Finite Group Databasebeta

← #14439494

Subgroups — #14439494

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91839C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3C3×#66159C211yesmaximal, characteristic, complemented
4#11754606C211yesmaximal, characteristic, complemented
5C2×#91315C211yesmaximal, characteristic, complemented
6C22×#6656C211yesmaximal, characteristic, complemented
7#11749339C212yesmaximal, complemented
8#11749312C212yesmaximal, complemented
9#11749094C212yesmaximal, complemented
10#11749067C212yesmaximal, complemented
11#11748320C211yesmaximal, characteristic, complemented
12#10615670—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91839—24no—
18C2×#6718C2211yescharacteristic, complemented
19C2×#6717C2211yescharacteristic, complemented
20C2×#6716C2211yescharacteristic, complemented
21C2×#6715C2211yescharacteristic, complemented
22C22×C3⋊#168C2211yescharacteristic
23C5×#949—24no—
24C2×C5×#215C2212yes—
25C2×C5×#213C2212yes—
26C2×C5×#208C2211yescharacteristic
27C3×#4090C2212yescomplemented
28C3×#4082C2212yescomplemented
29C3×#4081—22no—
30C3×#4072C2211yescharacteristic
31C3×#4070—22no—
32#91570—22no—
33#91466—22no—
34#91451C2212yes—
35#91373C2212yes—
36C2×#6662C2212yescomplemented
37#91315—24no—
38C2×#6658C2212yescomplemented
39C2×#6656—24no—
40C2×#6656C2212yes—
41C2×#6656C2212yes—
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83402—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66159D311yescharacteristic, complemented
47C2×#4096—31no—
48#66139—31no—
49C22×#687—31no—
50C2×#4055—31no—
51#65464—32no—
52#65456—32no—
53#65444—32no—
54#65443—32no—
55#65411—31no—
56C23×C5×D3—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×#1220—21no—
65#6817—22no—
66#6817—22no—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C2×C5×D12—22no—
71C2×C5×D12—22no—
72C2×C5×D12—21no—
73C2×C5×D12C2312yes—
74C22×C3×Dic5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79C2×#1203—24no—
80#6718—22no—
81#6717—22no—
82#6716—22no—
83#6715—22no—
84C2×C3⋊#168D414yescomplemented
85C2×C3⋊#168C2311yescharacteristic
86C2×C3⋊#168C2311yescharacteristic
87C5×#215—24no—
88C5×#213—24no—
89C5×#208D414yescomplemented
90C2×C5×C3⋊C8C2312yes—
91C3×C22⋊Dic5—24no—
92C3×C22⋊Dic5D412yes—
93C3×C4⋊Dic5D412yes—
94C3×#683—24no—
95C3×C4×Dic5C2312yes—
96(C2×D3)⋊Dic5—24no—
97#6662—24no—
98#6658—24no—
99#6656—24no—
100#6656—24no—
101C3×#536—51no—
102C2×#950—51no—
103C2×#949D511yescharacteristic, complemented
104C2×#942—51no—
105C22×#215—51no—
106#5525—51no—
107#5086—52no—
108#5085—52no—
109#5059—52no—
110#5058—52no—
111#4997—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×D4—31no—
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16—31no—
120#4099—62no—
121#4096—64no—
122#4090C2×D312yescomplemented
123C2×#689—31no—
124C2×#688—31no—
125#4086—32no—
126#4084—62no—
127#4082—32no—
128#4082C2×D312yescomplemented
129#4081—22no—
130C2×#687—31no—
131C2×#687—32no—
132C2×#687—32no—
133C2×#687—64no—
134C2×#686—31no—
135#4072C2×D311yescharacteristic
136#4070—22no—
137C22×#168—31no—
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C5×D3—22no—
148C22×C5×D3—42no—
149C22×C5×D3—82no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161#1220—42no—
162C2×Dic15—21no—
163D60—21no—
164D60—21no—
165C4×D15—42no—
166Dic30—21no—
167Dic30—21no—
168C5×D12—22no—
169C5×D12—22no—
170C5×D12—42no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—42no—
173C2×C3×Dic5C2×D414yes—
174C3×Dic10—22no—
175C3×Dic10—22no—
176C3×Dic10—42no—
177#1203—84no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×Q8—51no—
183C2×#235—51no—
184C22×D12C2×D511yescharacteristic
185C3×C4⋊Q8—52no—
186C3×#124—52no—
187C3×#123—102no—
188C3×C22⋊Q8—102no—
189C3×#117—51no—
190#950—104no—
191#949—24no—
192C2×#216—51no—
193C2×#216—52no—
194#942—104no—
195C2×#215—51no—
196C2×#215—52no—
197C2×#215—52no—
198C2×#215—52no—
199C2×#215—104no—
200C2×#215C2×D512yes—
201C2×#214—51no—
202C2×#213—51no—
203C2×#213C2×D512yes—
