Finite Group Databasebeta

← #14417111

Subgroups — #14417111

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
1#11756280C211yesmaximal, characteristic, complemented
2#11754492C211yesmaximal, characteristic, complemented
3C2×#91305C211yesmaximal, characteristic
4C5×#5002C211yesmaximal, characteristic, complemented
5C3×#65284C211yesmaximal, characteristic, complemented
6C2×#90968C211yesmaximal, characteristic, complemented
7#11748326C211yesmaximal, characteristic, complemented
8#11747280C212yesmaximal, complemented
9#11747279C212yesmaximal, complemented
10#11747236C212yesmaximal, complemented
11#11747233C212yesmaximal, complemented
12#10610551—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16#91815C2211yescharacteristic
17#91782C2212yes—
18#91782C2212yes—
19C22⋊C4×D15—22no—
20C4×D60—21no—
21C4×D60—21no—
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25Dic5×#67—22no—
26#91435C2212yescomplemented
27D3×C4⋊Dic5—21no—
28#91344C2212yescomplemented
29#91338—21no—
30C2×#6660C2212yes—
31#91305C418yescomplemented
32C2×#6654C2212yes—
33C5×#810C2211yescharacteristic, complemented
34C5×#810C2211yescharacteristic, complemented
35C5×#809C2211yescharacteristic, complemented
36C5×#809C2211yescharacteristic, complemented
37C3×#3940C2212yescomplemented
38C3×#3939C2212yescomplemented
39#90968C2212yes—
40#90968C2212yes—
41#90954C2212yescomplemented
42#90951C2212yescomplemented
43#79201—51nomaximal, Hall
44#66161—31no—
45C2×#4095—31no—
46#65855—31no—
47C5×#416—31no—
48C2×#3953—31no—
49#65390—31no—
50#65284D311yescharacteristic, complemented
51#65106—32no—
52#65077—32no—
53#65074—32no—
54#65045—32no—
55C23×D15—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×D60—21no—
58C2×D60—22no—
59C2×D60C2×C414yescomplemented
60C2×D60C2312yes—
61C2×C4×D15—22no—
62C2×C4×D15—22no—
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235C2×C414yescomplemented
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C22×C3×Dic5—21no—
70C2×D3×Dic5—22no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C22⋊C4—21no—
74C3×C42×C5—21no—
75#6719D412yes—
76#6714—22no—
77#6714—22no—
78C4⋊Dic15D411yescharacteristic
79C4⋊Dic15D411yescharacteristic
80C4×Dic15C2312yes—
81C2×C5×C3⋊C8—22no—
82C2×C5×C3⋊C8C2311yescharacteristic
83C2×C5×C3⋊C8C2311yescharacteristic
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yes—
86C3×#681C2×C414yescomplemented
87C2×C3×#168C2312yes—
88Dic3⋊Dic5—22no—
89(C2×D3)⋊Dic5—22no—
90Dic3×Dic5—22no—
91#6660C2×C418yescomplemented
92#6654C2×C418yescomplemented
93C2×#908—51no—
94#5521—51no—
95#5504—51no—
96C3×#428—51no—
97#5122—51no—
98#5002D511yescharacteristic, complemented
99C2×#809—51no—
100#4889—52no—
101#4872—52no—
102#4869—52no—
103#4852—52no—
104C2×C5×#41—31no—
105C22×D20—31no—
106C22×C5×C8—31no—
107C5×#117C2×D311yescharacteristic
108#4095—38no—
109Q8×Dic5—32no—
110C2×#688—32no—
111D4×Dic5—32no—
112D4×Dic5—62no—
113C2×#686—32no—
114#4072—31no—
115#4072—61no—
116C2×C4⋊Dic5—61no—
117C2×C4⋊Dic5C2×D311yescharacteristic
118C2×#681C2×D311yescharacteristic
119#4039—32no—
120#4039—32no—
121D5×C22⋊C4—62no—
122C4×D20—61no—
123C4×D20—61no—
124C5×#103—31no—
