Finite Group Databasebeta

← #14439261

Subgroups — #14439261

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
2C2×C5×#951C211yesmaximal, characteristic, complemented
3C3×#66166C211yesmaximal, characteristic
4C2×#91376C211yesmaximal, characteristic, complemented
5C2×#91313C211yesmaximal, characteristic, complemented
6C2×#91307C211yesmaximal, characteristic, complemented
7#11749353C212yesmaximal, complemented
8#11749347C212yesmaximal, complemented
9#11749107C212yesmaximal, complemented
10#11749106C212yesmaximal, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12#10615703—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17#91840—24no—
18C2×#6718C2212yes—
19C2×#6716C2212yes—
20C2×#6710C2211yescharacteristic
21C5×#951—24no—
22C2×C5×#216C2212yes—
23C2×C5×#214C2212yes—
24C2×C5×#208C2211yescharacteristic
25C3×#4093C2211yescharacteristic
26C3×#4090C2211yescharacteristic
27C3×#4086C2211yescharacteristic
28C3×#4085—22no—
29C3×#4082C2211yescharacteristic
30C3×C4×C22⋊D5—22no—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×#6668—22no—
33#91376—22no—
34#91376C2212yes—
35#91376C2212yes—
36C2×#6662C2212yes—
37C2×#6661C2212yes—
38#91313—24no—
39C2×#6657C2212yes—
40#91307—24no—
41C2×#6655C2212yes—
42#90952C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83288—51nomaximal, Hall
45C2×C5×#137—31no—
46#66166D311yescharacteristic
47C2×#4097—31no—
48C2×#4090—31no—
49C2×#4088—31no—
50C2×#4055—31no—
51#65479—32no—
52#65470—32no—
53#65464—32no—
54#65456—32no—
55M16×Dic5—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—
68C22×C5×Dic3—21no—
69C2×C5×Dic6—22no—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—21no—
72C2×C5×Dic6C2312yes—
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—22no—
75C22×C3×Dic5D412yes—
76C3×#709—22no—
77C3×#709—22no—
78C2×C3×D20C2311yescharacteristic
79C2×C3×C4×D5—21no—
80C2×C3×Dic10C2311yescharacteristic
81#6718—24no—
82#6716—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#216—24no—
86C5×#214—24no—
87C5×#208D414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×C22⋊Dic5—22no—
90C3×#685—22no—
91C3×#683—22no—
92C3×C4×Dic5D412yes—
93C3×C4×Dic5C2311yescharacteristic
94C3×C4×Dic5C2311yescharacteristic
95#6668—24no—
96#6668—24no—
97#6662—24no—
98#6661—24no—
99#6657—24no—
100#6655—24no—
101C3×#532—51no—
102C2×#951—51no—
103C2×#951—51no—
104C2×#951—51no—
105C2×#951D511yescharacteristic, complemented
106C2×#869—51no—
107#5092—52no—
108#5076—52no—
109#5060—52no—
110#5060—52no—
111C4×#208—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709C2×D311yescharacteristic
115C22×Dic10—31no—
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4097—64no—
121#4093C2×D311yescharacteristic
122#4090—32no—
123#4090—32no—
124#4090—62no—
125#4090C2×D311yescharacteristic
126C2×#689—32no—
127C2×#689—32no—
128#4088—64no—
129C2×#688—32no—
130#4086C2×D311yescharacteristic
131#4085—22no—
132#4082C2×D311yescharacteristic
133C2×#687—32no—
134C4×C22⋊D5—22no—
135C2×#683—62no—
