Finite Group Databasebeta

← #14439473

Subgroups — #14439473

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×#91831C211yesmaximal, characteristic, complemented
2C5×#5816C211yesmaximal, characteristic, complemented
3C22×C3×#688C211yesmaximal, characteristic, complemented
4#11754602C211yesmaximal, characteristic, complemented
5C2×#91303C211yesmaximal, characteristic, complemented
6C2×#91298C211yesmaximal, characteristic, complemented
7#11749344C212yesmaximal, complemented
8#11749342C212yesmaximal, complemented
9#11749319C212yesmaximal, complemented
10#11749317C212yesmaximal, complemented
11#11748323C211yesmaximal, characteristic, complemented
12#10615133—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C2×#6718C2212yescomplemented
18#91831—24no—
19C2×#6717C2212yescomplemented
20C2×#6710C2211yescharacteristic
21C5×#947C2212yescomplemented
22C5×#946—22no—
23C5×#944C2212yescomplemented
24C5×#929—22no—
25C5×#926C2211yescharacteristic
26C2×C3×#688—24no—
27C2×C3×#688C2212yes—
28C2×C3×#688C2212yes—
29C22×C3×#168C2211yescharacteristic
30#91564—22no—
31#91465—22no—
32#91458C2212yes—
33#91364C2212yes—
34C2×#6663C2211yescharacteristic, complemented
35C2×#6660C2211yescharacteristic, complemented
36C2×#6659C2211yescharacteristic, complemented
37C2×#6655C2212yes—
38#91303—24no—
39C2×#6654C2211yescharacteristic, complemented
40#91298—24no—
41C2×#6652C2212yes—
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83854—51nomaximal, Hall
45C5×#536—31no—
46C2×#4096—31no—
47C2×#4095—31no—
48C2×#4088—31no—
49C22×#688D311yescharacteristic, complemented
50#65859—31no—
51#65375—32no—
52#65374—32no—
53#65348—32no—
54#65347—32no—
55#65286—31no—
56C23×C3×D5—21no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C5×#67—21no—
70C5×#235—22no—
71C5×#235—22no—
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6C2311yescharacteristic
75C2×C3×D20—22no—
76C2×C3×D20—22no—
77C2×C3×D20—21no—
78C2×C3×D20C2312yes—
79C2×#1202—24no—
80#6718—24no—
81#6717—24no—
82#6710D414yescomplemented
83C2×C3⋊#168C2312yes—
84C5×#217D412yes—
85C5×(C2×D3)⋊C4—24no—
86C5×C4⋊Dic3D412yes—
87C5×Dic3⋊C4—24no—
88C4×C5×Dic3C2312yes—
89C3×#688—24no—
90C3×#688—24no—
91C2×C3×#168D414yescomplemented
92C2×C3×#168C2311yescharacteristic
93C2×C3×#168C2311yescharacteristic
94#6665—24no—
95#6663—22no—
96#6660—22no—
97#6659—22no—
98#6655—24no—
99#6654—22no—
100#6652—24no—
101C22×C3×SD16—51no—
102#5816D511yescharacteristic, complemented
103C2×#942—51no—
104#5805—51no—
105C2×#932—51no—
106C2×#904—51no—
107#5176—52no—
108#5175—52no—
109#5168—52no—
110#5167—52no—
111#5101—51no—
112C2×C5×#41—31no—
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C22×D20C2×D311yescharacteristic
116C5×C4⋊Q8—32no—
117C5×#124—32no—
118C5×#123—62no—
119C5×C22⋊Q8—62no—
120C5×#117—31no—
121#4096—64no—
122#4095—64no—
123C2×#689—32no—
124C2×#689—31no—
125#4088—64no—
126C2×#688—24no—
127C2×#688—32no—
128C2×#688—32no—
129C2×#688—31no—
130C2×#688C2×D312yes—
131C2×#688C2×D312yes—
132C2×#687—31no—
