Finite Group Databasebeta

← #14439463

Subgroups — #14439463

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×#904C211yesmaximal, characteristic, complemented
2C22×C3×#677C211yesmaximal, characteristic, complemented
3#11754600C211yesmaximal, characteristic, complemented
4#11754255C211yesmaximal, characteristic, complemented
5C2×#91309C211yesmaximal, characteristic, complemented
6C2×#91298C211yesmaximal, characteristic, complemented
7#11751202C211yesmaximal, characteristic, complemented
8#11748013C212yesmaximal, complemented
9#11748010C212yesmaximal, complemented
10#11747981C212yesmaximal, complemented
11#11747977C212yesmaximal, complemented
12#10615636—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×D20C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C22×C3×C5×C8C2211yescharacteristic
18#91815C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20C2×C5×Dic12C2211yescharacteristic, complemented
21C5×#904—24no—
22C2×C5×D24C2211yescharacteristic, complemented
23C2×C5×#204C2211yescharacteristic, complemented
24C2×C5×#204C2211yescharacteristic, complemented
25C2×C3×#677—24no—
26C2×C3×#677C2212yes—
27C2×C3×#677C2212yes—
28#91563—22no—
29#91539—22no—
30#91463C2212yes—
31#91456—22no—
32#91385C2212yescomplemented
33#91370C2212yescomplemented
34#91369—22no—
35#91368C2212yes—
36C2×#6661C2212yescomplemented
37#91309—24no—
38C2×#6656C2212yescomplemented
39C2×#6655C2212yes—
40#91298—24no—
41C2×#6652C2212yes—
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83854—51nomaximal, Hall
45C2×C5×#135—31no—
46#66164—31no—
47#66159—31no—
48C2×#4097—31no—
49C2×#4095—31no—
50C22×#677D311yescharacteristic, complemented
51#65479—32no—
52#65464—32no—
53#65457—32no—
54#65443—32no—
55#65390—31no—
56C23×C3×D5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×C5×#67—21no—
59C2×C5×#67—21no—
60C5×#235—22no—
61C5×#235—22no—
62C5×#235—22no—
63C5×#235—22no—
64C2×C5×D12C2311yescharacteristic
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3—21no—
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5—21no—
71C2×C3×D20—22no—
72C2×C3×D20—22no—
73C2×C3×D20—21no—
74C2×C3×D20C2312yes—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79C2×#1201—24no—
80C2×C3×C5×C8D414yescomplemented
81C2×C3×C5×C8C2311yescharacteristic
82C2×C3×C5×C8C2311yescharacteristic
83#6719D412yes—
84C4⋊Dic15D412yes—
85C4×Dic15C2312yes—
86#6710D414yescomplemented
87C2×C3⋊#168C2312yes—
88C5×Dic12—22no—
89C5×D24—22no—
90C5×#204—22no—
91C5×#204—22no—
92C3×#677—24no—
93C3×#677—24no—
94#6669—24no—
95(C2×D3)⋊Dic5—24no—
96#6665—24no—
97#6661—24no—
98#6656—24no—
99#6655—24no—
100#6652—24no—
101C22×C3×SD16—51no—
102#5816—51no—
103C2×#942—51no—
104#5805—51no—
105C2×#932—51no—
106C2×#904D511yescharacteristic, complemented
107#5176—52no—
108#5175—52no—
109#5168—52no—
110#5167—52no—
111#5101—51no—
112C2×C5×#41—31no—
113C2×C5×#41—31no—
114C22×D20C2×D311yescharacteristic
115C22×Dic10C2×D311yescharacteristic
116C5×#135—64no—
117C2×C5×Q16—31no—
118C2×C5×SD16—31no—
119C2×C5×SD16—31no—
120C2×C5×D8—31no—
121C22×C5×C8C2×D311yescharacteristic
122#4097—64no—
123#4095—64no—
124#4093—32no—
