Finite Group Databasebeta

← #14439251

Subgroups — #14439251

Order 1920.

1104 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×#91831C211yesmaximal, characteristic, complemented
2C2×C5×#944C211yesmaximal, characteristic, complemented
3C2×C3×#4088C211yesmaximal, characteristic, complemented
4#11754581C211yesmaximal, characteristic
5C2×#91321C211yesmaximal, characteristic, complemented
6C2×#91307C211yesmaximal, characteristic, complemented
7#11749357C212yesmaximal, complemented
8#11749344C212yesmaximal, complemented
9#11749324C212yesmaximal, complemented
10#11749319C212yesmaximal, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12#10614934—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6718C2212yes—
18#91831—24no—
19C2×#6717C2212yes—
20C2×#6710C2211yescharacteristic
21C5×#944—22no—
22C5×#944C2212yes—
23C5×#944C2212yes—
24C2×C5×Dic3⋊C4—22no—
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×#689C2212yes—
27C3×#4088—24no—
28C2×C3×#688C2212yes—
29C2×C3×#681C2211yescharacteristic
30#91569—22no—
31#91458C2211yescharacteristic
32C4×#1202—22no—
33#91389C2211yescharacteristic
34#91374C2211yescharacteristic
35#91364C2211yescharacteristic
36#91321—24no—
37C2×#6663C2212yes—
38C2×#6661C2212yes—
39C2×#6660C2212yes—
40#91307—24no—
41C2×#6655C2212yes—
42#90953C2212yes—
43Dic3×#168C2212yes—
44#83972—51nomaximal, Hall
45C2×C5×C4⋊Q8—31no—
46C2×#4088—31no—
47C2×#4088—31no—
48C2×#4088—31no—
49C2×#4088D311yescharacteristic, complemented
50#65811—31no—
51#65381—32no—
52#65375—32no—
53#65375—32no—
54#65374—32no—
55C4×#681—31no—
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8—22no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2312yes—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63#6817—22no—
64#6817—22no—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C22×C5×Dic3—21no—
69C22×C5×Dic3D412yes—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—22no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6C2312yes—
74C2×C3×C22⋊D5—21no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1202—22no—
81#6718—24no—
82#6717—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×Dic3⋊C4—24no—
86C5×Dic3⋊C4—24no—
87C4×C5×Dic3D412yes—
88C4×C5×Dic3C2311yescharacteristic
89C4×C5×Dic3C2311yescharacteristic
90C3×#689—24no—
91C3×#688—24no—
92C3×#681D414yescomplemented
93C2×C3×#168C2312yes—
94Dic3⋊Dic5—22no—
95#6667—22no—
96#6665—22no—
97#6663—24no—
98#6661—24no—
99#6660—24no—
100#6655—24no—
101C2×C3×#137—51no—
102#5832—51no—
103C2×#951—51no—
104C2×#944D511yescharacteristic, complemented
105C2×#942—51no—
106C2×#909—51no—
107#5190—52no—
108#5183—52no—
109#5175—52no—
110#5167—52no—
111Dic3×M16—51no—
112C22×C5×Q8—31no—
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C2×#709C2×D311yescharacteristic
116C5×C4⋊Q8—32no—
117C5×C4⋊Q8—32no—
118C5×C4⋊Q8—62no—
119C2×C5×C4⋊C4—62no—
120C2×C42×C5—31no—
121C2×#689—32no—
122C2×#689—32no—
123C2×#689—32no—
124C2×#689C2×D312yes—
125#4088—24no—
126#4088—64no—
127#4088—64no—
128#4088—64no—
129C2×#688—32no—
130C2×#688—32no—
131C2×#688—32no—
