Finite Group Databasebeta

← #14322451

Subgroups — #14322451

Order 1920.

2208 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1202C211yesmaximal, characteristic
2C2×C5×#877C211yesmaximal, characteristic, complemented
3C2×#91529C211yesmaximal, characteristic, complemented
4#11751056C211yesmaximal, characteristic, complemented
5C3×#65244C211yesmaximal, characteristic, complemented
6#11749502C211yesmaximal, characteristic, complemented
7#11749488C211yesmaximal, characteristic, complemented
8#11748913C214yesmaximal, complemented
9#11748912C214yesmaximal, complemented
10#10614000—31nomaximal, Hall
11C24×D15C2211yescharacteristic
12C24×C3×D5C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C22×#1202—24no—
15C22×#1202—24no—
16C22×#1202C418yescomplemented
17C22×#1202C2212yes—
18C22×#1202C2212yes—
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×#6719C2211yescharacteristic
21C2×#6714C2214yescomplemented
22C2×C5×#217C2211yescharacteristic
23C2×C5×Dic3⋊C4C2212yescomplemented
24C2×C4×C5×Dic3C2212yescomplemented
25C5×#877—24no—
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×#685C2214yescomplemented
28C2×Dic3⋊Dic5C2212yescomplemented
29C2×#6667C2214yescomplemented
30C2×#6665C2214yescomplemented
31#91529—24no—
32C2×Dic3×Dic5C2212yescomplemented
33#73819—51nomaximal, Hall
34C23×D20—31no—
35C2×C5×#117—31no—
36C2×#4072—31no—
37#65277—34no—
38#65244—31no—
39#65244—31no—
40#65244—31no—
41#65244D311yescharacteristic, complemented
42#65228—34no—
43C24×C3×C5C2311yescharacteristic
44C23×D15—22no—
45C23×D15—22no—
46C23×D15—44no—
47C23×D15C2×C414yes—
48C23×D15C2312yes—
49C23×C3×D5—22no—
50C23×C3×D5—22no—
51C23×C3×D5—44no—
52C23×C3×D5C2×C414yes—
53C23×C3×D5C2312yes—
54C22×C3×C4×C5C2312yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3C2×C414yes—
57C22×C5×Dic3D414yes—
58C22×C5×Dic3D414yes—
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2311yescharacteristic
62C22×C3×Dic5C2312yes—
63C2×#1202—232no—
64C2×#1202—24no—
65C2×#1202—24no—
66C2×#1202—24no—
67C2×#1202—24no—
68C2×#1202C2×C418yes—
69C2×#1202C2×C418yes—
70C3×C5×C22⋊C4—22no—
71#6719—22no—
72#6714—44no—
73C5×#217—22no—
74C5×Dic3⋊C4—24no—
75C4×C5×Dic3—24no—
76C3×C22⋊Dic5—22no—
77C3×#685—44no—
78Dic3⋊Dic5—24no—
79#6667—44no—
80#6665—44no—
81Dic3×Dic5—24no—
82C23×#67—51no—
83C2×#877—51no—
84C2×#877D511yescharacteristic, complemented
85C3×#379—51no—
86#5247—51no—
87#4957—54no—
88#4957—54no—
89#4955—51no—
90#4955—51no—
91C24×D5—31no—
92C24×D5C2×D311yescharacteristic
93C23×C4×C5—31no—
94C22×D20—38no—
95C22×D20—32no—
96C22×D20—32no—
97C22×D20—64no—
98C22×D20—64no—
99C5×#117—64no—
