Finite Group Databasebeta

← #14290930

Subgroups — #14290930

Order 1920.

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

normal subgroups only

This group has 460 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, complemented
2C3×#65356C211yesmaximal, characteristic, complemented
3#11747041C212yesmaximal, complemented
4#11746364C211yesmaximal, characteristic, complemented
5#11745847C212yesmaximal, complemented
6#10602745—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#896—22no—
9C5×#895—22no—
10C5×#894—22no—
11C5×#875C2212yes—
12C3×#4020C2211yescharacteristic
13C2×#6655—22no—
14C2×#6652—22no—
15#91087C2212yes—
16C3×#3941—22no—
17C3×#3935C2211yescharacteristic
18#71248—51nomaximal, Hall
19C5×#562—31no—
20#65356D311yescharacteristic, complemented
21#65347—32no—
22#64763—31no—
23#64760—32no—
24C2×C5×D12—22no—
25C2×C5×D12D412yes—
26C2×C4×C5×D3—22no—
27C2×C5×Dic6D412yes—
28C2×C3×D20—21no—
29C2×C3×D20—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C42×C5C2311yescharacteristic
33C2×C3⋊#168—22no—
34C5×(C2×D3)⋊C4—22no—
35C5×(C2×D3)⋊C4—22no—
36C5×(C2×D3)⋊C4—22no—
37C5×Dic3⋊C4—22no—
38C2×C3×#168—21no—
39#6655—44no—
40#6652—44no—
41#5700D511yescharacteristic, complemented
42C3×#490—51no—
43#5074—52no—
44#4543—51no—
45#4464—52no—
46C5×#125C2×D311yescharacteristic
47C5×#124—32no—
48C5×#123—62no—
49C5×C22⋊Q8—62no—
50C5×#121—62no—
51C2×#688—62no—
52C2×#686—62no—
53#4020C2×D311yescharacteristic
54#3941—22no—
55#3935—32no—
56#3935C2×D311yescharacteristic
57#1656—151noSylow
58C22×C5×D3—22no—
59C22×C3×D5—41no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D412yes—
62C2×C3×C4×C5C2×D411yescharacteristic
63C2×C5×Dic3—22no—
64C5×D12—42no—
65C5×D12—82no—
66C4×C5×D3—82no—
67C5×Dic6—42no—
68C3×D20—42no—
69C3×D20—42no—
70C3×D20—42no—
71C3⋊#168—24no—
72C3×#168—41no—
73C3×#127—51no—
74C3×#125C2×D511yescharacteristic
75C2×#214—102no—
76C2×#213—102no—
77#896—22no—
78#895—22no—
79#894—22no—
80#875C2×D512yes—
81C3×#102—102no—
82C3×#97—51no—
83#803—52no—
84C2×C5×Q8—32no—
85C2×C5×D4—32no—
86C2×C5×D4—62no—
87C22×C4×C5—62no—
88C2×D20—22no—
89C2×D20—21no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—62no—
92C5×C4⋊C4#6712yes—
93C5×C22⋊C4—62no—
94C5×C22⋊C4—62no—
95C5×C22⋊C4—62no—
96C42×C5C22×D311yescharacteristic
97#688—124no—
98#686—124no—
99C2×#168—21no—
100C2×#168—62no—
101#562—31no—
102#496—152no—
103#490—51no—
104#330—151no—
105#329—152no—
106C22×C3×C5#12011yescharacteristic
107C2×C5×D3—42no—
108C2×C5×D3—42no—
109C2×C5×D3—42no—
110C2×C3×D5—82no—
111C2×C3×D5—81no—
112C3×C4×C5—22no—
113C3×C4×C5—21no—
114C3×C4×C5—42no—
115C5×Dic3—42no—
116C2×C3×D4—101no—
117C2×C3×D4—102no—
118C2×D12—22no—
119C2×D12C22⋊D512yes—
120C2×C4×D3—22no—
121C2×Dic6C22⋊D512yes—
122C2×C3×C8—101no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4C22⋊D512yes—
125C3×C42C22×D511yescharacteristic
126#214—204no—
