Finite Group Databasebeta

← #14458295

Subgroups — #14458295

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
1C3×C5×D42C211yesmaximal, characteristic, complemented
2#11756314C211yesmaximal, characteristic, complemented
3#11751318C212yesmaximal, complemented
4C2×#91116C212yesmaximal, complemented
5#11751173C211yesmaximal, characteristic, complemented
6#11751171C211yesmaximal, characteristic, complemented
7#11751139C212yesmaximal, complemented
8#11751134C212yesmaximal, complemented
9C4×#6715C211yesmaximal, characteristic, complemented
10D4×C3⋊#168C211yesmaximal, characteristic, complemented
11#11751108C211yesmaximal, characteristic, complemented
12#10615213—31nomaximal, Hall
13C22×C3×C5×D4—21no—
14C22×C3×C5×D4C2212yes—
15C2×#6819—21no—
16C3×C5×#127C2211yescharacteristic
17C3×C5×#121—21no—
18C3×C5×#121C2212yes—
19C3×C5×#120—22no—
20C3×C4×C5×D4C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C2×#6715C2211yescharacteristic
23C2×#6715C2212yescomplemented
24#91819C2212yescomplemented
25C2×C4⋊Dic15C2212yescomplemented
26C22×C3⋊#168C2212yescomplemented
27#91786—21no—
28#91775—22no—
29C4×D60C2211yescharacteristic, complemented
30#91758C2211yescharacteristic, complemented
31#91116C2211yescharacteristic
32#91116C2212yes—
33#91116C2212yescomplemented
34#91116C2212yescomplemented
35#91116C2212yescomplemented
36#91114C2212yescomplemented
37#91093C2211yescharacteristic, complemented
38#91091C2212yescomplemented
39#91091C2211yescharacteristic, complemented
40C4⋊(C3⋊#168)C2211yescharacteristic, complemented
41C4×C3⋊#168C2211yescharacteristic, complemented
42#83482—51nomaximal, Hall
43C5×D42D311yescharacteristic, complemented
44#65889—31no—
45#65506—32no—
46C2×#3964—32no—
47#65361—31no—
48#65359—31no—
49#65327—32no—
50#65322—32no—
51C4×#686—31no—
52D4×#168—31no—
53#65296—31no—
54C24×C3×C5—22no—
55C2×C3×C5×D4—24no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4—42no—
61C2×C3×C5×D4—44no—
62C2×C3×C5×D4D411yescharacteristic
63C2×C3×C5×D4C2312yes—
64C2×C3×C5×D4C2311yescharacteristic
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5C2312yes—
67C2×#1220—22no—
68C22×Dic15—22no—
69#6819—44no—
70C2×D60C2311yescharacteristic
71C2×C4×D15—21no—
72C2×Dic30—21no—
73C3×C5×C4⋊C4D411yescharacteristic
74C3×C5×C4⋊C4C2311yescharacteristic
75C3×C5×C22⋊C4—21no—
76C3×C5×C22⋊C4—22no—
77C3×C5×C22⋊C4D412yes—
78C3×C42×C5C2311yescharacteristic
79#6715—22no—
80#6715—42no—
81#6714—21no—
82#6714—22no—
83C4⋊Dic15—21no—
84C4⋊Dic15—22no—
85C4⋊Dic15C2312yes—
86C4⋊Dic15C2311yescharacteristic
87C2×C3⋊#168—42no—
88C2×C3⋊#168C2311yescharacteristic
89C2×C3⋊#168C2312yes—
90C2×C3⋊#168C2311yescharacteristic
91C3×D42D511yescharacteristic, complemented
92#5555—51no—
93#5217—52no—
94C2×#832—52no—
95#5072—51no—
96#5070—51no—
97#5038—52no—
98#5033—52no—
99C4×#213—51no—
100D4×C3⋊C8—51no—
101#5007—51no—
102C22×C5×D4—21no—
103C22×C5×D4C2×D312yes—
104C2×#711—61no—
105C5×#127C2×D311yescharacteristic
106C5×#121—21no—
107C5×#121C2×D312yes—
108C5×#120—22no—
109C4×C5×D4C2×D311yescharacteristic
110C4×C5×D4C2×D311yescharacteristic
111C2×#686—31no—
112C2×#686—32no—
113#4076—32no—
114C2×C4⋊Dic5—32no—
115C22×#168—32no—
116#4043—61no—
117#4032—62no—
118C4×D20—31no—
119#4015—31no—
120#3964—32no—
121#3964—31no—
122#3964—32no—
123#3964—32no—
