Finite Group Databasebeta

← #14424500

Subgroups — #14424500

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×#92001C211yesmaximal, characteristic, complemented
2C3×#65859C211yesmaximal, characteristic, complemented
3C22×#6657C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic, complemented
5#11751105C211yesmaximal, characteristic, complemented
6C5×#5002C211yesmaximal, characteristic, complemented
7#11748342C211yesmaximal, characteristic, complemented
8#11747510C214yesmaximal, complemented
9#11747493C214yesmaximal, complemented
10#10610567—31nomaximal, Hall
11C22×Dic30C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C3×#709C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772C2212yescomplemented
17C2×D3×Dic10—21no—
18#92001—24no—
19#92001—24no—
20C2×#6765—21no—
21C2×D5×Dic6C2212yescomplemented
22C3×C5×#117C2211yescharacteristic
23C2×#6710C2211yescharacteristic
24C22×C5×C3⋊C8C2211yescharacteristic
25C3×#4041C2214yes—
26C3×#4028—22no—
27C3×#4021—21no—
28C3×#4020—21no—
29C2×#6657—24no—
30C2×#6657C2214yes—
31C2×#6655C2212yes—
32#91298—24no—
33C2×#6652C2212yes—
34#91094C2214yescomplemented
35C5×#810C2212yescomplemented
36C5×#809C2212yescomplemented
37#90955C2214yescomplemented
38#83390—51nomaximal, Hall
39C2×#4150—31no—
40C2×#4095—31no—
41C22×#677—31no—
42#65859D311yescharacteristic, complemented
43C5×#416—31no—
44#65399—31no—
45#65293—31no—
46#65095—34no—
47#65070—34no—
48C23×C3×D5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—21no—
51C2×Dic30—21no—
52C2×Dic30—22no—
53C2×Dic30D414yescomplemented
54C2×Dic30C2312yes—
55C2×C5×#67—21no—
56C5×#235—22no—
57C5×#235D414yescomplemented
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C5×Dic6C2311yescharacteristic
61C2×C3×C22⋊D5D412yes—
62C3×#709—22no—
63C3×#709—22no—
64C2×C3×D20—22no—
65C2×C3×D20—22no—
66C2×C3×D20—21no—
67C2×C3×D20—24no—
68C2×C3×D20D411yescharacteristic
69C2×C3×D20C2312yes—
70C2×C3×C4×D5C2312yes—
71C2×C3×Dic10D411yescharacteristic
72C2×#1204—22no—
73C2×#1201—22no—
74C2×D3×Dic5—22no—
75#6780—216no—
76C2×D5×Dic3—22no—
77#6772—24no—
78#6772—24no—
79D3×Dic10—28no—
80#6765—28no—
81D5×Dic6—24no—
82D5×Dic6—24no—
83C3×C5×C4⋊C4C2312yes—
84C3×C5×C22⋊C4—21no—
85C3×C42×C5—21no—
86#6710—22no—
87C2×C3⋊#168C2312yes—
88C2×C5×C3⋊C8—22no—
89C2×C5×C3⋊C8C2312yes—
90C3×#685—24no—
91#6657—28no—
92#6655—24no—
93#6652—24no—
94C2×#1010—51no—
95C3×#535—51no—
96C22×#214—51no—
97C2×#932—51no—
98#5234—51no—
99#5040—54no—
100#5037—54no—
101#5004—51no—
102#5002D511yescharacteristic, complemented
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—32no—
107C2×#711—32no—
108C2×#711—62no—
109C2×#709—61no—
110C2×#709C2×D311yescharacteristic
111C22×D20C2×D311yescharacteristic
112C22×Dic10—31no—
113C22×Dic10—61no—
114C22×C5×C8—31no—
115C5×#117C2×D311yescharacteristic
116#4095—64no—
117C2×#688—32no—
118C2×#686—32no—
119C2×#681—31no—
120C2×#677—34no—
121C2×#677—64no—
122#4041C2×D314yes—
123#4028—22no—