100C2×C5×C4⋊C4—32no—
101C2×C5×C22⋊C4—31no—
102C2×C5×C22⋊C4C2×D311yescharacteristic
103C2×C42×C5—32no—
104C2×C22⋊Dic5—31no—
105C2×C22⋊Dic5C2×D311yescharacteristic
106C2×#685—34no—
107C2×#685—34no—
108C2×#685—34no—
109C2×#685C2×D314yescomplemented
110#4072—64no—
111C2×C4⋊Dic5—32no—
112C2×C4×Dic5—32no—
113#2309—151noSylow
114C23×C3×C5—24no—
115C23×C3×C5C22×C412yes—
116C23×C3×C5C2×D412yes—
117C23×C3×C5C2×D412yes—
118C23×C3×C5C2411yescharacteristic
119C22×D15—28no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—24no—
123C22×D15—24no—
124C22×D15—48no—
125C22×D15—48no—
126C22×D15—48no—
127C22×D15C22×C414yes—
128C22×C3×D5—28no—
129C22×C3×D5—22no—
130C22×C3×D5—22no—
131C22×C3×D5—24no—
132C22×C3×D5—24no—
133C22×C3×D5—48no—
134C22×C3×D5—48no—
135C22×C3×D5—48no—
136C22×C3×D5C22×C414yes—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—24no—
139C2×Dic15—22no—
140C2×Dic15—24no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—24no—
143C2×C5×Dic3C22⋊C4116yescomplemented
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3C22×C412yes—
146C2×C5×Dic3C2×D412yes—
147C2×C5×Dic3C2×D412yes—
148C2×C5×Dic3C2×D412yes—
149C2×C5×Dic3C2×D412yes—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—24no—
152#1202—216no—
153#1202—216no—
154C25×C3—51no—
155C24×D3—51no—
156C22×#67—58no—
157C22×#67—52no—
158C22×#67—52no—
159C22×#67—104no—
160C22×#67—104no—
161C23×Dic3C2×D511yescharacteristic
162C2×C3×C22⋊C4—51no—
163C2×C3×C22⋊C4—54no—
164C2×C3×C22⋊C4C2×D511yescharacteristic
165C2×#217—51no—
166C2×#217—54no—
167C2×#217C2×D511yescharacteristic
168C2×(C2×D3)⋊C4—54no—
169C2×(C2×D3)⋊C4—54no—
170C2×Dic3⋊C4—52no—
171C2×Dic3⋊C4C2×D512yescomplemented
172C2×C4×Dic3—52no—
173C2×C4×Dic3C2×D512yescomplemented
174#877—24no—
175#877—104no—
176C24×C5C22×D311yescharacteristic
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—32no—
180C23×D5—34no—
181C23×D5—44no—
182C23×D5—62no—
183C23×D5—62no—
184C23×D5—124no—
185C23×D5C4×D314yes—
186C23×D5C22×D312yes—
187C22×C4×C5—34no—
188C22×C4×C5—34no—
189C22×C4×C5—34no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—32no—
193C22×C4×C5C22×D312yes—
194C22×Dic5—32no—
195C22×Dic5C22×D312yes—
196C2×D20—38no—
197C2×D20—38no—
198C2×D20—632no—
199C2×D20—64no—
200C2×D20—64no—
201C2×D20—64no—
202C2×D20—64no—
203C5×C4⋊C4—64no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—62no—
206C42×C5—64no—
207C22⋊Dic5—22no—
208C22⋊Dic5—62no—
209#685—44no—
210#685—124no—
211#685—124no—
212#685—124no—
213C4⋊Dic5—64no—
214C4×Dic5—64no—
215C23×D4—151no—
216C2×#117—31no—
217C2×#117—151no—
218#390—154no—
219#390—154no—
220#379—51no—
221#379—151no—
