Finite Group Databasebeta

← #14302557

Subgroups — #14302557

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic15C211yesmaximal, characteristic, complemented
2#11756581C211yesmaximal, characteristic
3C3×C5×#421C211yesmaximal, characteristic, complemented
4C2×#91109C211yesmaximal, characteristic, complemented
5#11751107C211yesmaximal, characteristic, complemented
6#11746377C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10601188—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13#91840C412yescomplemented
14#91839—22no—
15#91838C412yescomplemented
16Q8×Dic15—21no—
17#91831—21no—
18D4×Dic15—21no—
19D4×Dic15—22no—
20#91821—21no—
21#91815—21no—
22#91815C2211yescharacteristic
23C2×C4×Dic15—21no—
24C2×C4×Dic15C2211yescharacteristic
25C2×#6710C2211yescharacteristic
26C3×C5×#104—22no—
27#91109—21no—
28#91109—21no—
29#91090—22no—
30#70395—51nomaximal, Hall
31#41×Dic5—31no—
32#66156—31no—
33C5×#421D311yescharacteristic, complemented
34C2×#3957—31no—
35#65295—31no—
36#64776—31no—
37#64752—31no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41C2×C412yes—
41C3×C5×#41D412yes—
42C2×C3×C5×Q8D411yescharacteristic
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4D411yescharacteristic
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48C22×Dic15—22no—
49C22×Dic15—21no—
50#6817—21no—
51#6817—21no—
52#6817—21no—
53#6817—21no—
54C2×D60C2×C411yescharacteristic, complemented
55C2×C4×D15—21no—
56C2×Dic30C2×C411yescharacteristic, complemented
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C2×C3×C5×C8—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C42×C5—21no—
63#6719—22no—
64#6719D412yes—
65#6718—22no—
66#6717—22no—
67#6716—22no—
68#6715—22no—
69C4⋊Dic15—22no—
70C4⋊Dic15—21no—
71C4×Dic15—22no—
72C4×Dic15—21no—
73C4×Dic15—21no—
74C4×Dic15D411yescharacteristic
75C4×Dic15D411yescharacteristic
76#6710—21no—
77#6710C2×C412yescomplemented
78C2×C3⋊#168—21no—
79Dic3×#41—51no—
80#5822—51no—
81C3×#421D511yescharacteristic, complemented
82C2×#825—51no—
83#5006—51no—
84#4556—51no—
85#4532—51no—
86C2×C5×#41C2×D311yescharacteristic
87C2×#709—31no—
88C2×C5×M16C2×D311yescharacteristic
89C5×#117C2×D311yescharacteristic
90#4097—32no—
91#4096—62no—
92#4095—32no—
93Q8×Dic5—61no—
94#4088—61no—
95D4×Dic5—62no—
96D4×Dic5—61no—
97#4078—61no—
98#4072—31no—
99#4072—61no—
100C2×C4×Dic5—31no—
101C2×C4×Dic5—61no—
102C2×#681—31no—
103C5×#104—22no—
104#3957—61no—
105#3957—61no—
106#3938—62no—
107#1906—151noSylow
108C23×C3×C5—21no—
109C23×C3×C5C2×D411yescharacteristic
110C22×D15—21no—
111C3×C5×Q8—21no—
112C3×C5×Q8C22⋊C412yes—
113C3×C5×D4—22no—
114C3×C5×D4—22no—
115C3×C5×D4—21no—
116C3×C5×D4C22⋊C412yes—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—41no—
121C2×C3×C4×C5C22×C411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126C2×C3×C4×C5#4111yescharacteristic
127#1220—41no—
128#1220—41no—
129C2×Dic15—21no—
130C2×Dic15—21no—
131C2×Dic15—22no—
132C2×Dic15—21no—
133C2×Dic15—42no—
134C2×Dic15—44no—
135D60—21no—
136D60—21no—
137C4×D15—41no—
138C4×D15—41no—
139Dic30—21no—
140Dic30—21no—
141C3×C5×C8—41no—
142C3⋊#168—22no—
143C2×C3×#41C2×D511yescharacteristic
144C2×#235—51no—
145C2×C3×M16C2×D511yescharacteristic
146C3×#117C2×D511yescharacteristic
147#951—52no—
148#950—102no—
149#949—52no—
150Q8×Dic3—101no—
151#942—101no—
152D4×Dic3—102no—
153D4×Dic3—101no—
154#932—101no—
155#926—51no—
156#926—101no—
157C2×C4×Dic3—51no—
158C2×C4×Dic3—101no—
159C2×#208—51no—
160C3×#104—22no—
161#825—101no—
162#825—101no—
163#806—102no—
164C5×#41—21no—
165C5×#41—21no—
166C5×#41C4×D312yes—
167C5×#41#6712yes—
168C2×C5×Q8D1211yescharacteristic
169C2×C5×D4—21no—
170C2×C5×D4D1211yescharacteristic
171C22×C4×C5—21no—
172C22×C4×C5C22×D311yescharacteristic
173C2×C22⋊D5—61no—
174C22×Dic5—62no—
175C22×Dic5—61no—
