Finite Group Databasebeta

← #14316211

Subgroups — #14316211

Order 1920.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×D5×Dic12C211yesmaximal, characteristic
2C2×#91113C211yesmaximal, characteristic, complemented
3C2×C5×#829C211yesmaximal, characteristic, complemented
4C3×#65477C211yesmaximal, characteristic
5#11745901C211yesmaximal, characteristic, complemented
6#11745899C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic
8#10602295—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×Dic60C2211yescharacteristic
12C2×C5×Dic12C2211yescharacteristic
13C3×#4092—21no—
14C2×C3×C8×D5C2211yescharacteristic
15C2×#6663—21no—
16D5×Dic12—22no—
17D5×Dic12—22no—
18#91113—22no—
19C2×C3⋊#672C2211yescharacteristic
20C5×#829—22no—
21C2×C5×C3⋊C16C2211yescharacteristic
22C3×#3967—21no—
23C3×#3950C2211yescharacteristic
24#71087—51nomaximal, Hall
25C2×D5×Q16—31no—
26C2×C5×Q32—31no—
27#65477D311yescharacteristic
28C2×#3961—31no—
29#64784—31no—
30#64727—31no—
31#64723—31no—
32C2×C3×C5×Q8—21no—
33C2×Dic30—21no—
34C2×C5×Dic6—21no—
35C2×C3×C4×D5D411yescharacteristic
36C2×#1204—41no—
37C2×D5×Dic3—41no—
38D5×Dic6—24no—
39D5×Dic6—42no—
40C3×C5×Q16—21no—
41C3×C5×Q16—21no—
42C2×C3×C5×C8C2311yescharacteristic
43Dic60—21no—
44Dic60D412yes—
45C5×Dic12—21no—
46C5×Dic12D412yes—
47C3×#685—41no—
48C3×C4⋊Dic5—21no—
49C3×#683—41no—
50C2×C3×#168D411yescharacteristic
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6663—24no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C22×Dic12—51no—
57C3×#467—51no—
58C2×#829—51no—
59C2×#829D511yescharacteristic, complemented
60#4549—51no—
61#4492—51no—
62#4492—51no—
63C2×Q8×D5—61no—
64C2×C5×Q16—31no—
65C2×C5×Q16C2×D311yescharacteristic
66#4092—21no—
67C2×#689—61no—
68D5×Q16—62no—
69D5×Q16—62no—
70C2×Dic20—31no—
71C2×C8×D5C2×D311yescharacteristic
72C5×Q32—62no—
73C2×C5×C16—31no—
74#3967—21no—
75#3961—62no—
76#3950C2×D311yescharacteristic
77C2×#672—31no—
78#2188—151noSylow
79C22×C3×D5D811yescharacteristic
80C3×C5×Q8—41no—
81C3×C5×Q8—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×Dic15—41no—
85Dic30—22no—
86Dic30—41no—
87C2×C5×Dic3—41no—
88C5×Dic6—22no—
89C5×Dic6—41no—
90C2×C3×Dic5—41no—
91C2×C3×Dic5D811yescharacteristic
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94#1204—44no—
95D5×Dic3—44no—
96C3×C5×C8C2×D411yescharacteristic
97C3×C5×C8C2×D411yescharacteristic
98C3×#168—21no—
99C22×Dic6—101no—
100C2×C3×Q16C2×D511yescharacteristic
101C22×C3×C8—51no—
102C3×C22⋊Q8—101no—
103C2×Dic12—51no—
104C2×Dic12—102no—
105C2×Dic12—101no—
106C2×Dic12—102no—
107C2×Dic12C2×D511yescharacteristic
108C3×#107—51no—
109C3×#103—101no—
110#829—22no—
111#829—102no—
112C2×C3⋊C16—51no—
113C2×C3⋊C16C2×D511yescharacteristic
114C2×C5×Q8—21no—
115C2×C5×Q8—61no—
116Q8×D5—64no—
117Q8×D5—122no—
118C2×C4×D5—121no—
119C2×C4×D5#6711yescharacteristic
120C2×Dic10—61no—
121C2×Dic10—121no—
122C5×Q16—21no—
123C5×Q16—21no—
124C5×Q16—32no—
125C5×Q16—61no—
126C2×C5×C8C22×D311yescharacteristic
127#689—64no—
128#685—41no—
129C4⋊Dic5—21no—
130#683—41no—
131C2×#168#6711yescharacteristic
132Dic20—32no—
133Dic20—61no—
134C8×D5—21no—
135C8×D5—21no—
136C5×C16—61no—
137#672—61no—
138C22×Q16—151no—
139C2×Q32—31no—
140C2×Q32—151no—
141#467—51no—
142#358—151no—
143#358—151no—
144C22⋊C16—151no—
145C22×C3×C5C2×D811yescharacteristic
146C2×C3×D5—21no—
147C2×C3×D5—21no—
148C2×C3×D5Q3212yescomplemented
149C3×C4×C5—81no—
150C3×C4×C5#12011yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152Dic15—42no—
153C3×Dic5—21no—
154C3×Dic5—81no—
155C5×Dic3—42no—
156C2×C3×Q8—21no—
157C22×C3×C4—51no—
158C22×Dic3—201no—
159C2×Dic6—21no—
160C2×Dic6—104no—
161C2×Dic6—101no—
162C2×Dic6—202no—
163C2×Dic6—201no—
164C3×Q16—21no—
165C3×Q16—21no—
166C2×C3×C8—51no—
167C2×C3×C8—101no—
168C2×C3×C8—101no—
169C2×C3×C8C22×D511yescharacteristic
170C3×C4⋊C4—101no—