124#4021—21no—
125#4020—21no—
126C5×#103—32no—
127C5×#102—32no—
128#3952—34no—
129#3942—34no—
130#3010—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C5×D3—21no—
133C22×C3×D5—22no—
134C22×C3×D5—42no—
135C22×C3×D5—82no—
136C22×C3×D5C2×D412yes—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—24no—
143C2×Dic15—22no—
144Dic30—24no—
145Dic30—22no—
146Dic30C2×D414yes—
147C5×#67—24no—
148C2×C5×Dic3—21no—
149C5×D12—21no—
150C5×D12C2×D412yes—
151C4×C5×D3—24no—
152C5×Dic6—21no—
153C5×Dic6C2×D412yes—
154C3×C22⋊D5—24no—
155C2×C3×Dic5C2×D412yes—
156C3×D20—22no—
157C3×D20—22no—
158C3×D20—22no—
159C3×D20—42no—
160C3×D20—84no—
161C3×C4×D5—22no—
162C3×C4×D5—22no—
163C3×Dic10—22no—
164#1204—28no—
165#1201—28no—
166D3×Dic5—28no—
167D5×Dic3—28no—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C2×C3×#41—51no—
171C22×C3×D4—51no—
172#1010—104no—
173#1010—104no—
174C2×D3×Q8—101no—
175C2×#237—101no—
176C2×#237—102no—
177C2×#235—52no—
178C2×#235C2×D511yescharacteristic
179C22×Dic6—51no—
180C22×Dic6—52no—
181C3×#127—101no—
182C3×#124—101no—
183C3×#121—54no—
184C3×#120—102no—
185C3×#117C2×D511yescharacteristic
186C2×#214—52no—
187C2×#214—54no—
188C2×#214—104no—
189#932—104no—
190C2×#213—52no—
191C2×#208—51no—
192C22×C3⋊C8C2×D511yescharacteristic
193#830—54no—
194#810—54no—
195#810C2×D512yescomplemented
196#809C2×D512yescomplemented
197C23×D5—21no—
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—62no—
206C2×C22⋊D5#6712yes—
207C22×Dic5—61no—
208C22×Dic5—62no—
209Q8×D5—64no—
210Q8×D5—64no—
211#711—64no—
212#711—64no—
213#711—616no—
214#709—22no—
215#709—22no—
216#709—68no—
217C2×D20—22no—
218C2×D20—22no—
219C2×D20—21no—
220C2×D20—24no—
221C2×D20#6711yescharacteristic
222C2×D20C22×D312yes—
223C2×C4×D5—62no—
224C2×C4×D5C22×D312yes—
225C2×Dic10—34no—
226C2×Dic10—32no—
227C2×Dic10—68no—
228C2×Dic10—62no—
229C2×Dic10—61no—
230C2×Dic10—62no—
231C2×Dic10#6711yescharacteristic
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—24no—
240#681—62no—
241C2×#168—32no—
242#677—68no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—51no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—31no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×C5×D3—22no—
256C2×C5×D3—42no—
257C2×C3×D5—22no—
258C2×C3×D5—24no—
259C2×C3×D5—42no—
260C2×C3×D5—44no—
261C2×C3×D5—84no—
262C3×C4×C5—42no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—24no—
267C3×Dic5—22no—
268C5×Dic3—22no—
269C24×C3—101no—
270C3×#41—102no—
271C3×#41—102no—
272C2×C3×Q8—51no—
273C2×C3×D4—52no—
274C2×C3×D4—51no—
275C2×C3×D4—52no—
276C2×C3×D4—104no—
277C2×C3×D4—102no—
278C2×C3×D4—102no—
279C2×C3×D4—101no—
280C22×C3×C4—52no—
281C22×C3×C4C22×D511yescharacteristic
282C2×#67—21no—
283C2×#67—102no—
284C22×Dic3—102no—
285C22×Dic3—101no—
286D3×Q8—108no—
287#237—108no—
288#237—1016no—
289#235—22no—
290#235—104no—
291#235—104no—
292#235D2014yescomplemented
293C2×D12C22×D511yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—102no—
