Finite Group Databasebeta

← #14439484

Subgroups — #14439484

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#908C211yesmaximal, characteristic, complemented
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3#11754604C211yesmaximal, characteristic, complemented
4#11754255C211yesmaximal, characteristic, complemented
5C22×#6656C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7#11751223C211yesmaximal, characteristic, complemented
8#11748013C212yesmaximal, complemented
9#11748010C212yesmaximal, complemented
10#11747983C212yesmaximal, complemented
11#11747982C212yesmaximal, complemented
12#10615670—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91815C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C5×#908—24no—
21C2×C5×D24C2212yes—
22C2×C5×#204C2212yes—
23C3×#4055—24no—
24C2×C3×Dic20C2212yescomplemented
25C2×C3×#677C2212yescomplemented
26#91568—22no—
27#91539—22no—
28#91463C2212yes—
29#91449—22no—
30#91385C2212yescomplemented
31#91370C2212yes—
32#91370C2212yescomplemented
33#91369—22no—
34C2×#6661C2211yescharacteristic, complemented
35C2×#6656—24no—
36C2×#6656C2212yes—
37C2×#6656C2212yes—
38C2×#6656C2211yescharacteristic, complemented
39C2×#6655C2211yescharacteristic, complemented
40#91297—24no—
41C2×#6652C2211yescharacteristic, complemented
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83974—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66159—31no—
47C2×#4096—31no—
48#66139—31no—
49C22×#687—31no—
50C2×#4055D311yescharacteristic, complemented
51#65464—32no—
52#65456—32no—
53#65444—32no—
54#65443—32no—
55#65411—31no—
56C23×C5×D3—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×C5×#67—21no—
59C5×#235—22no—
60C5×#235—22no—
61C2×C5×D12—22no—
62C2×C5×D12—22no—
63C2×C5×D12—21no—
64C2×C5×D12C2312yes—
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3—21no—
67C2×C5×Dic6C2311yescharacteristic
68C2×C3×C22⋊D5—21no—
69C22×C3×Dic5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×Dic10—22no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10C2312yes—
78C2×C3×Dic10C2311yescharacteristic
79C2×#1201—24no—
80C3×C5×M16D414yescomplemented
81C2×C3×C5×C8C2312yes—
82#6719D412yes—
83C4⋊Dic15D412yes—
84C4×Dic15C2312yes—
85C2×C3⋊#168D414yescomplemented
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88C5×D24—24no—
89C5×#204—24no—
90C3×Dic20—24no—
91C3×#677—24no—
92#6669—24no—
93(C2×D3)⋊Dic5—24no—
94(C2×D3)⋊Dic5—24no—
95#6661—22no—
96#6656—22no—
97#6656—24no—
98#6656—24no—
99#6655—22no—
100#6652—22no—
101C2×C3×#137—51no—
102#5830—51no—
103C2×#950—51no—
104#5816—51no—
105C22×#215—51no—
106C2×#908D511yescharacteristic, complemented
107#5191—52no—
108#5190—52no—
109#5176—52no—
110#5175—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C22×C5×D4—31no—
114C2×#709C2×D311yescharacteristic
115C22×Dic10C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16C2×D311yescharacteristic
120#4099—62no—
121#4096—64no—
122#4090—32no—
123C2×#689—31no—
124C2×#688—31no—
125#4086—32no—
126#4084—62no—
127#4082—32no—
128#4082—32no—
129#4081—62no—
130C2×#687—32no—
131C2×#687—32no—