132C2×#688C2×D312yes—
133#4076—62no—
134C2×#681—31no—
135C2×#681C2×D311yescharacteristic
136#4021—31no—
137#4021—31no—
138#4020—31no—
139C4×D20—62no—
140#4015—31no—
141#3935—32no—
142C4×#168—32no—
143#3152—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C3×D5—21no—
147C3×C5×Q8—22no—
148C3×C5×Q8—22no—
149C3×C5×Q8—42no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2411yescharacteristic
156#1220—42no—
157C2×Dic15—21no—
158D60—21no—
159D60—21no—
160C4×D15—42no—
161Dic30—21no—
162Dic30—21no—
163C2×C5×Dic3—24no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—42no—
166C2×C5×Dic3C2×D412yes—
167C2×C5×Dic3C2×D412yes—
168C5×Dic6—22no—
169C5×Dic6—22no—
170C5×Dic6—42no—
171C3×C22⋊D5—42no—
172C2×C3×Dic5—21no—
173C3×D20—21no—
174C3×D20—21no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178#1202—44no—
179C3⋊#168C2×D414yes—
180C3×#168C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×Q8C2×D511yescharacteristic
183C2×#235—51no—
184C22×Dic6C2×D511yescharacteristic
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16—51no—
189#951—104no—
190#947—51no—
191#944—22no—
192#944—51no—
193#944C2×D512yes—
194#944C2×D512yes—
195C2×#216—52no—
196C2×#216—52no—
197#942—104no—
198C2×#215—52no—
199#940—51no—
200#939—102no—
201#936—51no—
202C2×#214—52no—
203C4×#67—102no—
204C2×Dic3⋊C4—22no—
205C2×C4×Dic3C2×D511yescharacteristic
206C2×#208—51no—
207#909—104no—
208C2×Dic12—52no—
209C2×#204—52no—
210#815—52no—
211C8×Dic3—52no—
212C2×C5×Q8—21no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8—32no—
216C2×C5×Q8—61no—
217C2×C5×Q8—62no—
218C2×C5×Q8—62no—
219C2×C5×Q8C22×D312yes—
220C22×C4×C5—21no—
221C22×C4×C5—32no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—21no—
225C2×C22⋊D5—61no—
226#709—22no—
227#709—22no—
228#709—62no—
229#709—62no—
230C2×D20—31no—
231C2×D20—62no—
232C2×D20C22×D311yescharacteristic
233C2×C4×D5—21no—
234C2×C4×D5—61no—
235C2×Dic10—31no—
236C2×Dic10C22×D311yescharacteristic
237C5×C4⋊C4—64no—
238C5×C4⋊C4—64no—
239C42×C5—32no—
240C42×C5—31no—
241C42×C5—31no—
242#689—24no—
243#689—64no—
244#689—64no—
245#689—64no—
246#688—24no—
247#688—64no—
248#688—64no—
249#688—64no—
250#685—62no—
251#685—62no—
252C4⋊Dic5—62no—
253#681—34no—
254#681#6714yescomplemented
255C2×#168—32no—
256C2×#168C22×D312yes—
257C2×#137—51no—
258C2×#137—151no—
259C2×#137—151no—
260C2×#137—151no—
261#532—151no—
262C2×C4⋊Q8—31no—
263#497—152no—
264#497—152no—
265#494—152no—
266#492—152no—
267C4×M16—151no—
268C22×C3×C5—22no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—41no—
272C2×D15—42no—
273C2×C3×D5—41no—
274C2×C3×D5—42no—
275C3×C4×C5—42no—
276C3×C4×C5#12712yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C22×D411yescharacteristic
279Dic15—41no—
280C3×Dic5—41no—
281C5×Dic3—22no—
282C5×Dic3—42no—
283C5×Dic3#13714yescomplemented
284C3×#41—102no—
285C3×#41—102no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8—51no—
290C2×C3×Q8C22×D512yes—
291C2×C3×D4—51no—
292C2×C3×D4—101no—
293C22×C3×C4—21no—
294C22×C3×C4—101no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—101no—
