Finite Group Databasebeta

← #14471451

Subgroups — #14471451

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
1#11752536C211yesmaximal, characteristic, complemented
2D12×Dic10C211yesmaximal, characteristic, complemented
3#11750947C211yesmaximal, characteristic, complemented
4C5×#4843C211yesmaximal, characteristic, complemented
5C3×#65119C211yesmaximal, characteristic, complemented
6#11747995C212yesmaximal, complemented
7#11747765C212yesmaximal, complemented
8#11747764C212yesmaximal, complemented
9Dic5×D24C212yesmaximal, complemented
10C4×#6654C211yesmaximal, characteristic, complemented
11#11746906C211yesmaximal, characteristic, complemented
12#10612049—31nomaximal, Hall
13C2×#6768—21no—
14C2×D3×Dic10—21no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C2×C5×D24C2212yes—
18C5×#874C2211yescharacteristic
19C4×C5×D12C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21#91468C2212yes—
22#91466—21no—
23#91451C2212yes—
24#91417—22no—
25#91416—22no—
26Dic5×D12C2212yes—
27Dic5×D12C2212yes—
28#91365—21no—
29C2×#6654C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91105C2212yes—
32#91102C2212yes—
33C5×#821C2212yes—
34C3×#3946C2212yes—
35C3×C8×Dic5C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90988C2211yescharacteristic
38#90969C2211yescharacteristic
39#90967C2212yes—
40#90967C2212yes—
41#90967C2211yescharacteristic
42#79924—51nomaximal, Hall
43#66052—31no—
44D4×Dic10—31no—
45C5×#459—31no—
46#65439—32no—
47D8×Dic5—32no—
48#65359—31no—
49C4×#686—31no—
50#65135—31no—
51#65119D311yescharacteristic, complemented
52#65049—32no—
53#65048—32no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30—21no—
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C3×Dic10D411yescharacteristic
63C2×#1204—22no—
64C2×#1203—22no—
65C2×#1203—22no—
66C2×D3×Dic5—22no—
67C2×D3×Dic5—22no—
68#6768—44no—
69D3×Dic10—44no—
70C2×C3×C5×C8C2312yes—
71C3×C42×C5C2311yescharacteristic
72#6714—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2311yescharacteristic
75C4⋊Dic15C2312yes—
76C5×(C2×D3)⋊C4—21no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×D24—24no—
79C3×C4⋊Dic5D411yescharacteristic
80C3×#683D412yes—
81C3×C4×Dic5C2312yes—
82C2×C3×#168C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84#6668—22no—
85(C2×D3)⋊Dic5—22no—
86(C2×D3)⋊Dic5—22no—
87#6654—22no—
88#5577—51no—
89Q8×D12—51no—
90C3×C8×Q8—51no—
91#4846—51no—
92#4846—52no—
93#4843—52no—
94#4843D511yescharacteristic, complemented
95#4694—51no—
96#4694—52no—
97C4×D24—52no—
98C4×D24—51no—
99C2×#711—61no—
100C22×Dic10—61no—
101C2×C5×D8—32no—
102C5×#127—31no—
103C4×C5×D4—31no—
104#4086—32no—
105#4085—62no—
106#4084—61no—
107D4×Dic5—32no—
108D4×Dic5—32no—
109C2×#686—31no—
110#4070—61no—
111#4034—32no—
112#4024—62no—
113C4×D20—31no—
114#4015—31no—
115C4×Dic10C2×D311yescharacteristic
