Finite Group Databasebeta

← #14424503

Subgroups — #14424503

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×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3#11754600C211yesmaximal, characteristic, complemented
4C22×#6655C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749278C214yesmaximal, complemented
7#11749035C214yesmaximal, complemented
8#11748409C211yesmaximal, characteristic, complemented
9#11748347C211yesmaximal, characteristic, complemented
10#10615844—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C5×#1010—24no—
13C5×#1010—24no—
14C2×C5×D3×Q8C2212yescomplemented
15C2×C5×#237—22no—
16C2×C5×#237C2212yescomplemented
17C2×C5×#235—21no—
18C2×C5×#235C2211yescharacteristic
19C22×C5×Dic6—21no—
20C22×C5×Dic6C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22#91815C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C3×#4095—24no—
25C2×C3×#688C2212yes—
26C2×C3×#686C2212yes—
27C2×C3×#681C2211yescharacteristic
28#91563—22no—
29#91463—21no—
30#91456C2214yes—
31#91368—21no—
32C2×#6655—24no—
33C2×#6655C2214yes—
34#91119C2212yescomplemented
35#91116C2212yescomplemented
36#90973C2214yescomplemented
37(C2×D3)⋊#168C2214yescomplemented
38#83948—51nomaximal, Hall
39C2×C5×2−1+4—31no—
40#66164—31no—
41C2×#4095D311yescharacteristic, complemented
42C22×#688—31no—
43#65527—34no—
44#65523—31no—
45#65522—31no—
46#65516—34no—
47#65514—31no—
48C23×C3×D5—21no—
49C3×C5×#41—22no—
50C3×C5×#41D414yescomplemented
51C2×C3×C5×Q8C2311yescharacteristic
52C2×C3×C5×D4—21no—
53C2×C3×C5×D4C2311yescharacteristic
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×#67—22no—
57C2×C5×#67D412yes—
58C22×C5×Dic3—21no—
59C22×C5×Dic3—22no—
60C5×D3×Q8—24no—
61C5×D3×Q8—24no—
62C5×#237—216no—
63C5×#237—24no—
64C5×#237—24no—
65C5×#235—28no—
66C5×#235—22no—
67C5×#235—22no—
68C2×C5×D12D411yescharacteristic
69C2×C4×C5×D3—22no—
70C2×C4×C5×D3C2312yes—
71C2×C5×Dic6—28no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6—22no—
74C2×C5×Dic6—22no—
75C2×C5×Dic6D411yescharacteristic
76C2×C5×Dic6D414yescomplemented
77C2×C5×Dic6C2312yes—
78C2×C3×D20—22no—
79C2×C3×D20—22no—
80C2×C3×D20—21no—
81C2×C3×D20C2312yes—
82C2×#1201—24no—
83#6719—21no—
84C4⋊Dic15C2312yes—
85C4×Dic15—21no—
86C2×C3⋊#168—22no—
87C2×C3⋊#168C2312yes—
88C3×#688—24no—
89C3×#686—24no—
90C3×#681—22no—
91C2×C3×#168C2312yes—
92#6665—24no—
93#6655—28no—
94C2×#1010D511yescharacteristic, complemented
95C2×C3×AGL(1,ℤ/8)—51no—
96#5805—51no—
97C22×#214—51no—
98#5233—51no—
99#5170—54no—
100#5158—54no—
101#5129—51no—
102#5120—51no—
103C5×2−1+4—64no—
104C5×2−1+4—64no—
105C2×C5×#41—31no—
106C2×C5×#41—32no—
107C2×C5×#41—61no—
108C2×C5×#41—62no—
109C2×C5×#41C2×D311yescharacteristic
110C22×C5×Q8—32no—
111C22×C5×Q8—31no—
112C22×C5×Q8—61no—
113C22×D20C2×D311yescharacteristic
114#4095—24no—
115#4093—61no—
116C2×#688—34no—
117C2×#688—64no—
118C2×#688C2×D312yes—
119#4086—61no—
120#4083—62no—
121C2×#686C2×D312yes—
122#4076—34no—
123#4072—31no—
124C2×#681C2×D311yescharacteristic
125C22×#168—31no—
126#3967—32no—
127#3967—34no—
128#3964—32no—
