Finite Group Databasebeta

← #14293671

Subgroups — #14293671

Order 1920.

396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 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#11751171C211yesmaximal, characteristic
2C5×#5076C211yesmaximal, characteristic
3C3×#65365C211yesmaximal, characteristic
4#11746955C211yesmaximal, characteristic, complemented
5#11746947C211yesmaximal, characteristic, complemented
6#11746921C211yesmaximal, characteristic, complemented
7#11745831C211yesmaximal, characteristic, complemented
8#10602050—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10#91758C2211yescharacteristic
11C2×C5×#214—22no—
12C5×#869C2211yescharacteristic
13C2×C3×#687—22no—
14C3×#4015C2211yescharacteristic
15#91116—22no—
16C4×C3⋊#168C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×C4×#168C2211yescharacteristic
19#90988—22no—
20#90986—22no—
21#90974—22no—
22#71258—51nomaximal, Hall
23C5×#492—31no—
24#65368—31no—
25#65367—31no—
26#65365D311yescharacteristic
27#65359—31no—
28#64970—31no—
29#64674—31no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×Dic30—21no—
34C2×C5×Dic6—21no—
35C2×C3×Dic10—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
39C2×C3⋊#168D412yes—
40C5×#214—44no—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C2×C5×C3⋊C8D412yes—
44C3×#687—44no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168D412yes—
48C3×#492—51no—
49#5093—51no—
50#5080—51no—
51#5076D511yescharacteristic
52#5070—51no—
53#4682—51no—
54#4455—51no—
55C2×C5×SD16—62no—
56C5×C4⋊Q8—31no—
57C5×#127C2×D311yescharacteristic
58C2×#687—22no—
59#4015—31no—
60#4015C2×D311yescharacteristic
61C4×C5×C8—31no—
62#3964—62no—
63#3948—62no—
64#3940—62no—
65#3939—62no—
66C4×#168—31no—
67C4×#168C2×D311yescharacteristic
68#1714—151noSylow
69C23×C3×C5—41no—
70C3×C5×D4—42no—
71C3×C5×D4—42no—
72C3×C5×D4—42no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×Dic15—41no—
77Dic30—42no—
78C2×C5×Dic3—41no—
79C5×Dic6—42no—
80C2×C3×Dic5—41no—
81C3×Dic10—42no—
82C3⋊#168—22no—
83C3×#168SD1614yescomplemented
84C5×C3⋊C8—22no—
85C2×C3×SD16—102no—
86C3×C4⋊Q8—51no—
87C3×#127C2×D511yescharacteristic
88C2×#214—22no—
89#869—51no—
90#869C2×D511yescharacteristic
91C3×C4×C8—51no—
92#832—102no—
93#818—102no—
94#810—102no—
95#808—102no—
96C4×C3⋊C8—51no—
97C4×C3⋊C8C2×D511yescharacteristic
98C2×C5×Q8—61no—
99C2×C5×D4—21no—
100C2×C5×D4—21no—
101C2×C5×D4—21no—
102C2×Dic10—21no—
103C2×Dic10—61no—
104C5×SD16—124no—
105C2×C5×C8—32no—
106C5×C4⋊C4—61no—
107C5×C4⋊C4—61no—
108C42×C5C22×D311yescharacteristic
109#687—44no—
110C4⋊Dic5—21no—
111C4⋊Dic5—21no—
112C4⋊Dic5—61no—
113C4⋊Dic5—61no—
114C2×#168—32no—
115C2×#168#6712yes—
116#500—151no—
117#498—151no—
118#492—31no—
119#492—51no—
120#487—151no—
121#486—151no—
122#322—151no—
123C22×C3×C5—81no—
124C22×C3×C5—81no—
125C22×C3×C5—81no—
126C22×C3×C5#12711yescharacteristic
127C3×C4×C5C2×SD1612yes—
128C3×C4×C5AGL(1,ℤ/8)12yes—
129C3×C4×C5#13712yes—
130Dic15—81no—
131C3×Dic5—81no—
132C5×Dic3—81no—
133C2×C3×Q8—101no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×Dic6—21no—
138C2×Dic6—101no—
139C3×SD16—204no—
140C2×C3×C8—52no—
141C3×C4⋊C4—101no—
142C3×C4⋊C4—101no—
143C3×C42C22×D511yescharacteristic
144#214—44no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—101no—
148C4⋊Dic3—101no—
