Finite Group Databasebeta

← #14458304

Subgroups — #14458304

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756476C211yesmaximal, characteristic, complemented
2#11756310C211yesmaximal, characteristic, complemented
3C3×C5×#459C211yesmaximal, characteristic, complemented
4#11751258C212yesmaximal, complemented
5#11751257C212yesmaximal, complemented
6#11751171C211yesmaximal, characteristic, complemented
7C4×#6715C211yesmaximal, characteristic, complemented
8#11750947C211yesmaximal, characteristic, complemented
9#11750935C211yesmaximal, characteristic, complemented
10#11750875C212yesmaximal, complemented
11D15×#102C212yesmaximal, complemented
12#10612083—31nomaximal, Hall
13C2×D4×D15—21no—
14C2×D4×D15C2212yes—
15C2×#6817—21no—
16C2×C3×C5×D8C2212yescomplemented
17C3×C5×#127C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic, complemented
19#91827—21no—
20#91827C2212yes—
21#91827C2212yescomplemented
22#91826—22no—
23C2×#6715C2211yescharacteristic
24#91813—21no—
25C2×C8×D15C2212yescomplemented
26C4⋊C4×D15C2212yescomplemented
27#91772—22no—
28C4×D60C2211yescharacteristic
29C4×D60C2211yescharacteristic
30#91758C2211yescharacteristic, complemented
31C3×C5×C4⋊C8C2211yescharacteristic, complemented
32C3×C5×#102C2212yescomplemented
33#91116C2212yescomplemented
34#91116C2212yescomplemented
35#91116C2211yescharacteristic, complemented
36#91105C2212yes—
37#91104C2212yescomplemented
38#91102C2212yescomplemented
39#91093C2211yescharacteristic
40#91091C2211yescharacteristic, complemented
41C4×C3⋊#168C2211yescharacteristic, complemented
42#80352—51nomaximal, Hall
43#66051—31no—
44#65885—31no—
45C5×#459D311yescharacteristic, complemented
46#65446—32no—
47#65445—32no—
48#65359—31no—
49C4×#686—31no—
50#65135—31no—
51#65123—31no—
52#65063—32no—
53D5×#102—32no—
54C23×D15—22no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2311yescharacteristic
58C2×C3×C5×D4C2312yes—
59C22×C3×C4×C5—21no—
60C2×#1220—22no—
61C2×#1220—22no—
62C2×#1220—22no—
63D4×D15—24no—
64D4×D15—42no—
65D4×D15—44no—
66#6817—44no—
67C2×D60D411yescharacteristic
68C2×D60C2311yescharacteristic
69C2×C4×D15—22no—
70C2×C4×D15—21no—
71C2×C4×D15C2312yes—
72C2×Dic30—21no—
73C3×C5×D8—42no—
74C2×C3×C5×C8C2312yes—
75C3×C5×C4⋊C4C2311yescharacteristic
76C3×C5×C22⋊C4—21no—
77C3×C42×C5C2311yescharacteristic
78#6719—22no—
79#6719—22no—
80#6715—22no—
81#6714—21no—
82#6714D412yes—
83C4⋊Dic15—21no—
84C4⋊Dic15D411yescharacteristic
85C4⋊Dic15C2312yes—
86C4⋊Dic15C2311yescharacteristic
87#6712—22no—
88C2×C3⋊#168C2311yescharacteristic
89C2×C3⋊#168C2311yescharacteristic
90C8×D15—42no—
91#5717—51no—
92#5551—51no—
93C3×#459D511yescharacteristic, complemented
94#5157—52no—
95#5156—52no—
96#5070—51no—
97C4×#213—51no—
98#4846—51no—
99#4834—51no—
100#4774—52no—
101D3×#102—52no—
102C2×D4×D5—32no—
103C2×D4×D5—61no—
104C2×#709—61no—
105C2×C5×D8C2×D312yescomplemented
106C5×#127C2×D311yescharacteristic
107C4×C5×D4C2×D311yescharacteristic, complemented
108#4084—32no—
109#4084—32no—
110#4084—61no—
111#4083—62no—
112C2×#686—31no—
113#4070—61no—
114C2×C8×D5—32no—
115D5×C4⋊C4—32no—
116#4029—62no—
117C4×D20—31no—
118C4×D20—31no—
119#4015—31no—
120C5×C4⋊C8C2×D311yescharacteristic, complemented
121C5×#102C2×D312yescomplemented
122#3964—31no—
123#3964—32no—
124#3964—32no—
