Finite Group Databasebeta

← #14424499

Subgroups — #14424499

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92004C211yesmaximal, characteristic, complemented
2#11756284C211yesmaximal, characteristic, complemented
3C22×#6658C211yesmaximal, characteristic, complemented
4C2×#91305C211yesmaximal, characteristic, complemented
5C5×#5002C211yesmaximal, characteristic, complemented
6C3×#65293C211yesmaximal, characteristic, complemented
7#11748350C211yesmaximal, characteristic, complemented
8#11747520C214yesmaximal, complemented
9#11747497C214yesmaximal, complemented
10#10610567—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C22×D60C2211yescharacteristic
13C2×C5×#235C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6782—22no—
16C2×D15⋊Q8C2212yescomplemented
17C2×#6769—21no—
18#92004—24no—
19#92004—24no—
20C2×#6768C2212yescomplemented
21C2×D3×Dic10—21no—
22C3×C5×#117C2211yescharacteristic
23#91784C2214yes—
24#91771—22no—
25#91764—21no—
26#91763—21no—
27C22×C5×C3⋊C8C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29C2×#6660C2212yes—
30C2×#6658—24no—
31C2×#6658C2214yes—
32#91305—24no—
33C2×#6654C2212yes—
34C5×#810C2212yescomplemented
35C5×#809C2212yescomplemented
36C3×#3942C2214yescomplemented
37#90957C2214yescomplemented
38#78960—51nomaximal, Hall
39C2×#4150—31no—
40C2×#4095—31no—
41C22×#677—31no—
42#65859—31no—
43C5×#416—31no—
44#65399—31no—
45#65293D311yescharacteristic, complemented
46#65095—34no—
47#65070—34no—
48C23×D15—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C2×#1220D412yes—
51#6817—22no—
52#6817—22no—
53C2×D60—22no—
54C2×D60—22no—
55C2×D60—21no—
56C2×D60—24no—
57C2×D60D411yescharacteristic
58C2×D60C2312yes—
59C2×C4×D15C2312yes—
60C2×Dic30D411yescharacteristic
61C2×C5×#67—21no—
62C5×#235—22no—
63C5×#235D414yescomplemented
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10—22no—
70C2×C3×Dic10D414yescomplemented
71C2×C3×Dic10C2312yes—
72C2×#1204—22no—
73C2×#1203—22no—
74C2×#1200—22no—
75#6782—216no—
76C2×D3×Dic5—22no—
77D15⋊Q8—24no—
78D15⋊Q8—24no—
79#6769—28no—
80#6768—24no—
81#6768—24no—
82D3×Dic10—28no—
83C3×C5×C4⋊C4C2312yes—
84C3×C5×C22⋊C4—21no—
85C3×C42×C5—21no—
86#6714—24no—
87C2×C5×C3⋊C8—22no—
88C2×C5×C3⋊C8C2312yes—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91#6660—24no—
92#6658—28no—
93#6654—24no—
94C2×#1007—51no—
95C22×#215—51no—
96C2×#908—51no—
97#5525—51no—
98C3×#419—51no—
99#5129—51no—
100#5002D511yescharacteristic, complemented
101#4810—54no—
102#4806—54no—
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—32no—
107C2×#711—32no—
108C2×#711—62no—
109C2×#709—31no—
110C2×#709—61no—
111C22×D20—31no—
112C22×Dic10—61no—
113C22×Dic10C2×D311yescharacteristic
114C22×C5×C8—31no—
115C5×#117C2×D311yescharacteristic
116#4095—64no—
117C2×#688—32no—
118C2×#686—32no—
119C2×#681C2×D311yescharacteristic
120C2×#677—34no—
121C2×#677—64no—
122#4041—34no—
123#4028—62no—
124#4021—61no—
125#4020—61no—
126C5×#103—32no—
127C5×#102—32no—
128#3952—34no—
