Finite Group Databasebeta

← #14417109

Subgroups — #14417109

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
1C5×#5521C211yesmaximal, characteristic, complemented
2#11754496C211yesmaximal, characteristic, complemented
3C2×#91304C211yesmaximal, characteristic
4#11751103C211yesmaximal, characteristic, complemented
5C3×#65284C211yesmaximal, characteristic, complemented
6C2×#90966C211yesmaximal, characteristic, complemented
7#11748327C211yesmaximal, characteristic, complemented
8#11747473C212yesmaximal, complemented
9#11747470C212yesmaximal, complemented
10#11747277C212yesmaximal, complemented
11#11747230C212yesmaximal, complemented
12#10614268—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C5×#893C2212yes—
19C5×#893C2212yes—
20C5×D3×C22⋊C4—22no—
21C4×C5×D12—21no—
22C4×C5×D12—21no—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91552—22no—
26#91437—21no—
27#91428C2212yescomplemented
28#91347—21no—
29#91340C2212yescomplemented
30C2×#6659C2212yes—
31#91304C418yescomplemented
32C2×#6654C2212yes—
33#91094C2211yescharacteristic, complemented
34#91094C2211yescharacteristic, complemented
35#91093C2211yescharacteristic, complemented
36#91093C2211yescharacteristic, complemented
37C3×#3940C2212yescomplemented
38C3×#3939C2212yescomplemented
39#90966C2212yes—
40#90966C2212yes—
41#90953C2212yescomplemented
42Dic3×#168C2212yescomplemented
43#79201—51nomaximal, Hall
44C5×#518—31no—
45C2×#4078—31no—
46#65857—31no—
47C2×#3964—31no—
48#65307—32no—
49C4×#687—32no—
50#65303—32no—
51C4×#686—32no—
52#65291—31no—
53#65286—31no—
54#65284D311yescharacteristic, complemented
55C23×C5×D3—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58#6817—22no—
59#6817C2×C414yescomplemented
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30C2311yescharacteristic
63C2×C5×D12—21no—
64C2×C5×D12—22no—
65C2×C5×D12C2×C414yescomplemented
66C2×C5×D12C2312yes—
67C2×C4×C5×D3—22no—
68C2×C4×C5×D3—22no—
69C22×C3×Dic5—21no—
70C2×#1200—22no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C22⋊C4—21no—
74C3×C42×C5—21no—
75C2×C3⋊#168—22no—
76C2×C3⋊#168C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C5×#217D412yes—
79C5×(C2×D3)⋊C4—22no—
80C5×(C2×D3)⋊C4—22no—
81C5×C4⋊Dic3D411yescharacteristic
82C5×C4⋊Dic3D411yescharacteristic
83C4×C5×Dic3C2312yes—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yes—
86C3×#681C2×C414yescomplemented
87C2×C3×#168C2312yes—
88#6669—22no—
89#6667—22no—
90Dic3×Dic5—22no—
91#6659C2×C418yescomplemented
92#6654C2×C418yescomplemented
93C2×#908—51no—
94#5521D511yescharacteristic, complemented
95#5504—51no—
96C3×#428—51no—
97#5122—51no—
98#5002—51no—
99C2×#809—51no—
100#4889—52no—
101#4872—52no—
102#4869—52no—
103#4852—52no—
104C22×C5×D4—31no—
105C2×#709—31no—
106C4×C5×D4—32no—
107C4×C5×D4—32no—
108C4×C5×D4—61no—
109C4×C5×D4—61no—
110C5×#117—31no—
111C5×#117C2×D311yescharacteristic
112C2×C5×C22⋊C4—62no—
113C2×#687—32no—
114#4078—38no—
115C2×#686—32no—
116C2×C4⋊Dic5C2×D311yescharacteristic
117C2×#681C2×D311yescharacteristic
118C22×#168—31no—
119#4038—61no—
120D5×C4⋊C4—61no—
121#4027—62no—
