Finite Group Databasebeta

← #14425690

Subgroups — #14425690

Order 1920.

1532 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757146C211yesmaximal, characteristic, complemented
2C5×#5828C211yesmaximal, characteristic, complemented
3#11754584C212yesmaximal, complemented
4C3×#65529C211yesmaximal, characteristic, complemented
5#11749186C214yesmaximal, complemented
6#11749180C214yesmaximal, complemented
7#11748626C212yesmaximal, complemented
8#10614667—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92101—22no—
11#92100—22no—
12#41×D15—24no—
13#92098—21no—
14#92095—21no—
15#92095C2214yes—
16C2×#6817—22no—
17C2×#6817C2212yes—
18C22×C4×C5×D3C2211yescharacteristic, complemented
19C5×#946—21no—
20C5×#938—21no—
21C5×#937C2212yescomplemented
22C5×#935C2212yescomplemented
23C4×C5×#67—22no—
24C5×#926C2211yescharacteristic, complemented
25C3×#4072C2212yescomplemented
26#91570C2214yescomplemented
27#91542C2214yescomplemented
28#91460—22no—
29C4×#1203—24no—
30#91365—22no—
31C3×#3966C2214yescomplemented
32#90997C2218yescomplemented
33#78690—51nomaximal, Hall
34#66283—31no—
35C5×#525—31no—
36#66125—32no—
37#65529D311yescharacteristic, complemented
38#65342—34no—
39#65321—34no—
40#65295—32no—
41C23×C5×D3C2311yescharacteristic
42C3×C5×#41—22no—
43C3×C5×#41—22no—
44C2×C3×C5×Q8D411yescharacteristic, complemented
45C2×C3×C5×D4D411yescharacteristic, complemented
46C2×C3×C5×D4C2312yes—
47C22×C3×C4×C5D412yescomplemented
48C22×C3×C4×C5C2311yescharacteristic
49C2×#1220—24no—
50C2×#1220C2314yes—
51#6821—24no—
52Q8×D15—24no—
53#6819—24no—
54#6819—28no—
55D4×D15—24no—
56D4×D15—28no—
57#6817—24no—
58#6817—24no—
59#6817—22no—
60#6817—24no—
61#6817—22no—
62#6817—22no—
63#6817—22no—
64C2×D60—22no—
65C2×D60D412yescomplemented
66C2×C4×D15—24no—
67C2×C4×D15D414yescomplemented
68C2×Dic30—22no—
69C2×Dic30D412yescomplemented
70C2×C5×#67—22no—
71C22×C5×Dic3C2311yescharacteristic
72C2×C4×C5×D3—22no—
73C2×C4×C5×D3—22no—
74C2×C4×C5×D3—21no—
75C2×C4×C5×D3—21no—
76C2×#1203—24no—
77C5×#217—22no—
78C5×#217C2312yes—
79C5×(C2×D3)⋊C4—22no—
80C5×C4⋊Dic3—21no—
81C5×Dic3⋊C4—22no—
82C4×C5×Dic3—21no—
83C3×C22⋊Dic5C2314yes—
84C3×C4⋊Dic5—22no—
85C3×C4×Dic5—22no—
86#6668—24no—
87#6667—24no—
88(C2×D3)⋊Dic5—24no—
89#5964—51no—
90#5828D511yescharacteristic, complemented
91#5524—52no—
92C3×#410—51no—
93#5006—52no—
94#4742—54no—
95#4741—54no—
96C2×C5×#41C2×D311yescharacteristic
97C23×C4×C5—31no—
98#4150—62no—
99#4149—62no—
100D5×#41—64no—
101#4147—61no—
102#4144—34no—
103#4144—61no—
104C2×#709—32no—
105C2×#709—62no—
106C5×#123—32no—
107C5×C22⋊Q8—61no—
108C5×#121—61no—
109C5×#120—32no—
110C4×C5×D4—62no—
111C5×#117—31no—
112#4099—34no—
113#4076—62no—
114#4075—34no—
115C4×C22⋊D5—64no—
116#4072C2×D312yescomplemented
117#4070—62no—
118#3966C2×D314yescomplemented
119#3938—38no—
120#3025—151noSylow
121C23×C3×C5C2×D412yes—
122C23×C3×C5C2411yescharacteristic
123C22×D15—24no—
124C22×D15C2×D414yes—
125C22×C5×D3—22no—
126C22×C5×D3—21no—
127C22×C5×D3—42no—
128C3×C5×Q8—22no—
129C3×C5×D4—24no—
130C3×C5×D4—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138#1220—28no—
139#1220—24no—
140#1220—24no—
141C2×Dic15—24no—
142C2×Dic15C2×D414yes—
143D60—24no—
144D60—22no—
145D60—22no—
146C4×D15—28no—
147C4×D15—24no—