129#3942C2×D314yescomplemented
130#3010—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—22no—
133C22×D15—42no—
134C22×D15—82no—
135C22×D15C2×D412yes—
136C22×C5×D3—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142#1220—24no—
143C2×Dic15C2×D412yes—
144D60—22no—
145D60—22no—
146D60—22no—
147D60—42no—
148D60—84no—
149C4×D15—22no—
150C4×D15—22no—
151Dic30—22no—
152C5×#67—24no—
153C2×C5×Dic3—21no—
154C5×D12—21no—
155C5×D12C2×D412yes—
156C4×C5×D3—24no—
157C5×Dic6—21no—
158C5×Dic6C2×D412yes—
159C2×C3×Dic5—24no—
160C2×C3×Dic5—22no—
161C3×Dic10—24no—
162C3×Dic10—22no—
163C3×Dic10C2×D414yes—
164#1204—28no—
165#1203—28no—
166#1200—28no—
167D3×Dic5—28no—
168C3×#168—22no—
169C5×C3⋊C8—22no—
170C22×C3×Q8—51no—
171#1007—104no—
172#1007—104no—
173C2×#239—52no—
174C2×#239—101no—
175C2×D3×Q8—52no—
176C2×D3×Q8—101no—
177C2×#235—51no—
178C2×#235—102no—
179C2×#235C2×D511yescharacteristic
180C22×D12—51no—
181C2×C3×M16—51no—
182C3×#117C2×D511yescharacteristic
183C2×#215—54no—
184C2×#215—104no—
185C22×C3⋊C8C2×D511yescharacteristic
186#908—104no—
187C2×D24—52no—
188C2×#204—52no—
189#895—54no—
190#882—102no—
191#875—101no—
192#874—101no—
193C3×#103—54no—
194(C2×D3)⋊C8—54no—
195#810C2×D512yescomplemented
196#809C2×D512yescomplemented
197C23×D5—61no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—32no—
206C2×C22⋊D5—62no—
207C22×Dic5—21no—
208C22×Dic5—62no—
209Q8×D5—64no—
210Q8×D5—64no—
211#711—64no—
212#711—616no—
213#711—64no—
214#709—68no—
215#709—62no—
216#709—62no—
217C2×D20—31no—
218C2×D20—32no—
219C2×D20—62no—
220C2×D20—62no—
221C2×D20—61no—
222C2×D20—64no—
223C2×C4×D5—32no—
224C2×C4×D5—62no—
225C2×Dic10—21no—
226C2×Dic10—22no—
227C2×Dic10—31no—
228C2×Dic10—68no—
229C2×Dic10—62no—
230C2×Dic10D1214yescomplemented
231C2×Dic10C22×D312yes—
232C2×C5×C8—32no—
233C2×C5×C8—62no—
234C5×C4⋊C4C22×D312yes—
235C5×C22⋊C4—21no—
236C42×C5—21no—
237#688—64no—
238#686—64no—
239#685—64no—
240#681—22no—
241C2×#168C22×D312yes—
242#677—68no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—51no—
250#416—31no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—22no—
256C2×D15—24no—
257C2×D15—42no—
258C2×D15—44no—
259C2×D15—84no—
260C2×C5×D3—22no—
261C2×C5×D3—42no—
262C3×C4×C5—42no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267C3×Dic5—24no—
268C5×Dic3—22no—
269C23×D3—101no—
270C2×C3×Q8—54no—
271C2×C3×Q8—52no—
272C2×C3×Q8—102no—
273C2×C3×Q8—101no—
274C22×C3×C4—101no—
275C22×C3×C4C22×D511yescharacteristic
276C2×#67—21no—
277C2×#67—52no—
278#239—108no—
279#239—104no—
280#239—104no—
281D3×Q8—104no—
282D3×Q8—108no—
283D3×Q8—104no—
284#235—22no—
285#235—1016no—
286#235—102no—
287#235—102no—
288#235D2014yescomplemented
289C2×D12—51no—
290C2×D12—52no—
291C2×D12—102no—
292C2×D12—102no—
293C2×D12—102no—
294C2×D12—101no—
295C2×D12—104no—
296C2×D12C22×D511yescharacteristic
297C2×C4×D3—21no—
298C2×C4×D3—52no—
299C2×C4×D3—102no—
300C2×C4×D3—102no—
301C2×Dic6—51no—
302C2×Dic6—102no—
303C2×Dic6C22×D511yescharacteristic
