Finite Group Databasebeta

← #14425689

Subgroups — #14425689

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
1C3×#66283C211yesmaximal, characteristic, complemented
2C5×#5828C211yesmaximal, characteristic, complemented
3#11754577C212yesmaximal, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11749181C214yesmaximal, complemented
6#11749175C214yesmaximal, complemented
7#11748624C212yesmaximal, complemented
8#10614667—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C4×C5×D3C2211yescharacteristic, complemented
11C3×#4150—22no—
12C3×#4149—22no—
13C3×D5×#41—24no—
14C3×#4147—21no—
15C3×#4144—21no—
16C3×#4144C2214yes—
17C2×C3×#709—22no—
18C2×C3×#709C2212yes—
19#91815C2212yescomplemented
20C5×#946—21no—
21C5×#938—21no—
22C5×#937C2212yescomplemented
23C5×#935C2212yescomplemented
24C4×C5×#67—22no—
25C5×#926C2211yescharacteristic, complemented
26#91568C2214yescomplemented
27#91536C2214yescomplemented
28#91456—22no—
29C4×#1201—24no—
30#91369—22no—
31#91118C2214yescomplemented
32#90995C2218yescomplemented
33#84125—51nomaximal, Hall
34#66283D311yescharacteristic, complemented
35C5×#525—31no—
36#66125—32no—
37#65529—31no—
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×C5×#67—22no—
50C22×C5×Dic3C2311yescharacteristic
51C2×C4×C5×D3—22no—
52C2×C4×C5×D3—22no—
53C2×C4×C5×D3—21no—
54C2×C4×C5×D3—21no—
55C2×C3×C22⋊D5—24no—
56C2×C3×C22⋊D5C2314yes—
57C3×#713—24no—
58C3×Q8×D5—24no—
59C3×#711—24no—
60C3×#711—28no—
61C3×D4×D5—24no—
62C3×D4×D5—28no—
63C3×#709—24no—
64C3×#709—24no—
65C3×#709—22no—
66C3×#709—24no—
67C3×#709—22no—
68C3×#709—22no—
69C3×#709—22no—
70C2×C3×D20—22no—
71C2×C3×D20D412yescomplemented
72C2×C3×C4×D5—24no—
73C2×C3×C4×D5D414yescomplemented
74C2×C3×Dic10—22no—
75C2×C3×Dic10D412yescomplemented
76C2×#1201—24no—
77#6719C2314yes—
78C4⋊Dic15—22no—
79C4×Dic15—22no—
80C5×#217—22no—
81C5×#217C2312yes—
82C5×(C2×D3)⋊C4—22no—
83C5×C4⋊Dic3—21no—
84C5×Dic3⋊C4—22no—
85C4×C5×Dic3—21no—
86#6669—24no—
87(C2×D3)⋊Dic5—24no—
88#6665—24no—
89C3×#585—51no—
90#5828—52no—
91#5828D511yescharacteristic, complemented
92#5244—54no—
93#5243—54no—
94#5240—51no—
95#5240—52no—
96C2×C5×#41C2×D311yescharacteristic
97C23×C4×C5—31no—
98#4150—22no—
99#4149—22no—
100D5×#41—24no—
101#4147—21no—
102#4144—21no—
103#4144C2×D314yes—
104C2×#709—22no—
105C2×#709C2×D312yes—
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#4072—32no—
117#4070—62no—
118#3966—34no—
119#3938—38no—
120#3025—151noSylow
121C23×C3×C5C2×D412yes—
122C23×C3×C5C2411yescharacteristic
123C22×C5×D3—22no—
124C22×C5×D3—21no—
125C22×C5×D3—42no—
126C22×C3×D5—24no—
127C22×C3×D5C2×D414yes—
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
138C2×Dic15—24no—
139C5×#67—44no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—21no—
143C4×C5×D3—41no—
144C4×C5×D3—42no—
145C4×C5×D3—41no—
146C3×C22⋊D5—28no—
147C3×C22⋊D5—24no—
148C3×C22⋊D5—24no—
149C2×C3×Dic5—24no—
150C2×C3×Dic5C2×D414yes—
151C3×D20—24no—
152C3×D20—22no—
153C3×D20—22no—
154C3×C4×D5—28no—
155C3×C4×D5—24no—
156C3×C4×D5—24no—