204C2×#208C2×D511yescharacteristic
205C22×C3⋊C8—51no—
206#895—102no—
207#882—102no—
208#875—52no—
209#874—52no—
210#803—52no—
211C4×C3⋊C8—52no—
212C24×C5—61no—
213C5×#41—22no—
214C5×#41—22no—
215C2×C5×Q8C22×D311yescharacteristic
216C2×C5×D4—21no—
217C2×C5×D4—32no—
218C2×C5×D4—62no—
219C2×C5×D4—62no—
220C2×C5×D4—61no—
221C2×C5×D4C22×D311yescharacteristic
222C22×C4×C5—21no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—61no—
225C2×C22⋊D5—64no—
226C22×Dic5—21no—
227#709—62no—
228#709—62no—
229C2×D20—31no—
230C2×C4×D5—61no—
231C2×Dic10—22no—
232C2×Dic10—22no—
233C2×Dic10—21no—
234C2×Dic10—31no—
235C2×Dic10C22×D312yes—
236C5×SD16—64no—
237C5×D8—64no—
238C5×M16—34no—
239C2×C5×C8—32no—
240C22⋊Dic5—24no—
241C22⋊Dic5—64no—
242C22⋊Dic5#6712yes—
243#689—62no—
244#688—62no—
245#687—64no—
246#687—64no—
247#687—62no—
248#686—62no—
249C4⋊Dic5#6712yes—
250#683—24no—
251C4×Dic5C22×D312yes—
252C2×#168—34no—
253C2×#168—31no—
254C2×#168—31no—
255Dic20—64no—
256#677—64no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—31no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—51no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×D15—41no—
274C2×D15—42no—
275C2×C5×D3—42no—
276C2×C5×D3—44no—
277C2×C5×D3—84no—
278C3×C4×C5—41no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C3×Dic5—24no—
284C3×Dic5—42no—
285C23×D3—21no—
286C3×#41—22no—
287C3×#41—22no—
288C2×C3×Q8—52no—
289C2×C3×Q8—101no—
290C2×C3×Q8—102no—
291C2×C3×Q8—102no—
292C2×C3×Q8C22×D511yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4C22×D511yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—101no—
299#235—102no—
300#235—102no—
301C2×D12—22no—
302C2×D12—22no—
303C2×D12—21no—
304C2×D12—51no—
305C2×D12—104no—
306C2×D12C22×D512yes—
307C2×C4×D3—101no—
308C2×Dic6—51no—
309C3×C4⋊C4—52no—
310C3×C4⋊C4—104no—
311C3×C22⋊C4—52no—
312C3×C22⋊C4—104no—
313C3×C42—52no—
314#216—102no—
315#216—104no—
316#215—24no—
317#215—104no—
318#215—104no—
319#215—102no—
320#215—104no—
321#214—102no—
322#213—24no—
323#213—102no—
324(C2×D3)⋊C4—104no—
325#208C22⋊D514yescomplemented
326C2×C3⋊C8—54no—
327C2×C3⋊C8—51no—
328C2×C3⋊C8—51no—
329C2×C3⋊C8C22×D512yes—
330C23×C5—21no—
331C23×C5—62no—
332C23×C5—122no—
333C23×C5—242no—
334C23×C5C2×#6711yescharacteristic
335C22×D5—61no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×D4—21no—
339C5×D4—21no—
340C5×D4—42no—
341C5×D4—62no—
342C5×D4—62no—
343C5×D4—122no—
344C2×C4×C5—21no—
345C2×C4×C5—42no—
346C2×C4×C5D3×D412yes—
347C2×C4×C5D3×D412yes—
348C2×C4×C5C2×#6711yescharacteristic
349C2×C4×C5C23×D311yescharacteristic
350C22⋊D5—122no—
351C22⋊D5—244no—
352C2×Dic5—22no—
353C2×Dic5—42no—
354C2×Dic5—61no—
355C2×Dic5C2×#6714yes—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—22no—
360Dic10—22no—
361Dic10—42no—
362Dic10—61no—
363Dic10—61no—
364C5×C8—34no—
365#168—32no—
366#168—32no—
367C2×#41—151no—
368C2×#41D3×D511yescharacteristic
369C22×Q8—51no—
370C22×D4—31no—
371#137—304no—
372AGL(1,ℤ/8)—64no—
373#135—304no—
374C2×Q16—152no—
375C2×Q16—151no—
376C2×SD16—32no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—151no—
381C2×SD16—151no—
382C2×SD16—304no—
383C2×D8—32no—
384C2×D8—151no—
385C2×M16—31no—
386C22×C8—151no—
387C4⋊Q8—52no—
388#127—152no—
389#124—52no—
390#124—152no—
391#123—102no—
392C22⋊Q8—102no—
393#121—302no—
394#120—302no—
395#117—51no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—81no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402D15—81no—
403C5×D3—82no—
404C23×C3—21no—
405C23×C3D4×D511yescharacteristic
406C22×D3—22no—
407C22×D3—42no—
408C22×D3—82no—
409C22×D3—101no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—102no—
413C3×Q8—102no—
414C3×Q8—202no—
415C3×D4—21no—
416C3×D4—21no—
417C3×D4—42no—
418C2×C3×C4—21no—
419C2×C3×C4—42no—
420C2×C3×C4—54no—
421C2×C3×C4—102no—
422C2×C3×C4—202no—
423C2×C3×C4D4×D511yescharacteristic
424C2×C3×C4D4×D512yes—
425C2×C3×C4C2×C22⋊D512yes—
426C2×C3×C4C23×D511yescharacteristic
427#67—202no—
428C2×Dic3—101no—
429D12—22no—
