Finite Group Databasebeta

← #14471678

Subgroups — #14471678

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756491C211yesmaximal, characteristic, complemented
2#11752641C211yesmaximal, characteristic, complemented
3C5×#5083C211yesmaximal, characteristic, complemented
4C3×#65370C211yesmaximal, characteristic, complemented
5#11749337C212yesmaximal, complemented
6#11749240C212yesmaximal, complemented
7#11749238C212yesmaximal
8#11749190C212yesmaximal, complemented
9C4×#6654C211yesmaximal, characteristic
10#11746942C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612146—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91836C2212yes—
15Q8×Dic15C2212yes—
16#91787—22no—
17#91786—21no—
18#91781—21no—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#215C2212yes—
22C4×C5×D12C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91435C2212yes—
25D3×C4⋊Dic5—21no—
26#91410—22no—
27#91384C2212yes—
28#91365—21no—
29C2×#6654C2211yescharacteristic
30C5×#835C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#3967C2212yes—
33C3×#3967C2212yes—
34C3×C4×#168C2211yescharacteristic
35#90988C2211yescharacteristic
36#90987C2212yes—
37#90983C2212yes—
38#90969C2211yescharacteristic
39#90968C2212yes—
40#90967C2211yescharacteristic
41#90951C2212yes—
42#81621—51nomaximal, Hall
43#66066—31no—
44#65877—31no—
45C5×#461—31no—
46#65454—32no—
47SD16×Dic5—32no—
48#65370D311yescharacteristic, complemented
49C4×#686—31no—
50#65131—31no—
51#65119—31no—
52#65089—32no—
53#65088—32no—
54C2×C3×C5×Q8C2312yes—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×Dic30D411yescharacteristic
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×Dic10—21no—
61C2×D3×Dic5—22no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65#6714—21no—
66#6714—22no—
67#6714—22no—
68C4⋊Dic15—22no—
69C4⋊Dic15D411yescharacteristic
70C4⋊Dic15C2311yescharacteristic
71#6712D412yes—
72C4×Dic15—22no—
73C4×Dic15C2312yes—
74C5×#215—24no—
75C5×(C2×D3)⋊C4—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C2×C5×C3⋊C8C2312yes—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82Dic3⋊Dic5—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85#6654—22no—
86#5732—51no—
87#5730—51no—
88C3×#487—51no—
89#5084—51no—
90#5083D511yescharacteristic, complemented
91#4819—52no—
92#4800—52no—
93#4796—52no—
94#4788—52no—
95C4×D24—51no—
96C8×Dic6—51no—
97C2×C5×SD16—32no—
98C5×C4⋊Q8C2×D311yescharacteristic
99C4×C5×D4—31no—
100#4093—32no—
101Q8×Dic5—32no—
102D4×Dic5—32no—
103C2×#686—31no—
104C2×C4⋊Dic5—61no—
105#4070—61no—
106#4044—62no—
107#4043—61no—
108#4038—61no—
109#4036—32no—
110#4024—62no—
111C4×D20—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C5×C4⋊C8—31no—
115C5×#103—32no—
116#3967C2×D312yes—
117#3967C2×D312yes—
118#3964—31no—
119#3953—32no—
120#3949—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—31no—
124#3939—31no—
125C4×#168C2×D311yescharacteristic
126#3360—151noSylow
127C22×D15—21no—
128C22×C5×D3—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15C2×D412yes—
137C2×Dic15C2×D412yes—
138D60—21no—
139D60—21no—
140C4×D15—42no—
141Dic30—22no—
142C2×C5×Dic3—21no—
143C5×D12—21no—
144C5×D12#4112yes—
145C4×C5×D3—42no—
146C2×C3×Dic5—22no—
147C3×Dic10—81no—
148D3×Dic5—82no—
149C3×#168—21no—
150C3×#168—21no—
151C5×C3⋊C8—22no—