125C5×#103—31no—
126C5×#102—31no—
127C5×#102—31no—
128#3953—32no—
129#3953—32no—
130#3947—32no—
131C8×Dic5—32no—
132#3940C2×D312yescomplemented
133#3939C2×D312yescomplemented
134#2946—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—22no—
137C22×D15—24no—
138C22×D15—81no—
139C22×D15—81no—
140C22×C5×D3—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5#4112yes—
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15C2×D412yes—
148C2×Dic15C2×D412yes—
149D60—24no—
150D60—22no—
151D60C22×C414yes—
152C4×D15—82no—
153C4×D15—82no—
154C5×#67—24no—
155C2×C5×Dic3—21no—
156C5×D12—21no—
157C5×D12C22×C412yes—
158C4×C5×D3—24no—
159C5×Dic6—21no—
160C5×Dic6C22×C412yes—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—81no—
163D3×Dic5—82no—
164C3×#168C22×C414yes—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—21no—
167C2×#235C2×D511yescharacteristic
168C22×D12—51no—
169C2×C3×M16—51no—
170C3×#117C2×D511yescharacteristic
171C2×C3×C4⋊C4—51no—
172C4×#67—102no—
173#926—51no—
174C22×C3⋊C8C2×D511yescharacteristic
175#908—58no—
176C2×D24—52no—
177C2×#204—52no—
178#893—52no—
179#893—52no—
180#893—52no—
181#892—101no—
182D3×C4⋊C4—101no—
183#887—52no—
184D3×C22⋊C4—102no—
185C4×D12—101no—
186C4×D12—101no—
187C3×#107—52no—
188C3×#106—52no—
189#815—52no—
190C8×Dic3—52no—
191#810C2×D511yescharacteristic, complemented
192#810C2×D511yescharacteristic, complemented
193#809—52no—
194#809—52no—
195#809C2×D511yescharacteristic, complemented
196#809C2×D511yescharacteristic, complemented
197C23×D5—61no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—21no—
206C22×Dic5—62no—
207C2×D20—34no—
208C2×D20—32no—
209C2×D20—61no—
210C2×D20—62no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C2×C5×C8—31no—
214C2×C5×C8—31no—
215C2×C5×C8—62no—
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C4⋊C4C22×D311yescharacteristic
218C5×C22⋊C4—21no—
219C42×C5—21no—
220C22⋊Dic5—32no—
221C22⋊Dic5—62no—
222#688—38no—
223#686—38no—
224#685—62no—
225#685—62no—
226C4⋊Dic5—21no—
227C4⋊Dic5—31no—
228C4⋊Dic5—31no—
229C4⋊Dic5—62no—
230C4⋊Dic5C22×D312yes—
231C4×Dic5—32no—
232C4×Dic5—62no—
233#681C4×D314yescomplemented
234C2×#168C22×D312yes—
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—51no—
243#416—31no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C4×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—24no—
251C2×D15—42no—
252C2×D15—42no—
253C2×D15—84no—
254C2×C5×D3—22no—
255C2×C5×D3—41no—
256C2×C5×D3—41no—
257C3×C4×C5—41no—
258C3×C4×C5—41no—
259C3×C4×C5C4×D412yes—
260C3×C4×C5C23×C411yescharacteristic
261C3×C4×C5C2×#4111yescharacteristic
262Dic15—22no—
263Dic15—22no—
264C3×Dic5—42no—
265C5×Dic3—22no—
266C23×D3—101no—
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—21no—
270#235—22no—
271#235C4×D514yescomplemented
272C2×D12—54no—
273C2×D12—52no—
274C2×D12—101no—
275C2×D12—102no—
276C2×D12C22×D511yescharacteristic
277C2×C4×D3—21no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C2×C4×D3—102no—
281C2×Dic6C22×D511yescharacteristic
282C3×M16—54no—
283C2×C3×C8—52no—
284C3×C4⋊C4—52no—
285C3×C4⋊C4—101no—
286C3×C4⋊C4C22×D511yescharacteristic
