Finite Group Databasebeta

← #14289029

Subgroups — #14289029

Order 1920.

456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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
1#11756481C211yesmaximal, characteristic, complemented
2C3×#65374C211yesmaximal, characteristic
3#11747083C212yesmaximal
4C5×#4546C211yesmaximal, characteristic, complemented
5#11745845C212yesmaximal, complemented
6#10599297—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8#91833—22no—
9#91777—22no—
10#91776—22no—
11C4×Dic30C2212yes—
12C2×C3×#688—22no—
13C3×#4020C2211yescharacteristic
14C2×#6657—22no—
15C5×C4⋊(C3⋊C8)C2212yes—
16C3×C4×#168C2211yescharacteristic
17#90965—22no—
18#71269—51nomaximal, Hall
19#66056—31no—
20#65374D311yescharacteristic
21#65137—32no—
22C5×#333—31no—
23#64704—32no—
24C2×C3×C5×Q8D412yes—
25C2×Dic30—22no—
26C2×Dic30D412yes—
27C2×C3×D20—21no—
28C2×C3×D20—22no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31C4⋊Dic15D412yes—
32#6712—24no—
33#6712—22no—
34C4×Dic15—22no—
35C4×Dic15—22no—
36C2×C5×C3⋊C8—22no—
37C3×#688—44no—
38C2×C3×#168—21no—
39#6657—44no—
40#5722—51no—
41C3×#492—51no—
42#5075—52no—
43#4546D511yescharacteristic, complemented
44#4456—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4090—62no—
47C2×#688—22no—
48C2×#677—62no—
49#4034—62no—
50#4033—62no—
51#4020C2×D311yescharacteristic
52C4×Dic10—32no—
53C5×C4⋊C8—32no—
54#3953—62no—
55C4×#168C2×D311yescharacteristic
56#1623—151noSylow
57C22×C3×D5—41no—
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15—22no—
63C2×Dic15—22no—
64Dic30—22no—
65Dic30—82no—
66Dic30SD1614yescomplemented
67C3×D20—42no—
68C3×D20—42no—
69C3×D20—42no—
70C3×#168—22no—
71C5×C3⋊C8—42no—
72C2×C3×SD16—102no—
73C3×C4⋊Q8C2×D511yescharacteristic
74C3×#127—51no—
75#944—102no—
76C2×#214—102no—
77#888—102no—
78#887—102no—
79C4×Dic6—52no—
80C3×C4×C8—51no—
81#832—102no—
82C4⋊(C3⋊C8)C2×D512yes—
83C2×C5×Q8#6712yes—
84C2×D20—22no—
85C2×D20—21no—
86C2×Dic10—32no—
87C2×Dic10—62no—
88C2×C5×C8—62no—
89C5×C4⋊C4—22no—
90C42×C5C22×D311yescharacteristic
91#688—44no—
92C4⋊Dic5—32no—
93#683—64no—
94#683—62no—
95C4×Dic5—62no—
96C4×Dic5—62no—
97C2×#168—21no—
98#677—124no—
99Q82—151no—
100#492—51no—
101#460—152no—
102#333—31no—
103Q8⋊C8—152no—
104C22×C3×C5#12011yescharacteristic
105C2×C3×D5—82no—
106C2×C3×D5—81no—
107C3×C4×C5—21no—
108C3×C4×C5—42no—
109C3×C4×C5C2×SD1612yes—
110C3×C4×C5#13712yes—
111Dic15—24no—
112Dic15—42no—
113C2×C3×Q8D2012yes—
114C2×C3×D4—101no—
115C2×C3×D4—102no—
116C2×Dic6—52no—
117C2×Dic6—102no—
118C3×SD16—204no—
119C2×C3×C8—101no—
120C3×C4⋊C4—22no—
121C3×C42C22×D511yescharacteristic
122#214—204no—
123C4⋊Dic3—52no—
124Dic3⋊C4—104no—
125Dic3⋊C4—102no—
