Finite Group Databasebeta

← #14458395

Subgroups — #14458395

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
1D12×D20C211yesmaximal, characteristic, complemented
2#11752533C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic, complemented
4C5×#4846C211yesmaximal, characteristic, complemented
5C3×#65123C211yesmaximal, characteristic, complemented
6#11748117C212yesmaximal, complemented
7D5×#821C212yesmaximal, complemented
8#11747899C212yesmaximal, complemented
9#11747616C212yesmaximal, complemented
10C4×#6654C211yesmaximal, characteristic, complemented
11#11746912C211yesmaximal, characteristic, complemented
12#10612711—31nomaximal, Hall
13C2×D3×D20—21no—
14C2×D5×D12C2212yes—
15C2×#6766—21no—
16C2×D120C2212yescomplemented
17#91763C2211yescharacteristic
18C4×D60C2211yescharacteristic, complemented
19C4×C5×D12C2211yescharacteristic
20C5×#869C2211yescharacteristic, complemented
21C2×C3×C8×D5C2212yescomplemented
22C3×C4×D20C2211yescharacteristic
23#91476—22no—
24#91460—21no—
25#91450C2212yes—
26#91450C2212yescomplemented
27#91413—22no—
28D5×C4⋊Dic3C2212yescomplemented
29#91383—21no—
30C2×#6654C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic, complemented
32#91105C2212yescomplemented
33C5×#821C2212yes—
34C5×#818C2212yescomplemented
35C3×#3952C2212yescomplemented
36C3×C4×#168C2211yescharacteristic, complemented
37#90988C2211yescharacteristic, complemented
38#90969C2212yescomplemented
39#90969C2212yescomplemented
40#90969C2211yescharacteristic, complemented
41#90967C2211yescharacteristic
42#79438—51nomaximal, Hall
43#66060—31no—
44D4×D20—31no—
45C5×#474—31no—
46#65377—31no—
47C4×#686—31no—
48#65172—32no—
49#65171—32no—
50#65132—31no—
51#65123D311yescharacteristic, complemented
52#65062—32no—
53D5×#102—32no—
54C22×D3×D5—22no—
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×D60C2311yescharacteristic
59C2×C4×D15—21no—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C5×Dic6—21no—
63C2×C3×D20D411yescharacteristic
64C2×C3×C4×D5C2312yes—
65C2×#1203—22no—
66C2×#1202—22no—
67C2×#1202—22no—
68C2×D5×Dic3—22no—
69D3×D20—44no—
70D5×D12—24no—
71D5×D12—42no—
72#6766—44no—
73C2×C3×C5×C8C2312yes—
74C3×C42×C5C2311yescharacteristic
75#6714—21no—
76C4⋊Dic15C2311yescharacteristic
77D120—42no—
78C5×(C2×D3)⋊C4—21no—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2312yes—
81C5×C4⋊Dic3C2311yescharacteristic
82C3×#685D412yes—
83C3×C4⋊Dic5D411yescharacteristic
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2311yescharacteristic
86C3×C8×D5—42no—
87#6668—22no—
88#6667—22no—
89#6667—22no—
90#6654—22no—
91#5555—51no—
92D4×D12—51no—
93C3×C8×D4—51no—
94#5115—52no—
95C2×#821—52no—
96#4846D511yescharacteristic, complemented
97#4843—51no—
98#4736—52no—
99#4732—52no—
100#4694—51no—
101C4×D24—51no—
102C2×#713—61no—
103C2×D4×D5—32no—
104C22×D20—61no—
105C5×C4⋊Q8—31no—
106C4×C5×D4—31no—
107#4092—61no—
108C2×#686—31no—
109#4076—61no—
110C2×D40—32no—
111C2×C8×D5C2×D312yescomplemented
112#4041—32no—
113#4041—32no—
114#4040—62no—
115D5×C4⋊C4—32no—
116#4028—62no—
117#4020—31no—
118C4×D20—31no—
119C4×D20C2×D311yescharacteristic
120C5×#107—32no—
121C5×C4⋊C8C2×D311yescharacteristic, complemented
122C5×#102—32no—
