Finite Group Databasebeta

← #14427838

Subgroups — #14427838

Order 1920.

1040 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
1#11756587C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic, complemented
3#11754592C211yesmaximal, characteristic, complemented
4C22×#6648C211yesmaximal, characteristic, complemented
5C3×#65522C211yesmaximal, characteristic, complemented
6#11749367C212yesmaximal, complemented
7#11749284C212yesmaximal, complemented
8#11749121C212yesmaximal, complemented
9#11749038C212yesmaximal, complemented
10#11748451C211yesmaximal, characteristic, complemented
11#11748388C211yesmaximal, characteristic, complemented
12#10615645—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16#91835C2212yes—
17#91827C2212yes—
18#91826—21no—
19#91824—21no—
20C4×#1220—22no—
21#91815C2211yescharacteristic
22C5×#950—24no—
23C2×C5×#216C2211yescharacteristic, complemented
24C2×C5×#215C2211yescharacteristic, complemented
25C2×C5×#214C2211yescharacteristic, complemented
26C2×C5×#213C2211yescharacteristic, complemented
27C22×C5×C3⋊C8C2211yescharacteristic
28C3×#4072C2211yescharacteristic
29C22×C3×#168C2211yescharacteristic
30#91573—21no—
31#91543—21no—
32#91466C2212yes—
33C4×#1203—22no—
34#91383C2212yes—
35C2×#6648—24no—
36C2×#6648C2212yes—
37C2×#6648C2212yes—
38C3×#3967C2212yescomplemented
39C3×#3964C2212yescomplemented
40#90990C2212yescomplemented
41#90987C2212yescomplemented
42#90973C2212yescomplemented
43#90967C2212yescomplemented
44#78838—51nomaximal, Hall
45C2×C5×#135—31no—
46#66162—31no—
47#66162—31no—
48C22×C8×D5—31no—
49#65522—31no—
50#65522D311yescharacteristic, complemented
51#65477—32no—
52#65460—32no—
53#65460—32no—
54#65446—32no—
55#65395—31no—
56C23×D15D411yescharacteristic
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—22no—
65C22×Dic15D411yescharacteristic
66C2×C4×D15—22no—
67C2×C4×D15—22no—
68C2×C4×D15D412yes—
69C2×C4×D15C2312yes—
70C2×C5×#67—21no—
71C5×#235—22no—
72C5×#235—22no—
73C2×C5×D12C2311yescharacteristic
74C2×C4×C5×D3—21no—
75C2×C5×Dic6C2311yescharacteristic
76C2×#1203—22no—
77#6719—21no—
78#6719—22no—
79#6714—22no—
80C4⋊Dic15C2312yes—
81#6712—22no—
82C4×Dic15—21no—
83C5×#216—22no—
84C5×#215—22no—
85C5×#214—22no—
86C5×#213—22no—
87C2×C5×C3⋊C8D414yescomplemented
88C2×C5×C3⋊C8C2311yescharacteristic
89C2×C5×C3⋊C8C2311yescharacteristic
90C3×C22⋊Dic5—21no—
91C3×C4⋊Dic5C2312yes—
92C3×C4×Dic5—21no—
93C2×C3×#168—22no—
94C2×C3×#168C2312yes—
95#6668—22no—
96#6667—22no—
97(C2×D3)⋊Dic5—22no—
98#6648—24no—
99#6648—24no—
100#5828—51no—
101C2×#950D511yescharacteristic, complemented
102C22×D3×C8—51no—
103#5524—51no—
104C3×#416—51no—
105#5113—51no—
106#4998—51no—
107#4813—52no—
108#4807—52no—
109#4778—52no—
110#4775—52no—
111C2×C5×#41—31no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C4×D5—31no—
114C5×#135—64no—
115C2×C5×Q16—31no—
116C2×C5×SD16—31no—
117C2×C5×SD16—31no—
118C2×C5×D8—31no—
119C22×C5×C8—31no—
120#4092—32no—
121#4092—32no—
122#4084—32no—
123#4084—32no—
124#4083—61no—
125#4083—61no—
126#4081—61no—
127#4081—61no—
128C4×C22⋊D5—62no—
129C4×C22⋊D5—62no—
130#4072—31no—
131#4072C2×D311yescharacteristic
132C22×#168C2×D311yescharacteristic
133C2×C8×D5—32no—
134C2×C8×D5—32no—
135C2×C8×D5—64no—
136#3967—32no—