148C4×D15—24no—
149Dic30—24no—
150Dic30—22no—
151Dic30—22no—
152C5×#67—44no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—21no—
156C4×C5×D3—41no—
157C4×C5×D3—42no—
158C4×C5×D3—41no—
159C2×C3×Dic5—24no—
160#1203—48no—
161C2×C3×#41C2×D511yescharacteristic
162#1010—102no—
163#1009—102no—
164D3×#41—104no—
165#1007—101no—
166#1004—54no—
167#1004—101no—
168C2×#235—52no—
169C2×#235—102no—
170C22×C4×D3C2×D511yescharacteristic, complemented
171C3×#117—52no—
172#946—21no—
173#938—21no—
174#937C2×D512yescomplemented
175#935C2×D512yescomplemented
176C4×#67—22no—
177#926C2×D511yescharacteristic, complemented
178#897—102no—
179#895—102no—
180#886—54no—
181#882—54no—
182C4×D12—104no—
183C3×#99—54no—
184#806—58no—
185C24×C5—31no—
186C5×#41—22no—
187C5×#41—22no—
188C2×C5×Q8D1211yescharacteristic, complemented
189C2×C5×D4—62no—
190C2×C5×D4D1211yescharacteristic, complemented
191C2×C5×D4C22×D312yes—
192C22×C4×C5—31no—
193C22×C4×C5—61no—
194C22×C4×C5—61no—
195C22×C4×C5—62no—
196C22×C4×C5—62no—
197C22×C4×C5D1212yescomplemented
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—34no—
200C2×C22⋊D5—64no—
201C2×C22⋊D5—64no—
202#713—64no—
203Q8×D5—64no—
204#711—68no—
205#711—64no—
206D4×D5—68no—
207D4×D5—64no—
208#709—64no—
209#709—64no—
210#709—62no—
211#709—62no—
212#709—64no—
213#709—62no—
214#709—62no—
215C2×D20—32no—
216C2×D20—62no—
217C2×C4×D5—34no—
218C2×C4×D5—64no—
219C2×Dic10—32no—
220C2×Dic10—62no—
221C5×C4⋊C4—61no—
222C5×C4⋊C4—62no—
223C5×C22⋊C4—32no—
224C5×C22⋊C4—62no—
225C5×C22⋊C4—62no—
226C42×C5—61no—
227C22⋊Dic5—64no—
228C22⋊Dic5C22×D314yes—
229#685—64no—
230C4⋊Dic5—22no—
231#683—64no—
232C4×Dic5—22no—
233#585—151no—
234#525—31no—
235#525—152no—
236#458—154no—
237B(4,𝔽2)—154no—
238#410—51no—
239#410—152no—
240C22×C3×C5—22no—
241C22×C3×C5—41no—
242C22×C3×C5—42no—
243C22×C3×C5C22×D412yes—
244C22×C3×C5C22×D411yescharacteristic
245C2×D15—24no—
246C2×D15—44no—
247C2×D15—84no—
248C2×C5×D3—24no—
249C2×C5×D3—22no—
250C2×C5×D3—41no—
251C2×C5×D3—42no—
252C2×C5×D3—41no—
253C3×C4×C5—22no—
254C3×C4×C5#12011yescharacteristic
255C3×C4×C5#12012yes—
256C3×C4×C5#12011yescharacteristic
257Dic15—24no—
258C3×Dic5—44no—
259C5×Dic3—42no—
260C5×Dic3—41no—
261C23×D3C22×D511yescharacteristic
262C3×#41—22no—
263C3×#41—22no—
264C2×C3×Q8C22⋊D511yescharacteristic, complemented
265C2×C3×D4C22⋊D511yescharacteristic, complemented
266C2×C3×D4C22×D512yes—
267C22×C3×C4C22⋊D512yescomplemented
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—22no—
270C2×#67—54no—
271C2×#67—104no—
272C22×Dic3C22×D511yescharacteristic
273#239—104no—
274D3×Q8—104no—
275#237—108no—
276#237—104no—
277D3×D4—108no—
278D3×D4—104no—
279#235—104no—
280#235—104no—
281#235—102no—
282#235—102no—
283#235—102no—
284#235—102no—
285#235—104no—
286C2×D12—52no—
287C2×D12—102no—
288C2×D12—104no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—54no—
294C2×C4×D3—104no—
295C2×Dic6—52no—
296C2×Dic6—102no—
297C3×C4⋊C4—102no—
298C3×C22⋊C4—54no—
299C3×C42—102no—
300#217—22no—
301#217C22×D512yes—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—104no—
304(C2×D3)⋊C4—104no—
305C4⋊Dic3—21no—
306C4⋊Dic3—104no—
307Dic3⋊C4—22no—
308C4×Dic3—21no—
309C23×C5—61no—
310C23×C5—62no—
311C23×C5—122no—
312C23×C5C2×D1212yes—
