Finite Group Databasebeta

← #14439460

Subgroups — #14439460

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
1C22×C5×#204C211yesmaximal, characteristic, complemented
2C2×C3×#4050C211yesmaximal, characteristic, complemented
3#11754604C211yesmaximal, characteristic, complemented
4#11754251C211yesmaximal, characteristic, complemented
5C2×#91307C211yesmaximal, characteristic, complemented
6C2×#91299C211yesmaximal, characteristic, complemented
7#11751202C211yesmaximal, characteristic, complemented
8#11748015C212yesmaximal, complemented
9#11748010C212yesmaximal, complemented
10#11747983C212yesmaximal, complemented
11#11747977C212yesmaximal, complemented
12#10615585—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C22×C3×C5×C8C2211yescharacteristic
18#91815C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20C2×C5×#204—24no—
21C2×C5×#204C2212yes—
22C2×C5×#204C2212yes—
23C2×C3×Dic20C2211yescharacteristic, complemented
24C3×#4050—24no—
25C2×C3×D40C2211yescharacteristic, complemented
26C2×C3×#677C2211yescharacteristic, complemented
27C2×C3×#677C2211yescharacteristic, complemented
28#91568—22no—
29#91536—22no—
30#91463C2212yes—
31#91449—22no—
32#91385C2212yescomplemented
33#91370C2212yes—
34#91368C2212yescomplemented
35#91359—22no—
36C2×#6661C2212yescomplemented
37C2×#6656C2212yes—
38#91307—24no—
39C2×#6655C2212yescomplemented
40#91299—24no—
41C2×#6652C2212yes—
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83905—51nomaximal, Hall
45C22×C5×SD16—31no—
46#66150—31no—
47C2×#4088—31no—
48#66139—31no—
49C2×#4078—31no—
50C2×#4050D311yescharacteristic, complemented
51#65465—32no—
52#65464—32no—
53#65457—32no—
54#65456—32no—
55#65390—31no—
56C23×C5×D3—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C5×Dic3—21no—
59C2×C5×D12—22no—
60C2×C5×D12—22no—
61C2×C5×D12—21no—
62C2×C5×D12C2312yes—
63C2×C5×Dic6—22no—
64C2×C5×Dic6—22no—
65C2×C5×Dic6—21no—
66C2×C5×Dic6C2312yes—
67C2×C3×C22⋊D5—21no—
68C2×C3×C22⋊D5—21no—
69C3×#709—22no—
70C3×#709—22no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20C2311yescharacteristic
74C2×C3×D20C2311yescharacteristic
75C2×C3×C4×D5—21no—
76C2×C3×C4×D5—21no—
77C2×C3×Dic10C2311yescharacteristic
78C2×C3×Dic10C2311yescharacteristic
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×#204—24no—
89C5×#204—24no—
90C3×Dic20—22no—
91C3×D40—22no—
92C3×#677—22no—
93C3×#677—22no—
94#6669—24no—
95(C2×D3)⋊Dic5—24no—
96#6665—24no—
97#6661—24no—
98#6656—24no—
99#6655—24no—
100#6652—24no—
101C2×C3×#135—51no—
102#5830—51no—
103#5825—51no—
104C2×#951—51no—
105C2×#949—51no—
106C22×#204D511yescharacteristic, complemented
107#5190—52no—
108#5175—52no—
109#5168—52no—
110#5154—52no—
111#5101—51no—
112C22×C5×Q8—31no—
113C22×C5×D4—31no—
114C2×#709C2×D311yescharacteristic
115C2×#709C2×D311yescharacteristic
116C2×C5×SD16—32no—
117C2×C5×SD16—32no—
118C2×C5×SD16—64no—
119C22×C5×C8C2×D311yescharacteristic
120#4099—62no—
121#4093—32no—
122#4092—62no—
123#4090—32no—
124C2×#689—32no—
125#4088—64no—
126C2×#688—32no—
