Finite Group Databasebeta

← #14319937

Subgroups — #14319937

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D5C211yesmaximal, characteristic
2C2×#91358C212yesmaximal, complemented
3#11751313C211yesmaximal, characteristic, complemented
4C5×#5212C211yesmaximal, characteristic, complemented
5#11749488C212yesmaximal
6Dic5×#217C212yesmaximal, complemented
7#11748759C212yesmaximal, complemented
8#11748737C212yesmaximal, complemented
9#11748702C212yesmaximal, complemented
10#10605593—31nomaximal, Hall
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×Dic5C2211yescharacteristic
14C22×C3×C4×D5—28no—
15C22×C3×C4×D5C418yescomplemented
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×#6719C2212yes—
21C2×C4⋊Dic15C2212yescomplemented
22C2×C5×#217C2212yes—
23C2×C5×C4⋊Dic3C2212yescomplemented
24C2×#6665C2214yes—
25C2×#6665C2214yes—
26C2×Dic3×Dic5C2214yescomplemented
27#91358—28no—
28#91115C2212yescomplemented
29C5×C3⋊#95C2212yescomplemented
30#90994C2214yescomplemented
31#84027—51nomaximal, Hall
32C23×C4×D5D311yescharacteristic
33C2×#4038—32no—
34C5×#380—31no—
35#65501—31no—
36#65276—32no—
37#65244—32no—
38C22⋊C4×Dic5—32no—
39#64955—32no—
40#64953—32no—
41C24×C3×C5C2311yescharacteristic
42C23×C3×D5—22no—
43C23×C3×D5—22no—
44C23×C3×D5—24no—
45C23×C3×D5—24no—
46C23×C3×D5C2×C414yes—
47C23×C3×D5C2311yescharacteristic
48C23×C3×D5C2311yescharacteristic
49C22×C3×C4×C5—24no—
50C22×C3×C4×C5C2×C414yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2314yes—
54C22×C5×Dic3C2314yes—
55C22×C3×Dic5—24no—
56C22×C3×Dic5C2×C414yes—
57C22×C3×Dic5C2311yescharacteristic
58C22×C3×Dic5C2311yescharacteristic
59C2×C3×C4×D5—24no—
60C2×C3×C4×D5—24no—
61C2×C3×C4×D5—24no—
62C2×C3×C4×D5—232no—
63C2×C3×C4×D5C2×C414yes—
64C2×C3×C4×D5C2×C414yes—
65C2×C3×C4×D5C2×C414yes—
66C2×C3×C4×D5C2×C414yes—
67C2×C3×C4×D5D418yes—
68#6719—24no—
69C4⋊Dic15—24no—
70C5×#217—24no—
71C5×C4⋊Dic3—24no—
72#6665—28no—
73#6665—28no—
74Dic3×Dic5—28no—
75C24×C3×C4—51no—
76C2×#926—52no—
77#5247—52no—
78#5212—51no—
79#5212—52no—
80#5212D511yescharacteristic, complemented
81#5211—52no—
82C4×#217—52no—
83C4×#217—52no—
84C24×D5C2×D311yescharacteristic
85C23×C4×C5C2×D311yescharacteristic
86C23×Dic5C2×D311yescharacteristic
87C22×C4×D5—28no—
88C22×C4×D5Dic318yescomplemented
89C22×C4×D5C2×D311yescharacteristic
90C22×C4×D5C2×D311yescharacteristic
91C22×C4×D5C2×D311yescharacteristic
92C22×C4×D5C2×D311yescharacteristic
93C2×C5×C4⋊C4—32no—
94C2×C5×C22⋊C4—32no—
95C2×C22⋊Dic5—32no—
96C2×#685—34no—
97C2×#685—34no—
98C2×C4⋊Dic5—32no—
99C2×C4×Dic5—34no—
100#4038—68no—
101C5×#95—32no—
