Finite Group Databasebeta

← #14425767

Subgroups — #14425767

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
1#11757146C211yesmaximal, characteristic, complemented
2C3×#66164C211yesmaximal, characteristic, complemented
3#11754602C212yesmaximal, complemented
4C5×#5240C211yesmaximal, characteristic, complemented
5#11749179C218yesmaximal, complemented
6#11748626C212yesmaximal, complemented
7#10610422—31nomaximal, Hall
8C2×C3×C5×#41C2211yescharacteristic
9#92101—22no—
10#92100—22no—
11#41×D15—24no—
12#92098—21no—
13#92095—21no—
14#92095C2214yes—
15C2×#6817—22no—
16C2×#6817C2212yes—
17C22×C3×D20C2211yescharacteristic, complemented
18C5×#926C2212yescomplemented
19C3×#4093—21no—
20C3×#4086—21no—
21C3×#4083C2214yescomplemented
22C3×#4076—22no—
23C3×#4072C2211yescharacteristic, complemented
24#91564C2218yescomplemented
25#91465—24no—
26#91458—22no—
27#91364—22no—
28C5×#834C2214yescomplemented
29#90997C2218yescomplemented
30#83396—51nomaximal, Hall
31#66283—31no—
32#66164D311yescharacteristic, complemented
33#65859—32no—
34C5×#410—31no—
35#65295—32no—
36#65030—38no—
37C23×C3×D5C2312yes—
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×#1220C2314yes—
47#6821—24no—
48Q8×D15—24no—
49#6819—24no—
50#6819—28no—
51D4×D15—24no—
52D4×D15—28no—
53#6817—24no—
54#6817—24no—
55#6817—22no—
56#6817—24no—
57#6817—22no—
58#6817—22no—
59#6817—22no—
60C2×D60—22no—
61C2×D60D412yescomplemented
62C2×C4×D15—24no—
63C2×C4×D15D414yescomplemented
64C2×Dic30—22no—
65C2×Dic30D412yescomplemented
66C2×C3×C22⋊D5—24no—
67C2×C3×D20—21no—
68C2×C3×D20—22no—
69C2×C3×D20—22no—
70C2×C3×D20—21no—
71C2×#1202—28no—
72C5×#217C2314yes—
73C5×C4⋊Dic3—22no—
74C4×C5×Dic3—22no—
75C3×C22⋊Dic5C2312yes—
76C3×#685—24no—
77C3×C4⋊Dic5—21no—
78C3×C4×Dic5—21no—
79#6665—28no—
80#5964—51no—
81C3×#535—51no—
82#5805—52no—
83#5240D511yescharacteristic, complemented
84#5032—58no—
85#5006—52no—
86C2×C5×#41C2×D311yescharacteristic
87#4150—62no—
88#4149—62no—
89D5×#41—64no—
90#4147—61no—
91#4144—34no—
92#4144—61no—
93C2×#709—32no—
94C2×#709—62no—
95C22×D20C2×D311yescharacteristic, complemented
96C5×#117—32no—
97#4093—21no—
98#4086—21no—
99#4083C2×D314yescomplemented
100#4076—22no—
101#4072C2×D311yescharacteristic, complemented
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×D15C2×D414yes—
113C22×C3×D5—24no—
114C22×C3×D5—22no—
115C22×C3×D5—82no—
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—28no—
127#1220—24no—
128#1220—24no—
129C2×Dic15—24no—
130C2×Dic15C2×D414yes—
131D60—24no—
132D60—22no—
133D60—22no—
134C4×D15—28no—
135C4×D15—24no—
136C4×D15—24no—
137Dic30—24no—
138Dic30—22no—
139Dic30—22no—
140C2×C5×Dic3—24no—
141C3×C22⋊D5—84no—
142C2×C3×Dic5—22no—
143C3×D20—41no—
144C3×D20—42no—
145C3×D20—41no—
146#1202—88no—
