Finite Group Databasebeta

← #14481713

Subgroups — #14481713

Order 1920.

2592 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D15C211yesmaximal, characteristic
2C5×#5483C211yesmaximal, characteristic, complemented
3C3×#65817C211yesmaximal, characteristic, complemented
4#11755432C212yesmaximal, complemented
5C2×#91561C212yesmaximal
6#11754484C214yesmaximal, complemented
7#11754383C214yesmaximal, complemented
8#11753060C218yesmaximal, complemented
9#11752850C218yesmaximal, complemented
10D5×#543—31nomaximal, Hall
11C24×D15C2211yescharacteristic
12C22×C4×D15C2212yes—
13C22×#1200C2214yes—
14C2×D15⋊Q8C2214yescomplemented
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C2×#6719C2211yescharacteristic
17C2×#6714C2212yes—
18C22⋊C4×D15C2214yes—
19C22⋊C4×D15C2214yes—
20C2×C5×#217C2212yes—
21C5×#924C2214yescomplemented
22C5×#878C2218yescomplemented
23C2×C3×C22⋊Dic5C2212yes—
24C3×#4070C2214yescomplemented
25C3×#4024C2218yescomplemented
26#91576C2218yescomplemented
27#91575C2218yescomplemented
28#91574C2218yescomplemented
29#91561C2214yes—
30#91561C2214yes—
31#91561C2214yes—
32#91561C2214yes—
33C2×#6667C2214yes—
34#91437C2214yescomplemented
35#91429C2218yescomplemented
36#91424C2218yescomplemented
37#91419C2218yescomplemented
38#91411C2218yescomplemented
39#91404C2218yescomplemented
40#91390C2214yescomplemented
41#91383C2214yescomplemented
42#91377C2218yescomplemented
43D3×#543—51nomaximal, Hall
44C5×#543—31no—
45#65968—34no—
46#65968—38no—
47D5×C22⋊Q8—34no—
48D5×C22⋊Q8—38no—
49C2×D5×C22⋊C4—31no—
50C2×D5×C22⋊C4—32no—
51#65817—32no—
52#65817D311yescharacteristic, complemented
53C24×C3×C5C2311yescharacteristic
54C23×D15—44no—
55C23×D15Q818yescomplemented
56C23×D15C2312yes—
57C23×D15C2311yescharacteristic
58C23×D15C2312yes—
59C23×D15C2311yescharacteristic
60C22×C3×C4×C5C2312yes—
61C22×Dic15C2312yes—
62C2×C4×D15—44no—
63C2×C4×D15C2314yes—
64C2×C4×D15C2314yes—
65C22×C5×Dic3C2314yes—
66C2×C5×Dic6C2314yescomplemented
67C22×C3×Dic5C2314yes—
68C2×C3×Dic10C2314yescomplemented
69C2×#1204C2318yescomplemented
70C2×#1200—48no—
71C2×#1200C2318yes—
72C2×#1200C2318yes—
73D15⋊Q8—48no—
74C3×C5×C22⋊C4C2314yes—
75#6719C2314yes—
76#6714C2318yes—
77C5×#217C2314yes—
78C5×#217C2314yes—
79C5×C4⋊Dic3C2314yescomplemented
80C5×Dic3⋊C4C2318yescomplemented
81C3×C22⋊Dic5C2314yes—
82C3×C22⋊Dic5C2314yes—
83C3×C4⋊Dic5C2314yescomplemented
84C3×#683C2318yescomplemented
85Dic3⋊Dic5C2318yescomplemented
86#6669C2318yescomplemented
87#6668C2318yescomplemented
88#6667C2318yes—
89#6667C2318yes—
90C3×#543—51no—
91#5634—54no—
92#5634—58no—
93D3×C22⋊Q8—54no—
94D3×C22⋊Q8—58no—
95C2×D3×C22⋊C4—51no—
