Finite Group Databasebeta

← #14320533

Subgroups — #14320533

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×C5×#117C211yesmaximal, characteristic, complemented
2C2×C4×#1220C211yesmaximal, characteristic
3C2×C42×D15C211yesmaximal, characteristic, complemented
4C4×#6719C211yesmaximal, characteristic, complemented
5#11751090C212yesmaximal, complemented
6#11751079C212yesmaximal, complemented
7#11751057C212yesmaximal
8#11751045C212yesmaximal, complemented
9C4×#6714C211yesmaximal, characteristic, complemented
10#11751033C211yesmaximal, characteristic, complemented
11C4×#6712C211yesmaximal, characteristic, complemented
12#10613999—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C4×D15C2211yescharacteristic
17C3×C5×#117—24no—
18C2×C3×C5×C4⋊C4C2212yes—
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×#6719C2212yes—
23C2×#6719C2211yescharacteristic
24C4×#1220C418yescomplemented
25C2×#6714C2212yes—
26C2×#6714C2211yescharacteristic
27C2×#6712C2212yes—
28C2×#6712C2211yescharacteristic
29C2×C4×Dic15C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31C2×C4×Dic15C2212yes—
32C2×C4×Dic15C2211yescharacteristic
33C42×D15—24no—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#82268—51nomaximal, Hall
40C2×C5×#117D311yescharacteristic, complemented
41C2×C4×C22⋊D5—31no—
42C2×C42×D5—31no—
43C4×C22⋊Dic5—31no—
44#65278—32no—
45#65267—32no—
46#65245—32no—
47#65233—32no—
48C4×#685—31no—
49#65221—31no—
50C4×#683—31no—
51C24×C3×C5C2311yescharacteristic
52C23×D15C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2312yes—
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—24no—
61C2×#1220C2×C414yes—
62C22×Dic15C2312yes—
63C22×Dic15C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2312yes—
67C2×C4×D15—24no—
68C2×C4×D15—24no—
69C2×C4×D15—22no—
70C2×C4×D15—22no—
71C2×C4×D15—24no—
72C2×C4×D15C2×C414yes—
73C3×C5×C4⋊C4—24no—
74C3×C5×C22⋊C4—24no—
75C3×C42×C5—22no—
76C3×C42×C5D414yescomplemented
77#6719—24no—
78#6719C2×C414yescomplemented
79#6714—24no—
80#6714C2×C414yes—
81#6712—24no—
82#6712C2×C414yescomplemented
83C4×Dic15—24no—
84C4×Dic15—22no—
85C4×Dic15—22no—
86C4×Dic15C2×C414yescomplemented
87C2×C3×#117D511yescharacteristic, complemented
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)⋊C4—51no—
96#4932—51no—
97C4×Dic3⋊C4—51no—
98C23×C4×C5C2×D311yescharacteristic
99C22×C22⋊D5—31no—
100C22×C4×D5—31no—
101C22×C4×D5—32no—
102C5×#117—24no—
103C2×C5×C4⋊C4C2×D312yes—
104C2×C5×C22⋊C4C2×D312yes—
105C2×C42×C5C2×D311yescharacteristic
106C2×C42×C5C2×D311yescharacteristic
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5—32no—
109C4×C22⋊D5—38no—
110C2×#685—31no—
111C2×#685—32no—
112C2×#683—31no—
113C2×#683—32no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—32no—
117C2×C4×Dic5—31no—
118C42×D5—64no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2290—151noSylow
125C23×C3×C5—21no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—21no—
129C23×C3×C5C22×C412yes—
130C23×C3×C5C2411yescharacteristic
131C22×D15—21no—
132C22×D15—21no—
133C22×D15—22no—
134C22×D15C22×C412yes—
