Finite Group Databasebeta

← #14291156

Subgroups — #14291156

Order 1920.

392 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×#5700C211yesmaximal, characteristic
2C3×#65358C211yesmaximal, characteristic, complemented
3#11746904C212yesmaximal, complemented
4#11746364C211yesmaximal, characteristic, complemented
5#11745847C212yesmaximal, complemented
6#10602747—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#896—22no—
9C5×#895—22no—
10C5×#894—22no—
11C5×#875C2212yes—
12C3×#4015C2211yescharacteristic
13#91087C2212yes—
14C3×#3942—22no—
15C3×#3935C2211yescharacteristic
16#90972—22no—
17#90966—22no—
18#71251—51nomaximal, Hall
19C5×#562—31no—
20#65358D311yescharacteristic, complemented
21#65344—32no—
22#64763—31no—
23#64760—32no—
24C2×C5×D12—22no—
25C2×C5×D12D412yes—
26C2×C4×C5×D3—22no—
27C2×C5×Dic6D412yes—
28C2×C3×Dic10—21no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4D412yes—
31C3×C42×C5C2311yescharacteristic
32C2×C3⋊#168—22no—
33C5×(C2×D3)⋊C4—22no—
34C5×(C2×D3)⋊C4—22no—
35C5×(C2×D3)⋊C4—22no—
36C5×Dic3⋊C4—22no—
37C3×C4⋊Dic5—22no—
38C2×C3×#168—21no—
39#5700D511yescharacteristic
40C3×#491—51no—
41#5089—52no—
42#4543—51no—
43#4464—52no—
44C5×#125C2×D311yescharacteristic
45C5×#124—32no—
46C5×#123—62no—
47C5×C22⋊Q8—62no—
48C5×#121—62no—
49#4015C2×D311yescharacteristic
50#3967—62no—
51#3964—62no—
52#3942—22no—
53#3935—32no—
54#3935C2×D311yescharacteristic
55#1662—151noSylow
56C22×C5×D3—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D412yes—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C5×Dic3—22no—
61C5×D12—42no—
62C5×D12—82no—
63C4×C5×D3—82no—
64C5×Dic6—42no—
65C2×C3×Dic5—41no—
66C3×Dic10—42no—
67C3⋊#168—42no—
68C3×#168—41no—
69C3×C4⋊Q8—51no—
70C3×#125C2×D511yescharacteristic
71#896—22no—
72#895—22no—
73#894—22no—
74#875C2×D512yes—
75C3×#103—102no—
76C3×#97—51no—
77#810—102no—
78#809—102no—
79#803—52no—
80C2×C5×Q8—32no—
81C2×C5×D4—32no—
82C2×C5×D4—62no—
83C22×C4×C5—62no—
84C2×Dic10—21no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—62no—
87C5×C4⋊C4#6712yes—
88C5×C22⋊C4—62no—
89C5×C22⋊C4—62no—
90C5×C22⋊C4—62no—
91C42×C5C22×D311yescharacteristic
92C4⋊Dic5—22no—
93C2×#168—21no—
94C2×#168—62no—
95#562—31no—
96#491—51no—
97#489—152no—
98#330—151no—
99#329—152no—
100C22×C3×C5#12011yescharacteristic
101C2×C5×D3—42no—
102C2×C5×D3—42no—
103C2×C5×D3—42no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×Dic5—81no—
108C5×Dic3—42no—
109C2×C3×Q8—101no—
110C2×D12—22no—
111C2×D12C22⋊D512yes—
112C2×C4×D3—22no—
113C2×Dic6C22⋊D512yes—
114C2×C3×C8—101no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—102no—
117C3×C4⋊C4C22⋊D512yes—
118C3×C42C22×D511yescharacteristic
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122Dic3⋊C4—22no—
123C2×C3⋊C8—102no—
124C23×C5—62no—
125C5×Q8—122no—
126C5×D4—122no—
127C5×D4—242no—
128C2×C4×C5—22no—
129C2×C4×C5—62no—
130C2×C4×C5—242no—
131C2×C4×C5D3×D412yes—
132C2×C4×C5C2×#6711yescharacteristic
133C2×Dic5—41no—
134Dic10—42no—
135#168—41no—
136#168—122no—
137C4⋊Q8—51no—
138#125D3×D511yescharacteristic
139#124—32no—
140#123—62no—
141C22⋊Q8—62no—
142#121—62no—
143#103—102no—
144#103—302no—
145#102—302no—
146#97—51no—
147#97—152no—
148C2×C3×C5#45411yescharacteristic
149C2×C3×C5#45512yes—
150C5×D3—82no—
151C22×D3—22no—
152C3×Q8—202no—
153C2×C3×C4—22no—
154C2×C3×C4—201no—
155C2×C3×C4C2×C22⋊D511yescharacteristic
156C2×C3×C4C2×C22⋊D512yes—
157C2×Dic3—22no—
158D12—42no—
159D12—82no—
160C4×D3—82no—
161Dic6—42no—
162C3×C8—201no—
163C3⋊C8—202no—
164C22×C5—122no—
165C22×C5—122no—
166C22×C5—122no—
167C22×C5#93711yescharacteristic
168C4×C5—22no—
169C4×C5—21no—
170C4×C5—42no—
171C4×C5—122no—
172Dic5—81no—
173C2×Q8—32no—
174C2×Q8—101no—
175C2×D4—32no—
176C2×D4—62no—
177C22×C4—62no—
178C2×C8—101no—
179C2×C8—302no—
180C4⋊C4—22no—
181C4⋊C4—62no—
182C4⋊C4—102no—
183C4⋊C4#120112yes—
184C22⋊C4—62no—
185C22⋊C4—62no—
186C22⋊C4—62no—
187C42C2×D3×D511yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3#409911yescharacteristic
190C2×D3—42no—
191C2×D3—42no—
192C2×D3—42no—
193C3×C4—22no—
194C3×C4—21no—
195C3×C4—42no—
196C3×C4—401no—
197Dic3—42no—
198C2×C5—242no—
199C2×C5#506211yescharacteristic
200C2×C5#520212yes—
201C23—62no—
202Q8—122no—
203Q8—202no—
204D4—122no—
205D4—242no—
206C2×C4—22no—
207C2×C4—62no—
208C2×C4—201no—
209C2×C4—242no—
210C2×C4C2×#120111yescharacteristic
211C2×C4D3×C22⋊D512yes—
212C8—201no—
213C8—602no—
214C2×C3#6553112yes—
215C2×C3#6553411yescharacteristic
216D3—82no—
217C5#7125111yescharacteristic, complemented, Sylow
218C22—122no—
219C22—122no—
220C22—122no—
221C22#9156811yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—122no—
226C4—401no—
227C3#1060274711yescharacteristic, complemented, Sylow
228C2—242no—
229C2#1174938611yescharacteristic
230C2#1174941612yes—
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC5×#5700C2
hypercenter#125D3×D5
hypocenterC3×C5#1662
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. C3×#65358C2semidirect
3. #11746904C2semidirect
4. #11746364C2semidirect
5. #11745847C2semidirect
20. #65358D3semidirect
188. C3×C5#1662semidirect
217. C5#71251semidirect
227. C3#10602747semidirect

Maximal subgroups

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

subgroupindex
C5×#57002
C3×#653582
#117469042
#117463642
#117458472
#106027473
#712515