297C2×#67—102no—
298C22×Dic3—21no—
299C22×Dic3C22⋊D512yes—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6—21no—
307C2×Dic6—51no—
308C2×Dic6C22×D512yes—
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16—54no—
312C2×C3×C8—52no—
313#217—102no—
314#216—104no—
315#216—104no—
316#215—104no—
317#214—104no—
318(C2×D3)⋊C4—102no—
319Dic3⋊C4—24no—
320Dic3⋊C4—24no—
321Dic3⋊C4—102no—
322C4×Dic3C22⋊D512yes—
323C4×Dic3C22×D511yescharacteristic
324C4×Dic3C22×D511yescharacteristic
325#208—54no—
326C2×C3⋊C8—52no—
327Dic12—104no—
328#204—104no—
329C23×C5D3×D411yescharacteristic
330C22×D5—21no—
331C22×D5—61no—
332C5×Q8—22no—
333C5×Q8—22no—
334C5×Q8—42no—
335C5×Q8—62no—
336C5×Q8—62no—
337C5×Q8—122no—
338C2×C4×C5—22no—
339C2×C4×C5—32no—
340C2×C4×C5—32no—
341C2×C4×C5—42no—
342C2×C4×C5—64no—
343C2×C4×C5—62no—
344C2×C4×C5—122no—
345C2×C4×C5D3×D411yescharacteristic
346C2×C4×C5D3×D412yes—
347C2×C4×C5C2×#6712yes—
348C2×C4×C5C23×D311yescharacteristic
349C22⋊D5—42no—
350C22⋊D5—122no—
351C2×Dic5—21no—
352C2×Dic5—61no—
353D20—21no—
354D20—21no—
355D20—61no—
356D20—61no—
357D20—124no—
358C4×D5—42no—
359C4×D5—122no—
360Dic10—21no—
361Dic10—21no—
362Dic10—61no—
363Dic10—61no—
364#168—34no—
365#168C2×#6714yes—
366C2×#41—51no—
367C2×#41—151no—
368C22×Q8—31no—
369C22×Q8D3×D511yescharacteristic
370#137—104no—
371#137—304no—
372#137—304no—
373#137—304no—
374C2×Q16—52no—
375C2×Q16—152no—
376C2×Q16—152no—
377C2×Q16—152no—
378C2×SD16—52no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×M16—51no—
383C2×M16—151no—
384C4⋊Q8—32no—
385C4⋊Q8—32no—
386C4⋊Q8—62no—
387C4⋊Q8—151no—
388#127—151no—
389#124—151no—
390#124—151no—
391#121—302no—
392C4×D4—302no—
393C2×C4⋊C4—62no—
394C2×C42—31no—
395#97—152no—
396C4×C8—152no—
397C2×C3×C5—22no—
398C2×C3×C5C2×#12711yescharacteristic
399C2×C3×C5C2×#13712yes—
400D15—81no—
401C3×D5—81no—
402C23×C3—101no—
403C23×C3C2×C22⋊D511yescharacteristic
404C22×D3—101no—
405C3×Q8—22no—
406C3×Q8—22no—
407C3×Q8—42no—
408C3×Q8—101no—
409C3×Q8—101no—
410C3×D4—101no—
411C3×D4—101no—
412C3×D4—202no—
413C2×C3×C4—22no—
414C2×C3×C4—42no—
415C2×C3×C4—101no—
416C2×C3×C4—202no—
417C2×C3×C4D4×D512yes—
418C2×C3×C4D4×D512yes—
419C2×C3×C4C2×C22⋊D511yescharacteristic
420C2×C3×C4C23×D511yescharacteristic
421#67—202no—
422#67—204no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3—42no—
426C2×Dic3—101no—
427C2×Dic3C2×C22⋊D512yes—
428C2×Dic3C2×C22⋊D512yes—
429D12—101no—
430D12—101no—
431C4×D3—202no—
432Dic6—22no—
433Dic6—22no—
434Dic6—42no—
435Dic6—101no—
436Dic6—101no—
437C3×C8—54no—
438C3⋊C8—54no—
439C22×C5—22no—
440C22×C5#94012yes—
441C22×C5C2×D3×D411yescharacteristic
442C2×D5—42no—
443C2×D5—41no—
444C2×D5—122no—
445C2×D5—121no—
446C4×C5—34no—
447C4×C5—42no—
448C4×C5—62no—
449C4×C5—122no—
450C4×C5#94012yes—
451C4×C5C2×D3×D411yescharacteristic
452C4×C5C22×#6711yescharacteristic
453Dic5—41no—
454Dic5—121no—
455#41—102no—
456#41—102no—
457#41—302no—
458#41—302no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—32no—
463C2×Q8—51no—
464C2×Q8—61no—
465C2×Q8—62no—
466C2×Q8—62no—