176#709—61no—
177#709—61no—
178#709—61no—
179#709—61no—
180C2×D20—31no—
181C2×C4×D5—61no—
182C2×Dic10—31no—
183C5×M16—21no—
184C5×M16—21no—
185C2×C5×C8—21no—
186C5×C4⋊C4—21no—
187C5×C22⋊C4—21no—
188C42×C5—21no—
189C22⋊Dic5—32no—
190C22⋊Dic5—62no—
191#689—62no—
192#688—62no—
193#687—62no—
194#686—62no—
195C4⋊Dic5—62no—
196C4⋊Dic5—61no—
197C4×Dic5—31no—
198C4×Dic5—31no—
199C4×Dic5—62no—
200C4×Dic5—61no—
201C4×Dic5—61no—
202#681—32no—
203#681—61no—
204C2×#168—61no—
205#575—151no—
206C4×#41—151no—
207#421D1511yescharacteristic, complemented
208C2×#104—151no—
209#410—151no—
210#344—151no—
211#339—151no—
212C22×C3×C5—22no—
213C22×C3×C5—41no—
214C22×C3×C5—42no—
215C22×C3×C5C4×D411yescharacteristic
216C22×C3×C5#12011yescharacteristic
217C22×C3×C5#12111yescharacteristic
218C2×D15—41no—
219C2×D15—81no—
220C3×C4×C5—22no—
221C3×C4×C5—81no—
222C3×C4×C5C2×C22⋊C411yescharacteristic
223C3×C4×C5C4×D411yescharacteristic
224C3×C4×C5#12111yescharacteristic
225C3×C4×C5#12311yescharacteristic
226Dic15—22no—
227Dic15—42no—
228Dic15—41no—
229Dic15—41no—
230C3×#41—21no—
231C3×#41—21no—
232C3×#41C4×D512yes—
233C3×#41C22⋊D512yes—
234C2×C3×Q8D2011yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4D2011yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4C22×D511yescharacteristic
239C2×#67—101no—
240C22×Dic3—102no—
241C22×Dic3—101no—
242#235—101no—
243#235—101no—
244#235—101no—
245#235—101no—
246C2×D12—51no—
247C2×C4×D3—101no—
248C2×Dic6—51no—
249C3×M16—21no—
250C3×M16—21no—
251C2×C3×C8—21no—
252C3×C4⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C42—21no—
255#217—52no—
256#217—102no—
257#216—102no—
258#215—102no—
259#214—102no—
260#213—102no—
261C4⋊Dic3—102no—
262C4⋊Dic3—101no—
263C4×Dic3—51no—
264C4×Dic3—51no—
265C4×Dic3—102no—
266C4×Dic3—101no—
267C4×Dic3—101no—
268#208—52no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5—21no—
272C23×C5D3×D411yescharacteristic
273C22×D5—61no—
274C5×Q8—21no—
275C5×Q8(C2×D3)⋊C412yes—
276C5×D4—22no—
277C5×D4—22no—
278C5×D4—21no—
279C5×D4(C2×D3)⋊C412yes—
280C2×C4×C5—21no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—41no—
284C2×C4×C5C2×C4×D311yescharacteristic
285C2×C4×C5C2×D1211yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5#23711yescharacteristic
288C2×C4×C5#23711yescharacteristic
289C2×C4×C5C2×#6711yescharacteristic
290C22⋊D5—121no—
291C22⋊D5—121no—
292C2×Dic5—61no—
293C2×Dic5—61no—
294C2×Dic5—61no—
295C2×Dic5—62no—
296C2×Dic5—122no—
297C2×Dic5—124no—
298D20—61no—
299D20—61no—
300C4×D5—121no—
301C4×D5—121no—
302Dic10—61no—
303Dic10—61no—
304C5×C8—41no—
305#168—62no—
306C2×#41—151no—
307C2×#41C2×D1511yescharacteristic
308#137—152no—
309#137—301no—
310AGL(1,ℤ/8)—152no—
311AGL(1,ℤ/8)—301no—
312#135—302no—
313C2×M16—151no—
314C2×M16C2×D1511yescharacteristic
315C4×Q8—301no—
316C4×D4—302no—
317C4×D4—301no—
318#117—151no—
319#117—301no—
320#117C2×D1511yescharacteristic
321C2×C42—151no—
322C2×C42—301no—
323#104—22no—
324#104—301no—
325#104—301no—
326#99—302no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5—21no—
330C2×C3×C5—42no—
331C2×C3×C5#38611yescharacteristic
332D15—81no—
333C23×C3—21no—
334C23×C3D4×D511yescharacteristic
335C22×D3—101no—
336C3×Q8—21no—
337C3×Q8#68512yes—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—21no—
341C3×D4#68512yes—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—41no—
346C2×C3×C4C2×C4×D511yescharacteristic
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4#71111yescharacteristic
350C2×C3×C4#71111yescharacteristic
351C2×C3×C4C2×C22⋊D511yescharacteristic
352#67—201no—
353#67—201no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—101no—
357C2×Dic3—102no—
358C2×Dic3—202no—
359C2×Dic3—204no—
360D12—101no—
361D12—101no—
362C4×D3—201no—
363C4×D3—201no—
364Dic6—101no—
365Dic6—101no—
366C3×C8—41no—