135C22×D15#4114yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—28no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C2×D414yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5#4112yes—
149#1220—28no—
150C2×Dic15—21no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15C22×C412yes—
160C2×Dic15C22×C412yes—
161C2×Dic15C22×C412yes—
162C2×Dic15#4114yes—
163C4×D15—216no—
164C4×D15—28no—
165C23×C3×C4C2×D511yescharacteristic
166C22×#67—51no—
167C22×C4×D3—51no—
168C22×C4×D3—52no—
169C3×#117—24no—
170C2×C3×C4⋊C4C2×D512yes—
171C2×C3×C22⋊C4C2×D512yes—
172C2×C3×C42C2×D511yescharacteristic
173C2×C3×C42C2×D511yescharacteristic
174C2×#217—51no—
175C2×#217—52no—
176C4×#67—58no—
177C2×(C2×D3)⋊C4—51no—
178C2×(C2×D3)⋊C4—52no—
179C2×Dic3⋊C4—51no—
180C2×Dic3⋊C4—52no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—51no—
184C2×C4×Dic3—52no—
185C42×D3—104no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C24×C5C22×D311yescharacteristic
192C23×D5—31no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5C4×D314yescomplemented
196C22×C4×C5C22×D312yes—
197C22×C4×C5C22×D311yescharacteristic
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—31no—
206C22×Dic5—32no—
207C2×C4×D5—34no—
208C2×C4×D5—64no—
209C2×C4×D5—64no—
210C2×C4×D5—62no—
211C2×C4×D5—64no—
212C2×C4×D5—62no—
213C5×C4⋊C4—24no—
214C5×C22⋊C4—24no—
215C42×C5—22no—
216C42×C5#6714yescomplemented
217C22⋊Dic5—34no—
218C22⋊Dic5—64no—
219#685—34no—
220#685—64no—
221#683—34no—
222#683—64no—
223C4×Dic5—34no—
224C4×Dic5—62no—
225C4×Dic5—64no—
226C4×Dic5—62no—
227C2×C4×D4—151no—
228C2×#117D1511yescharacteristic, complemented
229C22×C42—151no—
230#388—152no—
231#387—152no—
232#386—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C22⋊C4—151no—
236C4×C22⋊C4—151no—
237#376—151no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5C23×C411yescharacteristic
244C22×C3×C5C22×D411yescharacteristic
245C22×C3×C5C2×#4111yescharacteristic
246C22×C3×C5C2×#4112yes—
247C22×C3×C5C2×#4112yes—
248C2×D15—22no—
249C2×D15—22no—
250C2×D15—24no—
251C2×D15—24no—
252C2×D15#11714yescomplemented
253C3×C4×C5—22no—
254C3×C4×C5—24no—
255C3×C4×C5—42no—
256C3×C4×C5C4×D414yes—
257Dic15—22no—
258Dic15—22no—
259Dic15—22no—
260Dic15—24no—
261Dic15—42no—
262C24×C3C22×D511yescharacteristic
263C23×D3—51no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4C4×D514yescomplemented
267C22×C3×C4C22×D512yes—
268C22×C3×C4C22×D511yescharacteristic
269C22×C3×C4C22×D512yes—
270C22×C3×C4C22×D511yescharacteristic
271C2×#67—54no—
272C2×#67—104no—
273C22×Dic3—51no—
274C22×Dic3—51no—
275C22×Dic3—52no—
276C22×Dic3—51no—
277C22×Dic3—52no—
278C2×C4×D3—54no—
279C2×C4×D3—104no—
280C2×C4×D3—104no—
281C2×C4×D3—102no—
282C2×C4×D3—104no—
283C2×C4×D3—102no—
284C3×C4⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C42—22no—
287C3×C42C22⋊D514yescomplemented
288#217—54no—
289#217—104no—
290(C2×D3)⋊C4—54no—
291(C2×D3)⋊C4—104no—
292Dic3⋊C4—54no—
293Dic3⋊C4—104no—
294C4×Dic3—54no—
295C4×Dic3—102no—
296C4×Dic3—104no—
297C4×Dic3—102no—
298C23×C5—21no—
299C23×C5—22no—
300C23×C5—22no—
301C23×C5—21no—
302C23×C5C2×C4×D312yes—
303C23×C5C23×D311yescharacteristic
304C22×D5—32no—
305C22×D5—34no—
306C22×D5—61no—
307C22×D5—62no—
308C22×D5—61no—