123#3964—31no—
124#3953—32no—
125#3952C2×D312yescomplemented
126#3941—31no—
127#3941—32no—
128#3941—32no—
129#3939—31no—
130C4×#168C2×D311yescharacteristic, complemented
131#3294—151noSylow
132C22×D15—21no—
133C22×D15—22no—
134C22×C5×D3—21no—
135C22×C3×D5C2×D412yes—
136C2×D3×D5—44no—
137C2×D3×D5—44no—
138C2×D3×D5—82no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143D60—22no—
144D60—21no—
145D60—21no—
146D60—22no—
147D60—42no—
148D60—81no—
149C4×D15—42no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C5×D12—21no—
153C5×D12#4112yescomplemented
154C4×C5×D3—42no—
155C5×Dic6—42no—
156C2×C3×Dic5C2×D412yes—
157C3×D20D814yescomplemented
158C3×C4×D5—22no—
159C3×C4×D5—22no—
160#1203—44no—
161#1202—44no—
162#1202—44no—
163D5×Dic3—44no—
164C3×C5×C8—22no—
165C3×#168—21no—
166C3×#168—21no—
167C2×#237—101no—
168C2×D3×D4—101no—
169C22×D12—52no—
170C22×C3×C8—52no—
171C3×C4×D4—51no—
172#930—52no—
173#930—52no—
174C2×C4⋊Dic3—52no—
175C2×D24—51no—
176C2×D24—52no—
177#897—101no—
178#895—101no—
179#886—102no—
180#882—102no—
181#874—51no—
182C4×D12—51no—
183C4×D12C2×D511yescharacteristic
184#869C2×D511yescharacteristic, complemented
185C3×C4⋊C8C2×D511yescharacteristic, complemented
186C3×C22⋊C8—52no—
187C3×C4×C8—51no—
188#821—51no—
189#821—52no—
190#821—51no—
191#821—52no—
192#821—52no—
193#821C2×D512yes—
194#818—51no—
195#818C2×D512yescomplemented
196C23×D5—62no—
197C2×C5×Q8—61no—
198C2×C5×D4—31no—
199C22×C4×C5—61no—
200C2×C22⋊D5—62no—
201#713—124no—
202D4×D5—64no—
203D4×D5—122no—
204C2×D20—32no—
205C2×D20—31no—
206C2×D20—62no—
207C2×D20—62no—
208C2×D20—61no—
209C2×D20—61no—
210C2×D20—124no—
211C2×D20D1211yescharacteristic
212C2×C4×D5—62no—
213C2×C4×D5—61no—
214C2×C4×D5C22×D312yes—
215C2×C5×C8C22×D312yes—
216C5×C4⋊C4—31no—
217C5×C4⋊C4—32no—
218C5×C4⋊C4—61no—
219C5×C22⋊C4—61no—
220C42×C5C22×D311yescharacteristic
221#686—62no—
222#685—61no—
223#685—62no—
224#685—62no—
225#685D1212yes—
226C4⋊Dic5—31no—
227C4⋊Dic5D1211yescharacteristic
228#683—62no—
229C2×#168C22×D311yescharacteristic
230C2×#168C22×D311yescharacteristic
231D40—122no—
232C8×D5—42no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—31no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—151no—
242C8×D4—51no—
243C2×#102—152no—
244C22×C3×C5C22×D411yescharacteristic
245C2×D15—42no—
246C2×D15—41no—
247C2×D15—41no—
248C2×D15—42no—
249C2×D15—42no—
250C2×D15—41no—
251C2×C5×D3—22no—
252C2×C5×D3—41no—
253C2×C5×D3—41no—
254C2×C3×D5—22no—
255C2×C3×D5—22no—
256C2×C3×D5C2×D814yes—
257D3×D5—88no—
258C3×C4×C5—21no—
259C3×C4×C5C2×D812yes—
260C3×C4×C5C2×#4111yescharacteristic
261C3×C4×C5H(5,𝔽2)11yescharacteristic
262Dic15—41no—
263C3×Dic5—22no—
264C5×Dic3—42no—
265C5×Dic3—41no—
266C23×D3—102no—
267C2×C3×D4—51no—
268C22×C3×C4—52no—
269C2×#67—102no—
270C2×#67—102no—
271C22×Dic3—102no—
272#237—204no—
273D3×D4—204no—
274C2×D12—52no—
275C2×D12—51no—
276C2×D12—104no—
277C2×D12—102no—
278C2×D12—101no—
279C2×D12—101no—
280C2×D12—202no—
281C2×D12C22×D511yescharacteristic
282C2×C4×D3—21no—
283C2×C4×D3—101no—
284C2×Dic6—21no—
285C2×C3×C8—51no—
286C2×C3×C8—51no—
287C2×C3×C8—202no—
288C2×C3×C8C22×D512yes—
289C3×C4⋊C4—51no—
290C3×C22⋊C4—52no—
291C3×C42C22×D511yescharacteristic