149C2×C3⋊C8—52no—
150C2×C3⋊C8C22⋊D512yes—
151C23×C5—41no—
152C5×Q8—122no—
153C5×D4—42no—
154C5×D4—42no—
155C5×D4—42no—
156C2×C4×C5—121no—
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5D3×D411yescharacteristic
159C2×C4×C5C2×#6711yescharacteristic
160C2×Dic5—41no—
161C2×Dic5—121no—
162Dic10—42no—
163Dic10—122no—
164C5×C8—62no—
165#168—62no—
166#168#21414yescomplemented
167C2×SD16—62no—
168C2×SD16—102no—
169C4⋊Q8—31no—
170C4⋊Q8—51no—
171C4⋊Q8—151no—
172#127D3×D511yescharacteristic
173#107—302no—
174#106—302no—
175#103—302no—
176#102—302no—
177C4×C8—31no—
178C4×C8—51no—
179C4×C8—151no—
180C2×C3×C5—161no—
181C2×C3×C5#49211yescharacteristic
182C2×C3×C5#49611yescharacteristic
183C2×C3×C5#49711yescharacteristic
184C23×C3—41no—
185C3×Q8—202no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—42no—
189C2×C3×C4—201no—
190C2×C3×C4D4×D511yescharacteristic
191C2×C3×C4D4×D511yescharacteristic
192C2×C3×C4C2×C22⋊D511yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—201no—
195Dic6—42no—
196Dic6—202no—
197C3×C8—54no—
198C3⋊C8—22no—
199C3⋊C8—102no—
200C22×C5—81no—
201C22×C5—81no—
202C22×C5—81no—
203C22×C5#94011yescharacteristic
204C4×C5—241no—
205C4×C5#91412yes—
206C4×C5#91512yes—
207C4×C5C2×#21412yes—
208Dic5—81no—
209Dic5—241no—
210C2×Q8—61no—
211C2×Q8—101no—
212C2×Q8—301no—
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—21no—
216SD16—124no—
217SD16—204no—
218C2×C8—32no—
219C2×C8—52no—
220C2×C8—152no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—101no—
224C4⋊C4—101no—
225C4⋊C4—301no—
226C4⋊C4—301no—
227C42C2×D3×D511yescharacteristic
228C3×C5#171411yescharacteristic, complemented, Hall
229C22×C3—81no—
230C22×C3—81no—
231C22×C3—81no—
232C22×C3#408611yescharacteristic
233C3×C4—401no—
234C3×C4D5×SD1612yes—
235C3×C4#406112yes—
236C3×C4#407812yes—
237Dic3—81no—
238Dic3—401no—
239C2×C5—161no—
240C2×C5#507611yescharacteristic
241C2×C5#516711yescharacteristic
242C2×C5#517611yescharacteristic
243C23—41no—
244Q8—122no—
245Q8—202no—
246Q8—602no—
247D4—42no—
248D4—42no—
249D4—42no—
250C2×C4—121no—
251C2×C4—201no—
252C2×C4—601no—
253C2×C4D5×#6711yescharacteristic
254C2×C4D3×C22⋊D511yescharacteristic
255C2×C4#679011yescharacteristic
256C8—54no—
257C8—62no—
258C8—302no—
259C2×C3—161no—
260C2×C3#6536311yescharacteristic
261C2×C3#6545611yescharacteristic
262C2×C3#6546411yescharacteristic
263C5#7125811yescharacteristic, complemented, Sylow
264C22—81no—
265C22—81no—
266C22—81no—
267C22#9156711yescharacteristic
268C4—241no—
269C4—401no—
270C4—1201no—
271C4D5×#21412yes—
272C4#9148812yes—
273C4#9149612yes—
274C3#1060205011yescharacteristic, complemented, Sylow
275C2—161no—
276C2#1174907611yescharacteristic
277C2#1174910611yescharacteristic
278C2#1174911111yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#127
hypercenter#127D3×D5
hypocenterC3×C5#1714
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
4. #11746955C2semidirect
5. #11746947C2semidirect
6. #11746921C2semidirect
7. #11745831C2semidirect
83. C3×#168SD16semidirect
166. #168#214semidirect
228. C3×C5#1714semidirect
263. C5#71258semidirect
274. C3#10602050semidirect

Maximal subgroups

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

subgroupindex
#117511712
C5×#50762
C3×#653652
#117469552
#117469472
#117469212
#117458312
#106020503
#712585