129C22⋊#168—34no—
130#3010—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×C5×D3C2×D412yes—
134C22×C3×D5—22no—
135C22×C3×D5—42no—
136C22×C3×D5—82no—
137C3×C5×Q8—21no—
138C3×C5×Q8C2×D412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C2×D412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—22no—
149C5×#67—28no—
150C5×#67—24no—
151C2×C5×Dic3—28no—
152C2×C5×Dic3—24no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3C2×D412yes—
155C5×D12—22no—
156C4×C5×D3—28no—
157C4×C5×D3—22no—
158C4×C5×D3—22no—
159C5×Dic6—28no—
160C5×Dic6—22no—
161C5×Dic6—24no—
162C5×Dic6—22no—
163C5×Dic6C2×D414yes—
164C3×D20—22no—
165C3×D20—22no—
166C3×D20—42no—
167#1201—84no—
168C3⋊#168—22no—
169C3×#168—22no—
170C2×C3×#41C2×D511yescharacteristic
171C22×C3×D4—51no—
172#1010—24no—
173#1010—24no—
174C2×D3×Q8C2×D512yescomplemented
175C2×#237—22no—
176C2×#237C2×D512yescomplemented
177C2×#235—21no—
178C2×#235C2×D511yescharacteristic
179C22×Dic6—21no—
180C22×Dic6C2×D511yescharacteristic
181C3×AGL(1,ℤ/8)—104no—
182C2×C3×SD16—52no—
183C2×C3×D8—52no—
184C2×C3×M16—51no—
185#953—102no—
186#940—101no—
187#938—54no—
188#936—101no—
189C2×#214—54no—
190C2×#214—104no—
191#926—51no—
192C22×C3⋊C8—51no—
193#835—52no—
194#832—52no—
195(C2×D3)⋊C8—54no—
196#816—54no—
197C23×D5—21no—
198C5×#41—22no—
199C5×#41—68no—
200C5×#41—64no—
201C5×#41—616no—
202C5×#41—64no—
203C5×#41—62no—
204C5×#41—62no—
205C5×#41#6714yescomplemented
206C2×C5×Q8—31no—
207C2×C5×Q8—34no—
208C2×C5×Q8—32no—
209C2×C5×Q8—62no—
210C2×C5×Q8—68no—
211C2×C5×Q8—64no—
212C2×C5×Q8—64no—
213C2×C5×Q8—61no—
214C2×C5×Q8—62no—
215C2×C5×Q8C22×D311yescharacteristic
216C2×C5×D4—21no—
217C2×C5×D4—32no—
218C2×C5×D4—31no—
219C2×C5×D4—62no—
220C2×C5×D4C22×D311yescharacteristic
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—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20C22×D312yes—
232C22⋊Dic5—61no—
233#688—24no—
234#688—68no—
235#686—24no—
236#685—64no—
237C4⋊Dic5—32no—
238C4×Dic5—61no—
239#681—22no—
240C2×#168—32no—
241C2×#168—62no—
242C2×#168C22×D312yes—
243C2×2−1+4—31no—
244C2×AGL(1,ℤ/8)—51no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—42no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×C5×D3—22no—
258C2×C5×D3—24no—
259C2×C3×D5—42no—
260C2×C3×D5—44no—
261C2×C3×D5—84no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—42no—
267C5×Dic3—22no—
268C5×Dic3—24no—
269C24×C3—101no—
270C3×#41—22no—
271C3×#41C22⋊D514yescomplemented
272C2×C3×Q8C22×D511yescharacteristic
273C2×C3×D4—21no—
274C2×C3×D4—52no—
275C2×C3×D4—102no—
276C2×C3×D4—102no—
277C2×C3×D4—101no—
278C2×C3×D4C22×D511yescharacteristic
279C22×C3×C4—21no—
280C22×C3×C4C22×D511yescharacteristic
281C2×#67—22no—
282C2×#67—104no—
283C2×#67C22⋊D512yes—
284C22×Dic3—21no—
285C22×Dic3—22no—
286D3×Q8—24no—
287D3×Q8—24no—
288#237—216no—
289#237—24no—
290#237—24no—
291#235—28no—
292#235—22no—
293#235—22no—
294C2×D12C22⋊D511yescharacteristic
295C2×C4×D3—22no—
296C2×C4×D3C22×D512yes—
297C2×Dic6—28no—
298C2×Dic6—21no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6C22⋊D511yescharacteristic