136C2×C4×Dic5C2×D311yescharacteristic
137C2×#681—31no—
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3152—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×C3×D5—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—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—42no—
165C5×Dic6—22no—
166C5×Dic6—22no—
167C5×Dic6—42no—
168C3×C22⋊D5—42no—
169C3×C22⋊D5—44no—
170C2×C3×Dic5—24no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5C2×D412yes—
173C2×C3×Dic5C2×D412yes—
174C3×D20—21no—
175C3×D20—21no—
176C3×C4×D5—42no—
177C3×Dic10—21no—
178C3×Dic10—21no—
179C3⋊#168C2×D414yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41—51no—
182C2×C3×#41C2×D511yescharacteristic
183C22×Dic6—51no—
184C22×Dic6C2×D511yescharacteristic
185C3×C4⋊Q8—51no—
186C3×#127—51no—
187C3×#124—51no—
188C3×#124—51no—
189C3×#121—102no—
190C3×C4×D4—102no—
191C2×C3×C42—51no—
192#951—24no—
193#951—104no—
194#951—104no—
195#951—104no—
196C2×#216—52no—
197C2×#216—52no—
198C2×#216—52no—
199C2×#216C2×D512yes—
200C2×#214—52no—
201C2×#214—52no—
202C2×#214—52no—
203C2×#214C2×D512yes—
204C2×C4⋊Dic3—102no—
205C2×#208—51no—
206C2×#208C2×D511yescharacteristic
207#869—52no—
208#869—52no—
209#869—102no—
210#803—52no—
211C4×C3⋊C8—52no—
212C5×#41—22no—
213C5×#41—22no—
214C2×C5×Q8—32no—
215C2×C5×Q8—61no—
216C2×C5×Q8—62no—
217C2×C5×Q8—62no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4C22×D311yescharacteristic
221C22×C4×C5—21no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—21no—
225C2×C22⋊D5—22no—
226C22×Dic5—61no—
227C22×Dic5#6712yes—
228#709—22no—
229#709—22no—
230C2×D20C22×D311yescharacteristic
231C2×C4×D5—21no—
232C2×Dic10—32no—
233C2×Dic10—62no—
234C2×Dic10—62no—
235C2×Dic10—61no—
236C2×Dic10C22×D311yescharacteristic
237C5×Q16—64no—
238C5×SD16—64no—
239C5×M16—34no—
240C2×C5×C8—32no—
241C22⋊Dic5—22no—
242#689—64no—
243#689—64no—
244#688—64no—
245#687—64no—
246#685—22no—
247#683—22no—
248#683—64no—
249#683—64no—
250C4×Dic5#6712yes—
251C4×Dic5C22×D311yescharacteristic
252C4×Dic5C22×D311yescharacteristic
253#681—34no—
254C2×#168—32no—
255Dic20—64no—
256#677—64no—
257C2×#137—31no—
258C2×#137—151no—
259C2×#137—151no—
260C2×#137—151no—
261#532—51no—
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×C3×D5—41no—
274C2×C3×D5—42no—
275C3×C4×C5—41no—
276C3×C4×C5#12712yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C22×D411yescharacteristic
279Dic15—42no—
280C3×Dic5—22no—
281C3×Dic5—41no—
282C3×Dic5#13714yescomplemented
283C5×Dic3—42no—
284C3×#41—22no—
285C3×#41—22no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—51no—
289C2×C3×Q8C22×D511yescharacteristic
290C2×C3×D4—21no—
291C2×C3×D4—51no—
292C2×C3×D4—102no—
293C2×C3×D4—101no—
294C2×C3×D4C22×D511yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—52no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C22×Dic3—21no—
300C22×Dic3—101no—
301C2×Dic6—22no—
302C2×Dic6—22no—
303C2×Dic6—21no—
304C2×Dic6—52no—
305C2×Dic6—102no—
306C2×Dic6—102no—
