Finite Group Databasebeta

← #14424480

Subgroups — #14424480

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1007C211yesmaximal, characteristic, complemented
2C22×#6717C211yesmaximal, characteristic, complemented
3#11754610C211yesmaximal, characteristic, complemented
4C2×#91305C211yesmaximal, characteristic, complemented
5C3×#65514C211yesmaximal, characteristic, complemented
6#11749282C214yesmaximal, complemented
7#11749279C214yesmaximal, complemented
8#11748382C211yesmaximal, characteristic, complemented
9#11748347C211yesmaximal, characteristic, complemented
10#10615844—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C22×D60C2211yescharacteristic
13C5×#1007—24no—
14C5×#1007—24no—
15C2×C5×#239—21no—
16C2×C5×#239C2212yescomplemented
17C2×C5×D3×Q8—21no—
18C2×C5×D3×Q8C2212yescomplemented
19C2×C5×#235—22no—
20C2×C5×#235C2211yescharacteristic
21C2×C5×#235C2211yescharacteristic
22C2×#6717—24no—
23C2×#6717C2214yes—
24C22×C3⋊#168C2211yescharacteristic
25C3×#4072C2211yescharacteristic
26C2×C3×#681C2211yescharacteristic
27#91573—22no—
28#91460C2214yes—
29#91451—21no—
30#91375—21no—
31C2×#6660C2212yes—
32#91305—24no—
33C2×#6654C2212yes—
34C3×#3967C2214yescomplemented
35#90972C2212yescomplemented
36#90966C2212yescomplemented
37(C2×D3)⋊#168C2214yescomplemented
38#78960—51nomaximal, Hall
39C2×C5×2−1+4—31no—
40#66164—31no—
41C2×#4095—31no—
42C22×#688—31no—
43#65527—34no—
44#65523—31no—
45#65522—31no—
46#65516—34no—
47#65514D311yescharacteristic, complemented
48C23×D15—21no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8—22no—
51C2×C3×C5×Q8D414yescomplemented
52C2×C3×C5×Q8C2312yes—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C2×D60—22no—
56C2×D60—22no—
57C2×D60—21no—
58C2×D60C2312yes—
59C2×C5×#67—21no—
60C2×C5×#67D412yes—
61C5×#239—28no—
62C5×#239—24no—
63C5×#239—24no—
64C5×D3×Q8—28no—
65C5×D3×Q8—24no—
66C5×D3×Q8—24no—
67C5×#235—216no—
68C5×#235—22no—
69C5×#235—22no—
70C5×#235—22no—
71C5×#235D414yescomplemented
72C2×C5×D12—22no—
73C2×C5×D12D411yescharacteristic
74C2×C5×D12C2311yescharacteristic
75C2×C4×C5×D3—22no—
76C2×C4×C5×D3—21no—
77C2×C4×C5×D3—22no—
78C2×C4×C5×D3C2312yes—
79C2×C5×Dic6—22no—
80C2×C5×Dic6D411yescharacteristic
81C2×C5×Dic6C2311yescharacteristic
82C2×#1203—24no—
83#6717—28no—
84C2×C3⋊#168—22no—
85C2×C3⋊#168C2312yes—
86C3×C22⋊Dic5—21no—
87C3×C4⋊Dic5C2312yes—
88C3×C4×Dic5—21no—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91#6667—24no—
92#6660—24no—
93#6654—24no—
94C2×#1007D511yescharacteristic, complemented
95C22×#215—51no—
96C2×#908—51no—
97#5525—51no—
98C3×#419—51no—
99#5129—51no—
100#5002—51no—
101#4810—54no—
102#4806—54no—
103C5×2−1+4—64no—
104C5×2−1+4—64no—
105C2×C5×#41—31no—
106C2×C5×#41—32no—
107C2×C5×#41—31no—
108C2×C5×#41—62no—
109C2×C5×#41—61no—
110C22×C5×Q8—32no—
111C22×C5×Q8—61no—
112C22×C5×Q8C2×D311yescharacteristic
113C22×D20—31no—
114#4095—64no—
115#4093—61no—
116C2×#688—34no—
117C2×#688—32no—
118C2×#688—64no—
119#4086—61no—
120#4083—62no—
121C2×#686—32no—
122#4076—34no—
123#4072C2×D311yescharacteristic
124C2×#681C2×D311yescharacteristic
125C22×#168—31no—
126#3967—32no—