302C2×Dic6C22⋊D514yescomplemented
303C2×Dic6C22×D512yes—
304C3×SD16—104no—
305C3×D8—104no—
306C3×M16—102no—
307C2×C3×C8—52no—
308#217—101no—
309#217—104no—
310#214—108no—
311C4⋊Dic3—52no—
312C4×Dic3—101no—
313C2×C3⋊C8—52no—
314C2×C3⋊C8—102no—
315C23×C5—21no—
316C23×C5—32no—
317C23×C5D3×D411yescharacteristic
318C22×D5—22no—
319C22×D5—42no—
320C22×D5—82no—
321C5×Q8—21no—
322C5×Q8—34no—
323C5×Q8—68no—
324C5×Q8—62no—
325C5×Q8—64no—
326C5×Q8—62no—
327C5×Q8C2×#6712yes—
328C5×D4—24no—
329C5×D4—21no—
330C5×D4—68no—
331C5×D4—64no—
332C5×D4—62no—
333C5×D4C2×#6712yes—
334C2×C4×C5—21no—
335C2×C4×C5—24no—
336C2×C4×C5—32no—
337C2×C4×C5—68no—
338C2×C4×C5—68no—
339C2×C4×C5—64no—
340C2×C4×C5—62no—
341C2×C4×C5—62no—
342C2×C4×C5—62no—
343C2×C4×C5D3×D411yescharacteristic
344C2×C4×C5D3×D412yes—
345C2×C4×C5C2×#6712yes—
346C2×C4×C5C23×D311yescharacteristic
347C22⋊D5—244no—
348C2×Dic5—62no—
349D20—22no—
350D20—22no—
351D20—42no—
352#168—22no—
353#168—62no—
3542−1+4—64no—
3552−1+4—64no—
356C2×#41—31no—
357C2×#41—32no—
358C2×#41—61no—
359C2×#41—62no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—32no—
362C22×Q8—31no—
363C22×Q8—61no—
364C22×D4—51no—
365AGL(1,ℤ/8)—104no—
366C2×SD16—52no—
367C2×SD16—154no—
368C2×SD16—304no—
369C2×D8—52no—
370C2×M16—51no—
371C22×C8—151no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—151no—
377#103—154no—
378#103—152no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385C3×D5—82no—
386C5×D3—42no—
387C23×C3—21no—
388C23×C3—102no—
389C23×C3—202no—
390C23×C3—402no—
391C23×C3C2×C22⋊D511yescharacteristic
392C22×D3C2×C22⋊D512yes—
393C3×Q8—21no—
394C3×Q8C2×C22⋊D512yes—
395C3×D4—24no—
396C3×D4—21no—
397C3×D4—102no—
398C3×D4—102no—
399C3×D4—202no—
400C3×D4C2×C22⋊D512yes—
401C2×C3×C4—21no—
402C2×C3×C4—24no—
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C2×C22⋊D511yescharacteristic
405C2×C3×C4C2×C22⋊D512yes—
406C2×C3×C4C23×D511yescharacteristic
407#67—28no—
408#67—24no—
409#67—404no—
410C2×Dic3—28no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—102no—
414C2×Dic3C2×C22⋊D512yes—
415D12—22no—
416C4×D3—28no—
417C4×D3—22no—
418C4×D3—22no—
419Dic6—28no—
420Dic6—22no—
421Dic6—24no—
422Dic6—22no—
423Dic6C2×C22⋊D514yes—
424C3×C8—102no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—42no—
429C22×C5—64no—
430C22×C5—62no—
431C22×C5#93712yes—
432C22×C5C2×D3×D411yescharacteristic
433C2×D5—44no—
434C2×D5—42no—
435C2×D5—84no—
436C4×C5—22no—
437C4×C5—62no—
438C4×C5—64no—
439C4×C5#93712yes—
440C4×C5C2×D3×D411yescharacteristic
441C4×C5C22×#6711yescharacteristic
442Dic5—122no—
443C24—101no—
444#41—22no—
445#41—68no—
446#41—64no—
447#41—616no—
448#41—64no—
449#41—62no—
450#41—62no—
451#41#120114yescomplemented
452C2×Q8—31no—
453C2×Q8—34no—
454C2×Q8—32no—
455C2×Q8—62no—
456C2×Q8—68no—
457C2×Q8—64no—
458C2×Q8—64no—
459C2×Q8—62no—
460C2×Q8—61no—
461C2×Q8C2×D3×D511yescharacteristic
462C2×D4—21no—
463C2×D4—32no—
464C2×D4—31no—
465C2×D4—52no—
466C2×D4—62no—
467C2×D4—102no—
468C2×D4—102no—
469C2×D4—101no—
470C2×D4—304no—
471C2×D4C2×D3×D511yescharacteristic