313C23×C5C23×D311yescharacteristic
314C22×D5—34no—
315C22×D5—64no—
316C5×Q8—22no—
317C5×D4—24no—
318C5×D4—22no—
319C5×D4—124no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—62no—
323C2×C4×C5—61no—
324C2×C4×C5—62no—
325C2×C4×C5—121no—
326C2×C4×C5—122no—
327C2×C4×C5—121no—
328C2×C4×C5C2×D1212yes—
329C2×C4×C5C2×D1211yescharacteristic
330C2×C4×C5C2×D1211yescharacteristic
331C2×C4×C5D3×D412yes—
332C2×C4×C5D3×D412yes—
333C22⋊D5—68no—
334C22⋊D5—64no—
335C22⋊D5—64no—
336C22⋊D5—128no—
337C2×Dic5—24no—
338C2×Dic5—34no—
339C2×Dic5—64no—
340D20—64no—
341D20—62no—
342D20—62no—
343C4×D5—68no—
344C4×D5—64no—
345C4×D5—64no—
346Dic10—64no—
347Dic10—62no—
348Dic10—62no—
3492−1+4—302no—
3502−1+4—301no—
351H(5,𝔽2)—154no—
352H(5,𝔽2)—302no—
353H(5,𝔽2)—301no—
354C2×#41—152no—
355C2×#41—304no—
356C2×#41—302no—
357C2×#41D3×D511yescharacteristic
358C23×C4—31no—
359#123—32no—
360#123—154no—
361C22⋊Q8—61no—
362C22⋊Q8—302no—
363#121—61no—
364#121—302no—
365#120—32no—
366#120—154no—
367C4×D4—62no—
368C4×D4—304no—
369#117—31no—
370#117—52no—
371#99—54no—
372#99—158no—
373C2×C3×C5—21no—
374C2×C3×C5—22no—
375C2×C3×C5—42no—
376C2×C3×C5C2×#12011yescharacteristic
377D15—44no—
378C5×D3—42no—
379C23×C3C2×C22⋊D512yes—
380C23×C3C23×D511yescharacteristic
381C22×D3—22no—
382C22×D3—21no—
383C22×D3—42no—
384C22×D3—54no—
385C22×D3—104no—
386C3×Q8—22no—
387C3×D4—24no—
388C3×D4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—104no—
392C2×C3×C4D4×D512yes—
393C2×C3×C4D4×D512yes—
394C2×C3×C4C2×C22⋊D512yes—
395C2×C3×C4C2×C22⋊D511yescharacteristic
396C2×C3×C4C2×C22⋊D511yescharacteristic
397#67—44no—
398#67—108no—
399#67—104no—
400#67—104no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—54no—
405C2×Dic3—104no—
406D12—104no—
407D12—102no—
408D12—102no—
409D12—208no—
410C4×D3—41no—
411C4×D3—42no—
412C4×D3—41no—
413C4×D3—108no—
414C4×D3—104no—
415C4×D3—104no—
416Dic6—104no—
417Dic6—102no—
418Dic6—102no—
419C22×C5—22no—
420C22×C5—41no—
421C22×C5—42no—
422C22×C5—64no—
423C22×C5—62no—
424C22×C5—122no—
425C22×C5—121no—
426C22×C5—121no—
427C22×C5C22×D1211yescharacteristic
428C22×C5C2×D3×D412yes—
429C2×D5—64no—
430C2×D5—124no—
431C2×D5—244no—
432C4×C5—22no—
433C4×C5—122no—
434C4×C5—121no—
435C4×C5#88211yescharacteristic
436C4×C5#88212yes—
437C4×C5#88211yescharacteristic
438Dic5—44no—
439Dic5—64no—
440C24—31no—
441#41—22no—
442#41—22no—
443#41—304no—
444#41—304no—
445#41—308no—
446#41—304no—
447#41—304no—
448#41—302no—
449#41—302no—
450#41—304no—
451#41—302no—
452#41—302no—
453C2×Q8—152no—
454C2×Q8—302no—
455C2×Q8—304no—
456C2×Q8#120311yescharacteristic, complemented
457C2×D4—62no—
458C2×D4—154no—
459C2×D4—152no—
460C2×D4—302no—
461C2×D4—304no—
462C2×D4—308no—
463C2×D4—304no—
464C2×D4—304no—
465C2×D4#120311yescharacteristic, complemented
466C2×D4C2×D3×D512yes—
467C22×C4—31no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—154no—
473C22×C4—304no—
474C22×C4#120312yescomplemented
475C22×C4C2×D3×D511yescharacteristic
476C4⋊C4—61no—
477C4⋊C4—62no—
478C4⋊C4—102no—
479C4⋊C4—304no—
480C22⋊C4—32no—
481C22⋊C4—54no—
482C22⋊C4—62no—
483C22⋊C4—62no—
484C22⋊C4—304no—
485C22⋊C4—304no—
486C42—61no—
487C42—102no—
488C3×C5#302511yescharacteristic, complemented, Hall
489C22×C3—22no—
490C22×C3—41no—
491C22×C3—42no—
