Finite Group Databasebeta

← #14439348

Subgroups — #14439348

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×#91838C211yesmaximal, characteristic, complemented
2C5×#5832C211yesmaximal, characteristic, complemented
3C2×C3×#4097C211yesmaximal, characteristic, complemented
4C2×#91374C211yesmaximal, characteristic, complemented
5C2×#91309C211yesmaximal, characteristic, complemented
6C2×#91305C211yesmaximal, characteristic, complemented
7#11749324C212yesmaximal, complemented
8#11749323C212yesmaximal, complemented
9#11749078C212yesmaximal, complemented
10#11749076C212yesmaximal, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12#10615020—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91838—24no—
18C2×#6717C2212yes—
19C2×#6715C2212yes—
20C2×#6710C2211yescharacteristic
21C5×#947C2211yescharacteristic, complemented
22C5×#944C2211yescharacteristic, complemented
23C5×#940C2211yescharacteristic, complemented
24C5×#939—22no—
25C5×#936C2211yescharacteristic, complemented
26C4×C5×#67—22no—
27C2×C4×C5×Dic3C2211yescharacteristic
28C3×#4097—24no—
29C2×C3×#689C2212yescomplemented
30C2×C3×#687C2212yescomplemented
31C2×C3×#681C2211yescharacteristic
32C2×#6667—22no—
33#91374—22no—
34#91374C2212yes—
35#91374C2212yes—
36C2×#6661C2212yescomplemented
37C2×#6660C2212yes—
38#91309—24no—
39C2×#6656C2212yescomplemented
40#91305—24no—
41C2×#6654C2212yes—
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83973—51nomaximal, Hall
45C5×#532—31no—
46C2×#4097—31no—
47C2×#4097D311yescharacteristic, complemented
48C2×#4095—31no—
49C2×#4095—31no—
50C2×#4021—31no—
51#65375—32no—
52#65363—32no—
53#65348—32no—
54#65348—32no—
55C4×#681—31no—
56C23×D15—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×D60—22no—
65C2×D60—22no—
66C2×D60—21no—
67C2×D60C2312yes—
68C2×C5×#67—21no—
69C2×C5×#67—22no—
70C22×C5×Dic3D412yes—
71C5×#235—22no—
72C5×#235—22no—
73C2×C5×D12C2311yescharacteristic
74C2×C4×C5×D3—21no—
75C2×C5×Dic6C2311yescharacteristic
76C22×C3×Dic5—21no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10—21no—
80C2×C3×Dic10C2312yes—
81#6717—24no—
82#6715—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#217—22no—
86C5×(C2×D3)⋊C4—22no—
87C5×Dic3⋊C4—22no—
88C4×C5×Dic3D412yes—
89C4×C5×Dic3C2311yescharacteristic
90C4×C5×Dic3C2311yescharacteristic
91C3×#689—24no—
92C3×#687—24no—
93C3×#681D414yescomplemented
94C2×C3×#168C2312yes—
95#6667—24no—
96#6667—24no—
97#6661—24no—
98#6660—24no—
99#6656—24no—
100#6654—24no—
101C2×C3×#137—51no—
102#5832D511yescharacteristic, complemented
103C2×#949—51no—
104C2×#947—51no—
105C2×#942—51no—
106C2×#908—51no—
107#5191—52no—
108#5190—52no—
109#5176—52no—
110#5168—52no—
111Dic3×M16—51no—
112C2×C5×#41—31no—
113C2×C5×#41C2×D311yescharacteristic
114C22×D20—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×C4⋊Q8—31no—
117C5×#127—31no—
118C5×#124—31no—
119C5×#124—31no—
120C5×#121—62no—
121C4×C5×D4—62no—
122C2×C42×C5—31no—
123#4097—24no—
124#4097—64no—
125#4095—64no—
126#4095—64no—
127C2×#689—32no—
128C2×#689C2×D312yescomplemented
129C2×#688—32no—
130C2×#688—32no—
131C2×#687—32no—
132C2×#687C2×D312yescomplemented
133C2×#686—32no—
134C2×#686—32no—
135C2×#685—62no—
136C2×#681—31no—
137C2×#681C2×D311yescharacteristic
138#4021—32no—
139#4021—32no—
