Finite Group Databasebeta

← #14458358

Subgroups — #14458358

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#11756314C211yesmaximal, characteristic, complemented
2C3×D4×D20C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748518C212yesmaximal, complemented
5#11748512C212yesmaximal, complemented
6#11748377C212yesmaximal, complemented
7C2×#90965C212yesmaximal, complemented
8#11747043C211yesmaximal, characteristic, complemented
9C4×#6653C211yesmaximal, characteristic, complemented
10#11746890C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10611169—31nomaximal, Hall
13C2×#6819—21no—
14C2×C3×D4×D5—21no—
15C22×C3×D20C2212yes—
16C3×C4×C5×D4C2211yescharacteristic
17#91819C2212yescomplemented
18C2×C4⋊Dic15C2212yescomplemented
19#91786—21no—
20#91775—22no—
21C4×D60C2211yescharacteristic, complemented
22#91758C2211yescharacteristic, complemented
23C22×C5×C3⋊C8C2212yescomplemented
24C3×#4076C2212yes—
25C3×#4041—21no—
26C3×#4028—22no—
27C3×#4020C2211yescharacteristic
28C3×C4×D20C2211yescharacteristic
29C2×#6653C2211yescharacteristic
30C2×#6653C2212yescomplemented
31C5×#830C2212yescomplemented
32C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
33C4×C5×C3⋊C8C2211yescharacteristic, complemented
34#90990C2211yescharacteristic, complemented
35#90990C2212yescomplemented
36#90968C2211yescharacteristic, complemented
37#90965C2211yescharacteristic
38#90965C2212yes—
39#90965C2212yescomplemented
40#90965C2212yescomplemented
41#90965C2212yescomplemented
42#83482—51nomaximal, Hall
43#65889—31no—
44D4×D20D311yescharacteristic, complemented
45C5×C8×D4—31no—
46#65404—32no—
47C2×#3953—32no—
48#65135—31no—
49#65132—31no—
50#65025—32no—
51#65021—32no—
52#64983—31no—
53C4×D40—31no—
54C23×C3×D5—22no—
55C2×C3×C5×D4D411yescharacteristic
56C22×C3×C4×C5C2312yes—
57C2×#1220—22no—
58C22×Dic15—22no—
59#6819—44no—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30—21no—
63C2×C3×C22⋊D5—22no—
64C3×D4×D5—44no—
65C2×C3×D20—24no—
66C2×C3×D20—22no—
67C2×C3×D20—21no—
68C2×C3×D20—21no—
69C2×C3×D20—42no—
70C2×C3×D20C2312yes—
71C2×C3×D20C2311yescharacteristic
72C2×C3×C4×D5—21no—
73C3×C5×C4⋊C4D411yescharacteristic
74C3×C5×C22⋊C4D412yes—
75C3×C42×C5C2311yescharacteristic
76#6714—21no—
77#6714—22no—
78C4⋊Dic15—21no—
79C4⋊Dic15—22no—
80C4⋊Dic15C2312yes—
81C4⋊Dic15C2311yescharacteristic
82C2×C5×C3⋊C8—42no—
83C2×C5×C3⋊C8C2311yescharacteristic
84C2×C5×C3⋊C8C2312yes—
85C2×C5×C3⋊C8C2311yescharacteristic
86C3×#685—21no—
87C3×#685—22no—
88C3×C4⋊Dic5C2311yescharacteristic
89#6653—22no—
90#6653—42no—
91C3×D42—51no—
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⋊C8D511yescharacteristic, complemented
101#5007—51no—
102C2×#711—61no—
103C2×D4×D5—21no—
104C22×D20C2×D312yes—
105C22×C5×C8—32no—
106C4×C5×D4C2×D311yescharacteristic
107#4076—32no—
108#4076C2×D312yes—
109C2×C4⋊Dic5—32no—
110C2×D40—31no—
111C2×D40—32no—
112#4043—61no—
113#4041—21no—
114#4032—62no—
115#4028—22no—
116#4020C2×D311yescharacteristic
117C4×D20—31no—
118C4×D20C2×D311yescharacteristic
119#4015—31no—
120C5×C4⋊C8—31no—
121C5×C22⋊C8—32no—
122C4×C5×C8—31no—
123#3953—32no—
124#3953—32no—
125#3953—32no—
126#3953—31no—
