Finite Group Databasebeta

← #14417118

Subgroups — #14417118

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91797C211yesmaximal, characteristic
2#11754515C211yesmaximal, characteristic, complemented
3#11754506C211yesmaximal, characteristic, complemented
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65411C211yesmaximal, characteristic, complemented
6C2×#90969C211yesmaximal, characteristic, complemented
7#11748393C211yesmaximal, characteristic, complemented
8#11747778C212yesmaximal, complemented
9#11747772C212yesmaximal, complemented
10#11747766C212yesmaximal, complemented
11#11747760C212yesmaximal, complemented
12#10610932—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16#91797C418yescomplemented
17C2×D120C2212yes—
18C2×#6706C2212yes—
19C5×#926C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C3×#4072C2211yescharacteristic
22C22×C3×#168C2211yescharacteristic
23#91561—22no—
24#91556—22no—
25#91437—21no—
26#91428—21no—
27#91428—21no—
28#91418C2212yes—
29#91418C2212yes—
30#91418C2212yescomplemented
31#91347—21no—
32#91333C2212yescomplemented
33C5×#818C2212yescomplemented
34C5×#817C2212yescomplemented
35C3×#3947C2212yescomplemented
36C3×C8×Dic5C2212yescomplemented
37#90975C2211yescharacteristic, complemented
38#90975C2211yescharacteristic, complemented
39#90969C2212yes—
40#90969C2212yes—
41#90969C2211yescharacteristic, complemented
42#90969C2211yescharacteristic, complemented
43#78560—51nomaximal, Hall
44C2×#4054—31no—
45#65855—31no—
46#65838—31no—
47C5×#428—31no—
48#65411D311yescharacteristic, complemented
49#65291—31no—
50C2×#3941—31no—
51#65178—32no—
52#65161—32no—
53#65158—32no—
54#65141—32no—
55C23×D15—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58#6817—22no—
59#6817C2×C414yescomplemented
60C2×D60—21no—
61C2×D60—22no—
62C2×D60C2×C414yescomplemented
63C2×D60C2312yes—
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×Dic30C2311yescharacteristic
67C22×C5×Dic3—21no—
68C2×#1200—22no—
69C2×#1200—22no—
70C2×#1200—22no—
71C3×C5×M16C2×C414yescomplemented
72C2×C3×C5×C8C2312yes—
73D120C2×C418yescomplemented
74#6706C2×C418yescomplemented
75C5×#217—21no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×C4⋊Dic3C2311yescharacteristic
79C5×C4⋊Dic3C2312yes—
80C4×C5×Dic3—21no—
81C3×C22⋊Dic5D412yes—
82C3×C4⋊Dic5D411yescharacteristic
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4×Dic5C2312yes—
85C2×C3×#168—22no—
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88#6669—22no—
89#6667—22no—
90#6667—22no—
91#6667—22no—
92Dic3×Dic5—22no—
93C2×#908—51no—
94#5523—51no—
95#5521—51no—
96C3×#405—51no—
97#5121D511yescharacteristic, complemented
98#5113—51no—
99C2×#821—51no—
100#4711—52no—
101#4710—52no—
102C4×D24—52no—
103C4×#204—52no—
104C2×#709—31no—
105C22×D20—31no—
106C2×C5×M16C2×D311yescharacteristic
107C5×#117—31no—
108C2×C5×C4⋊C4—31no—
109C4×C22⋊D5—62no—
110#4072C2×D311yescharacteristic
111C22×#168C2×D311yescharacteristic
112#4054—38no—
113C2×D40—32no—
114C2×#677—32no—
115#4039—32no—
116#4039—32no—
117#4039—32no—
118#4038—61no—
119D5×C4⋊C4—61no—
120#4033—32no—
