Finite Group Databasebeta

← #14439482

Subgroups — #14439482

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×#91839C211yesmaximal, characteristic, complemented
2C2×C5×#951C211yesmaximal, characteristic, complemented
3C3×#66164C211yesmaximal, characteristic, complemented
4#11754270C211yesmaximal, characteristic, complemented
5C2×#91312C211yesmaximal, characteristic, complemented
6C22×#6655C211yesmaximal, characteristic, complemented
7#11749353C212yesmaximal, complemented
8#11749316C212yesmaximal, complemented
9#11749106C212yesmaximal, complemented
10#11749069C212yesmaximal, complemented
11#11748320C211yesmaximal, characteristic, complemented
12#10615705—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17#91839—24no—
18C2×#6718C2211yescharacteristic, complemented
19C2×#6717C2211yescharacteristic, complemented
20C2×#6716C2211yescharacteristic, complemented
21C2×#6715C2211yescharacteristic, complemented
22C22×C3⋊#168C2211yescharacteristic
23C5×#951—24no—
24C2×C5×#216C2212yescomplemented
25C2×C5×#214C2212yescomplemented
26C2×C5×#208C2211yescharacteristic
27C3×#4093C2212yes—
28C3×#4086C2212yes—
29C3×#4083—22no—
30C3×#4076—22no—
31C3×#4072C2211yescharacteristic
32#91542—22no—
33#91383—22no—
34#91376C2212yescomplemented
35#91375C2212yescomplemented
36#91312—24no—
37C2×#6657C2212yes—
38C2×#6655—24no—
39C2×#6655C2212yes—
40C2×#6655C2212yes—
41C2×#6653C2212yes—
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83381—51nomaximal, Hall
45C2×C5×#137—31no—
46#66164D311yescharacteristic, complemented
47C2×#4096—31no—
48#66150—31no—
49C22×#688—31no—
50C2×#4054—31no—
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65464—32no—
55#65411—31no—
56C23×C3×D5—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×#1220—21no—
65#6817—22no—
66#6817—22no—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C22×C5×Dic3—21no—
71C2×C5×Dic6—22no—
72C2×C5×Dic6—22no—
73C2×C5×Dic6—21no—
74C2×C5×Dic6C2312yes—
75C2×C3×C22⋊D5—24no—
76C2×C3×D20—22no—
77C2×C3×D20—22no—
78C2×C3×D20—21no—
79C2×C3×D20C2312yes—
80#6718—22no—
81#6717—22no—
82#6716—22no—
83#6715—22no—
84C2×C3⋊#168D414yescomplemented
85C2×C3⋊#168C2311yescharacteristic
86C2×C3⋊#168C2311yescharacteristic
87C5×#216—24no—
88C5×#214—24no—
89C5×#208D414yescomplemented
90C2×C5×C3⋊C8C2312yes—
91C3×C22⋊Dic5D412yes—
92C3×#685—24no—
93C3×C4⋊Dic5D412yes—
94C3×C4×Dic5C2312yes—
95#6668—24no—
96#6667—24no—
97#6657—24no—
98#6655—24no—
99#6655—24no—
100#6653—24no—
101C3×#535—51no—
102C2×#951D511yescharacteristic, complemented
103C2×#950—51no—
104C22×#214—51no—
105C2×#932—51no—
106#5526—51no—
107#5076—52no—
108#5074—52no—
109#5060—52no—
110#5059—52no—
111#4997—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×D20C2×D311yescharacteristic
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4096—64no—
121#4093—32no—
122#4093C2×D312yes—
123#4092—62no—
124#4090—32no—
125C2×#689—31no—
126C2×#688—31no—
127C2×#688—32no—
128C2×#688—32no—
129C2×#688—64no—
130#4086C2×D312yes—
131#4083—22no—
132C2×#687—31no—
133C2×#686—31no—
134#4076—22no—
135#4075—62no—
136#4072C2×D311yescharacteristic
137C22×#168—31no—
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C3×D5—22no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161#1220—42no—
162C2×Dic15—21no—
163D60—21no—
164D60—21no—
165C4×D15—42no—
166Dic30—21no—
167Dic30—21no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—42no—
170C5×Dic6—22no—
171C5×Dic6—22no—
172C5×Dic6—42no—
173C3×C22⋊D5—84no—
174C2×C3×Dic5C2×D414yes—
175C3×D20—22no—
176C3×D20—22no—
177C3×D20—42no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×D4—51no—
183C2×#235—51no—
184C22×Dic6C2×D511yescharacteristic
185C3×#127—52no—
186C3×#124—52no—
187C3×#121—102no—
188C3×#120—102no—
189C3×#117—51no—
190#951—24no—
191#950—104no—
192C2×#216—51no—
193C2×#216C2×D512yescomplemented
194C2×#215—51no—
195C2×#214—51no—
196C2×#214—52no—
197C2×#214—52no—
198C2×#214—52no—