124#3964—32no—
125C22⋊#168—32no—
126#3941—31no—
127#3939—32no—
128#3939—31no—
129C4⋊#168—31no—
130C4×#168—31no—
131#3294—151noSylow
132C23×C3×C5—21no—
133C23×C3×C5—22no—
134C23×C3×C5—44no—
135C23×C3×C5—44no—
136C23×C3×C5—82no—
137C23×C3×C5C2×D412yes—
138C22×D15—21no—
139C3×C5×D4—22no—
140C3×C5×D4—21no—
141C3×C5×D4—22no—
142C3×C5×D4—44no—
143C3×C5×D4—44no—
144C3×C5×D4—42no—
145C3×C5×D4—81no—
146C3×C5×D4D814yescomplemented
147C3×C5×D4#4112yescomplemented
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2411yescharacteristic
156#1220—44no—
157C2×Dic15—22no—
158C2×Dic15—21no—
159C2×Dic15—44no—
160D60—21no—
161D60—21no—
162C4×D15—42no—
163Dic30—42no—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C3⋊#168—22no—
167C22×C3×D4—21no—
168C22×C3×D4C2×D512yes—
169C2×#237—101no—
170C3×#127C2×D511yescharacteristic
171C3×#121—21no—
172C3×#121C2×D512yes—
173C3×#120—22no—
174C3×C4×D4C2×D511yescharacteristic
175C3×C4×D4C2×D511yescharacteristic
176C2×#213—51no—
177C2×#213—52no—
178#930—52no—
179C2×C4⋊Dic3—52no—
180C22×C3⋊C8—52no—
181#897—101no—
182#886—102no—
183C4×D12—51no—
184#869—51no—
185#832—51no—
186#832—52no—
187#832—52no—
188#832—52no—
189#832—52no—
190#830—52no—
191#809—51no—
192#807—52no—
193#807—51no—
194C4⋊(C3⋊C8)—51no—
195C4×C3⋊C8—51no—
196C24×C5—22no—
197C2×C5×D4—24no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4—21no—
201C2×C5×D4—21no—
202C2×C5×D4—42no—
203C2×C5×D4—44no—
204C2×C5×D4#6711yescharacteristic
205C2×C5×D4C22×D312yes—
206C2×C5×D4C22×D311yescharacteristic
207C22×C4×C5—21no—
208C22×C4×C5C22×D312yes—
209C2×C22⋊D5—62no—
210C22×Dic5—62no—
211#711—124no—
212C2×D20—31no—
213C2×C4×D5—61no—
214C2×Dic10—61no—
215C5×C4⋊C4#6711yescharacteristic
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C22⋊C4—21no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4#6712yes—
220C42×C5C22×D311yescharacteristic
221#686—62no—
222#686—122no—
223#685—61no—
224#685—62no—
225C4⋊Dic5—32no—
226C4⋊Dic5—31no—
227C4⋊Dic5—61no—
228C4⋊Dic5—62no—
229C2×#168—31no—
230C2×#168—31no—
231C2×#168—32no—
232C2×#168—122no—
233#547—151no—
234D42D1511yescharacteristic, complemented
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—151no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—22no—
245C22×C3×C5—22no—
246C22×C3×C5—22no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5—42no—
250C22×C3×C5—42no—
251C22×C3×C5—42no—
252C22×C3×C5—88no—
253C22×C3×C5C2×D814yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—41no—
256C2×D15—41no—
257C2×D15—41no—
258C3×C4×C5—22no—
259C3×C4×C5—21no—
260C3×C4×C5—41no—
261C3×C4×C5C2×D812yes—
262C3×C4×C5C2×#4111yescharacteristic
263C3×C4×C5H(5,𝔽2)11yescharacteristic
264Dic15—42no—
265Dic15—41no—
266C24×C3—22no—
267C2×C3×D4—24no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—42no—
273C2×C3×D4—44no—
274C2×C3×D4C22⋊D511yescharacteristic
275C2×C3×D4C22×D512yes—
276C2×C3×D4C22×D511yescharacteristic
277C22×C3×C4—21no—
278C22×C3×C4C22×D512yes—
279C2×#67—102no—
280C22×Dic3—102no—
281#237—204no—
282C2×D12—51no—
283C2×C4×D3—101no—
284C2×Dic6—101no—
285C3×C4⋊C4C22⋊D511yescharacteristic
286C3×C4⋊C4C22×D511yescharacteristic
287C3×C22⋊C4—21no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4C22⋊D512yes—
290C3×C42C22×D511yescharacteristic
291#213—102no—