127#3953—32no—
128#3953—31no—
129#3950—31no—
130#3950—32no—
131#3294—151noSylow
132C23×C3×C5C2×D412yes—
133C22×D15—21no—
134C22×C3×D5—21no—
135C22×C3×D5—22no—
136C22×C3×D5—44no—
137C22×C3×D5—44no—
138C22×C3×D5—82no—
139C3×C5×D4D814yescomplemented
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146#1220—44no—
147C2×Dic15—22no—
148C2×Dic15—21no—
149C2×Dic15—44no—
150D60—21no—
151D60—21no—
152C4×D15—42no—
153Dic30—42no—
154C3×C22⋊D5—44no—
155C2×C3×Dic5—21no—
156C3×D20—22no—
157C3×D20—21no—
158C3×D20—22no—
159C3×D20—44no—
160C3×D20—42no—
161C3×D20—81no—
162C3×D20#4112yescomplemented
163C3×C4×D5—42no—
164C5×C3⋊C8—21no—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—22no—
167C22×C3×D4—52no—
168C22×C3×D4—101no—
169C2×#237—101no—
170C3×#127—51no—
171C3×#121—52no—
172C3×#121—101no—
173C3×#120—102no—
174C3×C4×D4—51no—
175C3×C4×D4C2×D511yescharacteristic
176C2×#213—51no—
177C2×#213—52no—
178#930—52no—
179C2×C4⋊Dic3—52no—
180C22×C3⋊C8C2×D512yescomplemented
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#830C2×D512yescomplemented
191#809—51no—
192#807—52no—
193#807—51no—
194C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
195C4×C3⋊C8C2×D511yescharacteristic, complemented
196C23×D5—22no—
197C2×C5×D4#6711yescharacteristic
198C22×C4×C5C22×D312yes—
199C2×C22⋊D5—22no—
200C2×C22⋊D5—62no—
201C22×Dic5—62no—
202#711—124no—
203D4×D5—44no—
204C2×D20—24no—
205C2×D20—22no—
206C2×D20—21no—
207C2×D20—21no—
208C2×D20—31no—
209C2×D20—42no—
210C2×D20C22×D312yes—
211C2×D20C22×D311yescharacteristic
212C2×C4×D5—21no—
213C2×C4×D5—61no—
214C2×Dic10—61no—
215C2×C5×C8—31no—
216C2×C5×C8—32no—
217C2×C5×C8—31no—
218C2×C5×C8—122no—
219C5×C4⋊C4#6711yescharacteristic
220C5×C22⋊C4#6712yes—
221C42×C5C22×D311yescharacteristic
222#685—21no—
223#685—22no—
224#685—61no—
225#685—62no—
226C4⋊Dic5—32no—
227C4⋊Dic5—31no—
228C4⋊Dic5—61no—
229C4⋊Dic5—62no—
230C4⋊Dic5C22×D311yescharacteristic
231D40—62no—
232D40—122no—
233#547—151no—
234D42—51no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—151no—
242C8×D4—31no—
243C2×#102—152no—
244C22×C3×C5—22no—
245C22×C3×C5—22no—
246C22×C3×C5C2×D814yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—41no—
249C2×D15—41no—
250C2×D15—41no—
251C2×C3×D5—22no—
252C2×C3×D5—41no—
253C2×C3×D5—41no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5—42no—
257C2×C3×D5—88no—
258C3×C4×C5—22no—
259C3×C4×C5—21no—
260C3×C4×C5C2×D812yes—
261C3×C4×C5C2×#4111yescharacteristic
262C3×C4×C5H(5,𝔽2)11yescharacteristic
263Dic15—42no—
264Dic15—41no—
265C3×Dic5—41no—
266C24×C3—102no—
267C2×C3×D4—51no—
268C2×C3×D4—52no—
269C2×C3×D4—104no—
270C2×C3×D4—102no—
271C2×C3×D4—102no—
272C2×C3×D4—101no—
273C2×C3×D4—101no—
274C2×C3×D4—202no—
275C2×C3×D4—204no—
276C2×C3×D4D2011yescharacteristic
277C22×C3×C4—101no—
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⋊C4—51no—
286C3×C4⋊C4D2011yescharacteristic
287C3×C22⋊C4—101no—
288C3×C22⋊C4—102no—
289C3×C22⋊C4D2012yes—
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—42no—
300C2×C3⋊C8C22×D511yescharacteristic
301C2×C3⋊C8C22×D511yescharacteristic
302C2×C3⋊C8C22×D512yes—
303C23×C5C2×#6712yes—
304C22×D5—21no—
