Finite Group Databasebeta

← #14439334

Subgroups — #14439334

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×C5×#908C211yesmaximal, characteristic, complemented
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3#11754586C211yesmaximal, characteristic, complemented
4C2×#91370C211yesmaximal, characteristic, complemented
5C2×#91309C211yesmaximal, characteristic, complemented
6C2×#91299C211yesmaximal, characteristic, complemented
7M16×Dic15C211yesmaximal, characteristic, complemented
8#11748013C212yesmaximal, complemented
9#11747983C212yesmaximal, complemented
10#11747982C212yesmaximal, complemented
11#11747977C212yesmaximal, complemented
12#10615669—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20C5×#908—24no—
21C2×C5×D24C2212yes—
22C2×C5×#204C2212yes—
23C3×#4055—24no—
24C2×C3×Dic20C2212yescomplemented
25C2×C3×#677C2212yescomplemented
26#91571—22no—
27C2×(C2×D3)⋊Dic5—22no—
28#91463C2211yescharacteristic, complemented
29C4×#1201—22no—
30#91385C2211yescharacteristic, complemented
31#91370—22no—
32#91370C2212yes—
33#91370C2212yes—
34#91370C2211yescharacteristic, complemented
35#91368C2211yescharacteristic, complemented
36C2×#6661C2212yescomplemented
37#91309—24no—
38C2×#6656C2212yes—
39C2×#6656C2212yescomplemented
40#91299—24no—
41C2×#6652C2212yes—
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83973—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66166—31no—
47C2×#4097—31no—
48C2×#4082—31no—
49C2×#4078—31no—
50C2×#4055D311yescharacteristic, complemented
51#65457—32no—
52#65456—32no—
53#65444—32no—
54#65443—32no—
55M16×Dic5—31no—
56C23×C5×D3—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15D412yes—
59C2×C5×#67—21no—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12—22no—
63C2×C5×D12—22no—
64C2×C5×D12—21no—
65C2×C5×D12C2312yes—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×C22⋊D5—21no—
70C22×C3×Dic5—21no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20C2311yescharacteristic
74C2×C3×C4×D5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1201—22no—
81C3×C5×M16D414yescomplemented
82C2×C3×C5×C8C2312yes—
83C4×Dic15D412yes—
84C4×Dic15C2311yescharacteristic
85C4×Dic15C2311yescharacteristic
86#6710D414yescomplemented
87C2×C3⋊#168C2312yes—
88C5×D24—24no—
89C5×#204—24no—
90C3×Dic20—24no—
91C3×#677—24no—
92#6669—22no—
93(C2×D3)⋊Dic5—22no—
94(C2×D3)⋊Dic5—24no—
95(C2×D3)⋊Dic5—24no—
96#6665—22no—
97#6661—24no—
98#6656—24no—
99#6656—24no—
100#6652—24no—
101C2×C3×#137—51no—
102#5832—51no—
103C2×#949—51no—
104C2×#947—51no—
105C2×#942—51no—
106C2×#908D511yescharacteristic, complemented
107#5191—52no—
108#5190—52no—
109#5176—52no—
110#5168—52no—
111Dic3×M16—51no—
112C2×C5×#41—31no—
113C22×C5×D4—31no—
114C2×#709C2×D311yescharacteristic
115C22×Dic10C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16C2×D311yescharacteristic
120C2×C22⋊Dic5—62no—
121#4097—64no—
122#4093—31no—
123#4090—31no—
124C2×#689—32no—
125#4086—31no—
126#4085—62no—
127#4082—32no—
128#4082—32no—
129#4082—31no—
130#4082—62no—
131C2×#687—32no—
132C2×#687—32no—
133#4078—64no—
134C2×#686—32no—
135C4×C22⋊D5—62no—
136C2×C4×Dic5—31no—
137C2×#681—31no—
138#4055—24no—
139C2×Dic20C2×D312yescomplemented