292#213—202no—
293(C2×D3)⋊C4—101no—
294(C2×D3)⋊C4—102no—
295C4⋊Dic3—52no—
296C4⋊Dic3—51no—
297C4⋊Dic3—101no—
298C4⋊Dic3—102no—
299C2×C3⋊C8—51no—
300C2×C3⋊C8—51no—
301C2×C3⋊C8—52no—
302C2×C3⋊C8—202no—
303C23×C5—21no—
304C23×C5—22no—
305C23×C5—44no—
306C23×C5—44no—
307C23×C5—82no—
308C23×C5C2×#6712yes—
309C22×D5—61no—
310C5×D4—22no—
311C5×D4—21no—
312C5×D4—22no—
313C5×D4—44no—
314C5×D4—44no—
315C5×D4—42no—
316C5×D4—81no—
317C5×D4#21314yescomplemented
318C5×D4#23712yescomplemented
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—21no—
322C2×C4×C5—42no—
323C2×C4×C5C2×#6711yescharacteristic
324C2×C4×C5C2×#6712yes—
325C2×C4×C5C2×#6711yescharacteristic
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—124no—
328C2×Dic5—62no—
329C2×Dic5—61no—
330C2×Dic5—124no—
331D20—61no—
332D20—61no—
333C4×D5—122no—
334Dic10—122no—
335#168—61no—
336#168—61no—
337#168—62no—
338C2×#41—301no—
339C22×D4—21no—
340C22×D4C2×D1512yes—
341C2×D8—151no—
342C2×D8—152no—
343C22×C8—152no—
344C4⋊Q8—151no—
345#127C2×D1511yescharacteristic
346#123—302no—
347C22⋊Q8—301no—
348#121—21no—
349#121—152no—
350#121C2×D1512yes—
351#120—22no—
352C4×D4—151no—
353C4×D4C2×D1511yescharacteristic
354C4×D4C2×D1511yescharacteristic
355C2×C4⋊C4—152no—
356#107—151no—
357#107—152no—
358C4⋊C8—151no—
359#102—151no—
360#102—152no—
361#102—152no—
362#102—152no—
363#102—152no—
364#102—151no—
365C22⋊C8—152no—
366C4×C8—151no—
367C2×C3×C5—24no—
368C2×C3×C5—42no—
369C2×C3×C5—82no—
370C2×C3×C5#54611yescharacteristic
371C2×C3×C5C22×D811yescharacteristic
372C2×C3×C5#57711yescharacteristic
373D15—81no—
374C23×C3—21no—
375C23×C3—22no—
376C23×C3—44no—
377C23×C3—44no—
378C23×C3—82no—
379C23×C3C2×C22⋊D512yes—
380C22×D3—101no—
381C3×D4—22no—
382C3×D4—21no—
383C3×D4—22no—
384C3×D4—44no—
385C3×D4—44no—
386C3×D4—42no—
387C3×D4—81no—
388C3×D4#68614yescomplemented
389C3×D4#71112yescomplemented
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—42no—
394C2×C3×C4C2×C22⋊D511yescharacteristic
395C2×C3×C4C2×C22⋊D512yes—
396C2×C3×C4C2×C22⋊D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398#67—204no—
399C2×Dic3—102no—
400C2×Dic3—101no—
401C2×Dic3—204no—
402D12—101no—
403D12—101no—
404C4×D3—202no—
405Dic6—202no—
406C3⋊C8—101no—
407C3⋊C8—101no—
408C3⋊C8—102no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5—22no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—42no—
415C22×C5—42no—
416C22×C5—42no—
417C22×C5—88no—
418C22×C5C2×#21314yes—
419C22×C5C22×#6711yescharacteristic
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—121no—
423C4×C5—22no—
424C4×C5—21no—
425C4×C5—41no—
426C4×C5C2×#21312yes—
427C4×C5C2×#23711yescharacteristic
428C4×C5#100411yescharacteristic
429Dic5—122no—
430Dic5—121no—
431C24—22no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—24no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—151no—
442C2×D4—302no—
443C2×D4#122011yescharacteristic
444C2×D4C22×D1512yes—
445C2×D4C22×D1511yescharacteristic
446C22×C4—21no—
447C22×C4—302no—
448C22×C4—301no—
449C22×C4C22×D1512yes—
450D8—302no—
451D8—602no—
452C2×C8—151no—
453C2×C8—151no—
454C2×C8—152no—
455C2×C8—602no—
456C4⋊C4—151no—
457C4⋊C4—152no—
458C4⋊C4—302no—
459C4⋊C4—301no—
460C4⋊C4#122011yescharacteristic
461C4⋊C4C22×D1511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—22no—