127#4086—32no—
128#4084—62no—
129#4082—32no—
130C2×#687—32no—
131#4078—64no—
132C2×#686—32no—
133#4075—62no—
134#4072—31no—
135C2×#681—31no—
136C2×Dic20C2×D311yescharacteristic, complemented
137#4050—24no—
138C2×D40C2×D311yescharacteristic, complemented
139C2×#677C2×D311yescharacteristic, complemented
140C2×#677C2×D311yescharacteristic, complemented
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—22no—
146C22×C5×D3—42no—
147C22×C5×D3—82no—
148C22×C3×D5—21no—
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—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—42no—
157C5×D12—22no—
158C5×D12—22no—
159C5×D12—42no—
160C5×Dic6—22no—
161C5×Dic6—22no—
162C5×Dic6—42no—
163C3×C22⋊D5—42no—
164C3×C22⋊D5—42no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C3×D20—21no—
168C3×D20—21no—
169C3×D20—21no—
170C3×D20—21no—
171C3×C4×D5—42no—
172C3×C4×D5—42no—
173C3×Dic10—21no—
174C3×Dic10—21no—
175C3×Dic10—21no—
176C3×Dic10—21no—
177#1201—84no—
178C3×C5×C8C2×D412yes—
179C3×C5×C8C2×D412yes—
180C3⋊#168C2×D414yes—
181C2×C3×#41—51no—
182C2×C3×#41—51no—
183C22×D12C2×D511yescharacteristic
184C22×Dic6C2×D511yescharacteristic
185C3×#135—104no—
186C2×C3×Q16—51no—
187C2×C3×SD16—51no—
188C2×C3×SD16—51no—
189C2×C3×D8—51no—
190C22×C3×C8C2×D511yescharacteristic
191#951—104no—
192#949—104no—
193#947—52no—
194#944—52no—
195C2×#216—52no—
196C2×#215—52no—
197#940—52no—
198#937—102no—
199#936—52no—
200#935—102no—
201C2×#214—52no—
202C2×#213—52no—
203#930—102no—
204#926—51no—
205#924—102no—
206C2×#208—51no—
207C2×#204—24no—
208C2×#204C2×D512yes—
209C2×#204C2×D512yes—
210#815—52no—
211C8×Dic3—52no—
212C24×C5—61no—
213C2×C5×Q8—32no—
214C2×C5×Q8—61no—
215C2×C5×Q8—62no—
216C2×C5×Q8—62no—
217C2×C5×D4—32no—
218C2×C5×D4—62no—
219C2×C5×D4—61no—
220C2×C5×D4—62no—
221C22×C4×C5—61no—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—21no—
224C2×C22⋊D5—21no—
225C2×C22⋊D5—64no—
226#709—22no—
227#709—22no—
228#709—22no—
229#709—22no—
230C2×D20C22×D311yescharacteristic
231C2×D20C22×D311yescharacteristic
232C2×C4×D5—21no—
233C2×C4×D5—21no—
234C2×Dic10C22×D311yescharacteristic
235C2×Dic10C22×D311yescharacteristic
236C5×SD16—64no—
237C5×SD16—64no—
238C2×C5×C8#6714yescomplemented
239C2×C5×C8C22×D311yescharacteristic
240C2×C5×C8C22×D311yescharacteristic
241C22⋊Dic5—32no—
242C22⋊Dic5—64no—
243#689—64no—
244#688—64no—
245#687—64no—
246#686—64no—
247#685—64no—
248C4⋊Dic5—32no—
249#683—64no—
250C4×Dic5—32no—
251#681—34no—
252C2×#168—32no—
253Dic20—22no—
254D40—22no—
255#677—22no—
256#677—22no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—51no—
260C22×SD16—31no—
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—42no—
272C2×C5×D3—44no—
273C2×C5×D3—84no—
274C2×C3×D5—41no—
275C2×C3×D5—41no—
276C2×C3×D5—42no—
277C2×C3×D5—42no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—24no—
282C3×Dic5—41no—
283C3×Dic5—41no—
284C5×Dic3—42no—
285C23×D3—21no—
286C3×#41—102no—
287C3×#41—102no—
288C3×#41—102no—
289C3×#41—102no—
290C2×C3×Q8—51no—
291C2×C3×Q8—51no—
