Finite Group Databasebeta

← #14316214

Subgroups — #14316214

Order 1920.

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

normal subgroups only

This group has 432 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
1C2×C3×D5×Q16C211yesmaximal, characteristic
2C2×C5×#829C211yesmaximal, characteristic, complemented
3#11747942C211yesmaximal, characteristic
4C2×#90946C211yesmaximal, characteristic, complemented
5#11746385C211yesmaximal, characteristic, complemented
6#11745898C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic
8#10602295—31nomaximal, Hall
9C2×C3×Q8×D5—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×C5×Dic12C2211yescharacteristic
12C2×C3×#689—21no—
13C3×D5×Q16—22no—
14C3×D5×Q16—22no—
15C2×C3×Dic20C2211yescharacteristic
16C2×C3×C8×D5C2211yescharacteristic
17#91359—21no—
18#91102C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20C5×#829—22no—
21C2×C5×C3⋊C16C2211yescharacteristic
22#90973—21no—
23#90946—22no—
24#72064—51nomaximal, Hall
25C2×D5×Q16D311yescharacteristic
26C2×C5×Q32—31no—
27#65477—31no—
28C2×#3961—31no—
29#64784—31no—
30#64727—31no—
31#64723—31no—
32C2×C3×C5×Q8—21no—
33C2×C5×Dic6—21no—
34C3×Q8×D5—24no—
35C3×Q8×D5—42no—
36C2×C3×C4×D5—41no—
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×Dic10—21no—
39C2×C3×Dic10—41no—
40C3×C5×Q16—21no—
41C3×C5×Q16D412yes—
42C2×C3×C5×C8C2311yescharacteristic
43C4⋊Dic15—21no—
44C5×Dic12—21no—
45C5×Dic12—21no—
46C3×#689—24no—
47C2×C3×#168D411yescharacteristic
48C3×Dic20—21no—
49C3×Dic20D412yes—
50C3×C8×D5—21no—
51C3×C8×D5—21no—
52#6669—41no—
53#6665—41no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C22×C3×Q16—51no—
57C2×#829—51no—
58C2×#829D511yescharacteristic, complemented
59#5116—51no—
60#4564—51no—
61#4564—51no—
62#4549—51no—
63C2×Q8×D5—21no—
64C2×C5×Q16—31no—
65C2×C5×Q16C2×D311yescharacteristic
66#4092—61no—
67C2×#689—21no—
68D5×Q16—22no—
69D5×Q16—22no—
70C2×Dic20C2×D311yescharacteristic
71C2×C8×D5C2×D311yescharacteristic
72C5×Q32—62no—
73C2×C5×C16—31no—
74#3967—61no—
75#3961—62no—
76#3950—31no—
77C2×#672—31no—
78#2188—151noSylow
79C22×C3×D5D811yescharacteristic
80C3×C5×Q8—22no—
81C3×C5×Q8—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×Dic15—41no—
85C2×C5×Dic3—41no—
86C5×Dic6—41no—
87C5×Dic6—41no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5D811yescharacteristic
90C3×C4×D5—21no—
91C3×C4×D5—21no—
92C3×C4×D5—44no—
93C3×Dic10—22no—
94C3×Dic10—44no—
95C3×Dic10—41no—
96C3×C5×C8C2×D411yescharacteristic
97C3×C5×C8C2×D411yescharacteristic
98C3×#168—21no—
99C22×C3×Q8—101no—
100C2×C3×Q16—51no—
101C2×C3×Q16—101no—
102C2×C3×Q16—102no—
103C2×C3×Q16—102no—
104C2×C3×Q16C2×D511yescharacteristic
105C22×C3×C8—51no—
106#924—101no—
107C2×Dic12C2×D511yescharacteristic
108#829—22no—
109#829—102no—
110#818—51no—
111#816—101no—
112C2×C3⋊C16—51no—
113C2×C3⋊C16C2×D511yescharacteristic
114C2×C5×Q8—21no—
115C2×C5×Q8—61no—
116Q8×D5—24no—
117Q8×D5—42no—
118C2×C4×D5—41no—
119C2×C4×D5#6711yescharacteristic
120C2×Dic10—21no—
121C2×Dic10—41no—
122C5×Q16—21no—
123C5×Q16—61no—
124C5×Q16—61no—
125C5×Q16#6712yes—
126C2×C5×C8C22×D311yescharacteristic
127#689—24no—
128#685—121no—
129C4⋊Dic5—61no—
130#683—121no—
131C2×#168#6711yescharacteristic
132Dic20—21no—
133Dic20#6712yes—
134C8×D5—21no—
135C8×D5—21no—
136C5×C16—61no—
137#672—61no—
138C22×Q16—51no—
139C2×Q32—31no—
140C2×Q32—151no—
141#467—151no—
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—42no—
150C3×C4×C5#12011yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152Dic15—81no—
153C3×Dic5—21no—
154C3×Dic5—42no—
155C5×Dic3—81no—
156C2×C3×Q8—21no—
157C2×C3×Q8—104no—
158C2×C3×Q8—101no—
159C2×C3×Q8—201no—
160C2×C3×Q8—202no—
161C22×C3×C4—51no—
162C22×C3×C4—201no—
163C2×Dic6—21no—
