Finite Group Databasebeta

← #14293536

Subgroups — #14293536

Order 1920.

380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 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#11750782C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic
3#11747071C211yesmaximal, characteristic
4#11746948C211yesmaximal, characteristic, complemented
5#11746920C211yesmaximal, characteristic, complemented
6#11746890C211yesmaximal, characteristic
7C5×C8×C3⋊C8C211yesmaximal, characteristic, complemented
8#10598852—31nomaximal, Hall
9#91758C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6657—22no—
14C3×C4×C5×C8C2211yescharacteristic
15#91100—22no—
16C4×C5×C3⋊C8C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×#3953—22no—
19#90987—22no—
20#90971—22no—
21#90965—22no—
22#71181—51nomaximal, Hall
23#64983—31no—
24#64983D311yescharacteristic
25#64982—31no—
26#64970—31no—
27#64970—31no—
28#64969—31no—
29C5×C82—31no—
30C2×Dic30—21no—
31C2×Dic30—21no—
32C2×C3×D20—21no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8D412yes—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C4⋊Dic15—21no—
42C2×C5×C3⋊C8D412yes—
43C2×C5×C3⋊C8D412yes—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46#6657—44no—
47C3×#486—51no—
48#5080—51no—
49#5079—51no—
50#5076—51no—
51#5070—51no—
52#4681—51no—
53C8×C3⋊C8D511yescharacteristic, complemented
54C2×#677—62no—
55#4020C2×D311yescharacteristic
56#4015—31no—
57#4015—31no—
58#4015C2×D311yescharacteristic
59C4×C5×C8—31no—
60C4×C5×C8—31no—
61C4×C5×C8C2×D311yescharacteristic
62#3953—22no—
63#3953—62no—
64#3949—62no—
65#3948—62no—
66#3948—62no—
67#1708—151noSylow
68C22×C3×D5—41no—
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×Dic15—41no—
73C2×Dic15—41no—
74Dic30—42no—
75Dic30—42no—
76C2×C3×Dic5—41no—
77C3×D20—42no—
78C3×D20—42no—
79C3×D20—42no—
80C3×Dic10—42no—
81C3×C5×C8—22no—
82C5×C3⋊C8—22no—
83C5×C3⋊C8SD1614yes—
84C3×C4⋊Q8—51no—
85C3×#127—51no—
86C2×#214—102no—
87#869—51no—
88#869—51no—
89C3×#102—102no—
90C3×C4×C8C2×D511yescharacteristic
91#835—102no—
92#832—102no—
93#816—102no—
94#808—102no—
95C4×C3⋊C8C2×D511yescharacteristic
96C4×C3⋊C8C2×D511yescharacteristic
97C2×D20—21no—
98C2×D20—21no—
99C2×D20—21no—
100C2×Dic10—21no—
101C2×Dic10—61no—
102C2×Dic10—61no—
103C2×C5×C8—32no—
104C2×C5×C8—32no—
105C2×C5×C8#6712yes—
106C42×C5C22×D311yescharacteristic
107C4⋊Dic5—21no—
108C4⋊Dic5—21no—
109C4⋊Dic5—61no—
110C4⋊Dic5—61no—
111C4⋊Dic5—61no—
112C4⋊Dic5—61no—
113#677—124no—
114#498—151no—
115#492—151no—
116#487—151no—
117#487—151no—
118#486—51no—
119#486—151no—
120C82—31no—
121C22×C3×C5#12711yescharacteristic
122C2×C3×D5—81no—
123C2×C3×D5—81no—
124C2×C3×D5—81no—
125C3×C4×C5C2×SD1612yes—
126C3×C4×C5#13512yes—
127C3×C4×C5#13512yes—
128Dic15—81no—
129Dic15—81no—
130C3×Dic5—81no—
131C2×C3×Q8—101no—
132C2×C3×D4—101no—
133C2×C3×D4—101no—
134C2×C3×D4—101no—
135C2×Dic6—101no—
136C2×Dic6—101no—
137C2×C3×C8D2012yes—
138C3×C4⋊C4—101no—
139C3×C4⋊C4—101no—
140C3×C42C22×D511yescharacteristic
141#214—204no—
142C4⋊Dic3—101no—
143C4⋊Dic3—101no—
144C4⋊Dic3—101no—
145C4⋊Dic3—101no—
146C2×C3⋊C8D2012yes—
147C2×C3⋊C8D2012yes—
148C22×D5—41no—
149C2×C4×C5D3×D411yescharacteristic
