Finite Group Databasebeta

← #14439708

Subgroups — #14439708

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91798C211yesmaximal, characteristic, complemented
2C2×C5×#909C211yesmaximal, characteristic, complemented
3#11754271C211yesmaximal, characteristic, complemented
4#11754270C211yesmaximal, characteristic, complemented
5C22×#6663C211yesmaximal, characteristic, complemented
6C2×#91303C211yesmaximal, characteristic
7C3×#65411C211yesmaximal, characteristic, complemented
8#11748026C212yesmaximal, complemented
9#11748024C212yesmaximal, complemented
10#11748018C212yesmaximal, complemented
11#11747962C212yesmaximal, complemented
12#10615706—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C5×Dic6C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91798—24no—
19C2×Dic60C2212yes—
20C2×#6706C2212yes—
21C5×#909—24no—
22C2×C5×Dic12C2212yes—
23C2×C5×#204C2212yes—
24C3×#4072C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26#91543—22no—
27#91542—22no—
28#91383—22no—
29#91376C2212yes—
30#91376C2212yes—
31#91375C2212yes—
32#91373C2212yes—
33#91365—22no—
34C2×#6663—24no—
35C2×#6663C2212yes—
36C2×#6663C2211yescharacteristic
37C2×#6663C2212yes—
38C2×#6660C2211yescharacteristic
39C2×#6659C2211yescharacteristic
40#91303—24no—
41C2×#6654C2211yescharacteristic
42C3×#3947C2212yes—
43C3×C8×Dic5C2212yes—
44#78576—51nomaximal, Hall
45C2×C5×#137—31no—
46#66159—31no—
47C2×#4096—31no—
48#66150—31no—
49C22×#689—31no—
50C2×#4055—31no—
51#65479—32no—
52#65470—32no—
53#65457—32no—
54#65456—32no—
55#65411D311yescharacteristic, complemented
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30—22no—
64C2×Dic30—22no—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
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
79C3×C5×M16D414yes—
80C2×C3×C5×C8C2312yes—
81Dic60—24no—
82#6706—24no—
83C5×Dic12—24no—
84C5×#204—24no—
85C3×C22⋊Dic5D412yes—
86C3×C4⋊Dic5D412yes—
87C3×C4×Dic5C2312yes—
88C2×C3×#168D414yes—
89C2×C3×#168C2311yescharacteristic
90C2×C3×#168C2311yescharacteristic
91#6668—24no—
92#6668—24no—
93#6667—24no—
94(C2×D3)⋊Dic5—24no—
95#6663—22no—
96#6663—24no—
97#6663—24no—
98#6660—22no—
99#6659—22no—
100#6654—22no—
101C2×#909—51no—
102C2×#909D511yescharacteristic, complemented
103C22×Dic12—51no—
104C2×#904—51no—
105#5526—51no—
106#5526—51no—
107C3×#405—51no—
108#4715—52no—
109#4715—52no—
110#4699—52no—
111#4696—52no—
112C2×C5×#41—31no—
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×Dic10—31no—
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16C2×D311yescharacteristic
120#4096—64no—
121#4093—32no—
122#4092—62no—
123#4090—32no—
124#4090—32no—
125C2×#689—32no—
126C2×#689—32no—
127C2×#689—31no—
128C2×#689—64no—
129C2×#688—31no—
130#4082—32no—
131#4081—62no—
132C2×#687—31no—
133C2×#686—31no—
134#4075—62no—
135#4072C2×D311yescharacteristic
136#4070—62no—
137C22×#168C2×D311yescharacteristic