171C3×C4⋊C4—201no—
172C3×C22⋊C4—201no—
173Dic12—21no—
174Dic12—52no—
175Dic12—104no—
176Dic12—101no—
177Dic12C22⋊D512yes—
178C3⋊C16—21no—
179C3⋊C16—101no—
180C22×D5#21311yescharacteristic
181C5×Q8—41no—
182C5×Q8—41no—
183C5×Q8—62no—
184C5×Q8—121no—
185C2×C4×C5—41no—
186C2×C4×C5—121no—
187C2×C4×C5C2×#6711yescharacteristic
188C2×Dic5—41no—
189C2×Dic5—121no—
190C2×Dic5#21311yescharacteristic
191C4×D5—21no—
192C4×D5—21no—
193C4×D5—124no—
194Dic10—62no—
195Dic10—124no—
196Dic10—121no—
197C5×C8D3×D411yescharacteristic
198C5×C8D3×D411yescharacteristic
199#168—21no—
200C22×Q8—301no—
201C2×Q16—31no—
202C2×Q16—151no—
203C2×Q16—301no—
204C2×Q16—302no—
205C2×Q16—302no—
206C2×Q16D3×D511yescharacteristic
207C22×C8—51no—
208C22⋊Q8—101no—
209Q32—62no—
210Q32—302no—
211C2×C16—31no—
212C2×C16—151no—
213#107—51no—
214#103—101no—
215C2×C3×C5#44711yescharacteristic
216C2×C3×C5C2×Q3211yescharacteristic
217C2×C3×C5#51011yescharacteristic
218C3×D5—22no—
219C23×C3—51no—
220C3×Q8—41no—
221C3×Q8—41no—
222C2×C3×C4—41no—
223C2×C3×C4—51no—
224C2×C3×C4—101no—
225C2×C3×C4—101no—
226C2×C3×C4—201no—
227C2×C3×C4D4×D511yescharacteristic
228C2×Dic3—41no—
229C2×Dic3—204no—
230C2×Dic3—201no—
231Dic6—22no—
232Dic6—41no—
233Dic6—102no—
234Dic6—204no—
235Dic6—201no—
236C3×C8—101no—
237C3×C8D4×D511yescharacteristic
238C3×C8C2×C22⋊D511yescharacteristic
239C22×C5C2×#21311yescharacteristic
240C2×D5—21no—
241C2×D5—21no—
242C2×D5#82912yescomplemented
243C4×C5—81no—
244C4×C5—122no—
245C4×C5#93711yescharacteristic
246C4×C5#94911yescharacteristic
247Dic5—21no—
248Dic5—81no—
249Dic5—122no—
250C2×Q8—21no—
251C2×Q8—61no—
252C2×Q8—304no—
253C2×Q8—301no—
254C2×Q8—601no—
255C2×Q8—602no—
256C22×C4—51no—
257C22×C4—601no—
258Q16—21no—
259Q16—21no—
260Q16—32no—
261Q16—61no—
262Q16—152no—
263Q16—304no—
264Q16—301no—
265C2×C8—51no—
266C2×C8—101no—
267C2×C8—101no—
268C2×C8C2×D3×D511yescharacteristic
269C4⋊C4—101no—
270C4⋊C4—201no—
271C22⋊C4—201no—
272C16—61no—
273C16—301no—
274C3×C5#218811yescharacteristic, complemented, Hall
275C22×C3—52no—
276C22×C3—101no—
277C22×C3—101no—
278C22×C3D5×D811yescharacteristic
279C3×C4—81no—
280C3×C4—101no—
281C3×C4—401no—
282C3×C4#405711yescharacteristic
283C3×C4#408311yescharacteristic
284Dic3—42no—
285Dic3—202no—
286C2×C5#503611yescharacteristic
287C2×C5C2×#82911yescharacteristic
288C2×C5#519511yescharacteristic
289D5—22no—
290C23—51no—
291Q8—41no—
292Q8—41no—
293Q8—62no—
294Q8—121no—
295Q8—302no—
296Q8—604no—
297Q8—601no—
298C2×C4—41no—
299C2×C4—51no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—121no—
303C2×C4—201no—
304C2×C4—604no—
305C2×C4—601no—
306C2×C4D5×#6711yescharacteristic
307C8—101no—
308C8D3×C22⋊D511yescharacteristic
309C8#679011yescharacteristic
310C2×C3—102no—
311C2×C3D5×Q3211yescharacteristic
312C2×C3#6520711yescharacteristic
313C2×C3#6544511yescharacteristic
314C5#7108711yescharacteristic, complemented, Sylow
315C22—52no—
316C22—101no—
317C22—101no—
318C22D5×#21311yescharacteristic
319C4—81no—
320C4—101no—
321C4—122no—
322C4—401no—
323C4—602no—
324C4#9147811yescharacteristic
325C4#9157711yescharacteristic
326C3#1060229511yescharacteristic, complemented, Sylow
327C2—102no—
328C2D5×#82911yescharacteristic
329C2#1174829511yescharacteristic
330C2#1174915111yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
prime radicalC22×C3×D5D8
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2188
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#91113C2semidirect
3. C2×C5×#829C2semidirect
5. #11745901C2semidirect
6. #11745899C2semidirect
59. C2×#829D5semidirect
148. C2×C3×D5Q32semidirect
242. C2×D5#829semidirect
274. C3×C5#2188semidirect
314. C5#71087semidirect
326. C3#10602295semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic122
C2×#911132
C2×C5×#8292
C3×#654772
#117459012
#117458992
#117458792
#106022953
#710875