132C2×#687—31no—
133C2×#687—64no—
134C2×#686—31no—
135#4072—31no—
136#4070—62no—
137C22×#168—31no—
138#4055—24no—
139C2×Dic20C2×D312yescomplemented
140C2×#677C2×D312yescomplemented
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—21no—
146C22×C5×D3—22no—
147C22×C5×D3—42no—
148C22×C5×D3—82no—
149C22×C3×D5—21no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15C2×D414yes—
155C5×#67—42no—
156C2×C5×Dic3—21no—
157C5×D12—22no—
158C5×D12—21no—
159C5×D12—22no—
160C5×D12—21no—
161C5×D12—42no—
162C4×C5×D3—42no—
163C5×Dic6—21no—
164C5×Dic6—21no—
165C3×C22⋊D5—42no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—42no—
169C3×D20—21no—
170C3×D20—21no—
171C3×C4×D5—42no—
172C3×Dic10—22no—
173C3×Dic10—21no—
174C3×Dic10—22no—
175C3×Dic10—21no—
176C3×Dic10—42no—
177#1201—84no—
178C3×C5×C8C2×D414yes—
179C3⋊#168C2×D412yes—
180C3⋊#168C2×D412yes—
181C2×C3×#41—51no—
182C22×C3×Q8—51no—
183C2×#235C2×D511yescharacteristic
184C22×D12C2×D511yescharacteristic
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16C2×D511yescharacteristic
189#950—104no—
190#947—52no—
191#947—52no—
192#946—102no—
193#944—52no—
194C2×#216—51no—
195C2×#215—52no—
196C2×#215—52no—
197C2×#215—51no—
198C2×#215—104no—
199#940—52no—
200#937—102no—
201C2×#214—51no—
202C2×#213—51no—
203#930—102no—
204#929—102no—
205#926—51no—
206C22×C3⋊C8—51no—
207#908—24no—
208C2×D24C2×D512yes—
209C2×#204C2×D512yes—
210#815—52no—
211C8×Dic3—52no—
212C24×C5—61no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—31no—
216C2×C5×D4—31no—
217C2×C5×D4—32no—
218C2×C5×D4—61no—
219C2×C5×D4—62no—
220C2×C5×D4—61no—
221C2×C5×D4—62no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—21no—
225C2×C22⋊D5—64no—
226C22×Dic5—21no—
227#709—22no—
228#709—22no—
229C2×D20C22×D311yescharacteristic
230C2×C4×D5—21no—
231C2×Dic10—22no—
232C2×Dic10—22no—
233C2×Dic10—21no—
234C2×Dic10C22×D312yes—
235C2×Dic10C22×D311yescharacteristic
236C5×SD16—64no—
237C5×D8—64no—
238C5×M16#6714yescomplemented
239C2×C5×C8C22×D312yes—
240C22⋊Dic5—32no—
241C22⋊Dic5—64no—
242C22⋊Dic5—64no—
243#689—62no—
244#688—62no—
245#687—62no—
246#687—64no—
247#687—64no—
248#686—62no—
249C4⋊Dic5—32no—
250#683—64no—
251C4×Dic5—32no—
252C2×#168—34no—
253C2×#168—31no—
254C2×#168—31no—
255Dic20—24no—
256#677—24no—
257C2×#137—51no—
258C2×AGL(1,ℤ/8)—31no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×C5×D3—41no—
272C2×C5×D3—42no—
273C2×C5×D3—44no—
274C2×C5×D3—42no—
275C2×C5×D3—84no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—24no—
282C3×Dic5—42no—
283C3×Dic5—41no—
284C5×Dic3—41no—
285C23×D3—21no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—52no—
289C2×C3×Q8—51no—
290C2×C3×Q8—101no—
291C2×C3×Q8—102no—
292C2×C3×Q8—102no—
293C2×C3×D4—51no—
294C2×C3×D4—101no—
295C22×C3×C4—101no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—21no—
299C2×#67—104no—
300#235—22no—
301#235—22no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—21no—
305C2×D12C22×D512yes—
306C2×D12C22×D511yescharacteristic
307C2×C4×D3—21no—
308C2×Dic6C22×D511yescharacteristic
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16C22⋊D514yescomplemented