133C2×#686—32no—
134C2×#686—31no—
135C2×#681—31no—
136C22×#168C2×D311yescharacteristic
137#4041—62no—
138#4028—62no—
139#4021—32no—
140#4020—32no—
141#3935—32no—
142C4×#168—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C5×D3—21no—
147C22×C3×D5—22no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
150C3×C5×Q8—22no—
151C3×C5×Q8—22no—
152C3×C5×Q8—42no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—42no—
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5C2411yescharacteristic
159#1220—42no—
160C2×Dic15—21no—
161D60—21no—
162D60—21no—
163C4×D15—42no—
164Dic30—21no—
165Dic30—21no—
166C5×#67—42no—
167C2×C5×Dic3—21no—
168C2×C5×Dic3C2×D414yes—
169C5×D12—21no—
170C5×D12—21no—
171C4×C5×D3—42no—
172C5×Dic6—21no—
173C5×Dic6—21no—
174C3×D20—22no—
175C3×D20—22no—
176C3×D20—42no—
177#1202—84no—
178C3⋊#168C2×D414yes—
179C3×#168C2×D412yes—
180C3×#168C2×D412yes—
181C22×C3×Q8C2×D511yescharacteristic
182C22×C3×D4—51no—
183C2×#235—51no—
184C2×#235C2×D511yescharacteristic
185C2×C3×SD16—52no—
186C2×C3×SD16—52no—
187C2×C3×SD16—104no—
188C22×C3×C8—51no—
189#953—102no—
190#947C2×D512yescomplemented
191#946—22no—
192#944C2×D512yescomplemented
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—22no—
203#926C2×D511yescharacteristic
204C2×#208—51no—
205C2×Dic12—51no—
206#904—104no—
207C2×D24—51no—
208C2×#204—51no—
209C2×#204—51no—
210#815—52no—
211C8×Dic3—52no—
212C23×D5—21no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—21no—
216C2×C5×Q8—22no—
217C2×C5×Q8—22no—
218C2×C5×Q8—31no—
219C2×C5×Q8C22×D312yes—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C22×C4×C5—21no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—61no—
226#709—62no—
227#709—62no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20—31no—
232C2×D20—64no—
233C2×D20C22×D312yes—
234C2×C4×D5—61no—
235C2×Dic10—31no—
236C5×C4⋊C4—32no—
237C5×C4⋊C4—64no—
238C5×C22⋊C4—32no—
239C5×C22⋊C4—64no—
240C42×C5—32no—
241#689—64no—
242#689—62no—
243#688—24no—
244#688—24no—
245#688—64no—
246#688—64no—
247#688—62no—
248#687—62no—
249#686—64no—
250#686—62no—
251#685—64no—
252#681—34no—
253C2×#168—32no—
254C2×#168#6714yescomplemented
255C2×#168C22×D311yescharacteristic
256C2×#168C22×D311yescharacteristic
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—51no—
261#536—31no—
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×D15—41no—
272C2×D15—42no—
273C2×C5×D3—41no—
274C2×C5×D3—42no—
275C2×C3×D5—42no—
276C2×C3×D5—44no—
277C2×C3×D5—84no—
278C3×C4×C5—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C5×Dic3—24no—
284C5×Dic3—41no—
285C24×C3—101no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8C22×D512yes—
290C2×C3×D4—52no—
291C2×C3×D4—102no—
292C2×C3×D4—102no—
293C2×C3×D4—101no—
294C22×C3×C4—21no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—21no—
297C2×#67—101no—
298C2×#67—104no—
299#235—22no—
300#235—22no—
301#235—102no—
302#235—102no—
303C2×D12—51no—
304C2×D12C22×D511yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—101no—
307C2×Dic6—51no—
