Finite Group Databasebeta

← #14439338

Subgroups — #14439338

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91797C211yesmaximal, characteristic, complemented
2C2×C5×#909C211yesmaximal, characteristic, complemented
3#11754572C211yesmaximal, characteristic, complemented
4C2×#91375C211yesmaximal, characteristic, complemented
5C2×#91321C211yesmaximal, characteristic, complemented
6C2×#91305C211yesmaximal, characteristic, complemented
7C3×M16×Dic5C211yesmaximal, characteristic, complemented
8#11748026C212yesmaximal, complemented
9#11747997C212yesmaximal, complemented
10#11747965C212yesmaximal, complemented
11#11747962C212yesmaximal, complemented
12#10615704—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C5×Dic6C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91797—24no—
19C2×D120C2212yes—
20C2×#6706C2212yes—
21C5×#909—24no—
22C2×C5×Dic12C2212yescomplemented
23C2×C5×#204C2212yescomplemented
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91566—22no—
27C2×#6667—22no—
28#91451C2211yescharacteristic, complemented
29C4×#1203—22no—
30#91376C2211yescharacteristic, complemented
31#91375—22no—
32#91375C2212yes—
33#91375C2212yes—
34#91375C2211yescharacteristic, complemented
35#91373C2211yescharacteristic, complemented
36#91321—24no—
37C2×#6663C2212yescomplemented
38C2×#6660C2212yes—
39C2×#6660C2212yescomplemented
40#91305—24no—
41C2×#6654C2212yes—
42C3×#3947C2212yescomplemented
43C3×C8×Dic5C2212yescomplemented
44#78531—51nomaximal, Hall
45C2×C5×#137—31no—
46#66166—31no—
47C2×#4095—31no—
48C2×#4093—31no—
49C2×#4088—31no—
50C2×#4054—31no—
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65457—32no—
55M16×Dic5D311yescharacteristic, complemented
56C23×D15—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817—22no—
61C2×D60—22no—
62C2×D60—22no—
63C2×D60—21no—
64C2×D60C2311yescharacteristic
65C2×D60C2312yes—
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C2×C5×#67—21no—
69C22×C5×Dic3—21no—
70C5×#235—22no—
71C5×#235—22no—
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6—22no—
75C2×C5×Dic6—22no—
76C2×C5×Dic6—21no—
77C2×C5×Dic6C2312yes—
78C2×C5×Dic6C2311yescharacteristic
79C22×C3×Dic5D412yes—
80C2×#1203—22no—
81C3×C5×M16D414yescomplemented
82C2×C3×C5×C8C2312yes—
83D120—24no—
84#6706—24no—
85C5×Dic12—24no—
86C5×#204—24no—
87C3×C4×Dic5D412yes—
88C3×C4×Dic5C2311yescharacteristic
89C3×C4×Dic5C2311yescharacteristic
90C3×#681D414yescomplemented
91C2×C3×#168C2312yes—
92#6668—22no—
93#6667—22no—
94#6667—24no—
95#6667—24no—
96(C2×D3)⋊Dic5—22no—
97#6663—24no—
98#6660—24no—
99#6660—24no—
100#6654—24no—
101C2×#909—51no—
102C2×#909D511yescharacteristic, complemented
103C2×#908—51no—
104C2×#908—51no—
105#5477—51no—
106C2×#875—51no—
107C3×C4×M16—51no—
108#4715—52no—
109#4712—52no—
110#4696—52no—
111#4696—52no—
112C2×C5×#41—31no—
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×D20—31no—
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16C2×D311yescharacteristic
120#4095—64no—
121#4093—32no—
122#4093—32no—
123#4093—31no—
124#4093—62no—
125#4090—31no—
126C2×#689—32no—
127#4088—64no—
128C2×#688—32no—
129C2×#688—32no—
130#4086—31no—
131#4085—62no—
132#4082—31no—
133C2×#686—32no—
134C4×C22⋊D5—62no—
135C2×#685—62no—
136C2×C4×Dic5C2×D311yescharacteristic
