Finite Group Databasebeta

← #14418154

Subgroups — #14418154

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
1#11756504C211yesmaximal, characteristic, complemented
2#11754145C211yesmaximal, characteristic
3#11754125C211yesmaximal, characteristic, complemented
4C2×C5×#825C211yesmaximal, characteristic, complemented
5C3×#65413C211yesmaximal, characteristic, complemented
6C2×#90980C211yesmaximal, characteristic, complemented
7Dic3×#681C211yesmaximal, characteristic, complemented
8#11748177C214yesmaximal, complemented
9#11748176C214yesmaximal, complemented
10#10610711—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15#91796C2214yescomplemented
16M16×D15—22no—
17#91790—22no—
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91322C412yescomplemented
22#91321C412yescomplemented
23#91305C412yescomplemented
24#91304C412yescomplemented
25#91303C2214yes—
26#91288C2214yescomplemented
27D3×#681—22no—
28#91286—22no—
29C5×#825C2212yescomplemented
30C5×#825C2212yescomplemented
31C3×#3954C2214yescomplemented
32#90980C2212yescomplemented
33#90980C2212yescomplemented
34#90953C2212yescomplemented
35Dic3×#168C2212yescomplemented
36#79258—51nomaximal, Hall
37#66156—31no—
38#66153—31no—
39#66079—31no—
40C2×C5×#104—31no—
41#65413D311yescharacteristic, complemented
42C2×#3937—31no—
43C4×#681—31no—
44#65113—34no—
45#65112—34no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48#6817—21no—
49#6817—21no—
50#6817C2×C412yes—
51#6817C2312yes—
52C2×D60C2×C411yescharacteristic
53C2×C4×D15—21no—
54C2×Dic30C2×C411yescharacteristic
55C2×C5×#67—21no—
56C22×C5×Dic3—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—
67#6710D412yes—
68#6710D412yes—
69C2×C3⋊#168C2312yes—
70#6705—24no—
71C8×D15—24no—
72C4×C5×Dic3—21no—
73C4×C5×Dic3C2311yescharacteristic
74C4×C5×Dic3C2311yescharacteristic
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#6650—24no—
86D3×#168—24no—
87#5748—51no—
88#5745—51no—
89#5745—51no—
90C3×#430—51no—
91C2×#825—51no—
92C2×#825D511yescharacteristic, complemented
93Dic3×M16—51no—
94#4895—54no—
95#4894—54no—
96C2×C5×#41—31no—
97C2×#709—31no—
98C2×C5×M16C2×D311yescharacteristic
99C2×C42×C5—31no—
100#4097—32no—
101#4096—34no—
102#4095—32no—
103#4094—34no—
104#4094—62no—
105#4088—32no—
106#4078—32no—
107C2×#681—31no—
108C2×#681—62no—
109C2×#681C2×D311yescharacteristic
110C2×#681C2×D311yescharacteristic
111#4053—34no—
112D5×M16—62no—
113#4047—62no—
114C5×#104—32no—
115C5×#104—32no—
116#3954C2×D314yescomplemented
117#3937—32no—
118#3937—32no—
119#3935—32no—
120C4×#168—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—
134D60—21no—
135D60C22×C412yes—
136C4×D15—22no—
137C4×D15—22no—
138Dic30—21no—
139Dic30C22×C412yes—
140C5×#67—22no—
141C5×#67—22no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—42no—
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⋊#168C2×D414yes—
154C3×#168—22no—
155C3×#168C22×C414yes—
156C2×#235—51no—
157C2×#235C2×D511yescharacteristic
158C2×C3×M16—51no—
159C2×C3×M16—51no—
160C2×C3×M16C2×D511yescharacteristic
161C2×C4×Dic3C2×D511yescharacteristic
162C2×#208—51no—
163#909—52no—
164#909—52no—
165#908—52no—
166#908—52no—
167#907—54no—
168#907—54no—
169D3×M16—102no—
170D3×M16—102no—
171#904—54no—
172#901—102no—
173#901—102no—
174C3×#108—54no—
175#825—52no—
176#825—52no—
177#825C2×D512yescomplemented
178#825C2×D512yescomplemented
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×C5—61no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—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×M16C22×D312yes—
201C2×C5×C8—21no—
202C42×C5—31no—
203C42×C5—31no—
204C42×C5—61no—
205#689—34no—
206#688—34no—
207#687—34no—
208#686—34no—
209#681—21no—
210#681—32no—
211#681—32no—
212#681—64no—
213#681C4×D312yes—
214#681C4×D312yes—
215#681C22×D312yes—
216C2×#168—21no—
217C2×#168—32no—
218C2×#168—64no—
219C2×#168C22×D312yes—
220#676—64no—
221C8×D5—64no—
222#575—151no—
223#568—151no—
224#568—151no—
225#444—154no—
226#443—154no—
227#430—51no—
228C2×#104—31no—
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—
244C5×Dic3—22no—
245C5×Dic3—22no—
246C5×Dic3—41no—
247C22×C3×C4C22×D511yescharacteristic
248C2×#67—21no—
249C2×#67—101no—
250C22×Dic3—21no—
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—21no—
275C4×Dic3C22×D511yescharacteristic
276C4×Dic3C22×D511yescharacteristic
277#208—52no—
278#208—52no—
279C2×C3⋊C8—52no—
280Dic12—54no—
281D24—54no—
282#204—54no—
283#204—54no—
284ΓL(1,𝔽25)—104no—
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
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—61no—
299C2×C4×C5—62no—