140C2×#677C2×D312yescomplemented
141#3947—32no—
142C8×Dic5—32no—
143#3153—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—22no—
146C22×C5×D3—21no—
147C22×C5×D3—44no—
148C22×C5×D3—42no—
149C22×C3×D5—21no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15—42no—
155C2×Dic15C2×D412yes—
156C2×Dic15C2×D412yes—
157C5×#67—42no—
158C2×C5×Dic3—21no—
159C5×D12—21no—
160C5×D12—22no—
161C5×D12—22no—
162C5×D12—21no—
163C5×D12—42no—
164C4×C5×D3—42no—
165C5×Dic6—21no—
166C5×Dic6—21no—
167C3×C22⋊D5—42no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—42no—
171C3×D20—21no—
172C3×D20—21no—
173C3×C4×D5—42no—
174C3×Dic10—21no—
175C3×Dic10—22no—
176C3×Dic10—22no—
177C3×Dic10—21no—
178C3×Dic10—42no—
179#1201—44no—
180C3×C5×C8C2×D414yes—
181C3⋊#168C2×D414yes—
182C2×C3×#41—51no—
183C22×C3×Q8—51no—
184C2×#235C2×D511yescharacteristic
185C22×D12C2×D511yescharacteristic
186C3×#137—104no—
187C2×C3×Q16—52no—
188C2×C3×SD16—52no—
189C2×C3×M16C2×D511yescharacteristic
190#949—104no—
191#947—52no—
192#947—52no—
193#947—51no—
194#947—102no—
195#944—51no—
196C2×#216—52no—
197#942—104no—
198C2×#215—52no—
199C2×#215—52no—
200#940—51no—
201#939—102no—
202#936—51no—
203C2×#213—52no—
204C4×#67—102no—
205C2×(C2×D3)⋊C4—102no—
206C2×C4×Dic3—51no—
207C2×#208—51no—
208#908—24no—
209C2×D24C2×D512yes—
210C2×#204C2×D512yes—
211#815—52no—
212C8×Dic3—52no—
213C24×C5—61no—
214C5×#41—62no—
215C5×#41—62no—
216C2×C5×Q8—31no—
217C2×C5×D4—31no—
218C2×C5×D4—32no—
219C2×C5×D4—61no—
220C2×C5×D4—62no—
221C2×C5×D4—61no—
222C2×C5×D4—62no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226C2×C22⋊D5—62no—
227C22×Dic5—21no—
228C22×Dic5—32no—
229#709—22no—
230#709—22no—
231C2×D20C22×D311yescharacteristic
232C2×C4×D5—21no—
233C2×Dic10—22no—
234C2×Dic10—22no—
235C2×Dic10—21no—
236C2×Dic10C22×D312yes—
237C2×Dic10C22×D311yescharacteristic
238C5×SD16—64no—
239C5×D8—64no—
240C5×M16#6714yescomplemented
241C2×C5×C8C22×D312yes—
242C22⋊Dic5—64no—
243C22⋊Dic5—64no—
244C22⋊Dic5—62no—
245#689—64no—
246#687—64no—
247#687—64no—
248#686—64no—
249#685—62no—
250#683—62no—
251C4×Dic5—32no—
252C4×Dic5—31no—
253C4×Dic5—31no—
254#681—34no—
255C2×#168—32no—
256Dic20—24no—
257#677—24no—
258C2×#137—51no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—31no—
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—151no—
269C22×C3×C5—22no—
270C22×C3×C5#12712yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×C5×D3—41no—
273C2×C5×D3—42no—
274C2×C5×D3—42no—
275C2×C5×D3—44no—
276C2×C5×D3—84no—
277C2×C3×D5—41no—
278C2×C3×D5—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—22no—
283Dic15—22no—
284C3×Dic5—42no—
285C3×Dic5—41no—
286C5×Dic3—41no—
287C23×D3—21no—
288C3×#41—102no—
289C3×#41—102no—
290C2×C3×Q8—51no—
291C2×C3×Q8—52no—
292C2×C3×Q8—101no—
293C2×C3×Q8—102no—
294C2×C3×Q8—102no—
295C2×C3×D4—51no—
296C2×C3×D4—101no—
297C22×C3×C4—101no—
298C22×C3×C4—101no—
299C22×C3×C4C22×D511yescharacteristic
300C2×#67—21no—
301C2×#67—102no—
302C22×Dic3—52no—
303#235—22no—
304#235—22no—
305C2×D12—22no—
306C2×D12—22no—
307C2×D12—21no—
308C2×D12C22×D512yes—
309C2×D12C22×D511yescharacteristic
310C2×C4×D3—21no—
311C2×Dic6C22×D511yescharacteristic
312C3×Q16—104no—
313C3×SD16—104no—
314C3×M16C22⋊D514yescomplemented
