Finite Group Databasebeta

← #14472173

Subgroups — #14472173

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
1#11752491C211yesmaximal, characteristic
2#11752487C211yesmaximal, characteristic, complemented
3#11750950C211yesmaximal, characteristic, complemented
4C5×#4846C211yesmaximal, characteristic
5C3×#65119C211yesmaximal, characteristic, complemented
6#11747963C212yesmaximal
7#11747858C212yesmaximal, complemented
8#11747853C212yesmaximal
9#11747851C212yesmaximal, complemented
10C4×#6659C211yesmaximal, characteristic
11#11746930C211yesmaximal, characteristic, complemented
12#10612725—31nomaximal, Hall
13C2×Dic60C2212yes—
14#91758C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91388C2212yes—
20#91385—21no—
21#91373C2212yes—
22#91369—21no—
23#91344—21no—
24#91342—22no—
25#91338—21no—
26#91336—22no—
27#91333C2212yes—
28#91333C2212yes—
29C2×#6659C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91100C2212yes—
32C5×#821C2212yes—
33C5×#818C2212yes—
34C3×#3946C2212yes—
35C3×C8×Dic5C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90985C2211yescharacteristic
38#90975C2211yescharacteristic
39#90975C2212yes—
40#90975C2212yes—
41#90967C2211yescharacteristic
42#79934—51nomaximal, Hall
43#66055—31no—
44#65876—31no—
45C5×#474—31no—
46#65382—31no—
47C4×#687—31no—
48#65166—32no—
49#65162—32no—
50#65138—31no—
51#65119D311yescharacteristic, complemented
52#65057—32no—
53#65056—32no—
54C2×Dic30C2312yes—
55C2×Dic30C2311yescharacteristic
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C5×Dic6—21no—
59C2×C3×Dic10D411yescharacteristic
60C2×C3×C5×C8C2312yes—
61C3×C42×C5C2311yescharacteristic
62C4⋊Dic15—21no—
63C4⋊Dic15—21no—
64C4⋊Dic15C2311yescharacteristic
65#6712—21no—
66C4×Dic15—21no—
67Dic60—24no—
68C5×(C2×D3)⋊C4—21no—
69C5×C4⋊Dic3—21no—
70C5×C4⋊Dic3C2312yes—
71C5×C4⋊Dic3C2311yescharacteristic
72C3×C4⋊Dic5D411yescharacteristic
73C3×#683D412yes—
74C3×C4×Dic5C2312yes—
75C2×C3×#168C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77Dic3⋊Dic5—22no—
78#6669—22no—
79#6669—22no—
80#6669—22no—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6659—22no—
86#5584—51no—
87#5567—51no—
88C3×C8×Q8—51no—
89#4849—51no—
90#4846D511yescharacteristic
91#4845—52no—
92#4829—52no—
93C4×Dic12—52no—
94#4697—52no—
95C4×#204—51no—
96#4681—51no—
97C5×C4⋊Q8—31no—
98C4×C5×D4—31no—
99Q8×Dic5—61no—
100#4090—61no—
101#4082—32no—
102C2×#687—31no—
103#4072—61no—
104#4070—61no—
105C2×Dic20—32no—
106#4036—32no—
107#4035—62no—
108#4033—32no—
109#4033—32no—
110#4025—62no—
111#4015—31no—
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#107—32no—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102—32no—
117#3964—31no—
118#3948—32no—
119#3946C2×D312yes—
120C8×Dic5C2×D312yes—
121#3942—31no—
122#3942—32no—
123#3942—32no—
124#3940—31no—
125C4×#168C2×D311yescharacteristic
126#3364—151noSylow
127C22×C5×D3—21no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—21no—
132C2×Dic15—22no—
133C2×Dic15—21no—
134Dic30—21no—
135Dic30—22no—
136Dic30—22no—
137Dic30#4112yes—
138C2×C5×Dic3—21no—
139C2×C5×Dic3—22no—
140C5×D12—21no—
141C5×D12—21no—
142C4×C5×D3—42no—
143C5×Dic6—42no—