125#3953—32no—
126#3952—32no—
127#3950—32no—
128#3941—31no—
129#3939—31no—
130C4×#168—31no—
131#3294—151noSylow
132C23×C3×C5—21no—
133C23×C3×C5—22no—
134C22×D15—21no—
135C22×D15—44no—
136C22×D15—44no—
137C22×D15—82no—
138C22×D15C2×D412yes—
139C3×C5×D4—21no—
140C3×C5×D4—22no—
141C3×C5×D4—21no—
142C3×C5×D4—22no—
143C3×C5×D4—42no—
144C3×C5×D4—81no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—42no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2411yescharacteristic
150#1220—44no—
151#1220—44no—
152#1220—44no—
153C2×Dic15—22no—
154C2×Dic15—21no—
155C2×Dic15C2×D412yes—
156D60—21no—
157D60D814yescomplemented
158D60#4112yescomplemented
159C4×D15—22no—
160C4×D15—22no—
161C4×D15—44no—
162C4×D15—42no—
163Dic30—42no—
164C3×C5×C8—22no—
165C3⋊#168—21no—
166C3⋊#168—21no—
167C2×D3×D4—52no—
168C2×D3×D4—101no—
169C2×#235—101no—
170C2×C3×D8C2×D512yescomplemented
171C3×#127C2×D511yescharacteristic
172C3×C4×D4C2×D511yescharacteristic, complemented
173#938—52no—
174#938—52no—
175#938—101no—
176#937—102no—
177C2×#213—51no—
178#924—101no—
179C2×D3×C8—52no—
180D3×C4⋊C4—52no—
181#883—102no—
182C4×D12—51no—
183C4×D12—51no—
184#869—51no—
185C3×C4⋊C8C2×D511yescharacteristic, complemented
186C3×#102C2×D512yescomplemented
187#832—52no—
188#832—51no—
189#832—52no—
190#821—52no—
191(C2×D3)⋊C8—52no—
192#818—52no—
193#809—51no—
194#807—51no—
195C4×C3⋊C8—51no—
196C23×D5—62no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4C22×D311yescharacteristic
200C2×C5×D4C22×D312yes—
201C22×C4×C5—21no—
202C2×C22⋊D5—62no—
203C2×C22⋊D5—62no—
204C2×C22⋊D5—62no—
205D4×D5—64no—
206D4×D5—122no—
207D4×D5—124no—
208#709—124no—
209C2×D20—31no—
210C2×D20—31no—
211C2×C4×D5—32no—
212C2×C4×D5—62no—
213C2×C4×D5—61no—
214C2×Dic10—61no—
215C5×D8—42no—
216C2×C5×C8C22×D312yes—
217C5×C4⋊C4C22×D311yescharacteristic
218C5×C22⋊C4—21no—
219C42×C5C22×D311yescharacteristic
220C22⋊Dic5—62no—
221C22⋊Dic5—62no—
222#686—62no—
223#685—32no—
224#685—61no—
225C4⋊Dic5—31no—
226C4⋊Dic5—31no—
227C4⋊Dic5—32no—
228C4⋊Dic5—61no—
229#683—62no—
230C2×#168—31no—
231C2×#168—31no—
232C8×D5—122no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459D1511yescharacteristic, complemented
240#447—152no—
241C4×D8—151no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—42no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5—42no—
248C22×C3×C5—42no—
249C22×C3×C5—41no—
250C22×C3×C5C22×D411yescharacteristic
251C2×D15—22no—
252C2×D15—22no—
253C2×D15—22no—
254C2×D15—41no—
255C2×D15—41no—
256C2×D15—88no—
257C2×D15C2×D814yes—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5C2×D812yes—
261C3×C4×C5C2×#4111yescharacteristic
262C3×C4×C5H(5,𝔽2)11yescharacteristic
263Dic15—22no—
264Dic15—42no—
265Dic15—41no—
266C23×D3—102no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4C22×D512yes—
270C2×C3×D4C22×D511yescharacteristic
271C22×C3×C4—21no—
272C2×#67—102no—
273C2×#67—102no—
274C2×#67—102no—
275D3×D4—104no—
276D3×D4—202no—
277D3×D4—204no—
278#235—204no—
279C2×D12—51no—
280C2×D12—51no—
281C2×C4×D3—52no—
282C2×C4×D3—102no—
283C2×C4×D3—101no—
284C2×Dic6—101no—
285C3×D8—42no—
286C2×C3×C8C22×D512yes—
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C22⋊C4—21no—
289C3×C42C22×D511yescharacteristic
290#217—102no—
291#217—102no—
292#213—102no—
293(C2×D3)⋊C4—52no—