121D5×C22⋊C4—62no—
122C4×D20—61no—
123C4×D20—61no—
124C5×#107—32no—
125C5×#106—32no—
126#3947C2×D312yescomplemented
127C8×Dic5C2×D312yescomplemented
128#3942—31no—
129#3942—31no—
130#3941—31no—
131#3941—31no—
132#3941—32no—
133#3941—32no—
134#2946—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C22×D15—22no—
138C22×D15—24no—
139C22×D15—81no—
140C22×D15—81no—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4112yes—
144C2×C3×C4×C5C2411yescharacteristic
145#1220—24no—
146C2×Dic15—21no—
147D60—24no—
148D60—22no—
149D60—21no—
150D60C22×C414yes—
151D60C22×C412yes—
152C4×D15—24no—
153Dic30—21no—
154Dic30C22×C412yes—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—81no—
159C2×C3×Dic5C2×D412yes—
160C2×C3×Dic5C2×D412yes—
161#1200—82no—
162#1200—82no—
163#1200—82no—
164C3×C5×C8C22×C414yes—
165C3×#168—21no—
166C3×#168—21no—
167C2×#235—51no—
168C22×D12—51no—
169C2×C3×M16C2×D511yescharacteristic
170C22×C3×C8—51no—
171C3×#117—51no—
172#926C2×D511yescharacteristic
173C2×C4⋊Dic3C2×D511yescharacteristic
174#908—58no—
175C2×D24—52no—
176C2×#204—52no—
177#893—101no—
178#893—101no—
179#892—101no—
180D3×C4⋊C4—101no—
181#67⋊C4—102no—
182D3×C22⋊C4—102no—
183C4×D12—52no—
184C4×D12—52no—
185C4×D12—52no—
186C4×Dic6—52no—
187C3×#97—52no—
188C3×C4×C8—52no—
189#821—52no—
190#821—51no—
191#821—52no—
192#821—51no—
193#818C2×D512yescomplemented
194#817C2×D512yescomplemented
195#816—51no—
196#816—51no—
197C23×D5—61no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
201#709—34no—
202#709—62no—
203C2×D20—34no—
204C2×D20—32no—
205C2×D20—31no—
206C2×D20—61no—
207C2×D20—62no—
208C2×C4×D5—61no—
209C2×C4×D5—62no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10—31no—
213C5×M16C4×D314yescomplemented
214C2×C5×C8C22×D312yes—
215C5×C4⋊C4—32no—
216C5×C4⋊C4—31no—
217C5×C4⋊C4—31no—
218C5×C4⋊C4—61no—
219C5×C22⋊C4—61no—
220C42×C5—61no—
221C22⋊Dic5D1212yes—
222#685—62no—
223#685—62no—
224#685—62no—
225C4⋊Dic5D1211yescharacteristic
226C4⋊Dic5D1211yescharacteristic
227#683—62no—
228C4×Dic5—62no—
229C4×Dic5C22×D312yes—
230C2×#168—22no—
231C2×#168C22×D311yescharacteristic
232C2×#168C22×D311yescharacteristic
233D40—38no—
234#677—38no—
235C2×AGL(1,ℤ/8)—151no—
236#520—151no—
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—31no—
243#416—151no—
244C2×#102—151no—
245#405—51no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C4×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—22no—
251C2×D15—24no—
252C2×D15—41no—
253C2×D15—42no—
254C2×D15—42no—
255C2×D15—41no—
256C2×D15—84no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261C3×Dic5—22no—
262C3×Dic5—22no—
263C5×Dic3—41no—
264C5×Dic3—42no—
265C5×Dic3—41no—
266C23×D3—101no—
267C22×C3×C4C22×D511yescharacteristic
268C2×#67—101no—
269C22×Dic3—21no—
270#235—54no—
271#235—102no—
272C2×D12—54no—
273C2×D12—52no—
274C2×D12—51no—
275C2×D12—101no—
276C2×D12—102no—
277C2×C4×D3—101no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C2×C4×D3—102no—
281C2×Dic6—51no—
282C3×M16C4×D514yescomplemented
283C2×C3×C8—51no—
284C2×C3×C8—51no—
285C2×C3×C8—102no—
286C2×C3×C8C22×D512yes—
