Finite Group Databasebeta

← #14302993

Subgroups — #14302993

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756987C211yesmaximal, characteristic, complemented
2C3×#65987C211yesmaximal, characteristic
3D5⋊#834C211yesmaximal, characteristic, complemented
4C2×#91228C212yesmaximal, complemented
5#11746737C212yesmaximal, complemented
6#10604534—31nomaximal, Hall
7C2×C3×D4×D5C2211yescharacteristic
8C22×C3×D20C2211yescharacteristic
9C2×#6763—21no—
10C2×#6763C2212yes—
11C2×#6763C2212yes—
12D4×ΓL(1,𝔽16)—24no—
13#91989—21no—
14C3×C5×#123C411yescharacteristic, complemented
15C3×#4083C411yescharacteristic, complemented
16C3×#4075C411yescharacteristic, complemented
17C3×#4041—21no—
18C3×#4040—21no—
19C3×#4030—21no—
20C3×#4028—21no—
21C3×#4028C411yescharacteristic, complemented
22C3×D5×C22⋊C4C2211yescharacteristic
23#91240—21no—
24#91228—21no—
25#91228—24no—
26#71848—51nomaximal, Hall
27#66258—31no—
28#65987D311yescharacteristic
29D5⋊#99—31no—
30C2×#3999—32no—
31#64866—32no—
32C23×C3×D5C2×C411yescharacteristic, complemented
33C23×C3×D5D411yescharacteristic
34C23×C3×D5C2311yescharacteristic
35C22×ΓL(1,𝔽16)—22no—
36C22×ΓL(1,𝔽16)—22no—
37C22×ΓL(1,𝔽16)—22no—
38C2×C3×C5×D4C2×C411yescharacteristic
39C22×C3×C4×C5C2×C411yescharacteristic, complemented
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5C2×C411yescharacteristic
42C2×C3×C22⋊D5D411yescharacteristic
43C3×D4×D5—22no—
44C3×D4×D5—22no—
45C2×C3×D20—22no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—22no—
49C2×C3×D20—21no—
50C2×C3×D20D411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5D411yescharacteristic
53#6763—22no—
54#6763—22no—
55#6763—22no—
56#6763—22no—
57#6763D414yescomplemented
58C4⋊ΓL(1,𝔽16)—22no—
59C4×ΓL(1,𝔽16)—22no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
63C3×C22⋊Dic5C2×C411yescharacteristic, complemented
64C3×#685—21no—
65C3×#685—21no—
66C3×#685—21no—
67C3×#685—21no—
68C3×#683—21no—
69C3×#534—51no—
70#5798—51no—
71C2×#834—52no—
72C2×#834—51no—
73#4527—52no—
74C2×D4×D5C2×D311yescharacteristic
75C22×D20C2×D311yescharacteristic
76C2×C22⋊AGL(1,𝔽5)—32no—
77C2×C22⋊AGL(1,𝔽5)—32no—
78C2×C22⋊AGL(1,𝔽5)—61no—
79D4×AGL(1,𝔽5)—64no—
80#4130—61no—
81C5×#123Dic311yescharacteristic, complemented
82#4083Dic311yescharacteristic, complemented
83#4075Dic311yescharacteristic, complemented
84#4041—21no—
85#4040—21no—
86#4030—21no—
87#4028—21no—
88#4028Dic311yescharacteristic, complemented
89D5×C22⋊C4C2×D311yescharacteristic
90#4011—61no—
91#3999—64no—
92#3999—61no—
93#1913—151noSylow
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C22×C411yescharacteristic
96C22×C3×D5—21no—
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—22no—
100C22×C3×D5—81no—
101C22×C3×D5—81no—
102C22×C3×D5—81no—
103C22×C3×D5C22⋊C411yescharacteristic
104C22×C3×D5C2×D412yes—
105C22×C3×D5C2×D411yescharacteristic
106C22×C3×D5C2×D411yescharacteristic
107C22×C3×D5#4112yes—
108C2×ΓL(1,𝔽16)—24no—
109C2×ΓL(1,𝔽16)—42no—
110C2×ΓL(1,𝔽16)—82no—
111C2×ΓL(1,𝔽16)—82no—
112C2×ΓL(1,𝔽16)—82no—
113C3×C5×D4—22no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5C22⋊C411yescharacteristic
118C3×C22⋊D5—22no—
119C3×C22⋊D5—22no—