144C2×C3×Dic5C2×D412yes—
145C2×C3×Dic5C2×D412yes—
146C3×Dic10—22no—
147C3×C5×C8—22no—
148C3×#168—21no—
149C3×#168—21no—
150C3×C4×Q8—51no—
151#946—101no—
152#944—101no—
153C2×Dic12—52no—
154C2×#204—51no—
155#898—102no—
156#892—101no—
157#889—102no—
158#887—101no—
159#875—52no—
160C4×D12C2×D511yescharacteristic
161#870—52no—
162#869—51no—
163#869C2×D511yescharacteristic
164C4×Dic6—51no—
165C4×Dic6—52no—
166C4×Dic6—52no—
167C3×C4⋊C8—52no—
168C3×C4⋊C8C2×D511yescharacteristic
169C3×C4×C8—52no—
170C3×C4×C8—51no—
171#821—51no—
172#821C2×D512yes—
173#818C2×D512yes—
174#817—51no—
175#816—52no—
176#816—52no—
177#816—52no—
178#816—51no—
179C2×C5×Q8—61no—
180C2×C5×D4—31no—
181C22×C4×C5—61no—
182C2×Dic10—31no—
183C2×Dic10—32no—
184C2×Dic10D1211yescharacteristic
185C2×C5×C8C22×D312yes—
186C5×C4⋊C4—31no—
187C5×C4⋊C4—32no—
188C5×C4⋊C4—61no—
189C5×C22⋊C4—61no—
190C42×C5C22×D311yescharacteristic
191C22⋊Dic5—62no—
192C22⋊Dic5—62no—
193#687—62no—
194C4⋊Dic5—31no—
195C4⋊Dic5—61no—
196C4⋊Dic5—61no—
197C4⋊Dic5—62no—
198C4⋊Dic5D1211yescharacteristic
199#683—61no—
200#683—62no—
201#683—62no—
202#683—62no—
203#683D1212yes—
204C4×Dic5—61no—
205C4×Dic5—62no—
206C4×Dic5—62no—
207C4×Dic5C22×D312yes—
208C2×#168C22×D311yescharacteristic
209C2×#168C22×D311yescharacteristic
210Dic20—64no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—31no—
217#464—152no—
218#462—151no—
219C8×Q8—51no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C5×D3—41no—
224C2×C5×D3—41no—
225C2×C5×D3—41no—
226C3×C4×C5—21no—
227C3×C4×C5#13512yes—
228C3×C4×C5C2×#4111yescharacteristic
229C3×C4×C52−1+411yescharacteristic
230Dic15—22no—
231Dic15—42no—
232Dic15—41no—
233C3×Dic5—22no—
234C3×Dic5—22no—
235C5×Dic3—42no—
236C5×Dic3—41no—
237C2×C3×Q8—51no—
238C2×D12C22×D511yescharacteristic
239C2×C4×D3—21no—
240C2×Dic6—21no—
241C2×Dic6—51no—
242C2×Dic6—52no—
243C2×C3×C8—51no—
244C2×C3×C8—51no—
245C2×C3×C8C22×D512yes—
246C3×C4⋊C4—52no—
247C3×C4⋊C4—51no—
248C3×C42—52no—
249C3×C42C22×D511yescharacteristic
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—102no—
252(C2×D3)⋊C4—102no—
253C4⋊Dic3—21no—
254C4⋊Dic3—51no—
255C4⋊Dic3—101no—
256C4⋊Dic3—101no—
257C4⋊Dic3C22×D512yes—
258C4⋊Dic3C22×D511yescharacteristic
259Dic3⋊C4—102no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—101no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3—101no—
267Dic12—104no—
268#204—102no—
269C23×C5—61no—
270C5×Q8—122no—
271C5×D4—61no—
272C5×D4—61no—
273C2×C4×C5—61no—
274C2×C4×C5—62no—
275C2×C4×C5—122no—
276C2×C4×C5C2×D1211yescharacteristic
277C2×C4×C5C2×D1211yescharacteristic
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—61no—
280C2×Dic5—61no—
281C2×Dic5—62no—
282C2×Dic5C2×D1212yes—
283C2×Dic5C2×D1212yes—
284Dic10—22no—
285Dic10—32no—
286Dic10—61no—
287Dic10—62no—
288Dic10—62no—
289C5×C8—22no—
290#168—21no—
291#168—21no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—151no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—51no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4—31no—
308#117—301no—
309#107—32no—
310#106—151no—
311C4⋊C8—52no—
312C4⋊C8D3×D511yescharacteristic
313#103—151no—
314#103—152no—
315#103—152no—