96C2×D3×C22⋊C4—52no—
97#5483—52no—
98#5483D511yescharacteristic, complemented
99C24×D5—31no—
100C2×Q8×D5—34no—
101C22×C4×D5—32no—
102C22×C4×D5—34no—
103C5×C22⋊Q8—34no—
104C5×C22⋊Q8—38no—
105C2×C5×C22⋊C4—32no—
106C2×C5×C22⋊C4C2×D311yescharacteristic
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5C2×D312yes—
109#4092—34no—
110#4092—38no—
111C2×#685—32no—
112C2×#685—34no—
113#4070—38no—
114#4070C2×D314yescomplemented
115#4043—34no—
116#4043—38no—
117#4042—38no—
118#4042—38no—
119#4042—38no—
120D5×C4⋊C4—34no—
121D5×C4⋊C4—38no—
122D5×C22⋊C4—34no—
123D5×C22⋊C4—34no—
124D5×C22⋊C4—34no—
125D5×C22⋊C4—34no—
126D5×C22⋊C4—34no—
127D5×C22⋊C4—34no—
128#4024—38no—
129#4024—38no—
130#4024C2×D318yescomplemented
131C2×#543—151noSylow
132C23×C3×C5—42no—
133C23×C3×C5C2×Q814yescomplemented
134C23×C3×C5C2411yescharacteristic
135C23×C3×C5C2412yes—
136C22×D15—28no—
137C22×D15—24no—
138C22×D15—416no—
139C22×D15—42no—
140C22×D15—44no—
141C22×D15C2×Q818yes—
142C22×D15C2×Q814yes—
143C22×D15C2×Q818yescomplemented
144C22×D15C2×Q814yescomplemented
145C22×D15C2411yescharacteristic
146C22×D15C2412yes—
147C22×D15C2411yescharacteristic
148C2×C3×C4×C5—42no—
149C2×C3×C4×C5C2414yes—
150C2×Dic15—42no—
151C2×Dic15C2414yes—
152C4×D15—28no—
153C4×D15—44no—
154C2×C5×Dic3—44no—
155C2×C5×Dic3C2418yes—
156C5×Dic6—44no—
157C2×C3×Dic5—44no—
158C2×C3×Dic5C2418yes—
159C3×Dic10—44no—
160#1204—48no—
161#1200—216no—
162#1200—48no—
163C24×D3—51no—
164C2×D3×Q8—54no—
165C22×C4×D3—52no—
166C22×C4×D3—54no—
167C3×C22⋊Q8—54no—
168C3×C22⋊Q8—58no—
169C2×C3×C22⋊C4—52no—
170C2×C3×C22⋊C4C2×D511yescharacteristic
171C2×#217—51no—
172C2×#217C2×D512yes—
173#946—54no—
174#946—58no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4—54no—
177#924—58no—
178#924C2×D514yescomplemented
179#897—54no—
180#897—58no—
181#896—58no—
182#896—58no—
183#896—58no—
184D3×C4⋊C4—54no—
185D3×C4⋊C4—58no—
186D3×C22⋊C4—54no—
187D3×C22⋊C4—54no—
188D3×C22⋊C4—54no—
189D3×C22⋊C4—54no—
190D3×C22⋊C4—54no—
191D3×C22⋊C4—54no—
192#878—58no—
193#878—58no—
194#878C2×D518yescomplemented
195C24×C5C22×D311yescharacteristic
196C23×D5—32no—
197C23×D5—31no—
198C23×D5—38no—
199C23×D5—32no—
200C23×D5—31no—
201C23×D5—124no—
202C2×C5×Q8—34no—
203C22×C4×C5—34no—
204C22×C4×C5C22×D312yes—
205C22×Dic5—32no—
206C22×Dic5C22×D314yes—
207Q8×D5—128no—
208C2×C4×D5—34no—
209C2×C4×D5—38no—
210C2×C4×D5—34no—
211C2×C4×D5—38no—
212C2×C4×D5—128no—
213C2×C4×D5—124no—
214C2×Dic10—38no—
215C2×Dic10C22×D314yescomplemented
216C5×C4⋊C4—38no—
217C5×C4⋊C4—34no—
218C5×C22⋊C4—34no—
219C5×C22⋊C4—34no—
220C5×C22⋊C4C22×D314yes—
221C22⋊Dic5—34no—
222C22⋊Dic5C22×D314yes—
223C22⋊Dic5C22×D314yes—
