Finite Group Databasebeta

← #14458351

Subgroups — #14458351

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
1D4×D60C211yesmaximal, characteristic, complemented
2#11752561C211yesmaximal, characteristic, complemented
3C4×C5×#213C211yesmaximal, characteristic, complemented
4C3×#65296C211yesmaximal, characteristic, complemented
5#11749041C212yesmaximal, complemented
6#11748957C212yesmaximal, complemented
7#11747314C212yesmaximal, complemented
8#11747200C212yesmaximal, complemented
9#11747037C211yesmaximal, characteristic, complemented
10#11746994C211yesmaximal, characteristic, complemented
11#11746910C211yesmaximal, characteristic, complemented
12#10611339—31nomaximal, Hall
13C2×D4×D15C2212yes—
14C22×D60—21no—
15C2×#6769—21no—
16C3×C4×C5×D4C2211yescharacteristic
17#91819—21no—
18#91784C2212yes—
19#91771—22no—
20#91763C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C2×C5×#213C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic, complemented
24C3×#4015C2211yescharacteristic, complemented
25#91466C2212yescomplemented
26#91438—22no—
27#91437C2212yescomplemented
28#91369—21no—
29C2×#6654C2212yescomplemented
30C2×#6648C2212yescomplemented
31C5×#832C2211yescharacteristic
32C5×#809C2211yescharacteristic, complemented
33C5×#807C2211yescharacteristic, complemented
34C4×C5×C3⋊C8C2211yescharacteristic, complemented
35C3×#3964C2212yes—
36C3×#3939C2212yescomplemented
37C3×C4⋊#168C2211yescharacteristic, complemented
38#90969C2212yescomplemented
39#90968C2212yescomplemented
40#90968C2212yescomplemented
41#90957C2212yescomplemented
42#80980—51nomaximal, Hall
43#65885—31no—
44D4×D20—31no—
45C4×C5×D8—31no—
46#65445—32no—
47#65304—31no—
48#65296D311yescharacteristic, complemented
49#65171—32no—
50#65064—32no—
51D5×#102—32no—
52#64983—31no—
53C8×D20—31no—
54C23×D15—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58D4×D15—24no—
59D4×D15—42no—
60C2×D60—22no—
61C2×D60—21no—
62C2×D60—21no—
63C2×D60—44no—
64C2×D60D411yescharacteristic
65C2×D60C2312yes—
66C2×C4×D15C2312yes—
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C3×Dic10—21no—
70C2×#1203—22no—
71C2×#1200—22no—
72#6769—44no—
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C22⋊C4—21no—
75C3×C42×C5C2311yescharacteristic
76#6714—22no—
77#6714D412yes—
78C4⋊Dic15D411yescharacteristic
79C5×#213—22no—
80C5×(C2×D3)⋊C4—21no—
81C5×C4⋊Dic3C2311yescharacteristic
82C2×C5×C3⋊C8C2311yescharacteristic
83C2×C5×C3⋊C8C2311yescharacteristic
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yes—
86C2×C3×#168C2312yes—
87#6669—22no—
88(C2×D3)⋊Dic5—22no—
89#6654—42no—
90#6648—42no—
91#5726—51no—
92D4×D12—51no—
93C3×#474—51no—
94#5088—51no—
95C4×#213D511yescharacteristic, complemented
96#4883—52no—
97#4882—52no—
98#4843—51no—
99#4834—51no—
100#4773—52no—
101D3×#102—52no—
102C2×D4×D5—32no—
103C2×#709—61no—
104C22×D20—61no—
105C2×C5×D8—31no—
106C4×C5×D4—31no—
107C4×C5×D4C2×D311yescharacteristic
108#4084—32no—
109C2×#686—32no—
110#4076—61no—
111#4070—61no—
112C2×C8×D5—32no—
113#4041—32no—
114D5×C4⋊C4—32no—
115#4029—62no—
116#4028—62no—
117#4020—31no—
118C4×D20—31no—
119#4015C2×D311yescharacteristic, complemented
120C5×#107—31no—
121C5×#102—31no—
122C5×#102—31no—