147C2×C3×#41C2×D511yescharacteristic
148C22×C3×D4—51no—
149#1010—102no—
150#1009—102no—
151D3×#41—104no—
152#1007—101no—
153#1004—54no—
154#1004—101no—
155C2×#235—52no—
156C2×#235—102no—
157C3×#127—101no—
158C3×#124—101no—
159C3×#121—102no—
160C3×#120—54no—
161C3×#117—51no—
162#953—58no—
163#940—102no—
164#938—104no—
165#936—102no—
166#926C2×D512yescomplemented
167#834C2×D514yescomplemented
168#806—58no—
169C23×D5C22×D312yes—
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—34no—
179C2×C22⋊D5—64no—
180#713—64no—
181Q8×D5—64no—
182#711—68no—
183#711—64no—
184D4×D5—68no—
185D4×D5—64no—
186#709—64no—
187#709—64no—
188#709—62no—
189#709—62no—
190#709—62no—
191#709—62no—
192#709—64no—
193C2×D20—22no—
194C2×D20—22no—
195C2×D20—21no—
196C2×D20—21no—
197C2×D20—32no—
198C2×D20—62no—
199C2×D20—68no—
200C2×C4×D5—34no—
201C2×C4×D5—64no—
202C2×Dic10—32no—
203C2×Dic10—62no—
204C5×C4⋊C4—62no—
205C5×C22⋊C4—34no—
206C42×C5—62no—
207C22⋊Dic5C22×D312yes—
208#685—24no—
209#685—68no—
210C4⋊Dic5—21no—
211C4×Dic5—21no—
212#585—151no—
213#535—51no—
214#535—152no—
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—24no—
224C2×D15—44no—
225C2×D15—84no—
226C2×C3×D5—48no—
227C2×C3×D5—44no—
228C2×C3×D5—42no—
229C3×C4×C5—22no—
230C3×C4×C5#12011yescharacteristic
231C3×C4×C5#12012yes—
232C3×C4×C5#12011yescharacteristic
233Dic15—24no—
234C3×Dic5—42no—
235C5×Dic3—44no—
236C24×C3—52no—
237C3×#41—22no—
238C3×#41—22no—
239C2×C3×Q8D2011yescharacteristic, complemented
240C2×C3×D4—104no—
241C2×C3×D4—101no—
242C2×C3×D4—101no—
243C2×C3×D4—102no—
244C2×C3×D4—102no—
245C2×C3×D4D2011yescharacteristic, complemented
246C2×C3×D4C22×D512yes—
247C22×C3×C4D2012yescomplemented
248C22×C3×C4C22×D511yescharacteristic
249C2×#67—54no—
250C2×#67—108no—
251C2×#67—104no—
252#239—104no—
253D3×Q8—104no—
254#237—108no—
255#237—104no—
256D3×D4—108no—
257D3×D4—104no—
258#235—104no—
259#235—104no—
260#235—102no—
261#235—102no—
262#235—104no—
263#235—102no—
264#235—102no—
265C2×D12—52no—
266C2×D12—102no—
267C2×C4×D3—54no—
268C2×C4×D3—104no—
269C2×Dic6—52no—
270C2×Dic6—102no—
271C3×C4⋊C4—101no—
272C3×C22⋊C4—52no—
273C3×C22⋊C4—104no—
274C3×C42—101no—
275#217—108no—
276#217C22×D514yes—
277C4⋊Dic3—22no—
278C4×Dic3—22no—
279C23×C5C2×#6712yes—
280C23×C5C23×D311yescharacteristic
281C22×D5—24no—
282C22×D5—22no—
283C22×D5—34no—
284C22×D5—64no—
285C22×D5—82no—
286C5×Q8—22no—
287C5×D4—24no—
288C5×D4—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—64no—
292C2×C4×C5D3×D412yes—
293C2×C4×C5D3×D412yes—
294C2×C4×C5C2×#6712yes—
295C2×C4×C5C2×#6711yescharacteristic
296C2×C4×C5C2×#6711yescharacteristic
297C22⋊D5—68no—
298C22⋊D5—64no—
299C22⋊D5—64no—
300C22⋊D5—84no—
301C2×Dic5—22no—
302C2×Dic5—34no—
303C2×Dic5—64no—
304D20—41no—
305D20—42no—
306D20—41no—