199C2×#214—104no—
200C2×#214C2×D512yescomplemented
201#932—104no—
202C2×#213—51no—
203C2×#213—52no—
204C2×#208C2×D511yescharacteristic
205C22×C3⋊C8—51no—
206#897—102no—
207#886—102no—
208#875—52no—
209#869—52no—
210#803—52no—
211C4×C3⋊C8—52no—
212C23×D5—21no—
213C5×#41—22no—
214C5×#41—22no—
215C2×C5×Q8—32no—
216C2×C5×Q8—61no—
217C2×C5×Q8—62no—
218C2×C5×Q8—62no—
219C2×C5×Q8C22×D311yescharacteristic
220C2×C5×D4—21no—
221C2×C5×D4C22×D311yescharacteristic
222C22×C4×C5—21no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—24no—
226C2×C22⋊D5—61no—
227#709—62no—
228#709—62no—
229C2×D20—22no—
230C2×D20—22no—
231C2×D20—21no—
232C2×D20—31no—
233C2×D20C22×D312yes—
234C2×C4×D5—61no—
235C2×Dic10—31no—
236C5×Q16—64no—
237C5×SD16—64no—
238C5×M16—34no—
239C2×C5×C8—32no—
240C22⋊Dic5#6712yes—
241#689—62no—
242#688—64no—
243#688—64no—
244#688—62no—
245#687—62no—
246#686—62no—
247#685—24no—
248#685—64no—
249C4⋊Dic5#6712yes—
250#683—64no—
251C4×Dic5C22×D312yes—
252C2×#168—34no—
253C2×#168—31no—
254C2×#168—31no—
255D40—64no—
256#677—64no—
257C2×#137—31no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—51no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×D15—41no—
274C2×D15—42no—
275C2×C3×D5—42no—
276C2×C3×D5—44no—
277C2×C3×D5—84no—
278C3×C4×C5—41no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C3×Dic5—24no—
284C5×Dic3—42no—
285C24×C3—101no—
286C3×#41—22no—
287C3×#41—22no—
288C2×C3×Q8C22×D511yescharacteristic
289C2×C3×D4—21no—
290C2×C3×D4—52no—
291C2×C3×D4—104no—
292C2×C3×D4—102no—
293C2×C3×D4—101no—
294C2×C3×D4—102no—
295C2×C3×D4C22×D511yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—101no—
299C22×Dic3—21no—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6—21no—
307C2×Dic6—51no—
308C2×Dic6C22×D512yes—
309C3×C4⋊C4—52no—
310C3×C22⋊C4—52no—
311C3×C22⋊C4—104no—
312C3×C42—52no—
313#216—24no—
314#216—102no—
315#215—102no—
316#214—24no—
317#214—104no—
318#214—104no—
319#214—102no—
320#214—104no—
321#213—102no—
322#213—104no—
323(C2×D3)⋊C4—104no—
324C4⋊Dic3—104no—
325#208C22⋊D514yescomplemented
326C2×C3⋊C8—54no—
327C2×C3⋊C8—51no—
328C2×C3⋊C8—51no—
329C2×C3⋊C8C22×D512yes—
330C23×C5—21no—
331C23×C5C2×#6711yescharacteristic
332C22×D5—22no—
333C22×D5—42no—
334C22×D5—61no—
335C22×D5—82no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×Q8—62no—
339C5×Q8—62no—
340C5×Q8—122no—
341C5×D4—21no—
342C5×D4—21no—
343C5×D4—42no—
344C2×C4×C5—21no—
345C2×C4×C5—42no—
346C2×C4×C5—62no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D412yes—
349C2×C4×C5D3×D412yes—
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—84no—
353C22⋊D5—122no—
354C2×Dic5—61no—
355C2×Dic5C2×#6714yes—
356D20—22no—
357D20—22no—
358D20—42no—
359D20—61no—
360D20—61no—
361C4×D5—122no—
362Dic10—61no—
363Dic10—61no—
364C5×C8—34no—
365#168—32no—
366#168—32no—
367C2×#41—151no—
368C2×#41D3×D511yescharacteristic
369C22×Q8—31no—
370C22×D4—51no—
371#137—64no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—32no—
375C2×Q16—151no—
376C2×SD16—32no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—151no—
381C2×SD16—151no—
382C2×SD16—304no—
383C2×D8—152no—
384C2×D8—151no—
385C2×M16—31no—
386C22×C8—151no—
387C4⋊Q8—152no—
388#127—52no—
389#124—52no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—102no—
394#120—102no—
395#117—51no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—81no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402D15—81no—
403C3×D5—82no—
404C23×C3—21no—
405C23×C3—102no—
406C23×C3—202no—
407C23×C3—402no—
408C23×C3D4×D511yescharacteristic
409C22×D3—101no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×D4—21no—
413C3×D4—21no—
414C3×D4—42no—
415C3×D4—102no—
416C3×D4—102no—
417C3×D4—202no—
418C3×D4—404no—
419C2×C3×C4—21no—
420C2×C3×C4—42no—
421C2×C3×C4—54no—
422C2×C3×C4D4×D511yescharacteristic
423C2×C3×C4D4×D512yes—
424C2×C3×C4C2×C22⋊D512yes—
425C2×C3×C4C23×D511yescharacteristic
426#67—202no—
427C2×Dic3—22no—
428C2×Dic3—42no—
