Finite Group Databasebeta

← #14327705

Subgroups — #14327705

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic
2C2×C5×#926C211yesmaximal, characteristic, complemented
3C2×#91347C211yesmaximal, characteristic, complemented
4C3×#65501C211yesmaximal, characteristic, complemented
5#11749483C212yesmaximal
6#11749480C212yesmaximal, complemented
7#11748866C211yesmaximal, characteristic, complemented
8#11748854C212yesmaximal, complemented
9#11748799C211yesmaximal, characteristic, complemented
10#11748699C211yesmaximal, characteristic, complemented
11#11748645C212yesmaximal, complemented
12#10613972—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C2×#6719C2211yescharacteristic
17C4×#1220C418yescomplemented
18C2×#6714C2211yescharacteristic
19C2×#6712C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×#217C2212yes—
22C5×#926—24no—
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C4×C5×Dic3C2212yes—
26C2×C3×C22⋊Dic5C2212yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×#6669C2212yes—
30C2×#6669C2212yes—
31C2×#6667C2212yes—
32C2×#6667C2212yes—
33C2×Dic3×Dic5C2212yes—
34C2×Dic3×Dic5C2212yes—
35#91347—24no—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73885—51nomaximal, Hall
40C2×C5×#117—31no—
41C2×C4×C22⋊D5—31no—
42C2×#4038—31no—
43#65501D311yescharacteristic, complemented
44#65276—31no—
45#65265—31no—
46C4⋊C4×Dic5—31no—
47#65246—32no—
48#65233—32no—
49#65229—32no—
50C4×#683—32no—
51C24×C3×C5C2311yescharacteristic
52C23×D15C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—22no—
59C2×#1220—22no—
60C2×#1220C2×C414yes—
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C22×Dic15C2311yescharacteristic
64C2×C4×D15—22no—
65C2×C4×D15—22no—
66C2×C4×D15C2×C414yes—
67C22×C5×Dic3C2312yes—
68C22×C5×Dic3C2312yes—
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2312yes—
71#6719C2×C414yes—
72#6714C2×C414yes—
73#6712C2×C414yes—
74C4×Dic15C2×C414yes—
75C5×#217—24no—
76C5×C4⋊Dic3—22no—
77C5×C4⋊Dic3D414yescomplemented
78C4×C5×Dic3—24no—
79C3×C22⋊Dic5—42no—
80C3×C4⋊Dic5—22no—
81C3×C4⋊Dic5—22no—
82#6669—24no—
83#6669—42no—
84#6667—24no—
85#6667—42no—
86Dic3×Dic5—24no—
87Dic3×Dic5—24no—
88C2×C4×#67—51no—
89C2×#926D511yescharacteristic, complemented
90C2×#892—51no—
91C3×#380—51no—
92#4987—51no—
93#4975—51no—
94Dic3×C4⋊C4—51no—
95#4957—52no—
96#4945—52no—
97#4669—52no—
98#4649—52no—
99C23×C4×C5C2×D311yescharacteristic
100C22×C22⋊D5—31no—
101C22×C4×D5—31no—
102C5×#117—64no—
103C2×C5×C4⋊C4—31no—
104C2×C5×C4⋊C4—31no—
105C2×C5×C22⋊C4—32no—
106C2×C42×C5—32no—
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5C2×D312yes—
109C4×C22⋊D5—38no—
110C2×#685—31no—
111C2×#685—32no—
112C2×#685—32no—
113C2×C4⋊Dic5C2×D311yescharacteristic
114C2×C4⋊Dic5C2×D311yescharacteristic
115C2×#683—31no—
116C2×#683—32no—
117C2×#683—32no—
118C2×C4×Dic5—31no—
119C2×C4×Dic5—32no—
120C2×C4×Dic5—32no—
121#4038—64no—
122#3963—32no—
123#3963—32no—
124#3963C2×D312yes—
125#2354—151noSylow
126C23×C3×C5—21no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5C22×C412yes—
133C23×C3×C5C2411yescharacteristic
134C22×D15—21no—
135C22×D15—21no—
136C22×D15—21no—
137C22×D15—21no—
138C22×D15—21no—
139C22×D15—21no—
140C22×D15C22×C412yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—28no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5#4112yes—