309C2×C4×C5—21no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—21no—
313C2×C4×C5—28no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5C2×C4×D312yes—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5#23512yes—
320C2×C4×C5C2×#6714yes—
321C2×C4×C5C2×#6712yes—
322C22⋊D5—68no—
323C2×Dic5—32no—
324C2×Dic5—32no—
325C2×Dic5—32no—
326C2×Dic5—34no—
327C2×Dic5—61no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—61no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C4×D5—616no—
337C4×D5—68no—
338C22×D4—151no—
339C23×C4—151no—
340C23×C4—152no—
341C23×C4C2×D1511yescharacteristic
342C4×D4—158no—
343#117—24no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4C2×D1512yes—
347C2×C22⋊C4—151no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4C2×D1512yes—
352C2×C42—151no—
353C2×C42—152no—
354C2×C42—151no—
355C2×C42—151no—
356C2×C42—304no—
357C2×C42C2×D1511yescharacteristic
358C2×C42C2×D1511yescharacteristic
359#95—152no—
360#95—152no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5—42no—
365C2×C3×C5C2×#11711yescharacteristic
366C2×C3×C5C2×C4×D411yescharacteristic
367C2×C3×C5C4×#4111yescharacteristic
368C2×C3×C5#52512yes—
369C2×C3×C5#52912yes—
370D15—24no—
371C23×C3—21no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—21no—
375C23×C3C2×C4×D512yes—
376C23×C3C23×D511yescharacteristic
377C22×D3—52no—
378C22×D3—54no—
379C22×D3—101no—
380C22×D3—102no—
381C22×D3—101no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—28no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4C2×C4×D512yes—
392C2×C3×C4#70912yes—
393C2×C3×C4C2×C22⋊D514yes—
394C2×C3×C4C2×C22⋊D512yes—
395#67—108no—
396C2×Dic3—52no—
397C2×Dic3—52no—
398C2×Dic3—52no—
399C2×Dic3—54no—
400C2×Dic3—101no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—101no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—102no—
408C2×Dic3—102no—
409C4×D3—1016no—
410C4×D3—108no—
411C22×C5—22no—
412C22×C5—22no—
413C22×C5—22no—
414C22×C5—42no—
415C22×C5—42no—
416C22×C5C22×C4×D311yescharacteristic
417C22×C5C2×#23511yescharacteristic
418C22×C5D3×#4112yes—
419C22×C5D3×#4112yes—
420C22×C5C22×#6711yescharacteristic
421C2×D5—34no—
422C2×D5—62no—
423C2×D5—64no—
424C2×D5—62no—
425C2×D5—64no—
426C4×C5—22no—
427C4×C5—24no—
428C4×C5—42no—
429C4×C5C4×#6714yes—
430Dic5—62no—
431Dic5—62no—
432Dic5—62no—
433Dic5—64no—
434Dic5—122no—
435C24—151no—
436C24C22×D1511yescharacteristic
437C2×D4—154no—
438C2×D4—304no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—151no—
442C22×C4—151no—
443C22×C4—152no—
444C22×C4—151no—
445C22×C4—154no—
446C22×C4—152no—
447C22×C4—304no—
448C22×C4—304no—
449C22×C4—302no—
450C22×C4—304no—
451C22×C4—302no—
452C22×C4C4×D1514yescomplemented
453C22×C4C22×D1512yes—
454C22×C4C22×D1511yescharacteristic
455C22×C4C22×D1512yes—
456C22×C4C22×D1511yescharacteristic
457C4⋊C4—24no—
458C4⋊C4—154no—
459C4⋊C4—304no—
460C22⋊C4—24no—
461C22⋊C4—154no—
462C22⋊C4—154no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—22no—
466C42—154no—
467C42—302no—
468C42—304no—
469C42—302no—
470C42#122014yescomplemented
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3C22×C4×D511yescharacteristic