464C22⋊C4—301no—
465C22⋊C4—302no—
466C22⋊C4#122012yes—
467C42C22×D1511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—88no—
478C22×C3C2×#68614yes—
479C22×C3C22×C22⋊D511yescharacteristic
480C2×D3—201no—
481C2×D3—201no—
482C2×D3—201no—
483C3×C4—22no—
484C3×C4—21no—
485C3×C4—41no—
486C3×C4C2×#68612yes—
487C3×C4C2×#71111yescharacteristic
488C3×C4#414411yescharacteristic
489Dic3—202no—
490Dic3—201no—
491C2×C5—24no—
492C2×C5—42no—
493C2×C5—82no—
494C2×C5C22×#21311yescharacteristic
495C2×C5#580611yescharacteristic
496C2×C5#583611yescharacteristic
497D5—241no—
498C23—21no—
499C23—22no—
500C23—44no—
501C23—44no—
502C23—82no—
503C23—301no—
504C23C2×#122012yes—
505Q8—602no—
506D4—22no—
507D4—21no—
508D4—22no—
509D4—44no—
510D4—44no—
511D4—42no—
512D4—81no—
513D4—301no—
514D4—301no—
515D4—604no—
516D4#671514yescomplemented
517D4#681912yescomplemented
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—42no—
522C2×C4—301no—
523C2×C4—302no—
524C2×C4—604no—
525C2×C4—602no—
526C2×C4C2×#122011yescharacteristic
527C2×C4C2×#122012yes—
528C2×C4C2×#122011yescharacteristic
529C2×C4C23×D1511yescharacteristic
530C8—301no—
531C8—301no—
532C8—302no—
533C2×C3—24no—
534C2×C3—42no—
535C2×C3—82no—
536C2×C3C22×#68611yescharacteristic
537C2×C3#6614011yescharacteristic
538C2×C3#6617011yescharacteristic
539D3—401no—
540C5#8348211yescharacteristic, complemented, Sylow
541C22—22no—
542C22—22no—
543C22—22no—
544C22—41no—
545C22—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—88no—
550C22—601no—
551C22—601no—
552C22—601no—
553C22C2×#671514yes—
554C22C22×#122011yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—601no—
559C4—602no—
560C4C2×#671512yes—
561C4C2×#681911yescharacteristic
562C4#9209511yescharacteristic
563C3#1061521311yescharacteristic, complemented, Sylow
564C2—24no—
565C2—42no—
566C2—82no—
567C2—1201no—
568C2C22×#671511yescharacteristic
569C2#1175656511yescharacteristic
570C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×D42C2
socleC22×C3×C5C22×D4
hypercenterD42D15
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C3×C5×D42C2semidirect
2. #11756314C2semidirect
3. #11751318C2semidirect
4. C2×#91116C2semidirect
5. #11751173C2semidirect
6. #11751171C2semidirect
7. #11751139C2semidirect
8. #11751134C2semidirect
9. C4×#6715C2semidirect
10. D4×C3⋊#168C2semidirect
11. #11751108C2semidirect
23. C2×#6715C22semidirect
24. #91819C22semidirect
25. C2×C4⋊Dic15C22semidirect
26. C22×C3⋊#168C22semidirect
29. C4×D60C22semidirect
30. #91758C22semidirect
33. #91116C22semidirect
34. #91116C22semidirect
35. #91116C22semidirect
36. #91114C22semidirect
37. #91093C22semidirect
38. #91091C22semidirect
39. #91091C22semidirect
40. C4⋊(C3⋊#168)C22semidirect
41. C4×C3⋊#168C22semidirect
43. C5×D42D3semidirect
91. C3×D42D5semidirect
146. C3×C5×D4D8semidirect
147. C3×C5×D4#41semidirect
234. D42D15semidirect
317. C5×D4#213semidirect
318. C5×D4#237semidirect
388. C3×D4#686semidirect
389. C3×D4#711semidirect
468. C3×C5#3294semidirect
516. D4#6715semidirect
517. D4#6819semidirect
540. C5#83482semidirect
563. C3#10615213semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D422
#117563142
#117513182
C2×#911162
#117511732
#117511712
#117511392
#117511342
C4×#67152
D4×C3⋊#1682
#117511082
#106152133
#834825