Finite Group Databasebeta

← #14418156

Subgroups — #14418156

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
2#11754145C211yesmaximal, characteristic
3#11754130C211yesmaximal, characteristic, complemented
4C2×#91109C211yesmaximal, characteristic, complemented
5C3×#65413C211yesmaximal, characteristic, complemented
6C2×#90978C211yesmaximal, characteristic, complemented
7#11748328C211yesmaximal, characteristic, complemented
8#11748209C214yesmaximal, complemented
9#11748208C214yesmaximal, complemented
10#10615542—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×C4×Dic15C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C5×#907C2214yescomplemented
17C5×D3×M16—22no—
18C5×#901—22no—
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91322C412yescomplemented
22#91321C412yescomplemented
23#91305C412yescomplemented
24#91304C412yescomplemented
25#91303C2214yes—
26#91292—22no—
27#91291C2214yescomplemented
28#91290—22no—
29#91109C2212yescomplemented
30#91109C2212yescomplemented
31C3×#3954C2214yescomplemented
32#90978C2212yescomplemented
33#90978C2212yescomplemented
34#90954C2212yescomplemented
35#90951C2212yescomplemented
36#79258—51nomaximal, Hall
37C5×#568—31no—
38#66156—31no—
39#66079—31no—
40C2×#3969—31no—
41#65434—34no—
42#65433—34no—
43C2×#3957—31no—
44#65413D311yescharacteristic, complemented
45M16×Dic5—31no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48C22×Dic15—21no—
49#6817—21no—
50#6817—21no—
51#6817C2×C412yes—
52#6817C2312yes—
53C2×D60C2×C411yescharacteristic
54C2×C4×D15—21no—
55C2×Dic30C2×C411yescharacteristic
56C2×C5×#67—21no—
57C5×#235—21no—
58C5×#235—21no—
59C5×#235C2×C412yes—
60C5×#235C2312yes—
61C2×C5×D12C2×C411yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6C2×C411yescharacteristic
64C3×C5×M16—21no—
65C3×C5×M16C2312yes—
66C2×C3×C5×C8—21no—
67C4×Dic15—21no—
68C4×Dic15C2311yescharacteristic
69C4×Dic15C2311yescharacteristic
70C5×#208D412yes—
71C5×#208D412yes—
72C2×C5×C3⋊C8C2312yes—
73C5×ΓL(1,𝔽25)—24no—
74C5×D3×C8—24no—
75C3×#681—21no—
76C3×#681C2×C412yes—
77C3×#681C2×C412yes—
78C3×#681C2312yes—
79C2×C3×#168—21no—
80C2×C3×#168C2312yes—
81#6663C2×C414yescomplemented
82#6660C2×C414yescomplemented
83#6659C2×C414yescomplemented
84#6654C2×C414yescomplemented
85#6651—24no—
86#6648—24no—
87#5748—51no—
88#5745—51no—
89#5745D511yescharacteristic, complemented
90C3×#430—51no—
91C2×#825—51no—
92C2×#825—51no—
93Dic3×M16—51no—
94#4895—54no—
95#4894—54no—
96C2×C5×#41—31no—
97C2×#709—31no—
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×#681C2×D311yescharacteristic
110C2×#681C2×D311yescharacteristic
111#4053—62no—
112D5×M16—62no—
113#4047—34no—
114#3969—32no—
115#3969—32no—
116#3957—32no—
117#3957—32no—
118#3954C2×D314yescomplemented
119#3947—32no—
120C8×Dic5—32no—
121#2956—151noSylow
122C23×C3×C5#4111yescharacteristic
123C22×D15—21no—
124C22×C5×D3—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
131#1220—22no—
132#1220—22no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—42no—
137D60—21no—
138D60C22×C412yes—
139C4×D15—22no—
140C4×D15—22no—
141Dic30—21no—
142Dic30C22×C412yes—
143C5×#67—22no—
144C5×#67—22no—
145C2×C5×Dic3—21no—
146C5×D12—21no—
147C5×D12C22×C412yes—
148C4×C5×D3—22no—
149C4×C5×D3—22no—
150C5×Dic6—21no—
151C5×Dic6C22×C412yes—
152C3×C5×C8—22no—
153C3×#168—22no—
154C3×#168C22×C414yes—
155C5×C3⋊C8C2×D414yes—
156C2×#235—51no—
157C2×#235C2×D511yescharacteristic
158C2×C3×M16—51no—
159C2×C3×M16—51no—
160C2×C3×M16C2×D511yescharacteristic
161C2×C4×Dic3—51no—
162C2×#208C2×D511yescharacteristic
163#909—52no—
164#909—52no—
165#908—52no—
166#908—52no—
167#907—54no—