300C2×C4×C5—62no—
301C2×C4×C5—61no—
302C2×C4×C5—122no—
303C2×C4×C5C2×C4×D311yescharacteristic
304C2×C4×C5C2×C4×D311yescharacteristic
305C2×C4×C5D3×D411yescharacteristic
306C2×C4×C5D3×D411yescharacteristic
307C2×C4×C5#23911yescharacteristic
308C2×C4×C5C23×D311yescharacteristic
309C22⋊D5—62no—
310C22⋊D5—62no—
311C2×Dic5—61no—
312D20—32no—
313D20—61no—
314C4×D5—62no—
315C4×D5—62no—
316Dic10—32no—
317Dic10—61no—
318C5×C8—22no—
319#168—22no—
320#168—34no—
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—154no—
330#131—154no—
331#131—302no—
332#131—302no—
333C2×M16—51no—
334C2×M16—51no—
335C2×M16—151no—
336C2×M16—302no—
337C2×M16—302no—
338C2×M16D3×D511yescharacteristic
339C2×C42—31no—
340#108—54no—
341#104—32no—
342#104—32no—
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#71111yescharacteristic
354C22×D3—21no—
355C22×D3—101no—
356C2×C3×C4C2×C4×D511yescharacteristic
357C2×C3×C4C2×C4×D511yescharacteristic
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4#71111yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362#67—22no—
363#67—22no—
364#67—102no—
365#67—102no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—42no—
370C2×Dic3—101no—
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⋊C8—54no—
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—62no—
397C4×C5—121no—
398C4×C5#89311yescharacteristic
399C4×C5#89311yescharacteristic
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C2×D3×D411yescharacteristic
402Dic5—62no—
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—61no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—21no—
426M16—52no—
427M16—52no—
428M16—52no—
429M16—101no—
430M16—152no—
431M16—152no—
432M16—304no—
433M16—304no—
434M16C2×D3×D512yes—
435C2×C8—21no—
436C2×C8—52no—
437C2×C8—101no—
438C2×C8—152no—
439C2×C8—304no—
440C2×C8—304no—
441C42—31no—
442C42—31no—
443C42—61no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—41no—
446C22×C3#402711yescharacteristic
447C22×C3#402711yescharacteristic
448C22×C3C2×#71111yescharacteristic
449C2×D3—22no—
450C2×D3—81no—
451C2×D3—102no—
452C2×D3—401no—
453C3×C4#402711yescharacteristic
454C3×C4#402711yescharacteristic
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×D4×D511yescharacteristic
457Dic3—22no—
458Dic3—22no—
459Dic3—41no—
460Dic3—102no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—122no—
465C2×C5C2×#89311yescharacteristic
466D5—122no—
467C23—61no—
468C23—301no—
469C23#676811yescharacteristic
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—61no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—122no—
488C2×C4—301no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4#676811yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4C4×D3×D511yescharacteristic
494C2×C4#679011yescharacteristic
495C2×C4#679011yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—22no—
498C8—54no—
499C8—102no—
500C8—154no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3C2×#402711yescharacteristic
505D3—42no—
506D3—202no—
507C5#7925811yescharacteristic, complemented, Sylow
508C22—41no—
509C22—62no—
510C22—241no—
511C22—302no—
512C22—1201no—
513C22#9140611yescharacteristic
514C22#9140611yescharacteristic
515C22C2×#676811yescharacteristic
516C4—62no—
517C4—62no—
518C4—121no—
519C4—302no—
520C4#9140611yescharacteristic
521C4#9140611yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C2×#679011yescharacteristic
524C3#1061071111yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—122no—
529C2—602no—
530C2C2×#9140611yescharacteristic
subgroupG/H
centerC4C2×#6790
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. #11756504C2semidirect
3. #11754125C2semidirect
4. C2×C5×#825C2semidirect
5. C3×#65413C2semidirect
6. C2×#90980C2semidirect
7. Dic3×#681C2semidirect
8. #11748177C2semidirect
9. #11748176C2semidirect
15. #91796C22semidirect
21. #91322C4semidirect
22. #91321C4semidirect
23. #91305C4semidirect
24. #91304C4semidirect
26. #91288C22semidirect
29. C5×#825C22semidirect
30. C5×#825C22semidirect
31. C3×#3954C22semidirect
32. #90980C22semidirect
33. #90980C22semidirect
34. #90953C22semidirect
35. Dic3×#168C22semidirect
41. #65413D3semidirect
81. #6663C2×C4semidirect
82. #6660C2×C4semidirect
83. #6659C2×C4semidirect
84. #6654C2×C4semidirect
92. C2×#825D5semidirect
116. #3954C2×D3semidirect
177. #825C2×D5semidirect
178. #825C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#79258semidirect
524. C3#10610711semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117541452
#117541252
C2×C5×#8252
C3×#654132
C2×#909802
Dic3×#6812
#117481772
#117481762
#106107113
#792585