Finite Group Databasebeta

← #14471472

Subgroups — #14471472

Order 1920.

852 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic10C211yesmaximal, characteristic, complemented
2#11752536C211yesmaximal, characteristic, complemented
3C4×#6715C211yesmaximal, characteristic, complemented
4C5×#5015C211yesmaximal, characteristic, complemented
5#11749092C212yesmaximal, complemented
6Dic5×#213C212yesmaximal, complemented
7#11747237C212yesmaximal, complemented
8#11747138C212yesmaximal, complemented
9#11746971C211yesmaximal, characteristic, complemented
10#11746901C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612049—31nomaximal, Hall
13C22×C3×Dic10—21no—
14C2×#6768—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C2×#6715C2211yescharacteristic
17C4×D60C2211yescharacteristic
18C2×C5×#213C2212yes—
19C5×#874C2211yescharacteristic
20C3×D4×Dic5C2212yes—
21C3×#4070—21no—
22C3×#4034C2212yes—
23C3×#4024—22no—
24C3×#4015C2211yescharacteristic
25C3×C4×Dic10C2211yescharacteristic
26#91466—21no—
27#91451C2212yes—
28#91416—22no—
29Dic5×D12C2212yes—
30#91116C2211yescharacteristic
31#91093C2211yescharacteristic
32#91091C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#809C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36#90990C2212yes—
37#90982C2212yes—
38#90968C2212yes—
39#90966C2212yes—
40#90966C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83562—51nomaximal, Hall
43#66052—31no—
44D4×Dic10D311yescharacteristic, complemented
45C5×#459—31no—
46#65439—32no—
47D8×Dic5—32no—
48#65359—31no—
49C4×#686—31no—
50#65135—31no—
51#65119—31no—
52#65049—32no—
53#65048—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C5×D12—21no—
59C2×C5×D12—21no—
60C2×C5×D12C2312yes—
61C22×C3×Dic5—22no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—22no—
64C2×C3×Dic10—44no—
65C2×C3×Dic10D411yescharacteristic
66C2×#1203—22no—
67C2×#1203—22no—
68C2×D3×Dic5—22no—
69#6768—44no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73#6715—22no—
74#6714—21no—
75C4⋊Dic15C2311yescharacteristic
76C2×C3⋊#168C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C5×#213—24no—
79C2×C5×C3⋊C8C2312yes—
80C3×C22⋊Dic5—22no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5D411yescharacteristic
83C3×C4⋊Dic5C2312yes—
84C3×#683—22no—
85C3×#683D412yes—
86C3×C4×Dic5C2312yes—
87(C2×D3)⋊Dic5—22no—
88C3×D4×Q8—51no—
89#5577—51no—
90#5088—51no—
91#5088—52no—
92#5087—52no—
93#5087—51no—
94Q8×C3⋊C8—51no—
95#5015—52no—
96#5015D511yescharacteristic, complemented
97C4×#213—51no—
98C4×#213—52no—
99C2×#711—61no—
100C22×Dic10—21no—
101C2×C5×D8—32no—
102C5×#127—31no—
103C4×C5×D4C2×D311yescharacteristic
104#4086—32no—
105#4085—62no—
106#4084—61no—
107D4×Dic5—32no—
108D4×Dic5C2×D312yes—
109C2×#686—31no—
110#4070—21no—
111#4034C2×D312yes—
112#4024—22no—
113C4×D20—31no—
114#4015C2×D311yescharacteristic
