Finite Group Databasebeta

← #14472137

Subgroups — #14472137

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65876C211yesmaximal, characteristic
2#11752487C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic
4C5×#5007C211yesmaximal, characteristic
5#11749085C212yesmaximal
6#11749002C212yesmaximal
7#11747391C212yesmaximal, complemented
8#11747270C212yesmaximal, complemented
9#11747104C211yesmaximal, characteristic, complemented
10#11746924C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612725—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14C2×#6716C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×#4082C2212yes—
18C3×#4072—21no—
19C3×#4070—21no—
20C3×#4033C2212yes—
21C3×#4025—22no—
22C3×#4015C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91388C2212yes—
25#91385—21no—
26#91344—21no—
27#91336—22no—
28#91333C2212yes—
29C2×#6662C2212yes—
30#91116C2211yescharacteristic
31#91094C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#832C2212yes—
35C5×#807C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37#90982C2212yes—
38#90971C2212yes—
39#90970C2212yes—
40#90970C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83676—51nomaximal, Hall
43#66055—31no—
44#65876D311yescharacteristic
45C5×#474—31no—
46#65382—31no—
47C4×#687—31no—
48#65166—32no—
49#65162—32no—
50#65138—31no—
51#65119—31no—
52#65057—32no—
53#65056—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6—21no—
58C2×C3×Dic10D411yescharacteristic
59C2×C3×Dic10C2312yes—
60C3×C5×C4⋊C4C2311yescharacteristic
61C3×C5×C22⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63#6716—22no—
64C4⋊Dic15C2311yescharacteristic
65#6712—21no—
66C4×Dic15—21no—
67C2×C3⋊#168C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×C4⋊Dic3—21no—
70C5×C4⋊Dic3C2312yes—
71C2×C5×C3⋊C8C2312yes—
72C3×C22⋊Dic5—22no—
73C3×C22⋊Dic5—22no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5D411yescharacteristic
77C3×#683—22no—
78C3×#683D412yes—
79C3×C4×Dic5—22no—
80C3×C4×Dic5C2312yes—
81Dic3⋊Dic5—22no—
82#6669—22no—
83#6669—22no—
84Dic3×Dic5—22no—
85#6662—24no—
86C3×#556—51no—
87#5567—51no—
88#5090—51no—
89#5079—51no—
90#5056—52no—
91#5054—52no—
92C4×#216—52no—
93Q8×C3⋊C8—51no—
94#5022—52no—
95C4×#214—51no—
96#5007D511yescharacteristic
97C5×C4⋊Q8—31no—
98C4×C5×D4C2×D311yescharacteristic
99Q8×Dic5—61no—
100#4090—61no—
101#4082C2×D312yes—
102C2×#687—31no—
103#4072—21no—
104#4070—21no—
105C2×Dic20—32no—
106#4036—32no—
107#4035—62no—
108#4033—32no—
109#4033C2×D312yes—
110#4025—22no—
111#4015C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#107—32no—
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3964—31no—
118#3948—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3942—32no—
122#3942—32no—
123#3942—31no—
124#3940—31no—
125C4×#168—31no—
126#3364—151noSylow
127C23×C3×C5—21no—
128C3×C5×D4—21no—
129C3×C5×D4—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—42no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—21no—
137Dic30—21no—
138Dic30#4112yes—
139C2×C5×Dic3—22no—
140C5×Dic6—42no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5C2×D412yes—
143C2×C3×Dic5C2×D412yes—
144C3×Dic10—22no—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3⋊#168—21no—
148C3⋊#168—21no—
149C5×C3⋊C8—22no—
150C3×C4⋊Q8—51no—
151C3×#126—102no—
152C3×#124—52no—
153C3×C22⋊Q8—101no—
154C3×C4×Q8—51no—
155C3×C4×Q8—52no—
156C3×C4×D4C2×D511yescharacteristic
157C3×#117—101no—
158#944—101no—
159C2×#216—52no—
160C2×#214—51no—
161#889—102no—
162#887—101no—
163#870—52no—
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6—52no—
167#835—52no—
168#835—52no—
169#835—52no—
170#832—51no—
171#832C2×D512yes—
172#810—51no—
173#808—51no—
174#807C2×D512yes—
175C4⋊(C3⋊C8)—52no—
176C4⋊(C3⋊C8)C2×D511yescharacteristic
177C4×C3⋊C8—51no—
178C4×C3⋊C8—52no—
179C2×C5×Q8—61no—
180C2×C5×D4C22×D311yescharacteristic
181C22×C4×C5—21no—
182C2×Dic10—31no—
183C2×Dic10#6711yescharacteristic
184C2×Dic10C22×D312yes—
185C2×C5×C8—32no—
186C5×C4⋊C4—32no—
187C5×C4⋊C4—61no—
188C5×C4⋊C4C22×D311yescharacteristic
189C5×C22⋊C4—21no—
190C42×C5C22×D311yescharacteristic
191C22⋊Dic5—22no—
192C22⋊Dic5—22no—
193#687—62no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—31no—
197C4⋊Dic5—62no—
198C4⋊Dic5#6711yescharacteristic
199#683—22no—
200#683—61no—
201#683—62no—
202#683—62no—
203#683#6712yes—
204C4×Dic5—22no—
205C4×Dic5—61no—
206C4×Dic5—62no—
207C4×Dic5C22×D312yes—
208C2×#168—31no—
209C2×#168—31no—
210Dic20—64no—
211#557—151no—
212#556—51no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—31no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5—41no—
223C22×C3×C5—41no—
224C22×C3×C5—41no—
225C22×C3×C5C22×D411yescharacteristic
226C3×C4×C5—21no—
227C3×C4×C5—41no—
228C3×C4×C5#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—22no—
232Dic15—41no—
233C3×Dic5—22no—