152C3×C4⋊Q8—51no—
153C3×C4⋊Q8C2×D511yescharacteristic
154#947—52no—
155#946—102no—
156Q8×Dic3—52no—
157C2×#215C2×D512yes—
158C2×D24—51no—
159#898—102no—
160#897—101no—
161#897—101no—
162#893—52no—
163#892—101no—
164D3×C4⋊C4—101no—
165#890—52no—
166C4×D12—51no—
167C4×D12C2×D511yescharacteristic
168C4×Dic6—51no—
169C3×#103—52no—
170C3×#103—52no—
171C3×C4×C8—51no—
172#835C2×D512yes—
173#821—51no—
174#821—51no—
175#818—51no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—52no—
179#808—52no—
180C4⋊(C3⋊C8)C2×D511yescharacteristic
181C2×C5×Q8C22×D312yes—
182C2×C5×D4—31no—
183C22×C4×C5—61no—
184C22×Dic5—62no—
185C2×D20—31no—
186C2×C4×D5—61no—
187C2×Dic10—21no—
188C2×Dic10—31no—
189C5×SD16—64no—
190C2×C5×C8—32no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—31no—
194C5×C22⋊C4—61no—
195C42×C5C22×D311yescharacteristic
196C22⋊Dic5—62no—
197#686—62no—
198#685—62no—
199#685—62no—
200#685—61no—
201C4⋊Dic5—21no—
202C4⋊Dic5—31no—
203C4⋊Dic5—31no—
204C4⋊Dic5—62no—
205C4⋊Dic5—62no—
206C4⋊Dic5C22×D312yes—
207#683—32no—
208#683—62no—
209C4×Dic5—32no—
210C4×Dic5—62no—
211C2×#168C22×D311yescharacteristic
212C2×#168C22×D311yescharacteristic
213#556—151no—
214#554—151no—
215#488—152no—
216#487—51no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—31no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×D15—41no—
226C2×D15—41no—
227C2×D15—41no—
228C2×C5×D3—22no—
229C2×C5×D3—41no—
230C2×C5×D3—41no—
231C3×C4×C5—21no—
232C3×C4×C5—42no—
233C3×C4×C5#13512yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—22no—
237Dic15—22no—
238Dic15—41no—
239C3×Dic5—42no—
240C5×Dic3—41no—
241C2×C3×Q8—101no—
242C2×C3×Q8C22×D512yes—
243C2×D12—51no—
244C2×D12C22×D511yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—101no—
247C2×C4×D3—102no—
248C2×Dic6—51no—
249C2×C3×C8—51no—
250C2×C3×C8—51no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—52no—
254C3×C4⋊C4—101no—
255C3×C42C22×D511yescharacteristic
256#215—24no—
257(C2×D3)⋊C4—21no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—102no—
261(C2×D3)⋊C4—101no—
262C4⋊Dic3—51no—
263C4⋊Dic3—51no—
264C4⋊Dic3—102no—
265C4⋊Dic3—102no—
266C4⋊Dic3C22×D511yescharacteristic
267Dic3⋊C4—52no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8C22×D512yes—
272D24—102no—
273C23×C5—61no—
274C22×D5—61no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×D4—32no—
278C5×D4—61no—
279C2×C4×C5—22no—
280C2×C4×C5—61no—
281C2×C4×C5—122no—
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5C23×D311yescharacteristic
285C2×Dic5—22no—
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—61no—
289C2×Dic5—242no—
290D20—61no—
291D20—61no—
292C4×D5—122no—
293Dic10—62no—
294Dic10—81no—
295C5×C8—62no—
296#168—21no—
297#168—21no—
298C2×SD16—32no—
299C2×D8—151no—
300C4⋊Q8—51no—
301C4⋊Q8D3×D511yescharacteristic
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—151no—
309C4×Q8—152no—
310C4×D4—31no—
311C4×D4—152no—
312C4×D4—151no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—152no—
317C4⋊C8—31no—
318C4⋊C8—152no—
319#103—32no—
320#103—52no—
321#103—52no—
322#102—151no—
323#102—152no—
324#102—151no—
325C4×C8—51no—
326C4×C8—152no—
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—81no—
331C5×D3—42no—
332C22×D3—21no—
333C22×D3—101no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—401no—