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C22⋊C4—21no—
289C3×C42—21no—
290#217—52no—
291(C2×D3)⋊C4—102no—
292(C2×D3)⋊C4—102no—
293(C2×D3)⋊C4—102no—
294C4⋊Dic3—51no—
295C4⋊Dic3—51no—
296Dic3⋊C4—102no—
297C4×Dic3—52no—
298C4×Dic3—102no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8C22×D511yescharacteristic
301C2×C3⋊C8C22×D511yescharacteristic
302D24—58no—
303#204—58no—
304C23×C5—61no—
305C23×C5D3×D411yescharacteristic
306C22×D5—62no—
307C22×D5—64no—
308C22×D5—241no—
309C22×D5—241no—
310C5×Q8—32no—
311C5×Q8—61no—
312C5×D4—32no—
313C5×D4—64no—
314C5×D4—61no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—61no—
318C2×C4×C5—64no—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5D3×D411yescharacteristic
321C2×C4×C5#23912yes—
322C2×C4×C5C23×D311yescharacteristic
323C2×Dic5—22no—
324C2×Dic5—32no—
325C2×Dic5—32no—
326C2×Dic5—81no—
327C2×Dic5—242no—
328D20—34no—
329D20—64no—
330D20—62no—
331C4×D5—242no—
332C4×D5—242no—
333C5×C8—61no—
334C5×C8—61no—
335#168C2×C4×D314yes—
336C2×#41—31no—
337C22×D4—151no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—51no—
342C22×C8—31no—
343C4×Q8—152no—
344C4×D4—152no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—301no—
348C4×D4—301no—
349C4×D4—302no—
350#117—151no—
351#117—301no—
352#117D3×D511yescharacteristic
353C2×C4⋊C4—51no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—302no—
356#107—52no—
357#106—52no—
358#103—31no—
359#103—31no—
360#102—31no—
361#102—31no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—44no—
371C5×D3—42no—
372C23×C3D4×D511yescharacteristic
373C22×D3—21no—
374C22×D3—102no—
375C22×D3—104no—
376C22×D3—401no—
377C22×D3—401no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—102no—
381C2×C3×C4—401no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4#71112yes—
385C2×C3×C4C23×D511yescharacteristic
386#67—24no—
387C2×Dic3—21no—
388C2×Dic3—52no—
389C2×Dic3—52no—
390D12—21no—
391D12—54no—
392D12—102no—
393D12—104no—
394D12C2×C4×D512yes—
395C4×D3—24no—
396C4×D3—402no—
397C4×D3—402no—
398C4×D3—402no—
399Dic6—21no—
400Dic6C2×C4×D512yes—
401C3×C8—54no—
402C3⋊C8—21no—
403C3⋊C8—21no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—62no—
407C22×C5—121no—
408C22×C5—121no—
409C22×C5#89312yes—
410C22×C5C2×D3×D411yescharacteristic
411C2×D5—64no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—244no—
415C4×C5—41no—
416C4×C5—41no—
417C4×C5—62no—
418C4×C5#89312yes—
419C4×C5C22×C4×D311yescharacteristic
420C4×C5C2×#23911yescharacteristic
421Dic5—42no—
422Dic5—62no—
423Dic5—62no—
424C24—301no—
425#41—34no—
426#41—62no—
427C2×Q8—31no—
428C2×D4—31no—
429C2×D4—61no—
430C2×D4—154no—
431C2×D4—152no—
432C2×D4—302no—
433C2×D4—301no—
434C22×C4—61no—
435C22×C4—101no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—302no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—54no—
443C2×C8—31no—
444C2×C8—31no—
445C2×C8—52no—
446C2×C8—62no—
447C4⋊C4—52no—
448C4⋊C4—101no—
449C4⋊C4—151no—
450C4⋊C4—151no—
451C4⋊C4—302no—
452C4⋊C4C2×D3×D511yescharacteristic
453C4⋊C4C2×D3×D511yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—152no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—21no—
