Finite Group Databasebeta

← #12099215

Subgroups — #12099215

Order 1280.

1342 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#709C211yesmaximal, characteristic
2C2×#65009C212yesmaximal, complemented
3C5×#1817C211yesmaximal, characteristic, complemented
4#10602324C211yesmaximal, characteristic, complemented
5#10600749C212yesmaximal
6#10599456C212yesmaximal, complemented
7#10599455C211yesmaximal, characteristic, complemented
8#10599455C211yesmaximal, characteristic, complemented
9#10599394C212yesmaximal, complemented
10#10599393C211yesmaximal, characteristic, complemented
11#10599392C211yesmaximal, characteristic, complemented
12C22×#709C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C2×C4×C22⋊D5C411yescharacteristic
15C2×C4×C22⋊D5C411yescharacteristic
16C2×C4×C22⋊D5C411yescharacteristic
17C2×C4×C22⋊D5C411yescharacteristic
18C2×#4072C2211yescharacteristic
19C4×#709—28no—
20C2×C4×D20C411yescharacteristic
21C2×C4×D20C411yescharacteristic
22C2×#4018C2211yescharacteristic
23C2×#4018C2211yescharacteristic
24C2×C42×D5C2211yescharacteristic
25C2×C42×D5C2211yescharacteristic
26C2×C4×Dic10C411yescharacteristic
27C2×C4×Dic10C411yescharacteristic
28C2×C5×C22⋊C8C2212yes—
29C2×C22⋊#168C2212yes—
30C2×#3952C2212yes—
31C2×#3952C2212yes—
32C2×#3952C2212yes—
33C2×#3952C2212yes—
34C2×#3947C2212yes—
35C2×#3946C2212yes—
36C2×#3946C2212yes—
37C2×C8×Dic5C2212yes—
38#65009—28no—
39C5×#336C2211yescharacteristic
40C5×#336C2211yescharacteristic
41C5×#336C2212yes—
42#64744C2211yescharacteristic
43#64744C2211yescharacteristic
44#64744C2212yes—
45#20720—51nomaximal, Sylow
46C23×C4×C5C2×C411yescharacteristic
47C23×C4×C5C2×C411yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C22×C22⋊D5C2×C411yescharacteristic
50C22×C22⋊D5C2×C411yescharacteristic
51C2×#709—24no—
52C2×#709—24no—
53C2×#709—22no—
54C2×#709—22no—
55C22×D20C2×C411yescharacteristic
56C22×C4×D5C2×C411yescharacteristic
57C22×C4×D5C2×C411yescharacteristic
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5C2×C411yescharacteristic
60C22×C4×D5C2311yescharacteristic
61C22×C4×D5C2311yescharacteristic
62C22×Dic10C2×C411yescharacteristic
63C22×C5×C8C2312yes—
64C22×C5×C8C2312yes—
65C2×C42×C5—24no—
66C2×C42×C5C2×C411yescharacteristic
67C2×C42×C5C2×C411yescharacteristic
68C2×C42×C5C2311yescharacteristic
69C2×C42×C5C2311yescharacteristic
70C2×C22⋊Dic5C2×C411yescharacteristic
71C2×C22⋊Dic5C2×C411yescharacteristic
72C4×C22⋊D5—24no—
73C4×C22⋊D5—24no—
74C4×C22⋊D5—24no—
75C4×C22⋊D5—24no—
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#685C2×C411yescharacteristic
79C2×#685C2×C411yescharacteristic
80#4072D418yes—
81C2×C4⋊Dic5C2×C411yescharacteristic
82C2×C4⋊Dic5C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×C4×Dic5C2×C411yescharacteristic
88C2×C4×Dic5C2×C411yescharacteristic
89C2×C4×Dic5C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C22×#168C2312yes—
94C22×#168C2312yes—
95C4×D20—24no—
96C4×D20—24no—
97#4018—24no—
98#4018—24no—
99C42×D5—24no—
100C42×D5—24no—
101C4×Dic10—24no—
102C4×Dic10—24no—
103C5×C22⋊C8—24no—
104C22⋊#168—24no—
105#3952—24no—
106#3952—24no—
107#3952—24no—
108#3952—24no—
109#3947—24no—
110#3946—24no—
111#3946—24no—
112C8×Dic5—24no—
113C2×C4×#41—51no—
114C2×#433—52no—
115#1817—51no—