307D20—64no—
308D20—62no—
309D20—62no—
310D20—248no—
311C4×D5—68no—
312C4×D5—64no—
313C4×D5—64no—
314Dic10—64no—
315Dic10—62no—
316Dic10—62no—
3172−1+4—302no—
3182−1+4—301no—
319H(5,𝔽2)—154no—
320H(5,𝔽2)—302no—
321H(5,𝔽2)—301no—
322C2×#41—152no—
323C2×#41—304no—
324C2×#41—302no—
325C2×#41D3×D511yescharacteristic
326C22×D4—51no—
327#127—101no—
328#127—302no—
329#124—101no—
330#124—302no—
331#121—102no—
332#121—304no—
333#120—54no—
334#120—158no—
335#117—32no—
336#117—51no—
337#99—34no—
338#99—158no—
339C2×C3×C5—22no—
340C2×C3×C5—21no—
341C2×C3×C5—42no—
342C2×C3×C5C2×#12011yescharacteristic
343D15—44no—
344C3×D5—82no—
345C23×C3—102no—
346C23×C3—104no—
347C23×C3—402no—
348C23×C3C2×D2012yes—
349C23×C3C23×D511yescharacteristic
350C22×D3—54no—
351C22×D3—104no—
352C3×Q8—22no—
353C3×D4—24no—
354C3×D4—22no—
355C3×D4—201no—
356C3×D4—202no—
357C3×D4—201no—
358C3×D4—404no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—102no—
362C2×C3×C4C2×D2012yes—
363C2×C3×C4C2×D2011yescharacteristic
364C2×C3×C4C2×D2011yescharacteristic
365C2×C3×C4D4×D512yes—
366C2×C3×C4D4×D512yes—
367#67—108no—
368#67—104no—
369#67—104no—
370#67—408no—
371C2×Dic3—24no—
372C2×Dic3—54no—
373C2×Dic3—104no—
374D12—104no—
375D12—102no—
376D12—102no—
377C4×D3—108no—
378C4×D3—104no—
379C4×D3—104no—
380Dic6—104no—
381Dic6—102no—
382Dic6—102no—
383C22×C5—22no—
384C22×C5—41no—
385C22×C5—42no—
386C22×C5C2×D3×D412yes—
387C22×C5C22×#6711yescharacteristic
388C2×D5—48no—
389C2×D5—44no—
390C2×D5—42no—
391C2×D5—64no—
392C2×D5—124no—
393C2×D5—244no—
394C4×C5—22no—
395C4×C5—124no—
396C4×C5#93711yescharacteristic
397C4×C5#93712yes—
398C4×C5#93711yescharacteristic
399Dic5—42no—
400Dic5—64no—
401C24—52no—
402#41—22no—
403#41—22no—
404#41—304no—
405#41—304no—
406#41—308no—
407#41—304no—
408#41—304no—
409#41—302no—
410#41—302no—
411#41—304no—
412#41—302no—
413#41—302no—
414C2×Q8—152no—
415C2×Q8—302no—
416C2×Q8—304no—
417C2×Q8#120211yescharacteristic, complemented
418C2×D4—104no—
419C2×D4—101no—
420C2×D4—101no—
421C2×D4—102no—
422C2×D4—102no—
423C2×D4—154no—
424C2×D4—152no—
425C2×D4—302no—
426C2×D4—308no—
427C2×D4—308no—
428C2×D4—304no—
429C2×D4—304no—
430C2×D4#120211yescharacteristic, complemented
431C2×D4C2×D3×D512yes—
432C22×C4—154no—
433C22×C4—304no—
434C22×C4#120212yescomplemented
435C22×C4C2×D3×D511yescharacteristic
436C4⋊C4—62no—
437C4⋊C4—101no—
438C22⋊C4—34no—
439C22⋊C4—52no—
440C22⋊C4—104no—
441C22⋊C4—308no—
442C42—62no—
443C42—101no—
444C3×C5#302711yescharacteristic, complemented, Hall
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—42no—
448C22×C3—208no—
449C22×C3—204no—
450C22×C3—202no—
451C22×C3C22×D2011yescharacteristic
452C22×C3C2×D4×D512yes—
453C2×D3—104no—
454C2×D3—204no—
455C2×D3—404no—
456C3×C4—22no—
457C3×C4—202no—