304C3×M16—102no—
305C2×C3×C8—52no—
306C3×C4⋊C4C22×D512yes—
307C3×C22⋊C4—21no—
308C3×C42—21no—
309#215—108no—
310(C2×D3)⋊C4—104no—
311C2×C3⋊C8—22no—
312C2×C3⋊C8C22×D512yes—
313D24—104no—
314#204—104no—
315C23×C5—61no—
316C23×C5D3×D411yescharacteristic
317C22×D5—32no—
318C22×D5—62no—
319C22×D5—122no—
320C22×D5—242no—
321C5×Q8—32no—
322C5×Q8—61no—
323C5×D4—32no—
324C5×D4—64no—
325C5×D4—61no—
326C2×C4×C5—22no—
327C2×C4×C5—61no—
328C2×C4×C5—64no—
329C2×C4×C5C2×D1212yes—
330C2×C4×C5D3×D412yes—
331C2×C4×C5D3×D411yescharacteristic
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—68no—
334C22⋊D5—64no—
335C2×Dic5—24no—
336C2×Dic5—22no—
337C2×Dic5—32no—
338C2×Dic5—68no—
339D20—62no—
340D20—62no—
341D20—62no—
342D20—122no—
343D20—244no—
344C4×D5—68no—
345C4×D5—62no—
346C4×D5—62no—
347Dic10—24no—
348Dic10—22no—
349Dic10—68no—
350Dic10—62no—
351Dic10C2×D1214yes—
352C5×C8—62no—
353#168—22no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—151no—
358C2×#41—152no—
359C2×#41—301no—
360C2×#41—302no—
361C22×Q8—51no—
362C22×Q8—152no—
363C22×Q8—301no—
364C22×D4—151no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—51no—
371C22×C8—31no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117D3×D511yescharacteristic
377#103—32no—
378#103—54no—
379#102—32no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5C2×#12011yescharacteristic
383C2×C3×C5#57712yes—
384D15—42no—
385D15—82no—
386C5×D3—42no—
387C23×C3D4×D511yescharacteristic
388C22×D3—21no—
389C22×D3—52no—
390C22×D3—102no—
391C22×D3—202no—
392C22×D3—402no—
393C3×Q8—54no—
394C3×Q8—102no—
395C3×Q8—104no—
396C2×C3×C4—22no—
397C2×C3×C4—102no—
398C2×C3×C4—104no—
399C2×C3×C4C2×D2012yes—
400C2×C3×C4D4×D512yes—
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4C23×D511yescharacteristic
403#67—24no—
404#67—104no—
405C2×Dic3—21no—
406C2×Dic3—52no—
407D12—21no—
408D12—108no—
409D12—102no—
410D12—102no—
411D12—102no—
412D12—202no—
413D12—404no—
414D12C2×D2012yes—
415C4×D3—24no—
416C4×D3—108no—
417C4×D3—108no—
418C4×D3—102no—
419C4×D3—102no—
420Dic6—21no—
421Dic6—108no—
422Dic6—102no—
423Dic6C2×D2012yes—
424C3×C8—102no—
425C3⋊C8—22no—
426C22×C5—22no—
427C22×C5—62no—
428C22×C5—122no—
429C22×C5#88212yes—
430C22×C5C2×D3×D411yescharacteristic
431C2×D5—62no—
432C2×D5—64no—
433C2×D5—122no—
434C2×D5—124no—
435C2×D5—244no—
436C4×C5—42no—
437C4×C5—62no—
438C4×C5#88212yes—
439C4×C5C22×D1211yescharacteristic
440C4×C5C2×D3×D411yescharacteristic
441Dic5—24no—
442Dic5—62no—
443C24—301no—
444#41—34no—
445#41—62no—
446#41—308no—
447#41—3016no—
448#41—304no—
449#41—304no—
450#41—302no—
451#41—302no—
452C2×Q8—31no—
453C2×Q8—54no—
454C2×Q8—52no—
455C2×Q8—102no—
456C2×Q8—101no—
457C2×Q8—151no—
458C2×Q8—302no—
459C2×Q8—308no—
460C2×Q8—304no—
461C2×Q8—304no—
462C2×D4—31no—
463C2×D4—61no—
464C2×D4—152no—
465C2×D4—151no—
466C2×D4—152no—
467C2×D4—304no—
468C2×D4—302no—
469C2×D4—302no—
470C2×D4—302no—
471C2×D4—301no—
472C22×C4—61no—
473C22×C4—101no—