116#1817D511yescharacteristic, complemented
117#1798—52no—
118#1797—51no—
119#1797—51no—
120#1780—52no—
121#1750—52no—
122#1749—51no—
123C4×C22⋊C8—51no—
124C24×C5C22×C411yescharacteristic
125C23×D5C22×C411yescharacteristic
126C23×D5C22×C411yescharacteristic
127C22×C4×C5—22no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—41no—
135C22×C4×C5—41no—
136C22×C4×C5C22×C411yescharacteristic
137C22×C4×C5C22×C411yescharacteristic
138C22×C4×C5C22×C411yescharacteristic
139C22×C4×C5C22×C411yescharacteristic
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C2×D414yes—
142C22×C4×C5C2411yescharacteristic
143C2×C22⋊D5—22no—
144C2×C22⋊D5—22no—
145C2×C22⋊D5—22no—
146C2×C22⋊D5—22no—
147C2×C22⋊D5—22no—
148C2×C22⋊D5—22no—
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C22×Dic5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
155#709—216no—
156#709—216no—
157C2×D20—22no—
158C2×D20—22no—
159C2×D20—22no—
160C2×C4×D5—22no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—21no—
164C2×C4×D5—21no—
165C2×C4×D5—22no—
166C2×C4×D5—22no—
167C2×C4×D5—22no—
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—41no—
174C2×C4×D5—41no—
175C2×C4×D5—41no—
176C2×C4×D5—41no—
177C2×C4×D5#4114yes—
178C2×C4×D5#4112yes—
179C2×C4×D5#4112yes—
180C2×Dic10—22no—
181C2×Dic10—22no—
182C2×Dic10—22no—
183C2×C5×C8—22no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C42×C5—22no—
190C42×C5—22no—
191C42×C5—22no—
192C42×C5—22no—
193C22⋊Dic5C22⋊C414yes—
194C22⋊Dic5C22⋊C414yes—
195#685—22no—
196#685—22no—
197#685—22no—
198#685—22no—
199C4⋊Dic5C22⋊C414yes—
200C4⋊Dic5C22⋊C414yes—
201#683—22no—
202#683—22no—
203#683—22no—
204#683—22no—
205C4×Dic5—22no—
206C4×Dic5—22no—
207C4×Dic5—22no—
208C4×Dic5—22no—
209C4×Dic5C2×D414yes—
210C4×Dic5C2×D414yes—
211C2×#168—22no—
212C2×#168—22no—
213C2×#168—22no—
214C2×#168—22no—
215C2×#168—22no—
216C2×#168—22no—
217C22×#41—51no—
218C4×#41—108no—
219C2×C4×Q8—51no—
220C2×C4×Q8—51no—
221C2×C4×D4—51no—
222C2×C4×D4—51no—
223C2×C4×D4—51no—
224C2×C4×D4—51no—
225C2×C4×D4—51no—
226C2×C4×D4—51no—
227C2×#117—51no—
228C2×#117—51no—
229C2×#117—51no—
230C22×C42—51no—
231C22×C42—51no—
232C22×C42C2×D511yescharacteristic
233#433—108no—
234C2×C4⋊C8—52no—
235C2×C4⋊C8—52no—
236C2×C22⋊C8—52no—
237C2×C22⋊C8—52no—
238C2×C22⋊C8—52no—
239C2×C22⋊C8—52no—
240C2×C22⋊C8—52no—
241C2×C22⋊C8C2×D512yes—
242C2×#97—52no—
243C2×C4×C8—52no—
244#336—51no—
245#336—51no—
246#336—52no—
247#336C2×D511yescharacteristic
248#336C2×D511yescharacteristic
249#336C2×D512yes—
250C23×C5—21no—
251C23×C5—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5C2×C22⋊C412yes—
257C23×C5C23×C411yescharacteristic
258C22×D5—21no—
259C22×D5—21no—
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—21no—
269C22×D5—21no—
270C22×D5#11712yes—
271C22×D5#11712yes—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—24no—
279C2×C4×C5—24no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—44no—
287C2×C4×C5—44no—
288C2×C4×C5C2×C22⋊C412yes—
289C2×C4×C5#13112yes—
290C2×C4×C5#13112yes—
291C2×C4×C5C22×D412yes—
292C2×C4×C5C2×#4112yes—
293C2×C4×C5C2×#4111yescharacteristic
294C2×C4×C5C2×#4111yescharacteristic
295C22⋊D5—28no—
296C22⋊D5—28no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5C2×C22⋊C412yes—