137C2×#681C2×D311yescharacteristic
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947C2×D312yescomplemented
142C8×Dic5C2×D312yescomplemented
143#3153—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—22no—
146C22×D15—21no—
147C22×D15—44no—
148C22×D15—42no—
149C22×C5×D3—21no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2411yescharacteristic
154#1220—42no—
155C2×Dic15—21no—
156D60—21no—
157D60—22no—
158D60—22no—
159D60—21no—
160D60—42no—
161C4×D15—42no—
162Dic30—21no—
163Dic30—21no—
164C5×#67—42no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—21no—
167C2×C5×Dic3—42no—
168C5×D12—21no—
169C5×D12—21no—
170C4×C5×D3—42no—
171C5×Dic6—21no—
172C5×Dic6—22no—
173C5×Dic6—22no—
174C5×Dic6—21no—
175C5×Dic6—42no—
176C2×C3×Dic5—42no—
177C2×C3×Dic5C2×D412yes—
178C2×C3×Dic5C2×D412yes—
179#1203—44no—
180C3×C5×C8C2×D414yes—
181C3×#168C2×D414yes—
182C2×#235—51no—
183C2×#235C2×D511yescharacteristic
184C22×D12—51no—
185C22×Dic6C2×D511yescharacteristic
186C2×C3×M16—51no—
187C2×C3×M16C2×D511yescharacteristic
188C2×C3×C42—51no—
189#930—102no—
190C2×(C2×D3)⋊C4—102no—
191#909—24no—
192#909—104no—
193#908—104no—
194#908—104no—
195C2×Dic12—52no—
196C2×Dic12C2×D512yescomplemented
197C2×D24—52no—
198C2×D24—52no—
199C2×#204—52no—
200C2×#204—52no—
201C2×#204—52no—
202C2×#204C2×D512yescomplemented
203#875—51no—
204#875—52no—
205#875—51no—
206#875—52no—
207#875—102no—
208#874—51no—
209C4×D12—102no—
210#869—51no—
211C3×#97—52no—
212C3×C4×C8—52no—
213C23×D5—61no—
214C5×#41—62no—
215C5×#41—62no—
216C2×C5×Q8—32no—
217C2×C5×Q8—31no—
218C2×C5×Q8—61no—
219C2×C5×Q8—62no—
220C2×C5×Q8—62no—
221C2×C5×D4—31no—
222C2×C5×D4—61no—
223C22×C4×C5—61no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—61no—
227C2×C22⋊D5—62no—
228C22×Dic5D1212yes—
229#709—62no—
230#709—62no—
231C2×D20—32no—
232C2×D20—31no—
233C2×D20—62no—
234C2×D20—62no—
235C2×D20—61no—
236C2×C4×D5—61no—
237C2×Dic10—31no—
238C5×Q16—64no—
239C5×SD16—64no—
240C5×M16D1214yescomplemented
241C2×C5×C8C22×D312yes—
242C22⋊Dic5—62no—
243#689—64no—
244#688—64no—
245#688—64no—
246#686—64no—
247#685—64no—
248#685—64no—
249#685—62no—
250#683—62no—
251C4×Dic5D1212yes—
252C4×Dic5C22×D311yescharacteristic
253C4×Dic5C22×D311yescharacteristic
254#681D1214yescomplemented
255C2×#168C22×D312yes—
256D40—64no—
257#677—64no—
258C2×#137—31no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—151no—
261C2×AGL(1,ℤ/8)—151no—
262#532—151no—
263C2×#124—151no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—51no—
269C22×C3×C5—22no—
270C22×C3×C5#12712yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—41no—
273C2×D15—42no—
274C2×D15—42no—
275C2×D15—44no—
276C2×D15—84no—
277C2×C5×D3—41no—
278C2×C5×D3—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C3×Dic5—22no—
284C3×Dic5—22no—
285C5×Dic3—42no—
286C5×Dic3—41no—
287C23×D3—101no—
288C22×C3×C4—52no—
289C22×C3×C4C22×D511yescharacteristic
290C2×#67—21no—
291C2×#67—101no—
292C22×Dic3—21no—
293#235—22no—
294#235—22no—
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×D12—52no—
299C2×D12—102no—
300C2×D12—102no—
301C2×D12—102no—
302C2×D12—101no—
303C2×D12C22×D511yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—101no—
306C2×Dic6—22no—
307C2×Dic6—22no—
308C2×Dic6—21no—
309C2×Dic6—51no—
310C2×Dic6C22×D511yescharacteristic
