Finite Group Databasebeta

← #14332007

Subgroups — #14332007

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D15C211yesmaximal, characteristic
2C2×#91561C212yesmaximal
3C2×#91437C211yesmaximal, characteristic, complemented
4C2×#91404C212yesmaximal, complemented
5C5×#4949C211yesmaximal, characteristic, complemented
6C3×#65238C211yesmaximal, characteristic, complemented
7#11749505C212yesmaximal, complemented
8#11748888C211yesmaximal, characteristic, complemented
9#11748862C211yesmaximal, characteristic, complemented
10#11748835C211yesmaximal, characteristic, complemented
11#11748574C212yesmaximal, complemented
12D5×#399—31nomaximal, Hall
13C24×D15C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×#1200C2212yes—
17C22×#1200C2212yes—
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C2×#6714C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C22⋊C4×D15—24no—
23C2×C5×#217C2212yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
25C2×C5×Dic3⋊C4C2212yescomplemented
26C2×C3×C22⋊Dic5C2212yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
28C2×C3×#683C2212yescomplemented
29#91561—28no—
30C2×Dic3⋊Dic5C2212yescomplemented
31C2×#6669C2212yescomplemented
32C2×#6668C2212yescomplemented
33C2×#6667C2212yes—
34C2×#6667C2212yes—
35#91437—24no—
36#91404—28no—
37C5×C3⋊#95C2211yescharacteristic, complemented
38C3×#3963C2211yescharacteristic, complemented
39#90994C2212yescomplemented
40D3×#399—51nomaximal, Hall
41C2×D5×C4⋊C4—31no—
42C2×D5×C4⋊C4—32no—
43C2×D5×C22⋊C4—31no—
44C2×D5×C22⋊C4—32no—
45C5×#399—31no—
46#65281—32no—
47#65281—31no—
48#65238—32no—
49#65238D311yescharacteristic, complemented
50#64966—31no—
51D5×#95—31no—
52C24×C3×C5C2311yescharacteristic
53C23×D15—22no—
54C23×D15—24no—
55C23×D15—22no—
56C23×D15—24no—
57C23×D15Q814yes—
58C23×D15C2311yescharacteristic
59C23×D15C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C22×Dic15C2311yescharacteristic
64C2×C4×D15—24no—
65C2×C4×D15—24no—
66C2×C4×D15—22no—
67C2×C4×D15D414yes—
68C22×C5×Dic3C2312yes—
69C22×C5×Dic3C2312yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2312yes—
72C2×#1200—24no—
73C2×#1200—24no—
74C2×#1200—24no—
75C2×#1200—24no—
76C2×#1200—24no—
77C2×#1200D418yes—
78C3×C5×C22⋊C4—22no—
79#6719—22no—
80#6714—22no—
81#6714—22no—
82C5×#217—24no—
83C5×C4⋊Dic3—22no—
84C5×Dic3⋊C4—24no—
85C3×C22⋊Dic5—24no—
86C3×C4⋊Dic5—22no—
87C3×#683—24no—
88Dic3⋊Dic5—24no—
89#6669—24no—
90#6668—24no—
91#6667—24no—
92#6667—24no—
93C2×D3×C4⋊C4—51no—
94C2×D3×C4⋊C4—52no—
95C2×D3×C22⋊C4—51no—
96C2×D3×C22⋊C4—52no—
97C3×#399—51no—
98#4993—52no—
99#4993—51no—
100#4949—52no—
101#4949D511yescharacteristic, complemented
102#4677—51no—
103D3×#95—51no—
104C24×D5—31no—
105C22×C4×D5—31no—
106C22×C4×D5—32no—
107C22×C4×D5—31no—
108C22×C4×D5—32no—
109C2×C5×C4⋊C4—32no—
110C2×C5×C4⋊C4—31no—
111C2×C5×C22⋊C4—32no—
112C2×C5×C22⋊C4C2×D311yescharacteristic