150C2×C4×C5D3×D411yescharacteristic
151C2×C4×C5C2×#6711yescharacteristic
152C2×Dic5—41no—
153C2×Dic5—121no—
154C2×Dic5—121no—
155D20—42no—
156D20—42no—
157D20—42no—
158Dic10—42no—
159Dic10—122no—
160Dic10—122no—
161C5×C8—22no—
162C5×C8—34no—
163C5×C8—62no—
164C2×SD16—302no—
165C4⋊Q8—51no—
166C4⋊Q8—151no—
167C4⋊Q8—151no—
168#127—51no—
169#106—302no—
170#103—302no—
171#103—302no—
172#102—102no—
173#102—302no—
174C4×C8—31no—
175C4×C8—31no—
176C4×C8D3×D511yescharacteristic
177C2×C3×C5#49211yescharacteristic
178C2×C3×C5#49511yescharacteristic
179C2×C3×C5#49511yescharacteristic
180C3×D5—161no—
181C23×C3—201no—
182C3×Q8—202no—
183C3×D4—202no—
184C3×D4—202no—
185C3×D4—202no—
186C2×C3×C4—201no—
187C2×C3×C4C2×D2011yescharacteristic
188C2×C3×C4C2×D2011yescharacteristic
189C2×C3×C4C2×D2011yescharacteristic
190C2×Dic3—201no—
191C2×Dic3—201no—
192Dic6—202no—
193Dic6—202no—
194C3×C8—22no—
195C3⋊C8—22no—
196C3⋊C8#67714yes—
197C22×C5#94011yescharacteristic
198C2×D5—81no—
199C2×D5—81no—
200C2×D5—81no—
201C4×C5#91212yes—
202C4×C5D3×SD1612yes—
203C4×C5#95012yes—
204Dic5—81no—
205Dic5—241no—
206Dic5—241no—
207C2×Q8—101no—
208C2×Q8—301no—
209C2×Q8—301no—
210C2×D4—101no—
211C2×D4—101no—
212C2×D4—101no—
213SD16—604no—
214C2×C8—32no—
215C2×C8—32no—
216C2×C8#120212yes—
217C4⋊C4—101no—
218C4⋊C4—101no—
219C4⋊C4—301no—
220C4⋊C4—301no—
221C4⋊C4—301no—
222C4⋊C4—301no—
223C42C2×D3×D511yescharacteristic
224C3×C5#170811yescharacteristic, complemented, Hall
225C22×C3—401no—
226C22×C3—401no—
227C22×C3—401no—
228C22×C3#402011yescharacteristic
229C3×C4—401no—
230C3×C4C2×#67712yes—
231C3×C4#405012yes—
232C3×C4#405012yes—
233Dic3—401no—
234Dic3—401no—
235C2×C5#505911yescharacteristic
236C2×C5#515511yescharacteristic
237C2×C5#517511yescharacteristic
238D5—161no—
239C23—201no—
240Q8—202no—
241Q8—602no—
242Q8—602no—
243D4—202no—
244D4—202no—
245D4—202no—
246C2×C4—201no—
247C2×C4—601no—
248C2×C4—601no—
249C2×C4D3×D2011yescharacteristic
250C2×C4D3×D2011yescharacteristic
251C2×C4C2×#120211yescharacteristic
252C8—22no—
253C8—34no—
254C8—62no—
255C2×C3—801no—
256C2×C3#6498211yescharacteristic
257C2×C3#6498511yescharacteristic
258C2×C3#6498511yescharacteristic
259C5#7118111yescharacteristic, complemented, Sylow
260C22—401no—
261C22—401no—
262C22—401no—
263C22#9145811yescharacteristic
264C4—401no—
265C4—1201no—
266C4—1201no—
267C4D3×#67712yes—
268C4#9127312yes—
269C4#9131112yes—
270C3#1059885211yescharacteristic, complemented, Sylow
271C2—801no—
272C2#1174707211yescharacteristic
273C2#1174797111yescharacteristic
274C2#1174800211yescharacteristic
subgroupG/H
centerC22#91458
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#127
prime radicalC3×#4020C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1708
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11750782C2semidirect
4. #11746948C2semidirect
5. #11746920C2semidirect
7. C5×C8×C3⋊C8C2semidirect
53. C8×C3⋊C8D5semidirect
224. C3×C5#1708semidirect
259. C5#71181semidirect
270. C3#10598852semidirect

Maximal subgroups

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

subgroupindex
#117507822
C3×#649832
#117470712
#117469482
#117469202
#117468902
C5×C8×C3⋊C82
#105988523
#711815