—
64#874—51no—
65#874—51no—
66C3×#106—22no—
67C3×C4×C8C2×D511yescharacteristic
68#809—104no—
69C4×C3⋊C8—52no—
70C2×C5×Q8—22no—
71C2×D20—62no—
72C2×D20—62no—
73C2×D20—61no—
74C2×D20—61no—
75C2×C5×C8#6712yes—
76C5×C4⋊C4—22no—
77C5×C4⋊C4—22no—
78C42×C5C22×D311yescharacteristic
79#688—128no—
80C2×#168—34no—
81D40—124no—
82#498D1511yescharacteristic, complemented
83#493—151no—
84#492—152no—
85#486—152no—
86#322—151no—
87C22×C3×C5#12711yescharacteristic
88C2×D15—81no—
89C2×D15—81no—
90C2×D15—82no—
91C2×D15—82no—
92C3×C4×C5—82no—
93C3×C4×C5C2×SD1612yes—
94C3×C4×C5AGL(1,ℤ/8)14yes—
95C2×C3×Q8—22no—
96C2×D12—102no—
97C2×D12—102no—
98C2×D12—101no—
99C2×D12—101no—
100C2×C3×C8C22⋊D512yes—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C3×C42C22×D511yescharacteristic
104#215—208no—
105C2×C3⋊C8—54no—
106D24—204no—
107C22×D5—121no—
108C22×D5—121no—
109C5×Q8—44no—
110C2×C4×C5—42no—
111C2×C4×C5D3×D412yes—
112C2×C4×C5C2×#6711yescharacteristic
113D20—124no—
114D20—124no—
115D20—122no—
116D20—122no—
117C5×C8#21514yescomplemented
118#168—64no—
119C2×SD16—304no—
120C2×D8—302no—
121C4⋊Q8C2×D1512yes—
122#127—151no—
123#127—151no—
124#106—22no—
125#102—304no—
126C4×C8—152no—
127C4×C8C2×D1511yescharacteristic
128C2×C3×C5#49211yescharacteristic
129C2×C3×C5#49612yes—
130D15—161no—
131D15—161no—
132C22×D3—201no—
133C22×D3—201no—
134C3×Q8—44no—
135C2×C3×C4—42no—
136C2×C3×C4D4×D512yes—
137C2×C3×C4C2×C22⋊D511yescharacteristic
138D12—204no—
139D12—204no—
140D12—202no—
141D12—202no—
142C3×C8#68814yescomplemented
143C3⋊C8—104no—
144C22×C5#94011yescharacteristic
145C2×D5—242no—
146C2×D5—242no—
147C2×D5—241no—
148C2×D5—241no—
149C4×C5—82no—
150C4×C5#91414yes—
151C4×C5C2×#21512yes—
152C2×Q8—22no—
153C2×D4—302no—
154C2×D4—302no—
155C2×D4—301no—
156C2×D4—301no—
157SD16—608no—
158D8—604no—
159C2×C8—154no—
160C2×C8#122012yes—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C42C22×D1511yescharacteristic
164C3×C5#171511yescharacteristic, complemented, Hall
165C22×C3#408611yescharacteristic
166C2×D3—401no—
167C2×D3—401no—
168C2×D3—402no—
169C2×D3—402no—
170C3×C4—82no—
171C3×C4#406014yes—
172C3×C4C2×#68812yes—
173C2×C5#508511yescharacteristic
174C2×C5#517612yes—
175D5—481no—
176D5—481no—
177C23—601no—
178C23—601no—
179Q8—44no—
180D4—604no—
181D4—604no—
182D4—602no—
183D4—602no—
184C2×C4—42no—
185C2×C4D4×D1512yes—
186C2×C4C2×#122011yescharacteristic
187C8—304no—
188C8#671714yescomplemented
189C2×C3#6537411yescharacteristic
190C2×C3#6546512yes—
191D3—801no—
192D3—801no—
193C5#7133611yescharacteristic, complemented, Sylow
194C22—1201no—
195C22—1201no—
196C22—1202no—
197C22—1202no—
198C22#9182911yescharacteristic
199C4—82no—
200C4#9180314yes—
201C4C2×#671712yes—
202C3#1060212911yescharacteristic, complemented, Sylow
203C2—2401no—
204C2—2401no—
205C2#1175118611yescharacteristic
206C2#1175127712yes—
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#498C2
socleC22×C3×C5#127
prime radical#11750796C2
hypercenter#498D15
hypocenterC3×C5#1715
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. C3×C5×#498C2semidirect
2. #11751189C2semidirect
3. #11751186C2semidirect
5. #11746276C2semidirect
17. C5×#498D3semidirect
34. C3×#498D5semidirect
59. C3×C5×C8SD16semidirect
82. #498D15semidirect
117. C5×C8#215semidirect
142. C3×C8#688semidirect
164. C3×C5#1715semidirect
188. C8#6717semidirect
193. C5#71336semidirect
202. C3#10602129semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4982
#117511892
#117511862
#117507962
#117462762
#106021293
#713365