123C4×C5×C8—31no—
124#3964C2×D312yes—
125#3953—32no—
126#3953—32no—
127#3952—32no—
128#3941—32no—
129#3939C2×D312yescomplemented
130C4⋊#168C2×D311yescharacteristic, complemented
131#3294—151noSylow
132C23×C3×C5—21no—
133C22×D15—22no—
134C22×D15—44no—
135C22×D15—44no—
136C22×D15—82no—
137C22×D15C2×D412yes—
138C22×C5×D3—21no—
139C3×C5×D4—21no—
140C3×C5×D4#4112yescomplemented
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146#1220—44no—
147C2×Dic15C2×D412yes—
148D60—22no—
149D60—22no—
150D60—44no—
151D60—42no—
152D60—81no—
153D60D814yescomplemented
154C4×D15—22no—
155C4×D15—22no—
156C2×C5×Dic3—21no—
157C5×D12—21no—
158C5×D12—21no—
159C4×C5×D3—42no—
160C2×C3×Dic5—22no—
161C3×Dic10—42no—
162#1203—44no—
163#1200—44no—
164C3×#168—22no—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—21no—
167C2×#239—101no—
168C2×D3×D4—52no—
169C22×D12—101no—
170C3×C4⋊Q8—51no—
171C3×C4×D4C2×D511yescharacteristic
172#946—101no—
173C2×#213C2×D511yescharacteristic
174#930—101no—
175C2×D24—52no—
176C2×D3×C8—52no—
177#895—52no—
178#895—52no—
179#894—102no—
180D3×C4⋊C4—52no—
181#882—102no—
182#874—51no—
183C4×D12—51no—
184C4×D12C2×D511yescharacteristic, complemented
185C3×#107—52no—
186C3×C4⋊C8—51no—
187C3×#102—52no—
188#832C2×D511yescharacteristic
189#821—52no—
190(C2×D3)⋊C8—52no—
191#809—52no—
192#809—52no—
193#809C2×D511yescharacteristic, complemented
194#807C2×D511yescharacteristic, complemented
195C4×C3⋊C8C2×D511yescharacteristic, complemented
196C23×D5—62no—
197C2×C5×D4—31no—
198C2×C5×D4C22×D311yescharacteristic
199C22×C4×C5—21no—
200C22×C4×C5—61no—
201C2×C22⋊D5—62no—
202C2×C22⋊D5—62no—
203D4×D5—64no—
204D4×D5—122no—
205#709—124no—
206C2×D20—31no—
207C2×D20—32no—
208C2×D20—62no—
209C2×D20—61no—
210C2×D20—61no—
211C2×D20—124no—
212C2×C4×D5—32no—
213C2×C4×D5—62no—
214C2×Dic10—21no—
215C5×D8—62no—
216C2×C5×C8—31no—
217C2×C5×C8—31no—
218C5×C4⋊C4—31no—
219C5×C4⋊C4C22×D311yescharacteristic
220C5×C22⋊C4—21no—
221C5×C22⋊C4—61no—
222C42×C5C22×D311yescharacteristic
223C22⋊Dic5—62no—
224#686—122no—
225#685—32no—
226#685—62no—
227C4⋊Dic5—21no—
228C4⋊Dic5—31no—
229C4⋊Dic5C22×D312yes—
230#683—62no—
231C2×#168C22×D312yes—
232C8×D5—122no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—51no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—31no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—22no—
249C2×D15—22no—
250C2×D15—42no—
251C2×D15—42no—
252C2×D15—42no—
253C2×D15—88no—
254C2×D15C2×D814yes—
255C2×C5×D3—41no—
256C2×C5×D3—41no—
257C2×C5×D3—41no—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5C2×D812yes—
261C3×C4×C5C2×#4111yescharacteristic
262C3×C4×C5H(5,𝔽2)11yescharacteristic
263Dic15—22no—
264C3×Dic5—42no—
265C5×Dic3—41no—
266C23×D3—102no—
267C2×C3×Q8—101no—
268C2×C3×D4C22×D511yescharacteristic
269C22×C3×C4—21no—
270C2×#67—102no—
271#239—204no—
272D3×D4—104no—
273D3×D4—202no—
274C2×D12—51no—
275C2×D12—52no—
276C2×D12—102no—
277C2×D12—102no—
278C2×D12—101no—
279C2×D12—101no—
280C2×D12—204no—
281C2×D12C22×D511yescharacteristic
282C2×C4×D3—21no—
283C2×C4×D3—52no—
284C2×C4×D3—102no—
285C2×C3×C8—52no—
286C3×C4⋊C4—52no—
287C3×C4⋊C4—101no—
288C3×C4⋊C4C22×D511yescharacteristic
289C3×C22⋊C4—21no—