116C5×C4⋊C8C2×D311yescharacteristic
117C5×#102—32no—
118#3964—31no—
119#3964—32no—
120#3964—32no—
121#3953—32no—
122#3950—32no—
123#3946C2×D312yes—
124C8×Dic5C2×D312yes—
125#3941—31no—
126#3939—31no—
127C4×#168C2×D311yescharacteristic
128#3358—151noSylow
129C22×D15—21no—
130C22×C5×D3—21no—
131C22×C5×D3—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—22no—
137D60—21no—
138D60—21no—
139C4×D15—42no—
140Dic30—42no—
141C2×C5×Dic3—21no—
142C5×D12—22no—
143C5×D12—21no—
144C5×D12—22no—
145C5×D12—42no—
146C5×D12—81no—
147C5×D12#4112yescomplemented
148C4×C5×D3—42no—
149C2×C3×Dic5C2×D412yes—
150C2×C3×Dic5C2×D412yes—
151C3×Dic10D814yescomplemented
152#1204—44no—
153#1203—44no—
154#1203—82no—
155D3×Dic5—44no—
156D3×Dic5—44no—
157C3×C5×C8—22no—
158C3×#168—21no—
159C3×#168—21no—
160C2×#239—101no—
161C2×D3×Q8—101no—
162C3×C4×Q8—51no—
163C2×D24—51no—
164C2×D24C2×D512yes—
165#897—102no—
166#897—101no—
167#895—102no—
168#895—101no—
169#874—52no—
170#874C2×D511yescharacteristic
171C4×D12—52no—
172C4×D12—52no—
173C4×D12—51no—
174C4×D12C2×D511yescharacteristic
175#869—51no—
176#869—52no—
177C3×C4⋊C8—52no—
178C3×C4⋊C8C2×D511yescharacteristic
179C3×C4×C8—52no—
180C3×C4×C8—51no—
181#821—51no—
182#821—52no—
183#821—52no—
184#821—52no—
185#821—51no—
186#821C2×D512yes—
187#818—52no—
188#818—51no—
189C2×C5×D4—31no—
190C2×C5×D4—32no—
191C2×C5×D4—61no—
192C2×C5×D4—61no—
193C22×C4×C5—61no—
194C2×C22⋊D5—62no—
195C2×C22⋊D5—62no—
196C22×Dic5—62no—
197C22×Dic5—62no—
198#711—124no—
199C2×D20—31no—
200C2×C4×D5—61no—
201C2×Dic10—61no—
202C2×Dic10—62no—
203C2×Dic10—124no—
204C2×Dic10D1211yescharacteristic
205C5×D8—64no—
206C2×C5×C8C22×D312yes—
207C5×C4⋊C4—31no—
208C5×C22⋊C4—61no—
209C42×C5C22×D311yescharacteristic
210C22⋊Dic5—62no—
211C22⋊Dic5—62no—
212#686—62no—
213#685—61no—
214C4⋊Dic5—31no—
215C4⋊Dic5—32no—
216C4⋊Dic5—61no—
217C4⋊Dic5D1211yescharacteristic
218#683—62no—
219#683D1212yes—
220C4×Dic5C22×D312yes—
221C2×#168C22×D311yescharacteristic
222C2×#168C22×D311yescharacteristic
223#550—151no—
224D4×Q8—151no—
225#486—152no—
226#486—151no—
227#474—152no—
228#474—151no—
229#459—31no—
230#459—152no—
231C8×Q8—51no—
232C4×D8—151no—
233C4×D8—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—41no—
236C2×D15—41no—
237C2×D15—41no—
238C2×C5×D3—22no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C5×D3—42no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C3×C4×C5—21no—
245C3×C4×C5C2×D812yes—
246C3×C4×C5C2×#4111yescharacteristic
247C3×C4×C52−1+411yescharacteristic
248Dic15—41no—
249Dic15—42no—
250C3×Dic5—22no—
251C3×Dic5C2×D814yes—
252C5×Dic3—41no—
253C2×C3×Q8—51no—
254#239—204no—
255D3×Q8—204no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—51no—
259C2×D12—102no—
260C2×D12—102no—
261C2×D12C22×D512yes—
262C2×D12C22×D511yescharacteristic
263C2×C4×D3—21no—
264C2×C4×D3—102no—
