Finite Group Databasebeta

← #14320607

Subgroups — #14320607

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4018C211yesmaximal, characteristic, complemented
2C2×C4×#1201C211yesmaximal, characteristic
3C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
4C4×#6712C211yesmaximal, characteristic, complemented
5C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#11748911C212yesmaximal
7#11748892C212yesmaximal, complemented
8#11748707C212yesmaximal, complemented
9C4×#6665C211yesmaximal, characteristic, complemented
10#11748657C212yesmaximal, complemented
11#11748611C211yesmaximal, characteristic, complemented
12#10605169—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1201C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×#6712C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×(C2×D3)⋊C4C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×#685C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C3×#4018—24no—
27C2×#6669C2211yescharacteristic
28C2×(C2×D3)⋊Dic5C2211yescharacteristic
29C2×#6665C2212yes—
30C2×#6665C2211yescharacteristic
31C2×Dic3×Dic5C2212yes—
32C4×#1201C418yescomplemented
33C4×D3×Dic5—24no—
34#91115C2212yes—
35C5×C3⋊#95C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82268—51nomaximal, Hall
40C2×C4×C22⋊D5—31no—
41C22×C4×Dic5—31no—
42C2×#4018D311yescharacteristic, complemented
43C4×C5×C22⋊C4—31no—
44#65247—32no—
45#65235—32no—
46C4×#685—31no—
47#65221—31no—
48C4×#683—31no—
49#64958—32no—
50#64941—32no—
51C23×C5×D3C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2311yescharacteristic
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3—22no—
62C2×C4×C5×D3C2×C414yes—
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C414yescomplemented
68C2×#1201—24no—
69C2×#1201C2×C414yes—
70C2×D3×Dic5—24no—
71C2×D3×Dic5—24no—
72C2×D3×Dic5—24no—
73C3×C42×C5—22no—
74#6712—24no—
75C4×Dic15—22no—
76C4×Dic15C2×C414yescomplemented
77C5×(C2×D3)⋊C4—24no—
78C4×C5×Dic3—22no—
79C3×#685—24no—
80C3×#683—24no—
81C3×C4×Dic5D414yescomplemented
82#6669C2×C414yescomplemented
83(C2×D3)⋊Dic5C2×C414yes—
84#6665—24no—
85#6665C2×C414yescomplemented
86Dic3×Dic5—24no—
87C2×C3×#117—51no—
88C2×C4×#67—51no—
89C2×C42×D3—51no—
90C4×#217—51no—
91#4989—52no—
92#4978—52no—
93#4956—52no—
94#4944—52no—
95C4×(C2×D3)⋊C4D511yescharacteristic, complemented
96#4932—51no—
97C4×Dic3⋊C4—51no—
98C23×C4×C5—31no—
99C22×C22⋊D5—31no—
100C23×Dic5—32no—
101C22×C4×D5C2×D311yescharacteristic
102C2×C5×C22⋊C4—32no—
103C2×C42×C5—31no—
104C2×C42×C5C2×D311yescharacteristic
105C2×C22⋊Dic5—31no—
106C4×C22⋊D5—38no—
107C2×#685—31no—
108C2×#685—32no—
109C2×#685C2×D312yes—
110C2×#683—31no—
111C2×#683—32no—
112C2×#683C2×D312yes—
113C2×C4×Dic5—31no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—32no—
116C2×C4×Dic5—64no—
117C2×C4×Dic5C2×D311yescharacteristic
118#4018—24no—
119C5×#95—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2290—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×C5×D3—21no—
127C22×C5×D3—22no—
128C22×C5×D3—21no—
129C22×C5×D3C22×C412yes—
130C22×C5×D3#4114yes—
131C22×C3×D5—21no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—21no—
