Finite Group Databasebeta

← #14439469

Subgroups — #14439469

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
1C5×#5526C211yesmaximal, characteristic, complemented
2C3×#65859C211yesmaximal, characteristic, complemented
3C2×#91307C211yesmaximal, characteristic, complemented
4C22×#6655C211yesmaximal, characteristic, complemented
5C2×#91298C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7#11751098C211yesmaximal, characteristic, complemented
8#11747080C212yesmaximal, complemented
9#11747079C212yesmaximal, complemented
10#11747041C212yesmaximal, complemented
11#11747040C212yesmaximal, complemented
12#10615133—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C3×C5×#117C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C5×#897—22no—
21C5×#886—22no—
22C5×#875C2212yescomplemented
23C5×#869C2212yescomplemented
24C3×#4041—22no—
25C3×#4028—22no—
26C3×#4021C2212yes—
27C3×#4020C2212yes—
28C2×#6661C2211yescharacteristic, complemented
29C2×#6661C2212yescomplemented
30C2×#6656C2211yescharacteristic, complemented
31#91307—24no—
32C2×#6655—24no—
33C2×#6655C2212yes—
34C2×#6655C2212yes—
35C2×#6655C2212yes—
36C2×#6655C2211yescharacteristic, complemented
37C2×#6655C2212yescomplemented
38#91298—24no—
39#91297—24no—
40C2×#6652C2212yes—
41C2×#6652C2211yescharacteristic, complemented
42#91087C2212yescomplemented
43C4×C3⋊#168C2212yescomplemented
44#83381—51nomaximal, Hall
45C5×#536—31no—
46C2×#4096—31no—
47C2×#4095—31no—
48C2×#4088—31no—
49C22×#688—31no—
50#65859D311yescharacteristic, complemented
51#65375—32no—
52#65374—32no—
53#65348—32no—
54#65347—32no—
55#65286—31no—
56C23×C3×D5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×C5×#67—21no—
59C22×C5×Dic3—21no—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12C2311yescharacteristic
63C2×C4×C5×D3—21no—
64C2×C5×Dic6—22no—
65C2×C5×Dic6—22no—
66C2×C5×Dic6—21no—
67C2×C5×Dic6C2311yescharacteristic
68C2×C5×Dic6C2312yes—
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20—22no—
73C2×C3×D20—22no—
74C2×C3×D20—21no—
75C2×C3×D20—24no—
76C2×C3×D20C2312yes—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C3×C5×C4⋊C4D412yes—
81C3×C5×C22⋊C4D412yes—
82C3×C42×C5C2312yes—
83#6710D414yescomplemented
84C2×C3⋊#168D414yescomplemented
85C2×C3⋊#168C2312yes—
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88C5×(C2×D3)⋊C4—24no—
89C5×C4⋊Dic3—24no—
90C3×#685—24no—
91#6661—22no—
92#6661—24no—
93#6656—22no—
94#6655—22no—
95#6655—24no—
96#6655—24no—
97#6655—24no—
98#6655—24no—
99#6652—24no—
100#6652—22no—
101C3×#535—51no—
102C2×#951—51no—
103C2×#950—51no—
104C22×#214—51no—
105C2×#932—51no—
106#5526D511yescharacteristic, complemented
107#5076—52no—
108#5074—52no—
109#5060—52no—
110#5059—52no—
111#4997—51no—
112C2×C5×#41—31no—
113C22×C5×Q8—31no—
114C2×#709C2×D311yescharacteristic
115C22×D20C2×D311yescharacteristic
116C5×C4⋊Q8—32no—
117C5×#124—32no—
118C5×#123—62no—
119C5×C22⋊Q8—62no—
120C5×#117C2×D311yescharacteristic
121#4096—64no—
122#4095—64no—
123C2×#689—32no—
124C2×#689—31no—
125#4088—64no—
126C2×#688—32no—
127C2×#688—32no—
128C2×#688—32no—
129C2×#688—31no—
130C2×#688—32no—
