Finite Group Databasebeta

← #14282947

Subgroups — #14282947

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754176C211yesmaximal, characteristic
2C5×#4718C211yesmaximal, characteristic
3#11748667C211yesmaximal, characteristic
4#11746288C211yesmaximal, characteristic
5C3×#64687C211yesmaximal, characteristic
6#11745964C211yesmaximal, characteristic
7#11745960C211yesmaximal, characteristic
8#10601585—31nomaximal, Hall
9#91813C2211yescharacteristic
10C2×C4×C5×Dic3C2211yescharacteristic
11C3×#4070C2211yescharacteristic
12#91575—21no—
13C2×Dic3⋊Dic5—21no—
14#91529—21no—
15C2×Dic3×Dic5—21no—
16#91469C411yescharacteristic, complemented
17#91389C411yescharacteristic, complemented
18#91379—21no—
19#91340C411yescharacteristic, complemented
20Dic3×Dic10C411yescharacteristic, complemented
21#91324—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×Dic3⋊C8—21no—
26C5×C8×Dic3—21no—
27C3×#3963C2211yescharacteristic
28#68309—51nomaximal, Hall
29#65804—31no—
30C5×#431—31no—
31C4×C4⋊Dic5—31no—
32#64687—31no—
33#64687—31no—
34#64687—31no—
35#64687D311yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×Dic30C2×C411yescharacteristic
39C22×C5×Dic3D411yescharacteristic
40C22×C5×Dic3D411yescharacteristic
41C22×C3×Dic5—21no—
42C2×C3×Dic10C2×C411yescharacteristic
43C2×#1204—21no—
44C2×C3×C5×C8—21no—
45#6719—21no—
46C4⋊Dic15C2×C411yescharacteristic
47#6712—21no—
48C4×C5×Dic3C2×C411yescharacteristic
49C4×C5×Dic3C2×C411yescharacteristic
50C4×C5×Dic3D411yescharacteristic
51C4×C5×Dic3D411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×C22⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56Dic3⋊Dic5—24no—
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59Dic3⋊Dic5—21no—
60#6669—21no—
61#6668—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—42no—
65#5622—51no—
66#4718D511yescharacteristic
67#4649—51no—
68C3×#328—51no—
69#4538—51no—
70#4467—51no—
71#4452—51no—
72C2×C42×C5—31no—
73#4072—61no—
74C2×C4⋊Dic5—61no—
75#4070—31no—
76#4070—61no—
77#4070C2×D311yescharacteristic
78C2×C4×Dic5—61no—
79#4016—61no—
80#4015—31no—
81#4015—31no—
82C4×Dic10—31no—
83C4×Dic10—31no—
84C4×Dic10—61no—
85C5×C4⋊C8—61no—
86C5×C22⋊C8—31no—
87C5×C22⋊C8C2×D311yescharacteristic
88C4×C5×C8—61no—
89#3963—31no—
90#3963C2×D311yescharacteristic
91#1503—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—22no—
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—41no—
100C2×Dic15—41no—
101Dic30—41no—
102C2×C5×Dic3—22no—
103C2×C5×Dic3C22⋊C411yescharacteristic
104C2×C5×Dic3C22⋊C411yescharacteristic
105C2×C5×Dic3C22⋊C411yescharacteristic
106C2×C5×Dic3C22⋊C411yescharacteristic
107C2×C5×Dic3SD1612yes—
108C2×C5×Dic3Q1612yes—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C3×Dic10—41no—
115#1204—42no—
116C3×C5×C8—41no—
117C5×C3⋊C8—41no—
118C3×C22⋊Q8—51no—
119Q8×Dic3—51no—
120#944—51no—
121#924—51no—
122C2×Dic3⋊C4—101no—
123C2×C4×Dic3—101no—
124C2×C4×Dic3C2×D511yescharacteristic
125#889—101no—
126#888—51no—
127#887—51no—
128#887—101no—
129#878—101no—
130#877—101no—
131C3×C22⋊C8C2×D511yescharacteristic
132C3×#95—51no—