127#3967C2×D314yescomplemented
128#3964—32no—
129C22⋊#168—34no—
130#3010—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—22no—
133C22×D15—42no—
134C22×D15—82no—
135C22×C5×D3—21no—
136C22×C5×D3C2×D412yes—
137C3×C5×Q8—24no—
138C3×C5×Q8—22no—
139C3×C5×Q8C2×D414yes—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2411yescharacteristic
146D60—22no—
147D60—22no—
148D60—42no—
149C5×#67—24no—
150C5×#67—24no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3C2×D412yes—
153C5×D12—28no—
154C5×D12—22no—
155C5×D12—21no—
156C5×D12C2×D412yes—
157C4×C5×D3—28no—
158C4×C5×D3—28no—
159C4×C5×D3—24no—
160C4×C5×D3—22no—
161C4×C5×D3—22no—
162C5×Dic6—28no—
163C5×Dic6—22no—
164C5×Dic6—21no—
165C5×Dic6C2×D412yes—
166C2×C3×Dic5—22no—
167#1203—84no—
168C3⋊#168—22no—
169C3×#168—22no—
170C22×C3×Q8C2×D511yescharacteristic
171#1007—24no—
172#1007—24no—
173C2×#239—21no—
174C2×#239C2×D512yescomplemented
175C2×D3×Q8—21no—
176C2×D3×Q8C2×D512yescomplemented
177C2×#235—22no—
178C2×#235C2×D511yescharacteristic
179C2×#235C2×D511yescharacteristic
180C22×D12—51no—
181C2×C3×M16—51no—
182C3×#117—51no—
183C2×#215—54no—
184C2×#215—104no—
185C22×C3⋊C8—51no—
186#908—104no—
187C2×D24—52no—
188C2×#204—52no—
189#895—54no—
190#882—102no—
191#875—101no—
192#874—101no—
193C3×#103—54no—
194(C2×D3)⋊C8—54no—
195#810—52no—
196#809—52no—
197C23×D5—61no—
198C5×#41—34no—
199C5×#41—616no—
200C5×#41—64no—
201C5×#41—68no—
202C5×#41—64no—
203C5×#41—62no—
204C5×#41—62no—
205C5×#41—62no—
206C2×C5×Q8—21no—
207C2×C5×Q8—22no—
208C2×C5×Q8—31no—
209C2×C5×Q8—31no—
210C2×C5×Q8—62no—
211C2×C5×Q8—64no—
212C2×C5×Q8—68no—
213C2×C5×Q8—64no—
214C2×C5×Q8D1214yescomplemented
215C2×C5×Q8C22×D312yes—
216C2×C5×D4—32no—
217C2×C5×D4—31no—
218C2×C5×D4—31no—
219C2×C5×D4—62no—
220C2×C5×D4—61no—
221C22×C4×C5—21no—
222C22×C4×C5—32no—
223C22×C4×C5—62no—
224C22×C4×C5—62no—
225C22×C4×C5—61no—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—64no—
228C2×D20—32no—
229C2×D20—62no—
230C2×D20—62no—
231C2×D20—61no—
232C22⋊Dic5—21no—
233#688—64no—
234#688—68no—
235#686—64no—
236#685—64no—
237C4⋊Dic5C22×D312yes—
238C4×Dic5—21no—
239#681—22no—
240C2×#168—32no—
241C2×#168—62no—
242C2×#168C22×D312yes—
243C2×2−1+4—31no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—51no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—42no—
256C2×D15—44no—
257C2×D15—84no—
258C2×C5×D3—22no—
259C2×C5×D3—22no—
260C2×C5×D3—24no—
261C2×C5×D3—42no—
262C3×C4×C5—24no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266C3×Dic5—42no—
267C5×Dic3—22no—
268C5×Dic3—22no—
269C23×D3—101no—
270C2×C3×Q8—21no—
271C2×C3×Q8—22no—
272C2×C3×Q8C22⋊D514yescomplemented
273C2×C3×Q8C22×D512yes—
274C22×C3×C4—21no—
275C22×C3×C4C22×D511yescharacteristic
276C2×#67—21no—
277C2×#67C22⋊D512yes—
278#239—28no—
279#239—24no—
280#239—24no—
281D3×Q8—28no—
282D3×Q8—24no—
283D3×Q8—24no—
284#235—216no—
285#235—22no—
286#235—22no—
287#235—22no—
288#235C22⋊D514yescomplemented
289C2×D12—22no—
290C2×D12—52no—
291C2×D12—102no—
292C2×D12—102no—
293C2×D12—101no—
294C2×D12—104no—
295C2×D12C22⋊D511yescharacteristic
296C2×D12C22×D511yescharacteristic
297C2×C4×D3—22no—
298C2×C4×D3—21no—