122C4×D20—32no—
123C4×Dic10—32no—
124#3964—32no—
125#3964—32no—
126#3942—31no—
127#3942—31no—
128#3941—31no—
129#3941—31no—
130#3940C2×D312yescomplemented
131#3939C2×D312yescomplemented
132#3935—32no—
133C4×#168—32no—
134#2946—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C22×C5×D3—22no—
138C22×C5×D3—24no—
139C22×C5×D3—81no—
140C22×C5×D3—81no—
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
147#1220—24no—
148C2×Dic15—21no—
149D60—21no—
150D60C22×C412yes—
151C4×D15—24no—
152Dic30—21no—
153Dic30C22×C412yes—
154C2×C5×Dic3C2×D412yes—
155C2×C5×Dic3C2×D412yes—
156C5×D12—24no—
157C5×D12—22no—
158C5×D12C22×C414yes—
159C4×C5×D3—82no—
160C4×C5×D3—82no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—81no—
163#1200—82no—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C3×#168C22×C414yes—
167C2×#235—51no—
168C22×D12C2×D511yescharacteristic
169C2×C3×M16—51no—
170C3×#117C2×D511yescharacteristic
171C2×C3×C4⋊C4—51no—
172C4×#67—102no—
173#926C2×D511yescharacteristic
174C22×C3⋊C8—51no—
175#908—58no—
176C2×D24—52no—
177C2×#204—52no—
178#893—52no—
179#893C2×D512yes—
180#893C2×D512yes—
181#892—101no—
182D3×C4⋊C4—101no—
183#887—52no—
184D3×C22⋊C4—22no—
185C4×D12—21no—
186C4×D12—21no—
187C3×#107—52no—
188C3×#106—52no—
189#815—52no—
190C8×Dic3—52no—
191#810—51no—
192#810—51no—
193#809—52no—
194#809—52no—
195#809—51no—
196#809—51no—
197C24×C5—61no—
198C2×C5×D4—34no—
199C2×C5×D4—32no—
200C2×C5×D4—61no—
201C2×C5×D4—62no—
202C22×C4×C5—62no—
203C22×C4×C5—62no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—61no—
206C22×Dic5—21no—
207#709—34no—
208#709—62no—
209C2×D20—31no—
210C2×C4×D5—61no—
211C2×C4×D5—62no—
212C2×Dic10—31no—
213C5×C4⋊C4—31no—
214C5×C4⋊C4—31no—
215C5×C4⋊C4C22×D311yescharacteristic
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C22⋊C4—21no—
218C5×C22⋊C4—32no—
219C5×C22⋊C4—62no—
220C5×C22⋊C4—62no—
221C42×C5—21no—
222C42×C5—32no—
223#687—38no—
224#686—38no—
225#685—62no—
226C4⋊Dic5—21no—
227C4⋊Dic5C22×D312yes—
228#683—62no—
229C4×Dic5—62no—
230#681C4×D314yescomplemented
231C2×#168—31no—
232C2×#168—31no—
233C2×#168—62no—
234C2×#168C22×D312yes—
235C2×AGL(1,ℤ/8)—151no—
236#520—151no—
237#518—31no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—51no—
243#416—151no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C4×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—22no—
251C2×D15—41no—
252C2×D15—41no—
253C2×C5×D3—24no—
254C2×C5×D3—42no—
255C2×C5×D3—42no—
256C2×C5×D3—84no—
257C3×C4×C5—41no—
258C3×C4×C5—41no—
259C3×C4×C5C4×D412yes—
260C3×C4×C5C23×C411yescharacteristic
261C3×C4×C5C2×#4111yescharacteristic
262Dic15—22no—
263C3×Dic5—42no—
264C5×Dic3—22no—
265C5×Dic3—22no—
266C23×D3—21no—
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—101no—
270#235—54no—
271#235—102no—
272C2×D12—22no—
273C2×D12—21no—
274C2×D12—51no—
275C2×D12C4×D514yescomplemented
276C2×D12C22×D512yes—
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3—101no—
280C2×C4×D3—102no—
281C2×Dic6—51no—
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#217C22⋊D512yes—