296C2×Dic6—54no—
297C2×Dic6—52no—
298C2×Dic6—104no—
299C2×Dic6—102no—
300C2×Dic6—102no—
301C2×Dic6—101no—
302C2×Dic6—104no—
303C2×Dic6C22×D511yescharacteristic
304C3×C4⋊C4C22×D512yes—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—104no—
307C3×C42—21no—
308#214—108no—
309#214—104no—
310#213—104no—
311#208—102no—
312C2×C3⋊C8—22no—
313C2×C3⋊C8—52no—
314C2×C3⋊C8C22×D512yes—
315C23×C5—61no—
316C23×C5C2×#6711yescharacteristic
317C22×D5—22no—
318C22×D5—42no—
319C22×D5—82no—
320C22×D5C2×#6712yes—
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×C5D3×D412yes—
330C2×C4×C5D3×D412yes—
331C2×C4×C5C2×#6711yescharacteristic
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—24no—
334C22⋊D5—68no—
335C2×Dic5—68no—
336C2×Dic5—64no—
337C2×Dic5—62no—
338C2×Dic5C2×#6712yes—
339D20—22no—
340D20—22no—
341D20—22no—
342D20—42no—
343D20—84no—
344C4×D5—22no—
345C4×D5—22no—
346C4×D5—68no—
347Dic10—22no—
348Dic10—34no—
349Dic10—68no—
350Dic10—64no—
351Dic10—62no—
352C5×C8—62no—
353#168—62no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—51no—
358C2×#41—152no—
359C2×#41—301no—
360C2×#41—302no—
361C22×Q8—152no—
362C22×Q8—151no—
363C22×Q8—301no—
364C22×D4—51no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—151no—
371C22×C8—31no—
372#127—101no—
373#124—101no—
374#121—54no—
375#120—102no—
376#117D3×D511yescharacteristic
377#103—32no—
378#103—154no—
379#102—32no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5C2×#12011yescharacteristic
383C2×C3×C5#57712yes—
384C3×D5—42no—
385C3×D5—82no—
386C5×D3—42no—
387C23×C3—52no—
388C23×C3—102no—
389C23×C3—202no—
390C23×C3—402no—
391C23×C3D4×D511yescharacteristic
392C22×D3—21no—
393C3×Q8—102no—
394C3×D4—104no—
395C3×D4—102no—
396C3×D4—102no—
397C3×D4—102no—
398C3×D4—202no—
399C3×D4—404no—
400C2×C3×C4—22no—
401C2×C3×C4—52no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4C2×D2012yes—
405C2×C3×C4D4×D512yes—
406C2×C3×C4D4×D511yescharacteristic
407C2×C3×C4C23×D511yescharacteristic
408#67—24no—
409#67—108no—
410C2×Dic3—21no—
411C2×Dic3—108no—
412C2×Dic3—102no—
413C2×Dic3—104no—
414D12—21no—
415D12C2×D2012yes—
416C4×D3—24no—
417C4×D3—108no—
418Dic6—21no—
419Dic6—54no—
420Dic6—108no—
421Dic6—102no—
422Dic6—104no—
423Dic6C2×D2012yes—
424C3⋊C8—22no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—62no—
428C22×C5—122no—
429C22×C5#93712yes—
430C22×C5C22×#6711yescharacteristic
431C2×D5—22no—
432C2×D5—24no—
433C2×D5—42no—
434C2×D5—44no—
435C2×D5—84no—
436C4×C5—42no—
437C4×C5—62no—
438C4×C5#93712yes—
439C4×C5C2×D3×D411yescharacteristic
440C4×C5C2×D3×D411yescharacteristic
441Dic5—22no—
442Dic5—64no—
443C24—101no—
444#41—34no—
445#41—62no—
446#41—102no—
447#41—102no—
448#41—308no—
449#41—304no—
450#41—304no—
451#41—3016no—
452C2×Q8—31no—
453C2×Q8—51no—
454C2×Q8—154no—
455C2×Q8—152no—
456C2×Q8—302no—
457C2×Q8—308no—
458C2×Q8—304no—
459C2×Q8—304no—
460C2×Q8—302no—
461C2×Q8—301no—
462C2×D4—31no—
463C2×D4—52no—
