Finite Group Databasebeta

← #14424392

Subgroups — #14424392

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1009C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic, complemented
3#11754255C211yesmaximal, characteristic, complemented
4C22×#6656C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749305C214yesmaximal, complemented
7#11749058C214yesmaximal, complemented
8#11748389C211yesmaximal, characteristic, complemented
9#11748347C211yesmaximal, characteristic, complemented
10#10615836—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C5×#1009—24no—
13C5×#1009—24no—
14C2×C5×#239C2212yes—
15C2×C5×D3×D4—22no—
16C2×C5×D3×D4C2212yes—
17C2×C5×#235—21no—
18C2×C5×#235C2211yescharacteristic
19C22×C5×D12—21no—
20C22×C5×D12C2211yescharacteristic
21C22×C3×Dic10C2211yescharacteristic, complemented
22#91815C2211yescharacteristic, complemented
23C22×C3⋊#168C2211yescharacteristic, complemented
24C3×#4097—24no—
25C2×C3×#689C2212yescomplemented
26C2×C3×#687C2212yescomplemented
27C2×C3×#681C2211yescharacteristic, complemented
28#91539—22no—
29#91385—21no—
30#91370—21no—
31#91369C2214yescomplemented
32C2×#6656—24no—
33C2×#6656C2214yescomplemented
34#91119C2212yescomplemented
35#91116C2212yescomplemented
36#90967C2214yescomplemented
37(C2×D3)⋊#168C2214yescomplemented
38#83982—51nomaximal, Hall
39C2×C5×H(5,𝔽2)—31no—
40#66159—31no—
41C2×#4097D311yescharacteristic, complemented
42C22×#687—31no—
43#65528—34no—
44#65523—31no—
45#65522—31no—
46#65507—34no—
47#65504—31no—
48C23×C5×D3—21no—
49C23×C5×D3—22no—
50C3×C5×#41—22no—
51C3×C5×#41D414yes—
52C2×C3×C5×Q8C2311yescharacteristic
53C2×C3×C5×D4—21no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×C5×#67—22no—
58C2×C5×#67D412yes—
59C5×#239—24no—
60C5×#239—24no—
61C5×D3×D4—216no—
62C5×D3×D4—24no—
63C5×D3×D4—24no—
64C5×#235—28no—
65C5×#235—22no—
66C5×#235—22no—
67C2×C5×D12—28no—
68C2×C5×D12—22no—
69C2×C5×D12—21no—
70C2×C5×D12—22no—
71C2×C5×D12D411yescharacteristic
72C2×C5×D12D414yes—
73C2×C5×D12C2312yes—
74C2×C4×C5×D3—22no—
75C2×C4×C5×D3C2312yes—
76C2×C5×Dic6D411yescharacteristic
77C22×C3×Dic5—21no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10—22no—
80C2×C3×Dic10—21no—
81C2×C3×Dic10C2312yes—
82#6719—21no—
83C4⋊Dic15C2312yes—
84C4×Dic15—21no—
85C2×C3⋊#168—22no—
86C2×C3⋊#168C2312yes—
87C3×#689—24no—
88C3×#687—24no—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91#6669—24no—
92(C2×D3)⋊Dic5—24no—
93#6656—28no—
94C2×#1009D511yescharacteristic
95C2×C3×#137—51no—
96#5816—51no—
97C22×#215—51no—
98#5233—51no—
99#5187—54no—
100#5169—54no—
101#5131—51no—
102#5129—51no—
103C5×H(5,𝔽2)—64no—
104C5×H(5,𝔽2)—64no—
105C2×C5×#41—31no—
106C2×C5×#41—32no—
107C2×C5×#41—61no—
108C2×C5×#41C2×D311yescharacteristic
109C22×C5×D4—32no—
110C22×C5×D4—31no—
111C22×C5×D4—61no—
112C22×C5×D4—62no—
113C22×Dic10C2×D311yescharacteristic, complemented
114#4097—24no—
115#4090—61no—
116C2×#689C2×D312yescomplemented
117#4082—61no—
118#4081—62no—
119C2×#687—34no—
120C2×#687—64no—
121C2×#687C2×D312yescomplemented
122#4072—31no—
123#4070—34no—
124C2×#681C2×D311yescharacteristic, complemented
125C22×#168—31no—
126#3967—32no—
127#3964—32no—
128#3964—34no—
129C22⋊#168—34no—