299C2×C4×D3—22no—
300C2×C4×D3C22×D512yes—
301C2×Dic6—22no—
302C2×Dic6C22⋊D511yescharacteristic
303C2×Dic6C22×D511yescharacteristic
304C3×M16—102no—
305C2×C3×C8—52no—
306C3×C4⋊C4—52no—
307C3×C22⋊C4—101no—
308C3×C42—101no—
309#215—108no—
310(C2×D3)⋊C4—104no—
311C2×C3⋊C8—52no—
312C2×C3⋊C8—102no—
313D24—104no—
314#204—104no—
315C23×C5—32no—
316C23×C5—61no—
317C23×C5D3×D411yescharacteristic
318C22×D5—62no—
319C22×D5—122no—
320C22×D5—242no—
321C5×Q8—24no—
322C5×Q8—22no—
323C5×Q8—32no—
324C5×Q8—68no—
325C5×Q8—62no—
326C5×Q8—61no—
327C5×Q8C2×D1214yes—
328C5×D4—32no—
329C5×D4—68no—
330C5×D4—64no—
331C5×D4—64no—
332C5×D4—62no—
333C5×D4—61no—
334C2×C4×C5—24no—
335C2×C4×C5—22no—
336C2×C4×C5—32no—
337C2×C4×C5—68no—
338C2×C4×C5—68no—
339C2×C4×C5—61no—
340C2×C4×C5—64no—
341C2×C4×C5—62no—
342C2×C4×C5—62no—
343C2×C4×C5C2×D1212yes—
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5D3×D412yes—
346C2×C4×C5C23×D311yescharacteristic
347C22⋊D5—244no—
348C2×Dic5—22no—
349D20—62no—
350D20—62no—
351D20—122no—
352#168—22no—
353#168—62no—
3542−1+4—64no—
3552−1+4—64no—
356C2×#41—31no—
357C2×#41—32no—
358C2×#41—31no—
359C2×#41—62no—
360C2×#41—61no—
361C22×Q8—32no—
362C22×Q8—61no—
363C22×Q8D3×D511yescharacteristic
364C22×D4—151no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—152no—
367C2×SD16—154no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—51no—
371C22×C8—151no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—51no—
377#103—54no—
378#103—152no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5C2×#12011yescharacteristic
383C2×C3×C5#57712yes—
384D15—82no—
385C5×D3—42no—
386C5×D3—42no—
387C23×C3C2×C22⋊D511yescharacteristic
388C22×D3—21no—
389C22×D3—102no—
390C22×D3—202no—
391C22×D3—402no—
392C22×D3C2×C22⋊D512yes—
393C3×Q8—24no—
394C3×Q8—22no—
395C3×Q8C2×C22⋊D514yes—
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—102no—
399C2×C3×C4C2×C22⋊D512yes—
400C2×C3×C4C2×C22⋊D511yescharacteristic
401C2×C3×C4C2×C22⋊D512yes—
402C2×C3×C4C23×D511yescharacteristic
403#67—24no—
404#67—24no—
405C2×Dic3—21no—
406C2×Dic3C2×C22⋊D512yes—
407D12—28no—
408D12—22no—
409D12—21no—
410D12—102no—
411D12—102no—
412D12—202no—
413D12—404no—
414D12C2×C22⋊D512yes—
415C4×D3—28no—
416C4×D3—28no—
417C4×D3—24no—
418C4×D3—22no—
419C4×D3—22no—
420Dic6—28no—
421Dic6—22no—
422Dic6—21no—
423Dic6C2×C22⋊D512yes—
424C3×C8—102no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—62no—
428C22×C5—62no—
429C22×C5—64no—
430C22×C5—122no—
431C22×C5#88212yes—
432C22×C5C2×D3×D411yescharacteristic
433C2×D5—122no—
434C2×D5—124no—
435C2×D5—244no—
436C4×C5—24no—
437C4×C5—62no—
438C4×C5—62no—
439C4×C5#88212yes—
440C4×C5C22×D1211yescharacteristic
441C4×C5C2×D3×D411yescharacteristic
442Dic5—42no—
443C24—301no—
444#41—34no—
445#41—616no—
446#41—64no—
447#41—68no—
448#41—64no—
449#41—62no—
450#41—62no—
451#41—62no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—31no—
455C2×Q8—31no—
456C2×Q8—62no—
457C2×Q8—64no—
458C2×Q8—68no—
459C2×Q8—64no—
460C2×Q8#120314yescomplemented
461C2×Q8C2×D3×D512yes—
462C2×D4—32no—
463C2×D4—31no—
464C2×D4—31no—
465C2×D4—62no—
466C2×D4—61no—
467C2×D4—152no—