137#3967C2×D312yescomplemented
138#3964—32no—
139#3964C2×D312yescomplemented
140#3950—32no—
141#3949—32no—
142#3050—151noSylow
143C23×C3×C5—21no—
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—22no—
146C22×D15—24no—
147C22×D15C2×D412yes—
148C22×C5×D3—21no—
149C3×C5×Q8—21no—
150C3×C5×Q8—21no—
151C3×C5×D4—21no—
152C3×C5×D4—21no—
153C3×C5×D4—42no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—42no—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5#4112yes—
159C2×C3×C4×C5C2411yescharacteristic
160#1220—44no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15C2×D412yes—
164C4×D15—24no—
165C4×D15—22no—
166C4×D15—22no—
167C5×#67—42no—
168C2×C5×Dic3—21no—
169C5×D12—21no—
170C5×D12—21no—
171C4×C5×D3—42no—
172C5×Dic6—21no—
173C5×Dic6—21no—
174C2×C3×Dic5—22no—
175#1203—44no—
176C3×#168—22no—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41C2×D511yescharacteristic
180C2×#235C2×D511yescharacteristic
181C22×C4×D3—51no—
182C22×C3×C8—51no—
183C3×#117—51no—
184#950—24no—
185#946—52no—
186C2×#216C2×D511yescharacteristic, complemented
187C2×#215C2×D511yescharacteristic, complemented
188#938—52no—
189#937—101no—
190#935—101no—
191C2×#214C2×D511yescharacteristic, complemented
192C2×#213C2×D511yescharacteristic, complemented
193C4×#67—102no—
194#926—51no—
195C22×C3⋊C8C2×D511yescharacteristic
196C2×D3×C8—52no—
197C2×D3×C8—52no—
198C2×D3×C8—104no—
199#897—52no—
200#895—52no—
201#886—101no—
202#882—101no—
203C4×D12—102no—
204C3×#103—52no—
205C3×#102—52no—
206#821—52no—
207#816—52no—
208#808—52no—
209#807—52no—
210C23×D5—31no—
211C5×#41—22no—
212C5×#41—22no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—31no—
216C2×C5×Q8C22×D311yescharacteristic
217C2×C5×D4—21no—
218C2×C5×D4—31no—
219C2×C5×D4—61no—
220C2×C5×D4C22×D311yescharacteristic
221C22×C4×C5—21no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—62no—
225C2×C22⋊D5—62no—
226C22×Dic5—31no—
227C2×C4×D5—32no—
228C2×C4×D5—32no—
229C2×C4×D5—62no—
230C2×C4×D5—62no—
231C5×Q16—62no—
232C5×SD16—62no—
233C5×SD16—62no—
234C5×D8—62no—
235C2×C5×C8—34no—
236C2×C5×C8—31no—
237C2×C5×C8—31no—
238C22⋊Dic5—21no—
239C22⋊Dic5—62no—
240C22⋊Dic5—62no—
241C22⋊Dic5—61no—
242#685—62no—
243#685—62no—
244C4⋊Dic5—32no—
245C4⋊Dic5C22×D312yes—
246#683—62no—
247#683—62no—
248C4×Dic5—21no—
249C4×Dic5—61no—
250C2×#168—22no—
251C2×#168C22×D312yes—
252C8×D5—64no—
253C8×D5—64no—
254C2×#135—31no—
255C23×C8—151no—
256#525—151no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—51no—
264#416—151no—
265C22×C3×C5—22no—
266C22×C3×C5—41no—
267C22×C3×C5—42no—
268C22×C3×C5#12112yes—
269C22×C3×C5C22×D411yescharacteristic
270C2×D15—28no—
271C2×D15—22no—
272C2×D15—22no—
273C2×D15#13514yescomplemented
274C2×C5×D3—41no—
275C2×C5×D3—42no—
276C3×C4×C5—41no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—22no—
281Dic15—42no—
282C3×Dic5—42no—
283C5×Dic3—41no—
284C23×D3—51no—
285C3×#41—22no—
286C3×#41—22no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4C22×D511yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—21no—
293C2×#67—102no—
294C22×Dic3—51no—
295#235—22no—
296#235—22no—
297C2×D12—102no—
298C2×D12C22×D511yescharacteristic
299C2×C4×D3—21no—
300C2×C4×D3—52no—
301C2×C4×D3—52no—
302C2×C4×D3—102no—
303C2×C4×D3—102no—