130#3009—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×C5×D3—22no—
134C22×C5×D3—28no—
135C22×C5×D3—24no—
136C22×C5×D3—84no—
137C22×C5×D3—82no—
138C22×C5×D3C2×D412yes—
139C3×C5×Q8—21no—
140C3×C5×Q8C2×D412yes—
141C3×C5×D4—24no—
142C3×C5×D4—21no—
143C3×C5×D4C2×D412yes—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—24no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2411yescharacteristic
150C2×Dic15—22no—
151C5×#67—28no—
152C5×#67—24no—
153C2×C5×Dic3C2×D412yes—
154C5×D12—28no—
155C5×D12—22no—
156C5×D12—24no—
157C5×D12—22no—
158C5×D12C2×D414yes—
159C4×C5×D3—28no—
160C4×C5×D3—22no—
161C4×C5×D3—22no—
162C5×Dic6—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—42no—
165C3×Dic10—22no—
166C3×Dic10—22no—
167C3×Dic10—42no—
168C3⋊#168—22no—
169C3×#168—22no—
170C2×C3×#41C2×D511yescharacteristic
171C22×C3×Q8—51no—
172#1009—24no—
173#1009—24no—
174C2×#239C2×D512yes—
175C2×D3×D4—22no—
176C2×D3×D4C2×D512yes—
177C2×#235—21no—
178C2×#235C2×D511yescharacteristic
179C22×D12—21no—
180C22×D12C2×D511yescharacteristic
181C3×#137—104no—
182C2×C3×Q16—52no—
183C2×C3×SD16—52no—
184C2×C3×M16—51no—
185#947—101no—
186#946—54no—
187#944—101no—
188C2×#215—54no—
189C2×#215—104no—
190#929—102no—
191#926—51no—
192C22×C3⋊C8—51no—
193#835—52no—
194#832—52no—
195#821—54no—
196(C2×D3)⋊C8—54no—
197C24×C5—62no—
198C24×C5—61no—
199C5×#41—22no—
200C5×#41—68no—
201C5×#41—64no—
202C5×#41—64no—
203C5×#41—62no—
204C5×#41—62no—
205C5×#41#6714yes—
206C2×C5×Q8—31no—
207C2×C5×Q8C22×D311yescharacteristic
208C2×C5×D4—21no—
209C2×C5×D4—32no—
210C2×C5×D4—34no—
211C2×C5×D4—31no—
212C2×C5×D4—32no—
213C2×C5×D4—62no—
214C2×C5×D4—68no—
215C2×C5×D4—62no—
216C2×C5×D4—64no—
217C2×C5×D4—616no—
218C2×C5×D4—64no—
219C2×C5×D4—61no—
220C2×C5×D4—62no—
221C2×C5×D4C22×D311yescharacteristic
222C22×C4×C5—21no—
223C22×C4×C5—32no—
224C22×C4×C5—62no—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—21no—
227C2×Dic10—22no—
228C2×Dic10—22no—
229C2×Dic10—21no—
230C2×Dic10C22×D312yes—
231C22⋊Dic5—64no—
232C22⋊Dic5—61no—
233#689—24no—
234#687—24no—
235#687—68no—
236C4⋊Dic5—32no—
237#683—64no—
238C4×Dic5—61no—
239#681—22no—
240C2×#168—32no—
241C2×#168—62no—
242C2×#168C22×D312yes—
243C2×H(5,𝔽2)—31no—
244C2×#137—51no—
245C22×SD16—151no—
246#536—151no—
247#452—154no—
248#450—154no—
249#418—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×C5×D3—24no—
260C2×C5×D3—44no—
261C2×C5×D3—84no—
262C2×C5×D3—88no—
263C3×C4×C5—22no—
264C3×C4×C5#12012yes—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C22×D411yescharacteristic
267Dic15—42no—
268C3×Dic5—42no—
269C5×Dic3—22no—
270C23×D3—21no—
271C23×D3—22no—
272C3×#41—22no—
273C3×#41C22⋊D514yes—
274C2×C3×Q8—52no—
275C2×C3×Q8—101no—
276C2×C3×Q8—102no—
277C2×C3×Q8—102no—
278C2×C3×Q8C22×D511yescharacteristic
279C2×C3×D4—21no—
280C2×C3×D4C22×D511yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—101no—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—22no—
285C2×#67C22⋊D512yes—
286#239—24no—
287#239—24no—
288D3×D4—216no—
289D3×D4—24no—
290D3×D4—24no—
291#235—28no—
292#235—22no—
293#235—22no—
294C2×D12—28no—
295C2×D12—22no—
296C2×D12—21no—
297C2×D12—22no—
298C2×D12C22⋊D511yescharacteristic
299C2×D12C22⋊D514yes—
300C2×D12C22×D512yes—