468C2×D4—304no—
469C2×D4—302no—
470C2×D4—302no—
471C2×D4—301no—
472C22×C4—21no—
473C22×C4—32no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4—61no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—304no—
479SD16—308no—
480D8—304no—
481M16—102no—
482C2×C8—52no—
483C2×C8—152no—
484C2×C8—302no—
485C4⋊C4—52no—
486C22⋊C4—101no—
487C22⋊C4—304no—
488C42—101no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3#409912yes—
492C22×C3C22×C22⋊D511yescharacteristic
493C2×D3—24no—
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—42no—
497C2×D3—204no—
498C2×D3—202no—
499C2×D3—404no—
500C3×C4—24no—
501C3×C4—202no—
502C3×C4#409912yes—
503C3×C4C22×C22⋊D511yescharacteristic
504C3×C4C22×C22⋊D511yescharacteristic
505Dic3—22no—
506Dic3—22no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5—122no—
510C2×C5C2×#88211yescharacteristic
511C2×C5#577812yes—
512D5—242no—
513C23—32no—
514C23—61no—
515C23—302no—
516C23—602no—
517C23—1202no—
518C23D3×C22⋊D511yescharacteristic
519Q8—22no—
520Q8—24no—
521Q8—32no—
522Q8—68no—
523Q8—61no—
524Q8—62no—
525Q8C2×#120314yes—
526D4—32no—
527D4—68no—
528D4—64no—
529D4—64no—
530D4—61no—
531D4—62no—
532D4—302no—
533D4—302no—
534D4—602no—
535D4—1204no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—32no—
539C2×C4—68no—
540C2×C4—68no—
541C2×C4—61no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—64no—
545C2×C4—102no—
546C2×C4C2×#120312yes—
547C2×C4D3×C22⋊D512yes—
548C2×C4D3×C22⋊D511yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—102no—
551C8—302no—
552C2×C3—22no—
553C2×C3#6617112yes—
554C2×C3C2×#409911yescharacteristic
555D3—42no—
556D3—42no—
557D3—402no—
558C5#7896011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—64no—
561C22—62no—
562C22—62no—
563C22—122no—
564C22—604no—
565C22—602no—
566C22—1204no—
567C22#9157012yes—
568C22C2×D3×C22⋊D511yescharacteristic
569C4—24no—
570C4—62no—
571C4—62no—
572C4—202no—
573C4#9157012yes—
574C4C22×#120311yescharacteristic
575C4C2×D3×C22⋊D511yescharacteristic
576C3#1061584411yescharacteristic, complemented, Sylow
577C2—22no—
578C2—122no—
579C2—122no—
580C2—1202no—
581C2#1175509212yes—
582C2C2×#9157011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1007C2semidirect
2. C22×#6717C2semidirect
3. #11754610C2semidirect
4. C2×#91305C2semidirect
5. C3×#65514C2semidirect
6. #11749282C2semidirect
7. #11749279C2semidirect
8. #11748382C2semidirect
9. #11748347C2semidirect
16. C2×C5×#239C22semidirect
18. C2×C5×D3×Q8C22semidirect
34. C3×#3967C22semidirect
35. #90972C22semidirect
36. #90966C22semidirect
37. (C2×D3)⋊#168C22semidirect
47. #65514D3semidirect
51. C2×C3×C5×Q8D4semidirect
71. C5×#235D4semidirect
94. C2×#1007D5semidirect
127. #3967C2×D3semidirect
174. C2×#239C2×D5semidirect
176. C2×D3×Q8C2×D5semidirect
214. C2×C5×Q8D12semidirect
272. C2×C3×Q8C22⋊D5semidirect
288. #235C22⋊D5semidirect
460. C2×Q8#1203semidirect
489. C3×C5#3010semidirect
558. C5#78960semidirect
576. C3#10615844semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10072
C22×#67172
#117546102
C2×#913052
C3×#655142
#117492822
#117492792
#117483822
#117483472
#106158443
#789605