102#3963—32no—
103#3963—34no—
104#2280—151noSylow
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5C22×C412yes—
108C23×C3×C5#4112yes—
109C23×C3×C5#4112yes—
110C23×C3×C5C2411yescharacteristic
111C22×C3×D5—216no—
112C22×C3×D5—216no—
113C22×C3×D5—28no—
114C22×C3×D5—22no—
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—22no—
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5—28no—
121C22×C3×D5—28no—
122C22×C3×D5C22×C412yes—
123C22×C3×D5C22×C412yes—
124C22×C3×D5C2×D414yes—
125C22×C3×D5#4114yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—28no—
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5C2×D414yes—
131C2×Dic15—24no—
132C2×Dic15—24no—
133C2×Dic15—24no—
134C2×C5×Dic3—24no—
135C2×C5×Dic3—24no—
136C2×C5×Dic3—24no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—28no—
139C2×C3×Dic5C22×C412yes—
140C2×C3×Dic5C22×C412yes—
141C2×C3×Dic5C2×D414yes—
142C3×C4×D5—28no—
143C3×C4×D5—28no—
144C3×C4×D5—28no—
145C3×C4×D5C22⋊C4116yescomplemented
146C25×C3—51no—
147C23×C3×C4—51no—
148C23×C3×C4—51no—
149C23×C3×C4—58no—
150C23×C3×C4—51no—
151C23×C3×C4—51no—
152C23×C3×C4—51no—
153C23×C3×C4—108no—
154C23×C3×C4C2×D511yescharacteristic
155C2×#217—52no—
156C2×#217—54no—
157C2×#217—54no—
158C2×#217C2×D512yes—
159#926—108no—
160C2×C4⋊Dic3—52no—
161C2×C4⋊Dic3C2×D512yescomplemented
162C2×C4×Dic3—54no—
163C3⋊#95—52no—
164C3⋊#95—54no—
165C3⋊#95C2×D512yescomplemented
166C24×C5C22×D311yescharacteristic
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—24no—
170C23×D5—24no—
171C23×D5C2×Dic314yes—
172C23×D5C22×D311yescharacteristic
173C23×D5C22×D311yescharacteristic
174C22×C4×C5—24no—
175C22×C4×C5—34no—
176C22×C4×C5C2×Dic314yes—
177C22×C4×C5C22×D311yescharacteristic
178C22×C4×C5C22×D311yescharacteristic
179C22×Dic5—24no—
180C22×Dic5—34no—
181C22×Dic5C2×Dic314yes—
182C22×Dic5C22×D311yescharacteristic
183C22×Dic5C22×D311yescharacteristic
184C2×C4×D5—24no—
185C2×C4×D5—24no—
186C2×C4×D5—24no—
187C2×C4×D5—232no—
188C2×C4×D5C2×Dic314yes—
189C2×C4×D5C2×Dic314yes—
190C2×C4×D5C2×Dic314yes—
191C2×C4×D5C2×Dic314yes—
192C2×C4×D5#6718yes—
193C5×C4⋊C4—64no—
194C5×C22⋊C4—64no—
195C22⋊Dic5—64no—
196#685—68no—
197#685—68no—
198C4⋊Dic5—64no—
199C4×Dic5—68no—
200C24×C4—51no—
201C2×#117—152no—
202#381—152no—
203#380—31no—
204#380—152no—
205#380—151no—
206#379—152no—
207C4×C22⋊C4—152no—
208C4×C22⋊C4—152no—
209C22×C3×C5—22no—
210C22×C3×C5—22no—
211C22×C3×C5—24no—
212C22×C3×C5—24no—
213C22×C3×C5#11714yescomplemented
214C22×C3×C5C23×C411yescharacteristic
215C22×C3×C5C22×D412yes—
216C22×C3×C5C2×#4111yescharacteristic
217C22×C3×C5C2×#4111yescharacteristic
