Finite Group Databasebeta

← #14424425

Subgroups — #14424425

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×#92101C211yesmaximal, characteristic, complemented
2C3×C5×#535C211yesmaximal, characteristic, complemented
3C22×#6716C211yesmaximal, characteristic, complemented
4C2×#91821C211yesmaximal, characteristic, complemented
5#11751335C211yesmaximal, characteristic, complemented
6#11751141C214yesmaximal, complemented
7#11751138C214yesmaximal, complemented
8#11751105C211yesmaximal, characteristic, complemented
9#11751103C211yesmaximal, characteristic, complemented
10#10615121—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×C3×C5×D4C2211yescharacteristic
13#92101—24no—
14#92101—24no—
15C2×Q8×D15—21no—
16C2×#6819—21no—
17C2×#6819—22no—
18C2×#6817C2211yescharacteristic
19C2×#6817C2212yescomplemented
20C22×Dic30C2211yescharacteristic
21C22×Dic30C2212yescomplemented
22C3×C5×#127—21no—
23C3×C5×#124—21no—
24C3×C5×#121C2214yes—
25C3×C5×#120—22no—
26C3×C5×#117C2211yescharacteristic
27C2×#6716—24no—
28C2×#6716C2212yes—
29C2×#6716C2214yes—
30#91821—24no—
31C2×#6715C2212yes—
32C2×#6710C2211yescharacteristic
33C22×C3⋊#168C2211yescharacteristic
34#91114C2214yescomplemented
35#91094C2212yescomplemented
36#91094C2214yescomplemented
37#91093C2212yescomplemented
38#83390—51nomaximal, Hall
39C2×#4150—31no—
40C5×#535D311yescharacteristic, complemented
41C22×#687—31no—
42C2×#4078—31no—
43#65523—31no—
44#65329—34no—
45#65326—34no—
46#65293—31no—
47#65291—31no—
48C24×C3×C5—21no—
49C3×C5×#41—22no—
50C3×C5×#41—22no—
51C2×C3×C5×Q8D411yescharacteristic
52C2×C3×C5×D4—24no—
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4D412yes—
57C2×C3×C5×D4D411yescharacteristic
58C2×C3×C5×D4C2312yes—
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C2×#1220—21no—
62C2×#1220—22no—
63C22×Dic15—21no—
64C22×Dic15—22no—
65Q8×D15—28no—
66#6819—216no—
67#6819—28no—
68#6817—22no—
69#6817—24no—
70#6817—24no—
71#6817D414yescomplemented
72C2×D60C2311yescharacteristic
73C2×C4×D15—21no—
74C2×C4×D15—22no—
75C2×Dic30—21no—
76C2×Dic30—22no—
77C2×Dic30—22no—
78C2×Dic30—24no—
79C2×Dic30—24no—
80C2×Dic30D414yescomplemented
81C2×Dic30C2312yes—
82C2×Dic30C2311yescharacteristic
83C3×C5×C4⋊C4C2312yes—
84C3×C5×C22⋊C4—21no—
85C3×C5×C22⋊C4—24no—
86C3×C42×C5—21no—
87#6716—24no—
88#6716—28no—
89#6715—24no—
90#6710—22no—
91C2×C3⋊#168—22no—
92C2×C3⋊#168C2312yes—
93C2×C3⋊#168C2312yes—
94C2×#1010—51no—
95C3×#535D511yescharacteristic, complemented
96C22×#214—51no—
97C2×#932—51no—
98#5234—51no—
99#5040—54no—
100#5037—54no—
101#5004—51no—
102#5002—51no—
103C2×C5×#41C2×D311yescharacteristic
104C22×C5×D4C2×D311yescharacteristic
105#4150—64no—
106#4150—64no—
107C2×Q8×D5—61no—
108C2×#711—62no—
109C2×#711—61no—
110C2×#709—31no—
111C2×#709—32no—
112C22×Dic10—31no—
113C22×Dic10—32no—
114C5×#127—21no—
115C5×#124—21no—
116C5×#121C2×D314yes—
117C5×#120—22no—
118C5×#117C2×D311yescharacteristic
119C2×#687—34no—
120C2×#687—32no—
121C2×#687—64no—
122#4078—64no—
123C2×#686—32no—
124C2×#681—31no—
125C22×#168—31no—
126C22⋊#168—34no—
127#3942—32no—