429C2×Dic3—101no—
430D12—101no—
431D12—101no—
432C4×D3—202no—
433Dic6—22no—
434Dic6—22no—
435Dic6—42no—
436Dic6—101no—
437Dic6—101no—
438C3⋊C8—52no—
439C3⋊C8—52no—
440C3⋊C8C2×C22⋊D514yes—
441C22×C5—22no—
442C22×C5—41no—
443C22×C5—42no—
444C22×C5#94012yes—
445C22×C5C22×#6711yescharacteristic
446C2×D5—42no—
447C2×D5—44no—
448C2×D5—84no—
449C2×D5—121no—
450C2×D5—122no—
451C4×C5—41no—
452C4×C5—122no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C2×D3×D411yescharacteristic
456Dic5—24no—
457Dic5—121no—
458C24—101no—
459#41—22no—
460#41—22no—
461#41—302no—
462#41—302no—
463C2×Q8—32no—
464C2×Q8—61no—
465C2×Q8—62no—
466C2×Q8—62no—
467C2×Q8—151no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—52no—
471C2×D4—104no—
472C2×D4—101no—
473C2×D4—102no—
474C2×D4—102no—
475C2×D4—151no—
476C2×D4—301no—
477C2×D4C2×D3×D511yescharacteristic
478C22×C4—21no—
479C22×C4—61no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—64no—
483Q16—302no—
484SD16—64no—
485SD16—304no—
486SD16—302no—
487SD16—304no—
488SD16—304no—
489SD16—302no—
490D8—304no—
491D8—302no—
492M16—34no—
493C2×C8—32no—
494C2×C8—154no—
495C2×C8—151no—
496C2×C8—151no—
497C4⋊C4—52no—
498C4⋊C4—304no—
499C22⋊C4—52no—
500C22⋊C4—104no—
501C22⋊C4—304no—
502C42—52no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—42no—
506C22×C3—41no—
507C22×C3—204no—
508C22×C3—202no—
509C22×C3—404no—
510C22×C3#408612yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—202no—
513C2×D3—201no—
514C3×C4—41no—
515C3×C4—104no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C22×C22⋊D511yescharacteristic
519Dic3—42no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5C2×#94011yescharacteristic
524C2×C5#583612yes—
525D5—82no—
526D5—241no—
527C23—21no—
528C23—102no—
529C23—202no—
530C23—301no—
531C23—402no—
532C23D5×#6711yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—62no—
536Q8—62no—
537Q8—122no—
538Q8—301no—
539Q8—301no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—102no—
544D4—102no—
545D4—202no—
546D4—301no—
547D4—301no—
548D4—404no—
549D4—602no—
550C2×C4—21no—
551C2×C4—42no—
552C2×C4—54no—
553C2×C4—62no—
554C2×C4—122no—
555C2×C4—301no—
556C2×C4—602no—
557C2×C4D5×#6711yescharacteristic
558C2×C4D3×C22⋊D512yes—
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—34no—
562C8—152no—
563C8—152no—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3—402no—
567C2×C3#6611212yes—
568C2×C3C2×#408611yescharacteristic
569D3—401no—
570C5#8338111yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—41no—
574C22—204no—
575C22—202no—
576C22—404no—
577C22—602no—
578C22—601no—
579C22#9156712yes—
580C22C2×D5×#6711yescharacteristic
581C4—41no—
582C4—104no—
583C4—122no—
584C4—601no—
585C4#9156712yes—
586C4C2×D3×C22⋊D511yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061570511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—402no—
592C2—1201no—
593C2#1175533512yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91839C2semidirect
2. C2×C5×#951C2semidirect
3. C3×#66164C2semidirect
4. #11754270C2semidirect
5. C2×#91312C2semidirect
6. C22×#6655C2semidirect
7. #11749353C2semidirect
8. #11749316C2semidirect
9. #11749106C2semidirect
10. #11749069C2semidirect
11. #11748320C2semidirect
18. C2×#6718C22semidirect
19. C2×#6717C22semidirect
20. C2×#6716C22semidirect
21. C2×#6715C22semidirect
24. C2×C5×#216C22semidirect
25. C2×C5×#214C22semidirect
34. #91376C22semidirect
35. #91375C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
46. #66164D3semidirect
84. C2×C3⋊#168D4semidirect
89. C5×#208D4semidirect
102. C2×#951D5semidirect
193. C2×#216C2×D5semidirect
200. C2×#214C2×D5semidirect
325. #208C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83381semidirect
588. C3#10615705semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C2×C5×#9512
C3×#661642
#117542702
C2×#913122
C22×#66552
#117493532
#117493162
#117491062
#117490692
#117483202
#106157053
#833815