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—102no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—101no—
296C4⋊Dic3—21no—
297C4⋊Dic3—51no—
298C4⋊Dic3—102no—
299C4⋊Dic3C22×D511yescharacteristic
300C4⋊Dic3C22×D512yes—
301D24—102no—
302D24—202no—
303C23×C5—61no—
304C22×D5—61no—
305C22×D5—62no—
306C22×D5—124no—
307C22×D5—124no—
308C22×D5—242no—
309C22×D5C2×D1212yes—
310C5×Q8—122no—
311C5×D4—32no—
312C5×D4—61no—
313C2×C4×C5—62no—
314C2×C4×C5—61no—
315C2×C4×C5—122no—
316C2×C4×C5C2×D1211yescharacteristic
317C2×C4×C5C2×D1211yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C22⋊D5—124no—
320C2×Dic5—61no—
321C2×Dic5C2×D1212yes—
322D20—61no—
323D20—62no—
324D20—61no—
325D20—62no—
326D20—124no—
327D20—124no—
328D20—122no—
329D20—241no—
330D20D2414yescomplemented
331C4×D5—22no—
332C4×D5—22no—
333C4×D5—124no—
334C4×D5—122no—
335C5×C8—22no—
336#168—21no—
337#168—21no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—151no—
342C2×D8—152no—
343C22×C8—52no—
344C4⋊Q8—31no—
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—51no—
354C4×D4—151no—
355C2×C4⋊C4—152no—
356#107—32no—
357#107—151no—
358C4⋊C8D3×D511yescharacteristic, complemented
359#102—32no—
360#102—152no—
361#102—151no—
362#102—152no—
363#102—151no—
364#102—152no—
365C22⋊C8—52no—
366C4×C8—51no—
367C2×C3×C5#54611yescharacteristic
368C2×C3×C5C22×D811yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—82no—
371D15—81no—
372C3×D5—24no—
373C5×D3—42no—
374C23×C3—52no—
375C22×D3—21no—
376C22×D3—101no—
377C22×D3—102no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×D4—54no—
382C2×C3×C4—52no—
383C2×C3×C4—102no—
384C2×C3×C4—102no—
385C2×C3×C4D4×D511yescharacteristic
386C2×C3×C4D4×D511yescharacteristic
387C2×C3×C4C23×D511yescharacteristic
388#67—204no—
389#67—204no—
390C2×Dic3—22no—
391C2×Dic3—21no—
392C2×Dic3—101no—
393C2×Dic3—204no—
394D12—21no—
395D12—101no—
396D12—102no—
397D12—101no—
398D12—102no—
399D12—204no—
400D12—202no—
401D12—401no—
402D12#71312yescomplemented
403C4×D3—42no—
404C4×D3—202no—
405Dic6—42no—
406C3×C8—22no—
407C3×C8—101no—
408C3×C8—101no—
409C22×C5—62no—
410C22×C5—121no—
411C22×C5—121no—
412C22×C5C22×D1211yescharacteristic
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—121no—
416C2×D5—122no—
417C2×D5—122no—
418C2×D5—121no—
419C2×D5—122no—
420C2×D5—121no—
421C2×D5—248no—
422C2×D5C2×D2414yes—
423C4×C5—21no—
424C4×C5—122no—
425C4×C5—121no—
426C4×C5C2×D2412yes—
427C4×C5#100411yescharacteristic
428C4×C5D3×#4111yescharacteristic
429Dic5—22no—
430Dic5—121no—
431C24—302no—
432#41—604no—
433C2×Q8—61no—
434C2×D4—31no—
435C2×D4—51no—
436C2×D4—152no—
437C2×D4—151no—
438C2×D4—302no—
439C2×D4—302no—
440C2×D4—302no—
441C2×D4—304no—
442C2×D4—301no—
443C2×D4—301no—
444C2×D4—602no—
445C2×D4—604no—
446C22×C4—52no—
447C22×C4—61no—
448C22×C4—302no—
449C22×C4—301no—
450D8—302no—
451D8—602no—
452C2×C8—51no—
453C2×C8—51no—
454C2×C8—202no—
455C2×C8C2×D3×D512yes—
456C4⋊C4—32no—
457C4⋊C4—31no—
458C4⋊C4—51no—
459C4⋊C4—61no—
460C4⋊C4—151no—
461C4⋊C4—302no—
462C22⋊C4—52no—
463C22⋊C4—61no—
464C22⋊C4—302no—
465C22⋊C4—302no—
466C22⋊C4—301no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—54no—
470C22×C3—102no—
471C22×C3—102no—