128#3942—34no—
129#3941—32no—
130#3010—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—42no—
133C23×C3×C5—82no—
134C23×C3×C5C2×D412yes—
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C3×C5×Q8—22no—
138C3×C5×D4—24no—
139C3×C5×D4—22no—
140C3×C5×D4—22no—
141C3×C5×D4—22no—
142C3×C5×D4—42no—
143C3×C5×D4—84no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5C2411yescharacteristic
152#1220—28no—
153#1220—24no—
154C2×Dic15—28no—
155C2×Dic15—24no—
156C2×Dic15—22no—
157C2×Dic15—21no—
158D60—21no—
159D60C2×D412yes—
160C4×D15—28no—
161C4×D15—24no—
162Dic30—28no—
163Dic30—24no—
164Dic30—22no—
165Dic30—21no—
166Dic30C2×D412yes—
167Dic30C2×D414yes—
168C3⋊#168—22no—
169C3⋊#168—22no—
170C2×C3×#41C2×D511yescharacteristic
171C22×C3×D4C2×D511yescharacteristic
172#1010—104no—
173#1010—104no—
174C2×D3×Q8—101no—
175C2×#237—102no—
176C2×#237—101no—
177C2×#235—51no—
178C2×#235—52no—
179C22×Dic6—51no—
180C22×Dic6—52no—
181C3×#127—21no—
182C3×#124—21no—
183C3×#121C2×D514yes—
184C3×#120—22no—
185C3×#117C2×D511yescharacteristic
186C2×#214—52no—
187C2×#214—54no—
188C2×#214—104no—
189#932—104no—
190C2×#213—52no—
191C2×#208—51no—
192C22×C3⋊C8—51no—
193#830—54no—
194#810—52no—
195#810—54no—
196#809—52no—
197C24×C5—21no—
198C5×#41—22no—
199C5×#41—22no—
200C2×C5×Q8#6711yescharacteristic
201C2×C5×D4—24no—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—21no—
205C2×C5×D4#6712yes—
206C2×C5×D4#6711yescharacteristic
207C2×C5×D4C22×D312yes—
208C22×C4×C5C22×D312yes—
209C22×C4×C5C22×D311yescharacteristic
210C2×C22⋊D5—62no—
211C2×C22⋊D5—61no—
212C22×Dic5—62no—
213C22×Dic5—61no—
214Q8×D5—68no—
215#711—616no—
216#711—68no—
217#709—34no—
218#709—64no—
219#709—64no—
220#709—62no—
221C2×D20—31no—
222C2×C4×D5—62no—
223C2×C4×D5—61no—
224C2×Dic10—34no—
225C2×Dic10—32no—
226C2×Dic10—31no—
227C2×Dic10—64no—
228C2×Dic10—64no—
229C2×Dic10—62no—
230C2×Dic10—62no—
231C2×Dic10—61no—
232C5×C4⋊C4C22×D312yes—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—24no—
235C42×C5—21no—
236#687—64no—
237#687—68no—
238#686—64no—
239#681—62no—
240C2×#168—32no—
241C2×#168—32no—
242C2×#168—62no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535D1511yescharacteristic, complemented
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—24no—
255C22×C3×C5—42no—
256C22×C3×C5—44no—
257C22×C3×C5—84no—
258C22×C3×C5#12012yes—
259C22×C3×C5C22×D411yescharacteristic
260C2×D15—22no—
261C2×D15—42no—
262C3×C4×C5—22no—
263C3×C4×C5—42no—
264C3×C4×C5#12012yes—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C22×D411yescharacteristic
267Dic15—22no—
268Dic15—24no—
269C24×C3—21no—
270C3×#41—22no—
271C3×#41—22no—
272C2×C3×Q8C22⋊D511yescharacteristic
273C2×C3×D4—24no—
274C2×C3×D4—22no—
275C2×C3×D4—22no—
276C2×C3×D4—21no—
277C2×C3×D4C22⋊D512yes—
278C2×C3×D4C22⋊D511yescharacteristic
279C2×C3×D4C22×D512yes—
280C22×C3×C4C22×D512yes—
281C22×C3×C4C22×D511yescharacteristic
282C2×#67—102no—
283C2×#67—101no—
284C22×Dic3—102no—
285C22×Dic3—101no—
286D3×Q8—108no—
287#237—1016no—
288#237—108no—
289#235—54no—
290#235—104no—
291#235—104no—