305C22×D5—22no—
306C22×D5—44no—
307C22×D5—44no—
308C22×D5—61no—
309C22×D5—82no—
310C5×D4#21314yescomplemented
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C2×#6712yes—
315C2×C4×C5C2×#6711yescharacteristic
316C2×C4×C5C23×D311yescharacteristic
317C22⋊D5—44no—
318C22⋊D5—124no—
319C2×Dic5—21no—
320C2×Dic5—62no—
321C2×Dic5—61no—
322C2×Dic5—124no—
323D20—22no—
324D20—21no—
325D20—22no—
326D20—44no—
327D20—42no—
328D20—61no—
329D20—61no—
330D20—81no—
331D20#23712yescomplemented
332C4×D5—42no—
333C4×D5—122no—
334Dic10—122no—
335C5×C8—61no—
336C5×C8—62no—
337C5×C8—61no—
338C2×#41—301no—
339C22×D4—52no—
340C22×D4—101no—
341C2×D8—151no—
342C2×D8—152no—
343C22×C8—32no—
344C4⋊Q8—151no—
345#127—51no—
346#123—302no—
347C22⋊Q8—301no—
348#121—52no—
349#121—101no—
350#121—152no—
351#120—102no—
352C4×D4—51no—
353C4×D4—151no—
354C4×D4D3×D511yescharacteristic
355C2×C4⋊C4—152no—
356#107—151no—
357#107—152no—
358C4⋊C8—31no—
359#102—151no—
360#102—151no—
361#102—152no—
362#102—152no—
363#102—152no—
364#102—152no—
365C22⋊C8—32no—
366C4×C8—31no—
367C2×C3×C5—24no—
368C2×C3×C5#54611yescharacteristic
369C2×C3×C5C22×D811yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—81no—
372C3×D5—42no—
373C3×D5—82no—
374C23×C3—101no—
375C23×C3—102no—
376C23×C3—204no—
377C23×C3—204no—
378C23×C3—402no—
379C23×C3C2×D2012yes—
380C22×D3—101no—
381C3×D4—52no—
382C3×D4—101no—
383C3×D4—102no—
384C3×D4—102no—
385C3×D4—204no—
386C3×D4—204no—
387C3×D4—202no—
388C3×D4—401no—
389C3×D4D4014yescomplemented
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—101no—
393C2×C3×C4—202no—
394C2×C3×C4C2×D2011yescharacteristic
395C2×C3×C4C2×D2012yes—
396C2×C3×C4C2×D2011yescharacteristic
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—21no—
407C3⋊C8—22no—
408C3⋊C8—21no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5C2×#21314yes—
412C22×C5C22×#6711yescharacteristic
413C2×D5—22no—
414C2×D5—41no—
415C2×D5—41no—
416C2×D5—42no—
417C2×D5—42no—
418C2×D5—42no—
419C2×D5—88no—
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—121no—
423C4×C5—22no—
424C4×C5—21no—
425C4×C5C2×#21312yes—
426C4×C5C2×#23711yescharacteristic
427C4×C5#100411yescharacteristic
428Dic5—41no—
429Dic5—122no—
430Dic5—121no—
431C24—102no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—51no—
435C2×D4—52no—
436C2×D4—104no—
437C2×D4—102no—
438C2×D4—102no—
439C2×D4—101no—
440C2×D4—101no—
441C2×D4—151no—
442C2×D4—202no—
443C2×D4—204no—
444C2×D4—302no—
445C2×D4#120211yescharacteristic
446C22×C4—101no—
447C22×C4—302no—
448C22×C4—301no—
449C22×C4C2×D3×D512yes—
450D8—302no—
451D8—602no—
452C2×C8—31no—
453C2×C8—31no—
454C2×C8—32no—
455C2×C8—122no—
456C4⋊C4—51no—
457C4⋊C4—151no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—301no—
461C4⋊C4#120211yescharacteristic
462C22⋊C4—101no—
463C22⋊C4—102no—
464C22⋊C4—301no—
465C22⋊C4—302no—
466C22⋊C4#120212yes—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—102no—
472C22×C3—201no—
473C22×C3—201no—
474C22×C3—202no—
475C22×C3—202no—
476C22×C3—202no—
477C22×C3—408no—
478C22×C3C2×D4014yes—
479C22×C3C22×D2011yescharacteristic
480C2×D3—201no—
481C2×D3—201no—
482C2×D3—201no—
483C3×C4—21no—