120C3×C22⋊D5—81no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5C22⋊C411yescharacteristic
123C3×D20—22no—
124C3×D20—41no—
125C3×D20—42no—
126C3×D20—41no—
127C3×D20—81no—
128C3×C4×D5—21no—
129C3×C4×D5—21no—
130C3×C4×D5—81no—
131C22×C3×D4—51no—
132C22×C3×D4—51no—
133C3×#123—51no—
134C3×#123—101no—
135C3×#123AGL(1,𝔽5)11yescharacteristic, complemented
136C3×#121—101no—
137C3×#121—101no—
138C3×#120—51no—
139C3×#120—51no—
140C3×#120—101no—
141C2×C3×C22⋊C4—51no—
142C2×#217—52no—
143C2×#217—52no—
144C2×#217—101no—
145D4×Dic3—104no—
146#926—101no—
147#834—104no—
148#834—101no—
149#834—101no—
150C23×D5C2×Dic311yescharacteristic, complemented
151C23×D5#6711yescharacteristic
152C23×D5C22×D311yescharacteristic
153C22×AGL(1,𝔽5)—62no—
154C22×AGL(1,𝔽5)—62no—
155C22×AGL(1,𝔽5)—62no—
156C2×C5×D4C2×Dic311yescharacteristic
157C22×C4×C5C2×Dic311yescharacteristic, complemented
158C2×C22⋊D5—21no—
159C2×C22⋊D5C2×Dic311yescharacteristic
160C2×C22⋊D5#6711yescharacteristic
161D4×D5—22no—
162D4×D5—22no—
163C2×D20—22no—
164C2×D20—22no—
165C2×D20—21no—
166C2×D20—21no—
167C2×D20—21no—
168C2×D20#6711yescharacteristic
169C2×C4×D5—21no—
170C2×C4×D5#6711yescharacteristic
171C22⋊AGL(1,𝔽5)—34no—
172C22⋊AGL(1,𝔽5)—62no—
173C22⋊AGL(1,𝔽5)—62no—
174C22⋊AGL(1,𝔽5)—62no—
175C22⋊AGL(1,𝔽5)—62no—
176C4⋊AGL(1,𝔽5)—62no—
177C4×AGL(1,𝔽5)—62no—
178C5×C4⋊C4—21no—
179C5×C22⋊C4—21no—
180C5×C22⋊C4C2×Dic311yescharacteristic, complemented
181C22⋊Dic5C2×Dic311yescharacteristic, complemented
182#685—21no—
183#685—21no—
184#685—21no—
185#685—21no—
186#683—21no—
187#534—51no—
188#518—151no—
189C2×#99—152no—
190C2×#99—151no—
191#342—152no—
192C22×C3×C5—21no—
193C22×C3×C5—41no—
194C22×C3×C5—41no—
195C22×C3×C5C2×C22⋊C411yescharacteristic
196C22×C3×C5C4×D412yes—
197C2×C3×D5—21no—
198C2×C3×D5—41no—
199C2×C3×D5—42no—
200C2×C3×D5—42no—
201C2×C3×D5—41no—
202C2×C3×D5—42no—
203C2×C3×D5—41no—
204C2×C3×D5—41no—
205C2×C3×D5—41no—
206C2×C3×D5—41no—
207C2×C3×D5—81no—
208C2×C3×D5—82no—
209C2×C3×D5#12011yescharacteristic
210C2×C3×D5#12112yes—
211C2×C3×D5#12311yescharacteristic
212ΓL(1,𝔽16)—44no—
213ΓL(1,𝔽16)—82no—
214C3×C4×C5—21no—
215C3×C4×C5—41no—
216C3×C4×C5—41no—
217C3×Dic5—21no—
218C3×Dic5—41no—
219C24×C3—51no—
220C24×C3—51no—
221C24×C3—51no—
222C2×C3×D4—51no—
223C2×C3×D4—51no—
224C2×C3×D4—51no—
225C2×C3×D4—102no—
226C2×C3×D4—101no—
227C2×C3×D4—101no—
228C2×C3×D4—102no—
229C2×C3×D4—101no—
230C2×C3×D4—102no—
231C2×C3×D4—102no—
232C2×C3×D4—101no—
233C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
234C22×C3×C4—51no—
235C22×C3×C4—101no—
236C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
237C22×Dic3—102no—
238C22×Dic3—102no—
239C22×Dic3—102no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—101no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—51no—
244C3×C22⋊C4—101no—
245C3×C22⋊C4—101no—
246C3×C22⋊C4—101no—
247C3×C22⋊C4—101no—
248C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
249#217—54no—
250#217—102no—
251#217—102no—
252#217—102no—
253#217—102no—
254C4⋊Dic3—102no—
255C4×Dic3—102no—
256C23×C5#21711yescharacteristic
257C23×C5C22×Dic311yescharacteristic
258C22×D5—21no—
259C22×D5—21no—
260C22×D5—21no—
261C22×D5—22no—
262C22×D5—81no—
263C22×D5—81no—
264C22×D5—81no—
265C22×D5#21711yescharacteristic