307C2×Dic6—101no—
308C2×Dic6C22×D512yes—
309C3×C4⋊C4—102no—
310C3×C22⋊C4—102no—
311C3×C22⋊C4—102no—
312C3×C42—52no—
313C3×C42—51no—
314C3×C42—51no—
315#216—24no—
316#216—104no—
317#216—104no—
318#216—104no—
319#214—24no—
320#214—104no—
321#214—104no—
322#214—104no—
323C4⋊Dic3—104no—
324C4⋊Dic3—104no—
325#208—54no—
326#208C22⋊D514yescomplemented
327C2×C3⋊C8—52no—
328C2×C3⋊C8C22×D512yes—
329C23×C5—21no—
330C23×C5C2×#6711yescharacteristic
331C22×D5—21no—
332C5×Q8—21no—
333C5×Q8—21no—
334C5×Q8—62no—
335C5×Q8—62no—
336C5×Q8—122no—
337C5×D4—21no—
338C5×D4—21no—
339C5×D4—42no—
340C2×C4×C5—21no—
341C2×C4×C5—42no—
342C2×C4×C5—62no—
343C2×C4×C5—122no—
344C2×C4×C5D3×D412yes—
345C2×C4×C5D3×D412yes—
346C2×C4×C5C2×#6711yescharacteristic
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—42no—
349C22⋊D5—44no—
350C2×Dic5—24no—
351C2×Dic5—21no—
352C2×Dic5—62no—
353C2×Dic5—122no—
354C2×Dic5C2×#6712yes—
355C2×Dic5C2×#6712yes—
356D20—21no—
357D20—21no—
358C4×D5—42no—
359Dic10—21no—
360Dic10—21no—
361Dic10—62no—
362Dic10—62no—
363Dic10—122no—
364C5×C8—34no—
365#168—34no—
366C2×#41—51no—
367C2×#41D3×D511yescharacteristic
368C22×Q8—31no—
369C22×Q8—151no—
370#137—64no—
371#137—304no—
372#137—304no—
373#137—304no—
374C2×Q16—32no—
375C2×Q16—152no—
376C2×Q16—152no—
377C2×Q16—152no—
378C2×SD16—32no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×M16—31no—
383C2×M16—151no—
384C4⋊Q8—51no—
385C4⋊Q8—152no—
386C4⋊Q8—152no—
387C4⋊Q8—302no—
388#127—51no—
389#124—51no—
390#124—51no—
391#121—102no—
392C4×D4—102no—
393C2×C4⋊C4—302no—
394C2×C42—51no—
395#97—152no—
396C4×C8—152no—
397C2×C3×C5—22no—
398C2×C3×C5—81no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5C2×#13712yes—
401C3×D5—81no—
402C23×C3—21no—
403C23×C3—101no—
404C23×C3D4×D511yescharacteristic
405C3×Q8—21no—
406C3×Q8—21no—
407C3×Q8—101no—
408C3×Q8—101no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—42no—
412C3×D4—101no—
413C3×D4—101no—
414C3×D4—204no—
415C3×D4—202no—
416C2×C3×C4—21no—
417C2×C3×C4—42no—
418C2×C3×C4—52no—
419C2×C3×C4—52no—
420C2×C3×C4—104no—
421C2×C3×C4—101no—
422C2×C3×C4—202no—
423C2×C3×C4D4×D511yescharacteristic
424C2×C3×C4D4×D512yes—
425C2×C3×C4C2×C22⋊D512yes—
426C2×C3×C4C23×D511yescharacteristic
427C2×Dic3—22no—
428C2×Dic3—42no—
429C2×Dic3—102no—
430C2×Dic3—202no—
431Dic6—22no—
432Dic6—22no—
433Dic6—42no—
434Dic6—102no—
435Dic6—102no—
436Dic6—202no—
437C3⋊C8—54no—
438C3⋊C8C2×C22⋊D514yes—
439C22×C5—22no—
440C22×C5—41no—
441C22×C5—42no—
442C22×C5#94012yes—
443C22×C5C22×#6711yescharacteristic
444C2×D5—41no—
445C2×D5—42no—
446C4×C5—41no—
447C4×C5—122no—
448C4×C5#94012yes—
449C4×C5C2×D3×D411yescharacteristic
450C4×C5C2×D3×D411yescharacteristic
451Dic5—22no—
452Dic5—41no—
453Dic5—122no—
454Dic5#95114yescomplemented
455#41—22no—
456#41—22no—
457#41—102no—
458#41—102no—
459C2×Q8—32no—
460C2×Q8—51no—
461C2×Q8—61no—
462C2×Q8—62no—
463C2×Q8—62no—
464C2×Q8—152no—
465C2×Q8—301no—
466C2×Q8—302no—
467C2×Q8—302no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—51no—