131C2×#688—64no—
132C2×#687—31no—
133C2×#686—31no—
134C2×#686—32no—
135C2×#681—31no—
136C22×#168—31no—
137#4041—22no—
138#4028—22no—
139#4021C2×D312yes—
140#4020C2×D312yes—
141#3935—32no—
142C4×#168—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—21no—
146C22×C3×D5—22no—
147C22×C3×D5—21no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
150C2×C3×C4×C5C2×D414yes—
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2411yescharacteristic
155C5×#67—42no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—42no—
159C5×D12—21no—
160C5×D12—21no—
161C4×C5×D3—42no—
162C5×Dic6—22no—
163C5×Dic6—21no—
164C5×Dic6—22no—
165C5×Dic6—21no—
166C5×Dic6—42no—
167C3×C22⋊D5—42no—
168C2×C3×Dic5—21no—
169C3×D20—22no—
170C3×D20—22no—
171C3×D20—21no—
172C3×D20—21no—
173C3×D20—42no—
174C3×D20—84no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C3⋊#168C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×D4—51no—
183C2×#235C2×D511yescharacteristic
184C22×Dic6C2×D511yescharacteristic
185C3×#127—52no—
186C3×#124—52no—
187C3×#121—102no—
188C3×#120—102no—
189C3×#117C2×D511yescharacteristic
190#951—104no—
191#950—104no—
192C2×#216—51no—
193C2×#216—52no—
194C2×#215—51no—
195C2×#214—52no—
196C2×#214—52no—
197C2×#214—52no—
198C2×#214—51no—
199C2×#214—52no—
200C2×#214—104no—
201#932—104no—
202C2×#213—52no—
203C2×#213—51no—
204C2×#208—51no—
205C22×C3⋊C8—51no—
206#897—22no—
207#886—22no—
208#875C2×D512yescomplemented
209#869C2×D512yescomplemented
210#803—52no—
211C4×C3⋊C8—52no—
212C23×D5—21no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—32no—
216C2×C5×Q8—31no—
217C2×C5×Q8—61no—
218C2×C5×Q8—62no—
219C2×C5×Q8—62no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C22×C4×C5—61no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226#709—22no—
227#709—22no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20—24no—
232C2×D20C22×D312yes—
233C2×D20C22×D311yescharacteristic
234C2×C4×D5—21no—
235C2×Dic10C22×D311yescharacteristic
236C5×C4⋊C4—64no—
237C5×C4⋊C4#6712yes—
238C5×C22⋊C4—64no—
239C5×C22⋊C4#6712yes—
240C42×C5C22×D312yes—
241#689—62no—
242#689—64no—
243#688—62no—
244#688—64no—
245#688—64no—
246#688—64no—
247#688—64no—
248#687—62no—
249#686—62no—
250#686—64no—
251#685—24no—
252#681—34no—
253C2×#168—34no—
254C2×#168—31no—
255C2×#168—32no—
256C2×#168—31no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—31no—
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#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×C5×D3—41no—
272C2×C5×D3—42no—
273C2×C3×D5—41no—
274C2×C3×D5—42no—
275C2×C3×D5—42no—
276C2×C3×D5—44no—
277C2×C3×D5—84no—
278C3×C4×C5—24no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282C3×Dic5—41no—
283C5×Dic3—42no—
284C5×Dic3—41no—
285C24×C3—101no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—51no—
289C2×C3×D4—52no—
290C2×C3×D4—51no—
291C2×C3×D4—101no—
292C2×C3×D4—102no—
293C2×C3×D4—102no—
294C2×C3×D4—101no—
295C2×C3×D4—104no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—21no—
299C22×Dic3—21no—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6—21no—
307C2×Dic6C22×D511yescharacteristic