157C3×Dic10—24no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160#1201—48no—
161C3×2−1+4—102no—
162C3×2−1+4—101no—
163C3×H(5,𝔽2)—54no—
164C3×H(5,𝔽2)—102no—
165C3×H(5,𝔽2)—101no—
166C2×C3×#41—52no—
167C2×C3×#41—104no—
168C2×C3×#41—102no—
169C2×C3×#41C2×D511yescharacteristic
170C22×C4×D3C2×D511yescharacteristic, complemented
171#946—21no—
172#946—102no—
173#938—21no—
174#938—102no—
175#937—54no—
176#937C2×D512yescomplemented
177#935—54no—
178#935C2×D512yescomplemented
179C4×#67—22no—
180C4×#67—104no—
181#926—52no—
182#926C2×D511yescharacteristic, complemented
183#834—54no—
184#834—58no—
185C24×C5—31no—
186C5×#41—22no—
187C5×#41—22no—
188C2×C5×Q8#6711yescharacteristic, complemented
189C2×C5×D4—62no—
190C2×C5×D4#6711yescharacteristic, 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×C5#6712yescomplemented
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—24no—
200C2×C22⋊D5—64no—
201C2×C22⋊D5C22×D314yes—
202#713—24no—
203Q8×D5—24no—
204#711—24no—
205#711—28no—
206D4×D5—24no—
207D4×D5—28no—
208#709—24no—
209#709—24no—
210#709—22no—
211#709—24no—
212#709—22no—
213#709—22no—
214#709—22no—
215C2×D20—22no—
216C2×D20#6712yescomplemented
217C2×C4×D5—24no—
218C2×C4×D5#6714yescomplemented
219C2×Dic10—22no—
220C2×Dic10#6712yescomplemented
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—34no—
228C22⋊Dic5—64no—
229#685—64no—
230C4⋊Dic5—62no—
231#683—64no—
232C4×Dic5—62no—
233#585—51no—
234#525—31no—
235#525—152no—
236#458—154no—
237B(4,𝔽2)—154no—
238#410—152no—
239#410—151no—
240C22×C3×C5—22no—
241C22×C3×C5—41no—
242C22×C3×C5—42no—
243C22×C3×C5C22×D412yes—
244C22×C3×C5C22×D411yescharacteristic
245C2×C5×D3—24no—
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—42no—
249C2×C5×D3—41no—
250C2×C3×D5—24no—
251C2×C3×D5—44no—
252C2×C3×D5—84no—
253C3×C4×C5—22no—
254C3×C4×C5#12011yescharacteristic
255C3×C4×C5#12012yes—
256C3×C4×C5#12011yescharacteristic
257Dic15—44no—
258C3×Dic5—24no—
259C5×Dic3—42no—
260C5×Dic3—41no—
261C23×D3C22×D511yescharacteristic
262C3×#41—22no—
263C3×#41—22no—
264C3×#41—104no—
265C3×#41—104no—
266C3×#41—108no—
267C3×#41—104no—
268C3×#41—104no—
269C3×#41—102no—
270C3×#41—102no—
271C3×#41—102no—
272C3×#41—102no—
273C3×#41—104no—
274C2×C3×Q8—52no—
275C2×C3×Q8—102no—
276C2×C3×Q8—104no—
277C2×C3×Q8C22⋊D511yescharacteristic, complemented
278C2×C3×D4—54no—
279C2×C3×D4—52no—
280C2×C3×D4—102no—
281C2×C3×D4—108no—
282C2×C3×D4—104no—
283C2×C3×D4—104no—
284C2×C3×D4C22⋊D511yescharacteristic, complemented
285C2×C3×D4C22×D512yes—
286C22×C3×C4—54no—
287C22×C3×C4—104no—
288C22×C3×C4C22⋊D512yescomplemented
289C22×C3×C4C22×D511yescharacteristic
290C2×#67—22no—
291C2×#67—104no—
292C22×Dic3C22×D511yescharacteristic
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297#217—22no—
298#217—54no—
299#217—104no—
300#217C22×D512yes—
301(C2×D3)⋊C4—22no—
302(C2×D3)⋊C4—104no—
303C4⋊Dic3—21no—
304C4⋊Dic3—102no—
305Dic3⋊C4—22no—
306Dic3⋊C4—104no—
307C4×Dic3—21no—
308C4×Dic3—102no—
309C23×C5—62no—
310C23×C5—61no—
311C23×C5—122no—
312C23×C5C2×#6712yes—
313C23×C5C23×D311yescharacteristic
314C22×D5—24no—