224#685—38no—
225#685—38no—
226#685—38no—
227C4⋊Dic5—38no—
228C4⋊Dic5C22×D314yescomplemented
229#683—38no—
230#683—38no—
231#683C22×D318yescomplemented
232#543—31no—
233#543—51no—
234#543—152no—
235#543—154no—
236#543—158no—
237C2×C22⋊Q8—154no—
238C2×C22⋊Q8—158no—
239C22×C22⋊C4—152no—
240C22×C22⋊C4—151no—
241C22×C3×C5—24no—
242C22×C3×C5—22no—
243C22×C3×C5—44no—
244C22×C3×C5C22×Q812yes—
245C22×C3×C5C22×Q814yes—
246C22×C3×C5C2511yescharacteristic
247C2×D15—24no—
248C2×D15—22no—
249C2×D15—216no—
250C2×D15—28no—
251C2×D15—44no—
252C2×D15—48no—
253C2×D15C22×Q812yes—
254C2×D15C22×Q814yes—
255C2×D15C22×Q812yes—
256C2×D15H(5,𝔽2)14yes—
257C3×C4×C5—24no—
258Dic15—24no—
259C3×Dic5—28no—
260C5×Dic3—28no—
261C24×C3C22×D511yescharacteristic
262C23×D3—52no—
263C23×D3—51no—
264C23×D3—58no—
265C23×D3—52no—
266C23×D3—51no—
267C23×D3—204no—
268C2×C3×Q8—54no—
269C22×C3×C4—54no—
270C22×C3×C4C22×D512yes—
271C22×Dic3—52no—
272C22×Dic3C22×D514yes—
273D3×Q8—208no—
274C2×C4×D3—54no—
275C2×C4×D3—58no—
276C2×C4×D3—54no—
277C2×C4×D3—58no—
278C2×C4×D3—208no—
279C2×C4×D3—204no—
280C2×Dic6—58no—
281C2×Dic6C22×D514yescomplemented
282C3×C4⋊C4—58no—
283C3×C4⋊C4—54no—
284C3×C22⋊C4—54no—
285C3×C22⋊C4—54no—
286C3×C22⋊C4C22×D514yes—
287#217—54no—
288#217C22×D514yes—
289#217C22×D514yes—
290(C2×D3)⋊C4—58no—
291(C2×D3)⋊C4—58no—
292(C2×D3)⋊C4—58no—
293C4⋊Dic3—58no—
294C4⋊Dic3C22×D514yescomplemented
295Dic3⋊C4—58no—
296Dic3⋊C4—58no—
297Dic3⋊C4C22×D518yescomplemented
298C23×C5—42no—
299C23×C5D3×Q814yescomplemented
300C23×C5C23×D312yes—
301C23×C5C23×D311yescharacteristic
302C22×D5—31no—
303C22×D5—38no—
304C22×D5—34no—
305C22×D5—32no—
306C22×D5—31no—
307C22×D5—38no—
308C22×D5—34no—
309C22×D5—68no—
310C22×D5—64no—
311C22×D5—1216no—
312C22×D5—124no—
313C22×D5—122no—
314C5×Q8—124no—
315C2×C4×C5—38no—
316C2×C4×C5—42no—
317C2×C4×C5—124no—
318C2×C4×C5C23×D314yes—
319C2×Dic5—34no—
320C2×Dic5—44no—
321C2×Dic5—122no—
322C2×Dic5C23×D318yes—
323C4×D5—616no—
324C4×D5—68no—
325C4×D5—128no—
326C4×D5—124no—
327Dic10—44no—
328Dic10—128no—
329C25—151no—
330C22×Q8—154no—
331C23×C4—154no—
332C23×C4—152no—
333C22⋊Q8—34no—
334C22⋊Q8—38no—
335C22⋊Q8—54no—
336C22⋊Q8—58no—
337C22⋊Q8—158no—
338C22⋊Q8—158no—
339C22⋊Q8—158no—
340C22⋊Q8—158no—
341C22⋊Q8—158no—
342C22⋊Q8—158no—
343C22⋊Q8—158no—
344C22⋊Q8—154no—
345C22⋊Q8—158no—
346C22⋊Q8—154no—
347C2×C4⋊C4—158no—
348C2×C4⋊C4—154no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4—154no—
352C2×C22⋊C4—154no—
353C2×C22⋊C4—154no—
354C2×C22⋊C4—154no—
355C2×C22⋊C4—154no—
356C2×C22⋊C4—151no—
357C2×C22⋊C4—152no—
358C2×C22⋊C4—154no—
359C2×C22⋊C4—154no—
360C2×C22⋊C4D3×D511yescharacteristic