168#907C2×D514yescomplemented
169D3×M16—22no—
170D3×M16—102no—
171#904—54no—
172#901—22no—
173#901—102no—
174C3×#108—54no—
175#825—52no—
176#825—52no—
177#825—52no—
178#825—52no—
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—61no—
191C22×Dic5—61no—
192#709—32no—
193#709—32no—
194#709—61no—
195#709—61no—
196C2×D20—31no—
197C2×C4×D5—61no—
198C2×Dic10—31no—
199C5×M16—21no—
200C5×M16—32no—
201C5×M16—32no—
202C5×M16—64no—
203C5×M16C22×D312yes—
204C2×C5×C8—21no—
205C2×C5×C8—32no—
206C2×C5×C8—64no—
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#681C4×D312yes—
216#681C4×D312yes—
217#681C22×D312yes—
218C2×#168—21no—
219C2×#168C22×D312yes—
220#676—64no—
221C8×D5—64no—
222#575—151no—
223#568—31no—
224#568—151no—
225#444—154no—
226#443—154no—
227#430—51no—
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×D15—22no—
236C2×D15—81no—
237C2×C5×D3—22no—
238C2×C5×D3—81no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×D411yescharacteristic
243Dic15—22no—
244Dic15—22no—
245Dic15—41no—
246C5×Dic3—22no—
247C22×C3×C4C22×D511yescharacteristic
248C2×#67—21no—
249C2×#67—101no—
250C22×Dic3—101no—
251#235—21no—
252#235—21no—
253#235—52no—
254#235—52no—
255#235—101no—
256#235—101no—
257#235C4×D512yes—
258#235C22×D512yes—
259C2×D12—51no—
260C2×D12C4×D511yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—101no—
263C2×Dic6—51no—
264C2×Dic6C4×D511yescharacteristic
265C3×M16—21no—
266C3×M16—52no—
267C3×M16—52no—
268C3×M16—52no—
269C3×M16—101no—
270C3×M16C22×D512yes—
271C2×C3×C8—21no—
272C2×C3×C8—52no—
273C2×C3×C8—101no—
274C4×Dic3—51no—
275C4×Dic3—51no—
276C4×Dic3—101no—
277#208C22⋊D512yes—
278#208C22⋊D512yes—
279C2×C3⋊C8C22×D512yes—
280Dic12—54no—
281D24—54no—
282#204—54no—
283#204—54no—
284ΓL(1,𝔽25)—24no—
285ΓL(1,𝔽25)—104no—
286D3×C8—24no—
287D3×C8—104no—
288C23×C5—61no—
289C23×C5#23911yescharacteristic
290C22×D5—61no—
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×C5D3×D411yescharacteristic
303C2×C4×C5D3×D411yescharacteristic
304C2×C4×C5#23911yescharacteristic
305C2×C4×C5C23×D311yescharacteristic
306C22⋊D5—62no—
307C22⋊D5—62no—
308C2×Dic5—61no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—122no—
312D20—32no—
313D20—61no—
314C4×D5—62no—
315C4×D5—62no—
316Dic10—32no—
317Dic10—61no—
318C5×C8—22no—
319C5×C8—34no—
320#168—22no—
321#168C2×C4×D314yes—
322C2×#41—31no—
323C2×#41—151no—
324#137—152no—
325#137—152no—
326AGL(1,ℤ/8)—152no—
327AGL(1,ℤ/8)—152no—
328#135—154no—
329#131—34no—
330#131—62no—
331#131—154no—
332#131—302no—
333C2×M16—31no—
334C2×M16—51no—
335C2×M16—51no—
336C2×M16—62no—
337C2×M16—302no—
338C2×M16D3×D511yescharacteristic
339C2×C42—151no—
340#108—54no—
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
351D15—42no—
352C5×D3—42no—
353C23×C3#70911yescharacteristic
354C22×D3—21no—
355C22×D3—101no—
356C2×C3×C4C2×C4×D511yescharacteristic
357C2×C3×C4C2×C4×D511yescharacteristic
358C2×C3×C4#70911yescharacteristic
359C2×C3×C4C2×C22⋊D511yescharacteristic
360C2×C3×C4C2×C22⋊D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362#67—22no—
363#67—22no—
364#67—102no—
365#67—102no—
366C2×Dic3—21no—
367C2×Dic3—101no—
368C2×Dic3—101no—
369C2×Dic3—101no—
370C2×Dic3—202no—
371D12—21no—
372D12—52no—
373D12—101no—
374D12C2×C4×D512yes—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—102no—
378C4×D3—102no—
379Dic6—21no—
380Dic6—52no—
381Dic6—101no—
382Dic6C2×C4×D512yes—
383C3×C8—22no—
384C3×C8—54no—
385C3×C8—102no—
386C3⋊C8C2×C22⋊D514yes—
387C22×C5—41no—
388C22×C5—62no—
389C22×C5—241no—
390C22×C5#89311yescharacteristic
391C22×C5#89311yescharacteristic
392C22×C5C2×#23911yescharacteristic