474C22×C4—152no—
475C22×C4—302no—
476C22×C4—302no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—102no—
482C2×C8—32no—
483C2×C8—52no—
484C2×C8—62no—
485C4⋊C4C2×D3×D512yes—
486C22⋊C4—21no—
487C22⋊C4—304no—
488C42—21no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3#402812yes—
492C22×C3C2×D4×D511yescharacteristic
493C2×D3—22no—
494C2×D3—42no—
495C2×D3—102no—
496C2×D3—104no—
497C2×D3—202no—
498C2×D3—204no—
499C2×D3—404no—
500C3×C4—42no—
501C3×C4—104no—
502C3×C4#402812yes—
503C3×C4C22×D2011yescharacteristic
504C3×C4C2×D4×D511yescharacteristic
505Dic3—22no—
506Dic3—102no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5C2×#88211yescharacteristic
510C2×C5#577812yes—
511D5—122no—
512D5—242no—
513C23—61no—
514C23—152no—
515C23—302no—
516C23—602no—
517C23—1202no—
518C23#679011yescharacteristic
519Q8—32no—
520Q8—54no—
521Q8—61no—
522Q8—104no—
523Q8—102no—
524Q8—308no—
525Q8—302no—
526D4—32no—
527D4—64no—
528D4—61no—
529D4—308no—
530D4—304no—
531D4—302no—
532D4—302no—
533D4—302no—
534D4—602no—
535D4—1204no—
536C2×C4—22no—
537C2×C4—61no—
538C2×C4—64no—
539C2×C4—104no—
540C2×C4—102no—
541C2×C4—152no—
542C2×C4—308no—
543C2×C4—308no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4D5×D1212yes—
547C2×C4D3×D2012yes—
548C2×C4#679011yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—102no—
552C2×C3—22no—
553C2×C3C2×#402811yescharacteristic
554C2×C3#6610412yes—
555D3—42no—
556D3—202no—
557D3—402no—
558C5#7896011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—62no—
561C22—122no—
562C22—304no—
563C22—302no—
564C22—604no—
565C22—602no—
566C22—1204no—
567C22#9147612yes—
568C22C2×#679011yescharacteristic
569C4—42no—
570C4—62no—
571C4—104no—
572C4—302no—
573C4#9147612yes—
574C4C2×D5×D1211yescharacteristic
575C4C2×D3×D2011yescharacteristic
576C3#1061056711yescharacteristic, complemented, Sylow
577C2—22no—
578C2—122no—
579C2—602no—
580C2—1202no—
581C2C2×#9147611yescharacteristic
582C2#1175535412yes—
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
hypercenter#117D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#92004C2semidirect
2. #11756284C2semidirect
3. C22×#6658C2semidirect
4. C2×#91305C2semidirect
5. C5×#5002C2semidirect
6. C3×#65293C2semidirect
7. #11748350C2semidirect
8. #11747520C2semidirect
9. #11747497C2semidirect
16. C2×D15⋊Q8C22semidirect
20. C2×#6768C22semidirect
34. C5×#810C22semidirect
35. C5×#809C22semidirect
36. C3×#3942C22semidirect
37. #90957C22semidirect
45. #65293D3semidirect
63. C5×#235D4semidirect
70. C2×C3×Dic10D4semidirect
100. #5002D5semidirect
129. #3942C2×D3semidirect
195. #810C2×D5semidirect
196. #809C2×D5semidirect
230. C2×Dic10D12semidirect
288. #235D20semidirect
489. C3×C5#3010semidirect
558. C5#78960semidirect
576. C3#10610567semidirect

Maximal subgroups

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

subgroupindex
C2×#920042
#117562842
C22×#66582
C2×#913052
C5×#50022
C3×#652932
#117483502
#117475202
#117474972
#106105673
#789605