234C3×Dic5—22no—
235C3×Dic5—42no—
236C5×Dic3—42no—
237C2×C3×Q8—51no—
238C2×C3×Q8—52no—
239C2×C3×D4C22×D511yescharacteristic
240C22×C3×C4—21no—
241C2×Dic6—21no—
242C2×Dic6—51no—
243C3×C4⋊C4—52no—
244C3×C4⋊C4—51no—
245C3×C4⋊C4—102no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4C22×D511yescharacteristic
249C3×C22⋊C4—21no—
250C3×C22⋊C4—102no—
251C3×C22⋊C4—102no—
252C3×C42—52no—
253C3×C42—102no—
254C3×C42C22×D511yescharacteristic
255#216—104no—
256#214—102no—
257C4⋊Dic3—21no—
258C4⋊Dic3—51no—
259C4⋊Dic3C22×D512yes—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—101no—
264C4×Dic3—102no—
265C4×Dic3—101no—
266C2×C3⋊C8—51no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8C22×D512yes—
269C23×C5—21no—
270C5×Q8—122no—
271C5×D4—21no—
272C5×D4—21no—
273C2×C4×C5—21no—
274C2×C4×C5—42no—
275C2×C4×C5—62no—
276C2×C4×C5C2×#6711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—22no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5C2×#6712yes—
283C2×Dic5C2×#6712yes—
284Dic10—22no—
285Dic10—22no—
286Dic10—22no—
287Dic10—32no—
288Dic10—61no—
289C5×C8—62no—
290#168—61no—
291#168—61no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—51no—
296C4⋊Q8—301no—
297#126—102no—
298#125—152no—
299#125—302no—
300#124—52no—
301C22⋊Q8—101no—
302C4×Q8—51no—
303C4×Q8—52no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4D3×D511yescharacteristic
308#117—101no—
309#107—32no—
310#106—151no—
311C4⋊C8—31no—
312C4⋊C8—152no—
313#103—152no—
314#103—152no—
315#103—152no—
316#103—151no—
317#102—32no—
318#102—151no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5—81no—
322C2×C3×C5#54811yescharacteristic
323C2×C3×C5C2×#13511yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C23×C3—21no—
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—102no—
329C3×D4—21no—
330C3×D4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—42no—
333C2×C3×C4—52no—
334C2×C3×C4—52no—
335C2×C3×C4—102no—
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4C23×D511yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—101no—
341C2×Dic3—101no—
342Dic6—42no—
343Dic6—52no—
344Dic6—101no—
345C3⋊C8—22no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C22×#6711yescharacteristic
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—122no—
355C4×C5#95012yes—
356C4×C5D3×#4111yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—22no—
359Dic5—22no—
360Dic5—42no—
361Dic5—62no—
362Dic5—121no—
363C2×Q8—51no—
364C2×Q8—52no—
365C2×Q8—61no—
366C2×Q8—151no—
367C2×D4C2×D3×D511yescharacteristic
368C22×C4—21no—
369Q16—304no—
370SD16—302no—
371C2×C8—32no—
372C2×C8—151no—
373C2×C8—151no—
374C4⋊C4—32no—
375C4⋊C4—51no—
376C4⋊C4—52no—
377C4⋊C4—61no—
378C4⋊C4—102no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—151no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—301no—
386C4⋊C4C2×D3×D511yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—102no—
389C22⋊C4—102no—
390C42—52no—
391C42—102no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3C2×D4×D511yescharacteristic
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—102no—
403C3×C4—102no—
404C3×C4—202no—
405C3×C4#405812yes—
406C3×C4#414711yescharacteristic
407C3×C4D5×#4111yescharacteristic
408Dic3—42no—
409Dic3—102no—
410Dic3—201no—
411C2×C5—81no—
412C2×C5C2×#95011yescharacteristic
413C2×C5#583111yescharacteristic
414C2×C5#583811yescharacteristic
415C23—21no—
416Q8—102no—
417Q8—102no—
418Q8—102no—
419Q8—122no—
420Q8—152no—
421Q8—301no—
422D4—21no—
423D4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—52no—
427C2×C4—52no—
428C2×C4—62no—
429C2×C4—102no—
430C2×C4—301no—
431C2×C4—301no—
432C2×C4D5×#6711yescharacteristic
433C2×C4D5×#6711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—62no—
436C8—301no—
437C8—301no—
438C2×C3—81no—
439C2×C3#6596711yescharacteristic
440C2×C3C2×#405811yescharacteristic
441C2×C3#6611311yescharacteristic
442C5#8367611yescharacteristic, complemented, Sylow
443C22—41no—
444C22—41no—
445C22—41no—
446C22C2×D5×#6711yescharacteristic
447C4—21no—
448C4—41no—
449C4—102no—
450C4—102no—
451C4—122no—
452C4—202no—
453C4—302no—
454C4—601no—
455C4#9149012yes—
456C4#9200011yescharacteristic
457C4#9201611yescharacteristic
458C3#1061272511yescharacteristic, complemented, Sylow
459C2—81no—
460C2#1175421511yescharacteristic
461C2C2×#9149011yescharacteristic
462C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752487C2semidirect
7. #11747391C2semidirect
8. #11747270C2semidirect
9. #11747104C2semidirect
10. #11746924C2semidirect
11. #11746846C2semidirect
395. C3×C5#3364semidirect
442. C5#83676semidirect
458. C3#10612725semidirect

Maximal subgroups

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

subgroupindex
C3×#658762
#117524872
C4×#67162
C5×#50072
#117490852
#117490022
#117473912
#117472702
#117471042
#117469242
#117468462
#106127253
#836765