290C3×C42C22×D511yescharacteristic
291#213—22no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—52no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3—51no—
297C4⋊Dic3C22×D511yescharacteristic
298Dic3⋊C4—102no—
299C2×C3⋊C8C22×D511yescharacteristic
300C2×C3⋊C8C22×D511yescharacteristic
301D24—202no—
302D3×C8—202no—
303C23×C5—21no—
304C23×C5—61no—
305C22×D5—32no—
306C22×D5—62no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×D4—21no—
311C5×D4—61no—
312C5×D4—61no—
313C5×D4#23912yescomplemented
314C2×C4×C5—21no—
315C2×C4×C5—42no—
316C2×C4×C5—61no—
317C2×C4×C5—122no—
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—124no—
322C22⋊D5—124no—
323C2×Dic5—22no—
324C2×Dic5—32no—
325D20—34no—
326D20—62no—
327D20—62no—
328D20—124no—
329D20—122no—
330D20—241no—
331C4×D5—62no—
332C4×D5—62no—
333C4×D5—124no—
334Dic10—42no—
335C5×C8—61no—
336C5×C8—61no—
337#168—22no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—31no—
342C2×D8—152no—
343C22×C8—152no—
344C4⋊Q8—51no—
345#127—151no—
346#123—302no—
347C22⋊Q8—301no—
348#121—152no—
349#121—152no—
350#121—301no—
351#120—302no—
352C4×D4—31no—
353C4×D4—151no—
354C4×D4D3×D511yescharacteristic
355C2×C4⋊C4—152no—
356#107—31no—
357#107—52no—
358C4⋊C8—51no—
359#102—31no—
360#102—31no—
361#102—52no—
362#102—152no—
363#102—152no—
364#102—152no—
365C22⋊C8—152no—
366C4×C8—31no—
367C2×C3×C5—42no—
368C2×C3×C5#54611yescharacteristic
369C2×C3×C5C22×D811yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—24no—
372D15—82no—
373C5×D3—81no—
374C23×C3—21no—
375C22×D3—21no—
376C22×D3—52no—
377C22×D3—102no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×Q8—202no—
382C3×D4—21no—
383C3×D4#70912yescomplemented
384C2×C3×C4—21no—
385C2×C3×C4—42no—
386C2×C3×C4—102no—
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4C23×D511yescharacteristic
390#67—204no—
391C2×Dic3—21no—
392C2×Dic3—52no—
393D12—21no—
394D12—21no—
395D12—54no—
396D12—102no—
397D12—102no—
398D12—204no—
399D12—204no—
400D12—202no—
401D12—401no—
402C4×D3—42no—
403C4×D3—102no—
404C4×D3—102no—
405C4×D3—204no—
406C3×C8—102no—
407C3⋊C8—21no—
408C3⋊C8—21no—
409C22×C5—22no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5—121no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—34no—
417C2×D5—62no—
418C2×D5—62no—
419C2×D5—122no—
420C2×D5—122no—
421C2×D5—122no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—41no—
425C4×C5—121no—
426C4×C5D3×D812yes—
427C4×C5C2×#23911yescharacteristic
428C4×C5#100911yescharacteristic
429Dic5—42no—
430Dic5—62no—
431C24—302no—
432#41—604no—
433C2×Q8—101no—
434C2×D4—31no—
435C2×D4—151no—
436C2×D4—152no—
437C2×D4—302no—
438C2×D4—302no—
439C2×D4—302no—
440C2×D4—304no—
441C2×D4—301no—
442C2×D4—301no—
443C2×D4—604no—
444C2×D4—602no—
445C2×D4C2×D3×D511yescharacteristic
446C22×C4—21no—
447C22×C4—61no—
448C22×C4—152no—
449C22×C4—302no—
450D8—62no—
451D8—602no—
452C2×C8—31no—
453C2×C8—31no—
454C2×C8—52no—
455C2×C8—602no—
456C4⋊C4—31no—
457C4⋊C4—52no—
458C4⋊C4—101no—
459C4⋊C4—151no—
460C4⋊C4—302no—
461C4⋊C4C2×D3×D511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—61no—
464C22⋊C4—152no—
465C22⋊C4—302no—
466C22⋊C4—302no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3C2×D4×D511yescharacteristic