126C4×Dic3—102no—
127C4×Dic3—102no—
128C2×C3⋊C8—22no—
129C22×D5—41no—
130C5×Q8—42no—
131C2×C4×C5—22no—
132C2×C4×C5D3×D412yes—
133C2×C4×C5C2×#6711yescharacteristic
134C2×Dic5—62no—
135C2×Dic5—62no—
136D20—42no—
137D20—42no—
138D20—42no—
139Dic10—34no—
140Dic10—62no—
141Dic10—242no—
142C5×C8—122no—
143#168—22no—
144C2×SD16—102no—
145C2×SD16—302no—
146C4⋊Q8—302no—
147C4⋊Q8—302no—
148C4⋊Q8D3×D511yescharacteristic
149#127—51no—
150C4×Q8—152no—
151C4×Q8—302no—
152C4⋊C8—32no—
153#102—302no—
154C4×C8—51no—
155C2×C3×C5#44812yes—
156C2×C3×C5#45311yescharacteristic
157C3×D5—161no—
158C23×C3—201no—
159C3×Q8—42no—
160C3×D4—202no—
161C3×D4—202no—
162C3×D4—202no—
163C2×C3×C4—22no—
164C2×C3×C4C2×D2011yescharacteristic
165C2×C3×C4D4×D512yes—
166C2×Dic3—102no—
167C2×Dic3—102no—
168Dic6—54no—
169Dic6—102no—
170Dic6—402no—
171C3×C8—102no—
172C3⋊C8—42no—
173C22×C5#93711yescharacteristic
174C2×D5—82no—
175C2×D5—81no—
176C4×C5—21no—
177C4×C5—42no—
178C4×C5D3×SD1612yes—
179C4×C5#91512yes—
180Dic5—64no—
181Dic5—122no—
182C2×Q8—152no—
183C2×Q8—302no—
184C2×Q8#120212yes—
185C2×D4—101no—
186C2×D4—102no—
187SD16—204no—
188SD16—604no—
189C2×C8—62no—
190C2×C8—101no—
191C4⋊C4—22no—
192C4⋊C4—152no—
193C4⋊C4—304no—
194C4⋊C4—302no—
195C42—302no—
196C42—302no—
197C42C2×D3×D511yescharacteristic
198C3×C5#162311yescharacteristic, complemented, Hall
199C22×C3—401no—
200C22×C3—402no—
201C22×C3#402811yescharacteristic
202C3×C4—21no—
203C3×C4—42no—
204C3×C4D5×SD1612yes—
205C3×C4#406412yes—
206Dic3—104no—
207Dic3—202no—
208C2×C5#507711yescharacteristic
209C2×C5#517012yes—
210D5—161no—
211C23—201no—
212Q8—42no—
213Q8—154no—
214Q8—302no—
215Q8—1202no—
216D4—202no—
217D4—202no—
218D4—202no—
219C2×C4—22no—
220C2×C4—302no—
221C2×C4—302no—
222C2×C4C2×#120211yescharacteristic
223C2×C4#679012yes—
224C8—102no—
225C8—122no—
226C2×C3—801no—
227C2×C3#6503611yescharacteristic
228C2×C3#6509512yes—
229C5#7126911yescharacteristic, complemented, Sylow
230C22—401no—
231C22—402no—
232C22#9157211yescharacteristic
233C4—21no—
234C4—42no—
235C4—304no—
236C4—602no—
237C4#9150512yes—
238C4#9152212yes—
239C3#1059929711yescharacteristic, complemented, Sylow
240C2—801no—
241C2#1174914211yescharacteristic
242C2#1174928612yes—
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1623
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756481C2semidirect
4. C5×#4546C2semidirect
5. #11745845C2semidirect
43. #4546D5semidirect
66. Dic30SD16semidirect
198. C3×C5#1623semidirect
229. C5#71269semidirect
239. C3#10599297semidirect

Maximal subgroups

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

subgroupindex
#117564812
C3×#653742
#117470832
C5×#45462
#117458452
#105992973
#712695