113C2×C22⋊Dic5—31no—
114C2×C22⋊Dic5C2×D312yes—
115C2×#685—31no—
116C2×#685—31no—
117C2×#685—32no—
118C2×#685—32no—
119C2×C4⋊Dic5—32no—
120C2×C4⋊Dic5C2×D311yescharacteristic, complemented
121C2×#683—32no—
122C2×#683—32no—
123C2×#683C2×D312yescomplemented
124D5×C4⋊C4—68no—
125D5×C4⋊C4—64no—
126D5×C22⋊C4—68no—
127D5×C22⋊C4—64no—
128C5×#95—31no—
129#3963—32no—
130#3963C2×D311yescharacteristic, complemented
131C2×#399—151noSylow
132C23×C3×C5—22no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—22no—
136C23×C3×C5C2×Q812yes—
137C23×C3×C5C2411yescharacteristic
138C22×D15—22no—
139C22×D15—21no—
140C22×D15—21no—
141C22×D15—22no—
142C22×D15—28no—
143C22×D15—216no—
144C22×D15—48no—
145C22×D15—44no—
146C22×D15—44no—
147C22×D15C2×D414yes—
148C22×D15C2×D412yes—
149C22×D15C2×Q812yes—
150C22×D15C2×Q812yes—
151C22×D15#4112yes—
152C22×D15#4114yes—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5C2×D412yes—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—21no—
160C2×Dic15C2×D412yes—
161C4×D15—28no—
162C4×D15—44no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3C2×D414yes—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5C2×D414yes—
175#1200—216no—
176#1200—48no—
177C24×D3—51no—
178C22×C4×D3—51no—
179C22×C4×D3—52no—
180C22×C4×D3—51no—
181C22×C4×D3—52no—
182C2×C3×C4⋊C4—52no—
183C2×C3×C4⋊C4—51no—
184C2×C3×C22⋊C4—52no—
185C2×C3×C22⋊C4C2×D511yescharacteristic
186C2×#217—51no—
187C2×#217C2×D512yes—
188C2×(C2×D3)⋊C4—51no—
189C2×(C2×D3)⋊C4—51no—
190C2×(C2×D3)⋊C4—52no—
191C2×(C2×D3)⋊C4—52no—
192C2×C4⋊Dic3—52no—
193C2×C4⋊Dic3C2×D511yescharacteristic, complemented
194C2×Dic3⋊C4—52no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4C2×D512yescomplemented
197D3×C4⋊C4—108no—
198D3×C4⋊C4—104no—
199D3×C22⋊C4—108no—
200D3×C22⋊C4—104no—
201C3×#95—51no—
202C3⋊#95—52no—
203C3⋊#95C2×D511yescharacteristic, complemented
204C24×C5C22×D311yescharacteristic
205C23×D5—31no—
206C23×D5—34no—
207C23×D5—31no—
208C23×D5—64no—
209C23×D5—62no—
210C23×D5—62no—
211C23×D5—64no—
212C22×C4×C5—32no—
213C22×C4×C5—32no—
214C22×C4×C5C22×D311yescharacteristic
215C22×C4×C5C22×D311yescharacteristic
216C22×Dic5—31no—
217C22×Dic5—31no—
218C22×Dic5C22×D312yes—
219C22×Dic5C22×D312yes—
220C2×C4×D5—34no—
221C2×C4×D5—38no—
222C2×C4×D5—64no—
223C2×C4×D5—64no—
224C2×C4×D5—64no—
225C2×C4×D5—64no—
226C2×C4×D5—64no—
227C2×C4×D5—64no—
228C2×C4×D5—62no—
229C2×C4×D5—64no—
230C5×C4⋊C4—64no—
231C5×C4⋊C4—62no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—64no—
234C22⋊Dic5—24no—
235C22⋊Dic5—62no—
236#685—64no—
237#685—62no—
238#685—62no—
239#685—64no—
240C4⋊Dic5—22no—
241C4⋊Dic5—64no—
242#683—24no—
243#683—64no—
244#683—64no—
245C22×C4⋊C4—152no—
246C22×C4⋊C4—151no—
247C22×C22⋊C4—152no—
248C22×C22⋊C4—151no—
249#399—31no—
250#399—51no—
251#399—151no—
252#399—151no—
253#399—152no—
254#399—152no—
255C2×#95—151no—
256C22×C3×C5—24no—
