Finite Group Databasebeta

← #14418165

Subgroups — #14418165

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5745C211yesmaximal, characteristic, complemented
2C3×#66079C211yesmaximal, characteristic, complemented
3#11754138C211yesmaximal, characteristic
4M16×Dic15C211yesmaximal, characteristic, complemented
5#11748478C211yesmaximal, characteristic, complemented
6C2×#90978C211yesmaximal, characteristic, complemented
7C2×#90976C211yesmaximal, characteristic, complemented
8#11748075C214yesmaximal, complemented
9#11748074C214yesmaximal, complemented
10#10615542—31nomaximal, Hall
11C2×C5×#235C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×C4×Dic15C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C2×C5×#208C2211yescharacteristic
17C5×#907—22no—
18C5×D3×M16—22no—
19C5×#901C2214yescomplemented
20C2×C3×#681C2211yescharacteristic
21C3×#4053—22no—
22C3×D5×M16—22no—
23C3×#4047C2214yescomplemented
24#91309C412yescomplemented
25#91307C412yescomplemented
26#91299C412yescomplemented
27#91298C412yescomplemented
28#91297C2214yes—
29#91099C2212yescomplemented
30C8×Dic15C2212yescomplemented
31#90992C2214yescomplemented
32#90978C2212yescomplemented
33#90978C2212yescomplemented
34#90976C2212yescomplemented
35#90976C2212yescomplemented
36#83811—51nomaximal, Hall
37C5×#568—31no—
38#66156—31no—
39#66079D311yescharacteristic, complemented
40C2×#3969—31no—
41#65434—34no—
42#65433—34no—
43C2×#3957—31no—
44#65413—31no—
45M16×Dic5—31no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—21no—
48C2×C5×#67—21no—
49C5×#235—21no—
50C5×#235—21no—
51C5×#235C2×C412yes—
52C5×#235C2312yes—
53C2×C5×D12C2×C411yescharacteristic
54C2×C4×C5×D3—21no—
55C2×C5×Dic6C2×C411yescharacteristic
56C2×C3×C22⋊D5—21no—
57C3×#709—21no—
58C3×#709—21no—
59C3×#709C2×C412yes—
60C3×#709C2312yes—
61C2×C3×D20C2×C411yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×Dic10C2×C411yescharacteristic
64C3×C5×M16D412yes—
65C3×C5×M16D412yes—
66C2×C3×C5×C8C2312yes—
67C4×Dic15—21no—
68C4×Dic15C2311yescharacteristic
69C4×Dic15C2311yescharacteristic
70#6710C2×C412yes—
71#6710C2×C412yes—
72C2×C3⋊#168C2312yes—
73C5×#208—21no—
74C5×#208C2312yes—
75C2×C5×C3⋊C8—21no—
76C5×ΓL(1,𝔽25)—24no—
77C5×D3×C8—24no—
78C3×#681—21no—
79C3×#681C2312yes—
80C2×C3×#168—21no—
81C3×#676—24no—
82C3×C8×D5—24no—
83#6661C2×C414yescomplemented
84#6656C2×C414yescomplemented
85#6655C2×C414yescomplemented
86#6652C2×C414yescomplemented
87C3×#568—51no—
88#5822—51no—
89#5745D511yescharacteristic, complemented
90C2×#837—51no—
91#5145—54no—
92#5144—54no—
93C2×#825—51no—
94#5124—51no—
95Dic3×M16—51no—
96C2×C5×#41—31no—
97C2×#709C2×D311yescharacteristic
98C5×#131—34no—
99C5×#131—62no—
100C2×C5×M16—31no—
101C2×C5×M16—62no—
102C2×C5×M16C2×D311yescharacteristic
103#4097—32no—
104#4096—34no—
105#4095—32no—
106#4088—32no—
107#4078—32no—
108C2×C4×Dic5—31no—
109C2×#681—31no—
110C2×#681C2×D311yescharacteristic
111#4053—22no—
112D5×M16—22no—
113#4047C2×D314yescomplemented
114#3969—32no—
115#3969—32no—
116#3957—32no—
117#3957—32no—
118#3954—34no—
119#3947—32no—