265C2×C4×D3—102no—
266C2×C4×D3—101no—
267C2×Dic6—102no—
268C2×Dic6—101no—
269C2×C3×C8—51no—
270C2×C3×C8—51no—
271C2×C3×C8C22×D512yes—
272C3×C4⋊C4—52no—
273C3×C4⋊C4—51no—
274C3×C42—52no—
275C3×C42C22×D511yescharacteristic
276(C2×D3)⋊C4—21no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—102no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—51no—
281C4⋊Dic3—52no—
282C4⋊Dic3—102no—
283C4⋊Dic3—101no—
284C4⋊Dic3C22×D511yescharacteristic
285D24—24no—
286D24—102no—
287C23×C5—61no—
288C23×C5—62no—
289C22×D5—61no—
290C5×D4—32no—
291C5×D4—61no—
292C5×D4—62no—
293C5×D4—62no—
294C5×D4—122no—
295C5×D4—241no—
296C2×C4×C5—61no—
297C2×C4×C5—122no—
298C2×C4×C5C2×D1211yescharacteristic
299C2×C4×C5C2×D1211yescharacteristic
300C2×C4×C5C23×D311yescharacteristic
301C22⋊D5—124no—
302C22⋊D5—242no—
303C2×Dic5—62no—
304C2×Dic5—61no—
305C2×Dic5—124no—
306C2×Dic5—124no—
307C2×Dic5C2×D1212yes—
308C2×Dic5C2×D1212yes—
309D20—61no—
310D20—61no—
311C4×D5—122no—
312Dic10—122no—
313Dic10—124no—
314Dic10D2414yescomplemented
315C5×C8—22no—
316#168—21no—
317#168—21no—
318C2×#41—301no—
319C22×Q8—301no—
320C2×D8—32no—
321C2×D8—151no—
322C4⋊Q8—152no—
323C4⋊Q8—151no—
324#127—31no—
325#127—152no—
326C22⋊Q8—302no—
327C22⋊Q8—301no—
328#121—301no—
329#121—302no—
330C4×Q8—51no—
331C4×D4—31no—
332C4×D4—152no—
333C4×D4—152no—
334C4×D4—151no—
335#107—151no—
336#107—152no—
337C4⋊C8—52no—
338C4⋊C8D3×D511yescharacteristic
339#102—32no—
340#102—151no—
341#102—151no—
342#102—152no—
343#102—152no—
344#102—152no—
345C4×C8—52no—
346C4×C8—51no—
347C2×C3×C5#54811yescharacteristic
348C2×C3×C5C22×D811yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—81no—
351C5×D3—42no—
352C5×D3—82no—
353C22×D3—21no—
354C22×D3—22no—
355C22×D3—101no—
356C3×Q8—54no—
357C2×C3×C4—52no—
358C2×C3×C4—52no—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—102no—
364C2×Dic3—101no—
365D12—22no—
366D12—21no—
367D12—22no—
368D12—42no—
369D12—81no—
370D12—101no—
371D12—101no—
372D12—204no—
373D12—402no—
374D12#71112yescomplemented
375C4×D3—42no—
376C4×D3—204no—
377C4×D3—204no—
378C4×D3—202no—
379Dic6—204no—
380Dic6—202no—
381C3×C8—22no—
382C3×C8—101no—
383C3×C8—101no—
384C22×C5—62no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5—122no—
388C22×C5—122no—
389C22×C5—122no—
390C22×C5C22×D1211yescharacteristic
391C2×D5—121no—
392C2×D5—121no—
393C2×D5—121no—
394C4×C5—21no—
395C4×C5—121no—
396C4×C5C2×D2412yes—
397C4×C5#100711yescharacteristic
398C4×C5D3×#4111yescharacteristic
399Dic5—22no—
400Dic5—122no—
401Dic5—121no—
402Dic5C2×D2414yes—
403#41—604no—
404C2×Q8—51no—
405C2×Q8—302no—
406C2×Q8—301no—
407C2×Q8—604no—
408C2×D4—31no—
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—151no—
413C2×D4—302no—
414C2×D4—302no—
415C22×C4—61no—
416C22×C4—302no—
417C22×C4—302no—
418C22×C4—301no—
419D8—64no—
420D8—302no—