294(C2×D3)⋊C4—101no—
295C4⋊Dic3—51no—
296C4⋊Dic3—51no—
297C4⋊Dic3—52no—
298C4⋊Dic3—101no—
299Dic3⋊C4—102no—
300C2×C3⋊C8—51no—
301C2×C3⋊C8—51no—
302D3×C8—202no—
303C23×C5—21no—
304C23×C5—22no—
305C22×D5—32no—
306C22×D5—61no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×D4—21no—
311C5×D4—22no—
312C5×D4—21no—
313C5×D4—22no—
314C5×D4—42no—
315C5×D4—81no—
316C2×C4×C5—21no—
317C2×C4×C5—42no—
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—124no—
322C22⋊D5—124no—
323C22⋊D5—124no—
324C2×Dic5—32no—
325C2×Dic5—62no—
326C2×Dic5—61no—
327D20—34no—
328D20—32no—
329D20—61no—
330C4×D5—62no—
331C4×D5—62no—
332C4×D5—124no—
333C4×D5—122no—
334Dic10—122no—
335C5×C8—22no—
336#168—61no—
337#168—61no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—151no—
342C2×D8C2×D1512yescomplemented
343C22×C8—152no—
344C4⋊Q8—151no—
345#127C2×D1511yescharacteristic
346#123—302no—
347C22⋊Q8—301no—
348#121—152no—
349#121—152no—
350#121—301no—
351#120—302no—
352C4×D4—151no—
353C4×D4—151no—
354C4×D4C2×D1511yescharacteristic, complemented
355C2×C4⋊C4—152no—
356#107—152no—
357#107—151no—
358C4⋊C8C2×D1511yescharacteristic, complemented
359#102—152no—
360#102—151no—
361#102—152no—
362#102—152no—
363#102—151no—
364#102C2×D1512yescomplemented
365C22⋊C8—152no—
366C4×C8—151no—
367C2×C3×C5—82no—
368C2×C3×C5—81no—
369C2×C3×C5#54611yescharacteristic
370C2×C3×C5C22×D811yescharacteristic
371C2×C3×C5#57711yescharacteristic
372D15—24no—
373D15—42no—
374C23×C3—21no—
375C23×C3—22no—
376C22×D3—52no—
377C22×D3—101no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×D4—21no—
382C3×D4—22no—
383C3×D4—21no—
384C3×D4—22no—
385C3×D4—42no—
386C3×D4—81no—
387C2×C3×C4—21no—
388C2×C3×C4—42no—
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392#67—204no—
393#67—204no—
394#67—204no—
395C2×Dic3—52no—
396C2×Dic3—102no—
397C2×Dic3—101no—
398D12—52no—
399D12—54no—
400D12—101no—
401C4×D3—102no—
402C4×D3—102no—
403C4×D3—204no—
404C4×D3—202no—
405Dic6—202no—
406C3×C8—22no—
407C3⋊C8—101no—
408C3⋊C8—101no—
409C22×C5—41no—
410C22×C5—42no—
411C22×C5—42no—
412C22×C5—41no—
413C22×C5—42no—
414C22×C5—41no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—34no—
417C2×D5—62no—
418C2×D5—62no—
419C2×D5—62no—
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—41no—
425C4×C5D3×D812yes—
426C4×C5#100411yescharacteristic
427C4×C5D3×#4111yescharacteristic
428Dic5—62no—
429Dic5—122no—
430Dic5—121no—
431C24—302no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—151no—
437C2×D4—151no—
438C2×D4—302no—
439C2×D4—304no—
440C2×D4—302no—
441C2×D4—302no—
442C2×D4—602no—
443C2×D4—604no—
444C2×D4C22×D1512yes—
445C2×D4C22×D1511yescharacteristic
446C22×C4—21no—
447C22×C4—152no—
448C22×C4—302no—
449C22×C4—301no—
450D8—42no—
451D8—302no—
452C2×C8—151no—
453C2×C8—151no—
454C2×C8—602no—
455C2×C8C22×D1512yes—
456C4⋊C4—151no—
457C4⋊C4—152no—
458C4⋊C4—151no—
459C4⋊C4—302no—
460C4⋊C4—301no—
461C4⋊C4C22×D1511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—152no—
464C22⋊C4—302no—
465C22⋊C4—302no—
466C22⋊C4—301no—
467C42C22×D1511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—41no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—41no—
473C22×C3—42no—
474C22×C3—41no—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—54no—
477C2×D3—102no—
478C2×D3—102no—