222#379—151no—
223#379—151no—
224C22×C3×C5—24no—
225C22×C3×C5—24no—
226C22×C3×C5—24no—
227C22×C3×C5C2×C22⋊C414yes—
228C22×C3×C5C23×C411yescharacteristic
229C22×C3×C5C22×D411yescharacteristic
230C22×C3×C5C22×D411yescharacteristic
231C22×C3×C5H(5,𝔽2)14yes—
232C2×D15—24no—
233C2×D15—24no—
234C2×D15—24no—
235C2×D15—416no—
236C2×D15—44no—
237C2×D15—44no—
238C2×C3×D5—24no—
239C2×C3×D5—24no—
240C2×C3×D5—24no—
241C2×C3×D5—416no—
242C2×C3×D5—44no—
243C2×C3×D5—44no—
244C3×C4×C5—42no—
245Dic15—42no—
246C3×Dic5—42no—
247C5×Dic3—42no—
248C5×Dic3C2×C22⋊C414yes—
249C5×Dic3C2×C22⋊C414yes—
250C24×C3—52no—
251C24×C3—54no—
252C24×C3—102no—
253C24×C3—102no—
254C24×C3—204no—
255C24×C3C22×D511yescharacteristic
256C23×D3—52no—
257C23×D3—54no—
258C23×D3—102no—
259C23×D3—102no—
260C23×D3—204no—
261C22×C3×C4—52no—
262C22×C3×C4C22×D512yes—
263C2×#67—58no—
264C2×#67—58no—
265C2×#67—1032no—
266C2×#67—104no—
267C2×#67—104no—
268C2×#67—104no—
269C2×#67—104no—
270C22×Dic3—52no—
271C22×Dic3C4×D514yes—
272C22×Dic3D2014yes—
273C22×Dic3C22⋊D514yes—
274C22×Dic3C22×D512yes—
275C22×Dic3C22×D511yescharacteristic
276C22×Dic3C22×D511yescharacteristic
277C3×C22⋊C4—22no—
278C3×C22⋊C4—102no—
279C3×C22⋊C4—204no—
280#217—22no—
281#217—102no—
282#217—204no—
283(C2×D3)⋊C4—204no—
284(C2×D3)⋊C4—204no—
285Dic3⋊C4—24no—
286Dic3⋊C4—104no—
287C4×Dic3—24no—
288C4×Dic3—104no—
289C23×C5—24no—
290C23×C5C2×C4×D312yes—
291C23×C5D3×D412yes—
292C23×C5D3×D412yes—
293C23×C5C23×D311yescharacteristic
294C22×D5—28no—
295C22×D5—22no—
296C22×D5—22no—
297C22×D5—24no—
298C22×D5—24no—
299C22×D5—34no—
300C22×D5—48no—
301C22×D5—48no—
302C22×D5—48no—
303C22×D5—68no—
304C22×D5—62no—
305C22×D5—62no—
306C22×D5—64no—
307C22×D5—64no—
308C22×D5—128no—
309C22×D5—128no—
310C22×D5—128no—
311C22×D5C2×C4×D314yes—
312C2×C4×C5—22no—
313C2×C4×C5—24no—
314C2×C4×C5—316no—
315C2×C4×C5—32no—
316C2×C4×C5—32no—
317C2×C4×C5—32no—
318C2×C4×C5—32no—
319C2×C4×C5—32no—
320C2×C4×C5—32no—
321C2×C4×C5—62no—
322C2×C4×C5—64no—
323C2×Dic5—22no—
324C2×Dic5—24no—
325C2×Dic5—62no—
326C2×Dic5—64no—
327D20—616no—
328D20—616no—
329C25—51no—
330C25—151no—
331C22×D4—152no—
332C22×D4—152no—
333C22×D4—158no—
334C22×D4—304no—
335C22×D4—304no—
336C23×C4—31no—
337#117—64no—
338#117—304no—
339C2×C4⋊C4—32no—
340C2×C4⋊C4—152no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—51no—
343C2×C22⋊C4—54no—
344C2×C22⋊C4—151no—
345C2×C22⋊C4—154no—
346C2×C22⋊C4—154no—
347C2×C22⋊C4—154no—
348C2×C22⋊C4D3×D511yescharacteristic
349C2×C42—32no—
350C2×C42—152no—
351C2×C3×C5—24no—
352C2×C3×C5C22×C22⋊C411yescharacteristic
353C2×C3×C5#51812yes—
354C2×C3×C5#53512yes—