133C3⋊#95—51no—
134#830C2×D511yescharacteristic
135Dic3⋊C8—21no—
136C8×Dic3—21no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—21no—
141C22×Dic5—61no—
142C2×Dic10—31no—
143C2×Dic10—61no—
144C2×Dic10C4×D311yescharacteristic
145C2×C5×C8—21no—
146C2×C5×C8—61no—
147C42×C5—31no—
148C42×C5—31no—
149C42×C5—31no—
150C42×C5—31no—
151C22⋊Dic5—21no—
152C22⋊Dic5—61no—
153C4⋊Dic5—31no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—61no—
157C4⋊Dic5—64no—
158C4⋊Dic5C4×D311yescharacteristic
159#683—21no—
160#683—61no—
161#683—61no—
162#683—61no—
163C4×Dic5—61no—
164C4×Dic5—61no—
165C4×Dic5—122no—
166#533—151no—
167#431—31no—
168C4×C4⋊C4—151no—
169#328—51no—
170#328—151no—
171#328—151no—
172#328—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5C2×Q1611yescharacteristic
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180Dic15—42no—
181Dic15—41no—
182Dic15—41no—
183C3×Dic5—42no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C5×Dic3—21no—
187C5×Dic3#10312yes—
188C5×Dic3#10312yes—
189C5×Dic3#10412yes—
190C2×C3×Q8—51no—
191C22×C3×C4—101no—
192C22×C3×C4C22×D511yescharacteristic
193C22×Dic3—101no—
194C22×Dic3D2011yescharacteristic
195C22×Dic3D2011yescharacteristic
196C2×Dic6—51no—
197C2×Dic6—101no—
198C2×C3×C8—21no—
199C3×C4⋊C4—51no—
200C3×C4⋊C4—101no—
201C3×C22⋊C4—101no—
202#217—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3—101no—
205Dic3⋊C4—104no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211C4×Dic3—101no—
212C4×Dic3—101no—
213C4×Dic3—202no—
214C4×Dic3C4×D511yescharacteristic
215C4×Dic3C4×D511yescharacteristic
216C4×Dic3C22⋊D511yescharacteristic
217C4×Dic3C22⋊D511yescharacteristic
218C2×C3⋊C8—21no—
219C23×C5D3×D411yescharacteristic
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—32no—
224C2×C4×C5—32no—
225C2×C4×C5—31no—
226C2×C4×C5—41no—
227C2×C4×C5—62no—
228C2×C4×C5C2×C4×D311yescharacteristic
229C2×C4×C5D3×D411yescharacteristic
230C2×Dic5—22no—
231C2×Dic5—21no—
232C2×Dic5—21no—
233C2×Dic5—41no—
234C2×Dic5—41no—
235C2×Dic5—62no—
236C2×Dic5—61no—
237C2×Dic5—61no—
238C2×Dic5—121no—
239C2×Dic5—121no—
240Dic10—41no—
241Dic10—122no—
242Dic10—121no—
243C5×C8—41no—
244C5×C8—121no—
245C4⋊Q8—151no—
246C4⋊Q8—151no—
247#125—301no—
248C22⋊Q8—51no—
249C22⋊Q8—151no—
250C22⋊Q8—301no—
251C4×Q8—151no—
252C4×Q8—151no—
253C4×Q8—301no—
254#117—301no—
255C2×C4⋊C4—301no—
256C2×C42—31no—
257C2×C42—301no—
258C4⋊C8—61no—
259C22⋊C8—31no—
260C22⋊C8D3×D511yescharacteristic
261C4×C8—61no—
262#95—51no—
263#95—151no—
264C2×C3×C5—21no—
265C2×C3×C5—21no—
266C2×C3×C5#41011yescharacteristic
267C2×C3×C5C2×#10311yescharacteristic
268C2×C3×C5C2×#10411yescharacteristic
269C23×C3C2×D2011yescharacteristic
270C3×Q8—201no—
271C2×C3×C4—41no—
272C2×C3×C4—102no—
273C2×C3×C4—101no—
274C2×C3×C4—101no—
275C2×C3×C4—201no—
276C2×C3×C4—201no—
277C2×C3×C4C2×C4×D511yescharacteristic
278C2×C3×C4C2×C22⋊D511yescharacteristic
279C2×Dic3—22no—
280C2×Dic3—102no—
281C2×Dic3—101no—
282C2×Dic3—101no—
283C2×Dic3—201no—
284C2×Dic3—201no—
285C2×Dic3#67712yes—
286C2×Dic3Dic2012yes—
287C2×Dic3#68511yescharacteristic