479C2×D3—102no—
480C2×D3—201no—
481C2×D3—201no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4D5×D812yes—
486C3×C4#414411yescharacteristic
487C3×C4D5×#4111yescharacteristic
488Dic3—102no—
489Dic3—202no—
490Dic3—201no—
491C2×C5—82no—
492C2×C5—81no—
493C2×C5#561211yescharacteristic
494C2×C5C2×D3×D811yescharacteristic
495C2×C5#577511yescharacteristic
496D5—64no—
497D5—122no—
498C23—21no—
499C23—22no—
500C23—152no—
501C23—301no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—602no—
506D4—21no—
507D4—22no—
508D4—21no—
509D4—22no—
510D4—42no—
511D4—81no—
512D4—154no—
513D4—152no—
514D4—301no—
515D4—604no—
516D4—604no—
517D4—604no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—152no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—604no—
526C2×C4—602no—
527C2×C4D4×D1511yescharacteristic
528C2×C4D4×D1511yescharacteristic
529C2×C4C23×D1511yescharacteristic
530C8—22no—
531C8—301no—
532C8—301no—
533C2×C3—82no—
534C2×C3—81no—
535C2×C3#6594611yescharacteristic
536C2×C3C2×D5×D811yescharacteristic
537C2×C3#6610911yescharacteristic
538D3—104no—
539D3—202no—
540C5#8035211yescharacteristic, complemented, Sylow
541C22—42no—
542C22—41no—
543C22—41no—
544C22—42no—
545C22—42no—
546C22—41no—
547C22—154no—
548C22—302no—
549C22—302no—
550C22—302no—
551C22—601no—
552C22—601no—
553C22—1208no—
554C22C2×D4×D1511yescharacteristic
555C4—21no—
556C4—41no—
557C4—302no—
558C4—601no—
559C4—602no—
560C4D8×D1512yes—
561C4#9209511yescharacteristic
562C4#41×D1511yescharacteristic
563C3#1061208311yescharacteristic, complemented, Sylow
564C2—82no—
565C2—81no—
566C2—304no—
567C2—602no—
568C2#1175637111yescharacteristic
569C2C2×D8×D1511yescharacteristic
570C2#1175653411yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#459C2
socleC22×C3×C5C22×D4
hypercenter#459D15
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #11756476C2semidirect
2. #11756310C2semidirect
3. C3×C5×#459C2semidirect
4. #11751258C2semidirect
5. #11751257C2semidirect
6. #11751171C2semidirect
7. C4×#6715C2semidirect
8. #11750947C2semidirect
9. #11750935C2semidirect
10. #11750875C2semidirect
11. D15×#102C2semidirect
16. C2×C3×C5×D8C22semidirect
18. C3×C4×C5×D4C22semidirect
21. #91827C22semidirect
25. C2×C8×D15C22semidirect
26. C4⋊C4×D15C22semidirect
30. #91758C22semidirect
31. C3×C5×C4⋊C8C22semidirect
32. C3×C5×#102C22semidirect
33. #91116C22semidirect
34. #91116C22semidirect
35. #91116C22semidirect
37. #91104C22semidirect
38. #91102C22semidirect
40. #91091C22semidirect
41. C4×C3⋊#168C22semidirect
45. C5×#459D3semidirect
93. C3×#459D5semidirect
105. C2×C5×D8C2×D3semidirect
107. C4×C5×D4C2×D3semidirect
120. C5×C4⋊C8C2×D3semidirect
121. C5×#102C2×D3semidirect
157. D60D8semidirect
158. D60#41semidirect
170. C2×C3×D8C2×D5semidirect
172. C3×C4×D4C2×D5semidirect
185. C3×C4⋊C8C2×D5semidirect
186. C3×#102C2×D5semidirect
239. #459D15semidirect
342. C2×D8C2×D15semidirect
354. C4×D4C2×D15semidirect
358. C4⋊C8C2×D15semidirect
364. #102C2×D15semidirect
468. C3×C5#3294semidirect
540. C5#80352semidirect
563. C3#10612083semidirect

Maximal subgroups

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

subgroupindex
#117564762
#117563102
C3×C5×#4592
#117512582
#117512572
#117511712
C4×#67152
#117509472
#117509352
#117508752
D15×#1022
#106120833
#803525