218C22×C3×C5C2×#4112yes—
219C2×C3×D5—232no—
220C2×C3×D5—22no—
221C2×C3×D5—22no—
222C2×C3×D5—22no—
223C2×C3×D5—22no—
224C2×C3×D5—24no—
225C2×C3×D5—24no—
226C2×C3×D5—24no—
227C2×C3×D5—24no—
228C2×C3×D5C2×C22⋊C414yes—
229C2×C3×D5#11714yescomplemented
230C3×C4×C5—22no—
231C3×C4×C5C2×C22⋊C414yes—
232Dic15—44no—
233C3×Dic5—22no—
234C3×Dic5C2×C22⋊C414yes—
235C5×Dic3—44no—
236C24×C3—51no—
237C24×C3—51no—
238C24×C3—54no—
239C24×C3—104no—
240C24×C3—104no—
241C24×C3—102no—
242C24×C3—102no—
243C24×C3C22×D511yescharacteristic
244C22×C3×C4—24no—
245C22×C3×C4—51no—
246C22×C3×C4—54no—
247C22×C3×C4—58no—
248C22×C3×C4—54no—
249C22×C3×C4—51no—
250C22×C3×C4—54no—
251C22×C3×C4—54no—
252C22×C3×C4—54no—
253C22×C3×C4—104no—
254C22×C3×C4—1032no—
255C22×C3×C4—104no—
256C22×C3×C4—104no—
257C22×C3×C4—104no—
258C22×C3×C4C4×D514yes—
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D511yescharacteristic
261C22×Dic3—54no—
262C22×Dic3C22×D514yes—
263#217—24no—
264#217—108no—
265#217—108no—
266#217—104no—
267C4⋊Dic3—24no—
268C4⋊Dic3—104no—
269C4×Dic3—108no—
270C23×C5—22no—
271C23×C5—22no—
272C23×C5#23512yes—
273C23×C5#23512yes—
274C23×C5C22×Dic312yes—
275C23×C5C23×D311yescharacteristic
276C22×D5—216no—
277C22×D5—216no—
278C22×D5—28no—
279C22×D5—21no—
280C22×D5—21no—
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—22no—
284C22×D5—22no—
285C22×D5—28no—
286C22×D5—28no—
287C22×D5#23514yes—
288C22×D5C22×Dic312yes—
289C22×D5C22×Dic312yes—
290C22×D5C2×#6714yes—
291C2×C4×C5—22no—
292C2×C4×C5—28no—
293C2×C4×C5—64no—
294C2×C4×C5—64no—
295C2×C4×C5—64no—
296C2×C4×C5C22×Dic312yes—
297C2×C4×C5C22×Dic312yes—
298C2×C4×C5C2×#6714yes—
299C2×Dic5—22no—
300C2×Dic5—28no—
301C2×Dic5—64no—
302C2×Dic5—64no—
303C2×Dic5—64no—
304C2×Dic5C22×Dic312yes—
305C2×Dic5C22×Dic312yes—
306C2×Dic5C2×#6714yes—
307C4×D5—28no—
308C4×D5—28no—
309C4×D5—28no—
310C4×D5#217116yescomplemented
311C25—51no—
312C23×C4—51no—
313C23×C4—51no—
314C23×C4—58no—
315C23×C4—51no—
316C23×C4—51no—
317C23×C4—51no—
318C23×C4—108no—
319C23×C4D3×D511yescharacteristic
320#117—308no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—152no—
323C2×C22⋊C4—32no—
324C2×C22⋊C4—154no—
325C2×C22⋊C4—154no—
326C2×C22⋊C4—152no—
327C2×C42—154no—
328#95—32no—
329#95—154no—
330#95—152no—
331C2×C3×C5—24no—
332C2×C3×C5C22×C22⋊C411yescharacteristic
333C2×C3×C5C2×#11711yescharacteristic
334C2×C3×C5C2×#11711yescharacteristic
335C2×C3×C5#52512yes—
336C2×C3×C5#52512yes—
337C3×D5—24no—
338C3×D5—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—52no—
342C23×C3—52no—
343C23×C3—54no—
344C23×C3—54no—
345C23×C3—108no—