393C2×D5—62no—
394C2×D5—241no—
395C4×C5—62no—
396C4×C5#89311yescharacteristic
397C4×C5#89311yescharacteristic
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×D3×D411yescharacteristic
400Dic5—62no—
401Dic5—62no—
402Dic5—121no—
403#41—32no—
404#41—32no—
405#41—61no—
406#41—61no—
407#41—152no—
408#41—152no—
409#41—301no—
410#41—301no—
411C2×Q8—31no—
412C2×Q8—151no—
413C2×D4—31no—
414C2×D4—61no—
415C2×D4—151no—
416C2×D4—301no—
417C22×C4—61no—
418C22×C4—301no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—21no—
426M16—32no—
427M16—32no—
428M16—52no—
429M16—52no—
430M16—52no—
431M16—64no—
432M16—101no—
433M16—304no—
434M16C2×D3×D512yes—
435C2×C8—21no—
436C2×C8—32no—
437C2×C8—52no—
438C2×C8—64no—
439C2×C8—101no—
440C2×C8—304no—
441C42—151no—
442C42—151no—
443C42—301no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—41no—
446C22×C3C4×C22⋊D511yescharacteristic
447C22×C3C4×C22⋊D511yescharacteristic
448C22×C3C2×#70911yescharacteristic
449C2×D3—22no—
450C2×D3—81no—
451C2×D3—102no—
452C2×D3—401no—
453C3×C4C4×C22⋊D511yescharacteristic
454C3×C4C4×C22⋊D511yescharacteristic
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C22×C22⋊D511yescharacteristic
457Dic3—22no—
458Dic3—102no—
459Dic3—102no—
460Dic3—201no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—122no—
465C2×C5C2×#89311yescharacteristic
466D5—122no—
467C23—61no—
468C23—301no—
469C23#676911yescharacteristic
470Q8—32no—
471Q8—61no—
472Q8—152no—
473Q8—301no—
474D4—32no—
475D4—62no—
476D4—62no—
477D4—61no—
478D4—152no—
479D4—302no—
480D4—302no—
481D4—301no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4#676911yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4C4×D3×D511yescharacteristic
494C2×C4D3×C22⋊D511yescharacteristic
495C2×C4D3×C22⋊D511yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—22no—
498C8—34no—
499C8—54no—
500C8—102no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3C2×C4×C22⋊D511yescharacteristic
505D3—42no—
506D3—202no—
507C5#7925811yescharacteristic, complemented, Sylow
508C22—41no—
509C22—62no—
510C22—241no—
511C22—302no—
512C22—1201no—
513C22#9144611yescharacteristic
514C22#9144611yescharacteristic
515C22C2×#676911yescharacteristic
516C4—62no—
517C4—302no—
518C4—302no—
519C4—601no—
520C4#9144611yescharacteristic
521C4#9144611yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C2×D3×C22⋊D511yescharacteristic
524C3#1061554211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—122no—
529C2—602no—
530C2C2×#9144611yescharacteristic
subgroupG/H
centerC4C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C2×C4×D4
prime radical#11754145C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C5×#5745C2semidirect
3. #11754130C2semidirect
4. C2×#91109C2semidirect
5. C3×#65413C2semidirect
6. C2×#90978C2semidirect
7. #11748328C2semidirect
8. #11748209C2semidirect
9. #11748208C2semidirect
16. C5×#907C22semidirect
21. #91322C4semidirect
22. #91321C4semidirect
23. #91305C4semidirect
24. #91304C4semidirect
27. #91291C22semidirect
29. #91109C22semidirect
30. #91109C22semidirect
31. C3×#3954C22semidirect
32. #90978C22semidirect
33. #90978C22semidirect
34. #90954C22semidirect
35. #90951C22semidirect
44. #65413D3semidirect
81. #6663C2×C4semidirect
82. #6660C2×C4semidirect
83. #6659C2×C4semidirect
84. #6654C2×C4semidirect
89. #5745D5semidirect
118. #3954C2×D3semidirect
168. #907C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#79258semidirect
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
#117541452
#117541302
C2×#911092
C3×#654132
C2×#909782
#117483282
#117482092
#117482082
#106155423
#792585