115C4×Dic10C2×D311yescharacteristic
116C5×C4⋊C8—31no—
117C5×#102—32no—
118#3964—31no—
119#3964—32no—
120#3964—32no—
121#3953—32no—
122#3950—32no—
123#3946—32no—
124C8×Dic5—32no—
125#3941—31no—
126#3939—31no—
127C4×#168—31no—
128#3358—151noSylow
129C23×C3×C5—21no—
130C22×D15—21no—
131C22×C5×D3—22no—
132C3×C5×D4—21no—
133C3×C5×D4#4112yescomplemented
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140D60—21no—
141D60—21no—
142C4×D15—42no—
143C5×D12—22no—
144C5×D12—22no—
145C5×D12—42no—
146C5×D12—81no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—44no—
149C2×C3×Dic5C2×D412yes—
150C2×C3×Dic5C2×D412yes—
151C3×Dic10—42no—
152C3×Dic10—44no—
153C3×Dic10D814yescomplemented
154#1203—44no—
155#1203—82no—
156D3×Dic5—44no—
157C3⋊#168—21no—
158C3⋊#168—21no—
159C5×C3⋊C8—22no—
160C22×C3×Q8—101no—
161C2×#239—101no—
162C3×C4⋊Q8—52no—
163C3×C4⋊Q8—51no—
164C3×C22⋊Q8—102no—
165C3×C22⋊Q8—101no—
166C3×C4×Q8—51no—
167C3×C4×D4—52no—
168C3×C4×D4C2×D511yescharacteristic
169C2×#213—51no—
170C2×#213C2×D512yes—
171#895—102no—
172#895—101no—
173#874—52no—
174#874C2×D511yescharacteristic
175C4×D12—52no—
176C4×D12—51no—
177#832—51no—
178#809—52no—
179#809—52no—
180#809—51no—
181#809—52no—
182#809C2×D512yes—
183#807—51no—
184#807—52no—
185C4⋊(C3⋊C8)—52no—
186C4⋊(C3⋊C8)C2×D511yescharacteristic
187C4×C3⋊C8—51no—
188C4×C3⋊C8—52no—
189C2×C5×D4—32no—
190C2×C5×D4—61no—
191C2×C5×D4—61no—
192C2×C5×D4C22×D311yescharacteristic
193C22×C4×C5—21no—
194C2×C22⋊D5—62no—
195C2×C22⋊D5—62no—
196C22×Dic5—22no—
197C22×Dic5—62no—
198#711—124no—
199C2×D20—31no—
200C2×C4×D5—61no—
201C2×Dic10—21no—
202C2×Dic10—22no—
203C2×Dic10—44no—
204C2×Dic10#6711yescharacteristic
205C5×D8—64no—
206C2×C5×C8—32no—
207C5×C4⋊C4C22×D311yescharacteristic
208C5×C22⋊C4—21no—
209C42×C5C22×D311yescharacteristic
210C22⋊Dic5—22no—
211C22⋊Dic5—62no—
212#686—62no—
213#685—61no—
214C4⋊Dic5—21no—
215C4⋊Dic5—31no—
216C4⋊Dic5#6711yescharacteristic
217C4⋊Dic5C22×D312yes—
218#683—22no—
219#683#6712yes—
220C4×Dic5C22×D312yes—
221C2×#168—31no—
222C2×#168—31no—
223#550—151no—
224D4×Q8—51no—
225#486—152no—
226#486—151no—
227#474—152no—
228#474—151no—
229#459—31no—
230#459—152no—
231C8×Q8—151no—
232C4×D8—152no—
233C4×D8—151no—
234C22×C3×C5—22no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—41no—
239C2×D15—41no—
240C2×D15—41no—
241C2×C5×D3—42no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5C2×D812yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C52−1+411yescharacteristic
249Dic15—41no—
250C3×Dic5—22no—
251C3×Dic5—42no—
252C3×Dic5C2×D814yes—
253C2×C3×Q8—51no—
254C2×C3×Q8—102no—
255C2×C3×Q8—101no—
256C2×C3×Q8—204no—
257C2×C3×D4C22×D511yescharacteristic
258C22×C3×C4—21no—
259C22×C3×C4—102no—
260#239—204no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—51no—
264C2×D12—102no—
265C2×D12—102no—
266C2×D12C22×D512yes—
267C2×C4×D3—102no—
268C2×C4×D3—101no—