308C2×Dic6C22×D512yes—
309C3×C4⋊C4C22⋊D512yes—
310C3×C22⋊C4—104no—
311C3×C22⋊C4C22⋊D512yes—
312C3×C42C22×D512yes—
313#216—102no—
314#216—104no—
315#215—102no—
316#214—104no—
317#214—104no—
318#214—104no—
319#214—102no—
320#214—104no—
321#213—104no—
322#213—102no—
323(C2×D3)⋊C4—24no—
324C4⋊Dic3—24no—
325#208—54no—
326C2×C3⋊C8—54no—
327C2×C3⋊C8—51no—
328C2×C3⋊C8—52no—
329C2×C3⋊C8—51no—
330C23×C5—61no—
331C23×C5C2×#6711yescharacteristic
332C22×D5—22no—
333C22×D5—21no—
334C22×D5—42no—
335C22×D5—82no—
336C5×Q8—62no—
337C5×Q8—61no—
338C5×Q8—62no—
339C5×Q8—61no—
340C5×Q8—122no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—62no—
345C2×C4×C5—61no—
346C2×C4×C5—122no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D412yes—
349C2×C4×C5D3×D412yes—
350C2×C4×C5C2×#6714yes—
351C2×C4×C5C2×#6711yescharacteristic
352C2×C4×C5C23×D311yescharacteristic
353C22⋊D5—42no—
354C2×Dic5—21no—
355D20—22no—
356D20—21no—
357D20—22no—
358D20—21no—
359D20—42no—
360D20—84no—
361C4×D5—42no—
362Dic10—21no—
363Dic10—21no—
364#168—32no—
365#168—32no—
366#168—34no—
367C2×#41—31no—
368C2×#41—51no—
369C22×Q8—31no—
370C22×D4—51no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—151no—
375C2×Q16—152no—
376C2×SD16—151no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—151no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—151no—
384C2×D8—152no—
385C2×M16—151no—
386C22×C8—151no—
387C4⋊Q8—32no—
388#127—52no—
389#124—32no—
390#124—52no—
391#123—62no—
392C22⋊Q8—62no—
393#121—102no—
394#120—102no—
395#117D3×D511yescharacteristic
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401C3×D5—81no—
402C3×D5—82no—
403C5×D3—81no—
404C23×C3—102no—
405C23×C3—101no—
406C23×C3—202no—
407C23×C3—402no—
408C23×C3C2×C22⋊D511yescharacteristic
409C22×D3—21no—
410C3×Q8—101no—
411C3×Q8—101no—
412C3×D4—102no—
413C3×D4—101no—
414C3×D4—102no—
415C3×D4—101no—
416C3×D4—202no—
417C3×D4—202no—
418C3×D4—404no—
419C2×C3×C4—101no—
420C2×C3×C4—202no—
421C2×C3×C4D4×D512yes—
422C2×C3×C4D4×D512yes—
423C2×C3×C4C2×C22⋊D514yes—
424C2×C3×C4C2×C22⋊D511yescharacteristic
425C2×C3×C4C23×D511yescharacteristic
426#67—42no—
427C2×Dic3—21no—
428C2×Dic3—22no—
429C2×Dic3—42no—
430D12—21no—
431D12—21no—
432C4×D3—42no—
433Dic6—22no—
434Dic6—21no—
435Dic6—22no—
436Dic6—21no—
437Dic6—42no—
438C3⋊C8—52no—
439C3⋊C8—52no—
440C3⋊C8—54no—
441C22×C5—22no—
442C22×C5—121no—
443C22×C5—122no—
444C22×C5#94012yes—
445C22×C5C22×#6711yescharacteristic
446C2×D5—41no—
447C2×D5—42no—
448C2×D5—42no—
449C2×D5—44no—
450C2×D5—84no—
451C4×C5—24no—
452C4×C5—121no—
453C4×C5—122no—
454C4×C5#94012yes—
455C4×C5C2×D3×D411yescharacteristic
456C4×C5C2×D3×D411yescharacteristic
457Dic5—41no—
458C24—101no—
459#41—62no—
460#41—62no—
461#41—102no—
462#41—102no—
463C2×Q8—32no—
464C2×Q8—31no—
465C2×Q8—51no—
466C2×Q8—61no—
467C2×Q8—62no—
468C2×Q8—62no—
469C2×D4—31no—
470C2×D4—52no—
471C2×D4—51no—
472C2×D4—61no—
473C2×D4—101no—
474C2×D4—102no—
475C2×D4—102no—
476C2×D4—101no—
477C2×D4—104no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—302no—
483Q16—304no—
484SD16—302no—
485SD16—304no—
486SD16—304no—