164C3×Q16—21no—
165C3×Q16—52no—
166C3×Q16—104no—
167C3×Q16—101no—
168C3×Q16C22⋊D512yes—
169C2×C3×C8—51no—
170C2×C3×C8—101no—
171C2×C3×C8—101no—
172C2×C3×C8C22×D511yescharacteristic
173#217—201no—
174C4⋊Dic3—101no—
175Dic3⋊C4—201no—
176Dic12—21no—
177Dic12—21no—
178C3⋊C16—21no—
179C3⋊C16—101no—
180C22×D5#21311yescharacteristic
181C5×Q8—22no—
182C5×Q8—41no—
183C5×Q8—121no—
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—44no—
194Dic10—22no—
195Dic10—44no—
196Dic10—41no—
197C5×C8C2×#6711yescharacteristic
198C5×C8C2×#6711yescharacteristic
199#168—21no—
200C22×Q8—101no—
201C2×Q16—31no—
202C2×Q16—51no—
203C2×Q16—101no—
204C2×Q16—102no—
205C2×Q16—102no—
206C2×Q16D3×D511yescharacteristic
207C22×C8—51no—
208C22⋊Q8—301no—
209Q32—62no—
210Q32—302no—
211C2×C16—31no—
212C2×C16—151no—
213#107—151no—
214#103—301no—
215C2×C3×C5#44711yescharacteristic
216C2×C3×C5C2×Q3211yescharacteristic
217C2×C3×C5#51011yescharacteristic
218C3×D5—22no—
219C23×C3—51no—
220C3×Q8—22no—
221C3×Q8—41no—
222C3×Q8—102no—
223C3×Q8—204no—
224C3×Q8—201no—
225C2×C3×C4—41no—
226C2×C3×C4—51no—
227C2×C3×C4—101no—
228C2×C3×C4—101no—
229C2×C3×C4—204no—
230C2×C3×C4—201no—
231C2×C3×C4D4×D511yescharacteristic
232C2×Dic3—41no—
233C2×Dic3—201no—
234Dic6—41no—
235Dic6—41no—
236C3×C8—101no—
237C3×C8D4×D511yescharacteristic
238C3×C8C2×C22⋊D511yescharacteristic
239C22×C5C2×#21311yescharacteristic
240C2×D5—21no—
241C2×D5—21no—
242C2×D5#82912yescomplemented
243C4×C5—42no—
244C4×C5—241no—
245C4×C5#93211yescharacteristic
246C4×C5#95311yescharacteristic
247Dic5—21no—
248Dic5—42no—
249Dic5—241no—
250C2×Q8—21no—
251C2×Q8—61no—
252C2×Q8—104no—
253C2×Q8—101no—
254C2×Q8—201no—
255C2×Q8—202no—
256C22×C4—51no—
257C22×C4—201no—
258Q16—21no—
259Q16—52no—
260Q16—61no—
261Q16—61no—
262Q16—104no—
263Q16—101no—
264Q16#120112yes—
265C2×C8—51no—
266C2×C8—101no—
267C2×C8—101no—
268C2×C8C2×D3×D511yescharacteristic
269C4⋊C4—301no—
270C4⋊C4—601no—
271C22⋊C4—601no—
272C16—61no—
273C16—301no—
274C3×C5#218811yescharacteristic, complemented, Hall
275C22×C3—52no—
276C22×C3—101no—
277C22×C3—101no—
278C22×C3D5×D811yescharacteristic
279C3×C4—42no—
280C3×C4—101no—
281C3×C4—202no—
282C3×C4#405711yescharacteristic
283C3×C4#408311yescharacteristic
284Dic3—81no—
285Dic3—401no—
286C2×C5#517911yescharacteristic
287C2×C5C2×#82911yescharacteristic
288C2×C5#521711yescharacteristic
289D5—22no—
290C23—51no—
291Q8—22no—
292Q8—41no—
293Q8—102no—
294Q8—121no—
295Q8—121no—
296Q8—204no—
297Q8—201no—
298C2×C4—41no—
299C2×C4—51no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—121no—
303C2×C4—204no—
304C2×C4—201no—
305C2×C4—601no—
306C2×C4D5×#6711yescharacteristic
307C8—101no—
308C8C2×#120111yescharacteristic
309C8D5×#6711yescharacteristic
310C2×C3—102no—
311C2×C3D5×Q3211yescharacteristic
312C2×C3#6520711yescharacteristic
313C2×C3#6544511yescharacteristic
314C5#7206411yescharacteristic, complemented, Sylow
315C22—52no—
316C22—101no—
317C22—101no—
318C22D5×#21311yescharacteristic
319C4—42no—
320C4—101no—
321C4—202no—
322C4—241no—
323C4—1201no—
324C4#9148911yescharacteristic
325C4#9156311yescharacteristic
326C3#1060229511yescharacteristic, complemented, Sylow
327C2—102no—
328C2D5×#82911yescharacteristic
329C2#1174830211yescharacteristic
330C2#1174902111yescharacteristic
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×C5×#829C2semidirect
4. C2×#90946C2semidirect
5. #11746385C2semidirect
6. #11745898C2semidirect
58. C2×#829D5semidirect
148. C2×C3×D5Q32semidirect
242. C2×D5#829semidirect
274. C3×C5#2188semidirect
314. C5#72064semidirect
326. C3#10602295semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×Q162
C2×C5×#8292
#117479422
C2×#909462
#117463852
#117458982
#117458792
#106022953
#720645