472C22×C4—21no—
473C22×C4—32no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4—61no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—104no—
479SD16—308no—
480D8—104no—
481M16—102no—
482C2×C8—52no—
483C2×C8—152no—
484C2×C8—302no—
485C4⋊C4—152no—
486C22⋊C4—304no—
487C22⋊C4—301no—
488C42—301no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—42no—
493C22×C3—204no—
494C22×C3—202no—
495C22×C3—404no—
496C22×C3#409912yes—
497C22×C3C22×C22⋊D511yescharacteristic
498C2×D3—24no—
499C2×D3—22no—
500C3×C4—22no—
501C3×C4#409912yes—
502C3×C4C22×C22⋊D511yescharacteristic
503C3×C4C22×C22⋊D511yescharacteristic
504Dic3—22no—
505Dic3—24no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5—122no—
510C2×C5#577512yes—
511C2×C5C2×#93711yescharacteristic
512D5—82no—
513C23—21no—
514C23—32no—
515C23—102no—
516C23—202no—
517C23—402no—
518C23D3×C22⋊D511yescharacteristic
519Q8—21no—
520Q8—34no—
521Q8—68no—
522Q8—62no—
523Q8—62no—
524Q8—64no—
525Q8C2×#120112yes—
526D4—24no—
527D4—21no—
528D4—68no—
529D4—64no—
530D4—62no—
531D4—102no—
532D4—102no—
533D4—202no—
534D4—1204no—
535D4C2×#120112yes—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—32no—
539C2×C4—68no—
540C2×C4—68no—
541C2×C4—62no—
542C2×C4—64no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—302no—
546C2×C4C2×#120112yes—
547C2×C4D3×C22⋊D512yes—
548C2×C4D3×C22⋊D511yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—102no—
551C8—302no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—402no—
555C2×C3#6617112yes—
556C2×C3C2×#409911yescharacteristic
557D3—42no—
558C5#8394811yescharacteristic, complemented, Sylow
559C22—22no—
560C22—22no—
561C22—42no—
562C22—64no—
563C22—62no—
564C22—204no—
565C22—202no—
566C22—404no—
567C22#9156812yes—
568C22C2×D3×C22⋊D511yescharacteristic
569C4—22no—
570C4—62no—
571C4—64no—
572C4—602no—
573C4#9156812yes—
574C4C22×#120111yescharacteristic
575C4C2×D3×C22⋊D511yescharacteristic
576C3#1061584411yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—122no—
580C2—402no—
581C2#1175532412yes—
582C2C2×#9156811yescharacteristic
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#3010
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×C5×#1010C2semidirect
2. C2×C3×#4095C2semidirect
3. #11754600C2semidirect
4. C22×#6655C2semidirect
5. #11751334C2semidirect
6. #11749278C2semidirect
7. #11749035C2semidirect
8. #11748409C2semidirect
9. #11748347C2semidirect
14. C2×C5×D3×Q8C22semidirect
16. C2×C5×#237C22semidirect
34. #91119C22semidirect
35. #91116C22semidirect
36. #90973C22semidirect
37. (C2×D3)⋊#168C22semidirect
41. C2×#4095D3semidirect
50. C3×C5×#41D4semidirect
76. C2×C5×Dic6D4semidirect
94. C2×#1010D5semidirect
174. C2×D3×Q8C2×D5semidirect
176. C2×#237C2×D5semidirect
205. C5×#41#67semidirect
271. C3×#41C22⋊D5semidirect
302. C2×Dic6C22⋊D5semidirect
451. #41#1201semidirect
489. C3×C5#3010semidirect
558. C5#83948semidirect
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×#10102
C2×C3×#40952
#117546002
C22×#66552
#117513342
#117492782
#117490352
#117484092
#117483472
#106158443
#839485