287C3×C4⋊C4—51no—
288C3×C4⋊C4—51no—
289C3×C22⋊C4—52no—
290C3×C42—52no—
291#217—21no—
292(C2×D3)⋊C4—102no—
293(C2×D3)⋊C4—102no—
294(C2×D3)⋊C4—102no—
295C4⋊Dic3—21no—
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298C4⋊Dic3C22×D512yes—
299Dic3⋊C4—102no—
300C4×Dic3—21no—
301C4×Dic3—102no—
302D24—58no—
303#204—58no—
304C23×C5C2×D1211yescharacteristic
305C22×D5—61no—
306C22×D5—62no—
307C22×D5—64no—
308C22×D5—241no—
309C22×D5—241no—
310C2×C4×C5—62no—
311C2×C4×C5—61no—
312C2×C4×C5—61no—
313C2×C4×C5—241no—
314C2×C4×C5C2×C4×D312yes—
315C2×C4×C5C2×D1211yescharacteristic
316C2×C4×C5#23512yes—
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—64no—
319C2×Dic5—61no—
320C2×Dic5C2×D1212yes—
321C2×Dic5C2×D1212yes—
322D20—34no—
323D20—32no—
324D20—64no—
325D20—62no—
326D20—61no—
327C4×D5—64no—
328C4×D5—242no—
329C4×D5—242no—
330C4×D5—242no—
331Dic10—32no—
332Dic10—61no—
333C5×C8C2×C4×D314yes—
334#168—21no—
335#168—21no—
336C2×#41—151no—
337C22×D4—151no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16D3×D511yescharacteristic
342C22×C8—51no—
343C4×Q8—152no—
344C4×D4—152no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—301no—
348C4×D4—301no—
349C4×D4—302no—
350#117—31no—
351#117—51no—
352#117—301no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—302no—
356#107—32no—
357#106—32no—
358#103—151no—
359#103—151no—
360#102—152no—
361#102—152no—
362#102—151no—
363#102—151no—
364#97—52no—
365C4×C8—52no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—42no—
371D15—44no—
372C23×C3D4×D511yescharacteristic
373C22×D3—101no—
374C22×D3—102no—
375C22×D3—104no—
376C22×D3—401no—
377C22×D3—401no—
378C2×C3×C4—52no—
379C2×C3×C4—52no—
380C2×C3×C4C2×C4×D512yes—
381C2×C3×C4D4×D511yescharacteristic
382C2×C3×C4#71312yes—
383C2×C3×C4C23×D511yescharacteristic
384#67—104no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—81no—
389C2×Dic3—101no—
390D12—54no—
391D12—52no—
392D12—102no—
393D12—101no—
394D12—104no—
395C4×D3—104no—
396C4×D3—402no—
397C4×D3—402no—
398C4×D3—402no—
399Dic6—52no—
400Dic6—101no—
401C3×C8—101no—
402C3×C8—101no—
403C3×C8C2×C4×D514yes—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5C4×D1212yes—
407C22×C5C22×D1211yescharacteristic
408C2×D5—62no—
409C2×D5—64no—
410C2×D5—122no—
411C2×D5—121no—
412C2×D5—121no—
413C2×D5—122no—
414C2×D5—244no—
415C4×C5—121no—
416C4×C5—121no—
417C4×C5—122no—
418C4×C5C4×D1212yes—
419C4×C5C22×C4×D311yescharacteristic
420C4×C5C2×#23511yescharacteristic
421Dic5—22no—
422Dic5—22no—
423Dic5—62no—
424C24—301no—
425#41—154no—
426#41—302no—
427C2×Q8—151no—
428C2×D4—154no—
429C2×D4—151no—
430C2×D4—152no—
431C2×D4—301no—
432C2×D4—302no—
433C2×D4—301no—
434C22×C4—61no—
435C22×C4—302no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16#120014yescomplemented
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—102no—
446C2×C8C2×D3×D512yes—
447C4⋊C4—32no—
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—51no—
451C4⋊C4—51no—
452C4⋊C4—61no—
453C4⋊C4—302no—
454C22⋊C4—52no—
455C22⋊C4—61no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—52no—
