Finite Group Databasebeta

← #14439263

Subgroups — #14439263

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×#91840C211yesmaximal, characteristic, complemented
2C5×#5832C211yesmaximal, characteristic
3C2×C3×#4097C211yesmaximal, characteristic, complemented
4C2×#91389C211yesmaximal, characteristic, complemented
5C2×#91322C211yesmaximal, characteristic, complemented
6C2×#91309C211yesmaximal, characteristic, complemented
7#11749357C212yesmaximal, complemented
8#11749354C212yesmaximal, complemented
9#11749110C212yesmaximal, complemented
10#11749108C212yesmaximal, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12#10615019—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91840—24no—
18C2×#6718C2212yes—
19C2×#6716C2212yes—
20C2×#6710C2211yescharacteristic
21C5×#947C2211yescharacteristic
22C5×#944C2211yescharacteristic
23C5×#940C2211yescharacteristic
24C5×#939—22no—
25C5×#936C2211yescharacteristic
26C4×C5×#67—22no—
27C2×C4×C5×Dic3C2211yescharacteristic
28C3×#4097—24no—
29C2×C3×#689C2212yes—
30C2×C3×#687C2212yes—
31C2×C3×#681C2211yescharacteristic
32C2×Dic3⋊Dic5—22no—
33#91389—22no—
34#91389C2212yes—
35#91389C2212yes—
36#91322—24no—
37C2×#6663C2212yes—
38C2×#6661C2212yes—
39C2×#6659C2212yes—
40#91309—24no—
41C2×#6656C2212yes—
42#90953C2212yes—
43Dic3×#168C2212yes—
44#83972—51nomaximal, Hall
45C5×#532—31no—
46C2×#4097—31no—
47C2×#4097—31no—
48C2×#4097—31no—
49C2×#4097D311yescharacteristic, complemented
50C2×#4015—31no—
51#65381—32no—
52#65365—32no—
53#65349—32no—
54#65349—32no—
55C4×#681—31no—
56C3×C5×#41—22no—
57C3×C5×#41—22no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15—21no—
64C2×Dic30—22no—
65C2×Dic30—22no—
66C2×Dic30—21no—
67C2×Dic30C2312yes—
68C2×C5×#67—21no—
69C2×C5×#67—22no—
70C22×C5×Dic3D412yes—
71C5×#235—22no—
72C5×#235—22no—
73C2×C5×D12C2311yescharacteristic
74C2×C4×C5×D3—21no—
75C2×C5×Dic6C2311yescharacteristic
76C22×C3×Dic5—21no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10—21no—
80C2×C3×Dic10C2312yes—
81#6718—24no—
82#6716—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#217—22no—
86C5×(C2×D3)⋊C4—22no—
87C5×Dic3⋊C4—22no—
88C4×C5×Dic3D412yes—
89C4×C5×Dic3C2311yescharacteristic
90C4×C5×Dic3C2311yescharacteristic
91C3×#689—24no—
92C3×#687—24no—
93C3×#681D414yescomplemented
94C2×C3×#168C2312yes—
95Dic3⋊Dic5—24no—
96Dic3⋊Dic5—24no—
97#6663—24no—
98#6661—24no—
99#6659—24no—
100#6656—24no—
101C2×C3×#137—51no—
102#5832D511yescharacteristic
103C2×#951—51no—
104C2×#944—51no—
105C2×#942—51no—
106C2×#909—51no—
107#5190—52no—
108#5183—52no—
109#5175—52no—
110#5167—52no—
111Dic3×M16—51no—
112C2×C5×#41—31no—
113C2×C5×#41C2×D311yescharacteristic
114C22×Dic10—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×C4⋊Q8—31no—
117C5×#127—31no—
118C5×#124—31no—
119C5×#124—31no—
120C5×#121—62no—
121C4×C5×D4—62no—
122C2×C42×C5—31no—
123#4097—24no—
124#4097—64no—
125#4097—64no—
126#4097—64no—
127C2×#689—32no—
128C2×#689—32no—
