Finite Group Databasebeta

← #14425763

Subgroups — #14425763

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic, complemented
2C5×#5830C211yesmaximal, characteristic, complemented
3#11754604C212yesmaximal, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11749175C218yesmaximal, complemented
6#11748624C212yesmaximal, complemented
7#10615127—31nomaximal, Hall
8C2×C3×C5×#41C2211yescharacteristic
9C22×C5×D12C2211yescharacteristic, complemented
10C3×#4150—22no—
11C3×#4149—22no—
12C3×D5×#41—24no—
13C3×#4147—21no—
14C3×#4144—21no—
15C3×#4144C2214yes—
16C2×C3×#709—22no—
17C2×C3×#709C2212yes—
18#91815C2212yescomplemented
19C5×#947—21no—
20C5×#940—21no—
21C5×#937C2214yescomplemented
22C5×#930—22no—
23C5×#926C2211yescharacteristic, complemented
24#91568C2218yescomplemented
25#91463—22no—
26#91449—24no—
27#91370—22no—
28#91118C2214yescomplemented
29#90995C2218yescomplemented
30#84126—51nomaximal, Hall
31#66283D311yescharacteristic, complemented
32C5×#535—31no—
33#66139—32no—
34#65529—31no—
35#65321—38no—
36#65295—32no—
37C23×C5×D3C2312yes—
38C3×C5×#41—22no—
39C3×C5×#41—22no—
40C2×C3×C5×Q8D411yescharacteristic, complemented
41C2×C3×C5×D4D411yescharacteristic, complemented
42C2×C3×C5×D4C2312yes—
43C22×C3×C4×C5D412yescomplemented
44C22×C3×C4×C5C2311yescharacteristic
45C2×C5×#67—24no—
46C2×C5×D12—22no—
47C2×C5×D12—22no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C3×C22⋊D5—24no—
51C2×C3×C22⋊D5C2314yes—
52C3×#713—24no—
53C3×Q8×D5—24no—
54C3×#711—24no—
55C3×#711—28no—
56C3×D4×D5—24no—
57C3×D4×D5—28no—
58C3×#709—24no—
59C3×#709—24no—
60C3×#709—22no—
61C3×#709—24no—
62C3×#709—22no—
63C3×#709—22no—
64C3×#709—22no—
65C2×C3×D20—22no—
66C2×C3×D20D412yescomplemented
67C2×C3×C4×D5—24no—
68C2×C3×C4×D5D414yescomplemented
69C2×C3×Dic10—22no—
70C2×C3×Dic10D412yescomplemented
71C2×#1201—28no—
72#6719C2314yes—
73C4⋊Dic15—22no—
74C4×Dic15—22no—
75C5×#217C2312yes—
76C5×(C2×D3)⋊C4—24no—
77C5×C4⋊Dic3—21no—
78C4×C5×Dic3—21no—
79(C2×D3)⋊Dic5—28no—
80C3×#585—51no—
81#5830—52no—
82#5830D511yescharacteristic, complemented
83#5244—58no—
84#5240—51no—
85#5240—52no—
86C2×C5×#41C2×D311yescharacteristic
87C22×C5×D4—31no—
88#4150—22no—
89#4149—22no—
90D5×#41—24no—
91#4147—21no—
92#4144—21no—
93#4144C2×D314yes—
94C2×#709—22no—
95C2×#709C2×D312yes—
96C5×#127—61no—
97C5×#124—61no—
98C5×#121—62no—
99C5×#120—34no—
100C5×#117—31no—
101#4099—38no—
102#4086—62no—
103#4084—64no—
104#4082—62no—
105#4072—32no—
106#3966—34no—
107#3938—38no—
108#3027—151noSylow
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2411yescharacteristic
111C22×C5×D3—24no—
112C22×C5×D3—22no—
113C22×C5×D3—82no—
114C22×C3×D5—24no—
115C22×C3×D5C2×D414yes—
116C3×C5×Q8—22no—
117C3×C5×D4—24no—
118C3×C5×D4—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5C2×D412yes—
122C2×C3×C4×C5C2×D412yes—
123C2×C3×C4×C5C2×D412yes—
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×Dic15—24no—
127C5×#67—84no—
128C2×C5×Dic3—22no—
129C5×D12—41no—
130C5×D12—42no—
131C5×D12—41no—
132C3×C22⋊D5—28no—
133C3×C22⋊D5—24no—