301C2×C4×D3—22no—
302C2×C4×D3C22×D512yes—
303C2×Dic6C22⋊D511yescharacteristic
304C3×Q16—104no—
305C3×SD16—104no—
306C3×M16—102no—
307C2×C3×C8—52no—
308#217—101no—
309#215—108no—
310(C2×D3)⋊C4—104no—
311C4⋊Dic3—52no—
312Dic3⋊C4—104no—
313C4×Dic3—101no—
314C2×C3⋊C8—52no—
315C2×C3⋊C8—102no—
316C23×C5—21no—
317C23×C5—32no—
318C23×C5—68no—
319C23×C5—62no—
320C23×C5—64no—
321C23×C5—242no—
322C23×C5—244no—
323C23×C5D3×D411yescharacteristic
324C5×Q8—21no—
325C5×Q8—62no—
326C5×Q8C2×#6712yes—
327C5×D4—24no—
328C5×D4—21no—
329C5×D4—34no—
330C5×D4—68no—
331C5×D4—68no—
332C5×D4—64no—
333C5×D4—64no—
334C5×D4—62no—
335C5×D4—62no—
336C5×D4C2×#6712yes—
337C2×C4×C5—21no—
338C2×C4×C5—24no—
339C2×C4×C5—32no—
340C2×C4×C5—68no—
341C2×C4×C5—62no—
342C2×C4×C5—62no—
343C2×C4×C5D3×D411yescharacteristic
344C2×C4×C5D3×D412yes—
345C2×C4×C5C2×#6712yes—
346C2×C4×C5C23×D311yescharacteristic
347C2×Dic5—22no—
348C2×Dic5—42no—
349C2×Dic5—62no—
350Dic10—22no—
351Dic10—22no—
352Dic10—42no—
353#168—22no—
354#168—62no—
355H(5,𝔽2)—64no—
356H(5,𝔽2)—64no—
357C2×#41—31no—
358C2×#41—32no—
359C2×#41—61no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—51no—
362C22×D4—32no—
363C22×D4—31no—
364C22×D4—61no—
365C22×D4—62no—
366#137—104no—
367C2×Q16—52no—
368C2×SD16—52no—
369C2×SD16—154no—
370C2×SD16—304no—
371C2×M16—51no—
372C22×C8—151no—
373C4⋊Q8—301no—
374#124—301no—
375#123—302no—
376C22⋊Q8—154no—
377#117—151no—
378#103—152no—
379#102—154no—
380#102—152no—
381C22⋊C8—154no—
382C2×C3×C5—22no—
383C2×C3×C5—42no—
384C2×C3×C5C2×#12011yescharacteristic
385C2×C3×C5#57712yes—
386C5×D3—42no—
387C5×D3—44no—
388C23×C3—21no—
389C23×C3C2×C22⋊D511yescharacteristic
390C22×D3—22no—
391C22×D3—28no—
392C22×D3—24no—
393C22×D3—84no—
394C22×D3—82no—
395C22×D3C2×C22⋊D512yes—
396C3×Q8—21no—
397C3×Q8—102no—
398C3×Q8—102no—
399C3×Q8—202no—
400C3×Q8C2×C22⋊D512yes—
401C3×D4—24no—
402C3×D4—21no—
403C3×D4C2×C22⋊D512yes—
404C2×C3×C4—21no—
405C2×C3×C4—24no—
406C2×C3×C4—102no—
407C2×C3×C4—202no—
408C2×C3×C4C2×C22⋊D512yes—
409C2×C3×C4C2×C22⋊D511yescharacteristic
410C2×C3×C4C2×C22⋊D512yes—
411C2×C3×C4C23×D511yescharacteristic
412#67—28no—
413#67—24no—
414C2×Dic3—102no—
415C2×Dic3C2×C22⋊D512yes—
416D12—28no—
417D12—22no—
418D12—24no—
419D12—22no—
420D12C2×C22⋊D514yes—
421C4×D3—28no—
422C4×D3—22no—
423C4×D3—22no—
424Dic6—22no—
425C3×C8—102no—
426C3⋊C8—102no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—42no—
430C22×C5—64no—
431C22×C5—64no—
432C22×C5—62no—
433C22×C5—124no—
434C22×C5—244no—
435C22×C5—248no—
436C22×C5#93712yes—
437C22×C5C2×D3×D411yescharacteristic
438C4×C5—22no—
439C4×C5—62no—
440C4×C5#93712yes—
441C4×C5C2×D3×D411yescharacteristic
442C4×C5C22×#6711yescharacteristic
443Dic5—42no—
444Dic5—122no—
445C24—62no—
446C24—61no—
447#41—22no—
448#41—68no—
449#41—64no—
450#41—64no—
451#41—62no—
452#41—62no—
453#41#120114yes—
454C2×Q8—31no—
455C2×Q8—52no—
456C2×Q8—101no—
457C2×Q8—102no—
458C2×Q8—102no—
459C2×Q8C2×D3×D511yescharacteristic
460C2×D4—21no—
461C2×D4—32no—
462C2×D4—34no—
463C2×D4—31no—
464C2×D4—32no—
465C2×D4—62no—
466C2×D4—68no—
467C2×D4—62no—
468C2×D4—64no—
469C2×D4—616no—
470C2×D4—64no—
471C2×D4—62no—
472C2×D4—61no—
473C2×D4C2×D3×D511yescharacteristic