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947C2×D312yes—
142C8×Dic5C2×D312yes—
143#3156—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C5×D3—21no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—42no—
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—42no—
155D60—21no—
156D60—21no—
157C4×D15—42no—
158Dic30—21no—
159Dic30—22no—
160Dic30—22no—
161Dic30—21no—
162Dic30—42no—
163C5×#67—42no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3—42no—
167C5×D12—21no—
168C5×D12—21no—
169C4×C5×D3—42no—
170C5×Dic6—21no—
171C5×Dic6—22no—
172C5×Dic6—22no—
173C5×Dic6—21no—
174C5×Dic6—42no—
175C2×C3×Dic5C2×D414yes—
176C3×C5×C8C2×D414yes—
177C3×#168C2×D412yes—
178C3×#168C2×D412yes—
179C2×#235—51no—
180C2×#235C2×D511yescharacteristic
181C22×Dic6—51no—
182C22×Dic6C2×D511yescharacteristic
183C2×C3×M16C2×D511yescharacteristic
184C22×C3×C8—51no—
185C3×#117—51no—
186#909—24no—
187#909—104no—
188C2×Dic12—52no—
189C2×Dic12—51no—
190C2×Dic12—52no—
191C2×Dic12—52no—
192C2×Dic12—104no—
193C2×Dic12C2×D512yes—
194#904—104no—
195C2×D24—51no—
196C2×#204—51no—
197C2×#204—51no—
198C2×#204—52no—
199C2×#204C2×D512yes—
200#897—102no—
201#897—102no—
202#886—102no—
203#886—102no—
204#875—52no—
205#875—52no—
206#869—52no—
207#869—52no—
208C3×#97—52no—
209C3×C4×C8—52no—
210C5×#41—62no—
211C5×#41—62no—
212C2×C5×Q8—32no—
213C2×C5×Q8—31no—
214C2×C5×Q8—61no—
215C2×C5×Q8—62no—
216C2×C5×Q8—62no—
217C2×C5×D4—31no—
218C2×C5×D4—61no—
219C22×C4×C5—61no—
220C22×C4×C5—61no—
221C22×C4×C5C22×D311yescharacteristic
222C2×C22⋊D5—61no—
223C22×Dic5—61no—
224#709—62no—
225#709—62no—
226C2×D20—31no—
227C2×C4×D5—61no—
228C2×Dic10—32no—
229C2×Dic10—31no—
230C2×Dic10—62no—
231C2×Dic10—62no—
232C2×Dic10—61no—
233C5×Q16—64no—
234C5×SD16—64no—
235C5×M16D1214yes—
236C2×C5×C8C22×D312yes—
237C22⋊Dic5—64no—
238C22⋊Dic5D1212yes—
239#689—62no—
240#689—64no—
241#689—64no—
242#688—62no—
243#687—62no—
244#686—62no—
245#685—64no—
246C4⋊Dic5D1212yes—
247#683—64no—
248#683—64no—
249C4×Dic5C22×D312yes—
250C2×#168D1214yes—
251C2×#168C22×D311yescharacteristic
252C2×#168C22×D311yescharacteristic
253Dic20—64no—
254#677—64no—
255C2×#137—31no—
256C2×#137—151no—
257C2×#135—151no—
258C22×Q16—151no—
259#536—151no—
260#536—151no—
261#497—152no—
262#497—152no—
263#495—152no—
264#494—152no—
265#405—51no—
266C22×C3×C5—22no—
267C22×C3×C5#12712yes—
268C22×C3×C5C22×D411yescharacteristic
269C2×D15—41no—
270C2×D15—42no—
271C2×C5×D3—41no—
272C2×C5×D3—42no—
273C3×C4×C5#12712yes—
274C3×C4×C5C22×D411yescharacteristic
275C3×C4×C5C22×D411yescharacteristic
276Dic15—42no—
277Dic15—41no—
278C3×Dic5—24no—
279C5×Dic3—42no—
280C5×Dic3—41no—
281C22×C3×C4C22×D511yescharacteristic
282C2×#67—21no—
283C2×#67—101no—
284C22×Dic3—21no—
285C22×Dic3—101no—
286#235—22no—
287#235—22no—
288#235—102no—
289#235—102no—
290C2×D12—51no—
291C2×D12C22×D511yescharacteristic
292C2×C4×D3—21no—
293C2×C4×D3—101no—
294C2×Dic6—22no—
295C2×Dic6—22no—