134C3×C22⋊D5—24no—
135C2×C3×Dic5—24no—
136C2×C3×Dic5C2×D414yes—
137C3×D20—24no—
138C3×D20—22no—
139C3×D20—22no—
140C3×C4×D5—28no—
141C3×C4×D5—24no—
142C3×C4×D5—24no—
143C3×Dic10—24no—
144C3×Dic10—22no—
145C3×Dic10—22no—
146#1201—88no—
147C3×2−1+4—102no—
148C3×2−1+4—101no—
149C3×H(5,𝔽2)—54no—
150C3×H(5,𝔽2)—102no—
151C3×H(5,𝔽2)—101no—
152C2×C3×#41—52no—
153C2×C3×#41—104no—
154C2×C3×#41—102no—
155C2×C3×#41C2×D511yescharacteristic
156C22×D12C2×D511yescharacteristic, complemented
157#947—21no—
158#947—102no—
159#940—21no—
160#940—102no—
161#937—58no—
162#937C2×D514yescomplemented
163#930—22no—
164#930—104no—
165#926—52no—
166#926C2×D511yescharacteristic, complemented
167#834—54no—
168#834—58no—
169C24×C5—32no—
170C5×#41—22no—
171C5×#41—22no—
172C2×C5×Q8#6711yescharacteristic, complemented
173C2×C5×D4—64no—
174C2×C5×D4—61no—
175C2×C5×D4—61no—
176C2×C5×D4—62no—
177C2×C5×D4—62no—
178C2×C5×D4#6711yescharacteristic, complemented
179C2×C5×D4C22×D312yes—
180C22×C4×C5#6712yescomplemented
181C22×C4×C5C22×D311yescharacteristic
182C2×C22⋊D5—24no—
183C2×C22⋊D5—68no—
184C2×C22⋊D5C22×D314yes—
185#713—24no—
186Q8×D5—24no—
187#711—24no—
188#711—28no—
189D4×D5—24no—
190D4×D5—28no—
191#709—24no—
192#709—24no—
193#709—22no—
194#709—24no—
195#709—22no—
196#709—22no—
197#709—22no—
198C2×D20—22no—
199C2×D20#6712yescomplemented
200C2×C4×D5—24no—
201C2×C4×D5#6714yescomplemented
202C2×Dic10—22no—
203C2×Dic10#6712yescomplemented
204C5×C4⋊C4—61no—
205C5×C22⋊C4—32no—
206C5×C22⋊C4—64no—
207C42×C5—61no—
208C22⋊Dic5—34no—
209C22⋊Dic5—68no—
210C4⋊Dic5—62no—
211C4×Dic5—62no—
212#585—51no—
213#535—31no—
214#535—152no—
215B(4,𝔽2)—158no—
216#410—152no—
217#410—151no—
218C22×C3×C5—22no—
219C22×C3×C5—41no—
220C22×C3×C5—42no—
221C22×C3×C5C22×D412yes—
222C22×C3×C5C22×D411yescharacteristic
223C2×C5×D3—48no—
224C2×C5×D3—44no—
225C2×C5×D3—42no—
226C2×C3×D5—24no—
227C2×C3×D5—44no—
228C2×C3×D5—84no—
229C3×C4×C5—22no—
230C3×C4×C5#12011yescharacteristic
231C3×C4×C5#12012yes—
232C3×C4×C5#12011yescharacteristic
233Dic15—44no—
234C3×Dic5—24no—
235C5×Dic3—42no—
236C23×D3C22×D512yes—
237C3×#41—22no—
238C3×#41—22no—
239C3×#41—104no—
240C3×#41—104no—
241C3×#41—108no—
242C3×#41—104no—
243C3×#41—104no—
244C3×#41—102no—
245C3×#41—102no—
246C3×#41—102no—
247C3×#41—102no—
248C3×#41—104no—
249C2×C3×Q8—52no—
250C2×C3×Q8—102no—
251C2×C3×Q8—104no—
252C2×C3×Q8C22⋊D511yescharacteristic, complemented
253C2×C3×D4—54no—
254C2×C3×D4—52no—
255C2×C3×D4—102no—
256C2×C3×D4—108no—
257C2×C3×D4—104no—
258C2×C3×D4—104no—
259C2×C3×D4C22⋊D511yescharacteristic, complemented
260C2×C3×D4C22×D512yes—
261C22×C3×C4—54no—
262C22×C3×C4—104no—
263C22×C3×C4C22⋊D512yescomplemented
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—24no—
266C2×#67—108no—
267C2×D12—22no—
268C2×D12—22no—
269C2×D12—21no—
270C2×D12—21no—
271#217—54no—
272#217C22×D512yes—
273(C2×D3)⋊C4—24no—
274(C2×D3)⋊C4—108no—
275C4⋊Dic3—21no—
276C4⋊Dic3—102no—
277C4×Dic3—21no—
278C4×Dic3—102no—
279C23×C5—64no—
280C23×C5—62no—
281C23×C5—242no—
282C23×C5C2×#6712yes—