458C3×C4#402811yescharacteristic
459C3×C4#402812yes—
460C3×C4#402811yescharacteristic
461Dic3—44no—
462Dic3—104no—
463C2×C5—21no—
464C2×C5—22no—
465C2×C5—42no—
466C2×C5C2×#93711yescharacteristic
467D5—82no—
468D5—124no—
469C23—102no—
470C23—104no—
471C23—154no—
472C23—304no—
473C23—402no—
474C23C2×#120212yes—
475C23C22×D3×D511yescharacteristic
476Q8—22no—
477Q8—304no—
478Q8—302no—
479Q8—302no—
480D4—24no—
481D4—22no—
482D4—201no—
483D4—201no—
484D4—202no—
485D4—304no—
486D4—308no—
487D4—304no—
488D4—304no—
489D4—302no—
490D4—302no—
491D4—404no—
492D4—1208no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—64no—
496C2×C4—102no—
497C2×C4—154no—
498C2×C4—308no—
499C2×C4—304no—
500C2×C4—304no—
501C2×C4—304no—
502C2×C4C2×#120212yes—
503C2×C4C2×#120211yescharacteristic
504C2×C4C2×#120211yescharacteristic
505C2×C4#679012yes—
506C2×C4#679012yes—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—42no—
510C2×C3—402no—
511C2×C3C2×#402811yescharacteristic
512D3—204no—
513C5#8339611yescharacteristic, complemented, Sylow
514C22—22no—
515C22—41no—
516C22—42no—
517C22—204no—
518C22—208no—
519C22—202no—
520C22—304no—
521C22—604no—
522C22—1204no—
523C22C22×#120211yescharacteristic
524C22C2×#679012yes—
525C4—22no—
526C4—124no—
527C4—202no—
528C4—304no—
529C4#9157211yescharacteristic
530C4#9157211yescharacteristic
531C4#9157212yes—
532C3#1061042211yescharacteristic, complemented, Sylow
533C2—22no—
534C2—21no—
535C2—42no—
536C2—402no—
537C2—604no—
538C2C2×#9157211yescharacteristic
subgroupG/H
centerC2C2×#91572
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. #11757146C2semidirect
2. C3×#66164C2semidirect
3. #11754602C2semidirect
4. C5×#5240C2semidirect
5. #11749179C2semidirect
6. #11748626C2semidirect
17. C22×C3×D20C22semidirect
18. C5×#926C22semidirect
21. C3×#4083C22semidirect
23. C3×#4072C22semidirect
24. #91564C22semidirect
28. C5×#834C22semidirect
29. #90997C22semidirect
32. #66164D3semidirect
40. C2×C3×C5×Q8D4semidirect
41. C2×C3×C5×D4D4semidirect
43. C22×C3×C4×C5D4semidirect
61. C2×D60D4semidirect
63. C2×C4×D15D4semidirect
65. C2×Dic30D4semidirect
83. #5240D5semidirect
95. C22×D20C2×D3semidirect
99. #4083C2×D3semidirect
101. #4072C2×D3semidirect
166. #926C2×D5semidirect
167. #834C2×D5semidirect
172. C2×C5×Q8#67semidirect
173. C2×C5×D4#67semidirect
175. C22×C4×C5#67semidirect
239. C2×C3×Q8D20semidirect
245. C2×C3×D4D20semidirect
247. C22×C3×C4D20semidirect
417. C2×Q8#1202semidirect
430. C2×D4#1202semidirect
434. C22×C4#1202semidirect
444. C3×C5#3027semidirect
513. C5#83396semidirect
532. C3#10610422semidirect

Maximal subgroups

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

subgroupindex
#117571462
C3×#661642
#117546022
C5×#52402
#117491792
#117486262
#106104223
#833965