148#1220—28no—
149C2×Dic15—21no—
150C2×Dic15—21no—
151C2×Dic15—21no—
152C2×Dic15—21no—
153C2×Dic15C22×C412yes—
154C2×Dic15C22×C412yes—
155C2×Dic15C22×C412yes—
156C2×Dic15#4112yes—
157C2×Dic15#4112yes—
158C4×D15—28no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3C2×D414yes—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C23×C3×C4C2×D511yescharacteristic
172C22×#67—51no—
173C22×C4×D3—51no—
174C2×C3×C4⋊C4—51no—
175C2×C3×C4⋊C4—51no—
176C2×C3×C22⋊C4—52no—
177C2×#217—51no—
178C2×#217C2×D512yes—
179C4×#67—58no—
180C2×(C2×D3)⋊C4—51no—
181C2×(C2×D3)⋊C4—52no—
182C2×(C2×D3)⋊C4—52no—
183#926—24no—
184C2×C4⋊Dic3C2×D511yescharacteristic
185C2×C4⋊Dic3C2×D511yescharacteristic
186C2×Dic3⋊C4—51no—
187C2×Dic3⋊C4—52no—
188C2×Dic3⋊C4—52no—
189C2×C4×Dic3—51no—
190C2×C4×Dic3—52no—
191C2×C4×Dic3—52no—
192C2×C4×Dic3C2×D512yes—
193#892—104no—
194C3×#95—52no—
195C3⋊#95—52no—
196C3⋊#95—52no—
197C24×C5C22×D311yescharacteristic
198C23×D5—31no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—32no—
202C22×C4×C5—32no—
203C22×C4×C5C4×D314yes—
204C22×C4×C5C22×D311yescharacteristic
205C22×C4×C5C22×D311yescharacteristic
206C2×C22⋊D5—34no—
207C2×C22⋊D5—62no—
208C2×C22⋊D5—62no—
209C22×Dic5—31no—
210C22×Dic5—31no—
211C22×Dic5—31no—
212C22×Dic5C22×D312yes—
213C22×Dic5C22×D312yes—
214C2×C4×D5—34no—
215C2×C4×D5—62no—
216C2×C4×D5—62no—
217C5×C4⋊C4—34no—
218C5×C4⋊C4—62no—
219C5×C22⋊C4—64no—
220C42×C5—64no—
221C22⋊Dic5—34no—
222C22⋊Dic5—42no—
223#685—34no—
224#685—64no—
225#685—122no—
226C4⋊Dic5—22no—
227C4⋊Dic5—22no—
228#683—34no—
229#683—64no—
230#683—122no—
231C4×Dic5—34no—
232C4×Dic5—64no—
233C4×Dic5—64no—
234C2×C4×D4—151no—
235C2×#117—31no—
236C2×#117—151no—
237#390—152no—
238#388—152no—
239#388—152no—
240#384—151no—
241#380—51no—
242#380—151no—
243C4×C4⋊C4—152no—
244C4×C4⋊C4—151no—
245C22×C3×C5—22no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5—41no—
252C22×C3×C5C23×C411yescharacteristic
253C22×C3×C5C22×D411yescharacteristic
254C22×C3×C5C2×#4111yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5H(5,𝔽2)11yescharacteristic
258C22×C3×C52−1+411yescharacteristic
259C2×D15—22no—
260C2×D15—22no—
261C2×D15—22no—
262C2×D15—41no—
263C2×D15—41no—
264C2×D15—41no—
265C2×D15—41no—
266C3×C4×C5—22no—
267C3×C4×C5C4×D414yes—
268Dic15—22no—
269Dic15—22no—
270Dic15#11714yescomplemented
271C3×Dic5—42no—
272C3×Dic5—42no—
273C5×Dic3—24no—
274C5×Dic3—42no—
275C24×C3C22×D511yescharacteristic
276C23×D3—51no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—52no—
280C22×C3×C4—52no—
281C22×C3×C4C4×D514yes—
282C22×C3×C4C22×D511yescharacteristic
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—54no—
285C2×#67—102no—
286C2×#67—102no—
287C22×Dic3—51no—
288C22×Dic3—51no—
289C22×Dic3—51no—
290C22×Dic3C22×D512yes—
291C22×Dic3C22×D512yes—
292C2×C4×D3—54no—
293C2×C4×D3—102no—
294C2×C4×D3—102no—
295C3×C4⋊C4—102no—
296C3×C4⋊C4—102no—
297C3×C22⋊C4—202no—
298#217—24no—
299#217—54no—
300(C2×D3)⋊C4—54no—
301(C2×D3)⋊C4—104no—
302(C2×D3)⋊C4—202no—
303C4⋊Dic3—22no—
304C4⋊Dic3C22⋊D514yescomplemented
305Dic3⋊C4—54no—
306Dic3⋊C4—104no—
307Dic3⋊C4—202no—
308C4×Dic3—24no—
309C4×Dic3—54no—
310C4×Dic3—104no—
311C4×Dic3—104no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5C2×C4×D312yes—
319C23×C5C23×D311yescharacteristic
320C22×D5—32no—