487SD16—302no—
488SD16—304no—
489SD16—304no—
490D8—302no—
491D8—304no—
492M16—154no—
493C2×C8—154no—
494C2×C8—151no—
495C2×C8—152no—
496C2×C8—151no—
497C4⋊C4—64no—
498C4⋊C4#120112yes—
499C22⋊C4—64no—
500C22⋊C4—104no—
501C22⋊C4#120112yes—
502C42C2×D3×D512yes—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—201no—
506C22×C3—202no—
507C22×C3—202no—
508C22×C3—204no—
509C22×C3—404no—
510C22×C3#408612yes—
511C22×C3C22×C22⋊D511yescharacteristic
512C2×D3—41no—
513C2×D3—42no—
514C3×C4—24no—
515C3×C4—201no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C2×D4×D511yescharacteristic
519Dic3—42no—
520Dic3—41no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5C2×#94011yescharacteristic
524C2×C5#583612yes—
525D5—82no—
526D5—81no—
527C23—61no—
528C23—102no—
529C23—101no—
530C23—202no—
531C23—402no—
532C23C2×#120111yescharacteristic
533Q8—62no—
534Q8—61no—
535Q8—62no—
536Q8—61no—
537Q8—101no—
538Q8—101no—
539Q8—122no—
540D4—61no—
541D4—61no—
542D4—102no—
543D4—101no—
544D4—102no—
545D4—101no—
546D4—122no—
547D4—202no—
548D4—202no—
549D4—404no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—101no—
553C2×C4—122no—
554C2×C4—122no—
555C2×C4—202no—
556C2×C4#677712yes—
557C2×C4#677712yes—
558C2×C4C2×#120114yes—
559C2×C4C2×#120111yescharacteristic
560C2×C4C22×D3×D511yescharacteristic
561C8—152no—
562C8—152no—
563C8—154no—
564C2×C3—22no—
565C2×C3—402no—
566C2×C3—401no—
567C2×C3C2×#408611yescharacteristic
568C2×C3#6617112yes—
569D3—81no—
570C5#8338111yescharacteristic, complemented, Sylow
571C22—22no—
572C22—122no—
573C22—121no—
574C22—202no—
575C22—204no—
576C22—201no—
577C22—202no—
578C22—404no—
579C22#9146312yes—
580C22C22×#120111yescharacteristic
581C4—24no—
582C4—121no—
583C4—122no—
584C4—201no—
585C4#9146312yes—
586C4C2×#677711yescharacteristic
587C4C2×#677711yescharacteristic
588C3#1061513311yescharacteristic, complemented, Sylow
589C2—22no—
590C2—241no—
591C2—402no—
592C2—401no—
593C2C2×#9146311yescharacteristic
594C2#1175530312yes—
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
hypercenter#117D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5526C2semidirect
2. C3×#65859C2semidirect
3. C2×#91307C2semidirect
4. C22×#6655C2semidirect
5. C2×#91298C2semidirect
6. C2×#91297C2semidirect
7. #11751098C2semidirect
8. #11747080C2semidirect
9. #11747079C2semidirect
10. #11747041C2semidirect
11. #11747040C2semidirect
22. C5×#875C22semidirect
23. C5×#869C22semidirect
28. C2×#6661C22semidirect
29. C2×#6661C22semidirect
30. C2×#6656C22semidirect
36. C2×#6655C22semidirect
37. C2×#6655C22semidirect
41. C2×#6652C22semidirect
42. #91087C22semidirect
43. C4×C3⋊#168C22semidirect
50. #65859D3semidirect
83. #6710D4semidirect
84. C2×C3⋊#168D4semidirect
106. #5526D5semidirect
208. #875C2×D5semidirect
209. #869C2×D5semidirect
503. C3×C5#3154semidirect
570. C5#83381semidirect
588. C3#10615133semidirect

Maximal subgroups

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

subgroupindex
C5×#55262
C3×#658592
C2×#913072
C22×#66552
C2×#912982
C2×#912972
#117510982
#117470802
#117470792
#117470412
#117470402
#106151333
#833815