315C22×D5C2×#6714yes—
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—62no—
324C2×C4×C5—61no—
325C2×C4×C5—121no—
326C2×C4×C5—122no—
327C2×C4×C5—121no—
328C2×C4×C5C2×#6712yes—
329C2×C4×C5C2×#6711yescharacteristic
330C2×C4×C5C2×#6711yescharacteristic
331C2×C4×C5C2×#6712yes—
332C2×C4×C5C2×#6712yes—
333C22⋊D5—28no—
334C22⋊D5—24no—
335C22⋊D5—24no—
336C22⋊D5—128no—
337C2×Dic5—24no—
338C2×Dic5—64no—
339C2×Dic5C2×#6714yes—
340D20—24no—
341D20—22no—
342D20—22no—
343C4×D5—28no—
344C4×D5—24no—
345C4×D5—24no—
346Dic10—24no—
347Dic10—22no—
348Dic10—22no—
3492−1+4—102no—
3502−1+4—101no—
351H(5,𝔽2)—54no—
352H(5,𝔽2)—102no—
353H(5,𝔽2)—101no—
354C2×#41—52no—
355C2×#41—104no—
356C2×#41—102no—
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—152no—
371#99—158no—
372#99—154no—
373C2×C3×C5—21no—
374C2×C3×C5—22no—
375C2×C3×C5—42no—
376C2×C3×C5C2×#12011yescharacteristic
377C3×D5—44no—
378C5×D3—42no—
379C23×C3—54no—
380C23×C3—104no—
381C23×C3C2×C22⋊D512yes—
382C23×C3C23×D511yescharacteristic
383C22×D3—22no—
384C22×D3—21no—
385C22×D3—42no—
386C3×Q8—22no—
387C3×Q8—104no—
388C3×Q8—102no—
389C3×Q8—102no—
390C3×D4—24no—
391C3×D4—22no—
392C3×D4—104no—
393C3×D4—108no—
394C3×D4—104no—
395C3×D4—104no—
396C3×D4—102no—
397C3×D4—102no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—54no—
401C2×C3×C4—108no—
402C2×C3×C4—104no—
403C2×C3×C4—104no—
404C2×C3×C4—104no—
405C2×C3×C4D4×D512yes—
406C2×C3×C4D4×D512yes—
407C2×C3×C4C2×C22⋊D512yes—
408C2×C3×C4C2×C22⋊D511yescharacteristic
409C2×C3×C4C2×C22⋊D511yescharacteristic
410#67—44no—
411#67—208no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—21no—
415C2×Dic3—104no—
416C4×D3—41no—
417C4×D3—42no—
418C4×D3—41no—
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×#6711yescharacteristic
428C22×C5C22×#6712yes—
429C2×D5—24no—
430C2×D5—44no—
431C2×D5—84no—
432C4×C5—22no—
433C4×C5—122no—
434C4×C5—121no—
435C4×C5#95311yescharacteristic
436C4×C5#95312yes—
437C4×C5#95311yescharacteristic
438Dic5—24no—
439Dic5—124no—
440C24—31no—
441#41—22no—
442#41—22no—
443#41—104no—
444#41—104no—
445#41—108no—
446#41—104no—
447#41—104no—
448#41—102no—
449#41—102no—
450#41—104no—
451#41—102no—
452#41—102no—
453C2×Q8—52no—
454C2×Q8—102no—
455C2×Q8—104no—
456C2×Q8#120111yescharacteristic, complemented
457C2×D4—54no—
458C2×D4—52no—
459C2×D4—62no—
460C2×D4—102no—
461C2×D4—108no—
462C2×D4—104no—
463C2×D4—104no—
464C2×D4—304no—
465C2×D4#120111yescharacteristic, complemented
466C2×D4C2×D3×D512yes—
467C22×C4—31no—
468C22×C4—54no—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—104no—
474C22×C4#120112yescomplemented
475C22×C4C2×D3×D511yescharacteristic
476C4⋊C4—61no—
477C4⋊C4—62no—
478C4⋊C4—304no—
479C4⋊C4—302no—
480C22⋊C4—32no—
481C22⋊C4—62no—
482C22⋊C4—62no—
483C22⋊C4—154no—
484C22⋊C4—304no—
485C22⋊C4—304no—
486C42—61no—
487C42—302no—
488C3×C5#302511yescharacteristic, complemented, Hall
489C22×C3—22no—
490C22×C3—41no—
491C22×C3—42no—
492C22×C3—104no—
493C22×C3—204no—
494C22×C3—404no—
495C22×C3C2×D4×D512yes—
496C22×C3C22×C22⋊D511yescharacteristic
497C2×D3—22no—