288C2×Dic3#68511yescharacteristic
289C2×Dic3#68511yescharacteristic
290C2×Dic3#68511yescharacteristic
291Dic6—202no—
292Dic6—201no—
293C3×C8—41no—
294C3⋊C8—41no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5D3×C22⋊C411yescharacteristic
298C22×C5D3×SD1611yescharacteristic
299C22×C5D3×Q1611yescharacteristic
300C4×C5—21no—
301C4×C5—21no—
302C4×C5—32no—
303C4×C5—32no—
304C4×C5—32no—
305C4×C5—61no—
306Dic5—42no—
307Dic5—41no—
308Dic5—41no—
309Dic5—122no—
310Dic5—121no—
311Dic5—121no—
312C2×Q8—51no—
313C2×Q8—151no—
314C2×Q8—301no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—101no—
318C22×C4—301no—
319C22×C4C2×D3×D511yescharacteristic
320C2×C8—21no—
321C2×C8—61no—
322C4⋊C4—51no—
323C4⋊C4—101no—
324C4⋊C4—151no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—304no—
331C4⋊C4—301no—
332C22⋊C4—101no—
333C22⋊C4—301no—
334C42—31no—
335C42—31no—
336C42—31no—
337C42—31no—
338C42—301no—
339C42—301no—
340C42—602no—
341C3×C5#150311yescharacteristic, complemented, Hall
342C22×C3—21no—
343C22×C3—21no—
344C22×C3C2×#67711yescharacteristic
345C22×C3C2×Dic2011yescharacteristic
346C22×C3C2×#68511yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—202no—
350C3×C4—201no—
351C3×C4—201no—
352Dic3—21no—
353Dic3—202no—
354Dic3—201no—
355Dic3—201no—
356Dic3#394812yes—
357Dic3#394812yes—
358Dic3#395712yes—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5#474011yescharacteristic
362C2×C5D3×#10311yescharacteristic
363C2×C5D3×#10411yescharacteristic
364C23D3×D2011yescharacteristic
365Q8—201no—
366Q8—601no—
367Q8—602no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—32no—
372C2×C4—32no—
373C2×C4—31no—
374C2×C4—41no—
375C2×C4—62no—
376C2×C4—102no—
377C2×C4—101no—
378C2×C4—101no—
379C2×C4—201no—
380C2×C4—201no—
381C2×C4—302no—
382C2×C4—301no—
383C2×C4—301no—
384C2×C4—601no—
385C2×C4—601no—
386C2×C4C4×D3×D511yescharacteristic
387C2×C4D3×C22⋊D511yescharacteristic
388C8—41no—
389C8—121no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3#6529511yescharacteristic
393C2×C3C2×#394811yescharacteristic
394C2×C3C2×#395711yescharacteristic
395C5#6830911yescharacteristic, complemented, Sylow
396C22—21no—
397C22—21no—
398C22D3×#67711yescharacteristic
399C22D3×Dic2011yescharacteristic
400C22D3×#68511yescharacteristic
401C4—21no—
402C4—21no—
403C4—32no—
404C4—32no—
405C4—32no—
406C4—61no—
407C4—202no—
408C4—201no—
409C4—201no—
410C4—602no—
411C4—601no—
412C4—601no—
413C3#1060158511yescharacteristic, complemented, Sylow
414C2—21no—
415C2—21no—
416C2#1174713011yescharacteristic
417C2D3×#394811yescharacteristic
418C2D3×#395711yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1503
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
16. #91469C4semidirect
17. #91389C4semidirect
19. #91340C4semidirect
20. Dic3×Dic10C4semidirect
341. C3×C5#1503semidirect
395. C5#68309semidirect
413. C3#10601585semidirect

Maximal subgroups

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

subgroupindex
#117541762
C5×#47182
#117486672
#117462882
C3×#646872
#117459642
#117459602
#106015853
#683095