266C22×D5D3×D412yes—
267C22×D5#23712yes—
268C22×D5C2×#6711yescharacteristic
269C22×D5C2×#6711yescharacteristic
270C2×AGL(1,𝔽5)—64no—
271C2×AGL(1,𝔽5)—122no—
272C2×AGL(1,𝔽5)—242no—
273C2×AGL(1,𝔽5)—242no—
274C2×AGL(1,𝔽5)—242no—
275C5×D4—22no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5#21711yescharacteristic
280C22⋊D5—22no—
281C22⋊D5—22no—
282C22⋊D5—81no—
283C2×Dic5—21no—
284C2×Dic5#21711yescharacteristic
285D20—22no—
286D20—41no—
287D20—41no—
288D20—42no—
289D20—81no—
290C4×D5—21no—
291C4×D5—21no—
292C4×D5—81no—
293C22×D4—51no—
294C22×D4—51no—
295#123—51no—
296#123—101no—
297#123ΓL(1,𝔽16)11yescharacteristic, complemented
298#121—101no—
299#121—101no—
300#120—51no—
301#120—51no—
302#120—101no—
303C4×D4—304no—
304#117—301no—
305C2×C22⋊C4—51no—
306C2×C22⋊C4—152no—
307C2×C22⋊C4—152no—
308C2×C22⋊C4—301no—
309#99—304no—
310#99—301no—
311#99—301no—
312C2×C3×C5—21no—
313C2×C3×C5—22no—
314C2×C3×C5—41no—
315C2×C3×C5#38611yescharacteristic
316C3×D5—21no—
317C3×D5—22no—
318C3×D5—21no—
319C3×D5—41no—
320C3×D5—81no—
321C23×C3—52no—
322C23×C3—52no—
323C23×C3—51no—
324C23×C3—51no—
325C23×C3—51no—
326C23×C3—101no—
327C23×C3—101no—
328C23×C3—101no—
329C23×C3—102no—
330C23×C3—401no—
331C23×C3—401no—
332C23×C3—401no—
333C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
334C23×C3C22×AGL(1,𝔽5)11yescharacteristic
335C3×D4—22no—
336C3×D4—102no—
337C3×D4—102no—
338C3×D4—102no—
339C3×D4—201no—
340C3×D4—202no—
341C3×D4—201no—
342C3×D4—401no—
343C3×D4—401no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—51no—
348C2×C3×C4—101no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—401no—
352C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
353C2×Dic3—104no—
354C2×Dic3—202no—
355C2×Dic3—402no—
356C2×Dic3—402no—
357C2×Dic3—402no—
358C22×C5—21no—
359C22×C5—41no—
360C22×C5—41no—
361C22×C5D4×Dic312yes—
362C22×C5C2×#21711yescharacteristic
363C2×D5—21no—
364C2×D5—41no—
365C2×D5—42no—
366C2×D5—42no—
367C2×D5—41no—
368C2×D5—42no—
369C2×D5—41no—
370C2×D5—41no—
371C2×D5—41no—
372C2×D5—41no—
373C2×D5—81no—
374C2×D5—82no—
375C2×D5#93511yescharacteristic
376C2×D5#93711yescharacteristic
377C2×D5#93912yes—
378AGL(1,𝔽5)—124no—
379AGL(1,𝔽5)—242no—
380C4×C5—21no—
381C4×C5—41no—
382C4×C5—41no—
383Dic5—21no—
384Dic5—41no—
385C24—51no—
386C24—51no—
387C24—51no—
388C2×D4—51no—
389C2×D4—51no—
390C2×D4—51no—
391C2×D4—102no—
392C2×D4—101no—
393C2×D4—101no—
394C2×D4—102no—
395C2×D4—101no—
396C2×D4—102no—
397C2×D4—102no—
398C2×D4—101no—
399C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
400C22×C4—51no—
401C22×C4—101no—
402C22×C4—302no—
403C22×C4—302no—
404C22×C4—302no—
405C22×C4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
406C4⋊C4—21no—
407C4⋊C4—101no—
408C4⋊C4—302no—
409C22⋊C4—21no—
410C22⋊C4—51no—
411C22⋊C4—101no—
412C22⋊C4—101no—
413C22⋊C4—101no—
414C22⋊C4—101no—
415C22⋊C4—154no—
416C22⋊C4—302no—
417C22⋊C4—302no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
421C42—302no—
422C3×C5#191311yescharacteristic, complemented, Hall
423C22×C3—21no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—51no—
427C22×C3—52no—
428C22×C3—51no—
429C22×C3—101no—
430C22×C3—202no—
431C22×C3—202no—
432C22×C3—201no—