308C2×Dic6C22×D511yescharacteristic
309C3×SD16—104no—
310C3×SD16—104no—
311C2×C3×C8—54no—
312C2×C3×C8—51no—
313C2×C3×C8—51no—
314#217—104no—
315#217C22⋊D512yes—
316#216—104no—
317#215—104no—
318#214—104no—
319#213—104no—
320(C2×D3)⋊C4—24no—
321C4⋊Dic3C22⋊D512yes—
322Dic3⋊C4—24no—
323C4×Dic3C22×D512yes—
324#208—54no—
325C2×C3⋊C8—52no—
326Dic12—102no—
327D24—102no—
328#204—102no—
329#204—102no—
330C23×C5—61no—
331C23×C5D3×D411yescharacteristic
332C22×D5—22no—
333C22×D5—42no—
334C22×D5—61no—
335C22×D5—82no—
336C5×Q8—22no—
337C5×Q8—22no—
338C5×Q8—42no—
339C5×Q8—61no—
340C5×Q8—61no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—22no—
345C2×C4×C5—34no—
346C2×C4×C5—42no—
347C2×C4×C5—61no—
348C2×C4×C5—122no—
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5D3×D412yes—
351C2×C4×C5C2×#6712yes—
352C2×C4×C5C23×D311yescharacteristic
353C22⋊D5—122no—
354C2×Dic5—61no—
355D20—22no—
356D20—22no—
357D20—42no—
358D20—61no—
359D20—61no—
360D20—244no—
361C4×D5—122no—
362Dic10—61no—
363Dic10—61no—
364#168—34no—
365#168C2×#6712yes—
366#168C2×#6712yes—
367C2×#41—31no—
368C2×#41—151no—
369C22×Q8D3×D511yescharacteristic
370C22×D4—51no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—151no—
375C2×Q16—152no—
376C2×SD16—52no—
377C2×SD16—52no—
378C2×SD16—104no—
379C2×SD16—151no—
380C2×SD16—151no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×D8—151no—
384C2×D8—152no—
385C2×M16—151no—
386C22×C8—51no—
387C4⋊Q8—32no—
388#127—152no—
389#124—32no—
390#124—152no—
391#123—62no—
392C22⋊Q8—62no—
393#121—302no—
394#120—302no—
395#117—31no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401D15—81no—
402C3×D5—82no—
403C5×D3—81no—
404C23×C3—102no—
405C23×C3—202no—
406C23×C3—402no—
407C23×C3C2×C22⋊D511yescharacteristic
408C22×D3—21no—
409C22×D3—101no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—42no—
413C3×D4—102no—
414C3×D4—102no—
415C3×D4—202no—
416C2×C3×C4—22no—
417C2×C3×C4—42no—
418C2×C3×C4D4×D512yes—
419C2×C3×C4D4×D512yes—
420C2×C3×C4C2×C22⋊D511yescharacteristic
421C2×C3×C4C23×D511yescharacteristic
422#67—42no—
423#67—202no—
424#67—404no—
425C2×Dic3—21no—
426C2×Dic3—101no—
427C2×Dic3C2×C22⋊D514yes—
428D12—21no—
429D12—21no—
430D12—101no—
431D12—101no—
432C4×D3—42no—
433C4×D3—202no—
434Dic6—21no—
435Dic6—21no—
436Dic6—101no—
437Dic6—101no—
438C3×C8—52no—
439C3×C8—52no—
440C3⋊C8—54no—
441C22×C5—22no—
442C22×C5—122no—
443C22×C5—121no—
444C22×C5#94012yes—
445C22×C5C2×D3×D411yescharacteristic
446C2×D5—44no—
447C2×D5—42no—
448C2×D5—84no—
449C2×D5—122no—
450C2×D5—121no—
451C4×C5—42no—
452C4×C5—64no—
453C4×C5—121no—
454C4×C5#94012yes—
455C4×C5C2×D3×D411yescharacteristic
456C4×C5C22×#6711yescharacteristic
457Dic5—121no—
458C24—101no—
459#41—62no—
460#41—62no—
461#41—302no—
462#41—302no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—31no—
467C2×Q8—151no—
468C2×Q8C2×D3×D512yes—
469C2×D4—31no—
470C2×D4—52no—
471C2×D4—61no—
472C2×D4—102no—
473C2×D4—101no—
474C2×D4—102no—
475C2×D4—151no—
476C2×D4—304no—
477C2×D4—301no—