492C22×C3C2×D4×D512yes—
493C22×C3C22×C22⋊D511yescharacteristic
494C2×D3—24no—
495C2×D3—22no—
496C2×D3—41no—
497C2×D3—42no—
498C2×D3—41no—
499C2×D3—104no—
500C2×D3—204no—
501C2×D3—404no—
502C3×C4—22no—
503C3×C4—204no—
504C3×C4#408311yescharacteristic
505C3×C4#408312yes—
506C3×C4#408311yescharacteristic
507Dic3—42no—
508Dic3—41no—
509Dic3—104no—
510C2×C5—22no—
511C2×C5—21no—
512C2×C5—42no—
513C2×C5—122no—
514C2×C5C2×#88211yescharacteristic
515D5—124no—
516C23—61no—
517C23—62no—
518C23—122no—
519C23—154no—
520C23—304no—
521C23C2×#120312yes—
522C23C22×D3×D511yescharacteristic
523Q8—22no—
524Q8—304no—
525Q8—302no—
526Q8—302no—
527D4—24no—
528D4—22no—
529D4—124no—
530D4—304no—
531D4—308no—
532D4—304no—
533D4—304no—
534D4—302no—
535D4—302no—
536D4—608no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—62no—
540C2×C4—61no—
541C2×C4—62no—
542C2×C4—104no—
543C2×C4—121no—
544C2×C4—122no—
545C2×C4—121no—
546C2×C4—154no—
547C2×C4—308no—
548C2×C4—304no—
549C2×C4—304no—
550C2×C4—304no—
551C2×C4C2×#120312yes—
552C2×C4C2×#120311yescharacteristic
553C2×C4C2×#120311yescharacteristic
554C2×C4#679012yes—
555C2×C4#679012yes—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—42no—
559C2×C3C2×#408311yescharacteristic
560D3—42no—
561D3—204no—
562C5#7869011yescharacteristic, complemented, Sylow
563C22—22no—
564C22—41no—
565C22—42no—
566C22—62no—
567C22—64no—
568C22—121no—
569C22—122no—
570C22—121no—
571C22—304no—
572C22—604no—
573C22—1204no—
574C22C22×#120311yescharacteristic
575C22C2×#679012yes—
576C4—22no—
577C4—122no—
578C4—121no—
579C4—204no—
580C4—304no—
581C4#9157311yescharacteristic
582C4#9157312yes—
583C4#9157311yescharacteristic
584C3#1061466711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—22no—
587C2—42no—
588C2—122no—
589C2—604no—
590C2C2×#9157311yescharacteristic
subgroupG/H
centerC4#91573
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3025
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11757146C2semidirect
2. C5×#5828C2semidirect
3. #11754584C2semidirect
4. C3×#65529C2semidirect
5. #11749186C2semidirect
6. #11749180C2semidirect
7. #11748626C2semidirect
18. C22×C4×C5×D3C22semidirect
21. C5×#937C22semidirect
22. C5×#935C22semidirect
24. C5×#926C22semidirect
25. C3×#4072C22semidirect
26. #91570C22semidirect
27. #91542C22semidirect
31. C3×#3966C22semidirect
32. #90997C22semidirect
37. #65529D3semidirect
44. C2×C3×C5×Q8D4semidirect
45. C2×C3×C5×D4D4semidirect
47. C22×C3×C4×C5D4semidirect
65. C2×D60D4semidirect
67. C2×C4×D15D4semidirect
69. C2×Dic30D4semidirect
90. #5828D5semidirect
116. #4072C2×D3semidirect
118. #3966C2×D3semidirect
170. C22×C4×D3C2×D5semidirect
174. #937C2×D5semidirect
175. #935C2×D5semidirect
177. #926C2×D5semidirect
188. C2×C5×Q8D12semidirect
190. C2×C5×D4D12semidirect
197. C22×C4×C5D12semidirect
264. C2×C3×Q8C22⋊D5semidirect
265. C2×C3×D4C22⋊D5semidirect
267. C22×C3×C4C22⋊D5semidirect
456. C2×Q8#1203semidirect
465. C2×D4#1203semidirect
474. C22×C4#1203semidirect
488. C3×C5#3025semidirect
562. C5#78690semidirect
584. C3#10614667semidirect

Maximal subgroups

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

subgroupindex
#117571462
C5×#58282
#117545842
C3×#655292
#117491862
#117491802
#117486262
#106146673
#786905