269C3×C4⋊C4—52no—
270C3×C4⋊C4—51no—
271C3×C4⋊C4—52no—
272C3×C4⋊C4—102no—
273C3×C4⋊C4—101no—
274C3×C4⋊C4C22×D511yescharacteristic
275C3×C22⋊C4—21no—
276C3×C22⋊C4—102no—
277C3×C42—52no—
278C3×C42C22×D511yescharacteristic
279#213—24no—
280#213—102no—
281(C2×D3)⋊C4—102no—
282(C2×D3)⋊C4—101no—
283C4⋊Dic3—51no—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8C22×D512yes—
287C23×C5—21no—
288C23×C5—62no—
289C22×D5—61no—
290C5×D4—21no—
291C5×D4—62no—
292C5×D4—62no—
293C5×D4—122no—
294C5×D4—241no—
295C5×D4#23912yescomplemented
296C2×C4×C5—21no—
297C2×C4×C5—42no—
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C2×#6711yescharacteristic
300C2×C4×C5C23×D311yescharacteristic
301C22⋊D5—124no—
302C22⋊D5—242no—
303C2×Dic5—22no—
304C2×Dic5—44no—
305C2×Dic5—61no—
306C2×Dic5—124no—
307C2×Dic5C2×#6712yes—
308C2×Dic5C2×#6712yes—
309D20—61no—
310D20—61no—
311C4×D5—122no—
312Dic10—42no—
313Dic10—44no—
314Dic10#21314yescomplemented
315C5×C8—62no—
316#168—61no—
317#168—61no—
318C2×#41—301no—
319C22×Q8—101no—
320C2×D8—32no—
321C2×D8—151no—
322C4⋊Q8—52no—
323C4⋊Q8—51no—
324#127—31no—
325#127—152no—
326C22⋊Q8—102no—
327C22⋊Q8—101no—
328#121—301no—
329#121—302no—
330C4×Q8—51no—
331C4×D4—52no—
332C4×D4—152no—
333C4×D4—151no—
334C4×D4D3×D511yescharacteristic
335#107—152no—
336#107—151no—
337C4⋊C8—31no—
338C4⋊C8—152no—
339#102—32no—
340#102—152no—
341#102—152no—
342#102—152no—
343#102—151no—
344#102—151no—
345C4×C8—152no—
346C4×C8—151no—
347C2×C3×C5—42no—
348C2×C3×C5#54811yescharacteristic
349C2×C3×C5C22×D811yescharacteristic
350C2×C3×C5#57711yescharacteristic
351D15—81no—
352C5×D3—82no—
353C23×C3—21no—
354C22×D3—22no—
355C22×D3—101no—
356C3×Q8—54no—
357C3×Q8—204no—
358C3×Q8—202no—
359C3×D4—21no—
360C3×D4#71112yescomplemented
361C2×C3×C4—21no—
362C2×C3×C4—42no—
363C2×C3×C4—52no—
364C2×C3×C4—52no—
365C2×C3×C4—102no—
366C2×C3×C4—204no—
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4C23×D511yescharacteristic
370C2×Dic3—101no—
371D12—22no—
372D12—22no—
373D12—42no—
374D12—81no—
375D12—101no—
376D12—101no—
377D12—204no—
378D12—402no—
379C4×D3—204no—
380C4×D3—202no—
381C3⋊C8—22no—
382C3⋊C8—101no—
383C3⋊C8—101no—
384C22×C5—22no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5—122no—
388C22×C5—122no—
389C22×C5—122no—
390C22×C5C22×#6711yescharacteristic
391C2×D5—121no—
392C2×D5—121no—
393C2×D5—121no—
394C4×C5—21no—
395C4×C5—41no—
396C4×C5C2×#21312yes—
397C4×C5C2×#23911yescharacteristic
398C4×C5#100711yescharacteristic
399Dic5—22no—
400Dic5—42no—
401Dic5—121no—
402Dic5C2×#21314yes—
403#41—604no—
404C2×Q8—51no—
405C2×Q8—102no—
406C2×Q8—101no—
407C2×Q8—204no—
408C2×D4—32no—
409C2×D4—61no—
410C2×D4—61no—
411C2×D4—151no—
412C2×D4—302no—
413C2×D4—302no—
414C2×D4C2×D3×D511yescharacteristic
415C22×C4—21no—
416C22×C4—102no—
417C22×C4—302no—
418C22×C4—301no—
419D8—64no—
420D8—302no—
421C2×C8—32no—