292#235—102no—
293C2×D12—51no—
294C2×C4×D3—102no—
295C2×C4×D3—101no—
296C2×Dic6—54no—
297C2×Dic6—52no—
298C2×Dic6—51no—
299C2×Dic6—104no—
300C2×Dic6—104no—
301C2×Dic6—102no—
302C2×Dic6—102no—
303C2×Dic6—101no—
304C3×C4⋊C4C22×D512yes—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—24no—
307C3×C42—21no—
308#214—104no—
309#214—108no—
310#213—104no—
311#208—102no—
312C2×C3⋊C8—52no—
313C2×C3⋊C8—52no—
314C2×C3⋊C8—102no—
315C23×C5—22no—
316C23×C5—42no—
317C23×C5—82no—
318C23×C5C2×#6712yes—
319C23×C5C2×#6711yescharacteristic
320C22×D5—61no—
321C5×Q8—22no—
322C5×D4—24no—
323C5×D4—22no—
324C5×D4—22no—
325C5×D4—22no—
326C5×D4—42no—
327C5×D4—84no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5D3×D412yes—
332C2×C4×C5D3×D412yes—
333C2×C4×C5C2×#6712yes—
334C2×C4×C5C2×#6711yescharacteristic
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—68no—
337C22⋊D5—64no—
338C2×Dic5—68no—
339C2×Dic5—64no—
340C2×Dic5—62no—
341C2×Dic5—61no—
342D20—32no—
343D20—61no—
344C4×D5—68no—
345C4×D5—64no—
346Dic10—34no—
347Dic10—32no—
348Dic10—68no—
349Dic10—64no—
350Dic10—61no—
351Dic10—62no—
352#168—62no—
353#168—62no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—151no—
357C2×#41—152no—
358C2×#41—302no—
359C2×#41—301no—
360C2×#41C2×D1511yescharacteristic
361C22×Q8—151no—
362C22×Q8—152no—
363C22×Q8—301no—
364C22×D4C2×D1511yescharacteristic
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—151no—
371C22×C8—151no—
372#127—21no—
373#124—21no—
374#121C2×D1514yes—
375#120—22no—
376#117C2×D1511yescharacteristic
377#103—152no—
378#103—154no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5—82no—
384C2×C3×C5C2×#12011yescharacteristic
385C2×C3×C5#57712yes—
386D15—42no—
387C23×C3—22no—
388C23×C3—42no—
389C23×C3—82no—
390C23×C3C2×C22⋊D512yes—
391C23×C3C2×C22⋊D511yescharacteristic
392C22×D3—101no—
393C3×Q8—22no—
394C3×D4—24no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—42no—
399C3×D4—84no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4D4×D512yes—
404C2×C3×C4D4×D512yes—
405C2×C3×C4C2×C22⋊D512yes—
406C2×C3×C4C2×C22⋊D511yescharacteristic
407C2×C3×C4C23×D511yescharacteristic
408#67—108no—
409#67—104no—
410C2×Dic3—108no—
411C2×Dic3—102no—
412C2×Dic3—101no—
413C2×Dic3—104no—
414D12—52no—
415D12—101no—
416C4×D3—108no—
417C4×D3—104no—
418Dic6—54no—
419Dic6—52no—
420Dic6—108no—
421Dic6—101no—
422Dic6—102no—
423Dic6—104no—
424C3⋊C8—102no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—24no—
429C22×C5—42no—
430C22×C5—44no—
431C22×C5—84no—
432C22×C5#93712yes—
433C22×C5C22×#6711yescharacteristic
434C2×D5—62no—
435C2×D5—122no—
436C4×C5—22no—
437C4×C5—42no—
438C4×C5#93712yes—
439C4×C5C2×D3×D411yescharacteristic
440C4×C5C2×D3×D411yescharacteristic
441Dic5—64no—
442Dic5—62no—
443C24—21no—
444#41—22no—
445#41—22no—
446#41—154no—
447#41—304no—
448#41—304no—
449#41—3016no—
450#41—308no—
451#41—302no—
452C2×Q8—154no—
453C2×Q8—152no—
454C2×Q8—151no—
455C2×Q8—304no—
456C2×Q8—304no—
457C2×Q8—308no—
458C2×Q8—302no—
459C2×Q8—302no—
460C2×Q8—301no—
461C2×Q8#122011yescharacteristic