474C22×C4—21no—
475C22×C4—32no—
476C22×C4—62no—
477C22×C4—101no—
478C22×C4C2×D3×D511yescharacteristic
479Q16—104no—
480SD16—104no—
481SD16—308no—
482M16—102no—
483C2×C8—52no—
484C2×C8—152no—
485C2×C8—302no—
486C4⋊C4—152no—
487C4⋊C4—304no—
488C22⋊C4—304no—
489C22⋊C4—301no—
490C42—301no—
491C3×C5#300911yescharacteristic, complemented, Hall
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—42no—
495C22×C3#409912yes—
496C22×C3C22×C22⋊D511yescharacteristic
497C2×D3—24no—
498C2×D3—22no—
499C2×D3—24no—
500C2×D3—44no—
501C2×D3—84no—
502C2×D3—88no—
503C3×C4—22no—
504C3×C4—202no—
505C3×C4#409912yes—
506C3×C4C22×C22⋊D511yescharacteristic
507C3×C4C22×C22⋊D511yescharacteristic
508Dic3—22no—
509Dic3—202no—
510C2×C5—22no—
511C2×C5—42no—
512C2×C5—122no—
513C2×C5—124no—
514C2×C5#577812yes—
515C2×C5C2×#93711yescharacteristic
516C23—21no—
517C23—32no—
518C23—68no—
519C23—62no—
520C23—64no—
521C23—242no—
522C23—244no—
523C23D3×C22⋊D511yescharacteristic
524Q8—21no—
525Q8—62no—
526Q8—102no—
527Q8—102no—
528Q8—202no—
529Q8C2×#120112yes—
530D4—24no—
531D4—21no—
532D4—34no—
533D4—68no—
534D4—68no—
535D4—64no—
536D4—62no—
537D4—64no—
538D4—62no—
539D4C2×#120112yes—
540C2×C4—21no—
541C2×C4—24no—
542C2×C4—32no—
543C2×C4—68no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—102no—
547C2×C4—202no—
548C2×C4—302no—
549C2×C4C2×#120112yes—
550C2×C4D3×C22⋊D512yes—
551C2×C4D3×C22⋊D511yescharacteristic
552C2×C4C22×D3×D511yescharacteristic
553C8—102no—
554C8—302no—
555C2×C3—22no—
556C2×C3—42no—
557C2×C3#6617012yes—
558C2×C3C2×#409911yescharacteristic
559D3—42no—
560D3—44no—
561C5#8398211yescharacteristic, complemented, Sylow
562C22—22no—
563C22—22no—
564C22—42no—
565C22—64no—
566C22—64no—
567C22—62no—
568C22—124no—
569C22—244no—
570C22—248no—
571C22#9156812yes—
572C22C2×D3×C22⋊D511yescharacteristic
573C4—22no—
574C4—62no—
575C4—202no—
576C4—602no—
577C4#9156812yes—
578C4C22×#120111yescharacteristic
579C4C2×D3×C22⋊D511yescharacteristic
580C3#1061583611yescharacteristic, complemented, Sylow
581C2—22no—
582C2—42no—
583C2—122no—
584C2—124no—
585C2#1175534012yes—
586C2C2×#9156811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1009C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3009
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
2. C2×C3×#4097C2semidirect
3. #11754255C2semidirect
4. C22×#6656C2semidirect
5. #11751334C2semidirect
6. #11749305C2semidirect
7. #11749058C2semidirect
8. #11748389C2semidirect
9. #11748347C2semidirect
21. C22×C3×Dic10C22semidirect
22. #91815C22semidirect
23. C22×C3⋊#168C22semidirect
25. C2×C3×#689C22semidirect
26. C2×C3×#687C22semidirect
27. C2×C3×#681C22semidirect
31. #91369C22semidirect
33. C2×#6656C22semidirect
34. #91119C22semidirect
35. #91116C22semidirect
36. #90967C22semidirect
37. (C2×D3)⋊#168C22semidirect
41. C2×#4097D3semidirect
113. C22×Dic10C2×D3semidirect
116. C2×#689C2×D3semidirect
121. C2×#687C2×D3semidirect
124. C2×#681C2×D3semidirect
491. C3×C5#3009semidirect
561. C5#83982semidirect
580. C3#10615836semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10092
C2×C3×#40972
#117542552
C22×#66562
#117513342
#117493052
#117490582
#117483892
#117483472
#106158363
#839825