Finite Group Databasebeta

← #14425768

Subgroups — #14425768

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
2#11756589C211yesmaximal, characteristic, complemented
3#11754609C212yesmaximal, complemented
4C5×#5240C211yesmaximal, characteristic, complemented
5#11749176C218yesmaximal, complemented
6#11748624C212yesmaximal, complemented
7#10610422—31nomaximal, Hall
8C2×C3×C5×#41C2211yescharacteristic
9C22×D60C2211yescharacteristic, 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#91836—21no—
19#91829—21no—
20#91826C2214yescomplemented
21#91819—22no—
22#91815C2211yescharacteristic, complemented
23C5×#926C2212yescomplemented
24#91572C2218yescomplemented
25#91458—22no—
26#91450—24no—
27#91374—22no—
28C5×#834C2214yescomplemented
29#90995C2218yescomplemented
30#84126—51nomaximal, Hall
31#66283D311yescharacteristic, complemented
32#66164—31no—
33#65859—32no—
34C5×#410—31no—
35#65295—32no—
36#65030—38no—
37C23×D15C2312yes—
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×#1220—24no—
46C2×D60—22no—
47C2×D60—22no—
48C2×D60—21no—
49C2×D60—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×#1202—28no—
72#6719C2312yes—
73#6714—24no—
74C4⋊Dic15—21no—
75C4×Dic15—21no—
76C5×#217C2314yes—
77C5×C4⋊Dic3—22no—
78C4×C5×Dic3—22no—
79#6667—28no—
80C3×#585—51no—
81#5830—51no—
82#5830—52no—
83#5244—58no—
84#5240—52no—
85#5240D511yescharacteristic, complemented
86C2×C5×#41C2×D311yescharacteristic
87#4150—22no—
88#4149—22no—
89D5×#41—24no—
90#4147—21no—
91#4144—21no—
92#4144C2×D314yes—
93C2×#709—22no—
94C2×#709C2×D312yes—
95C22×D20—31no—
96C5×#117—32no—
97#4093—61no—
98#4086—61no—
99#4083—34no—
100#4076—62no—
101#4072—31no—
102#4041—64no—
103#4028—38no—
104#4021—62no—
105#4020—62no—
106C5×#99—34no—
107#3938—38no—
108#3027—151noSylow
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2411yescharacteristic
111C22×D15—24no—
112C22×D15—22no—
113C22×D15—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×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D412yes—
125C2×C3×C4×C5C2×D412yes—
126#1220—84no—
127C2×Dic15—22no—
128D60—41no—
129D60—42no—
130D60—41no—
131C2×C5×Dic3—24no—
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#1202—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×D12—51no—
157#947—102no—
158#947—101no—
159#940—102no—
160#940—101no—
161#937—54no—
162#937—58no—
163#930—104no—
164#930—102no—
165#926—51no—
166#926C2×D512yescomplemented
167#834—58no—
168#834C2×D514yescomplemented
169C23×D5—32no—
170C5×#41—22no—
171C5×#41—22no—
172C2×C5×Q8#6711yescharacteristic, complemented
173C2×C5×D4#6711yescharacteristic, complemented
174C2×C5×D4C22×D312yes—
175C22×C4×C5#6712yescomplemented
176C22×C4×C5C22×D311yescharacteristic
177C2×C22⋊D5—24no—
178C2×C22⋊D5—64no—
179C2×C22⋊D5C22×D314yes—
180#713—24no—
181Q8×D5—24no—
182#711—24no—
183#711—28no—
184D4×D5—24no—
185D4×D5—28no—
186#709—24no—
187#709—24no—
188#709—22no—
189#709—24no—
190#709—22no—
191#709—22no—
192#709—22no—
193C2×D20—22no—
194C2×D20—62no—
195C2×D20—62no—
196C2×D20—61no—
197C2×D20—61no—
198C2×D20—68no—
199C2×D20#6712yescomplemented
200C2×C4×D5—24no—
201C2×C4×D5#6714yescomplemented