292C2×C3×D4—51no—
293C2×C3×D4—51no—
294C2×C3×D4—101no—
295C2×C3×D4—101no—
296C22×C3×C4—101no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—104no—
300C22×Dic3—21no—
301C2×D12—22no—
302C2×D12—22no—
303C2×D12—21no—
304C2×D12C22×D512yes—
305C2×Dic6—22no—
306C2×Dic6—22no—
307C2×Dic6—21no—
308C2×Dic6C22×D512yes—
309C3×Q16—102no—
310C3×SD16—102no—
311C3×SD16—102no—
312C3×D8—102no—
313C2×C3×C8C22⋊D514yescomplemented
314C2×C3×C8C22×D511yescharacteristic
315C2×C3×C8C22×D511yescharacteristic
316#217—52no—
317#217—104no—
318#216—104no—
319#215—104no—
320#214—104no—
321#213—104no—
322(C2×D3)⋊C4—104no—
323C4⋊Dic3—52no—
324Dic3⋊C4—104no—
325C4×Dic3—52no—
326#208—54no—
327C2×C3⋊C8—52no—
328#204—24no—
329#204—24no—
330C23×C5—62no—
331C23×C5—122no—
332C23×C5—242no—
333C23×C5D3×D411yescharacteristic
334C22×D5—21no—
335C22×D5—21no—
336C5×Q8—62no—
337C5×Q8—62no—
338C5×Q8—122no—
339C5×D4—62no—
340C5×D4—62no—
341C5×D4—122no—
342C2×C4×C5—62no—
343C2×C4×C5—122no—
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5D3×D412yes—
346C2×C4×C5C2×#6712yes—
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—42no—
349C22⋊D5—42no—
350C22⋊D5—244no—
351C2×Dic5—21no—
352C2×Dic5—21no—
353C2×Dic5—34no—
354D20—21no—
355D20—21no—
356D20—21no—
357D20—21no—
358C4×D5—42no—
359C4×D5—42no—
360Dic10—21no—
361Dic10—21no—
362Dic10—21no—
363Dic10—21no—
364C5×C8C2×#6712yes—
365C5×C8C2×#6712yes—
366#168—34no—
367C2×#41—51no—
368C2×#41—51no—
369C22×Q8—31no—
370C22×D4—31no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—104no—
374C2×Q16—51no—
375C2×Q16—152no—
376C2×SD16—32no—
377C2×SD16—32no—
378C2×SD16—51no—
379C2×SD16—51no—
380C2×SD16—64no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×D8—51no—
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—81no—
402C3×D5—81no—
403C5×D3—82no—
404C23×C3—101no—
405C23×C3—101no—
406C23×C3D4×D511yescharacteristic
407C22×D3—22no—
408C22×D3—42no—
409C22×D3—82no—
410C3×Q8—101no—
411C3×Q8—101no—
412C3×Q8—101no—
413C3×Q8—101no—
414C3×D4—101no—
415C3×D4—101no—
416C3×D4—101no—
417C3×D4—101no—
418C3×D4—202no—
419C3×D4—202no—
420C2×C3×C4—101no—
421C2×C3×C4—101no—
422C2×C3×C4—202no—
423C2×C3×C4—202no—
424C2×C3×C4D4×D512yes—
425C2×C3×C4D4×D511yescharacteristic
426C2×C3×C4C2×C22⋊D512yes—
427C2×C3×C4C23×D511yescharacteristic
428#67—404no—
429C2×Dic3—22no—
430C2×Dic3—42no—
431C2×Dic3—54no—
432D12—22no—
433D12—22no—
434D12—42no—
435Dic6—22no—
436Dic6—22no—
437Dic6—42no—
438C3×C8C2×C22⋊D512yes—
439C3×C8C2×C22⋊D512yes—
440C3⋊C8—54no—
441C22×C5—22no—
442C22×C5—124no—
443C22×C5—122no—
444C22×C5—244no—
445C22×C5#94012yes—
446C22×C5C2×D3×D411yescharacteristic
447C2×D5—42no—
448C2×D5—42no—
449C2×D5—41no—
450C2×D5—41no—
451C4×C5—122no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C22×#6711yescharacteristic
455Dic5—41no—
456Dic5—41no—
457Dic5—64no—
458C24—61no—
459#41—102no—
460#41—102no—
461#41—102no—
462#41—102no—
463C2×Q8—32no—
464C2×Q8—51no—
465C2×Q8—51no—
466C2×Q8—61no—
467C2×Q8—62no—
468C2×Q8—62no—
469C2×D4—32no—
470C2×D4—51no—