140#4021—62no—
141#3935—32no—
142C4×#168—32no—
143#3153—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—22no—
147C22×D15—44no—
148C22×D15—42no—
149C22×C5×D3—21no—
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
161D60—22no—
162D60—22no—
163D60—42no—
164C5×#67—44no—
165C5×#67—42no—
166C2×C5×Dic3—21no—
167C2×C5×Dic3—42no—
168C2×C5×Dic3C2×D412yes—
169C2×C5×Dic3C2×D412yes—
170C5×D12—21no—
171C5×D12—21no—
172C4×C5×D3—42no—
173C5×Dic6—21no—
174C5×Dic6—21no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—42no—
177C3×Dic10—22no—
178C3×Dic10—22no—
179C3×Dic10—42no—
180C3⋊#168C2×D414yes—
181C3×#168C2×D414yes—
182C2×C3×#41C2×D511yescharacteristic
183C22×C3×Q8—51no—
184C2×#235C2×D511yescharacteristic
185C22×D12—51no—
186C3×#137—104no—
187C2×C3×Q16—52no—
188C2×C3×SD16—52no—
189C2×C3×M16—51no—
190#949—104no—
191#947—52no—
192#947—52no—
193#947—102no—
194#947C2×D511yescharacteristic, complemented
195#944C2×D511yescharacteristic, complemented
196C2×#216—52no—
197#942—104no—
198C2×#215—52no—
199C2×#215—52no—
200#940C2×D511yescharacteristic, complemented
201#939—22no—
202#936C2×D511yescharacteristic, complemented
203C2×#213—52no—
204C4×#67—22no—
205C2×(C2×D3)⋊C4—102no—
206C2×C4×Dic3C2×D511yescharacteristic
207C2×#208—51no—
208#908—104no—
209C2×D24—52no—
210C2×#204—52no—
211#815—52no—
212C8×Dic3—52no—
213C23×D5—61no—
214C5×#41—22no—
215C5×#41—22no—
216C5×#41—62no—
217C5×#41—62no—
218C2×C5×Q8—31no—
219C2×C5×Q8C22×D311yescharacteristic
220C2×C5×D4—21no—
221C2×C5×D4—31no—
222C2×C5×D4—62no—
223C2×C5×D4—61no—
224C2×C5×D4C22×D311yescharacteristic
225C22×C4×C5—21no—
226C22×C4×C5—32no—
227C22×C4×C5—61no—
228C22×C4×C5C22×D311yescharacteristic
229C22×Dic5—21no—
230C2×D20—32no—
231C2×D20—62no—
232C2×D20—62no—
233C2×D20—61no—
234C2×Dic10—22no—
235C2×Dic10—22no—
236C2×Dic10—21no—
237C2×Dic10C22×D312yes—
238C5×C4⋊C4—62no—
239C5×C22⋊C4—62no—
240C5×C22⋊C4—62no—
241C42×C5—32no—
242C42×C5—31no—
243C42×C5—31no—
244#689—24no—
245#689—64no—
246#688—64no—
247#688—64no—
248#687—24no—
249#687—64no—
250#686—64no—
251#686—64no—
252#685—64no—
253#685—64no—
254#681—34no—
255#681#6714yescomplemented
256C2×#168—32no—
257C2×#168C22×D312yes—
258C2×#137—51no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—151no—
261C2×AGL(1,ℤ/8)—151no—
262#532—31no—
263C2×#124—151no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—151no—
269C22×C3×C5—22no—
270C22×C3×C5—41no—
271C22×C3×C5—42no—
272C22×C3×C5#12712yes—
273C22×C3×C5C22×D411yescharacteristic
274C2×D15—42no—
275C2×D15—44no—
276C2×D15—84no—
277C2×C5×D3—41no—
278C2×C5×D3—42no—
279C3×C4×C5—41no—
280C3×C4×C5#12712yes—
281C3×C4×C5C22×D411yescharacteristic
282C3×C4×C5C22×D411yescharacteristic
283C3×Dic5—42no—
284C5×Dic3—22no—
285C5×Dic3—22no—
286C5×Dic3—41no—
287C23×D3—101no—
288C3×#41—22no—
289C3×#41—22no—
290C2×C3×Q8—52no—
291C2×C3×Q8—101no—
292C2×C3×Q8—102no—
293C2×C3×Q8—102no—
294C2×C3×Q8C22×D511yescharacteristic
295C2×C3×D4—21no—
296C2×C3×D4C22×D511yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—101no—
299C22×C3×C4C22×D511yescharacteristic
300C2×#67—21no—
301C2×#67—22no—
302C22×Dic3C22⋊D512yes—
303#235—22no—
304#235—22no—
305C2×D12—52no—
306C2×D12—102no—
307C2×D12—102no—
308C2×D12—101no—
309C2×D12C22×D511yescharacteristic