129C2×#689—32no—
130C2×#689C2×D312yes—
131C2×#687—32no—
132C2×#687—32no—
133C2×#687—32no—
134C2×#687C2×D312yes—
135C2×C4⋊Dic5—62no—
136C2×#681—31no—
137C2×#681C2×D311yescharacteristic
138#4015—32no—
139#4015—32no—
140#4015—62no—
141#3935—32no—
142C4×#168—32no—
143#3152—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—21no—
147C3×C5×Q8—21no—
148C3×C5×Q8—21no—
149C3×C5×D4—21no—
150C3×C5×D4—21no—
151C3×C5×D4—42no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—42no—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2411yescharacteristic
158C2×Dic15—22no—
159C2×Dic15—42no—
160Dic30—22no—
161Dic30—22no—
162Dic30—42no—
163C5×#67—42no—
164C5×#67—44no—
165C2×C5×Dic3—24no—
166C2×C5×Dic3—21no—
167C2×C5×Dic3C2×D412yes—
168C2×C5×Dic3C2×D412yes—
169C5×D12—21no—
170C5×D12—21no—
171C4×C5×D3—42no—
172C5×Dic6—21no—
173C5×Dic6—21no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—42no—
176C3×Dic10—22no—
177C3×Dic10—22no—
178C3×Dic10—42no—
179C3⋊#168C2×D414yes—
180C3×#168C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×Q8—51no—
183C2×#235C2×D511yescharacteristic
184C22×Dic6—51no—
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16—51no—
189#951—104no—
190#947C2×D511yescharacteristic
191#944—52no—
192#944—52no—
193#944—102no—
194#944C2×D511yescharacteristic
195C2×#216—52no—
196C2×#216—52no—
197#942—104no—
198C2×#215—52no—
199#940C2×D511yescharacteristic
200#939—22no—
201#936C2×D511yescharacteristic
202C2×#214—52no—
203C4×#67—22no—
204C2×Dic3⋊C4—102no—
205C2×C4×Dic3C2×D511yescharacteristic
206C2×#208—51no—
207#909—104no—
208C2×Dic12—52no—
209C2×#204—52no—
210#815—52no—
211C8×Dic3—52no—
212C5×#41—22no—
213C5×#41—22no—
214C5×#41—62no—
215C5×#41—62no—
216C2×C5×Q8—31no—
217C2×C5×Q8C22×D311yescharacteristic
218C2×C5×D4—21no—
219C2×C5×D4—31no—
220C2×C5×D4—62no—
221C2×C5×D4—61no—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—32no—
225C22×C4×C5—61no—
226C22×C4×C5C22×D311yescharacteristic
227C22×Dic5—21no—
228C22×Dic5—61no—
229C2×Dic10—22no—
230C2×Dic10—22no—
231C2×Dic10—21no—
232C2×Dic10—32no—
233C2×Dic10—62no—
234C2×Dic10—62no—
235C2×Dic10—61no—
236C2×Dic10C22×D312yes—
237C5×C4⋊C4—62no—
238C5×C22⋊C4—62no—
239C5×C22⋊C4—62no—
240C42×C5—32no—
241C42×C5—31no—
242C42×C5—31no—
243#689—24no—
244#689—64no—
245#689—64no—
246#689—64no—
247#687—24no—
248#687—64no—
249#687—64no—
250#687—64no—
251C4⋊Dic5—64no—
252C4⋊Dic5—64no—
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—31no—
262C2×C4⋊Q8—151no—
263#497—152no—
264#497—152no—
265#494—152no—
266#492—152no—
267C4×M16—151no—
268C22×C3×C5—22no—
269C22×C3×C5—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×C5×D3—41no—
274C2×C5×D3—42no—
275C3×C4×C5—41no—
276C3×C4×C5#12712yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C22×D411yescharacteristic
279Dic15—42no—
280C3×Dic5—42no—
281C5×Dic3—22no—
282C5×Dic3—41no—
283C5×Dic3#13714yescomplemented
284C3×#41—22no—
285C3×#41—22no—
286C2×C3×Q8—52no—