312C2×C3×C8C22×D512yes—
313#217—52no—
314#216—102no—
315#215—104no—
316#215—104no—
317#215—102no—
318#214—102no—
319#213—102no—
320(C2×D3)⋊C4—104no—
321(C2×D3)⋊C4—104no—
322C4⋊Dic3—52no—
323Dic3⋊C4—104no—
324C4×Dic3—52no—
325C2×C3⋊C8—54no—
326C2×C3⋊C8—51no—
327C2×C3⋊C8—51no—
328D24—24no—
329#204—24no—
330C23×C5—61no—
331C23×C5—62no—
332C23×C5—122no—
333C23×C5—242no—
334C23×C5D3×D411yescharacteristic
335C22×D5—21no—
336C5×Q8—61no—
337C5×Q8—61no—
338C5×D4—61no—
339C5×D4—62no—
340C5×D4—61no—
341C5×D4—62no—
342C5×D4—122no—
343C5×D4—122no—
344C2×C4×C5—61no—
345C2×C4×C5—122no—
346C2×C4×C5D3×D411yescharacteristic
347C2×C4×C5D3×D412yes—
348C2×C4×C5C2×#6712yes—
349C2×C4×C5C23×D311yescharacteristic
350C22⋊D5—42no—
351C22⋊D5—244no—
352C2×Dic5—22no—
353C2×Dic5—21no—
354C2×Dic5—34no—
355C2×Dic5—42no—
356D20—21no—
357D20—21no—
358C4×D5—42no—
359Dic10—22no—
360Dic10—21no—
361Dic10—22no—
362Dic10—21no—
363Dic10—42no—
364C5×C8C2×#6714yes—
365#168—32no—
366#168—32no—
367C2×#41—31no—
368C2×#41—51no—
369C22×Q8—51no—
370C22×D4—31no—
371#137—104no—
372AGL(1,ℤ/8)—64no—
373#135—304no—
374C2×Q16—52no—
375C2×Q16—151no—
376C2×SD16—32no—
377C2×SD16—52no—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—151no—
381C2×SD16—151no—
382C2×SD16—304no—
383C2×D8—32no—
384C2×D8—151no—
385C2×M16D3×D511yescharacteristic
386C22×C8—151no—
387C4⋊Q8—152no—
388#127—152no—
389#124—152no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—302no—
394#120—302no—
395#117—151no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401C3×D5—81no—
402C5×D3—81no—
403C5×D3—82no—
404C23×C3—101no—
405C23×C3D4×D511yescharacteristic
406C22×D3—21no—
407C22×D3—22no—
408C22×D3—42no—
409C22×D3—82no—
410C3×Q8—102no—
411C3×Q8—101no—
412C3×Q8—102no—
413C3×Q8—101no—
414C3×Q8—202no—
415C3×D4—101no—
416C3×D4—101no—
417C3×D4—202no—
418C2×C3×C4—102no—
419C2×C3×C4—101no—
420C2×C3×C4—202no—
421C2×C3×C4—202no—
422C2×C3×C4D4×D512yes—
423C2×C3×C4D4×D511yescharacteristic
424C2×C3×C4C2×C22⋊D512yes—
425C2×C3×C4C23×D511yescharacteristic
426#67—42no—
427#67—404no—
428C2×Dic3—21no—
429C2×Dic3—54no—
430D12—21no—
431D12—22no—
432D12—22no—
433D12—21no—
434D12—42no—
435C4×D3—42no—
436Dic6—21no—
437Dic6—21no—
438C3×C8C2×C22⋊D514yes—
439C3⋊C8—52no—
440C3⋊C8—52no—
441C22×C5—22no—
442C22×C5—124no—
443C22×C5—122no—
444C22×C5—121no—
445C22×C5—122no—
446C22×C5—244no—
447C22×C5#94012yes—
448C22×C5C2×D3×D411yescharacteristic
449C2×D5—42no—
450C2×D5—41no—
451C4×C5—121no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C22×#6711yescharacteristic
455Dic5—42no—
456Dic5—41no—
457Dic5—64no—
458C24—61no—
459#41—62no—
460#41—62no—
461#41—102no—
462#41—102no—
463C2×Q8—31no—
464C2×Q8—51no—
465C2×Q8—52no—
466C2×Q8—101no—
467C2×Q8—102no—
468C2×Q8—102no—
469C2×D4—31no—
470C2×D4—32no—
471C2×D4—51no—
472C2×D4—61no—
473C2×D4—62no—
474C2×D4—61no—
475C2×D4—62no—
476C2×D4—101no—
477C2×D4—304no—
478C22×C4—61no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—104no—
483Q16—302no—
484SD16—64no—
485SD16—104no—
486SD16—304no—
487SD16—304no—
488SD16—302no—