283C23×C5C23×D311yescharacteristic
284C22×D5—24no—
285C22×D5C2×#6714yes—
286C5×Q8—22no—
287C5×D4—24no—
288C5×D4—22no—
289C5×D4—121no—
290C5×D4—122no—
291C5×D4—121no—
292C5×D4—244no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—62no—
296C2×C4×C5C2×#6712yes—
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C2×#6712yes—
300C2×C4×C5C2×#6712yes—
301C22⋊D5—28no—
302C22⋊D5—24no—
303C22⋊D5—24no—
304C22⋊D5—248no—
305C2×Dic5—24no—
306C2×Dic5—64no—
307C2×Dic5C2×#6714yes—
308D20—24no—
309D20—22no—
310D20—22no—
311C4×D5—28no—
312C4×D5—24no—
313C4×D5—24no—
314Dic10—24no—
315Dic10—22no—
316Dic10—22no—
3172−1+4—102no—
3182−1+4—101no—
319H(5,𝔽2)—54no—
320H(5,𝔽2)—102no—
321H(5,𝔽2)—101no—
322C2×#41—52no—
323C2×#41—104no—
324C2×#41—102no—
325C2×#41D3×D511yescharacteristic
326C22×D4—31no—
327#127—61no—
328#127—302no—
329#124—61no—
330#124—302no—
331#121—62no—
332#121—304no—
333#120—34no—
334#120—158no—
335#117—31no—
336#117—152no—
337#99—158no—
338#99—154no—
339C2×C3×C5—21no—
340C2×C3×C5—22no—
341C2×C3×C5—42no—
342C2×C3×C5C2×#12011yescharacteristic
343C3×D5—44no—
344C5×D3—82no—
345C23×C3—54no—
346C23×C3—104no—
347C23×C3C2×C22⋊D512yes—
348C23×C3C23×D511yescharacteristic
349C22×D3—24no—
350C22×D3—22no—
351C22×D3—82no—
352C3×Q8—22no—
353C3×Q8—104no—
354C3×Q8—102no—
355C3×Q8—102no—
356C3×D4—24no—
357C3×D4—22no—
358C3×D4—104no—
359C3×D4—108no—
360C3×D4—104no—
361C3×D4—104no—
362C3×D4—102no—
363C3×D4—102no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—54no—
367C2×C3×C4—108no—
368C2×C3×C4—104no—
369C2×C3×C4—104no—
370C2×C3×C4—104no—
371C2×C3×C4D4×D512yes—
372C2×C3×C4D4×D512yes—
373C2×C3×C4C2×C22⋊D512yes—
374C2×C3×C4C2×C22⋊D511yescharacteristic
375C2×C3×C4C2×C22⋊D511yescharacteristic
376#67—84no—
377#67—408no—
378C2×Dic3—22no—
379C2×Dic3—104no—
380D12—41no—
381D12—41no—
382D12—42no—
383C22×C5—22no—
384C22×C5—41no—
385C22×C5—42no—
386C22×C5—128no—
387C22×C5—124no—
388C22×C5—122no—
389C22×C5C22×#6711yescharacteristic
390C22×C5C22×#6712yes—
391C2×D5—24no—
392C2×D5—44no—
393C2×D5—84no—
394C4×C5—22no—
395C4×C5—122no—
396C4×C5#95311yescharacteristic
397C4×C5#95312yes—
398C4×C5#95311yescharacteristic
399Dic5—24no—
400Dic5—124no—
401C24—32no—
402#41—22no—
403#41—22no—
404#41—104no—
405#41—104no—
406#41—108no—
407#41—104no—
408#41—104no—
409#41—102no—
410#41—102no—
411#41—104no—
412#41—102no—
413#41—102no—
414C2×Q8—52no—
415C2×Q8—102no—
416C2×Q8—104no—
417C2×Q8#120111yescharacteristic, complemented
418C2×D4—54no—
419C2×D4—52no—
420C2×D4—64no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—62no—
424C2×D4—62no—
425C2×D4—102no—
426C2×D4—108no—
427C2×D4—104no—
428C2×D4—104no—
429C2×D4—308no—
430C2×D4#120111yescharacteristic, complemented
431C2×D4C2×D3×D512yes—
432C22×C4—54no—
433C22×C4—104no—
434C22×C4#120112yescomplemented
435C22×C4C2×D3×D511yescharacteristic
436C4⋊C4—61no—
437C4⋊C4—302no—
438C22⋊C4—32no—
439C22⋊C4—64no—
440C22⋊C4—154no—
441C22⋊C4—308no—
442C42—61no—
443C42—302no—
444C3×C5#302711yescharacteristic, complemented, Hall