310C2×C4×D3—21no—
311C2×Dic6C22×D511yescharacteristic
312C3×Q16—104no—
313C3×SD16—104no—
314C3×M16—54no—
315C2×C3×C8—52no—
316#217—22no—
317#216—104no—
318#215—104no—
319#215—104no—
320#213—104no—
321(C2×D3)⋊C4—22no—
322(C2×D3)⋊C4—104no—
323(C2×D3)⋊C4—104no—
324Dic3⋊C4—22no—
325C4×Dic3C22⋊D512yes—
326C4×Dic3C22×D511yescharacteristic
327C4×Dic3C22×D511yescharacteristic
328#208—54no—
329C2×C3⋊C8—52no—
330D24—104no—
331#204—104no—
332C23×C5—21no—
333C23×C5—61no—
334C23×C5D3×D411yescharacteristic
335C22×D5—62no—
336C22×D5—124no—
337C22×D5—122no—
338C5×Q8—21no—
339C5×Q8—21no—
340C5×Q8—61no—
341C5×Q8—61no—
342C5×D4—21no—
343C5×D4—21no—
344C5×D4—42no—
345C5×D4—61no—
346C5×D4—61no—
347C5×D4—124no—
348C5×D4—122no—
349C2×C4×C5—21no—
350C2×C4×C5—32no—
351C2×C4×C5—32no—
352C2×C4×C5—42no—
353C2×C4×C5—61no—
354C2×C4×C5—122no—
355C2×C4×C5—122no—
356C2×C4×C5D3×D411yescharacteristic
357C2×C4×C5D3×D412yes—
358C2×C4×C5C2×#6712yes—
359C2×C4×C5C23×D311yescharacteristic
360C2×Dic5—22no—
361C2×Dic5—42no—
362D20—62no—
363D20—62no—
364D20—122no—
365Dic10—22no—
366Dic10—22no—
367Dic10—42no—
368#168—34no—
369#168C2×#6714yes—
370C2×#41—31no—
371C2×#41D3×D511yescharacteristic
372C22×Q8—51no—
373C22×D4—151no—
374#137—104no—
375#137—304no—
376AGL(1,ℤ/8)—304no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—52no—
379C2×Q16—152no—
380C2×SD16—52no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—152no—
385C2×D8—152no—
386C2×M16—51no—
387C2×M16—151no—
388C4⋊Q8—31no—
389#127—31no—
390#124—31no—
391#124—31no—
392#124—152no—
393#124—152no—
394#124—302no—
395#121—62no—
396C4×D4—62no—
397C2×C22⋊C4—302no—
398C2×C42—31no—
399#97—152no—
400C4×C8—152no—
401C2×C3×C5—22no—
402C2×C3×C5—81no—
403C2×C3×C5C2×#12711yescharacteristic
404C2×C3×C5#57512yes—
405D15—82no—
406C5×D3—81no—
407C23×C3—21no—
408C23×C3C2×C22⋊D511yescharacteristic
409C22×D3—21no—
410C22×D3—102no—
411C22×D3—204no—
412C22×D3—202no—
413C3×Q8—21no—
414C3×Q8—21no—
415C3×Q8—102no—
416C3×Q8—102no—
417C3×Q8—202no—
418C3×D4—21no—
419C3×D4—21no—
420C3×D4—42no—
421C2×C3×C4—21no—
422C2×C3×C4—42no—
423C2×C3×C4—102no—
424C2×C3×C4—202no—
425C2×C3×C4D4×D512yes—
426C2×C3×C4D4×D512yes—
427C2×C3×C4C2×C22⋊D511yescharacteristic
428C2×C3×C4C23×D511yescharacteristic
429#67—44no—
430#67—42no—
431C2×Dic3—21no—
432C2×Dic3—42no—
433C2×Dic3C2×C22⋊D512yes—
434C2×Dic3C2×C22⋊D512yes—
435D12—21no—
436D12—21no—
437D12—102no—
438D12—102no—
439D12—202no—
440C4×D3—42no—
441Dic6—21no—
442Dic6—21no—
443C3×C8—54no—
444C3⋊C8—54no—
445C22×C5—22no—
446C22×C5—42no—
447C22×C5—41no—
448C22×C5—122no—
449C22×C5—121no—
450C22×C5#94012yes—
451C22×C5C2×D3×D411yescharacteristic
452C2×D5—124no—
453C2×D5—122no—
454C2×D5—244no—
455C4×C5—41no—
456C4×C5—62no—
457C4×C5—62no—
458C4×C5—121no—
459C4×C5#94012yes—
460C4×C5C2×D3×D411yescharacteristic
461C4×C5C22×#6711yescharacteristic
462Dic5—42no—
463C24—301no—
464#41—22no—
465#41—22no—
466#41—62no—
467#41—62no—
468C2×Q8—31no—
469C2×Q8—52no—
470C2×Q8—101no—
471C2×Q8—102no—
472C2×Q8—102no—
473C2×Q8C2×D3×D511yescharacteristic
474C2×D4—21no—
475C2×D4—31no—
476C2×D4—62no—
477C2×D4—61no—
478C2×D4—152no—
479C2×D4—302no—
480C2×D4—301no—
481C2×D4—302no—
482C2×D4C2×D3×D511yescharacteristic
483C22×C4—21no—
484C22×C4—32no—
485C22×C4—61no—