135C22×C3×D5C22×C412yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15C22×C412yes—
147C2×Dic15C22×C412yes—
148C2×Dic15#4114yes—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3C22×C412yes—
155C4×C5×D3—28no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C2×D414yes—
162C3×C4×D5—28no—
163#1201—28no—
164D3×Dic5—216no—
165C23×C3×C4—51no—
166C22×#67—51no—
167C22×C4×D3—52no—
168C22×C4×D3C2×D511yescharacteristic
169C3×#117—104no—
170C2×C3×C4⋊C4—52no—
171C2×C3×C22⋊C4—52no—
172C2×C3×C42—51no—
173C2×C3×C42C2×D511yescharacteristic
174C2×#217—51no—
175C2×#217—52no—
176C4×#67—58no—
177C2×(C2×D3)⋊C4—51no—
178C2×(C2×D3)⋊C4C2×D512yes—
179C2×Dic3⋊C4—51no—
180C2×Dic3⋊C4—52no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—52no—
184C2×C4×Dic3C2×D511yescharacteristic
185C42×D3—104no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95C2×D512yes—
191C24×C5—31no—
192C23×D5C22×D311yescharacteristic
193C22×C4×C5—31no—
194C22×C4×C5—34no—
195C22×C4×C5—32no—
196C22×C4×C5—62no—
197C22×C4×C5—62no—
198C22×C4×C5C22×D312yes—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—34no—
201C2×C22⋊D5—64no—
202C22×Dic5—31no—
203C22×Dic5—32no—
204C22×Dic5—31no—
205C22×Dic5—64no—
206C22×Dic5—64no—
207C22×Dic5—64no—
208C22×Dic5C22×D311yescharacteristic
209C22×Dic5C22×D312yes—
210C2×C4×D5—22no—
211C2×C4×D5—22no—
212C2×C4×D5C4×D314yescomplemented
213C5×C22⋊C4—64no—
214C42×C5—22no—
215C42×C5—62no—
216C22⋊Dic5—34no—
217#685—24no—
218#685—34no—
219#685—64no—
220#683—24no—
221#683—34no—
222#683—64no—
223C4×Dic5—34no—
224C4×Dic5—62no—
225C4×Dic5—64no—
226C4×Dic5#6714yescomplemented
227C2×C4×D4—151no—
228C2×#117—51no—
229C22×C42—151no—
230#388—152no—
231#387—152no—
232#386—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C22⋊C4—31no—
236C4×C22⋊C4—151no—
237#376—151no—
238C22×C3×C5C23×C411yescharacteristic
239C22×C3×C5C22×D411yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4112yes—
243C2×C5×D3—22no—
244C2×C5×D3—22no—
245C2×C5×D3—24no—
246C2×C5×D3—24no—
247C2×C5×D3#11714yescomplemented
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—22no—
251C2×C3×D5—42no—
252C2×C3×D5—42no—
253C3×C4×C5—42no—
254C3×C4×C5C4×D414yes—
255Dic15—22no—
256Dic15—22no—
257Dic15—24no—
258C3×Dic5—22no—
259C3×Dic5—24no—
260C5×Dic3—22no—
261C5×Dic3—42no—
262C24×C3—51no—
263C23×D3C22×D511yescharacteristic
264C22×C3×C4—52no—
265C22×C3×C4—51no—
266C22×C3×C4—54no—
267C22×C3×C4—102no—
268C22×C3×C4—102no—
269C22×C3×C4C22×D512yes—
270C22×C3×C4C22×D511yescharacteristic
271C2×#67—54no—
272C2×#67—104no—
273C22×Dic3—51no—
274C22×Dic3—52no—
275C22×Dic3—51no—
276C22×Dic3C22×D512yes—
277C22×Dic3C22×D511yescharacteristic
278C2×C4×D3—22no—
279C2×C4×D3—22no—
280C2×C4×D3—104no—
281C2×C4×D3—104no—
282C2×C4×D3—104no—
283C2×C4×D3C4×D514yes—
284C3×C4⋊C4—104no—
285C3×C22⋊C4—104no—
286C3×C42—22no—
287C3×C42—54no—
288#217—54no—
289#217—104no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—54no—
292Dic3⋊C4—54no—
293Dic3⋊C4—104no—
294C4×Dic3—22no—
295C4×Dic3—54no—
296C4×Dic3—104no—
297C4×Dic3—102no—
298C23×C5—32no—
299C23×C5—34no—
300C23×C5—61no—