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—42no—
448C22×C3—104no—
449C22×C3—204no—
450C22×C3—404no—
451C22×C3C2×D4×D512yes—
452C22×C3C22×C22⋊D511yescharacteristic
453C2×D3—44no—
454C2×D3—48no—
455C2×D3—42no—
456C3×C4—22no—
457C3×C4—104no—
458C3×C4#408311yescharacteristic
459C3×C4#408311yescharacteristic
460C3×C4#408312yes—
461Dic3—42no—
462Dic3—204no—
463C2×C5—22no—
464C2×C5—21no—
465C2×C5—42no—
466C2×C5—242no—
467C2×C5C2×#95311yescharacteristic
468D5—44no—
469C23—54no—
470C23—62no—
471C23—64no—
472C23—104no—
473C23—242no—
474C23C2×#120112yes—
475C23C22×D3×D511yescharacteristic
476Q8—22no—
477Q8—104no—
478Q8—102no—
479Q8—102no—
480D4—24no—
481D4—22no—
482D4—104no—
483D4—108no—
484D4—104no—
485D4—104no—
486D4—102no—
487D4—102no—
488D4—121no—
489D4—121no—
490D4—122no—
491D4—244no—
492D4—1208no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—54no—
496C2×C4—62no—
497C2×C4—108no—
498C2×C4—104no—
499C2×C4—104no—
500C2×C4—104no—
501C2×C4—304no—
502C2×C4C2×#120112yes—
503C2×C4C2×#120111yescharacteristic
504C2×C4C2×#120111yescharacteristic
505C2×C4D5×#6712yes—
506C2×C4D5×#6712yes—
507C2×C3—21no—
508C2×C3—22no—
509C2×C3—42no—
510C2×C3—204no—
511C2×C3C2×#408311yescharacteristic
512D3—82no—
513C5#8412611yescharacteristic, complemented, Sylow
514C22—22no—
515C22—41no—
516C22—42no—
517C22—104no—
518C22—124no—
519C22—128no—
520C22—122no—
521C22—204no—
522C22—404no—
523C22C22×#120111yescharacteristic
524C22C2×D5×#6712yes—
525C4—22no—
526C4—104no—
527C4—122no—
528C4—604no—
529C4#9156311yescharacteristic
530C4#9156311yescharacteristic
531C4#9156312yes—
532C3#1061512711yescharacteristic, complemented, Sylow
533C2—21no—
534C2—22no—
535C2—42no—
536C2—204no—
537C2—242no—
538C2C2×#9156311yescharacteristic
subgroupG/H
centerC2C2×#91563
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3027
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#66283C2semidirect
2. C5×#5830C2semidirect
3. #11754604C2semidirect
4. #11751341C2semidirect
5. #11749175C2semidirect
6. #11748624C2semidirect
9. C22×C5×D12C22semidirect
18. #91815C22semidirect
21. C5×#937C22semidirect
23. C5×#926C22semidirect
24. #91568C22semidirect
28. #91118C22semidirect
29. #90995C22semidirect
31. #66283D3semidirect
40. C2×C3×C5×Q8D4semidirect
41. C2×C3×C5×D4D4semidirect
43. C22×C3×C4×C5D4semidirect
66. C2×C3×D20D4semidirect
68. C2×C3×C4×D5D4semidirect
70. C2×C3×Dic10D4semidirect
82. #5830D5semidirect
156. C22×D12C2×D5semidirect
162. #937C2×D5semidirect
166. #926C2×D5semidirect
172. C2×C5×Q8#67semidirect
178. C2×C5×D4#67semidirect
180. C22×C4×C5#67semidirect
199. C2×D20#67semidirect
201. C2×C4×D5#67semidirect
203. C2×Dic10#67semidirect
252. C2×C3×Q8C22⋊D5semidirect
259. C2×C3×D4C22⋊D5semidirect
263. C22×C3×C4C22⋊D5semidirect
417. C2×Q8#1201semidirect
430. C2×D4#1201semidirect
434. C22×C4#1201semidirect
444. C3×C5#3027semidirect
513. C5#84126semidirect
532. C3#10615127semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
C5×#58302
#117546042
#117513412
#117491752
#117486242
#106151273
#841265