296C2×Dic6—21no—
297C2×Dic6—51no—
298C2×Dic6—52no—
299C2×Dic6—102no—
300C2×Dic6—102no—
301C2×Dic6—101no—
302C2×Dic6C22×D511yescharacteristic
303C2×Dic6C22×D512yes—
304C3×M16C22⋊D514yes—
305C2×C3×C8—54no—
306C2×C3×C8—51no—
307C2×C3×C8—51no—
308C2×C3×C8C22×D512yes—
309C3×C4⋊C4—52no—
310C3×C22⋊C4—52no—
311C3×C42—52no—
312(C2×D3)⋊C4—104no—
313(C2×D3)⋊C4—104no—
314C4⋊Dic3—104no—
315C4⋊Dic3—104no—
316Dic12—24no—
317Dic12—102no—
318Dic12—104no—
319Dic12—104no—
320Dic12—104no—
321D24—102no—
322#204—24no—
323#204—102no—
324#204—102no—
325#204—104no—
326C23×C5—61no—
327C23×C5C2×D1211yescharacteristic
328C22×D5—61no—
329C5×Q8—61no—
330C5×Q8—62no—
331C5×Q8—62no—
332C5×Q8—61no—
333C5×Q8—122no—
334C5×D4—61no—
335C5×D4—61no—
336C5×D4—122no—
337C2×C4×C5—61no—
338C2×C4×C5—62no—
339C2×C4×C5—122no—
340C2×C4×C5—122no—
341C2×C4×C5C2×D1211yescharacteristic
342C2×C4×C5C2×D1212yes—
343C2×C4×C5C2×D1212yes—
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—122no—
346C2×Dic5—61no—
347C2×Dic5—62no—
348C2×Dic5—122no—
349C2×Dic5C2×D1214yes—
350D20—61no—
351D20—61no—
352C4×D5—122no—
353Dic10—62no—
354Dic10—61no—
355Dic10—61no—
356Dic10—62no—
357Dic10—122no—
358C5×C8C2×D1214yes—
359#168C2×D1212yes—
360#168C2×D1212yes—
361C2×#41—31no—
362C2×#41—151no—
363C22×Q8—31no—
364C22×Q8—151no—
365#137—64no—
366#137—304no—
367#135—304no—
368C2×Q16—32no—
369C2×Q16—152no—
370C2×Q16—152no—
371C2×Q16—151no—
372C2×Q16—152no—
373C2×Q16—304no—
374C2×SD16—32no—
375C2×SD16—151no—
376C2×SD16—151no—
377C2×SD16—152no—
378C2×D8—151no—
379C2×M16D3×D511yescharacteristic
380C22×C8—51no—
381C4⋊Q8—152no—
382C4⋊Q8—152no—
383#124—152no—
384#124—152no—
385#123—302no—
386#123—302no—
387C22⋊Q8—302no—
388C22⋊Q8—302no—
389#117—51no—
390#97—52no—
391C4×C8—52no—
392C2×C3×C5—22no—
393C2×C3×C5C2×#12711yescharacteristic
394C2×C3×C5#57812yes—
395D15—81no—
396C5×D3—81no—
397C23×C3D4×D511yescharacteristic
398C22×D3—21no—
399C22×D3—101no—
400C2×C3×C4—54no—
401C2×C3×C4D4×D512yes—
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—42no—
406#67—202no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—42no—
410C2×Dic3—101no—
411C2×Dic3—102no—
412C2×Dic3—202no—
413D12—21no—
414D12—21no—
415D12—101no—
416D12—101no—
417C4×D3—42no—
418C4×D3—202no—
419Dic6—21no—
420Dic6—22no—
421Dic6—22no—
422Dic6—21no—
423Dic6—42no—
424Dic6—101no—
425Dic6—102no—
426Dic6—102no—
427Dic6—101no—
428Dic6—202no—
429C3×C8—52no—
430C3×C8—52no—
431C3×C8C2×C22⋊D514yes—
432C22×C5—22no—
433C22×C5—121no—
434C22×C5—122no—
435C22×C5#87412yes—
436C22×C5C22×D1211yescharacteristic
437C2×D5—121no—
438C2×D5—122no—
439C4×C5—121no—
440C4×C5—122no—
441C4×C5#87412yes—
442C4×C5C22×D1211yescharacteristic
443C4×C5C22×D1211yescharacteristic
444Dic5—24no—
445Dic5—122no—
446Dic5—121no—
447#41—62no—
448#41—62no—
449#41—302no—
450#41—302no—
451C2×Q8—32no—
452C2×Q8—31no—
453C2×Q8—61no—
454C2×Q8—62no—
455C2×Q8—62no—
456C2×Q8—152no—