127#213—204no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—22no—
131Dic3⋊C4—22no—
132C2×C3⋊C8—102no—
133C23×C5—62no—
134C22×D5—41no—
135C5×Q8—122no—
136C5×D4—122no—
137C5×D4—242no—
138C2×C4×C5—22no—
139C2×C4×C5—62no—
140C2×C4×C5—242no—
141C2×C4×C5D3×D412yes—
142C2×C4×C5C2×#6711yescharacteristic
143D20—42no—
144D20—42no—
145D20—42no—
146#168—41no—
147#168—64no—
148C2×SD16—302no—
149C2×D8—302no—
150#127—51no—
151#125D3×D511yescharacteristic
152#124—32no—
153#123—62no—
154C22⋊Q8—62no—
155#121—62no—
156#102—102no—
157#97—51no—
158#97—152no—
159C2×C3×C5#45312yes—
160C2×C3×C5#45411yescharacteristic
161C3×D5—161no—
162C5×D3—82no—
163C23×C3—201no—
164C22×D3—22no—
165C3×D4—202no—
166C3×D4—202no—
167C3×D4—202no—
168C2×C3×C4—22no—
169C2×C3×C4C2×C22⋊D511yescharacteristic
170C2×C3×C4C2×C22⋊D512yes—
171C2×Dic3—22no—
172D12—42no—
173D12—82no—
174C4×D3—82no—
175Dic6—42no—
176C3×C8—201no—
177C3⋊C8—104no—
178C22×C5—122no—
179C22×C5—122no—
180C22×C5—122no—
181C22×C5#93711yescharacteristic
182C2×D5—82no—
183C2×D5—81no—
184C4×C5—22no—
185C4×C5—21no—
186C4×C5—42no—
187C4×C5—122no—
188C2×Q8—32no—
189C2×D4—32no—
190C2×D4—62no—
191C2×D4—101no—
192C2×D4—102no—
193C22×C4—62no—
194SD16—604no—
195D8—604no—
196C2×C8—101no—
197C2×C8—302no—
198C4⋊C4—22no—
199C4⋊C4—62no—
200C4⋊C4#120112yes—
201C22⋊C4—62no—
202C22⋊C4—62no—
203C22⋊C4—62no—
204C42C2×D3×D511yescharacteristic
205C3×C5#165611yescharacteristic, complemented, Hall
206C22×C3—402no—
207C22×C3—401no—
208C22×C3#409911yescharacteristic
209C2×D3—42no—
210C2×D3—42no—
211C2×D3—42no—
212C3×C4—22no—
213C3×C4—21no—
214C3×C4—42no—
215Dic3—42no—
216C2×C5—242no—
217C2×C5#506211yescharacteristic
218C2×C5#519812yes—
219D5—161no—
220C23—62no—
221C23—201no—
222Q8—122no—
223D4—122no—
224D4—202no—
225D4—202no—
226D4—202no—
227D4—242no—
228C2×C4—22no—
229C2×C4—62no—
230C2×C4—242no—
231C2×C4C2×#120111yescharacteristic
232C2×C4D3×C22⋊D512yes—
233C8—201no—
234C8—304no—
235C2×C3—801no—
236C2×C3#6553012yes—
237C2×C3#6553411yescharacteristic
238D3—82no—
239C5#7124811yescharacteristic, complemented, Sylow
240C22—122no—
241C22—122no—
242C22—122no—
243C22—401no—
244C22—402no—
245C22#9156811yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4—122no—
250C3#1060274511yescharacteristic, complemented, Sylow
251C2—242no—
252C2—801no—
253C2#1174938611yescharacteristic
254C2#1174941912yes—
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
hypercenter#125D3×D5
hypocenterC3×C5#1656
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
1. C5×#5700C2semidirect
2. C3×#65356C2semidirect
3. #11747041C2semidirect
4. #11746364C2semidirect
5. #11745847C2semidirect
20. #65356D3semidirect
41. #5700D5semidirect
205. C3×C5#1656semidirect
239. C5#71248semidirect
250. C3#10602745semidirect

Maximal subgroups

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

subgroupindex
C5×#57002
C3×#653562
#117470412
#117463642
#117458472
#106027453
#712485