421C2×C8—51no—
422C2×C8—51no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—31no—
425C4⋊C4—52no—
426C4⋊C4—51no—
427C4⋊C4—152no—
428C4⋊C4—151no—
429C4⋊C4—302no—
430C4⋊C4—301no—
431C22⋊C4—61no—
432C22⋊C4—302no—
433C22⋊C4—302no—
434C22⋊C4—301no—
435C42—52no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3C2×D4×D511yescharacteristic
439C2×D3—22no—
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—201no—
446C2×D3—201no—
447C2×D3—201no—
448C3×C4—21no—
449C3×C4—54no—
450C3×C4—102no—
451C3×C4D5×D812yes—
452C3×C4C2×#71111yescharacteristic
453C3×C4#415011yescharacteristic
454Dic3—41no—
455Dic3—202no—
456Dic3—201no—
457C2×C5—122no—
458C2×C5—242no—
459C2×C5#557611yescharacteristic
460C2×C5C22×D2411yescharacteristic
461C2×C5#575111yescharacteristic
462D5—241no—
463C23—61no—
464C23—62no—
465C23—301no—
466Q8—54no—
467Q8—604no—
468Q8—602no—
469D4—32no—
470D4—62no—
471D4—61no—
472D4—62no—
473D4—122no—
474D4—241no—
475D4—301no—
476D4—301no—
477D4—604no—
478D4—1202no—
479C2×C4—52no—
480C2×C4—52no—
481C2×C4—61no—
482C2×C4—122no—
483C2×C4—301no—
484C2×C4—302no—
485C2×C4—604no—
486C2×C4—604no—
487C2×C4—602no—
488C2×C4D5×D1211yescharacteristic
489C2×C4D5×D1211yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—22no—
492C8—101no—
493C8—101no—
494C2×C3#6593211yescharacteristic
495C2×C3C2×D5×D811yescharacteristic
496C2×C3#6610911yescharacteristic
497D3—42no—
498D3—82no—
499D3—401no—
500C5#7992411yescharacteristic, complemented, Sylow
501C22—62no—
502C22—121no—
503C22—121no—
504C22—122no—
505C22—122no—
506C22—122no—
507C22—601no—
508C22—601no—
509C22—601no—
510C22C2×D5×D1211yescharacteristic
511C4—21no—
512C4—54no—
513C4—102no—
514C4—121no—
515C4—601no—
516C4—602no—
517C4D5×D2412yes—
518C4D3×#71111yescharacteristic
519C4#9203011yescharacteristic
520C3#1061204911yescharacteristic, complemented, Sylow
521C2—122no—
522C2—242no—
523C2—1201no—
524C2#1175343711yescharacteristic
525C2C2×D5×D2411yescharacteristic
526C2#1175402311yescharacteristic
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#3358
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. #11752536C2semidirect
2. D12×Dic10C2semidirect
3. #11750947C2semidirect
4. C5×#4843C2semidirect
5. C3×#65119C2semidirect
6. #11747995C2semidirect
7. #11747765C2semidirect
8. #11747764C2semidirect
9. Dic5×D24C2semidirect
10. C4×#6654C2semidirect
11. #11746906C2semidirect
51. #65119D3semidirect
94. #4843D5semidirect
147. C5×D12#41semidirect
151. C3×Dic10D8semidirect
314. Dic10D24semidirect
374. D12#711semidirect
437. C3×C5#3358semidirect
500. C5#79924semidirect
520. C3#10612049semidirect

Maximal subgroups

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

subgroupindex
#117525362
D12×Dic102
#117509472
C5×#48432
C3×#651192
#117479952
#117477652
#117477642
Dic5×D242
C4×#66542
#117469062
#106120493
#799245