473C2×D3—41no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—54no—
477C2×D3—102no—
478C2×D3—102no—
479C2×D3—202no—
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4—202no—
486C3×C4D5×D812yes—
487C3×C4C2×#70911yescharacteristic
488C3×C4#414911yescharacteristic
489Dic3—41no—
490Dic3—102no—
491C2×C5—42no—
492C2×C5—241no—
493C2×C5#563011yescharacteristic
494C2×C5C2×D3×D811yescharacteristic
495C2×C5#577811yescharacteristic
496D5—64no—
497D5—242no—
498C23—21no—
499C23—61no—
500C23—152no—
501C23—302no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—202no—
506D4—21no—
507D4—61no—
508D4—61no—
509D4—154no—
510D4—302no—
511D4—302no—
512D4—604no—
513D4—604no—
514D4—604no—
515D4—602no—
516D4—1201no—
517D4#676912yescomplemented
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—61no—
521C2×C4—102no—
522C2×C4—122no—
523C2×C4—152no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4#679011yescharacteristic
528C2×C4#679011yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—61no—
531C8—61no—
532C8—102no—
533C2×C3—42no—
534C2×C3#6588411yescharacteristic
535C2×C3C2×D5×D811yescharacteristic
536C2×C3#6610411yescharacteristic
537D3—81no—
538D3—104no—
539D3—402no—
540C5#8098011yescharacteristic, complemented, Sylow
541C22—22no—
542C22—41no—
543C22—41no—
544C22—121no—
545C22—121no—
546C22—121no—
547C22—154no—
548C22—302no—
549C22—302no—
550C22—602no—
551C22—602no—
552C22—602no—
553C22—1208no—
554C22C2×#679011yescharacteristic
555C4—21no—
556C4—41no—
557C4—121no—
558C4—202no—
559C4—302no—
560C4#9148112yes—
561C4C2×#676911yescharacteristic
562C4#9201911yescharacteristic
563C3#1061133911yescharacteristic, complemented, Sylow
564C2—42no—
565C2—241no—
566C2—304no—
567C2—1202no—
568C2#1175438211yescharacteristic
569C2C2×#9148111yescharacteristic
570C2#1175535411yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×D60C2semidirect
2. #11752561C2semidirect
3. C4×C5×#213C2semidirect
4. C3×#65296C2semidirect
5. #11749041C2semidirect
6. #11748957C2semidirect
7. #11747314C2semidirect
8. #11747200C2semidirect
9. #11747037C2semidirect
10. #11746994C2semidirect
11. #11746910C2semidirect
23. C4×C5×D12C22semidirect
24. C3×#4015C22semidirect
25. #91466C22semidirect
27. #91437C22semidirect
29. C2×#6654C22semidirect
30. C2×#6648C22semidirect
32. C5×#809C22semidirect
33. C5×#807C22semidirect
34. C4×C5×C3⋊C8C22semidirect
36. C3×#3939C22semidirect
37. C3×C4⋊#168C22semidirect
38. #90969C22semidirect
39. #90968C22semidirect
40. #90968C22semidirect
41. #90957C22semidirect
48. #65296D3semidirect
95. C4×#213D5semidirect
119. #4015C2×D3semidirect
129. #3939C2×D3semidirect
130. C4⋊#168C2×D3semidirect
140. C3×C5×D4#41semidirect
153. D60D8semidirect
184. C4×D12C2×D5semidirect
193. #809C2×D5semidirect
194. #807C2×D5semidirect
195. C4×C3⋊C8C2×D5semidirect
313. C5×D4#239semidirect
383. C3×D4#709semidirect
468. C3×C5#3294semidirect
517. D4#6769semidirect
540. C5#80980semidirect
563. C3#10611339semidirect

Maximal subgroups

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

subgroupindex
D4×D602
#117525612
C4×C5×#2132
C3×#652962
#117490412
#117489572
#117473142
#117472002
#117470372
#117469942
#117469102
#106113393
#809805