257C22×C3×C5—22no—
258C22×C3×C5—42no—
259C22×C3×C5—41no—
260C22×C3×C5—41no—
261C22×C3×C5C22×D412yes—
262C22×C3×C5C22×D411yescharacteristic
263C22×C3×C5C22×Q811yescharacteristic
264C22×C3×C5C2×#4111yescharacteristic
265C22×C3×C5C2×#4112yes—
266C2×D15—24no—
267C2×D15—22no—
268C2×D15—42no—
269C2×D15—41no—
270C2×D15—41no—
271C2×D15—416no—
272C2×D15C22⋊Q818yes—
273C2×D15C22⋊Q814yes—
274C2×D15#12318yes—
275C2×D15#12314yes—
276C2×D15#12714yes—
277C3×C4×C5—22no—
278C3×C4×C5—41no—
279Dic15—22no—
280Dic15—41no—
281C3×Dic5—24no—
282C3×Dic5—42no—
283C5×Dic3—24no—
284C5×Dic3—42no—
285C24×C3C22×D511yescharacteristic
286C23×D3—51no—
287C23×D3—54no—
288C23×D3—51no—
289C23×D3—104no—
290C23×D3—102no—
291C23×D3—102no—
292C23×D3—104no—
293C22×C3×C4—52no—
294C22×C3×C4—52no—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×Dic3—51no—
298C22×Dic3—51no—
299C22×Dic3C22×D512yes—
300C22×Dic3C22×D512yes—
301C2×C4×D3—54no—
302C2×C4×D3—58no—
303C2×C4×D3—104no—
304C2×C4×D3—104no—
305C2×C4×D3—104no—
306C2×C4×D3—104no—
307C2×C4×D3—104no—
308C2×C4×D3—104no—
309C2×C4×D3—102no—
310C2×C4×D3—104no—
311C3×C4⋊C4—104no—
312C3×C4⋊C4—102no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—104no—
315#217—24no—
316#217—102no—
317(C2×D3)⋊C4—104no—
318(C2×D3)⋊C4—102no—
319(C2×D3)⋊C4—102no—
320(C2×D3)⋊C4—104no—
321C4⋊Dic3—22no—
322C4⋊Dic3—104no—
323Dic3⋊C4—24no—
324Dic3⋊C4—104no—
325Dic3⋊C4—104no—
326C23×C5—22no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—22no—
330C23×C5D3×Q812yes—
331C23×C5C23×D311yescharacteristic
332C22×D5—34no—
333C22×D5—32no—
334C22×D5—32no—
335C22×D5—32no—
336C22×D5—34no—
337C22×D5—32no—
338C22×D5—68no—
339C22×D5—616no—
340C22×D5—62no—
341C22×D5—61no—
342C22×D5—61no—
343C22×D5—62no—
344C22×D5—124no—
345C22×D5—128no—
346C22×D5—124no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—21no—
350C2×C4×C5—34no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5—62no—
354C2×C4×C5—62no—
355C2×C4×C5—62no—
356C2×C4×C5D3×D412yes—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—32no—
363C2×Dic5—62no—
364C2×Dic5—62no—
365C2×Dic5—61no—
366C2×Dic5D3×D414yes—
367C4×D5—616no—
368C4×D5—68no—
369C4×D5—128no—
370C4×D5—124no—
371C25—151no—
372C23×C4—152no—
373C23×C4—152no—
374C23×C4—151no—
375C23×C4—151no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—52no—
379C2×C4⋊C4—51no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—152no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—308no—
384C2×C4⋊C4—304no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—52no—
387C2×C22⋊C4—152no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—151no—
390C2×C22⋊C4—151no—
391C2×C22⋊C4—151no—
392C2×C22⋊C4—304no—
393C2×C22⋊C4—308no—
394C2×C22⋊C4D3×D511yescharacteristic
395#95—31no—
396#95—51no—
397#95—152no—
398C2×C3×C5—42no—
399C2×C3×C5C2×C22⋊Q811yescharacteristic
400C2×C3×C5C2×C22⋊Q812yes—