361C2×C3×C5—24no—
362C2×C3×C5—22no—
363C2×C3×C5C23×Q811yescharacteristic
364C2×C3×C5C2×H(5,𝔽2)12yes—
365D15—24no—
366D15—22no—
367D15#54314yescomplemented
368C23×C3—42no—
369C23×C3Q8×D514yescomplemented
370C23×C3C23×D512yes—
371C23×C3C23×D511yescharacteristic
372C22×D3—51no—
373C22×D3—58no—
374C22×D3—54no—
375C22×D3—52no—
376C22×D3—51no—
377C22×D3—58no—
378C22×D3—54no—
379C22×D3—108no—
380C22×D3—104no—
381C22×D3—2016no—
382C22×D3—204no—
383C22×D3—202no—
384C3×Q8—204no—
385C2×C3×C4—42no—
386C2×C3×C4—58no—
387C2×C3×C4—204no—
388C2×C3×C4C23×D514yes—
389C2×Dic3—44no—
390C2×Dic3—54no—
391C2×Dic3—202no—
392C2×Dic3C23×D518yes—
393C4×D3—1016no—
394C4×D3—108no—
395C4×D3—208no—
396C4×D3—204no—
397Dic6—44no—
398Dic6—208no—
399C22×C5—24no—
400C22×C5—22no—
401C22×C5—44no—
402C22×C5C2×D3×Q814yes—
403C22×C5C2×D3×Q812yes—
404C22×C5C24×D311yescharacteristic
405C2×D5—32no—
406C2×D5—34no—
407C2×D5—32no—
408C2×D5—34no—
409C2×D5—616no—
410C2×D5—68no—
411C2×D5—64no—
412C2×D5—62no—
413C2×D5—128no—
414C2×D5—124no—
415C4×C5—24no—
416C4×C5—68no—
417Dic5—28no—
418Dic5—64no—
419C24—151no—
420C24—152no—
421C24—158no—
422C24—151no—
423C24—152no—
424C24—604no—
425C24C2×D3×D511yescharacteristic
426C2×Q8—34no—
427C2×Q8—54no—
428C2×Q8—158no—
429C2×Q8—608no—
430C22×C4—34no—
431C22×C4—54no—
432C22×C4—158no—
433C22×C4—158no—
434C22×C4—152no—
435C22×C4—154no—
436C22×C4—154no—
437C22×C4—604no—
438C22×C4—608no—
439C22×C4C2×D3×D512yes—
440C4⋊C4—38no—
441C4⋊C4—34no—
442C4⋊C4—58no—
443C4⋊C4—54no—
444C4⋊C4—158no—
445C4⋊C4—158no—
446C4⋊C4—158no—
447C22⋊C4—34no—
448C22⋊C4—34no—
449C22⋊C4—54no—
450C22⋊C4—54no—
451C22⋊C4—158no—
452C22⋊C4—158no—
453C22⋊C4—154no—
454C22⋊C4—158no—
455C22⋊C4C2×D3×D514yes—
456C3×C5C2×#54311yescharacteristic, complemented, Hall
457C22×C3—24no—
458C22×C3—22no—
459C22×C3—44no—
460C22×C3C2×Q8×D514yes—
461C22×C3C2×Q8×D512yes—
462C22×C3C24×D511yescharacteristic
463C2×D3—52no—
464C2×D3—54no—
465C2×D3—52no—
466C2×D3—54no—
467C2×D3—1016no—
468C2×D3—108no—
469C2×D3—104no—
470C2×D3—102no—
471C2×D3—208no—
472C2×D3—204no—
473C3×C4—24no—
474C3×C4—108no—
475Dic3—28no—
476Dic3—104no—
477C2×C5—24no—
478C2×C5—22no—
479C2×C5C22×D3×Q811yescharacteristic
480C2×C5D3×H(5,𝔽2)12yes—
481D5—34no—
482D5—64no—
483D5—62no—
484C23—42no—
485C23—151no—
486C23—154no—
487C23—158no—
488C23—151no—
489C23—152no—
490C23—154no—
491C23—158no—
492C23—304no—
493C23—308no—
494C23—602no—
495C23—604no—
496C23—6016no—
497C23D15⋊Q814yescomplemented
498C23C22×D3×D511yescharacteristic
499C23C22×D3×D512yes—
500Q8—124no—
501Q8—204no—
502Q8—608no—
503C2×C4—38no—
504C2×C4—42no—
505C2×C4—58no—
506C2×C4—124no—