433C22×C3—201no—
434C22×C3—201no—
435C22×C3—201no—
436C22×C3—201no—
437C22×C3—202no—
438C22×C3—201no—
439C22×C3—402no—
440C22×C3—401no—
441C22×C3D4×AGL(1,𝔽5)12yes—
442C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
443C3×C4—21no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—101no—
447C3×C4—201no—
448Dic3—204no—
449Dic3—402no—
450C2×C5—21no—
451C2×C5—22no—
452C2×C5—41no—
453C2×C5#522011yescharacteristic
454D5—21no—
455D5—22no—
456D5—21no—
457D5—41no—
458D5—81no—
459C23—52no—
460C23—52no—
461C23—51no—
462C23—51no—
463C23—51no—
464C23—101no—
465C23—101no—
466C23—101no—
467C23—102no—
468C23—401no—
469C23—401no—
470C23—401no—
471C23#676311yescharacteristic
472C23C22×ΓL(1,𝔽16)11yescharacteristic
473D4—22no—
474D4—102no—
475D4—102no—
476D4—102no—
477D4—201no—
478D4—201no—
479D4—202no—
480D4—401no—
481D4—401no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—51no—
486C2×C4—101no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—304no—
490C2×C4—401no—
491C2×C4—602no—
492C2×C4—1202no—
493C2×C4—1202no—
494C2×C4—1202no—
495C2×C4#676311yescharacteristic
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—41no—
499C2×C3—101no—
500C2×C3—102no—
501C2×C3—101no—
502C2×C3—201no—
503C2×C3—401no—
504C2×C3#6577911yescharacteristic
505C5#7184811yescharacteristic, complemented, Sylow
506C22—21no—
507C22—41no—
508C22—41no—
509C22—51no—
510C22—51no—
511C22—52no—
512C22—101no—
513C22—201no—
514C22—202no—
515C22—202no—
516C22—201no—
517C22—201no—
518C22—201no—
519C22—201no—
520C22—202no—
521C22—201no—
522C22—402no—
523C22—401no—
524C22D4×ΓL(1,𝔽16)12yes—
525C22C2×#676311yescharacteristic
526C4—21no—
527C4—41no—
528C4—41no—
529C4—101no—
530C4—201no—
531C4—604no—
532C4—1202no—
533C3#1060453411yescharacteristic, complemented, Sylow
534C2—21no—
535C2—22no—
536C2—41no—
537C2—101no—
538C2—102no—
539C2—101no—
540C2—201no—
541C2—401no—
542C2#1175243811yescharacteristic
subgroupG/H
centerC2#11752438
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC3×C5×#123C4
socleC2×C3×C5#386
prime radicalC3×#65987C2
cosocleC23×C3×D5C23
hypercenter#123ΓL(1,𝔽16)
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #11756987C2semidirect
3. D5⋊#834C2semidirect
4. C2×#91228C2semidirect
5. #11746737C2semidirect
14. C3×C5×#123C4semidirect
15. C3×#4083C4semidirect
16. C3×#4075C4semidirect
21. C3×#4028C4semidirect
32. C23×C3×D5C2×C4semidirect
39. C22×C3×C4×C5C2×C4semidirect
57. #6763D4semidirect
62. C3×C5×C22⋊C4C2×C4semidirect
63. C3×C22⋊Dic5C2×C4semidirect
81. C5×#123Dic3semidirect
82. #4083Dic3semidirect
83. #4075Dic3semidirect
88. #4028Dic3semidirect
135. C3×#123AGL(1,𝔽5)semidirect
150. C23×D5C2×Dic3semidirect
157. C22×C4×C5C2×Dic3semidirect
180. C5×C22⋊C4C2×Dic3semidirect
181. C22⋊Dic5C2×Dic3semidirect
236. C22×C3×C4C2×AGL(1,𝔽5)semidirect
248. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
297. #123ΓL(1,𝔽16)semidirect
405. C22×C4C2×ΓL(1,𝔽16)semidirect
420. C22⋊C4C2×ΓL(1,𝔽16)semidirect
422. C3×C5#1913semidirect
505. C5#71848semidirect
533. C3#10604534semidirect

Maximal subgroups

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

subgroupindex
#117569872
C3×#659872
D5⋊#8342
C2×#912282
#117467372
#106045343
#718485