478C22×C4—21no—
479C22×C4—61no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—302no—
483Q16—304no—
484SD16—104no—
485SD16—104no—
486SD16—302no—
487SD16—302no—
488SD16—304no—
489SD16—304no—
490D8—302no—
491D8—304no—
492M16—154no—
493C2×C8—54no—
494C2×C8—51no—
495C2×C8—51no—
496C2×C8—152no—
497C4⋊C4—32no—
498C4⋊C4—64no—
499C22⋊C4—32no—
500C22⋊C4—64no—
501C22⋊C4—304no—
502C42—32no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—202no—
506C22×C3—204no—
507C22×C3—404no—
508C22×C3#408612yes—
509C22×C3C22×C22⋊D511yescharacteristic
510C2×D3—41no—
511C2×D3—42no—
512C2×D3—201no—
513C2×D3—202no—
514C3×C4—42no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C2×D4×D511yescharacteristic
518Dic3—24no—
519Dic3—41no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5#576212yes—
524C2×C5C2×#94011yescharacteristic
525D5—82no—
526D5—241no—
527C23—61no—
528C23—102no—
529C23—202no—
530C23—301no—
531C23—402no—
532C23D3×C22⋊D511yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—61no—
537Q8—61no—
538Q8—301no—
539Q8—301no—
540D4—61no—
541D4—61no—
542D4—102no—
543D4—102no—
544D4—122no—
545D4—202no—
546D4—301no—
547D4—301no—
548D4—602no—
549D4—1204no—
550C2×C4—22no—
551C2×C4—34no—
552C2×C4—42no—
553C2×C4—61no—
554C2×C4—122no—
555C2×C4—301no—
556C2×C4—602no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D511yescharacteristic
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—52no—
562C8—52no—
563C8—154no—
564C2×C3—22no—
565C2×C3—402no—
566C2×C3C2×#408611yescharacteristic
567C2×C3#6617112yes—
568D3—81no—
569D3—401no—
570C5#8385411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—122no—
573C22—121no—
574C22—204no—
575C22—202no—
576C22—404no—
577C22—602no—
578C22—601no—
579C22#9156712yes—
580C22C2×D3×C22⋊D511yescharacteristic
581C4—42no—
582C4—64no—
583C4—121no—
584C4—601no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061513311yescharacteristic, complemented, Sylow
589C2—22no—
590C2—241no—
591C2—402no—
592C2—1201no—
593C2#1175509112yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#91831C2semidirect
2. C5×#5816C2semidirect
3. C22×C3×#688C2semidirect
4. #11754602C2semidirect
5. C2×#91303C2semidirect
6. C2×#91298C2semidirect
7. #11749344C2semidirect
8. #11749342C2semidirect
9. #11749319C2semidirect
10. #11749317C2semidirect
11. #11748323C2semidirect
17. C2×#6718C22semidirect
19. C2×#6717C22semidirect
21. C5×#947C22semidirect
23. C5×#944C22semidirect
34. C2×#6663C22semidirect
35. C2×#6660C22semidirect
36. C2×#6659C22semidirect
39. C2×#6654C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
49. C22×#688D3semidirect
82. #6710D4semidirect
91. C2×C3×#168D4semidirect
102. #5816D5semidirect
190. #947C2×D5semidirect
192. #944C2×D5semidirect
254. C2×#168#67semidirect
503. C3×C5#3154semidirect
570. C5#83854semidirect
588. C3#10615133semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C5×#58162
C22×C3×#6882
#117546022
C2×#913032
C2×#912982
#117493442
#117493422
#117493192
#117493172
#117483232
#106151333
#838545