489SD16—302no—
490D8—64no—
491D8—302no—
492M16#120114yescomplemented
493C2×C8—154no—
494C2×C8—151no—
495C2×C8—151no—
496C2×C8C2×D3×D512yes—
497C4⋊C4—152no—
498C4⋊C4—304no—
499C22⋊C4—152no—
500C22⋊C4—304no—
501C22⋊C4—304no—
502C42—152no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—202no—
506C22×C3—201no—
507C22×C3#408612yes—
508C22×C3C2×D4×D511yescharacteristic
509C2×D3—44no—
510C2×D3—42no—
511C2×D3—41no—
512C2×D3—42no—
513C2×D3—84no—
514C3×C4—201no—
515C3×C4—202no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C22×C22⋊D511yescharacteristic
519Dic3—41no—
520Dic3—104no—
521C2×C5—22no—
522C2×C5—242no—
523C2×C5—241no—
524C2×C5#577812yes—
525C2×C5C2×#94011yescharacteristic
526D5—81no—
527C23—61no—
528C23—62no—
529C23—101no—
530C23—122no—
531C23—242no—
532C23#677711yescharacteristic
533Q8—61no—
534Q8—61no—
535Q8—102no—
536Q8—101no—
537Q8—102no—
538Q8—101no—
539Q8—202no—
540D4—61no—
541D4—62no—
542D4—61no—
543D4—62no—
544D4—101no—
545D4—101no—
546D4—122no—
547D4—122no—
548D4—202no—
549D4—1204no—
550C2×C4—61no—
551C2×C4—101no—
552C2×C4—102no—
553C2×C4—122no—
554C2×C4—154no—
555C2×C4—202no—
556C2×C4—202no—
557C2×C4#677711yescharacteristic
558C2×C4#677712yes—
559C2×C4C2×#120112yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—152no—
562C8—152no—
563C8C2×#120114yes—
564C2×C3—22no—
565C2×C3—401no—
566C2×C3#6610912yes—
567C2×C3C2×#408611yescharacteristic
568D3—82no—
569D3—81no—
570C5#8397411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—124no—
573C22—122no—
574C22—121no—
575C22—122no—
576C22—202no—
577C22—201no—
578C22—244no—
579C22#9146312yes—
580C22C2×#677711yescharacteristic
581C4—121no—
582C4—201no—
583C4—202no—
584C4—304no—
585C4#9146312yes—
586C4C2×#677711yescharacteristic
587C4C22×#120111yescharacteristic
588C3#1061567011yescharacteristic, complemented, Sylow
589C2—22no—
590C2—242no—
591C2—241no—
592C2—401no—
593C2#1175403912yes—
594C2C2×#9146311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
hypercenterC2×M16D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C5×#908C2semidirect
2. C2×C3×#4055C2semidirect
3. #11754604C2semidirect
4. #11754255C2semidirect
5. C22×#6656C2semidirect
6. C2×#91297C2semidirect
7. #11751223C2semidirect
8. #11748013C2semidirect
9. #11748010C2semidirect
10. #11747983C2semidirect
11. #11747982C2semidirect
24. C2×C3×Dic20C22semidirect
25. C2×C3×#677C22semidirect
30. #91385C22semidirect
32. #91370C22semidirect
34. C2×#6661C22semidirect
38. C2×#6656C22semidirect
39. C2×#6655C22semidirect
41. C2×#6652C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
50. C2×#4055D3semidirect
80. C3×C5×M16D4semidirect
85. C2×C3⋊#168D4semidirect
106. C2×#908D5semidirect
139. C2×Dic20C2×D3semidirect
140. C2×#677C2×D3semidirect
238. C5×M16#67semidirect
311. C3×M16C22⋊D5semidirect
492. M16#1201semidirect
503. C3×C5#3154semidirect
570. C5#83974semidirect
588. C3#10615670semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9082
C2×C3×#40552
#117546042
#117542552
C22×#66562
C2×#912972
#117512232
#117480132
#117480102
#117479832
#117479822
#106156703
#839745