401C2×C3×C5C2×#12312yes—
402C2×C3×C5C2×#12311yescharacteristic
403C2×C3×C5C2×#12711yescharacteristic
404D15—42no—
405D15#39918yescomplemented
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3Q8×D512yes—
411C23×C3C23×D511yescharacteristic
412C22×D3—54no—
413C22×D3—52no—
414C22×D3—52no—
415C22×D3—52no—
416C22×D3—54no—
417C22×D3—52no—
418C22×D3—108no—
419C22×D3—1016no—
420C22×D3—102no—
421C22×D3—101no—
422C22×D3—101no—
423C22×D3—102no—
424C22×D3—204no—
425C22×D3—204no—
426C22×D3—208no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—54no—
431C2×C3×C4—102no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4D4×D512yes—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—52no—
443C2×Dic3—102no—
444C2×Dic3—102no—
445C2×Dic3—101no—
446C2×Dic3D4×D514yes—
447C4×D3—1016no—
448C4×D3—108no—
449C4×D3—208no—
450C4×D3—204no—
451C22×C5—22no—
452C22×C5—24no—
453C22×C5—41no—
454C22×C5—42no—
455C22×C5—41no—
456C22×C5C2×D3×D412yes—
457C22×C5C2×D3×D411yescharacteristic
458C22×C5C2×D3×Q811yescharacteristic
459C22×C5D3×#4111yescharacteristic
460C22×C5D3×#4112yes—
461C2×D5—34no—
462C2×D5—38no—
463C2×D5—34no—
464C2×D5—34no—
465C2×D5—38no—
466C2×D5—62no—
467C2×D5—64no—
468C2×D5—1216no—
469C2×D5—121no—
470C2×D5—122no—
471C2×D5—121no—
472C4×C5—22no—
473C4×C5—41no—
474C4×C5—64no—
475C4×C5—122no—
476Dic5—24no—
477Dic5—42no—
478Dic5—62no—
479Dic5—121no—
480C24—151no—
481C24—154no—
482C24—151no—
483C24—304no—
484C24—302no—
485C24—302no—
486C24—304no—
487C24C2×D3×D511yescharacteristic
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—52no—
491C22×C4—52no—
492C22×C4—158no—
493C22×C4—151no—
494C22×C4—154no—
495C22×C4—151no—
496C22×C4—304no—
497C22×C4—302no—
498C22×C4—304no—
499C22×C4—304no—
500C22×C4—304no—
501C22×C4—304no—
502C22×C4—304no—
503C22×C4—304no—
504C22×C4C2×D3×D511yescharacteristic
505C22×C4C2×D3×D511yescharacteristic
506C4⋊C4—64no—
507C4⋊C4—62no—
508C4⋊C4—104no—
509C4⋊C4—102no—
510C4⋊C4—304no—
511C4⋊C4—304no—
512C4⋊C4—304no—
513C22⋊C4—22no—
514C22⋊C4—64no—
515C22⋊C4—104no—
516C22⋊C4—302no—
517C22⋊C4—304no—
518C22⋊C4—304no—
519C22⋊C4—302no—
520C22⋊C4—302no—
521C3×C5C2×#39911yescharacteristic, complemented, Hall
522C22×C3—22no—
523C22×C3—24no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—42no—
527C22×C3C2×D4×D512yes—
528C22×C3C2×D4×D511yescharacteristic
529C22×C3C2×Q8×D511yescharacteristic
530C22×C3D5×#4111yescharacteristic
531C22×C3D5×#4112yes—
532C2×D3—54no—
533C2×D3—54no—
534C2×D3—58no—
535C2×D3—54no—
536C2×D3—58no—
537C2×D3—102no—
538C2×D3—104no—
539C2×D3—2016no—
540C2×D3—201no—
541C2×D3—201no—
542C2×D3—202no—
543C3×C4—22no—
544C3×C4—41no—
545C3×C4—104no—
546C3×C4—202no—
547Dic3—24no—
548Dic3—42no—
549Dic3—102no—
550Dic3—201no—
551C2×C5—42no—
552C2×C5D3×C22⋊Q811yescharacteristic
553C2×C5D3×C22⋊Q812yes—
554C2×C5D3×#12311yescharacteristic
555C2×C5D3×#12312yes—
556C2×C5D3×#12711yescharacteristic