304C2×Dic6C22×D511yescharacteristic
305C2×C3×C8—52no—
306C2×C3×C8—102no—
307C3×C4⋊C4—52no—
308C3×C22⋊C4—101no—
309C3×C42—101no—
310#217—102no—
311#217—101no—
312#216—22no—
313#215—22no—
314#214—22no—
315#213—22no—
316(C2×D3)⋊C4—102no—
317(C2×D3)⋊C4—102no—
318(C2×D3)⋊C4—102no—
319C4⋊Dic3—52no—
320C4⋊Dic3—102no—
321Dic3⋊C4—102no—
322C4×Dic3—101no—
323C2×C3⋊C8C22⋊D514yescomplemented
324C2×C3⋊C8C22×D511yescharacteristic
325C2×C3⋊C8C22×D511yescharacteristic
326D3×C8—104no—
327D3×C8—104no—
328C23×C5—21no—
329C23×C5—61no—
330C23×C5D3×D411yescharacteristic
331C22×D5—32no—
332C22×D5—64no—
333C22×D5—62no—
334C5×Q8—21no—
335C5×Q8—21no—
336C5×Q8—61no—
337C5×Q8—61no—
338C5×D4—21no—
339C5×D4—21no—
340C5×D4—42no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—21no—
345C2×C4×C5—42no—
346C2×C4×C5—61no—
347C2×C4×C5—122no—
348C2×C4×C5#23512yes—
349C2×C4×C5D3×D412yes—
350C2×C4×C5D3×D411yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—124no—
353C22⋊D5—124no—
354C2×Dic5—22no—
355C2×Dic5—32no—
356C2×Dic5—62no—
357C2×Dic5—62no—
358C4×D5—64no—
359C4×D5—62no—
360C4×D5—62no—
361C5×C8—32no—
362C5×C8—32no—
363#168—22no—
364C2×#41—31no—
365C2×#41D3×D511yescharacteristic
366C23×C4—151no—
367#135—64no—
368C2×Q16—31no—
369C2×SD16—31no—
370C2×SD16—31no—
371C2×D8—31no—
372C22×C8—31no—
373C22×C8—51no—
374C22×C8—152no—
375C22×C8—152no—
376C22×C8—304no—
377#123—301no—
378#123—301no—
379C22⋊Q8—152no—
380C22⋊Q8—152no—
381#121—152no—
382#121—152no—
383#120—301no—
384#120—301no—
385C4×D4—302no—
386C4×D4—302no—
387#117—51no—
388#117—151no—
389#107—152no—
390#106—152no—
391#103—52no—
392#103—152no—
393#102—52no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5—81no—
397C2×C3×C5C2×#12111yescharacteristic
398C2×C3×C5C2×#13512yes—
399D15—24no—
400C5×D3—81no—
401C23×C3—21no—
402C23×C3D4×D511yescharacteristic
403C22×D3—21no—
404C22×D3—52no—
405C22×D3—104no—
406C22×D3—102no—
407C3×Q8—21no—
408C3×Q8—21no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—42no—
412C2×C3×C4—21no—
413C2×C3×C4—42no—
414C2×C3×C4—102no—
415C2×C3×C4D4×D511yescharacteristic
416C2×C3×C4#71112yes—
417C2×C3×C4C2×C22⋊D512yes—
418C2×C3×C4C23×D511yescharacteristic
419#67—42no—
420#67—204no—
421C2×Dic3—21no—
422C2×Dic3—52no—
423C2×Dic3—102no—
424C2×Dic3—102no—
425D12—21no—
426D12—21no—
427D12—204no—
428C4×D3—42no—
429C4×D3—102no—
430C4×D3—102no—
431C4×D3—104no—
432Dic6—21no—
433Dic6—21no—
434C3×C8—102no—
435C3⋊C8C2×C22⋊D512yes—
436C3⋊C8C2×C22⋊D512yes—
437C22×C5—22no—
438C22×C5—41no—
439C22×C5—42no—
440C22×C5—121no—
441C22×C5—122no—
442C22×C5#88412yes—
443C22×C5C2×D3×D411yescharacteristic
444C2×D5—34no—
445C2×D5—68no—
446C2×D5—62no—
447C2×D5—62no—
448C4×C5—41no—
449C4×C5—121no—
450C4×C5#88412yes—
451C4×C5C2×#23511yescharacteristic
452C4×C5C2×D3×D411yescharacteristic
453Dic5—42no—
454Dic5—62no—
455Dic5—122no—
456C24—151no—
457#41—22no—
458#41—22no—
459#41—62no—
460#41—62no—
461C2×Q8—31no—
462C2×Q8C2×D3×D511yescharacteristic
463C2×D4—21no—
464C2×D4—31no—
465C2×D4—61no—
466C2×D4—302no—
467C2×D4—302no—
468C2×D4C2×D3×D511yescharacteristic
469C22×C4—21no—
470C22×C4—61no—
471C22×C4—151no—
472C22×C4—152no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—62no—
478SD16—62no—
479SD16—62no—
480D8—62no—