346C23×C3—108no—
347C23×C3—1016no—
348C23×C3—1016no—
349C23×C3—102no—
350C23×C3—101no—
351C23×C3—101no—
352C23×C3—101no—
353C23×C3—101no—
354C23×C3—102no—
355C23×C3—108no—
356C23×C3C2×C4×D512yes—
357C23×C3#71112yes—
358C23×C3#71312yes—
359C23×C3C23×D511yescharacteristic
360C2×C3×C4—22no—
361C2×C3×C4—28no—
362C2×C3×C4—52no—
363C2×C3×C4—54no—
364C2×C3×C4—516no—
365C2×C3×C4—52no—
366C2×C3×C4—108no—
367C2×C3×C4—108no—
368C2×C3×C4—108no—
369C2×C3×C4—102no—
370C2×C3×C4—108no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4C2×C4×D512yes—
373C2×C3×C4D4×D514yes—
374C2×Dic3—24no—
375C2×Dic3—24no—
376C2×Dic3—24no—
377C2×Dic3—104no—
378C2×Dic3—104no—
379C2×Dic3—104no—
380C22×C5—22no—
381C22×C5—24no—
382C22×C5—24no—
383C22×C5—22no—
384C22×C5#92614yescomplemented
385C22×C5C2×#23511yescharacteristic
386C22×C5C2×#23511yescharacteristic
387C22×C5C2×#23512yes—
388C22×C5C23×Dic311yescharacteristic
389C22×C5C22×#6712yes—
390C2×D5—232no—
391C2×D5—22no—
392C2×D5—22no—
393C2×D5—22no—
394C2×D5—24no—
395C2×D5—24no—
396C2×D5—24no—
397C2×D5—24no—
398C2×D5—22no—
399C2×D5#92614yescomplemented
400C2×D5C2×#21714yes—
401C4×C5—22no—
402C4×C5—124no—
403C4×C5C2×#21714yes—
404Dic5—22no—
405Dic5—124no—
406Dic5C2×#21714yes—
407C24—51no—
408C24—51no—
409C24—54no—
410C24—104no—
411C24—104no—
412C24—102no—
413C24—102no—
414C24C2×D3×D511yescharacteristic
415C22×C4—24no—
416C22×C4—34no—
417C22×C4—51no—
418C22×C4—54no—
419C22×C4—58no—
420C22×C4—54no—
421C22×C4—51no—
422C22×C4—54no—
423C22×C4—54no—
424C22×C4—54no—
425C22×C4—104no—
426C22×C4—1032no—
427C22×C4—104no—
428C22×C4—104no—
429C22×C4—104no—
430C22×C4—154no—
431C22×C4D5×Dic314yes—
432C22×C4C2×D3×D511yescharacteristic
433C22×C4C2×D3×D511yescharacteristic
434C4⋊C4—64no—
435C4⋊C4—304no—
436C22⋊C4—64no—
437C22⋊C4—308no—
438C22⋊C4—308no—
439C22⋊C4—304no—
440C42—308no—
441C3×C5#228011yescharacteristic, complemented, Hall
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—54no—
447C22×C3—54no—
448C22×C3—1032no—
449C22×C3—102no—
450C22×C3—102no—
451C22×C3—102no—
452C22×C3—102no—
453C22×C3—104no—
454C22×C3—104no—
455C22×C3—104no—
456C22×C3—104no—
457C22×C3#403814yescomplemented
458C22×C3C22×C4×D511yescharacteristic
459C22×C3C2×D4×D512yes—
460C22×C3C2×#71111yescharacteristic
461C22×C3C2×#71311yescharacteristic
462C22×C3D5×#4112yes—
463C3×C4—22no—
464C3×C4—54no—
465C3×C4—102no—
466C3×C4D5×C22⋊C414yes—
467Dic3—44no—
468Dic3—204no—
469C2×C5—24no—
470C2×C5C2×#92611yescharacteristic
471C2×C5C2×#92611yescharacteristic
472C2×C5#579112yes—
473C2×C5#579112yes—
474C2×C5C22×#21711yescharacteristic
475D5—24no—
