Finite Group Databasebeta

← #14302563

Subgroups — #14302563

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
1C3×C4×C5×#41C211yesmaximal, characteristic, complemented
2#11756581C211yesmaximal, characteristic
3#11751337C211yesmaximal, characteristic, complemented
4#11751107C211yesmaximal, characteristic, complemented
5C2×#91089C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10602438—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C3×C4×C5×Q8—21no—
12C3×C4×C5×D4—21no—
13C3×C4×C5×D4—22no—
14C3×C5×#117—21no—
15C3×C5×#117C2211yescharacteristic
16C2×C3×C42×C5—21no—
17C2×C3×C42×C5C2211yescharacteristic
18#91840C412yescomplemented
19#91839—22no—
20#91838C412yescomplemented
21#91831—21no—
22#91821—21no—
23#91815C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25C2×#6710C2211yescharacteristic
26#91121—22no—
27#91090—22no—
28#91089—21no—
29#91089—21no—
30#71645—51nomaximal, Hall
31C4×C5×#41D311yescharacteristic, complemented
32#66156—31no—
33#65525—31no—
34#65295—31no—
35C2×#3937—31no—
36#64753—31no—
37#64743—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×C5—22no—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5C2311yescharacteristic
49C2×#1220—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×C4⋊C4—22no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C22⋊C4—22no—
60C3×C5×C22⋊C4D412yes—
61C3×C42×C5—22no—
62C3×C42×C5—21no—
63C3×C42×C5—21no—
64C3×C42×C5D411yescharacteristic
65C3×C42×C5D411yescharacteristic
66#6719—21no—
67#6718—22no—
68#6717—22no—
69#6716—22no—
70#6715—22no—
71C4⋊Dic15—21no—
72C4×Dic15—21no—
73#6710—21no—
74#6710—21no—
75#6710—21no—
76#6710C2×C412yescomplemented
77C2×C3⋊#168—21no—
78C2×C3⋊#168—21no—
79C3×C4×#41D511yescharacteristic, complemented
80#5822—51no—
81#5236—51no—
82#5006—51no—
83C2×#805—51no—
84#4533—51no—
85#4523—51no—
86C2×C5×#41C2×D311yescharacteristic
87C2×#709—31no—
88C4×C5×Q8—21no—
89C4×C5×D4—21no—
90C4×C5×D4—22no—
91C5×#117—21no—
92C5×#117C2×D311yescharacteristic
93C2×C42×C5—21no—
94C2×C42×C5C2×D311yescharacteristic
95#4097—32no—
96#4096—62no—
97#4095—32no—
98#4088—61no—
99#4078—61no—
100#4072—31no—
101C2×#681—31no—
102C2×#681—31no—
103#3969—62no—
104#3938—62no—
105#3937—61no—
106#3937—61no—
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—21no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—42no—
124C2×C3×C4×C5—44no—
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5#4111yescharacteristic
131#1220—41no—
132#1220—41no—
133C2×Dic15—21no—
134C2×Dic15—41no—
135D60—21no—
136D60—21no—
137C4×D15—41no—
138C4×D15—41no—
139Dic30—21no—
140Dic30—21no—
141C3⋊#168—22no—
142C3⋊#168—41no—
143C2×C3×#41C2×D511yescharacteristic
144C2×#235—51no—
145C3×C4×Q8—21no—
146C3×C4×D4—21no—
147C3×C4×D4—22no—
148C3×#117—21no—
149C3×#117C2×D511yescharacteristic
150C2×C3×C42—21no—
151C2×C3×C42C2×D511yescharacteristic
152#951—52no—
153#950—102no—
154#949—52no—
155#942—101no—
156#932—101no—
157#926—51no—
158C2×#208—51no—
159C2×#208—51no—
160#837—102no—
161#806—102no—
162#805—101no—
163#805—101no—
164C5×#41—21no—
165C5×#41—21no—
166C5×#41C4×D312yes—
167C5×#41D1212yes—
168C2×C5×Q8#6711yescharacteristic
169C2×C5×D4—21no—
170C2×C5×D4#6711yescharacteristic
171C22×C4×C5—21no—
172C22×C4×C5—22no—
173C22×C4×C5—21no—
174C22×C4×C5C22×D311yescharacteristic
175C2×C22⋊D5—61no—
176#709—61no—
177#709—61no—
178#709—61no—
179#709—61no—
180C2×D20—31no—