291(C2×D3)⋊C4—22no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—102no—
294C4⋊Dic3C22⋊D511yescharacteristic
295C4⋊Dic3C22⋊D511yescharacteristic
296Dic3⋊C4—102no—
297C4×Dic3—102no—
298C4×Dic3C22×D512yes—
299C2×C3⋊C8—51no—
300C2×C3⋊C8—51no—
301C2×C3⋊C8—102no—
302D24—58no—
303#204—58no—
304C23×C5—62no—
305C23×C5—64no—
306C23×C5—241no—
307C23×C5—241no—
308C23×C5D3×D411yescharacteristic
309C22×D5—61no—
310C5×D4—34no—
311C5×D4—64no—
312C5×D4—62no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—32no—
316C2×C4×C5—32no—
317C2×C4×C5—242no—
318C2×C4×C5—242no—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5D3×D411yescharacteristic
321C2×C4×C5#23912yes—
322C2×C4×C5C23×D311yescharacteristic
323C22⋊D5—64no—
324C2×Dic5—22no—
325C2×Dic5—61no—
326C2×Dic5—81no—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—242no—
331Dic10—32no—
332Dic10—61no—
333#168—61no—
334#168—61no—
335#168C2×C4×D314yes—
336C2×#41—151no—
337C22×D4—31no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—51no—
342C22×C8—151no—
343C4×Q8—152no—
344C4×D4—32no—
345C4×D4—32no—
346C4×D4—61no—
347C4×D4—61no—
348C4×D4—152no—
349C4×D4—302no—
350#117—31no—
351#117—301no—
352#117D3×D511yescharacteristic
353C2×C4⋊C4—51no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—62no—
356#107—52no—
357#106—52no—
358#103—151no—
359#103—151no—
360#102—152no—
361#102—152no—
362#102—151no—
363#102—151no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—42no—
371C5×D3—44no—
372C23×C3C2×C22⋊D511yescharacteristic
373C22×D3—22no—
374C22×D3—24no—
375C22×D3—81no—
376C22×D3—81no—
377C22×D3—101no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—102no—
381C2×C3×C4—401no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4#70912yes—
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386#67—104no—
387C2×Dic3—101no—
388C2×Dic3C2×C22⋊D512yes—
389C2×Dic3C2×C22⋊D512yes—
390D12—22no—
391D12—24no—
392D12—52no—
393D12—101no—
394D12C2×C4×D514yes—
395C4×D3—82no—
396C4×D3—82no—
397C4×D3—104no—
398C4×D3—402no—
399Dic6—52no—
400Dic6—101no—
401C3×C8—54no—
402C3⋊C8—101no—
403C3⋊C8—101no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—64no—
407C22×C5—122no—
408C22×C5—122no—
409C22×C5—244no—
410C22×C5#89312yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—62no—
413C2×D5—121no—
414C2×D5—121no—
415C4×C5—41no—
416C4×C5—41no—
417C4×C5—62no—
418C4×C5—62no—
419C4×C5#89312yes—
420C4×C5C22×C4×D311yescharacteristic
421C4×C5C2×#23911yescharacteristic
422Dic5—42no—
423Dic5—62no—
424C24—61no—
425#41—154no—
426#41—302no—
427C2×Q8—151no—
428C2×D4—34no—
429C2×D4—32no—
430C2×D4—62no—
431C2×D4—61no—
432C2×D4—151no—
433C2×D4—301no—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4—101no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—54no—
443C2×C8—52no—
444C2×C8—151no—
445C2×C8—151no—
446C2×C8—302no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—52no—
450C4⋊C4—101no—
451C4⋊C4—302no—
452C4⋊C4C2×D3×D511yescharacteristic
453C4⋊C4C2×D3×D511yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—32no—
456C22⋊C4—62no—
457C22⋊C4—62no—
458C22⋊C4—302no—
459C42—21no—