476D5—24no—
477C23—22no—
478C23—22no—
479C23—54no—
480C23—52no—
481C23—52no—
482C23—54no—
483C23—108no—
484C23—108no—
485C23—1016no—
486C23—1016no—
487C23—101no—
488C23—101no—
489C23—101no—
490C23—101no—
491C23—102no—
492C23—102no—
493C23—108no—
494C23#677212yes—
495C23#677312yes—
496C23C2×D5×Dic312yes—
497C23C22×D3×D511yescharacteristic
498C2×C4—22no—
499C2×C4—28no—
500C2×C4—52no—
501C2×C4—54no—
502C2×C4—516no—
503C2×C4—52no—
504C2×C4—64no—
505C2×C4—64no—
506C2×C4—64no—
507C2×C4—108no—
508C2×C4—108no—
509C2×C4—108no—
510C2×C4—102no—
511C2×C4—108no—
512C2×C4—304no—
513C2×C4—304no—
514C2×C4—304no—
515C2×C4C2×D5×Dic312yes—
516C2×C4C2×D5×Dic312yes—
517C2×C4D5×#6714yes—
518C2×C3—24no—
519C2×C3—104no—
520C2×C3—104no—
521C2×C3C2×D5×C22⋊C411yescharacteristic
522C2×C3C2×#403811yescharacteristic
523C2×C3D5×#11711yescharacteristic
524C2×C3#6594012yes—
525C2×C3#6596112yes—
526C5#8402711yescharacteristic, complemented, Sylow
527C22—24no—
528C22—24no—
529C22—22no—
530C22—22no—
531C22—54no—
532C22—54no—
533C22—1032no—
534C22—104no—
535C22—104no—
536C22—104no—
537C22—104no—
538C22—102no—
539C22—102no—
540C22—102no—
541C22—102no—
542C22#9135814yescomplemented
543C22C2×#677211yescharacteristic
544C22C2×#677311yescharacteristic
545C22D5×#23512yes—
546C22C22×D5×Dic311yescharacteristic
547C22C2×D5×#6712yes—
548C4—22no—
549C4—54no—
550C4—102no—
551C4—124no—
552C4—604no—
553C4D5×#21714yes—
554C3#1060559311yescharacteristic, complemented, Sylow
555C2—24no—
556C2—104no—
557C2—104no—
558C2C2×#9135811yescharacteristic
559C2D5×#92611yescharacteristic
560C2#1175452612yes—
561C2#1175452712yes—
562C2C2×D5×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91358C2semidirect
3. #11751313C2semidirect
4. C5×#5212C2semidirect
6. Dic5×#217C2semidirect
7. #11748759C2semidirect
8. #11748737C2semidirect
9. #11748702C2semidirect
15. C22×C3×C4×D5C4semidirect
21. C2×C4⋊Dic15C22semidirect
23. C2×C5×C4⋊Dic3C22semidirect
26. C2×Dic3×Dic5C22semidirect
28. #91115C22semidirect
29. C5×C3⋊#95C22semidirect
30. #90994C22semidirect
80. #5212D5semidirect
88. C22×C4×D5Dic3semidirect
145. C3×C4×D5C22⋊C4semidirect
161. C2×C4⋊Dic3C2×D5semidirect
165. C3⋊#95C2×D5semidirect
213. C22×C3×C5#117semidirect
229. C2×C3×D5#117semidirect
310. C4×D5#217semidirect
384. C22×C5#926semidirect
399. C2×D5#926semidirect
441. C3×C5#2280semidirect
457. C22×C3#4038semidirect
526. C5#84027semidirect
542. C22#91358semidirect
554. C3#10605593semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C2×#913582
#117513132
C5×#52122
#117494882
Dic5×#2172
#117487592
#117487372
#117487022
#106055933
#840275