471C2×D4—51no—
472C2×D4—62no—
473C2×D4—61no—
474C2×D4—62no—
475C2×D4—101no—
476C2×D4—101no—
477C2×D4—304no—
478C22×C4—61no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—102no—
483Q16—304no—
484SD16—64no—
485SD16—64no—
486SD16—102no—
487SD16—102no—
488SD16—304no—
489SD16—304no—
490D8—102no—
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—202no—
506C22×C3—202no—
507C22×C3—201no—
508C22×C3—201no—
509C22×C3#408612yes—
510C22×C3C2×D4×D511yescharacteristic
511C2×D3—44no—
512C2×D3—42no—
513C2×D3—84no—
514C3×C4—201no—
515C3×C4—201no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C22×C22⋊D511yescharacteristic
519Dic3—42no—
520Dic3—104no—
521C2×C5—22no—
522C2×C5—242no—
523C2×C5#577012yes—
524C2×C5C2×#94011yescharacteristic
525D5—81no—
526D5—81no—
527C23—62no—
528C23—101no—
529C23—101no—
530C23—122no—
531C23—242no—
532C23#677711yescharacteristic
533Q8—62no—
534Q8—62no—
535Q8—101no—
536Q8—101no—
537Q8—101no—
538Q8—101no—
539Q8—122no—
540D4—62no—
541D4—62no—
542D4—101no—
543D4—101no—
544D4—101no—
545D4—101no—
546D4—122no—
547D4—202no—
548D4—202no—
549D4—1204no—
550C2×C4—62no—
551C2×C4—101no—
552C2×C4—101no—
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—154no—
562C8C2×#120112yes—
563C8C2×#120112yes—
564C2×C3—22no—
565C2×C3—401no—
566C2×C3—401no—
567C2×C3#6609612yes—
568C2×C3C2×#408611yescharacteristic
569D3—82no—
570C5#8390511yescharacteristic, complemented, Sylow
571C22—22no—
572C22—122no—
573C22—124no—
574C22—201no—
575C22—201no—
576C22—202no—
577C22—202no—
578C22—244no—
579C22#9146312yes—
580C22C2×#677711yescharacteristic
581C4—122no—
582C4—201no—
583C4—201no—
584C4—304no—
585C4#9146312yes—
586C4C2×#677711yescharacteristic
587C4C22×#120111yescharacteristic
588C3#1061558511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—242no—
591C2—401no—
592C2—401no—
593C2#1175398212yes—
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. C22×C5×#204C2semidirect
2. C2×C3×#4050C2semidirect
3. #11754604C2semidirect
4. #11754251C2semidirect
5. C2×#91307C2semidirect
6. C2×#91299C2semidirect
7. #11751202C2semidirect
8. #11748015C2semidirect
9. #11748010C2semidirect
10. #11747983C2semidirect
11. #11747977C2semidirect
23. C2×C3×Dic20C22semidirect
25. C2×C3×D40C22semidirect
26. C2×C3×#677C22semidirect
27. C2×C3×#677C22semidirect
32. #91385C22semidirect
34. #91368C22semidirect
36. C2×#6661C22semidirect
39. C2×#6655C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
50. C2×#4050D3semidirect
80. C2×C3×C5×C8D4semidirect
86. #6710D4semidirect
106. C22×#204D5semidirect
136. C2×Dic20C2×D3semidirect
138. C2×D40C2×D3semidirect
139. C2×#677C2×D3semidirect
140. C2×#677C2×D3semidirect
238. C2×C5×C8#67semidirect
313. C2×C3×C8C22⋊D5semidirect
494. C2×C8#1201semidirect
503. C3×C5#3154semidirect
570. C5#83905semidirect
588. C3#10615585semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2042
C2×C3×#40502
#117546042
#117542512
C2×#913072
C2×#912992
#117512022
#117480152
#117480102
#117479832
#117479772
#106155853
#839055