125#4090—32no—
126C2×#689—32no—
127C2×#688—32no—
128#4086—32no—
129#4083—62no—
130#4082—32no—
131#4081—62no—
132C2×#687—32no—
133C2×#686—32no—
134#4076—62no—
135#4072—31no—
136#4070—62no—
137C2×#681—31no—
138C2×#677—24no—
139C2×#677C2×D312yes—
140C2×#677C2×D312yes—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—21no—
146C22×C5×D3—21no—
147C22×C3×D5—22no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
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—
156C5×#67—42no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C5×D12—21no—
160C5×D12—21no—
161C5×D12—21no—
162C5×D12—21no—
163C4×C5×D3—42no—
164C4×C5×D3—42no—
165C5×Dic6—21no—
166C5×Dic6—21no—
167C5×Dic6—21no—
168C5×Dic6—21no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—42no—
171C3×D20—22no—
172C3×D20—22no—
173C3×D20—42no—
174C3×Dic10—22no—
175C3×Dic10—22no—
176C3×Dic10—42no—
177#1201—84no—
178C3×C5×C8C2×D412yes—
179C3×C5×C8C2×D412yes—
180C3⋊#168C2×D414yes—
181C22×C3×Q8—51no—
182C22×C3×D4—51no—
183C2×#235C2×D511yescharacteristic
184C2×#235C2×D511yescharacteristic
185C2×C3×SD16—52no—
186C2×C3×SD16—52no—
187C2×C3×SD16—104no—
188C22×C3×C8C2×D511yescharacteristic
189#953—102no—
190#947—52no—
191#946—102no—
192#944—52no—
193C2×#216—52no—
194#942—104no—
195C2×#215—52no—
196#940—52no—
197#938—102no—
198#936—52no—
199C2×#214—52no—
200#932—104no—
201C2×#213—52no—
202#929—102no—
203#926—51no—
204C2×#208—51no—
205C2×Dic12C2×D511yescharacteristic, complemented
206#904—24no—
207C2×D24C2×D511yescharacteristic, complemented
208C2×#204C2×D511yescharacteristic, complemented
209C2×#204C2×D511yescharacteristic, complemented
210#815—52no—
211C8×Dic3—52no—
212C23×D5—21no—
213C5×#41—62no—
214C5×#41—62no—
215C5×#41—62no—
216C5×#41—62no—
217C2×C5×Q8—31no—
218C2×C5×Q8—31no—
219C2×C5×D4—31no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C2×C5×D4—61no—
223C22×C4×C5—61no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—64no—
227C22×Dic5—21no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20C22×D312yes—
232C2×Dic10—22no—
233C2×Dic10—22no—
234C2×Dic10—21no—
235C2×Dic10C22×D312yes—
236C5×Q16—62no—
237C5×SD16—62no—
238C5×SD16—62no—
239C5×D8—62no—
240C2×C5×C8#6714yescomplemented
241C2×C5×C8C22×D311yescharacteristic
242C2×C5×C8C22×D311yescharacteristic
243C22⋊Dic5—32no—
244C22⋊Dic5—64no—
245#689—64no—
246#688—64no—
247#687—64no—
248#686—64no—
249#685—64no—
250C4⋊Dic5—32no—
251#683—64no—
252C4×Dic5—32no—
253#681—34no—
254C2×#168—32no—
255#677—24no—
256#677—24no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—31no—
260C22×SD16—51no—
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—41no—
273C2×C5×D3—42no—
274C2×C5×D3—42no—
275C2×C3×D5—42no—
276C2×C3×D5—44no—
277C2×C3×D5—84no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—24no—
282C3×Dic5—42no—
283C5×Dic3—41no—
284C5×Dic3—41no—
285C24×C3—101no—
286C2×C3×Q8—52no—
287C2×C3×Q8—101no—
288C2×C3×Q8—102no—
289C2×C3×Q8—102no—
290C2×C3×D4—52no—
291C2×C3×D4—102no—
292C2×C3×D4—101no—
293C2×C3×D4—102no—
294C22×C3×C4—101no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—21no—
297C2×#67—21no—
298C2×#67—104no—