422C2×C8—151no—
423C2×C8—151no—
424C4⋊C4—52no—
425C4⋊C4—51no—
426C4⋊C4—52no—
427C4⋊C4—102no—
428C4⋊C4—101no—
429C4⋊C4—151no—
430C4⋊C4C2×D3×D511yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—102no—
433C22⋊C4—302no—
434C22⋊C4—301no—
435C42—52no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3—22no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3C2×D4×D511yescharacteristic
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—201no—
446C2×D3—201no—
447C2×D3—201no—
448C3×C4—21no—
449C3×C4—41no—
450C3×C4—54no—
451C3×C4—102no—
452C3×C4—202no—
453C3×C4D5×D812yes—
454C3×C4C2×#71111yescharacteristic
455C3×C4#415011yescharacteristic
456Dic3—201no—
457C2×C5—42no—
458C2×C5—242no—
459C2×C5C22×#21311yescharacteristic
460C2×C5#581711yescharacteristic
461C2×C5#583711yescharacteristic
462D5—241no—
463C23—21no—
464C23—62no—
465C23—301no—
466Q8—54no—
467Q8—204no—
468Q8—202no—
469D4—21no—
470D4—62no—
471D4—62no—
472D4—122no—
473D4—241no—
474D4—301no—
475D4—301no—
476D4—604no—
477D4—1202no—
478D4#676812yescomplemented
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—52no—
482C2×C4—52no—
483C2×C4—102no—
484C2×C4—204no—
485C2×C4—301no—
486C2×C4—604no—
487C2×C4—602no—
488C2×C4D5×#6711yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—62no—
492C8—301no—
493C8—301no—
494C2×C3—42no—
495C2×C3#6593211yescharacteristic
496C2×C3C2×D5×D811yescharacteristic
497C2×C3#6610911yescharacteristic
498D3—82no—
499D3—401no—
500C5#8356211yescharacteristic, complemented, Sylow
501C22—22no—
502C22—41no—
503C22—41no—
504C22—122no—
505C22—122no—
506C22—122no—
507C22—601no—
508C22—601no—
509C22—601no—
510C22C2×D5×#6711yescharacteristic
511C4—21no—
512C4—41no—
513C4—54no—
514C4—102no—
515C4—202no—
516C4—601no—
517C4D5×#21312yes—
518C4C2×#676811yescharacteristic
519C4#9200411yescharacteristic
520C3#1061204911yescharacteristic, complemented, Sylow
521C2—42no—
522C2—242no—
523C2—1201no—
524C2#1175431911yescharacteristic
525C2C2×D5×#21311yescharacteristic
526C2#1175531711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3358
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. C3×D4×Dic10C2semidirect
2. #11752536C2semidirect
3. C4×#6715C2semidirect
4. C5×#5015C2semidirect
5. #11749092C2semidirect
6. Dic5×#213C2semidirect
7. #11747237C2semidirect
8. #11747138C2semidirect
9. #11746971C2semidirect
10. #11746901C2semidirect
11. #11746846C2semidirect
44. D4×Dic10D3semidirect
96. #5015D5semidirect
133. C3×C5×D4#41semidirect
153. C3×Dic10D8semidirect
295. C5×D4#239semidirect
314. Dic10#213semidirect
360. C3×D4#711semidirect
437. C3×C5#3358semidirect
478. D4#6768semidirect
500. C5#83562semidirect
520. C3#10612049semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic102
#117525362
C4×#67152
C5×#50152
#117490922
Dic5×#2132
#117472372
#117471382
#117469712
#117469012
#117468462
#106120493
#835625