287C2×C3×Q8—101no—
288C2×C3×Q8—102no—
289C2×C3×Q8—102no—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×D4—21no—
292C2×C3×D4C22×D511yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—101no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—21no—
297C2×#67—22no—
298C22×Dic3—101no—
299C22×Dic3C22⋊D512yes—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6—52no—
305C2×Dic6—102no—
306C2×Dic6—102no—
307C2×Dic6—101no—
308C2×Dic6C22×D511yescharacteristic
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16—54no—
312C2×C3×C8—52no—
313#217—22no—
314#216—104no—
315#216—104no—
316#215—104no—
317#214—104no—
318(C2×D3)⋊C4—22no—
319Dic3⋊C4—22no—
320Dic3⋊C4—104no—
321Dic3⋊C4—104no—
322C4×Dic3C22⋊D512yes—
323C4×Dic3C22×D511yescharacteristic
324C4×Dic3C22×D511yescharacteristic
325#208—54no—
326C2×C3⋊C8—52no—
327Dic12—104no—
328#204—104no—
329C23×C5—21no—
330C23×C5—61no—
331C23×C5D3×D411yescharacteristic
332C5×Q8—21no—
333C5×Q8—21no—
334C5×Q8—61no—
335C5×Q8—61no—
336C5×D4—21no—
337C5×D4—21no—
338C5×D4—42no—
339C5×D4—61no—
340C5×D4—61no—
341C5×D4—124no—
342C5×D4—122no—
343C2×C4×C5—21no—
344C2×C4×C5—32no—
345C2×C4×C5—32no—
346C2×C4×C5—42no—
347C2×C4×C5—64no—
348C2×C4×C5—61no—
349C2×C4×C5—122no—
350C2×C4×C5D3×D411yescharacteristic
351C2×C4×C5D3×D412yes—
352C2×C4×C5C2×#6712yes—
353C2×C4×C5C23×D311yescharacteristic
354C2×Dic5—22no—
355C2×Dic5—42no—
356C2×Dic5—62no—
357C2×Dic5—122no—
358Dic10—22no—
359Dic10—22no—
360Dic10—42no—
361Dic10—62no—
362Dic10—62no—
363Dic10—122no—
364#168—34no—
365#168C2×#6714yes—
366C2×#41—31no—
367C2×#41D3×D511yescharacteristic
368C22×Q8—51no—
369C22×Q8—151no—
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—31no—
385C4⋊Q8—152no—
386C4⋊Q8—152no—
387C4⋊Q8—302no—
388#127—31no—
389#124—31no—
390#124—31no—
391#121—62no—
392C4×D4—62no—
393C2×C4⋊C4—302no—
394C2×C42—31no—
395#97—152no—
396C4×C8—152no—
397C2×C3×C5—22no—
398C2×C3×C5—81no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5C2×#13712yes—
401C5×D3—81no—
402C23×C3—21no—
403C23×C3C2×C22⋊D511yescharacteristic
404C22×D3—21no—
405C3×Q8—21no—
406C3×Q8—21no—
407C3×Q8—102no—
408C3×Q8—102no—
409C3×Q8—202no—
410C3×D4—21no—
411C3×D4—21no—
412C3×D4—42no—
413C2×C3×C4—21no—
414C2×C3×C4—42no—
415C2×C3×C4—102no—
416C2×C3×C4—202no—
417C2×C3×C4D4×D512yes—
418C2×C3×C4D4×D512yes—
419C2×C3×C4C2×C22⋊D511yescharacteristic
420C2×C3×C4C23×D511yescharacteristic
421#67—42no—
422#67—44no—
423C2×Dic3—24no—
424C2×Dic3—21no—
425C2×Dic3—102no—
426C2×Dic3—202no—
427C2×Dic3C2×C22⋊D512yes—
428C2×Dic3C2×C22⋊D512yes—
429D12—21no—
430D12—21no—
431C4×D3—42no—
432Dic6—21no—
433Dic6—21no—
434Dic6—102no—
435Dic6—102no—
436Dic6—202no—
437C3×C8—54no—
438C3⋊C8—54no—
439C22×C5—22no—
440C22×C5—42no—
441C22×C5—41no—
442C22×C5—122no—
443C22×C5—121no—
444C22×C5#94012yes—
445C22×C5C2×D3×D411yescharacteristic
446C4×C5—34no—
447C4×C5—41no—
448C4×C5—62no—
449C4×C5—121no—
450C4×C5#94012yes—
451C4×C5C2×D3×D411yescharacteristic