311C2×Dic6C22×D512yes—
312C3×M16—54no—
313C3×M16C22⋊D514yescomplemented
314C2×C3×C8—52no—
315C2×C3×C8C22×D512yes—
316C3×C42—52no—
317C3×C42—51no—
318C3×C42—51no—
319(C2×D3)⋊C4—102no—
320(C2×D3)⋊C4—104no—
321(C2×D3)⋊C4—104no—
322(C2×D3)⋊C4—102no—
323C4⋊Dic3—102no—
324Dic12—24no—
325Dic12—104no—
326D24—104no—
327D24—104no—
328#204—24no—
329#204—104no—
330#204—104no—
331#204—104no—
332C23×C5—61no—
333C23×C5C2×D1211yescharacteristic
334C22×D5—62no—
335C22×D5—61no—
336C22×D5—124no—
337C22×D5—122no—
338C5×Q8—61no—
339C5×Q8—62no—
340C5×Q8—62no—
341C5×Q8—61no—
342C5×Q8—122no—
343C5×D4—61no—
344C5×D4—61no—
345C5×D4—122no—
346C2×C4×C5—61no—
347C2×C4×C5—62no—
348C2×C4×C5—122no—
349C2×C4×C5—122no—
350C2×C4×C5C2×D1211yescharacteristic
351C2×C4×C5C2×D1212yes—
352C2×C4×C5C2×D1212yes—
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—124no—
355C22⋊D5—122no—
356C2×Dic5—42no—
357C2×Dic5—61no—
358C2×Dic5C2×D1212yes—
359C2×Dic5C2×D1212yes—
360D20—62no—
361D20—61no—
362D20—62no—
363D20—61no—
364D20—122no—
365C4×D5—122no—
366Dic10—61no—
367Dic10—61no—
368C5×C8C2×D1214yes—
369#168C2×D1214yes—
370C2×#41—31no—
371C2×#41—151no—
372C22×Q8—31no—
373C22×D4—151no—
374#137—64no—
375#137—304no—
376AGL(1,ℤ/8)—304no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—32no—
379C2×Q16—152no—
380C2×SD16—32no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—152no—
385C2×D8—152no—
386C2×M16—51no—
387C2×M16D3×D511yescharacteristic
388C4⋊Q8—151no—
389#127—151no—
390#124—151no—
391#124—152no—
392#124—152no—
393#124—151no—
394#124—302no—
395#121—302no—
396C4×D4—302no—
397C2×C22⋊C4—302no—
398C2×C42—51no—
399#97—52no—
400C4×C8—52no—
401C2×C3×C5—22no—
402C2×C3×C5C2×#12711yescharacteristic
403C2×C3×C5#57512yes—
404D15—81no—
405D15—82no—
406C5×D3—81no—
407C23×C3D4×D511yescharacteristic
408C22×D3—21no—
409C22×D3—102no—
410C22×D3—101no—
411C22×D3—204no—
412C22×D3—202no—
413C2×C3×C4—52no—
414C2×C3×C4—52no—
415C2×C3×C4—202no—
416C2×C3×C4D4×D512yes—
417C2×C3×C4D4×D511yescharacteristic
418C2×C3×C4C2×C22⋊D512yes—
419C2×C3×C4C23×D511yescharacteristic
420#67—42no—
421#67—202no—
422C2×Dic3—21no—
423C2×Dic3—22no—
424C2×Dic3—42no—
425C2×Dic3—101no—
426D12—21no—
427D12—21no—
428D12—101no—
429D12—102no—
430D12—102no—
431D12—101no—
432D12—204no—
433D12—202no—
434C4×D3—42no—
435C4×D3—202no—
436Dic6—21no—
437Dic6—22no—
438Dic6—22no—
439Dic6—21no—
440Dic6—42no—
441Dic6—101no—
442Dic6—101no—
443C3×C8—54no—
444C3×C8C2×C22⋊D514yes—
445C22×C5—22no—
446C22×C5—121no—
447C22×C5—122no—
448C22×C5#87412yes—
449C22×C5C22×D1211yescharacteristic
450C2×D5—121no—
451C2×D5—122no—
452C2×D5—122no—
453C2×D5—124no—
454C2×D5—244no—
455C4×C5—121no—
456C4×C5—122no—
457C4×C5#87412yes—
458C4×C5C22×D1211yescharacteristic
459C4×C5C22×D1211yescharacteristic
460Dic5—22no—
461Dic5—22no—
462Dic5—121no—
463C24—301no—
464#41—62no—
465#41—62no—
466#41—302no—
467#41—302no—
468C2×Q8—32no—
469C2×Q8—31no—
470C2×Q8—61no—
471C2×Q8—62no—
472C2×Q8—62no—
473C2×Q8—151no—
474C2×D4—31no—
475C2×D4—61no—
476C2×D4—152no—
477C2×D4—151no—
478C2×D4—302no—
479C2×D4—301no—
480C2×D4—302no—
481C2×D4—301no—
482C2×D4—302no—
483C22×C4—52no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—64no—
489Q16—304no—
490SD16—64no—
491SD16—304no—
492SD16—304no—
493SD16—304no—