181C2×C4×D5—61no—
182C2×Dic10—31no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—21no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4#6712yes—
187C42×C5—22no—
188C42×C5—21no—
189C42×C5—21no—
190C42×C5#6711yescharacteristic
191C42×C5#6711yescharacteristic
192C22⋊Dic5—61no—
193#689—62no—
194#688—62no—
195#687—62no—
196#686—62no—
197C4⋊Dic5—61no—
198C4×Dic5—61no—
199#681—32no—
200#681—61no—
201#681—61no—
202#681—61no—
203C2×#168—61no—
204C2×#168—61no—
205#575—151no—
206C4×#41D1511yescharacteristic, complemented
207#421—151no—
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—22no—
222C3×C4×C5—42no—
223C3×C4×C5—41no—
224C3×C4×C5C2×C22⋊C411yescharacteristic
225C3×C4×C5C4×D411yescharacteristic
226C3×C4×C5#12111yescharacteristic
227C3×C4×C5#12311yescharacteristic
228Dic15—41no—
229Dic15—81no—
230C3×#41—21no—
231C3×#41—21no—
232C3×#41C4×D512yes—
233C3×#41D2012yes—
234C2×C3×Q8C22⋊D511yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4C22⋊D511yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4C22×D511yescharacteristic
241C2×#67—101no—
242#235—101no—
243#235—101no—
244#235—101no—
245#235—101no—
246C2×D12—51no—
247C2×C4×D3—101no—
248C2×Dic6—51no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—21no—
251C3×C22⋊C4—22no—
252C3×C22⋊C4C22⋊D512yes—
253C3×C42—22no—
254C3×C42—21no—
255C3×C42—21no—
256C3×C42C22⋊D511yescharacteristic
257C3×C42C22⋊D511yescharacteristic
258#217—101no—
259#216—102no—
260#215—102no—
261#214—102no—
262#213—102no—
263C4⋊Dic3—101no—
264C4×Dic3—101no—
265#208—52no—
266#208—101no—
267#208—101no—
268#208—101no—
269C2×C3⋊C8—101no—
270C2×C3⋊C8—101no—
271C23×C5—21no—
272C23×C5C2×#6711yescharacteristic
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—21no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—21no—
286C2×C4×C5—42no—
287C2×C4×C5—44no—
288C2×C4×C5C2×C4×D311yescharacteristic
289C2×C4×C5C2×D1211yescharacteristic
290C2×C4×C5#23511yescharacteristic
291C2×C4×C5#23511yescharacteristic
292C2×C4×C5C2×#6711yescharacteristic
293C2×C4×C5C2×#6711yescharacteristic
294C22⋊D5—121no—
295C22⋊D5—121no—
296C2×Dic5—61no—
297C2×Dic5—121no—
298D20—61no—
299D20—61no—
300C4×D5—121no—
301C4×D5—121no—
302Dic10—61no—
303Dic10—61no—
304#168—62no—
305#168—121no—
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×M16—151no—
315C4×Q8—21no—
316C4×D4—21no—
317C4×D4—22no—
318#117—21no—
319#117—151no—
320#117C2×D1511yescharacteristic
321C2×C42—21no—
322C2×C42C2×D1511yescharacteristic
323#104—302no—
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×C3C2×C22⋊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—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—42no—
349C2×C3×C4—44no—
350C2×C3×C4C2×C4×D511yescharacteristic
351C2×C3×C4C2×D2011yescharacteristic
352C2×C3×C4#70911yescharacteristic
353C2×C3×C4#70911yescharacteristic
354C2×C3×C4C2×C22⋊D511yescharacteristic
355C2×C3×C4C2×C22⋊D511yescharacteristic
356#67—201no—
357#67—201no—
358C2×Dic3—101no—
359C2×Dic3—201no—
360D12—101no—
361D12—101no—
362C4×D3—201no—
363C4×D3—201no—
364Dic6—101no—
365Dic6—101no—
366C3⋊C8—102no—
367C3⋊C8—201no—
368C22×C5—22no—
369C22×C5—41no—
370C22×C5—42no—
371C22×C5C4×#6711yescharacteristic
372C22×C5#93011yescharacteristic
373C22×C5#95311yescharacteristic
374C2×D5—121no—
375C2×D5—241no—
376C4×C5—22no—
377C4×C5—22no—
378C4×C5—42no—
379C4×C5—41no—
380C4×C5C2×(C2×D3)⋊C411yescharacteristic