355C2×C3×C5#53512yes—
356D15—44no—
357C3×D5—44no—
358C23×C3—24no—
359C23×C3—54no—
360C23×C3—102no—
361C23×C3—104no—
362C23×C3—104no—
363C23×C3—102no—
364C23×C3—108no—
365C23×C3—208no—
366C23×C3—208no—
367C23×C3—208no—
368C23×C3C2×C4×D512yes—
369C23×C3C2×D2012yes—
370C23×C3C2×C22⋊D512yes—
371C23×C3C23×D511yescharacteristic
372C22×D3—54no—
373C22×D3—102no—
374C22×D3—104no—
375C22×D3—104no—
376C22×D3—102no—
377C22×D3—108no—
378C22×D3—208no—
379C22×D3—208no—
380C22×D3—208no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—102no—
384C2×C3×C4—104no—
385#67—1016no—
386#67—1016no—
387C2×Dic3—24no—
388C2×Dic3—22no—
389C2×Dic3—102no—
390C2×Dic3—104no—
391C2×Dic3#685116yescomplemented
392C2×Dic3C2×C4×D512yes—
393C2×Dic3C2×C4×D512yes—
394C2×Dic3C2×D2012yes—
395C2×Dic3C2×D2012yes—
396C2×Dic3C2×C22⋊D512yes—
397C2×Dic3C2×C22⋊D512yes—
398C22×C5—24no—
399C22×C5—24no—
400C22×C5—24no—
401C22×C5D3×C22⋊C414yes—
402C22×C5C22×C4×D311yescharacteristic
403C22×C5C2×D3×D411yescharacteristic
404C22×C5C2×D3×D411yescharacteristic
405C22×C5#100414yes—
406C2×D5—24no—
407C2×D5—24no—
408C2×D5—24no—
409C2×D5—416no—
410C2×D5—44no—
411C2×D5—44no—
412C2×D5—64no—
413C2×D5—64no—
414C2×D5—64no—
415C2×D5—1216no—
416C2×D5—124no—
417C2×D5—124no—
418C4×C5—34no—
419C4×C5—34no—
420C4×C5—42no—
421C4×C5—122no—
422Dic5—42no—
423Dic5—122no—
424C24—52no—
425C24—54no—
426C24—102no—
427C24—102no—
428C24—152no—
429C24—154no—
430C24—204no—
431C24—302no—
432C24—302no—
433C24—604no—
434C24C2×D3×D511yescharacteristic
435C2×D4—158no—
436C2×D4—158no—
437C2×D4—3032no—
438C2×D4—304no—
439C2×D4—304no—
440C2×D4—304no—
441C2×D4—304no—
442C22×C4—34no—
443C22×C4—34no—
444C22×C4—34no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—52no—
449C22×C4—152no—
450C22×C4C2×D3×D512yes—
451C4⋊C4—64no—
452C4⋊C4—304no—
453C22⋊C4—22no—
454C22⋊C4—62no—
455C22⋊C4—102no—
456C22⋊C4—204no—
457C22⋊C4—302no—
458C22⋊C4—604no—
459C22⋊C4—604no—
460C22⋊C4—604no—
461C42—64no—
462C42—304no—
463C3×C5#230911yescharacteristic, complemented, Hall
464C22×C3—24no—
465C22×C3—24no—
466C22×C3—24no—
467C22×C3—104no—
468C22×C3—104no—
469C22×C3—104no—
470C22×C3—2016no—
471C22×C3—204no—
472C22×C3—204no—
473C22×C3C2×#68514yes—
474C22×C3C22×C4×D511yescharacteristic
475C22×C3C22×D2011yescharacteristic
476C22×C3#414914yes—
477C22×C3C22×C22⋊D511yescharacteristic
478C2×D3—104no—
479C2×D3—104no—
480C2×D3—104no—
481C2×D3—2016no—
482C2×D3—204no—
483C2×D3—204no—
484C3×C4—42no—
485C3×C4—202no—
486Dic3—42no—
487Dic3—202no—
488Dic3C2×#68514yes—
489Dic3C2×#68514yes—
490C2×C5—24no—
491C2×C5C2×D3×C22⋊C411yescharacteristic
492C2×C5#548612yes—
493C2×C5#559212yes—