316#103—152no—
317#102—32no—
318#102—151no—
319C4×C8—52no—
320C4×C8—51no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C5×D3—81no—
325C22×D3—21no—
326C3×Q8—102no—
327C2×C3×C4—52no—
328C2×C3×C4—52no—
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4C23×D511yescharacteristic
332C2×Dic3—21no—
333C2×Dic3—22no—
334C2×Dic3—101no—
335C2×Dic3—101no—
336C2×Dic3—102no—
337D12—21no—
338D12—21no—
339C4×D3—42no—
340Dic6—42no—
341Dic6—52no—
342Dic6—101no—
343Dic6—102no—
344Dic6—102no—
345C3×C8—22no—
346C3×C8—101no—
347C3×C8—101no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5C22×D1211yescharacteristic
352C4×C5—21no—
353C4×C5—121no—
354C4×C5—122no—
355C4×C5#90412yes—
356C4×C5#100711yescharacteristic
357C4×C5D3×#4111yescharacteristic
358Dic5—22no—
359Dic5—22no—
360Dic5—62no—
361Dic5—121no—
362Dic5—122no—
363C2×Q8—51no—
364C2×Q8—61no—
365C2×Q8—151no—
366C2×Q8—152no—
367C2×D4—31no—
368C22×C4—61no—
369Q16—304no—
370SD16—302no—
371C2×C8—51no—
372C2×C8—51no—
373C2×C8C2×D3×D512yes—
374C4⋊C4—32no—
375C4⋊C4—31no—
376C4⋊C4—51no—
377C4⋊C4—52no—
378C4⋊C4—61no—
379C4⋊C4—151no—
380C4⋊C4—302no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—301no—
385C4⋊C4—301no—
386C4⋊C4—301no—
387C22⋊C4—61no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—52no—
391C42—302no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—102no—
402C3×C4—102no—
403C3×C4#405812yes—
404C3×C4#414711yescharacteristic
405C3×C4D5×#4111yescharacteristic
406Dic3—42no—
407Dic3—41no—
408Dic3—102no—
409Dic3—201no—
410Dic3—202no—
411C2×C5—241no—
412C2×C5#557611yescharacteristic
413C2×C5C2×#90411yescharacteristic
414C2×C5#575311yescharacteristic
415C23—61no—
416Q8—102no—
417Q8—122no—
418Q8—152no—
419Q8—301no—
420Q8—302no—
421Q8—302no—
422D4—61no—
423D4—61no—
424C2×C4—52no—
425C2×C4—52no—
426C2×C4—61no—
427C2×C4—62no—
428C2×C4—122no—
429C2×C4—301no—
430C2×C4—302no—
431C2×C4—301no—
432C2×C4D5×D1211yescharacteristic
433C2×C4D5×D1211yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—22no—
436C8—101no—
437C8—101no—
438C2×C3#6596711yescharacteristic
439C2×C3C2×#405811yescharacteristic
440C2×C3#6611311yescharacteristic
441D3—81no—
442C5#7993411yescharacteristic, complemented, Sylow
443C22—121no—
444C22—121no—
445C22—121no—
446C22C2×D5×D1211yescharacteristic
447C4—21no—
448C4—102no—
449C4—102no—
450C4—121no—
451C4—122no—
452C4—302no—
453C4—601no—
454C4—602no—
455C4#9127012yes—
456C4#9202411yescharacteristic
457C4#9202911yescharacteristic
458C3#1061272511yescharacteristic, complemented, Sylow
459C2—241no—
460C2#1175334111yescharacteristic
461C2C2×#9127011yescharacteristic
462C2#1175404011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752487C2semidirect
3. #11750950C2semidirect
5. C3×#65119C2semidirect
7. #11747858C2semidirect
9. #11747851C2semidirect
11. #11746930C2semidirect
51. #65119D3semidirect
395. C3×C5#3364semidirect
442. C5#79934semidirect
458. C3#10612725semidirect

Maximal subgroups

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

subgroupindex
#117524912
#117524872
#117509502
C5×#48462
C3×#651192
#117479632
#117478582
#117478532
#117478512
C4×#66592
#117469302
#106127253
#799345