457C2×Q8—151no—
458C2×Q8—301no—
459C2×Q8—302no—
460C2×Q8—302no—
461C2×D4—31no—
462C2×D4—61no—
463C2×D4—151no—
464C2×D4—301no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—301no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—64no—
471Q16—304no—
472Q16—304no—
473Q16—302no—
474Q16—304no—
475SD16—64no—
476SD16—302no—
477SD16—302no—
478SD16—304no—
479D8—302no—
480M16#120314yes—
481C2×C8—54no—
482C2×C8—51no—
483C2×C8—51no—
484C2×C8C2×D3×D512yes—
485C4⋊C4—52no—
486C4⋊C4—304no—
487C4⋊C4—304no—
488C22⋊C4—52no—
489C22⋊C4—304no—
490C22⋊C4—304no—
491C42—52no—
492C3×C5#315611yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3#408612yes—
495C22×C3C2×D4×D511yescharacteristic
496C2×D3—42no—
497C2×D3—41no—
498C2×D3—202no—
499C2×D3—201no—
500C3×C4—104no—
501C3×C4#408612yes—
502C3×C4C2×D4×D511yescharacteristic
503C3×C4C22×C22⋊D511yescharacteristic
504Dic3—42no—
505Dic3—41no—
506Dic3—202no—
507Dic3—201no—
508C2×C5—22no—
509C2×C5—241no—
510C2×C5C2×#87411yescharacteristic
511C2×C5#575312yes—
512D5—241no—
513C23—61no—
514C23—301no—
515C23D5×D1211yescharacteristic
516Q8—61no—
517Q8—62no—
518Q8—62no—
519Q8—61no—
520Q8—122no—
521Q8—301no—
522Q8—302no—
523Q8—302no—
524Q8—301no—
525Q8—602no—
526D4—61no—
527D4—61no—
528D4—122no—
529D4—301no—
530D4—301no—
531D4—602no—
532C2×C4—54no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—122no—
536C2×C4—122no—
537C2×C4—302no—
538C2×C4—301no—
539C2×C4—602no—
540C2×C4—602no—
541C2×C4D5×D1211yescharacteristic
542C2×C4D5×D1212yes—
543C2×C4C2×#120312yes—
544C2×C4C22×D3×D511yescharacteristic
545C8—52no—
546C8—52no—
547C8C2×#120314yes—
548C2×C3—22no—
549C2×C3#6611312yes—
550C2×C3C2×#408611yescharacteristic
551D3—81no—
552D3—401no—
553C5#7857611yescharacteristic, complemented, Sylow
554C22—22no—
555C22—121no—
556C22—122no—
557C22—601no—
558C22—602no—
559C22#9145112yes—
560C22C2×D5×D1211yescharacteristic
561C4—104no—
562C4—121no—
563C4—122no—
564C4—601no—
565C4—602no—
566C4#9145112yes—
567C4C2×D5×D1211yescharacteristic
568C4C22×#120311yescharacteristic
569C3#1061570611yescharacteristic, complemented, Sylow
570C2—22no—
571C2—241no—
572C2—1201no—
573C2#1175404012yes—
574C2C2×#9145111yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#91303C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3156
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×#91798C2semidirect
2. C2×C5×#909C2semidirect
3. #11754271C2semidirect
4. #11754270C2semidirect
5. C22×#6663C2semidirect
7. C3×#65411C2semidirect
8. #11748026C2semidirect
9. #11748024C2semidirect
10. #11748018C2semidirect
11. #11747962C2semidirect
55. #65411D3semidirect
102. C2×#909D5semidirect
492. C3×C5#3156semidirect
553. C5#78576semidirect
569. C3#10615706semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
C2×C5×#9092
#117542712
#117542702
C22×#66632
C2×#913032
C3×#654112
#117480262
#117480242
#117480182
#117479622
#106157063
#785765