478C22×C3C2×#70911yescharacteristic
479C22×C3D5×#4112yes—
480C22×C3D5×#4112yes—
481C22×C3C22×C22⋊D511yescharacteristic
482C2×D3—54no—
483C2×D3—102no—
484C2×D3—104no—
485C2×D3—102no—
486C2×D3—104no—
487C3×C4—22no—
488C3×C4—24no—
489C3×C4—42no—
490C3×C4C4×C22⋊D514yes—
491Dic3—102no—
492Dic3—102no—
493Dic3—102no—
494Dic3—104no—
495Dic3—202no—
496C2×C5—42no—
497C2×C5D3×#11711yescharacteristic
498C2×C5#552211yescharacteristic
499C2×C5#552812yes—
500C2×C5C2×C4×#6711yescharacteristic
501C2×C5#582812yes—
502D5—64no—
503C23—21no—
504C23—22no—
505C23—22no—
506C23—21no—
507C23—152no—
508C23—154no—
509C23—301no—
510C23—302no—
511C23—301no—
512C23C2×C4×D1512yes—
513C23C23×D1511yescharacteristic
514D4—308no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—28no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—152no—
524C2×C4—152no—
525C2×C4—152no—
526C2×C4—154no—
527C2×C4—3016no—
528C2×C4—301no—
529C2×C4—302no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—301no—
533C2×C4—302no—
534C2×C4—308no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4C2×C4×D1512yes—
539C2×C4C2×C4×D1512yes—
540C2×C4#681712yes—
541C2×C4C2×#122014yes—
542C2×C4C2×#122012yes—
543C2×C3—42no—
544C2×C3D5×#11711yescharacteristic
545C2×C3#6585611yescharacteristic
546C2×C3#6586212yes—
547C2×C3C2×C4×C22⋊D511yescharacteristic
548C2×C3#6616212yes—
549D3—104no—
550C5#8226811yescharacteristic, complemented, Sylow
551C22—22no—
552C22—22no—
553C22—22no—
554C22—42no—
555C22—42no—
556C22—154no—
557C22—302no—
558C22—304no—
559C22—302no—
560C22—304no—
561C22C22×C4×D1511yescharacteristic
562C22C2×#681711yescharacteristic
563C22#41×D1512yes—
564C22#41×D1512yes—
565C22C22×#122011yescharacteristic
566C4—22no—
567C4—24no—
568C4—42no—
569C4—302no—
570C4—304no—
571C4—302no—
572C4—302no—
573C4—602no—
574C4C4×#122014yes—
575C3#1061399911yescharacteristic, complemented, Sylow
576C2—42no—
577C2—304no—
578C2D15×#11711yescharacteristic
579C2#1175628111yescharacteristic
580C2#1175628712yes—
581C2C2×C4×#122011yescharacteristic
582C2#1175658712yes—
subgroupG/H
centerC22×C4C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC2×C3×C5×#117C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×#117D15
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
3. C2×C42×D15C2semidirect
4. C4×#6719C2semidirect
5. #11751090C2semidirect
6. #11751079C2semidirect
8. #11751045C2semidirect
9. C4×#6714C2semidirect
10. #11751033C2semidirect
11. C4×#6712C2semidirect
24. C4×#1220C4semidirect
40. C2×C5×#117D3semidirect
55. C22×C3×C4×C5C2×C4semidirect
76. C3×C42×C5D4semidirect
78. #6719C2×C4semidirect
82. #6712C2×C4semidirect
86. C4×Dic15C2×C4semidirect
87. C2×C3×#117D5semidirect
195. C22×C4×C5C4×D3semidirect
216. C42×C5#67semidirect
228. C2×#117D15semidirect
252. C2×D15#117semidirect
266. C22×C3×C4C4×D5semidirect
287. C3×C42C22⋊D5semidirect
452. C22×C4C4×D15semidirect
470. C42#1220semidirect
471. C3×C5#2290semidirect
550. C5#82268semidirect
575. C3#10613999semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C2×C4×#12202
C2×C42×D152
C4×#67192
#117510902
#117510792
#117510572
#117510452
C4×#67142
#117510332
C4×#67122
#106139993
#822685