481C2×C8—34no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—52no—
485C2×C8—102no—
486C2×C8—304no—
487C2×C8—304no—
488C4⋊C4—52no—
489C4⋊C4—152no—
490C4⋊C4—302no—
491C4⋊C4—302no—
492C22⋊C4—101no—
493C22⋊C4—302no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—101no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—42no—
503C22×C3—41no—
504C22×C3#408412yes—
505C22×C3C2×D4×D511yescharacteristic
506C2×D3—42no—
507C2×D3—41no—
508C2×D3—54no—
509C2×D3—108no—
510C2×D3—102no—
511C2×D3—102no—
512C3×C4—41no—
513C3×C4—202no—
514C3×C4#408412yes—
515C3×C4C2×#71111yescharacteristic
516C3×C4C22×C22⋊D511yescharacteristic
517Dic3—41no—
518Dic3—102no—
519Dic3—202no—
520C2×C5—22no—
521C2×C5—81no—
522C2×C5—241no—
523C2×C5C2×#88411yescharacteristic
524C2×C5D3×#13512yes—
525D5—64no—
526C23—21no—
527C23—61no—
528C23—152no—
529C23—304no—
530C23—302no—
531C23#679011yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—61no—
535Q8—61no—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—61no—
540D4—61no—
541D4—122no—
542D4—604no—
543D4—604no—
544C2×C4—21no—
545C2×C4—42no—
546C2×C4—61no—
547C2×C4—102no—
548C2×C4—122no—
549C2×C4—152no—
550C2×C4—302no—
551C2×C4—302no—
552C2×C4—302no—
553C2×C4—304no—
554C2×C4—302no—
555C2×C4#678212yes—
556C2×C4D3×C22⋊D512yes—
557C2×C4#679011yescharacteristic
558C2×C4C22×D3×D511yescharacteristic
559C8—32no—
560C8—32no—
561C8—102no—
562C2×C3—22no—
563C2×C3—81no—
564C2×C3D5×#13512yes—
565C2×C3C2×#408411yescharacteristic
566D3—81no—
567D3—104no—
568C5#7883811yescharacteristic, complemented, Sylow
569C22—22no—
570C22—42no—
571C22—41no—
572C22—122no—
573C22—121no—
574C22—154no—
575C22—308no—
576C22—302no—
577C22—302no—
578C22#9155712yes—
579C22C2×#679011yescharacteristic
580C4—41no—
581C4—121no—
582C4—202no—
583C4—302no—
584C4—602no—
585C4#9155712yes—
586C4C2×#678211yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061564511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—241no—
592C2—304no—
593C2#1175532812yes—
594C2C2×#9155711yescharacteristic
subgroupG/H
centerC2×C4#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11756587C2semidirect
2. C2×C5×#950C2semidirect
3. #11754592C2semidirect
4. C22×#6648C2semidirect
5. C3×#65522C2semidirect
6. #11749367C2semidirect
7. #11749284C2semidirect
8. #11749121C2semidirect
9. #11749038C2semidirect
10. #11748451C2semidirect
11. #11748388C2semidirect
23. C2×C5×#216C22semidirect
24. C2×C5×#215C22semidirect
25. C2×C5×#214C22semidirect
26. C2×C5×#213C22semidirect
38. C3×#3967C22semidirect
39. C3×#3964C22semidirect
40. #90990C22semidirect
41. #90987C22semidirect
42. #90973C22semidirect
43. #90967C22semidirect
50. #65522D3semidirect
87. C2×C5×C3⋊C8D4semidirect
101. C2×#950D5semidirect
137. #3967C2×D3semidirect
139. #3964C2×D3semidirect
186. C2×#216C2×D5semidirect
187. C2×#215C2×D5semidirect
191. C2×#214C2×D5semidirect
192. C2×#213C2×D5semidirect
273. C2×D15#135semidirect
323. C2×C3⋊C8C22⋊D5semidirect
500. C3×C5#3050semidirect
568. C5#78838semidirect
588. C3#10615645semidirect

Maximal subgroups

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

subgroupindex
#117565872
C2×C5×#9502
#117545922
C22×#66482
C3×#655222
#117493672
#117492842
#117491212
#117490382
#117484512
#117483882
#106156453
#788385