Finite Group Databasebeta

← #14291157

Subgroups — #14291157

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
2#11751170C211yesmaximal, characteristic, complemented
3#11746909C212yesmaximal, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5#11745847C212yesmaximal, complemented
6#10602747—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91758C2211yescharacteristic
9C5×#896—22no—
10C5×#895—22no—
11C5×#894—22no—
12C5×#875C2212yes—
13#91094—22no—
14#91087C2211yescharacteristic
15C3×#3935C2212yes—
16#90973—22no—
17#90967—22no—
18#68374—51nomaximal, Hall
19C5×#562—31no—
20#65358—31no—
21#65344—32no—
22#64763D311yescharacteristic, complemented
23#64760—32no—
24C2×Dic30—21no—
25C2×C5×D12—22no—
26C2×C5×D12D412yes—
27C2×C4×C5×D3—22no—
28C2×C5×Dic6D412yes—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4D412yes—
31C3×C42×C5C2311yescharacteristic
32C4⋊Dic15—22no—
33C2×C3⋊#168—21no—
34C5×(C2×D3)⋊C4—22no—
35C5×(C2×D3)⋊C4—22no—
36C5×(C2×D3)⋊C4—22no—
37C5×Dic3⋊C4—22no—
38C2×C3×#168—22no—
39#5700D511yescharacteristic
40#5069—51no—
41#4714—52no—
42C3×#330—51no—
43#4464—52no—
44C5×#125C2×D311yescharacteristic
45C5×#124—32no—
46C5×#123—62no—
47C5×C22⋊Q8—62no—
48C5×#121—62no—
49#4015—31no—
50#3967—62no—
51#3964—62no—
52#3942—62no—
53#3935—31no—
54#3935C2×D312yes—
55#1662—151noSylow
56C22×C5×D3—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—41no—
61Dic30—42no—
62C2×C5×Dic3—22no—
63C5×D12—42no—
64C5×D12—82no—
65C4×C5×D3—82no—
66C5×Dic6—42no—
67C3⋊#168—41no—
68C3×#168—42no—
69C3×#125C2×D511yescharacteristic
70#896—22no—
71#895—22no—
72#894—22no—
73#875C2×D512yes—
74#869—51no—
75C3×#97—52no—
76#821—102no—
77#816—102no—
78#810—102no—
79#803—51no—
80C2×C5×Q8—32no—
81C2×C5×D4—32no—
82C2×C5×D4—62no—
83C22×C4×C5—62no—
84C2×Dic10—61no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—62no—
87C5×C4⋊C4D1212yes—
88C5×C22⋊C4—62no—
89C5×C22⋊C4—62no—
90C5×C22⋊C4—62no—
91C42×C5C22×D311yescharacteristic
92C4⋊Dic5—62no—
93C2×#168—22no—
94C2×#168—61no—
95#562—31no—
96#491—151no—
97#489—152no—
98#330—51no—
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—
107Dic15—81no—
108C5×Dic3—42no—
109C2×D12—22no—
110C2×D12C22⋊D512yes—
111C2×C4×D3—22no—
112C2×Dic6—101no—
113C2×Dic6C22⋊D512yes—
114C2×C3×C8—102no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4C22⋊D512yes—
117C3×C42C22×D511yescharacteristic
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121C4⋊Dic3—102no—
122Dic3⋊C4—22no—
123C2×C3⋊C8—101no—
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×C5C2×D1211yescharacteristic
132C2×C4×C5D3×D412yes—
133C2×Dic5—121no—
134Dic10—122no—
135#168—42no—
136#168—121no—
137C4⋊Q8—151no—
138#125D3×D511yescharacteristic
139#124—32no—
140#123—62no—
141C22⋊Q8—62no—
142#121—62no—
143#103—302no—
144#103—302no—
145#102—302no—
146#97—52no—
147#97—151no—
148C2×C3×C5#45411yescharacteristic
149C2×C3×C5#45512yes—
150C5×D3—82no—
151C22×D3—22no—
152C2×C3×C4—22no—
153C2×C3×C4C2×C22⋊D511yescharacteristic
154C2×C3×C4C2×C22⋊D512yes—
155C2×Dic3—22no—
156C2×Dic3—201no—
157D12—42no—
158D12—82no—
159C4×D3—82no—
160Dic6—42no—
161Dic6—202no—
162C3×C8—202no—
163C3⋊C8—201no—
164C22×C5—122no—
165C22×C5—122no—
166C22×C5—122no—
167C22×C5#88211yescharacteristic
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—42no—
171C4×C5—122no—
172Dic5—241no—
173C2×Q8—32no—
174C2×Q8—301no—
175C2×D4—32no—
176C2×D4—62no—
177C22×C4—62no—
178C2×C8—102no—
179C2×C8—301no—
180C4⋊C4—22no—
181C4⋊C4—62no—
182C4⋊C4—302no—
183C4⋊C4#120312yes—
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—
196Dic3—42no—
197Dic3—401no—
198C2×C5—242no—
199C2×C5#475311yescharacteristic
200C2×C5#482512yes—
201C23—62no—
202Q8—122no—
203Q8—602no—
204D4—122no—
205D4—242no—
206C2×C4—22no—
207C2×C4—62no—
208C2×C4—242no—
209C2×C4—601no—
210C2×C4C2×#120311yescharacteristic
211C2×C4D3×C22⋊D512yes—
212C8—202no—
213C8—601no—
214C2×C3#6553112yes—
215C2×C3#6553411yescharacteristic
216D3—82no—
217C5#6837411yescharacteristic, complemented, Sylow
218C22—122no—
219C22—122no—
220C22—122no—
221C22#9157011yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—122no—
226C4—1201no—
227C3#1060274711yescharacteristic, complemented, Sylow
228C2—242no—
229C2#1174938711yescharacteristic
230C2#1174946612yes—
subgroupG/H
centerC22#91570
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. #11751170C2semidirect
3. #11746909C2semidirect
4. C3×#64763C2semidirect
5. #11745847C2semidirect
22. #64763D3semidirect
188. C3×C5#1662semidirect
217. C5#68374semidirect
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
#117511702
#117469092
C3×#647632
#117458472
#106027473
#683745