202C2×Dic10—22no—
203C2×Dic10#6712yescomplemented
204C5×C4⋊C4—62no—
205C5×C22⋊C4—34no—
206C42×C5—62no—
207C22⋊Dic5—32no—
208#685—64no—
209#685—68no—
210C4⋊Dic5—61no—
211C4×Dic5—61no—
212#585—51no—
213#535—152no—
214#535—151no—
215B(4,𝔽2)—158no—
216#410—31no—
217#410—152no—
218C22×C3×C5—22no—
219C22×C3×C5—41no—
220C22×C3×C5—42no—
221C22×C3×C5C22×D411yescharacteristic
222C22×C3×C5C22×D412yes—
223C2×D15—48no—
224C2×D15—44no—
225C2×D15—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—42no—
234C3×Dic5—24no—
235C5×Dic3—44no—
236C23×D3—52no—
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—104no—
247C3×#41—102no—
248C3×#41—102no—
249C2×C3×Q8—52no—
250C2×C3×Q8—102no—
251C2×C3×Q8—104no—
252C2×C3×Q8D2011yescharacteristic, 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×D4D2011yescharacteristic, complemented
260C2×C3×D4C22×D512yes—
261C22×C3×C4—54no—
262C22×C3×C4—104no—
263C22×C3×C4D2012yescomplemented
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—108no—
266C2×#67—104no—
267C2×D12—101no—
268C2×D12—101no—
269C2×D12—102no—
270C2×D12—102no—
271#217—52no—
272#217C22×D514yes—
273(C2×D3)⋊C4—108no—
274(C2×D3)⋊C4—104no—
275C4⋊Dic3—22no—
276C4⋊Dic3—101no—
277C4×Dic3—22no—
278C4×Dic3—101no—
279C23×C5C2×#6712yes—
280C23×C5C23×D311yescharacteristic
281C22×D5—24no—
282C22×D5—64no—
283C22×D5—62no—
284C22×D5—242no—
285C22×D5C2×#6714yes—
286C5×Q8—22no—
287C5×D4—24no—
288C5×D4—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—64no—
292C2×C4×C5C2×#6712yes—
293C2×C4×C5C2×#6711yescharacteristic
294C2×C4×C5C2×#6711yescharacteristic
295C2×C4×C5C2×#6712yes—
296C2×C4×C5C2×#6712yes—
297C22⋊D5—28no—
298C22⋊D5—24no—
299C22⋊D5—24no—
300C22⋊D5—244no—
301C2×Dic5—24no—
302C2×Dic5—62no—
303C2×Dic5C2×#6714yes—
304D20—24no—
305D20—22no—
306D20—22no—
307D20—121no—
308D20—122no—
309D20—121no—
310D20—248no—
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—151no—
327#127—302no—
328#127—301no—
329#124—302no—
330#124—301no—
331#121—304no—
332#121—302no—
333#120—158no—
334#120—154no—
335#117—32no—
336#117—151no—
337#99—34no—
338#99—158no—
339C2×C3×C5—22no—
340C2×C3×C5—21no—
341C2×C3×C5—42no—
342C2×C3×C5C2×#12011yescharacteristic
343D15—82no—
344C3×D5—44no—
345C23×C3—54no—
346C23×C3—104no—
347C23×C3C2×D2012yes—
348C23×C3C23×D511yescharacteristic
349C22×D3—102no—
350C22×D3—104no—
351C22×D3—402no—
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×C4C2×D2012yes—
372C2×C3×C4C2×D2011yescharacteristic
373C2×C3×C4C2×D2011yescharacteristic
374C2×C3×C4D4×D512yes—
375C2×C3×C4D4×D512yes—
376#67—408no—
377#67—404no—
378C2×Dic3—24no—
379C2×Dic3—102no—
380D12—201no—
381D12—201no—
382D12—202no—
383C22×C5—22no—
384C22×C5—41no—
385C22×C5—42no—
386C22×C5C22×#6711yescharacteristic
387C22×C5C22×#6712yes—
388C2×D5—24no—
389C2×D5—44no—
390C2×D5—84no—
391C2×D5—128no—
392C2×D5—124no—
393C2×D5—122no—
394C4×C5—22no—
395C4×C5—124no—
396C4×C5#95311yescharacteristic
397C4×C5#95312yes—
398C4×C5#95311yescharacteristic
399Dic5—24no—
400Dic5—122no—
401C24—152no—
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#120211yescharacteristic, complemented
418C2×D4—54no—
419C2×D4—52no—
420C2×D4—102no—