472C22×C3C2×D4×D511yescharacteristic
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—201no—
477C2×D3—202no—
478C2×D3—202no—
479C2×D3—201no—
480C2×D3—202no—
481C2×D3—201no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—102no—
485C3×C4D5×D812yes—
486C3×C4C2×#71311yescharacteristic
487C3×C4#414911yescharacteristic
488Dic3—42no—
489Dic3—41no—
490Dic3—201no—
491C2×C5—122no—
492C2×C5#555411yescharacteristic
493C2×C5C22×D2411yescharacteristic
494C2×C5#575111yescharacteristic
495D5—24no—
496D5—242no—
497D5—241no—
498C23—52no—
499C23—61no—
500C23—301no—
501C23—302no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—122no—
506D4—32no—
507D4—54no—
508D4—61no—
509D4—301no—
510D4—302no—
511D4—301no—
512D4—302no—
513D4—604no—
514D4—604no—
515D4—604no—
516D4—602no—
517D4—1201no—
518C2×C4—52no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—122no—
524C2×C4—301no—
525C2×C4—604no—
526C2×C4—602no—
527C2×C4D5×D1211yescharacteristic
528C2×C4D5×D1211yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—22no—
531C8—101no—
532C8—101no—
533C2×C3—104no—
534C2×C3#6596411yescharacteristic
535C2×C3C2×D5×D811yescharacteristic
536C2×C3#6611211yescharacteristic
537D3—42no—
538D3—402no—
539D3—401no—
540C5#7943811yescharacteristic, complemented, Sylow
541C22—54no—
542C22—62no—
543C22—102no—
544C22—102no—
545C22—121no—
546C22—121no—
547C22—602no—
548C22—601no—
549C22—602no—
550C22—601no—
551C22—601no—
552C22—602no—
553C22—1208no—
554C22C2×D5×D1211yescharacteristic
555C4—21no—
556C4—102no—
557C4—121no—
558C4—122no—
559C4—601no—
560C4D5×D2412yes—
561C4#9202611yescharacteristic
562C4D3×#71311yescharacteristic
563C3#1061271111yescharacteristic, complemented, Sylow
564C2—104no—
565C2—122no—
566C2—1202no—
567C2—1201no—
568C2#1175387611yescharacteristic
569C2C2×D5×D2411yescharacteristic
570C2#1175402511yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. D12×D20C2semidirect
2. #11752533C2semidirect
3. #11750944C2semidirect
4. C5×#4846C2semidirect
5. C3×#65123C2semidirect
6. #11748117C2semidirect
7. D5×#821C2semidirect
8. #11747899C2semidirect
9. #11747616C2semidirect
10. C4×#6654C2semidirect
11. #11746912C2semidirect
16. C2×D120C22semidirect
18. C4×D60C22semidirect
20. C5×#869C22semidirect
21. C2×C3×C8×D5C22semidirect
26. #91450C22semidirect
28. D5×C4⋊Dic3C22semidirect
31. C3×C5×C4⋊C8C22semidirect
32. #91105C22semidirect
34. C5×#818C22semidirect
35. C3×#3952C22semidirect
36. C3×C4×#168C22semidirect
37. #90988C22semidirect
38. #90969C22semidirect
39. #90969C22semidirect
40. #90969C22semidirect
51. #65123D3semidirect
96. #4846D5semidirect
111. C2×C8×D5C2×D3semidirect
121. C5×C4⋊C8C2×D3semidirect
125. #3952C2×D3semidirect
130. C4×#168C2×D3semidirect
153. C5×D12#41semidirect
157. C3×D20D8semidirect
184. #869C2×D5semidirect
185. C3×C4⋊C8C2×D5semidirect
195. #818C2×D5semidirect
330. D20D24semidirect
358. C4⋊C8D3×D5semidirect
402. D12#713semidirect
468. C3×C5#3294semidirect
540. C5#79438semidirect
563. C3#10612711semidirect

Maximal subgroups

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

subgroupindex
D12×D202
#117525332
#117509442
C5×#48462
C3×#651232
#117481172
D5×#8212
#117478992
#117476162
C4×#66542
#117469122
#106127113
#794385