299#235—22no—
300#235—22no—
301#235—22no—
302#235—22no—
303C2×D12C22×D511yescharacteristic
304C2×D12C22×D511yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×Dic6C22×D511yescharacteristic
308C2×Dic6C22×D511yescharacteristic
309C3×SD16—104no—
310C3×SD16—104no—
311C2×C3×C8C22⋊D514yescomplemented
312C2×C3×C8C22×D511yescharacteristic
313C2×C3×C8C22×D511yescharacteristic
314#217—52no—
315#217—104no—
316#216—104no—
317#215—104no—
318#214—104no—
319#213—104no—
320(C2×D3)⋊C4—104no—
321C4⋊Dic3—52no—
322Dic3⋊C4—104no—
323C4×Dic3—52no—
324#208—54no—
325C2×C3⋊C8—52no—
326Dic12—22no—
327D24—22no—
328#204—22no—
329#204—22no—
330C23×C5—61no—
331C23×C5—61no—
332C23×C5D3×D411yescharacteristic
333C22×D5—22no—
334C22×D5—42no—
335C22×D5—82no—
336C5×Q8—61no—
337C5×Q8—61no—
338C5×Q8—61no—
339C5×Q8—61no—
340C5×D4—61no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—61no—
344C5×D4—122no—
345C5×D4—122no—
346C2×C4×C5—61no—
347C2×C4×C5—61no—
348C2×C4×C5—122no—
349C2×C4×C5—122no—
350C2×C4×C5D3×D411yescharacteristic
351C2×C4×C5D3×D412yes—
352C2×C4×C5C2×#6712yes—
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—244no—
355C2×Dic5—22no—
356C2×Dic5—34no—
357C2×Dic5—42no—
358D20—22no—
359D20—22no—
360D20—42no—
361Dic10—22no—
362Dic10—22no—
363Dic10—42no—
364C5×C8C2×#6712yes—
365C5×C8C2×#6712yes—
366#168—34no—
367C2×#41—31no—
368C2×#41—31no—
369C22×Q8—51no—
370C22×D4—51no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—64no—
374C2×Q16—31no—
375C2×Q16—152no—
376C2×SD16—31no—
377C2×SD16—31no—
378C2×SD16—52no—
379C2×SD16—52no—
380C2×SD16—104no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×D8—31no—
384C2×D8—152no—
385C2×M16—151no—
386C22×C8D3×D511yescharacteristic
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—82no—
402C5×D3—81no—
403C5×D3—81no—
404C23×C3—102no—
405C23×C3—202no—
406C23×C3—402no—
407C23×C3D4×D511yescharacteristic
408C22×D3—21no—
409C22×D3—21no—
410C3×Q8—102no—
411C3×Q8—102no—
412C3×Q8—202no—
413C3×D4—102no—
414C3×D4—102no—
415C3×D4—202no—
416C2×C3×C4—102no—
417C2×C3×C4—202no—
418C2×C3×C4D4×D512yes—
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4C2×C22⋊D512yes—
421C2×C3×C4C23×D511yescharacteristic
422#67—42no—
423#67—42no—
424#67—404no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—54no—
428D12—21no—
429D12—21no—
430D12—21no—
431D12—21no—
432C4×D3—42no—
433C4×D3—42no—
434Dic6—21no—
435Dic6—21no—
436Dic6—21no—
437Dic6—21no—
438C3×C8C2×C22⋊D512yes—
439C3×C8C2×C22⋊D512yes—
440C3⋊C8—54no—
441C22×C5—22no—
442C22×C5—122no—
443C22×C5—122no—
444C22×C5—121no—
445C22×C5—121no—
446C22×C5#94012yes—
447C22×C5C2×D3×D411yescharacteristic
448C2×D5—44no—
449C2×D5—42no—
450C2×D5—84no—
451C4×C5—121no—
452C4×C5—121no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—42no—
457Dic5—64no—
458C24—101no—
459#41—62no—
460#41—62no—
461#41—62no—
462#41—62no—
463C2×Q8—31no—
464C2×Q8—31no—
465C2×Q8—52no—
466C2×Q8—101no—
467C2×Q8—102no—
468C2×Q8—102no—
469C2×D4—31no—
470C2×D4—31no—
471C2×D4—52no—
472C2×D4—61no—
473C2×D4—61no—
474C2×D4—102no—
475C2×D4—101no—
476C2×D4—102no—
477C2×D4—304no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—62no—