486C22×C4—101no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—104no—
489Q16—304no—
490SD16—104no—
491SD16—304no—
492SD16—304no—
493SD16—304no—
494D8—304no—
495D8—304no—
496M16—54no—
497M16—154no—
498C2×C8—52no—
499C2×C8—152no—
500C4⋊C4—62no—
501C22⋊C4—62no—
502C22⋊C4—62no—
503C22⋊C4—304no—
504C22⋊C4—304no—
505C42—32no—
506C42—31no—
507C42—31no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—41no—
511C22×C3—42no—
512C22×C3#408612yes—
513C22×C3C22×C22⋊D511yescharacteristic
514C2×D3—41no—
515C2×D3—42no—
516C2×D3—202no—
517C2×D3—204no—
518C2×D3—404no—
519C3×C4—41no—
520C3×C4—202no—
521C3×C4#408612yes—
522C3×C4C2×D4×D511yescharacteristic
523C3×C4C2×D4×D511yescharacteristic
524Dic3—22no—
525Dic3—22no—
526Dic3—41no—
527C2×C5—22no—
528C2×C5—81no—
529C2×C5—241no—
530C2×C5#577712yes—
531C2×C5C2×#94011yescharacteristic
532D5—242no—
533C23—21no—
534C23—61no—
535C23—302no—
536C23—604no—
537C23—602no—
538C23D3×C22⋊D511yescharacteristic
539Q8—21no—
540Q8—21no—
541Q8—61no—
542Q8—61no—
543Q8—102no—
544Q8—102no—
545Q8—202no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—61no—
550D4—61no—
551D4—124no—
552D4—122no—
553D4—302no—
554D4—302no—
555D4—602no—
556C2×C4—21no—
557C2×C4—32no—
558C2×C4—32no—
559C2×C4—42no—
560C2×C4—61no—
561C2×C4—102no—
562C2×C4—122no—
563C2×C4—122no—
564C2×C4—202no—
565C2×C4D5×#6712yes—
566C2×C4D3×C22⋊D511yescharacteristic
567C2×C4#679012yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—54no—
570C8—154no—
571C2×C3—22no—
572C2×C3—81no—
573C2×C3C2×#408611yescharacteristic
574C2×C3#6615612yes—
575D3—81no—
576D3—402no—
577C5#8397311yescharacteristic, complemented, Sylow
578C22—22no—
579C22—42no—
580C22—41no—
581C22—122no—
582C22—121no—
583C22—604no—
584C22—602no—
585C22—1204no—
586C22#9156712yes—
587C22C2×D3×C22⋊D511yescharacteristic
588C4—41no—
589C4—62no—
590C4—62no—
591C4—121no—
592C4—202no—
593C4#9156712yes—
594C4C2×D5×#6711yescharacteristic
595C4C2×#679011yescharacteristic
596C3#1061502011yescharacteristic, complemented, Sylow
597C2—22no—
598C2—81no—
599C2—241no—
600C2—1202no—
601C2#1175534812yes—
602C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3153
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×#91838C2semidirect
2. C5×#5832C2semidirect
3. C2×C3×#4097C2semidirect
4. C2×#91374C2semidirect
5. C2×#91309C2semidirect
6. C2×#91305C2semidirect
7. #11749324C2semidirect
8. #11749323C2semidirect
9. #11749078C2semidirect
10. #11749076C2semidirect
11. Dic3×#681C2semidirect
21. C5×#947C22semidirect
22. C5×#944C22semidirect
23. C5×#940C22semidirect
25. C5×#936C22semidirect
29. C2×C3×#689C22semidirect
30. C2×C3×#687C22semidirect
36. C2×#6661C22semidirect
39. C2×#6656C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
47. C2×#4097D3semidirect
83. #6710D4semidirect
93. C3×#681D4semidirect
102. #5832D5semidirect
128. C2×#689C2×D3semidirect
132. C2×#687C2×D3semidirect
194. #947C2×D5semidirect
195. #944C2×D5semidirect
200. #940C2×D5semidirect
202. #936C2×D5semidirect
255. #681#67semidirect
508. C3×C5#3153semidirect
577. C5#83973semidirect
596. C3#10615020semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C5×#58322
C2×C3×#40972
C2×#913742
C2×#913092
C2×#913052
#117493242
#117493232
#117490782
#117490762
Dic3×#6812
#106150203
#839735