464C2×D4—51no—
465C2×D4—52no—
466C2×D4—61no—
467C2×D4—104no—
468C2×D4—102no—
469C2×D4—102no—
470C2×D4—101no—
471C2×D4—302no—
472C22×C4—52no—
473C22×C4—61no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—302no—
482C2×C8—32no—
483C2×C8—62no—
484C2×C8—152no—
485C4⋊C4C2×D3×D512yes—
486C22⋊C4—21no—
487C22⋊C4—104no—
488C42—21no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—102no—
492C22×C3—104no—
493C22×C3—202no—
494C22×C3—204no—
495C22×C3—404no—
496C22×C3#402812yes—
497C22×C3C2×D4×D511yescharacteristic
498C2×D3—22no—
499C2×D3—42no—
500C3×C4—42no—
501C3×C4—102no—
502C3×C4#402812yes—
503C3×C4C22×D2011yescharacteristic
504C3×C4C2×D4×D511yescharacteristic
505Dic3—22no—
506Dic3—104no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5C2×#93711yescharacteristic
510C2×C5#583612yes—
511D5—42no—
512D5—82no—
513C23—52no—
514C23—61no—
515C23—102no—
516C23—202no—
517C23—402no—
518C23D5×#6711yescharacteristic
519Q8—32no—
520Q8—61no—
521Q8—102no—
522Q8—154no—
523Q8—308no—
524Q8—304no—
525Q8—302no—
526D4—32no—
527D4—64no—
528D4—61no—
529D4—104no—
530D4—102no—
531D4—102no—
532D4—102no—
533D4—202no—
534D4—308no—
535D4—404no—
536C2×C4—22no—
537C2×C4—52no—
538C2×C4—61no—
539C2×C4—64no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—308no—
543C2×C4—308no—
544C2×C4—304no—
545C2×C4—302no—
546C2×C4D3×D2012yes—
547C2×C4#677712yes—
548C2×C4D5×#6711yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—302no—
552C2×C3—22no—
553C2×C3—202no—
554C2×C3—402no—
555C2×C3C2×#402811yescharacteristic
556C2×C3#6610412yes—
557D3—42no—
558C5#8339011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—62no—
561C22—104no—
562C22—102no—
563C22—122no—
564C22—204no—
565C22—202no—
566C22—404no—
567C22#9147412yes—
568C22C2×D5×#6711yescharacteristic
569C4—42no—
570C4—62no—
571C4—102no—
572C4—304no—
573C4#9147412yes—
574C4C2×D3×D2011yescharacteristic
575C4C2×#677711yescharacteristic
576C3#1061056711yescharacteristic, complemented, Sylow
577C2—22no—
578C2—122no—
579C2—202no—
580C2—402no—
581C2C2×#9147411yescharacteristic
582C2#1175533712yes—
subgroupG/H
centerC22C2×D5×#67
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×#92001C2semidirect
2. C3×#65859C2semidirect
3. C22×#6657C2semidirect
4. C2×#91298C2semidirect
5. #11751105C2semidirect
6. C5×#5002C2semidirect
7. #11748342C2semidirect
8. #11747510C2semidirect
9. #11747493C2semidirect
16. C2×#6772C22semidirect
21. C2×D5×Dic6C22semidirect
34. #91094C22semidirect
35. C5×#810C22semidirect
36. C5×#809C22semidirect
37. #90955C22semidirect
42. #65859D3semidirect
53. C2×Dic30D4semidirect
57. C5×#235D4semidirect
102. #5002D5semidirect
195. #810C2×D5semidirect
196. #809C2×D5semidirect
292. #235D20semidirect
489. C3×C5#3010semidirect
558. C5#83390semidirect
576. C3#10610567semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C3×#658592
C22×#66572
C2×#912982
#117511052
C5×#50022
#117483422
#117475102
#117474932
#106105673
#833905