498C2×D3—24no—
499C2×D3—41no—
500C2×D3—42no—
501C2×D3—41no—
502C3×C4—22no—
503C3×C4—104no—
504C3×C4#408311yescharacteristic
505C3×C4#408312yes—
506C3×C4#408311yescharacteristic
507Dic3—42no—
508Dic3—41no—
509Dic3—204no—
510C2×C5—22no—
511C2×C5—21no—
512C2×C5—42no—
513C2×C5—122no—
514C2×C5C2×#95311yescharacteristic
515D5—44no—
516C23—54no—
517C23—61no—
518C23—62no—
519C23—104no—
520C23—122no—
521C23C2×#120112yes—
522C23C22×D3×D511yescharacteristic
523Q8—22no—
524Q8—104no—
525Q8—102no—
526Q8—102no—
527D4—24no—
528D4—22no—
529D4—104no—
530D4—108no—
531D4—104no—
532D4—104no—
533D4—102no—
534D4—102no—
535D4—124no—
536D4—608no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—54no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—62no—
543C2×C4—108no—
544C2×C4—104no—
545C2×C4—104no—
546C2×C4—104no—
547C2×C4—121no—
548C2×C4—122no—
549C2×C4—121no—
550C2×C4—304no—
551C2×C4C2×#120112yes—
552C2×C4C2×#120111yescharacteristic
553C2×C4C2×#120111yescharacteristic
554C2×C4D5×#6712yes—
555C2×C4D5×#6712yes—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—42no—
559C2×C3—204no—
560C2×C3C2×#408311yescharacteristic
561D3—42no—
562C5#8412511yescharacteristic, complemented, Sylow
563C22—22no—
564C22—41no—
565C22—42no—
566C22—62no—
567C22—64no—
568C22—104no—
569C22—121no—
570C22—122no—
571C22—121no—
572C22—204no—
573C22—404no—
574C22C22×#120111yescharacteristic
575C22C2×D5×#6712yes—
576C4—22no—
577C4—104no—
578C4—122no—
579C4—121no—
580C4—604no—
581C4#9156311yescharacteristic
582C4#9156312yes—
583C4#9156311yescharacteristic
584C3#1061466711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—22no—
587C2—42no—
588C2—122no—
589C2—204no—
590C2C2×#9156311yescharacteristic
subgroupG/H
centerC4#91563
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. C3×#66283C2semidirect
2. C5×#5828C2semidirect
3. #11754577C2semidirect
4. #11751341C2semidirect
5. #11749181C2semidirect
6. #11749175C2semidirect
7. #11748624C2semidirect
10. C22×C4×C5×D3C22semidirect
19. #91815C22semidirect
22. C5×#937C22semidirect
23. C5×#935C22semidirect
25. C5×#926C22semidirect
26. #91568C22semidirect
27. #91536C22semidirect
31. #91118C22semidirect
32. #90995C22semidirect
34. #66283D3semidirect
44. C2×C3×C5×Q8D4semidirect
45. C2×C3×C5×D4D4semidirect
47. C22×C3×C4×C5D4semidirect
71. C2×C3×D20D4semidirect
73. C2×C3×C4×D5D4semidirect
75. C2×C3×Dic10D4semidirect
91. #5828D5semidirect
170. C22×C4×D3C2×D5semidirect
176. #937C2×D5semidirect
178. #935C2×D5semidirect
182. #926C2×D5semidirect
188. C2×C5×Q8#67semidirect
190. C2×C5×D4#67semidirect
197. C22×C4×C5#67semidirect
216. C2×D20#67semidirect
218. C2×C4×D5#67semidirect
220. C2×Dic10#67semidirect
277. C2×C3×Q8C22⋊D5semidirect
284. C2×C3×D4C22⋊D5semidirect
288. C22×C3×C4C22⋊D5semidirect
456. C2×Q8#1201semidirect
465. C2×D4#1201semidirect
474. C22×C4#1201semidirect
488. C3×C5#3025semidirect
562. C5#84125semidirect
584. C3#10614667semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
C5×#58282
#117545772
#117513412
#117491812
#117491752
#117486242
#106146673
#841255