120C8×Dic5—32no—
121#2956—151noSylow
122C23×C3×C5#4111yescharacteristic
123C22×C5×D3—21no—
124C22×C3×D5—21no—
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×C3×C4×C5C22×C411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—21no—
132C2×Dic15—21no—
133C2×Dic15—42no—
134C5×#67—22no—
135C5×#67—22no—
136C2×C5×Dic3—21no—
137C5×D12—21no—
138C5×D12C22×C412yes—
139C4×C5×D3—22no—
140C4×C5×D3—22no—
141C5×Dic6—21no—
142C5×Dic6C22×C412yes—
143C3×C22⋊D5—22no—
144C3×C22⋊D5—22no—
145C2×C3×Dic5—21no—
146C3×D20—21no—
147C3×D20C22×C412yes—
148C3×C4×D5—22no—
149C3×C4×D5—22no—
150C3×Dic10—21no—
151C3×Dic10C22×C412yes—
152C3×C5×C8C2×D414yes—
153C3⋊#168C22×C414yes—
154C3×#168—22no—
155C5×C3⋊C8—22no—
156C2×C3×#41—51no—
157C2×#235C2×D511yescharacteristic
158C3×#131—54no—
159C3×#131—102no—
160C2×C3×M16—51no—
161C2×C3×M16—102no—
162C2×C3×M16C2×D511yescharacteristic
163#951—52no—
164#950—54no—
165#949—52no—
166#942—52no—
167#932—52no—
168C2×C4×Dic3—51no—
169C2×#208—51no—
170C2×#208C2×D511yescharacteristic
171#907—22no—
172D3×M16—22no—
173#901C2×D514yescomplemented
174#837—52no—
175#837—52no—
176#825—52no—
177#825—52no—
178#822—54no—
179#815—52no—
180C8×Dic3—52no—
181C5×#41—32no—
182C5×#41—32no—
183C5×#41—61no—
184C5×#41—61no—
185C2×C5×Q8—31no—
186C2×C5×D4—31no—
187C2×C5×D4—61no—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—21no—
191C22×Dic5—61no—
192#709—21no—
193#709—21no—
194#709C4×D312yes—
195#709C22×D312yes—
196C2×D20C4×D311yescharacteristic
197C2×C4×D5—21no—
198C2×Dic10C4×D311yescharacteristic
199C5×M16—32no—
200C5×M16—61no—
201C5×M16—64no—
202C5×M16#6712yes—
203C5×M16#6712yes—
204C2×C5×C8—61no—
205C2×C5×C8—64no—
206C2×C5×C8C22×D312yes—
207#689—34no—
208#688—34no—
209#687—34no—
210#686—34no—
211C4×Dic5—31no—
212C4×Dic5—31no—
213C4×Dic5—61no—
214#681—21no—
215#681—32no—
216#681—32no—
217#681C22×D312yes—
218C2×#168—21no—
219C2×#168—32no—
220#676—24no—
221C8×D5—24no—
222#575—151no—
223#568—31no—
224#568—51no—
225#444—154no—
226#443—154no—
227#430—151no—
228C2×#104—151no—
229C2×#104—151no—
230C4×M16—151no—
231C22×C3×C5—41no—
232C22×C3×C5C4×D411yescharacteristic
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C2×C5×D3—22no—
236C2×C5×D3—81no—
237C2×C3×D5—22no—
238C2×C3×D5—81no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×D411yescharacteristic
243Dic15—22no—
244Dic15—41no—
245C3×Dic5—22no—
246C5×Dic3—22no—
247C3×#41—52no—
248C3×#41—52no—
249C3×#41—101no—
250C3×#41—101no—
251C2×C3×Q8—51no—
252C2×C3×D4—51no—
253C2×C3×D4—101no—
254C22×C3×C4—101no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—21no—
257C22×Dic3—101no—
258#235—21no—
259#235—21no—
260#235C4×D512yes—
261#235C22×D512yes—
262C2×D12C4×D511yescharacteristic
263C2×C4×D3—21no—
264C2×Dic6C4×D511yescharacteristic
265C3×M16—52no—
266C3×M16—101no—
267C3×M16—104no—
268C3×M16C22⋊D512yes—
269C3×M16C22⋊D512yes—
270C2×C3×C8—101no—
271C2×C3×C8—104no—
272C2×C3×C8C22×D512yes—
273#216—54no—
274#215—54no—
275#214—54no—
276#213—54no—
277C4×Dic3—51no—
278C4×Dic3—51no—
279C4×Dic3—101no—
280#208—21no—
281#208—52no—