301C23×C5—62no—
302C23×C5—61no—
303C23×C5C23×D311yescharacteristic
304C22×D5—21no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5—21no—
308C22×D5C2×C4×D312yes—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—32no—
313C2×C4×C5—61no—
314C2×C4×C5—61no—
315C2×C4×C5—68no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5—62no—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5#23512yes—
321C2×C4×C5C2×#6712yes—
322C22⋊D5—68no—
323C2×Dic5—21no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—21no—
327C2×Dic5—32no—
328C2×Dic5—32no—
329C2×Dic5—34no—
330C2×Dic5—616no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5C2×C4×D312yes—
336C2×Dic5C2×#6714yes—
337C4×D5—28no—
338C22×D4—151no—
339C23×C4—31no—
340C23×C4—51no—
341C23×C4—152no—
342C4×D4—158no—
343#117—104no—
344C2×C4⋊C4—52no—
345C2×C4⋊C4—151no—
346C2×C4⋊C4—152no—
347C2×C22⋊C4—32no—
348C2×C22⋊C4—52no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—151no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—51no—
354C2×C42—151no—
355C2×C42—152no—
356C2×C42—151no—
357C2×C42—304no—
358C2×C42D3×D511yescharacteristic
359#95—32no—
360#95—152no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5C2×#11711yescharacteristic
365C2×C3×C5C2×C4×D411yescharacteristic
366C2×C3×C5C4×#4111yescharacteristic
367C2×C3×C5#52512yes—
368C2×C3×C5#52912yes—
369C3×D5—42no—
370C5×D3—24no—
371C23×C3—52no—
372C23×C3—102no—
373C23×C3—101no—
374C23×C3—101no—
375C23×C3—102no—
376C23×C3C23×D511yescharacteristic
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—22no—
380C22×D3C2×C4×D512yes—
381C22×D3#70914yes—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—52no—
386C2×C3×C4—54no—
387C2×C3×C4—102no—
388C2×C3×C4—101no—
389C2×C3×C4—101no—
390C2×C3×C4—102no—
391C2×C3×C4—108no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4D4×D512yes—
394C2×C3×C4#71112yes—
395#67—108no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—52no—
402C2×Dic3—52no—
403C2×Dic3—54no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—102no—
408C2×Dic3C2×C4×D512yes—
409C4×D3—28no—
410C4×D3—1016no—
411C22×C5—34no—
412C22×C5—62no—
413C22×C5—64no—
414C22×C5—62no—
415C22×C5—64no—
416C22×C5C22×C4×D311yescharacteristic
417C22×C5C2×#23511yescharacteristic
418C22×C5D3×#4112yes—
419C22×C5D3×#4112yes—
420C22×C5C22×#6711yescharacteristic
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—22no—
424C2×D5—42no—
425C2×D5—42no—
426C4×C5—42no—
427C4×C5—62no—
428C4×C5—122no—
429C4×C5C4×#6714yes—
430Dic5—22no—
431Dic5—24no—
432Dic5—62no—
433Dic5—62no—
434Dic5—64no—
435C24—31no—
436C24—51no—
437C2×D4—154no—
438C2×D4—304no—
439C22×C4—31no—
440C22×C4—34no—
441C22×C4—32no—
442C22×C4—52no—
443C22×C4—51no—
444C22×C4—54no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—151no—
450C22×C4—152no—
451C22×C4—151no—
452C22×C4—304no—
453C22×C4—304no—
454C22×C4—304no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—104no—
458C4⋊C4—154no—
459C4⋊C4—304no—
460C22⋊C4—64no—
461C22⋊C4—104no—
462C22⋊C4—154no—
463C22⋊C4—154no—
464C22⋊C4—304no—
465C42—22no—
466C42—54no—
467C42—62no—
468C42—154no—
469C42—304no—
470C42—302no—