494D8—304no—
495D8—304no—
496M16—54no—
497M16#120314yescomplemented
498C2×C8—52no—
499C2×C8C2×D3×D512yes—
500C4⋊C4—302no—
501C22⋊C4—304no—
502C22⋊C4—304no—
503C22⋊C4—302no—
504C22⋊C4—302no—
505C42—52no—
506C42—51no—
507C42—51no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3#408612yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—42no—
513C2×D3—41no—
514C2×D3—202no—
515C2×D3—204no—
516C2×D3—201no—
517C2×D3—202no—
518C2×D3—404no—
519C3×C4—102no—
520C3×C4—102no—
521C3×C4#408612yes—
522C3×C4C2×D4×D511yescharacteristic
523C3×C4C22×C22⋊D511yescharacteristic
524Dic3—42no—
525Dic3—41no—
526Dic3—201no—
527C2×C5—22no—
528C2×C5—241no—
529C2×C5C2×#87411yescharacteristic
530C2×C5#574812yes—
531D5—242no—
532D5—241no—
533C23—61no—
534C23—302no—
535C23—301no—
536C23—604no—
537C23—602no—
538C23D5×D1211yescharacteristic
539Q8—61no—
540Q8—62no—
541Q8—62no—
542Q8—61no—
543Q8—122no—
544Q8—301no—
545Q8—301no—
546D4—61no—
547D4—61no—
548D4—122no—
549D4—302no—
550D4—301no—
551D4—301no—
552D4—302no—
553D4—604no—
554D4—602no—
555D4—602no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—62no—
559C2×C4—61no—
560C2×C4—122no—
561C2×C4—122no—
562C2×C4—202no—
563C2×C4—301no—
564C2×C4—602no—
565C2×C4D5×D1211yescharacteristic
566C2×C4D5×D1212yes—
567C2×C4C2×#120312yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—54no—
570C8C2×#120314yes—
571C2×C3—22no—
572C2×C3#6611112yes—
573C2×C3C2×#408611yescharacteristic
574D3—81no—
575D3—402no—
576D3—401no—
577C5#7853111yescharacteristic, complemented, Sylow
578C22—22no—
579C22—122no—
580C22—121no—
581C22—602no—
582C22—604no—
583C22—601no—
584C22—602no—
585C22—1204no—
586C22#9145112yes—
587C22C2×D5×D1211yescharacteristic
588C4—102no—
589C4—102no—
590C4—121no—
591C4—122no—
592C4—601no—
593C4#9145112yes—
594C4C2×D5×D1211yescharacteristic
595C4C22×#120311yescharacteristic
596C3#1061570411yescharacteristic, complemented, Sylow
597C2—22no—
598C2—241no—
599C2—1202no—
600C2—1201no—
601C2#1175402112yes—
602C2C2×#9145111yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
hypercenterC2×M16D3×D5
hypocenterC3×C5#3153
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#91797C2semidirect
2. C2×C5×#909C2semidirect
3. #11754572C2semidirect
4. C2×#91375C2semidirect
5. C2×#91321C2semidirect
6. C2×#91305C2semidirect
7. C3×M16×Dic5C2semidirect
8. #11748026C2semidirect
9. #11747997C2semidirect
10. #11747965C2semidirect
11. #11747962C2semidirect
22. C2×C5×Dic12C22semidirect
23. C2×C5×#204C22semidirect
28. #91451C22semidirect
30. #91376C22semidirect
34. #91375C22semidirect
35. #91373C22semidirect
37. C2×#6663C22semidirect
39. C2×#6660C22semidirect
42. C3×#3947C22semidirect
43. C3×C8×Dic5C22semidirect
55. M16×Dic5D3semidirect
81. C3×C5×M16D4semidirect
90. C3×#681D4semidirect
102. C2×#909D5semidirect
141. #3947C2×D3semidirect
142. C8×Dic5C2×D3semidirect
196. C2×Dic12C2×D5semidirect
202. C2×#204C2×D5semidirect
240. C5×M16D12semidirect
254. #681D12semidirect
313. C3×M16C22⋊D5semidirect
497. M16#1203semidirect
508. C3×C5#3153semidirect
577. C5#78531semidirect
596. C3#10615704semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
C2×C5×#9092
#117545722
C2×#913752
C2×#913212
C2×#913052
C3×M16×Dic52
#117480262
#117479972
#117479652
#117479622
#106157043
#785315