321C22×D5—61no—
322C22×D5—61no—
323C22×D5—61no—
324C22×D5—61no—
325C22×D5—61no—
326C22×D5—61no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—28no—
330C2×C4×C5—34no—
331C2×C4×C5—62no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5C2×C4×D312yes—
337C2×C4×C5C2×C4×D312yes—
338C2×C4×C5D3×D412yes—
339C2×C4×C5#23712yes—
340C22⋊D5—68no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—32no—
348C2×Dic5—32no—
349C2×Dic5—32no—
350C2×Dic5—32no—
351C2×Dic5—32no—
352C2×Dic5—61no—
353C2×Dic5—61no—
354C2×Dic5—61no—
355C2×Dic5—61no—
356C4×D5—68no—
357C22×D4—151no—
358C23×C4—151no—
359C23×C4D3×D511yescharacteristic
360C4×D4—158no—
361#117—64no—
362#117—304no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—152no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—52no—
372C2×C22⋊C4—151no—
373C2×C22⋊C4—151no—
374C2×C22⋊C4—152no—
375C2×C22⋊C4—152no—
376C2×C42—32no—
377C2×C42—151no—
378C2×C42—152no—
379C2×C42—152no—
380#95—52no—
381#95—152no—
382#95—152no—
383C2×C3×C5—42no—
384C2×C3×C5C2×#11711yescharacteristic
385C2×C3×C5C2×C4×D411yescharacteristic
386C2×C3×C5#52011yescharacteristic
387C2×C3×C5#54711yescharacteristic
388C2×C3×C5#55011yescharacteristic
389C2×C3×C5#55511yescharacteristic
390C2×C3×C5#55611yescharacteristic
391D15—42no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3C2×C4×D512yes—
399C23×C3C23×D511yescharacteristic
400C22×D3—52no—
401C22×D3—101no—
402C22×D3—101no—
403C22×D3—101no—
404C22×D3—101no—
405C22×D3—101no—
406C22×D3—101no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—28no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4—102no—
413C2×C3×C4—102no—
414C2×C3×C4—102no—
415C2×C3×C4—102no—
416C2×C3×C4C2×C4×D512yes—
417C2×C3×C4C2×C4×D512yes—
418C2×C3×C4#70912yes—
419C2×C3×C4C2×C22⋊D512yes—
420#67—108no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—52no—
427C2×Dic3—52no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—52no—
431C2×Dic3—101no—
432C2×Dic3—101no—
433C2×Dic3—101no—
434C2×Dic3—101no—
435C2×Dic3C2×C22⋊D514yes—
436C4×D3—108no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5C22×C4×D311yescharacteristic
445C22×C5C2×D3×D411yescharacteristic
446C22×C5C2×#23711yescharacteristic
447C22×C5#100411yescharacteristic
448C22×C5#100711yescharacteristic
449C22×C5D3×#4111yescharacteristic
450C22×C5D3×#4111yescharacteristic
451C2×D5—62no—
452C2×D5—62no—
453C2×D5—62no—
454C2×D5—121no—
455C2×D5—121no—
456C2×D5—121no—
457C2×D5—121no—
458C4×C5—22no—
459C4×C5—64no—
460C4×C5—122no—
461C4×C5#67⋊C414yes—
462Dic5—34no—
463Dic5—42no—
464Dic5—42no—
465Dic5—62no—
466Dic5—62no—
467C24—151no—
468C24C2×D3×D511yescharacteristic
469C2×D4—154no—
470C2×D4—302no—
471C2×D4—302no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—32no—
475C22×C4—32no—
476C22×C4—52no—
477C22×C4—52no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—151no—
481C22×C4—154no—
482C22×C4—302no—
483C22×C4—302no—
484C22×C4#120014yes—
485C22×C4C2×D3×D511yescharacteristic
486C22×C4C2×D3×D511yescharacteristic
487C4⋊C4—34no—
488C4⋊C4—62no—
489C4⋊C4—102no—
490C4⋊C4—102no—
491C4⋊C4—154no—
492C4⋊C4—304no—
493C4⋊C4—602no—
494C22⋊C4—64no—
495C22⋊C4—154no—
496C22⋊C4—154no—
497C22⋊C4—202no—
498C22⋊C4—304no—
499C22⋊C4—602no—
500C42—64no—
501C42—154no—
502C42—304no—
503C42—304no—
504C3×C5#235411yescharacteristic, complemented, Hall