315C2×C3×C8C22×D512yes—
316#217—102no—
317#216—104no—
318#215—104no—
319#215—104no—
320#213—104no—
321(C2×D3)⋊C4—104no—
322(C2×D3)⋊C4—104no—
323(C2×D3)⋊C4—102no—
324Dic3⋊C4—102no—
325C4×Dic3—52no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328#208—54no—
329C2×C3⋊C8—52no—
330D24—24no—
331#204—24no—
332C23×C5—62no—
333C23×C5—61no—
334C23×C5—124no—
335C23×C5—122no—
336C23×C5D3×D411yescharacteristic
337C22×D5—21no—
338C5×Q8—61no—
339C5×Q8—61no—
340C5×D4—62no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—62no—
344C5×D4—122no—
345C5×D4—122no—
346C2×C4×C5—61no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D411yescharacteristic
349C2×C4×C5D3×D412yes—
350C2×C4×C5C2×#6712yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—42no—
353C22⋊D5—124no—
354C2×Dic5—21no—
355C2×Dic5—22no—
356C2×Dic5—32no—
357C2×Dic5—32no—
358C2×Dic5—42no—
359C2×Dic5—122no—
360D20—21no—
361D20—21no—
362C4×D5—42no—
363Dic10—21no—
364Dic10—22no—
365Dic10—22no—
366Dic10—21no—
367Dic10—42no—
368C5×C8C2×#6714yes—
369#168—34no—
370C2×#41—31no—
371C2×#41—51no—
372C22×Q8—51no—
373C22×D4—31no—
374#137—104no—
375#137—304no—
376AGL(1,ℤ/8)—64no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—52no—
379C2×Q16—152no—
380C2×SD16—32no—
381C2×SD16—52no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—32no—
385C2×D8—152no—
386C2×M16—151no—
387C2×M16D3×D511yescharacteristic
388C4⋊Q8—151no—
389#127—151no—
390#124—152no—
391#124—152no—
392#124—151no—
393#124—151no—
394#124—302no—
395#121—302no—
396C4×D4—302no—
397C2×C22⋊C4—302no—
398C2×C42—151no—
399#97—152no—
400C4×C8—152no—
401C2×C3×C5—22no—
402C2×C3×C5C2×#12711yescharacteristic
403C2×C3×C5#57512yes—
404C3×D5—81no—
405C5×D3—81no—
406C5×D3—82no—
407C23×C3—101no—
408C23×C3D4×D511yescharacteristic
409C22×D3—22no—
410C22×D3—21no—
411C22×D3—44no—
412C22×D3—42no—
413C3×Q8—101no—
414C3×Q8—102no—
415C3×Q8—102no—
416C3×Q8—101no—
417C3×Q8—202no—
418C3×D4—101no—
419C3×D4—101no—
420C3×D4—202no—
421C2×C3×C4—101no—
422C2×C3×C4—102no—
423C2×C3×C4—202no—
424C2×C3×C4—202no—
425C2×C3×C4D4×D512yes—
426C2×C3×C4D4×D511yescharacteristic
427C2×C3×C4C2×C22⋊D512yes—
428C2×C3×C4C23×D511yescharacteristic
429#67—42no—
430#67—204no—
431C2×Dic3—21no—
432C2×Dic3—52no—
433C2×Dic3—52no—
434C2×Dic3—202no—
435D12—22no—
436D12—21no—
437D12—22no—
438D12—21no—
439D12—42no—
440C4×D3—42no—
441Dic6—21no—
442Dic6—21no—
443C3×C8C2×C22⋊D514yes—
444C3⋊C8—54no—
445C22×C5—22no—
446C22×C5—122no—
447C22×C5—124no—
448C22×C5—121no—
449C22×C5—122no—
450C22×C5—244no—
451C22×C5#94012yes—
452C22×C5C2×D3×D411yescharacteristic
453C2×D5—42no—
454C2×D5—41no—
455C4×C5—121no—
456C4×C5#94012yes—
457C4×C5C2×D3×D411yescharacteristic
458C4×C5C22×#6711yescharacteristic
459Dic5—42no—
460Dic5—41no—
461Dic5—62no—
462Dic5—62no—
463C24—61no—
464#41—62no—
465#41—62no—
466#41—102no—
467#41—102no—
468C2×Q8—31no—
469C2×Q8—52no—
470C2×Q8—51no—
471C2×Q8—101no—
472C2×Q8—102no—
473C2×Q8—102no—
474C2×D4—32no—
475C2×D4—31no—
476C2×D4—51no—
477C2×D4—61no—
478C2×D4—62no—
479C2×D4—61no—
480C2×D4—62no—
481C2×D4—101no—
482C2×D4—302no—
483C22×C4—61no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—152no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—104no—