557D5—38no—
558D5—122no—
559C23—21no—
560C23—22no—
561C23—22no—
562C23—21no—
563C23—152no—
564C23—152no—
565C23—154no—
566C23—154no—
567C23—152no—
568C23—152no—
569C23—308no—
570C23—3016no—
571C23—301no—
572C23—302no—
573C23—302no—
574C23—301no—
575C23—604no—
576C23—604no—
577C23—608no—
578C23D15⋊Q812yes—
579C23C22×D3×D511yescharacteristic
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—34no—
584C2×C4—54no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—102no—
591C2×C4—102no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—102no—
595C2×C4—152no—
596C2×C4—308no—
597C2×C4—3016no—
598C2×C4—302no—
599C2×C4—302no—
600C2×C4—301no—
601C2×C4—604no—
602C2×C4—608no—
603C2×C4#679012yes—
604C2×C3—42no—
605C2×C3D5×C22⋊Q811yescharacteristic
606C2×C3D5×C22⋊Q812yes—
607C2×C3D5×#12311yescharacteristic
608C2×C3D5×#12312yes—
609C2×C3D5×#12711yescharacteristic
610D3—58no—
611D3—202no—
612C5D3×#39911yescharacteristic, complemented, Sylow
613C22—22no—
614C22—24no—
615C22—41no—
616C22—41no—
617C22—42no—
618C22—154no—
619C22—154no—
620C22—154no—
621C22—158no—
622C22—158no—
623C22—302no—
624C22—304no—
625C22—6016no—
626C22—601no—
627C22—601no—
628C22—602no—
629C22C2×D15⋊Q811yescharacteristic
630C22#9201611yescharacteristic
631C22D3×D4×D512yes—
632C22#9202412yes—
633C22C2×#679011yescharacteristic
634C4—22no—
635C4—41no—
636C4—64no—
637C4—104no—
638C4—122no—
639C4—202no—
640C4—302no—
641C4—601no—
642C3D5×#39911yescharacteristic, complemented, Sylow
643C2—42no—
644C2—158no—
645C2—602no—
646C2#1175285012yes—
647C2#1175321012yes—
648C2#1175438311yescharacteristic
649C2#1175483011yescharacteristic
650C2#1175505211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC2×C3×C5×C22⋊C4C22
prime radicalC24×D15C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#399
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#91437C2semidirect
4. C2×#91404C2semidirect
5. C5×#4949C2semidirect
6. C3×#65238C2semidirect
7. #11749505C2semidirect
8. #11748888C2semidirect
9. #11748862C2semidirect
10. #11748835C2semidirect
11. #11748574C2semidirect
24. C2×C5×C4⋊Dic3C22semidirect
25. C2×C5×Dic3⋊C4C22semidirect
27. C2×C3×C4⋊Dic5C22semidirect
28. C2×C3×#683C22semidirect
30. C2×Dic3⋊Dic5C22semidirect
31. C2×#6669C22semidirect
32. C2×#6668C22semidirect
37. C5×C3⋊#95C22semidirect
38. C3×#3963C22semidirect
39. #90994C22semidirect
49. #65238D3semidirect
101. #4949D5semidirect
120. C2×C4⋊Dic5C2×D3semidirect
123. C2×#683C2×D3semidirect
130. #3963C2×D3semidirect
193. C2×C4⋊Dic3C2×D5semidirect
196. C2×Dic3⋊C4C2×D5semidirect
203. C3⋊#95C2×D5semidirect
405. D15#399semidirect
521. C3×C5C2×#399semidirect
612. C5D3×#399semidirect
642. C3D5×#399semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D152
C2×#915612
C2×#914372
C2×#914042
C5×#49492
C3×#652382
#117495052
#117488882
#117488622
#117488352
#117485742
D5×#3993
D3×#3995