460C42—152no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3#402712yes—
466C22×C3C2×D4×D511yescharacteristic
467C2×D3—22no—
468C2×D3—41no—
469C2×D3—41no—
470C2×D3—104no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—404no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—202no—
477C3×C4#402712yes—
478C3×C4C22×C4×D511yescharacteristic
479C3×C4C2×#71111yescharacteristic
480Dic3—22no—
481Dic3—102no—
482Dic3—102no—
483C2×C5—22no—
484C2×C5—122no—
485C2×C5C2×#89311yescharacteristic
486C2×C5#577411yescharacteristic
487C2×C5#577811yescharacteristic
488D5—124no—
489C23—61no—
490C23—302no—
491C23—304no—
492C23—1201no—
493C23—1201no—
494C23#679011yescharacteristic
495Q8—32no—
496Q8—61no—
497D4—32no—
498D4—64no—
499D4—61no—
500D4—154no—
501D4—304no—
502D4—302no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—61no—
506C2×C4—64no—
507C2×C4—102no—
508C2×C4—152no—
509C2×C4—152no—
510C2×C4—401no—
511C2×C4—1202no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4#676812yes—
515C2×C4C4×D3×D512yes—
516C2×C4#679011yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—54no—
519C8—61no—
520C8—61no—
521C2×C3—22no—
522C2×C3C2×#402711yescharacteristic
523C2×C3#6610311yescharacteristic
524C2×C3#6610411yescharacteristic
525D3—42no—
526D3—204no—
527C5#7920111yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—62no—
531C22—121no—
532C22—121no—
533C22—304no—
534C22—602no—
535C22—602no—
536C22—1204no—
537C22#9140612yes—
538C22C2×#679011yescharacteristic
539C4—41no—
540C4—41no—
541C4—62no—
542C4—202no—
543C4—302no—
544C4—302no—
545C4#9140612yes—
546C4C2×#676811yescharacteristic
547C4C2×C4×D3×D511yescharacteristic
548C3#1061055111yescharacteristic, complemented, Sylow
549C2—22no—
550C2—122no—
551C2—604no—
552C2C2×#9140611yescharacteristic
553C2#1175533011yescharacteristic
554C2#1175535411yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91305C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756280C2semidirect
2. #11754492C2semidirect
4. C5×#5002C2semidirect
5. C3×#65284C2semidirect
6. C2×#90968C2semidirect
7. #11748326C2semidirect
8. #11747280C2semidirect
9. #11747279C2semidirect
10. #11747236C2semidirect
11. #11747233C2semidirect
26. #91435C22semidirect
28. #91344C22semidirect
31. #91305C4semidirect
33. C5×#810C22semidirect
34. C5×#810C22semidirect
35. C5×#809C22semidirect
36. C5×#809C22semidirect
37. C3×#3940C22semidirect
38. C3×#3939C22semidirect
41. #90954C22semidirect
42. #90951C22semidirect
50. #65284D3semidirect
59. C2×D60C2×C4semidirect
65. C5×#235C2×C4semidirect
86. C3×#681C2×C4semidirect
91. #6660C2×C4semidirect
92. #6654C2×C4semidirect
98. #5002D5semidirect
132. #3940C2×D3semidirect
133. #3939C2×D3semidirect
191. #810C2×D5semidirect
192. #810C2×D5semidirect
195. #809C2×D5semidirect
196. #809C2×D5semidirect
233. #681C4×D3semidirect
271. #235C4×D5semidirect
462. C3×C5#2946semidirect
527. C5#79201semidirect
548. C3#10610551semidirect

Maximal subgroups

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

subgroupindex
#117562802
#117544922
C2×#913052
C5×#50022
C3×#652842
C2×#909682
#117483262
#117472802
#117472792
#117472362
#117472332
#106105513
#792015