367C3⋊C8—102no—
368C22×C5—22no—
369C22×C5—41no—
370C22×C5—42no—
371C22×C5#67⋊C411yescharacteristic
372C22×C5#88211yescharacteristic
373C22×C5#93911yescharacteristic
374C2×D5—121no—
375C2×D5—241no—
376C4×C5—22no—
377C4×C5—81no—
378C4×C5#67⋊C411yescharacteristic
379C4×C5#88611yescharacteristic
380C4×C5C2×(C2×D3)⋊C411yescharacteristic
381C4×C5#93911yescharacteristic
382Dic5—62no—
383Dic5—121no—
384Dic5—122no—
385Dic5—121no—
386#41—21no—
387#41—21no—
388#41—301no—
389#41—301no—
390#41—301no—
391#41—301no—
392#41C4×D1512yes—
393#41#122012yes—
394C2×Q8—151no—
395C2×Q8D6011yescharacteristic
396C2×D4—21no—
397C2×D4—151no—
398C2×D4—301no—
399C2×D4D6011yescharacteristic
400C22×C4—21no—
401C22×C4—302no—
402C22×C4—301no—
403C22×C4—301no—
404C22×C4C22×D1511yescharacteristic
405Q16—302no—
406SD16—302no—
407SD16—302no—
408D8—302no—
409M16—21no—
410M16—21no—
411M16—152no—
412M16—301no—
413C2×C8—21no—
414C2×C8—301no—
415C4⋊C4—21no—
416C4⋊C4—302no—
417C4⋊C4—301no—
418C22⋊C4—21no—
419C22⋊C4—152no—
420C22⋊C4—302no—
421C42—21no—
422C42—151no—
423C42—151no—
424C42—302no—
425C42—301no—
426C42—301no—
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—22no—
429C22×C3—41no—
430C22×C3—42no—
431C22×C3#402711yescharacteristic
432C22×C3#402811yescharacteristic
433C22×C3#408511yescharacteristic
434C2×D3—201no—
435C2×D3—401no—
436C3×C4—22no—
437C3×C4—81no—
438C3×C4#402711yescharacteristic
439C3×C4#403211yescharacteristic
440C3×C4C2×#68511yescharacteristic
441C3×C4#408511yescharacteristic
442Dic3—102no—
443Dic3—201no—
444Dic3—202no—
445Dic3—201no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5—42no—
450C2×C5#495811yescharacteristic
451D5—241no—
452C23—21no—
453C23—301no—
454C23D4×D1511yescharacteristic
455Q8—21no—
456Q8—301no—
457Q8—301no—
458Q8#671412yes—
459D4—22no—
460D4—22no—
461D4—21no—
462D4—301no—
463D4—301no—
464D4—601no—
465D4—601no—
466D4#671412yes—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—301no—
472C2×C4—301no—
473C2×C4—301no—
474C2×C4—302no—
475C2×C4—602no—
476C2×C4—604no—
477C2×C4—601no—
478C2×C4—601no—
479C2×C4C2×C4×D1511yescharacteristic
480C2×C4C2×D6011yescharacteristic
481C2×C4D4×D1511yescharacteristic
482C2×C4#681911yescharacteristic
483C2×C4#681911yescharacteristic
484C2×C4C2×#122011yescharacteristic
485C8—41no—
486C8—302no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—42no—
491C2×C3#6524711yescharacteristic
492D3—401no—
493C5#7039511yescharacteristic, complemented, Sylow
494C22—22no—
495C22—41no—
496C22—42no—
497C22—601no—
498C22—1201no—
499C22#9177011yescharacteristic
500C22#9177111yescharacteristic
501C22#9182811yescharacteristic
502C4—22no—
503C4—81no—
504C4—302no—
505C4—601no—
506C4—602no—
507C4—601no—
508C4#9177011yescharacteristic
509C4#9177511yescharacteristic
510C4C2×#671411yescharacteristic
511C4#9182811yescharacteristic
512C3#1060118811yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—42no—
517C2—1201no—
518C2#1175105911yescharacteristic
subgroupG/H
centerC4#91828
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radical#11756581C2
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1906
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #41×Dic15C2semidirect
3. C3×C5×#421C2semidirect
4. C2×#91109C2semidirect
5. #11751107C2semidirect
6. #11746377C2semidirect
7. #11746353C2semidirect
13. #91840C4semidirect
15. #91838C4semidirect
33. C5×#421D3semidirect
54. C2×D60C2×C4semidirect
56. C2×Dic30C2×C4semidirect
77. #6710C2×C4semidirect
81. C3×#421D5semidirect
207. #421D15semidirect
427. C3×C5#1906semidirect
493. C5#70395semidirect
512. C3#10601188semidirect

Maximal subgroups

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

subgroupindex
#41×Dic152
#117565812
C3×C5×#4212
C2×#911092
#117511072
#117463772
#117463532
#106011883
#703955