494C2×C5#559212yes—
495D5—44no—
496D5—124no—
497C23—24no—
498C23—54no—
499C23—108no—
500C23—102no—
501C23—104no—
502C23—104no—
503C23—102no—
504C23—154no—
505C23—208no—
506C23—208no—
507C23—208no—
508C23—308no—
509C23—302no—
510C23—304no—
511C23—304no—
512C23—302no—
513C23—608no—
514C23—608no—
515C23—608no—
516C23C4×D3×D512yes—
517C23D3×D2012yes—
518C23D3×C22⋊D512yes—
519C23C22×D3×D511yescharacteristic
520D4—3016no—
521D4—3016no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—316no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—32no—
530C2×C4—32no—
531C2×C4—64no—
532C2×C4—62no—
533C2×C4—102no—
534C2×C4—104no—
535C2×C4—302no—
536C2×C4—304no—
537C2×C3—24no—
538C2×C3—204no—
539C2×C3#6585512yes—
540C2×C3#6585912yes—
541C2×C3C22×#68511yescharacteristic
542C2×C3#6616412yes—
543D3—204no—
544C5#7381911yescharacteristic, complemented, Sylow
545C22—24no—
546C22—24no—
547C22—24no—
548C22—104no—
549C22—104no—
550C22—104no—
551C22—2016no—
552C22—204no—
553C22—204no—
554C22—304no—
555C22—304no—
556C22—304no—
557C22—6016no—
558C22—604no—
559C22—604no—
560C22D3×#68514yes—
561C22C2×C4×D3×D511yescharacteristic
562C22C2×D3×D2011yescharacteristic
563C22#9202614yes—
564C22C2×D3×C22⋊D511yescharacteristic
565C4—34no—
566C4—34no—
567C4—42no—
568C4—122no—
569C4—202no—
570C4—602no—
571C3#1061400011yescharacteristic, complemented, Sylow
572C2—24no—
573C2—204no—
574C2—604no—
575C2#1175287712yes—
576C2#1175306612yes—
577C2C2×D3×#68511yescharacteristic
578C2#1175494712yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×#1202C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2309
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#877C2semidirect
3. C2×#91529C2semidirect
4. #11751056C2semidirect
5. C3×#65244C2semidirect
6. #11749502C2semidirect
7. #11749488C2semidirect
8. #11748913C2semidirect
9. #11748912C2semidirect
16. C22×#1202C4semidirect
21. C2×#6714C22semidirect
23. C2×C5×Dic3⋊C4C22semidirect
24. C2×C4×C5×Dic3C22semidirect
27. C2×C3×#685C22semidirect
28. C2×Dic3⋊Dic5C22semidirect
29. C2×#6667C22semidirect
30. C2×#6665C22semidirect
32. C2×Dic3×Dic5C22semidirect
41. #65244D3semidirect
84. C2×#877D5semidirect
109. C2×#685C2×D3semidirect
143. C2×C5×Dic3C22⋊C4semidirect
171. C2×Dic3⋊C4C2×D5semidirect
173. C2×C4×Dic3C2×D5semidirect
391. C2×Dic3#685semidirect
463. C3×C5#2309semidirect
544. C5#73819semidirect
571. C3#10614000semidirect

Maximal subgroups

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

subgroupindex
C23×#12022
C2×C5×#8772
C2×#915292
#117510562
C3×#652442
#117495022
#117494882
#117489132
#117489122
#106140003
#738195