282#208—52no—
283#208C22×D512yes—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—52no—
286ΓL(1,𝔽25)—24no—
287D3×C8—24no—
288C23×C5—61no—
289C23×C5#23511yescharacteristic
290C22×D5—21no—
291C5×Q8—32no—
292C5×Q8—61no—
293C5×D4—32no—
294C5×D4—62no—
295C5×D4—62no—
296C5×D4—61no—
297C2×C4×C5—61no—
298C2×C4×C5—62no—
299C2×C4×C5—62no—
300C2×C4×C5C2×C4×D311yescharacteristic
301C2×C4×C5C2×C4×D311yescharacteristic
302C2×C4×C5#23511yescharacteristic
303C2×C4×C5C2×#6711yescharacteristic
304C2×C4×C5C2×#6711yescharacteristic
305C2×C4×C5C23×D311yescharacteristic
306C22⋊D5—22no—
307C22⋊D5—22no—
308C2×Dic5—21no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—122no—
312D20—21no—
313D20C2×C4×D312yes—
314C4×D5—22no—
315C4×D5—22no—
316Dic10—21no—
317Dic10C2×C4×D312yes—
318C5×C8—62no—
319C5×C8C2×#6714yes—
320#168—22no—
321#168—34no—
322C2×#41—31no—
323C2×#41—51no—
324#137—152no—
325#137—152no—
326AGL(1,ℤ/8)—152no—
327AGL(1,ℤ/8)—152no—
328#135—154no—
329#131—34no—
330#131—54no—
331#131—62no—
332#131—102no—
333C2×M16—31no—
334C2×M16—51no—
335C2×M16—62no—
336C2×M16—102no—
337C2×M16—151no—
338C2×M16D3×D511yescharacteristic
339C2×C42—151no—
340#108—154no—
341#104—152no—
342#104—152no—
343#104—152no—
344#104—152no—
345#97—152no—
346C4×C8—152no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5—21no—
350C2×C3×C5C2×C4×D411yescharacteristic
351C3×D5—42no—
352C5×D3—42no—
353C23×C3—101no—
354C23×C3#70911yescharacteristic
355C22×D3—21no—
356C3×Q8—52no—
357C3×Q8—101no—
358C3×D4—52no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—101no—
362C2×C3×C4—101no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4C2×C4×D511yescharacteristic
366C2×C3×C4C2×C4×D511yescharacteristic
367C2×C3×C4#70911yescharacteristic
368C2×C3×C4C2×C22⋊D511yescharacteristic
369C2×C3×C4C2×C22⋊D511yescharacteristic
370C2×C3×C4C23×D511yescharacteristic
371#67—22no—
372#67—22no—
373C2×Dic3—21no—
374C2×Dic3—101no—
375C2×Dic3—101no—
376C2×Dic3—202no—
377D12—21no—
378D12C2×C4×D512yes—
379C4×D3—22no—
380C4×D3—22no—
381Dic6—21no—
382Dic6C2×C4×D512yes—
383C3×C8—102no—
384C3×C8C2×C22⋊D514yes—
385C3⋊C8—22no—
386C3⋊C8—54no—
387C22×C5—41no—
388C22×C5—62no—
389C22×C5—241no—
390C22×C5C4×#6711yescharacteristic
391C22×C5C4×#6711yescharacteristic
392C22×C5C2×#23511yescharacteristic
393C2×D5—22no—
394C2×D5—81no—
395C4×C5—62no—
396C4×C5C4×#6711yescharacteristic
397C4×C5C4×#6711yescharacteristic
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C22×#6711yescharacteristic
400Dic5—22no—
401Dic5—62no—
402Dic5—121no—
403#41—32no—
404#41—32no—
405#41—52no—
406#41—52no—
407#41—61no—
408#41—61no—
409#41—101no—
410#41—101no—
411C2×Q8—31no—
412C2×Q8—51no—
413C2×D4—31no—
414C2×D4—51no—
415C2×D4—61no—
416C2×D4—101no—
417C22×C4—61no—
418C22×C4—101no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—32no—
426M16—52no—
427M16—61no—
428M16—64no—
429M16—101no—
430M16—104no—
431M16—152no—
432M16—152no—
433M16#120112yes—
434M16#120112yes—
435C2×C8—61no—
436C2×C8—64no—
437C2×C8—101no—
438C2×C8—104no—
439C2×C8—152no—
440C2×C8C2×D3×D512yes—