489Q16—304no—
490SD16—64no—
491SD16—104no—
492SD16—304no—
493SD16—304no—
494D8—64no—
495D8—304no—
496M16—154no—
497M16#120114yescomplemented
498C2×C8—152no—
499C2×C8C2×D3×D512yes—
500C4⋊C4—302no—
501C22⋊C4—302no—
502C22⋊C4—304no—
503C22⋊C4—304no—
504C22⋊C4—302no—
505C42—152no—
506C42—151no—
507C42—151no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—202no—
511C22×C3—201no—
512C22×C3#408612yes—
513C22×C3C2×D4×D511yescharacteristic
514C2×D3—42no—
515C2×D3—44no—
516C2×D3—41no—
517C2×D3—42no—
518C2×D3—84no—
519C3×C4—201no—
520C3×C4—202no—
521C3×C4#408612yes—
522C3×C4C2×D4×D511yescharacteristic
523C3×C4C22×C22⋊D511yescharacteristic
524Dic3—41no—
525Dic3—102no—
526Dic3—102no—
527C2×C5—22no—
528C2×C5—242no—
529C2×C5—241no—
530C2×C5#577712yes—
531C2×C5C2×#94011yescharacteristic
532D5—81no—
533C23—62no—
534C23—61no—
535C23—101no—
536C23—124no—
537C23—122no—
538C23#677711yescharacteristic
539Q8—61no—
540Q8—61no—
541Q8—101no—
542Q8—102no—
543Q8—102no—
544Q8—101no—
545Q8—202no—
546D4—62no—
547D4—61no—
548D4—61no—
549D4—62no—
550D4—101no—
551D4—101no—
552D4—122no—
553D4—122no—
554D4—202no—
555D4—604no—
556C2×C4—61no—
557C2×C4—102no—
558C2×C4—101no—
559C2×C4—122no—
560C2×C4—152no—
561C2×C4—152no—
562C2×C4—202no—
563C2×C4—202no—
564C2×C4—602no—
565C2×C4#677711yescharacteristic
566C2×C4#677712yes—
567C2×C4C2×#120112yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—154no—
570C8C2×#120114yes—
571C2×C3—22no—
572C2×C3—401no—
573C2×C3#6610712yes—
574C2×C3C2×#408611yescharacteristic
575D3—82no—
576D3—81no—
577C5#8397311yescharacteristic, complemented, Sylow
578C22—22no—
579C22—122no—
580C22—124no—
581C22—121no—
582C22—122no—
583C22—202no—
584C22—201no—
585C22—244no—
586C22#9146312yes—
587C22C2×#677711yescharacteristic
588C4—121no—
589C4—201no—
590C4—202no—
591C4—302no—
592C4—302no—
593C4#9146312yes—
594C4C2×#677711yescharacteristic
595C4C22×#120111yescharacteristic
596C3#1061566911yescharacteristic, complemented, Sylow
597C2—22no—
598C2—242no—
599C2—241no—
600C2—401no—
601C2#1175403512yes—
602C2C2×#9146311yescharacteristic
subgroupG/H
centerC22C2×#6777
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×C5×#908C2semidirect
2. C2×C3×#4055C2semidirect
3. #11754586C2semidirect
4. C2×#91370C2semidirect
5. C2×#91309C2semidirect
6. C2×#91299C2semidirect
7. M16×Dic15C2semidirect
8. #11748013C2semidirect
9. #11747983C2semidirect
10. #11747982C2semidirect
11. #11747977C2semidirect
24. C2×C3×Dic20C22semidirect
25. C2×C3×#677C22semidirect
28. #91463C22semidirect
30. #91385C22semidirect
34. #91370C22semidirect
35. #91368C22semidirect
36. C2×#6661C22semidirect
39. C2×#6656C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
50. C2×#4055D3semidirect
81. C3×C5×M16D4semidirect
86. #6710D4semidirect
106. C2×#908D5semidirect
139. C2×Dic20C2×D3semidirect
140. C2×#677C2×D3semidirect
240. C5×M16#67semidirect
314. C3×M16C22⋊D5semidirect
497. M16#1201semidirect
508. C3×C5#3153semidirect
577. C5#83973semidirect
596. C3#10615669semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9082
C2×C3×#40552
#117545862
C2×#913702
C2×#913092
C2×#912992
M16×Dic152
#117480132
#117479832
#117479822
#117479772
#106156693
#839735