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—102no—
473C22×C3—102no—
474C22×C3—102no—
475C22×C3—202no—
476C22×C3—202no—
477C22×C3C22×C4×D511yescharacteristic
478C22×C3C2×#70912yes—
479C22×C3C2×D4×D511yescharacteristic
480C22×C3C2×#71111yescharacteristic
481C22×C3D5×#4112yes—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—24no—
485C2×D3—24no—
486C2×D3#401814yescomplemented
487C3×C4—42no—
488C3×C4—102no—
489C3×C4—104no—
490C3×C4#402714yes—
491Dic3—22no—
492Dic3—42no—
493Dic3—102no—
494Dic3—102no—
495Dic3—104no—
496C2×C5—64no—
497C2×C5D3×#11711yescharacteristic
498C2×C5#552211yescharacteristic
499C2×C5#552812yes—
500C2×C5C2×C4×#6711yescharacteristic
501C2×C5#582812yes—
502D5—42no—
503C23—32no—
504C23—34no—
505C23—52no—
506C23—61no—
507C23—62no—
508C23—61no—
509C23—101no—
510C23—102no—
511C23—102no—
512C23—101no—
513C23C22×D3×D511yescharacteristic
514D4—308no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—32no—
519C2×C4—52no—
520C2×C4—54no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—68no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—101no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—101no—
531C2×C4—108no—
532C2×C4—152no—
533C2×C4—152no—
534C2×C4—154no—
535C2×C4—3016no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4—302no—
540C2×C4#677212yes—
541C2×C4C4×D3×D512yes—
542C2×C4D5×#6712yes—
543C2×C3—202no—
544C2×C3C2×#401811yescharacteristic
545C2×C3C2×#402711yescharacteristic
546C2×C3#6585611yescharacteristic
547C2×C3#6587212yes—
548C2×C3#6588112yes—
549D3—24no—
550C5#8226811yescharacteristic, complemented, Sylow
551C22—34no—
552C22—62no—
553C22—64no—
554C22—62no—
555C22—64no—
556C22—102no—
557C22—102no—
558C22—102no—
559C22—202no—
560C22—202no—
561C22C2×#677211yescharacteristic
562C22C2×C4×D3×D511yescharacteristic
563C22D3×#70912yes—
564C22#9201612yes—
565C22C2×D5×#6711yescharacteristic
566C4—42no—
567C4—62no—
568C4—102no—
569C4—104no—
570C4—122no—
571C4—302no—
572C4—304no—
573C4—302no—
574C4#9144014yes—
575C3#1060516911yescharacteristic, complemented, Sylow
576C2—64no—
577C2—202no—
578C2#1175266711yescharacteristic
579C2#1175269412yes—
580C2D3×#401811yescharacteristic
581C2C2×#9144011yescharacteristic
582C2#1175463112yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4018C2semidirect
3. C2×C4×D3×Dic5C2semidirect
4. C4×#6712C2semidirect
5. C4×C5×(C2×D3)⋊C4C2semidirect
7. #11748892C2semidirect
8. #11748707C2semidirect
9. C4×#6665C2semidirect
10. #11748657C2semidirect
11. #11748611C2semidirect
32. C4×#1201C4semidirect
42. C2×#4018D3semidirect
67. C2×C3×C4×D5C2×C4semidirect
76. C4×Dic15C2×C4semidirect
81. C3×C4×Dic5D4semidirect
82. #6669C2×C4semidirect
85. #6665C2×C4semidirect
95. C4×(C2×D3)⋊C4D5semidirect
212. C2×C4×D5C4×D3semidirect
226. C4×Dic5#67semidirect
247. C2×C5×D3#117semidirect
471. C3×C5#2290semidirect
486. C2×D3#4018semidirect
550. C5#82268semidirect
575. C3#10605169semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40182
C2×C4×#12012
C2×C4×D3×Dic52
C4×#67122
C4×C5×(C2×D3)⋊C42
#117489112
#117488922
#117487072
C4×#66652
#117486572
#117486112
#106051693
#822685