452C4×C5C22×#6711yescharacteristic
453Dic5—42no—
454Dic5—122no—
455#41—22no—
456#41—22no—
457#41—62no—
458#41—62no—
459C2×Q8—31no—
460C2×Q8—52no—
461C2×Q8—101no—
462C2×Q8—102no—
463C2×Q8—102no—
464C2×Q8—152no—
465C2×Q8—301no—
466C2×Q8—302no—
467C2×Q8—302no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—31no—
471C2×D4—62no—
472C2×D4—61no—
473C2×D4C2×D3×D511yescharacteristic
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—62no—
493C4⋊C4—304no—
494C4⋊C4—304no—
495C22⋊C4—62no—
496C22⋊C4—62no—
497C42—32no—
498C42—31no—
499C42—31no—
500C3×C5#315211yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3#408612yes—
505C22×C3C22×C22⋊D511yescharacteristic
506C2×D3—41no—
507C2×D3—42no—
508C3×C4—41no—
509C3×C4—202no—
510C3×C4#408612yes—
511C3×C4C2×D4×D511yescharacteristic
512C3×C4C2×D4×D511yescharacteristic
513Dic3—22no—
514Dic3—41no—
515Dic3—202no—
516Dic3#409714yescomplemented
517C2×C5—22no—
518C2×C5—81no—
519C2×C5—241no—
520C2×C5D3×#13712yes—
521C2×C5C2×#94011yescharacteristic
522C23—21no—
523C23—61no—
524C23D3×C22⋊D511yescharacteristic
525Q8—21no—
526Q8—21no—
527Q8—61no—
528Q8—61no—
529Q8—102no—
530Q8—102no—
531Q8—202no—
532Q8—302no—
533Q8—302no—
534Q8—602no—
535D4—21no—
536D4—21no—
537D4—42no—
538D4—61no—
539D4—61no—
540D4—124no—
541D4—122no—
542C2×C4—21no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—42no—
546C2×C4—64no—
547C2×C4—61no—
548C2×C4—102no—
549C2×C4—122no—
550C2×C4—202no—
551C2×C4—302no—
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—81no—
561C2×C3C2×#408611yescharacteristic
562C2×C3C2×#409712yes—
563D3—81no—
564C5#8397211yescharacteristic, complemented, Sylow
565C22—22no—
566C22—42no—
567C22—41no—
568C22—122no—
569C22—121no—
570C22#9156712yes—
571C22C2×D3×C22⋊D511yescharacteristic
572C4—34no—
573C4—41no—
574C4—62no—
575C4—121no—
576C4—202no—
577C4—602no—
578C4#9156712yes—
579C4C2×D5×#6711yescharacteristic
580C4C2×#679011yescharacteristic
581C3#1061501911yescharacteristic, complemented, Sylow
582C2—22no—
583C2—81no—
584C2—241no—
585C2D3×#409712yes—
586C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC5×#5832C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3152
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×#91840C2semidirect
3. C2×C3×#4097C2semidirect
4. C2×#91389C2semidirect
5. C2×#91322C2semidirect
6. C2×#91309C2semidirect
7. #11749357C2semidirect
8. #11749354C2semidirect
9. #11749110C2semidirect
10. #11749108C2semidirect
11. Dic3×#681C2semidirect
49. C2×#4097D3semidirect
83. #6710D4semidirect
93. C3×#681D4semidirect
254. #681#67semidirect
283. C5×Dic3#137semidirect
500. C3×C5#3152semidirect
516. Dic3#4097semidirect
564. C5#83972semidirect
581. C3#10615019semidirect

Maximal subgroups

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

subgroupindex
C2×#918402
C5×#58322
C2×C3×#40972
C2×#913892
C2×#913222
C2×#913092
#117493572
#117493542
#117491102
#117491082
Dic3×#6812
#106150193
#839725