460C42—61no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3#403912yes—
466C22×C3C2×D4×D511yescharacteristic
467C2×D3—102no—
468C2×D3—104no—
469C2×D3—201no—
470C2×D3—202no—
471C2×D3—202no—
472C2×D3—201no—
473C2×D3—404no—
474C3×C4—102no—
475C3×C4—102no—
476C3×C4#403912yes—
477C3×C4C22×C4×D511yescharacteristic
478C3×C4C2×#71311yescharacteristic
479Dic3—41no—
480Dic3—42no—
481Dic3—41no—
482Dic3—102no—
483C2×C5—22no—
484C2×C5C2×C4×D1211yescharacteristic
485C2×C5#575111yescharacteristic
486C2×C5#575211yescharacteristic
487D5—124no—
488D5—122no—
489C23—301no—
490C23—302no—
491C23—304no—
492C23—1201no—
493C23—1201no—
494C23D5×D1211yescharacteristic
495Q8—152no—
496Q8—301no—
497D4—152no—
498D4—154no—
499D4—304no—
500D4—304no—
501D4—302no—
502D4—301no—
503C2×C4—52no—
504C2×C4—52no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—62no—
508C2×C4—241no—
509C2×C4—301no—
510C2×C4—304no—
511C2×C4—1202no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4#677312yes—
515C2×C4D5×D1211yescharacteristic
516C2×C4C2×#120012yes—
517C2×C4C22×D3×D511yescharacteristic
518C8—101no—
519C8—101no—
520C8C2×#120014yes—
521C2×C3—22no—
522C2×C3C2×#403911yescharacteristic
523C2×C3#6610811yescharacteristic
524C2×C3#6611211yescharacteristic
525D3—204no—
526D3—202no—
527C5#7856011yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—302no—
531C22—304no—
532C22—601no—
533C22—602no—
534C22—602no—
535C22—601no—
536C22—1204no—
537C22#9141812yes—
538C22C2×D5×D1211yescharacteristic
539C4—102no—
540C4—102no—
541C4—122no—
542C4—121no—
543C4—121no—
544C4—302no—
545C4#9141812yes—
546C4C2×#677311yescharacteristic
547C4C22×#120011yescharacteristic
548C3#1061093211yescharacteristic, complemented, Sylow
549C2—22no—
550C2—604no—
551C2—602no—
552C2#1175402411yescharacteristic
553C2#1175402511yescharacteristic
554C2C2×#9141811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#91797C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754515C2semidirect
3. #11754506C2semidirect
4. C5×#5121C2semidirect
5. C3×#65411C2semidirect
6. C2×#90969C2semidirect
7. #11748393C2semidirect
8. #11747778C2semidirect
9. #11747772C2semidirect
10. #11747766C2semidirect
11. #11747760C2semidirect
16. #91797C4semidirect
30. #91418C22semidirect
32. #91333C22semidirect
33. C5×#818C22semidirect
34. C5×#817C22semidirect
35. C3×#3947C22semidirect
36. C3×C8×Dic5C22semidirect
37. #90975C22semidirect
38. #90975C22semidirect
41. #90969C22semidirect
42. #90969C22semidirect
48. #65411D3semidirect
59. #6817C2×C4semidirect
62. C2×D60C2×C4semidirect
71. C3×C5×M16C2×C4semidirect
73. D120C2×C4semidirect
74. #6706C2×C4semidirect
97. #5121D5semidirect
126. #3947C2×D3semidirect
127. C8×Dic5C2×D3semidirect
193. #818C2×D5semidirect
194. #817C2×D5semidirect
213. C5×M16C4×D3semidirect
282. C3×M16C4×D5semidirect
442. M16#1200semidirect
462. C3×C5#2946semidirect
527. C5#78560semidirect
548. C3#10610932semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
#117545152
#117545062
C5×#51212
C3×#654112
C2×#909692
#117483932
#117477782
#117477722
#117477662
#117477602
#106109323
#785605