507C2×C4—154no—
508C2×C4—204no—
509C2×C4—308no—
510C2×C4—3016no—
511C2×C4—604no—
512C2×C4—608no—
513C2×C4—602no—
514C2×C4C22×D3×D514yes—
515C2×C3—24no—
516C2×C3—22no—
517C2×C3C22×Q8×D511yescharacteristic
518C2×C3D5×H(5,𝔽2)12yes—
519D3—54no—
520D3—104no—
521D3—102no—
522C5D3×#54311yescharacteristic, complemented, Sylow
523C22—22no—
524C22—24no—
525C22—44no—
526C22—152no—
527C22—154no—
528C22—152no—
529C22—154no—
530C22—308no—
531C22—3016no—
532C22—302no—
533C22—304no—
534C22—604no—
535C22—608no—
536C22C2×D15⋊Q812yes—
537C22C2×D15⋊Q814yes—
538C22C23×D3×D511yescharacteristic
539C4—24no—
540C4—68no—
541C4—108no—
542C4—304no—
543C3D5×#54311yescharacteristic, complemented, Sylow
544C2—22no—
545C2—24no—
546C2—154no—
547C2—302no—
548C2—304no—
549C2C22×D15⋊Q811yescharacteristic
550C2#1175703012yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×C22⋊C4C22
prime radicalC24×D15C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#543
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#5483C2semidirect
3. C3×#65817C2semidirect
4. #11755432C2semidirect
6. #11754484C2semidirect
7. #11754383C2semidirect
8. #11753060C2semidirect
9. #11752850C2semidirect
14. C2×D15⋊Q8C22semidirect
21. C5×#924C22semidirect
22. C5×#878C22semidirect
24. C3×#4070C22semidirect
25. C3×#4024C22semidirect
26. #91576C22semidirect
27. #91575C22semidirect
28. #91574C22semidirect
34. #91437C22semidirect
35. #91429C22semidirect
36. #91424C22semidirect
37. #91419C22semidirect
38. #91411C22semidirect
39. #91404C22semidirect
40. #91390C22semidirect
41. #91383C22semidirect
42. #91377C22semidirect
52. #65817D3semidirect
55. C23×D15Q8semidirect
66. C2×C5×Dic6C23semidirect
68. C2×C3×Dic10C23semidirect
69. C2×#1204C23semidirect
79. C5×C4⋊Dic3C23semidirect
80. C5×Dic3⋊C4C23semidirect
83. C3×C4⋊Dic5C23semidirect
84. C3×#683C23semidirect
85. Dic3⋊Dic5C23semidirect
86. #6669C23semidirect
87. #6668C23semidirect
98. #5483D5semidirect
114. #4070C2×D3semidirect
130. #4024C2×D3semidirect
133. C23×C3×C5C2×Q8semidirect
143. C22×D15C2×Q8semidirect
144. C22×D15C2×Q8semidirect
178. #924C2×D5semidirect
194. #878C2×D5semidirect
215. C2×Dic10C22×D3semidirect
228. C4⋊Dic5C22×D3semidirect
231. #683C22×D3semidirect
281. C2×Dic6C22×D5semidirect
294. C4⋊Dic3C22×D5semidirect
297. Dic3⋊C4C22×D5semidirect
299. C23×C5D3×Q8semidirect
367. D15#543semidirect
369. C23×C3Q8×D5semidirect
456. C3×C5C2×#543semidirect
497. C23D15⋊Q8semidirect
522. C5D3×#543semidirect
543. C3D5×#543semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D152
C5×#54832
C3×#658172
#117554322
C2×#915612
#117544842
#117543832
#117530602
#117528502
D5×#5433
D3×#5435