483Q16—304no—
484SD16—62no—
485SD16—62no—
486SD16—104no—
487SD16—104no—
488SD16—304no—
489SD16—304no—
490D8—62no—
491D8—304no—
492M16—154no—
493C2×C8—152no—
494C2×C8#120114yescomplemented
495C2×C8C2×D3×D511yescharacteristic
496C2×C8C2×D3×D511yescharacteristic
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—204no—
506C22×C3—202no—
507C22×C3—404no—
508C22×C3#408612yes—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—42no—
511C2×D3—42no—
512C2×D3—41no—
513C2×D3—41no—
514C3×C4—202no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—41no—
519Dic3—41no—
520Dic3—104no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5—241no—
524C2×C5#576212yes—
525C2×C5C2×#94011yescharacteristic
526D5—82no—
527C23—61no—
528C23—61no—
529C23—102no—
530C23—202no—
531C23—402no—
532C23#677711yescharacteristic
533Q8—61no—
534Q8—61no—
535Q8—61no—
536Q8—61no—
537Q8—102no—
538Q8—102no—
539Q8—202no—
540D4—61no—
541D4—61no—
542D4—61no—
543D4—61no—
544D4—102no—
545D4—102no—
546D4—122no—
547D4—122no—
548D4—202no—
549D4—1204no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—102no—
553C2×C4—122no—
554C2×C4—122no—
555C2×C4—154no—
556C2×C4—202no—
557C2×C4#677711yescharacteristic
558C2×C4#677712yes—
559C2×C4C2×#120112yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—154no—
562C8C2×#120112yes—
563C8C2×#120112yes—
564C2×C3—22no—
565C2×C3—402no—
566C2×C3#6610412yes—
567C2×C3C2×#408611yescharacteristic
568D3—81no—
569D3—81no—
570C5#8385411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—121no—
573C22—121no—
574C22—122no—
575C22—122no—
576C22—202no—
577C22—204no—
578C22—404no—
579C22#9146312yes—
580C22C2×#677711yescharacteristic
581C4—121no—
582C4—121no—
583C4—202no—
584C4—304no—
585C4#9146312yes—
586C4C2×#677711yescharacteristic
587C4C22×#120111yescharacteristic
588C3#1061563611yescharacteristic, complemented, Sylow
589C2—22no—
590C2—241no—
591C2—241no—
592C2—402no—
593C2#1175398012yes—
594C2C2×#9146311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C5×#904C2semidirect
2. C22×C3×#677C2semidirect
3. #11754600C2semidirect
4. #11754255C2semidirect
5. C2×#91309C2semidirect
6. C2×#91298C2semidirect
7. #11751202C2semidirect
8. #11748013C2semidirect
9. #11748010C2semidirect
10. #11747981C2semidirect
11. #11747977C2semidirect
20. C2×C5×Dic12C22semidirect
22. C2×C5×D24C22semidirect
23. C2×C5×#204C22semidirect
24. C2×C5×#204C22semidirect
32. #91385C22semidirect
33. #91370C22semidirect
36. C2×#6661C22semidirect
38. C2×#6656C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
50. C22×#677D3semidirect
80. C2×C3×C5×C8D4semidirect
86. #6710D4semidirect
106. C2×#904D5semidirect
205. C2×Dic12C2×D5semidirect
207. C2×D24C2×D5semidirect
208. C2×#204C2×D5semidirect
209. C2×#204C2×D5semidirect
240. C2×C5×C8#67semidirect
311. C2×C3×C8C22⋊D5semidirect
494. C2×C8#1201semidirect
503. C3×C5#3154semidirect
570. C5#83854semidirect
588. C3#10615636semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9042
C22×C3×#6772
#117546002
#117542552
C2×#913092
C2×#912982
#117512022
#117480132
#117480102
#117479812
#117479772
#106156363
#838545