460C42—32no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3C4×C22⋊D512yes—
466C22×C3C22×C22⋊D511yescharacteristic
467C2×D3—24no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—84no—
471C2×D3—102no—
472C2×D3—201no—
473C2×D3—201no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—202no—
477C3×C4C4×C22⋊D512yes—
478C3×C4C22×C4×D511yescharacteristic
479C3×C4C2×#70911yescharacteristic
480Dic3—22no—
481Dic3—22no—
482Dic3—102no—
483C2×C5—22no—
484C2×C5—124no—
485C2×C5C2×#89311yescharacteristic
486C2×C5#577411yescharacteristic
487C2×C5#577811yescharacteristic
488D5—122no—
489C23—62no—
490C23—64no—
491C23—241no—
492C23—241no—
493C23—301no—
494C23D3×C22⋊D511yescharacteristic
495Q8—152no—
496Q8—301no—
497D4—34no—
498D4—64no—
499D4—62no—
500D4—152no—
501D4—304no—
502D4—301no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—32no—
506C2×C4—32no—
507C2×C4—102no—
508C2×C4—242no—
509C2×C4—242no—
510C2×C4—301no—
511C2×C4—304no—
512C2×C4—401no—
513C2×C4—1202no—
514C2×C4#676912yes—
515C2×C4C4×D3×D512yes—
516C2×C4D3×C22⋊D511yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—54no—
519C8—301no—
520C8—301no—
521C2×C3—22no—
522C2×C3C2×C4×C22⋊D511yescharacteristic
523C2×C3#6616911yescharacteristic
524C2×C3#6617011yescharacteristic
525D3—44no—
526D3—202no—
527C5#7920111yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—64no—
531C22—122no—
532C22—122no—
533C22—244no—
534C22—302no—
535C22—601no—
536C22—601no—
537C22#9144612yes—
538C22C2×D3×C22⋊D511yescharacteristic
539C4—41no—
540C4—41no—
541C4—62no—
542C4—62no—
543C4—202no—
544C4—302no—
545C4#9144612yes—
546C4C2×#676911yescharacteristic
547C4C2×C4×D3×D511yescharacteristic
548C3#1061426811yescharacteristic, complemented, Sylow
549C2—22no—
550C2—124no—
551C2—602no—
552C2C2×#9144611yescharacteristic
553C2#1175532311yescharacteristic
554C2#1175534011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91304C2
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. C5×#5521C2semidirect
2. #11754496C2semidirect
4. #11751103C2semidirect
5. C3×#65284C2semidirect
6. C2×#90966C2semidirect
7. #11748327C2semidirect
8. #11747473C2semidirect
9. #11747470C2semidirect
10. #11747277C2semidirect
11. #11747230C2semidirect
27. #91428C22semidirect
29. #91340C22semidirect
31. #91304C4semidirect
33. #91094C22semidirect
34. #91094C22semidirect
35. #91093C22semidirect
36. #91093C22semidirect
37. C3×#3940C22semidirect
38. C3×#3939C22semidirect
41. #90953C22semidirect
42. Dic3×#168C22semidirect
54. #65284D3semidirect
59. #6817C2×C4semidirect
65. C2×C5×D12C2×C4semidirect
86. C3×#681C2×C4semidirect
91. #6659C2×C4semidirect
92. #6654C2×C4semidirect
94. #5521D5semidirect
130. #3940C2×D3semidirect
131. #3939C2×D3semidirect
230. #681C4×D3semidirect
275. C2×D12C4×D5semidirect
462. C3×C5#2946semidirect
527. C5#79201semidirect
548. C3#10614268semidirect

Maximal subgroups

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

subgroupindex
C5×#55212
#117544962
C2×#913042
#117511032
C3×#652842
C2×#909662
#117483272
#117474732
#117474702
#117472772
#117472302
#106142683
#792015