484C3×C4—22no—
485C3×C4—201no—
486C3×C4C2×D4012yes—
487C3×C4#414411yescharacteristic
488C3×C4D5×#4111yescharacteristic
489Dic3—202no—
490Dic3—201no—
491C2×C5—24no—
492C2×C5C22×#21311yescharacteristic
493C2×C5#580611yescharacteristic
494C2×C5#583611yescharacteristic
495D5—42no—
496D5—82no—
497D5—241no—
498C23—101no—
499C23—102no—
500C23—204no—
501C23—204no—
502C23—301no—
503C23—402no—
504C23C2×#120212yes—
505Q8—602no—
506D4—52no—
507D4—102no—
508D4—101no—
509D4—102no—
510D4—204no—
511D4—204no—
512D4—202no—
513D4—301no—
514D4—301no—
515D4—401no—
516D4—604no—
517D4#665314yescomplemented
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—101no—
521C2×C4—202no—
522C2×C4—301no—
523C2×C4—302no—
524C2×C4—604no—
525C2×C4—602no—
526C2×C4C2×#120211yescharacteristic
527C2×C4C2×#120212yes—
528C2×C4C2×#120211yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—61no—
531C8—61no—
532C8—62no—
533C2×C3—24no—
534C2×C3—202no—
535C2×C3—402no—
536C2×C3#6588811yescharacteristic
537C2×C3C22×D4011yescharacteristic
538C2×C3#6608511yescharacteristic
539D3—401no—
540C5#8348211yescharacteristic, complemented, Sylow
541C22—22no—
542C22—22no—
543C22—102no—
544C22—201no—
545C22—201no—
546C22—202no—
547C22—202no—
548C22—202no—
549C22—408no—
550C22—601no—
551C22—601no—
552C22—601no—
553C22C2×#665314yes—
554C22C22×#120211yescharacteristic
555C4—21no—
556C4—22no—
557C4—201no—
558C4—601no—
559C4—602no—
560C4C2×#665312yes—
561C4D5×#23711yescharacteristic
562C4#9202511yescharacteristic
563C3#1061116911yescharacteristic, complemented, Sylow
564C2—24no—
565C2—202no—
566C2—402no—
567C2—1201no—
568C2C22×#665311yescharacteristic
569C2#1175496311yescharacteristic
570C2#1175530911yescharacteristic
subgroupG/H
centerC22C22×#1202
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 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756314C2semidirect
2. C3×D4×D20C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748518C2semidirect
5. #11748512C2semidirect
6. #11748377C2semidirect
7. C2×#90965C2semidirect
8. #11747043C2semidirect
9. C4×#6653C2semidirect
10. #11746890C2semidirect
11. #11746889C2semidirect
17. #91819C22semidirect
18. C2×C4⋊Dic15C22semidirect
21. C4×D60C22semidirect
22. #91758C22semidirect
23. C22×C5×C3⋊C8C22semidirect
30. C2×#6653C22semidirect
31. C5×#830C22semidirect
32. C5×C4⋊(C3⋊C8)C22semidirect
33. C4×C5×C3⋊C8C22semidirect
34. #90990C22semidirect
35. #90990C22semidirect
36. #90968C22semidirect
39. #90965C22semidirect
40. #90965C22semidirect
41. #90965C22semidirect
44. D4×D20D3semidirect
100. D4×C3⋊C8D5semidirect
139. C3×C5×D4D8semidirect
162. C3×D20#41semidirect
180. C22×C3⋊C8C2×D5semidirect
190. #830C2×D5semidirect
194. C4⋊(C3⋊C8)C2×D5semidirect
195. C4×C3⋊C8C2×D5semidirect
310. C5×D4#213semidirect
331. D20#237semidirect
389. C3×D4D40semidirect
468. C3×C5#3294semidirect
517. D4#6653semidirect
540. C5#83482semidirect
563. C3#10611169semidirect

Maximal subgroups

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

subgroupindex
#117563142
C3×D4×D202
C5×D4×C3⋊C82
#117485182
#117485122
#117483772
C2×#909652
#117470432
C4×#66532
#117468902
#117468892
#106111693
#834825