421C2×D4—108no—
422C2×D4—104no—
423C2×D4—104no—
424C2×D4—308no—
425C2×D4—304no—
426C2×D4—301no—
427C2×D4—301no—
428C2×D4—302no—
429C2×D4—302no—
430C2×D4#120211yescharacteristic, complemented
431C2×D4C2×D3×D512yes—
432C22×C4—54no—
433C22×C4—104no—
434C22×C4#120212yescomplemented
435C22×C4C2×D3×D511yescharacteristic
436C4⋊C4—62no—
437C4⋊C4—301no—
438C22⋊C4—34no—
439C22⋊C4—152no—
440C22⋊C4—308no—
441C22⋊C4—304no—
442C42—62no—
443C42—301no—
444C3×C5#302711yescharacteristic, complemented, Hall
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—42no—
448C22×C3—104no—
449C22×C3—204no—
450C22×C3—404no—
451C22×C3C22×D2011yescharacteristic
452C22×C3C2×D4×D512yes—
453C2×D3—208no—
454C2×D3—204no—
455C2×D3—202no—
456C3×C4—22no—
457C3×C4—104no—
458C3×C4#402811yescharacteristic
459C3×C4#402811yescharacteristic
460C3×C4#402812yes—
461Dic3—44no—
462Dic3—202no—
463C2×C5—21no—
464C2×C5—22no—
465C2×C5—42no—
466C2×C5C2×#95311yescharacteristic
467D5—44no—
468D5—242no—
469C23—54no—
470C23—104no—
471C23—302no—
472C23—304no—
473C23—1202no—
474C23C2×#120212yes—
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—601no—
489D4—601no—
490D4—602no—
491D4—1208no—
492D4—1204no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—54no—
496C2×C4—64no—
497C2×C4—108no—
498C2×C4—104no—
499C2×C4—104no—
500C2×C4—104no—
501C2×C4—302no—
502C2×C4C2×#120212yes—
503C2×C4C2×#120211yescharacteristic
504C2×C4C2×#120211yescharacteristic
505C2×C4D5×#6712yes—
506C2×C4D5×#6712yes—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—42no—
510C2×C3—204no—
511C2×C3C2×#402811yescharacteristic
512D3—402no—
513C5#8412611yescharacteristic, complemented, Sylow
514C22—22no—
515C22—41no—
516C22—42no—
517C22—104no—
518C22—204no—
519C22—404no—
520C22—608no—
521C22—604no—
522C22—602no—
523C22C22×#120211yescharacteristic
524C22C2×D5×#6712yes—
525C4—22no—
526C4—104no—
527C4—124no—
528C4—602no—
529C4#9156411yescharacteristic
530C4#9156411yescharacteristic
531C4#9156412yes—
532C3#1061042211yescharacteristic, complemented, Sylow
533C2—22no—
534C2—21no—
535C2—42no—
536C2—204no—
537C2—1202no—
538C2C2×#9156411yescharacteristic
subgroupG/H
centerC2C2×#91564
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. #11756589C2semidirect
3. #11754609C2semidirect
4. C5×#5240C2semidirect
5. #11749176C2semidirect
6. #11748624C2semidirect
9. C22×D60C22semidirect
20. #91826C22semidirect
22. #91815C22semidirect
23. C5×#926C22semidirect
24. #91572C22semidirect
28. C5×#834C22semidirect
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
85. #5240D5semidirect
166. #926C2×D5semidirect
168. #834C2×D5semidirect
172. C2×C5×Q8#67semidirect
173. C2×C5×D4#67semidirect
175. C22×C4×C5#67semidirect
199. C2×D20#67semidirect
201. C2×C4×D5#67semidirect
203. C2×Dic10#67semidirect
252. C2×C3×Q8D20semidirect
259. C2×C3×D4D20semidirect
263. C22×C3×C4D20semidirect
417. C2×Q8#1202semidirect
430. C2×D4#1202semidirect
434. C22×C4#1202semidirect
444. C3×C5#3027semidirect
513. C5#84126semidirect
532. C3#10610422semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
#117565892
#117546092
C5×#52402
#117491762
#117486242
#106104223
#841265