467C2×Q8—151no—
468C2×Q8C2×D3×D512yes—
469C2×D4—51no—
470C2×D4—101no—
471C2×D4—151no—
472C2×D4—302no—
473C2×D4—301no—
474C22×C4—21no—
475C22×C4—32no—
476C22×C4—61no—
477C22×C4—101no—
478C22×C4—301no—
479C22×C4C2×D3×D511yescharacteristic
480Q16—104no—
481Q16—304no—
482Q16—304no—
483Q16—304no—
484SD16—104no—
485SD16—304no—
486SD16—304no—
487SD16—304no—
488M16—54no—
489M16—154no—
490C2×C8—52no—
491C2×C8—152no—
492C4⋊C4—64no—
493C4⋊C4—64no—
494C4⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C42—32no—
498C42—31no—
499C42—31no—
500C3×C5#315211yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—201no—
503C22×C3—202no—
504C22×C3#408612yes—
505C22×C3C22×C22⋊D511yescharacteristic
506C2×D3—201no—
507C2×D3—202no—
508C3×C4—42no—
509C3×C4—201no—
510C3×C4#408612yes—
511C3×C4C2×D4×D511yescharacteristic
512C3×C4C2×D4×D511yescharacteristic
513Dic3—22no—
514Dic3—42no—
515Dic3—201no—
516Dic3#408814yescomplemented
517C2×C5—22no—
518C2×C5D3×#13712yes—
519C2×C5C2×#94011yescharacteristic
520D5—81no—
521D5—241no—
522C23—101no—
523C23—301no—
524C23D3×C22⋊D511yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—42no—
528Q8—62no—
529Q8—62no—
530Q8—101no—
531Q8—101no—
532Q8—122no—
533Q8—301no—
534Q8—301no—
535D4—101no—
536D4—101no—
537D4—202no—
538D4—301no—
539D4—301no—
540D4—604no—
541D4—602no—
542C2×C4—22no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—42no—
546C2×C4—64no—
547C2×C4—62no—
548C2×C4—101no—
549C2×C4—122no—
550C2×C4—202no—
551C2×C4—301no—
552C2×C4—602no—
553C2×C4D5×#6712yes—
554C2×C4D3×C22⋊D511yescharacteristic
555C2×C4#679012yes—
556C2×C4C22×D3×D511yescharacteristic
557C8—54no—
558C8—154no—
559C2×C3—22no—
560C2×C3—401no—
561C2×C3C2×#408611yescharacteristic
562C2×C3C2×#408812yes—
563D3—401no—
564C5#8397211yescharacteristic, complemented, Sylow
565C22—22no—
566C22—202no—
567C22—201no—
568C22—602no—
569C22—601no—
570C22#9156712yes—
571C22C2×D3×C22⋊D511yescharacteristic
572C4—34no—
573C4—42no—
574C4—62no—
575C4—122no—
576C4—201no—
577C4—601no—
578C4#9156712yes—
579C4C2×D5×#6711yescharacteristic
580C4C2×#679011yescharacteristic
581C3#1061493411yescharacteristic, complemented, Sylow
582C2—22no—
583C2—401no—
584C2—1201no—
585C2D3×#408812yes—
586C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11754581C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3152
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×#91831C2semidirect
2. C2×C5×#944C2semidirect
3. C2×C3×#4088C2semidirect
5. C2×#91321C2semidirect
6. C2×#91307C2semidirect
7. #11749357C2semidirect
8. #11749344C2semidirect
9. #11749324C2semidirect
10. #11749319C2semidirect
11. Dic3×#681C2semidirect
49. C2×#4088D3semidirect
83. #6710D4semidirect
92. C3×#681D4semidirect
104. C2×#944D5semidirect
254. #681#67semidirect
283. C5×Dic3#137semidirect
500. C3×C5#3152semidirect
516. Dic3#4088semidirect
564. C5#83972semidirect
581. C3#10614934semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C2×C5×#9442
C2×C3×#40882
#117545812
C2×#913212
C2×#913072
#117493572
#117493442
#117493242
#117493192
Dic3×#6812
#106149343
#839725