310C2×Dic5C2×C22⋊C412yes—
311C2×Dic5C2×C22⋊C412yes—
312C2×Dic5C2×C22⋊C412yes—
313C2×Dic5#11712yes—
314C2×Dic5#11712yes—
315D20—28no—
316C4×D5—24no—
317C4×D5—24no—
318C4×D5—24no—
319C4×D5—24no—
320C4×D5—44no—
321C4×D5—44no—
322C4×D5—44no—
323C4×D5—44no—
324Dic10—28no—
325C5×C8—42no—
326C5×C8—42no—
327#168—42no—
328#168—42no—
329C2×#41—104no—
330C2×#41—102no—
331C2×#41—102no—
332C2×#41—104no—
333C22×Q8—51no—
334C22×D4—51no—
335C22×D4—51no—
336C22×D4—51no—
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4C4×D511yescharacteristic
344C23×C4C4×D511yescharacteristic
345C23×C4C22×D511yescharacteristic
346C22×C8—52no—
347C22×C8—52no—
348C22×C8C22×D512yes—
349C22×C8C22×D512yes—
350C4×Q8—104no—
351C4×Q8—104no—
352C4×D4—104no—
353C4×D4—104no—
354C4×D4—104no—
355C4×D4—104no—
356C4×D4—104no—
357C4×D4—104no—
358#117—58no—
359#117—104no—
360#117—104no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4—51no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C22⋊C4—51no—
368C2×C22⋊C4—51no—
369C2×C22⋊C4—51no—
370C2×C22⋊C4—51no—
371C2×C22⋊C4—51no—
372C2×C22⋊C4—51no—
373C2×C42—24no—
374C2×C42—51no—
375C2×C42—51no—
376C2×C42—51no—
377C2×C42—51no—
378C2×C42—51no—
379C2×C42—51no—
380C2×C42—104no—
381C2×C42—104no—
382C2×C42C4×D511yescharacteristic
383C2×C42C4×D511yescharacteristic
384C2×C42C22×D511yescharacteristic
385C2×C42C22×D511yescharacteristic
386C4⋊C8—104no—
387C4⋊C8—104no—
388C22⋊C8—24no—
389C22⋊C8—104no—
390C22⋊C8—104no—
391C22⋊C8—104no—
392C22⋊C8—104no—
393C22⋊C8—104no—
394#97—104no—
395C4×C8—104no—
396C22×C5—22no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5C22×C22⋊C411yescharacteristic
404C22×C5C2×#11711yescharacteristic
405C22×C5C2×#11711yescharacteristic
406C22×C5C2×#13111yescharacteristic
407C22×C5C2×#13111yescharacteristic
408C22×C5#56811yescharacteristic
409C22×C5#56811yescharacteristic
410C2×D5—22no—
411C2×D5—22no—
412C2×D5—22no—
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—22no—
416C2×D5—41no—
417C2×D5—41no—
418C2×D5—41no—
419C2×D5—41no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—41no—
424C4×C5—22no—
425C4×C5—22no—
426C4×C5—22no—
427C4×C5—41no—
428C4×C5—41no—
429C4×C5#52512yes—
430C4×C5#52512yes—
431Dic5—22no—
432Dic5—22no—
433Dic5—22no—
434Dic5—22no—
435Dic5—22no—
436Dic5—22no—
437C24—51no—
438C24—51no—
439C24C2×C4×D511yescharacteristic
440#41—1016no—
441#41—1016no—
442C2×Q8—102no—
443C2×Q8—102no—
444C2×Q8—102no—
445C2×D4—102no—
446C2×D4—102no—
447C2×D4—102no—
448C2×D4—102no—
449C2×D4—102no—
450C2×D4—102no—
451C2×D4—102no—
452C2×D4—102no—
453C2×D4—102no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—51no—
464C22×C4—51no—
465C22×C4—51no—
466C22×C4—51no—
467C22×C4—51no—
468C22×C4—51no—
469C22×C4—54no—
470C22×C4—52no—
471C22×C4—52no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—102no—
477C22×C4—102no—
478C22×C4—102no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—102no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—102no—
485C22×C4—201no—
486C22×C4—201no—
487C22×C4—201no—
488C22×C4—201no—
489C22×C4C2×C4×D511yescharacteristic
490C22×C4C2×C4×D511yescharacteristic
491C22×C4C2×C4×D511yescharacteristic
492C22×C4C2×C4×D511yescharacteristic
493C22×C4C2×C4×D511yescharacteristic
494C22×C4D4×D514yes—