381C4×C5C4×#6711yescharacteristic
382C4×C5#92911yescharacteristic
383C4×C5#93011yescharacteristic
384Dic5—121no—
385Dic5—241no—
386#41—21no—
387#41—21no—
388#41—301no—
389#41—301no—
390#41—301no—
391#41—301no—
392#41C4×D1512yes—
393#41D6012yes—
394C2×Q8—151no—
395C2×Q8#122011yescharacteristic
396C2×D4—21no—
397C2×D4—151no—
398C2×D4—301no—
399C2×D4#122011yescharacteristic
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—301no—
404C22×C4C22×D1511yescharacteristic
405Q16—302no—
406SD16—302no—
407SD16—302no—
408D8—302no—
409M16—152no—
410M16—301no—
411M16—301no—
412M16—301no—
413C2×C8—301no—
414C2×C8—301no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—301no—
418C22⋊C4—22no—
419C22⋊C4—301no—
420C22⋊C4#122012yes—
421C42—22no—
422C42—21no—
423C42—21no—
424C42—301no—
425C42#122011yescharacteristic
426C42#122011yescharacteristic
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—22no—
429C22×C3—41no—
430C22×C3—42no—
431C22×C3C4×C22⋊D511yescharacteristic
432C22×C3#407611yescharacteristic
433C22×C3#409911yescharacteristic
434C2×D3—201no—
435C2×D3—401no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—42no—
439C3×C4—41no—
440C3×C4C2×#68511yescharacteristic
441C3×C4C4×C22⋊D511yescharacteristic
442C3×C4#407511yescharacteristic
443C3×C4#407611yescharacteristic
444Dic3—201no—
445Dic3—401no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5—42no—
450C2×C5#521311yescharacteristic
451D5—241no—
452C23—21no—
453C23—301no—
454C23C2×#122011yescharacteristic
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—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—301no—
476C2×C4—601no—
477C2×C4—601no—
478C2×C4—601no—
479C2×C4C2×C4×D1511yescharacteristic
480C2×C4C2×D6011yescharacteristic
481C2×C4#681711yescharacteristic
482C2×C4#681711yescharacteristic
483C2×C4C2×#122011yescharacteristic
484C2×C4C2×#122011yescharacteristic
485C8—302no—
486C8—601no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—42no—
491C2×C3#6550211yescharacteristic
492D3—401no—
493C5#7164511yescharacteristic, complemented, Sylow
494C22—22no—
495C22—41no—
496C22—42no—
497C22—601no—
498C22—1201no—
499C22C4×#122011yescharacteristic
500C22#9181911yescharacteristic
501C22#9184211yescharacteristic
502C4—22no—
503C4—22no—
504C4—42no—
505C4—41no—
506C4—601no—
507C4—1201no—
508C4C2×#671411yescharacteristic
509C4C4×#122011yescharacteristic
510C4#9181811yescharacteristic
511C4#9181911yescharacteristic
512C3#1060243811yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—42no—
517C2—1201no—
518C2#1175131411yescharacteristic
subgroupG/H
centerC4#91819
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C4×C5×#41C2
socleC2×C3×C5#386
prime radical#11756581C2
cosocleC22×C3×C4×C5C23
hypercenterC4×#41D15
hypocenterC3×C5#1906
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C3×C4×C5×#41C2semidirect
3. #11751337C2semidirect
4. #11751107C2semidirect
5. C2×#91089C2semidirect
6. #11746354C2semidirect
7. #11746344C2semidirect
18. #91840C4semidirect
20. #91838C4semidirect
31. C4×C5×#41D3semidirect
54. C2×D60C2×C4semidirect
56. C2×Dic30C2×C4semidirect
76. #6710C2×C4semidirect
79. C3×C4×#41D5semidirect
206. C4×#41D15semidirect
427. C3×C5#1906semidirect
493. C5#71645semidirect
512. C3#10602438semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C5×#412
#117565812
#117513372
#117511072
C2×#910892
#117463542
#117463442
#106024383
#716455