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—151no—
467C2×D4—302no—
468C2×D4—301no—
469C2×D4#122012yes—
470C2×D4#122011yescharacteristic
471C2×D4C22×D1512yes—
472C22×C4—302no—
473C22×C4—301no—
474C22×C4—302no—
475C22×C4—301no—
476C22×C4C22×D1512yes—
477C22×C4C22×D1511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—302no—
482C2×C8—152no—
483C2×C8—152no—
484C2×C8—302no—
485C4⋊C4C22×D1512yes—
486C22⋊C4—21no—
487C22⋊C4—24no—
488C42—21no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—24no—
493C22×C3—42no—
494C22×C3—44no—
495C22×C3—84no—
496C22×C3#408312yes—
497C22×C3C22×C22⋊D511yescharacteristic
498C2×D3—102no—
499C2×D3—202no—
500C3×C4—22no—
501C3×C4—42no—
502C3×C4#408312yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C2×D4×D511yescharacteristic
505Dic3—104no—
506Dic3—102no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5—82no—
510C2×C5C2×#93711yescharacteristic
511C2×C5#583612yes—
512D5—122no—
513C23—22no—
514C23—42no—
515C23—82no—
516C23—301no—
517C23C2×#122012yes—
518C23C2×#122011yescharacteristic
519Q8—22no—
520Q8—154no—
521Q8—152no—
522Q8—308no—
523Q8—304no—
524Q8—302no—
525Q8—301no—
526D4—24no—
527D4—22no—
528D4—22no—
529D4—22no—
530D4—42no—
531D4—84no—
532D4—152no—
533D4—308no—
534D4—304no—
535D4—301no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—308no—
540C2×C4—308no—
541C2×C4—304no—
542C2×C4—302no—
543C2×C4—301no—
544C2×C4—304no—
545C2×C4D4×D1512yes—
546C2×C4D4×D1512yes—
547C2×C4C2×#122012yes—
548C2×C4C2×#122011yescharacteristic
549C2×C4C23×D1511yescharacteristic
550C8—302no—
551C8—302no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—82no—
555C2×C3C2×#408311yescharacteristic
556C2×C3#6617012yes—
557D3—202no—
558C5#8339011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—22no—
561C22—24no—
562C22—42no—
563C22—44no—
564C22—84no—
565C22—302no—
566C22—602no—
567C22#9182612yes—
568C22C22×#122011yescharacteristic
569C4—22no—
570C4—42no—
571C4—304no—
572C4—302no—
573C4#9182612yes—
574C4C2×D4×D1511yescharacteristic
575C4C2×D4×D1511yescharacteristic
576C3#1061512111yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—82no—
580C2—602no—
581C2C2×#9182611yescharacteristic
582C2#1175659512yes—
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#535C2
socleC22×C3×C5C22×D4
hypercenter#535D15
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#92101C2semidirect
2. C3×C5×#535C2semidirect
3. C22×#6716C2semidirect
4. C2×#91821C2semidirect
5. #11751335C2semidirect
6. #11751141C2semidirect
7. #11751138C2semidirect
8. #11751105C2semidirect
9. #11751103C2semidirect
19. C2×#6817C22semidirect
21. C22×Dic30C22semidirect
34. #91114C22semidirect
35. #91094C22semidirect
36. #91094C22semidirect
37. #91093C22semidirect
40. C5×#535D3semidirect
71. #6817D4semidirect
80. C2×Dic30D4semidirect
95. C3×#535D5semidirect
246. #535D15semidirect
489. C3×C5#3010semidirect
558. C5#83390semidirect
576. C3#10615121semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C3×C5×#5352
C22×#67162
C2×#918212
#117513352
#117511412
#117511382
#117511052
#117511032
#106151213
#833905