471C2×D4—102no—
472C2×D4—101no—
473C2×D4C2×D3×D511yescharacteristic
474C22×C4—21no—
475C22×C4—52no—
476C22×C4—61no—
477C22×C4—101no—
478C22×C4—301no—
479C22×C4C2×D3×D511yescharacteristic
480Q16—64no—
481Q16—304no—
482Q16—304no—
483Q16—304no—
484SD16—64no—
485SD16—304no—
486SD16—304no—
487SD16—304no—
488M16—34no—
489M16—154no—
490C2×C8—32no—
491C2×C8—152no—
492C4⋊C4—102no—
493C4⋊C4—304no—
494C4⋊C4—304no—
495C22⋊C4—102no—
496C22⋊C4—102no—
497C42—52no—
498C42—51no—
499C42—51no—
500C3×C5#315211yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—42no—
503C22×C3—41no—
504C22×C3—202no—
505C22×C3—201no—
506C22×C3#408612yes—
507C22×C3C2×D4×D511yescharacteristic
508C3×C4—41no—
509C3×C4—54no—
510C3×C4—102no—
511C3×C4—201no—
512C3×C4#408612yes—
513C3×C4C2×D4×D511yescharacteristic
514C3×C4C22×C22⋊D511yescharacteristic
515Dic3—42no—
516Dic3—202no—
517C2×C5—22no—
518C2×C5—81no—
519C2×C5C2×#94011yescharacteristic
520C2×C5C2×#95112yes—
521D5—81no—
522C23—21no—
523C23—101no—
524C23D5×#6711yescharacteristic
525Q8—21no—
526Q8—21no—
527Q8—62no—
528Q8—62no—
529Q8—101no—
530Q8—101no—
531Q8—122no—
532Q8—302no—
533Q8—302no—
534Q8—602no—
535D4—21no—
536D4—21no—
537D4—42no—
538D4—101no—
539D4—101no—
540D4—204no—
541D4—202no—
542C2×C4—21no—
543C2×C4—42no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—62no—
547C2×C4—104no—
548C2×C4—101no—
549C2×C4—122no—
550C2×C4—202no—
551C2×C4—302no—
552C2×C4—602no—
553C2×C4D5×#6711yescharacteristic
554C2×C4D3×C22⋊D512yes—
555C2×C4#679012yes—
556C2×C4C22×D3×D511yescharacteristic
557C8—34no—
558C8—154no—
559C2×C3—22no—
560C2×C3—81no—
561C2×C3—401no—
562C2×C3D5×#13712yes—
563C2×C3C2×#408611yescharacteristic
564C5#8328811yescharacteristic, complemented, Sylow
565C22—22no—
566C22—42no—
567C22—41no—
568C22—202no—
569C22—201no—
570C22#9156712yes—
571C22C2×D5×#6711yescharacteristic
572C4—41no—
573C4—54no—
574C4—102no—
575C4—122no—
576C4—201no—
577C4—602no—
578C4#9156712yes—
579C4C2×D3×C22⋊D511yescharacteristic
580C4C2×#679011yescharacteristic
581C3#1061570311yescharacteristic, complemented, Sylow
582C2—22no—
583C2—81no—
584C2—401no—
585C2D5×#95112yes—
586C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC3×#66166C2
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
2. C2×C5×#951C2semidirect
4. C2×#91376C2semidirect
5. C2×#91313C2semidirect
6. C2×#91307C2semidirect
7. #11749353C2semidirect
8. #11749347C2semidirect
9. #11749107C2semidirect
10. #11749106C2semidirect
11. Dic5×#208C2semidirect
83. #6710D4semidirect
87. C5×#208D4semidirect
105. C2×#951D5semidirect
282. C3×Dic5#137semidirect
326. #208C22⋊D5semidirect
454. Dic5#951semidirect
500. C3×C5#3152semidirect
564. C5#83288semidirect
581. C3#10615703semidirect

Maximal subgroups

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

subgroupindex
C2×#918402
C2×C5×#9512
C3×#661662
C2×#913762
C2×#913132
C2×#913072
#117493532
#117493472
#117491072
#117491062
Dic5×#2082
#106157033
#832885