430D12—22no—
431D12—42no—
432D12—101no—
433D12—101no—
434D12—404no—
435C4×D3—202no—
436Dic6—101no—
437Dic6—101no—
438C3⋊C8—52no—
439C3⋊C8—52no—
440C3⋊C8C2×C22⋊D514yes—
441C22×C5—22no—
442C22×C5—41no—
443C22×C5—42no—
444C22×C5—122no—
445C22×C5—124no—
446C22×C5—244no—
447C22×C5#94012yes—
448C22×C5C22×#6711yescharacteristic
449C2×D5—121no—
450C2×D5—122no—
451C4×C5—41no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C2×D3×D411yescharacteristic
455Dic5—24no—
456Dic5—42no—
457Dic5—121no—
458C24—61no—
459#41—22no—
460#41—22no—
461#41—302no—
462#41—302no—
463C2×Q8—52no—
464C2×Q8—101no—
465C2×Q8—102no—
466C2×Q8—102no—
467C2×Q8—151no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—32no—
471C2×D4—61no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—151no—
475C2×D4—304no—
476C2×D4—301no—
477C2×D4C2×D3×D511yescharacteristic
478C22×C4—21no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—304no—
483Q16—302no—
484SD16—64no—
485SD16—304no—
486SD16—302no—
487SD16—304no—
488SD16—304no—
489SD16—302no—
490D8—64no—
491D8—302no—
492M16—34no—
493C2×C8—32no—
494C2×C8—154no—
495C2×C8—151no—
496C2×C8—151no—
497C4⋊C4—52no—
498C4⋊C4—104no—
499C22⋊C4—52no—
500C22⋊C4—104no—
501C22⋊C4—304no—
502C42—52no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—42no—
506C22×C3—41no—
507C22×C3#408612yes—
508C22×C3C2×D4×D511yescharacteristic
509C2×D3—44no—
510C2×D3—42no—
511C2×D3—84no—
512C2×D3—202no—
513C2×D3—201no—
514C3×C4—41no—
515C3×C4—104no—
516C3×C4—202no—
517C3×C4#408612yes—
518C3×C4C2×D4×D511yescharacteristic
519C3×C4C22×C22⋊D511yescharacteristic
520Dic3—201no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5—242no—
524C2×C5C2×#94011yescharacteristic
525C2×C5#583712yes—
526D5—241no—
527C23—21no—
528C23—62no—
529C23—122no—
530C23—242no—
531C23—301no—
532C23D5×#6711yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—102no—
536Q8—102no—
537Q8—202no—
538Q8—301no—
539Q8—301no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—62no—
544D4—62no—
545D4—122no—
546D4—301no—
547D4—301no—
548D4—602no—
549D4—1204no—
550C2×C4—21no—
551C2×C4—42no—
552C2×C4—54no—
553C2×C4—102no—
554C2×C4—202no—
555C2×C4—301no—
556C2×C4—602no—
557C2×C4D5×#6711yescharacteristic
558C2×C4D3×C22⋊D512yes—
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—34no—
562C8—152no—
563C8—152no—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3#6610912yes—
567C2×C3C2×#408611yescharacteristic
568D3—82no—
569D3—401no—
570C5#8340211yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—41no—
574C22—124no—
575C22—122no—
576C22—244no—
577C22—602no—
578C22—601no—
579C22#9156712yes—
580C22C2×D5×#6711yescharacteristic
581C4—41no—
582C4—104no—
583C4—202no—
584C4—601no—
585C4#9156712yes—
586C4C2×D3×C22⋊D511yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061567011yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—242no—
592C2—1201no—
593C2#1175531712yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3154
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×#91839C2semidirect
2. C2×C5×#949C2semidirect
3. C3×#66159C2semidirect
4. #11754606C2semidirect
5. C2×#91315C2semidirect
6. C22×#6656C2semidirect
7. #11749339C2semidirect
8. #11749312C2semidirect
9. #11749094C2semidirect
10. #11749067C2semidirect
11. #11748320C2semidirect
18. C2×#6718C22semidirect
19. C2×#6717C22semidirect
20. C2×#6716C22semidirect
21. C2×#6715C22semidirect
27. C3×#4090C22semidirect
28. C3×#4082C22semidirect
36. C2×#6662C22semidirect
38. C2×#6658C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
46. #66159D3semidirect
84. C2×C3⋊#168D4semidirect
89. C5×#208D4semidirect
103. C2×#949D5semidirect
122. #4090C2×D3semidirect
128. #4082C2×D3semidirect
325. #208C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83402semidirect
588. C3#10615670semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C2×C5×#9492
C3×#661592
#117546062
C2×#913152
C22×#66562
#117493392
#117493122
#117490942
#117490672
#117483202
#106156703
#834025