441C42—151no—
442C42—151no—
443C42—301no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—41no—
446C22×C3—102no—
447C22×C3—401no—
448C22×C3C4×C22⋊D511yescharacteristic
449C22×C3C4×C22⋊D511yescharacteristic
450C22×C3C2×#70911yescharacteristic
451C2×D3—22no—
452C2×D3—81no—
453C3×C4—102no—
454C3×C4C4×C22⋊D511yescharacteristic
455C3×C4C4×C22⋊D511yescharacteristic
456C3×C4C22×C4×D511yescharacteristic
457C3×C4C22×C22⋊D511yescharacteristic
458Dic3—22no—
459Dic3—102no—
460Dic3—201no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—122no—
465C2×C5C2×C4×#6711yescharacteristic
466D5—42no—
467C23—61no—
468C23—101no—
469C23#677111yescharacteristic
470Q8—32no—
471Q8—52no—
472Q8—61no—
473Q8—101no—
474D4—32no—
475D4—52no—
476D4—62no—
477D4—62no—
478D4—61no—
479D4—102no—
480D4—102no—
481D4—101no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—101no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—301no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4#677111yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4C4×D3×D511yescharacteristic
494C2×C4C2×#120111yescharacteristic
495C2×C4C2×#120111yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—62no—
498C8—102no—
499C8—154no—
500C8C2×#120114yes—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—202no—
505C2×C3C2×C4×C22⋊D511yescharacteristic
506D3—42no—
507C5#8381111yescharacteristic, complemented, Sylow
508C22—41no—
509C22—62no—
510C22—102no—
511C22—241no—
512C22—401no—
513C22C4×#120111yescharacteristic
514C22C4×#120111yescharacteristic
515C22C2×#677111yescharacteristic
516C4—62no—
517C4—102no—
518C4—302no—
519C4—601no—
520C4C4×#120111yescharacteristic
521C4C4×#120111yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C22×#120111yescharacteristic
524C3#1061554211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—122no—
529C2—202no—
530C2C2×C4×#120111yescharacteristic
subgroupG/H
centerC4C22×#1201
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C2×C4×D4
prime radical#11754138C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C5×#5745C2semidirect
2. C3×#66079C2semidirect
4. M16×Dic15C2semidirect
5. #11748478C2semidirect
6. C2×#90978C2semidirect
7. C2×#90976C2semidirect
8. #11748075C2semidirect
9. #11748074C2semidirect
19. C5×#901C22semidirect
23. C3×#4047C22semidirect
24. #91309C4semidirect
25. #91307C4semidirect
26. #91299C4semidirect
27. #91298C4semidirect
29. #91099C22semidirect
30. C8×Dic15C22semidirect
31. #90992C22semidirect
32. #90978C22semidirect
33. #90978C22semidirect
34. #90976C22semidirect
35. #90976C22semidirect
39. #66079D3semidirect
83. #6661C2×C4semidirect
84. #6656C2×C4semidirect
85. #6655C2×C4semidirect
86. #6652C2×C4semidirect
89. #5745D5semidirect
113. #4047C2×D3semidirect
173. #901C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#83811semidirect
524. C3#10615542semidirect

Maximal subgroups

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

subgroupindex
C5×#57452
C3×#660792
#117541382
M16×Dic152
#117484782
C2×#909782
C2×#909762
#117480752
#117480742
#106155423
#838115