337C2×C3×C4—22no—
338C2×C3×C4—102no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—52no—
344C2×Dic3—52no—
345C2×Dic3—101no—
346D12—21no—
347D12—101no—
348D12—101no—
349D12#71112yes—
350C4×D3—42no—
351C4×D3—202no—
352C4×D3—402no—
353Dic6—102no—
354C3×C8—101no—
355C3×C8—101no—
356C3⋊C8—22no—
357C22×C5—62no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C2×D3×D411yescharacteristic
361C2×D5—121no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—42no—
366C4×C5—121no—
367C4×C5#91912yes—
368C4×C5D3×#4111yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—42no—
371Dic5—62no—
372Dic5—62no—
373Dic5—121no—
374C2×Q8—101no—
375C2×Q8—151no—
376C2×Q8C2×D3×D512yes—
377C2×D4—31no—
378C2×D4—151no—
379C22×C4—61no—
380C22×C4—302no—
381C22×C4—301no—
382SD16—64no—
383D8—302no—
384C2×C8—32no—
385C2×C8—51no—
386C2×C8—51no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—31no—
390C4⋊C4—52no—
391C4⋊C4—101no—
392C4⋊C4—151no—
393C4⋊C4—152no—
394C4⋊C4—151no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C22⋊C4—61no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—301no—
403C42—152no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3C2×D4×D511yescharacteristic
408C2×D3—22no—
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—42no—
416C3×C4—202no—
417C3×C4#406212yes—
418C3×C4C2×#71111yescharacteristic
419C3×C4#415011yescharacteristic
420Dic3—41no—
421Dic3—102no—
422Dic3—102no—
423Dic3—201no—
424C2×C5—122no—
425C2×C5#567711yescharacteristic
426C2×C5#576211yescharacteristic
427C2×C5C2×#91911yescharacteristic
428D5—241no—
429C23—61no—
430C23—301no—
431Q8—22no—
432Q8—22no—
433Q8—302no—
434Q8—401no—
435D4—32no—
436D4—61no—
437D4—301no—
438D4—301no—
439C2×C4—22no—
440C2×C4—61no—
441C2×C4—102no—
442C2×C4—122no—
443C2×C4—152no—
444C2×C4—152no—
445C2×C4—301no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4#679011yescharacteristic
449C2×C4#679011yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—62no—
452C8—101no—
453C8—101no—
454C2×C3#6593211yescharacteristic
455C2×C3C2×#406211yescharacteristic
456C2×C3#6611211yescharacteristic
457D3—42no—
458D3—401no—
459C5#8162111yescharacteristic, complemented, Sylow
460C22—62no—
461C22—121no—
462C22—121no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C2×#679011yescharacteristic
467C4—21no—
468C4—42no—
469C4—121no—
470C4—202no—
471C4—302no—
472C4—302no—
473C4—601no—
474C4#9152312yes—
475C4#9202011yescharacteristic
476C4D3×#71111yescharacteristic
477C3#1061214611yescharacteristic, complemented, Sylow
478C2—122no—
479C2—1201no—
480C2#1175482711yescharacteristic
481C2#1175509711yescharacteristic
482C2C2×#9152311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6654C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756491C2semidirect
2. #11752641C2semidirect
3. C5×#5083C2semidirect
4. C3×#65370C2semidirect
5. #11749337C2semidirect
6. #11749240C2semidirect
8. #11749190C2semidirect
10. #11746942C2semidirect
11. #11746851C2semidirect
48. #65370D3semidirect
90. #5083D5semidirect
406. C3×C5#3360semidirect
459. C5#81621semidirect
477. C3#10612146semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117526412
C5×#50832
C3×#653702
#117493372
#117492402
#117492382
#117491902
C4×#66542
#117469422
#117468512
#106121463
#816215