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3C22×C4×D511yescharacteristic
513C22×C3C2×#70911yescharacteristic
514C22×C3D5×#4111yescharacteristic
515C22×C3D5×#4111yescharacteristic
516C22×C3#414911yescharacteristic
517C22×C3#415011yescharacteristic
518C22×C3C22×C22⋊D511yescharacteristic
519C2×D3—102no—
520C2×D3—102no—
521C2×D3—102no—
522C2×D3—201no—
523C2×D3—201no—
524C2×D3—201no—
525C2×D3—201no—
526C3×C4—22no—
527C3×C4—202no—
528C3×C4—202no—
529C3×C4C4×C22⋊D514yes—
530Dic3—24no—
531Dic3—42no—
532Dic3—54no—
533Dic3—102no—
534Dic3—102no—
535C2×C5—42no—
536C2×C5C2×#67⋊C411yescharacteristic
537C2×C5#550411yescharacteristic
538C2×C5D3×#11711yescharacteristic
539C2×C5#559911yescharacteristic
540C2×C5#561611yescharacteristic
541C2×C5#563111yescharacteristic
542C2×C5#564111yescharacteristic
543D5—122no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—152no—
551C23—301no—
552C23—301no—
553C23—301no—
554C23—301no—
555C23—301no—
556C23—301no—
557C23C2×#120012yes—
558C23C22×D3×D511yescharacteristic
559D4—308no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—28no—
563C2×C4—34no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—102no—
574C2×C4—102no—
575C2×C4—152no—
576C2×C4—152no—
577C2×C4—152no—
578C2×C4—152no—
579C2×C4—152no—
580C2×C4—301no—
581C2×C4—301no—
582C2×C4—301no—
583C2×C4—301no—
584C2×C4—308no—
585C2×C4#677912yes—
586C2×C4C2×#120012yes—
587C2×C4C2×#120012yes—
588C2×C4D3×C22⋊D512yes—
589C2×C3—42no—
590C2×C3D5×#11711yescharacteristic
591C2×C3#6585711yescharacteristic
592C2×C3#6586611yescharacteristic
593C2×C3#6586711yescharacteristic
594C2×C3C2×C4×C22⋊D511yescharacteristic
595C2×C3#6615811yescharacteristic
596C2×C3#6616811yescharacteristic
597D3—202no—
598C5#7388511yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—302no—
607C22—302no—
608C22—302no—
609C22—601no—
610C22—601no—
611C22—601no—
612C22—601no—
613C22#9200411yescharacteristic
614C22#9201611yescharacteristic
615C22#9201611yescharacteristic
616C22#9201711yescharacteristic
617C22C2×#677911yescharacteristic
618C22C22×#120011yescharacteristic
619C22C2×D3×C22⋊D511yescharacteristic
620C4—22no—
621C4—64no—
622C4—122no—
623C4—154no—
624C4—202no—
625C4—202no—
626C4—302no—
627C4—302no—
628C4#9155614yes—
629C3#1061397211yescharacteristic, complemented, Sylow
630C2—42no—
631C2—602no—
632C2#1175417811yescharacteristic
633C2#1175435011yescharacteristic
634C2#1175444711yescharacteristic
635C2#1175446111yescharacteristic
636C2#1175449611yescharacteristic
637C2#1175453511yescharacteristic
638C2C2×#9155611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2354
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×C5×#926C2semidirect
3. C2×#91347C2semidirect
4. C3×#65501C2semidirect
6. #11749480C2semidirect
7. #11748866C2semidirect
8. #11748854C2semidirect
9. #11748799C2semidirect
10. #11748699C2semidirect
11. #11748645C2semidirect
17. C4×#1220C4semidirect
43. #65501D3semidirect
77. C5×C4⋊Dic3D4semidirect
89. C2×#926D5semidirect
270. Dic15#117semidirect
304. C4⋊Dic3C22⋊D5semidirect
504. C3×C5#2354semidirect
598. C5#73885semidirect
629. C3#10613972semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C5×#9262
C2×#913472
C3×#655012
#117494832
#117494802
#117488662
#117488542
#117487992
#117486992
#117486452
#106139723
#738855