495C22×C4C23×D511yescharacteristic
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—102no—
503C2×C8—102no—
504C2×C8—102no—
505C2×C8—102no—
506C2×C8—102no—
507C2×C8—102no—
508C4⋊C4—54no—
509C4⋊C4—54no—
510C4⋊C4—102no—
511C4⋊C4—102no—
512C4⋊C4—102no—
513C4⋊C4—102no—
514C22⋊C4—54no—
515C22⋊C4—54no—
516C22⋊C4—102no—
517C22⋊C4—102no—
518C22⋊C4—102no—
519C22⋊C4—102no—
520C42—22no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—54no—
525C42—54no—
526C42—102no—
527C42—102no—
528C42—102no—
529C42—102no—
530C2×C5—42no—
531C2×C5#228011yescharacteristic
532C2×C5#288011yescharacteristic
533C2×C5#288011yescharacteristic
534C2×C5#292211yescharacteristic
535C2×C5#292311yescharacteristic
536C2×C5#292511yescharacteristic
537C2×C5#292511yescharacteristic
538D5—42no—
539D5—42no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—52no—
547C23—52no—
548C23—101no—
549C23—101no—
550C23—101no—
551C23—101no—
552C23—101no—
553C23—101no—
554C23—101no—
555C23—101no—
556C23—101no—
557C23—101no—
558C23—101no—
559C23—101no—
560C23D5×C22⋊C412yes—
561C23C22×C4×D511yescharacteristic
562Q8—108no—
563D4—108no—
564D4—108no—
565D4—108no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—52no—
583C2×C4—52no—
584C2×C4—52no—
585C2×C4—52no—
586C2×C4—52no—
587C2×C4—52no—
588C2×C4—101no—
589C2×C4—101no—
590C2×C4—101no—
591C2×C4—101no—
592C2×C4—101no—
593C2×C4—101no—
594C2×C4—101no—
595C2×C4—101no—
596C2×C4—101no—
597C2×C4—101no—
598C2×C4—101no—
599C2×C4—101no—
600C2×C4—104no—
601C2×C4—104no—
602C2×C4—104no—
603C2×C4—104no—
604C2×C4—204no—
605C2×C4—204no—
606C2×C4—204no—
607C2×C4—204no—
608C2×C4D5×C22⋊C412yes—
609C2×C4#404712yes—
610C2×C4#405312yes—
611C2×C4C2×D4×D512yes—
612C2×C4D5×#4112yes—
613C2×C4D5×#4111yescharacteristic
614C2×C4D5×#4111yescharacteristic
615C8—42no—
616C8—42no—
617C8—202no—
618C8—202no—
619C5#2072011yescharacteristic, complemented, Sylow
620C22—22no—
621C22—22no—
622C22—22no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—102no—
628C22—102no—
629C22—102no—
630C22—102no—
631C22—102no—
632C22—102no—
633C22—201no—
634C22—201no—
635C22—201no—
636C22—201no—
637C22—201no—
638C22—201no—
639C22—201no—
640C22—201no—
641C22C2×D5×C22⋊C411yescharacteristic
642C22D5×#11711yescharacteristic
643C22D5×#11711yescharacteristic
644C22C2×#404711yescharacteristic
645C22C2×#405311yescharacteristic
646C22#6607911yescharacteristic
647C22#6607911yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—102no—
654C4—102no—
655C4—102no—
656C4—102no—
657C4—102no—
658C4—102no—
659C4#6599012yes—
660C4#6599012yes—
661C2—42no—
662C2—202no—
663C2—202no—
664C2#1060578111yescharacteristic
665C2#1061033111yescharacteristic
666C2#1061036211yescharacteristic
667C2#1061101411yescharacteristic
668C2#1061101611yescharacteristic
669C2#1061106311yescharacteristic
670C2#1061106511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1817C2
prime radicalC22×#709C22
cosocleC22×C4×C5C24
hypercenter#1817D5
hypocenterC5#20720
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#65009C2semidirect
3. C5×#1817C2semidirect
4. #10602324C2semidirect
6. #10599456C2semidirect
7. #10599455C2semidirect
8. #10599455C2semidirect
9. #10599394C2semidirect
10. #10599393C2semidirect
11. #10599392C2semidirect
116. #1817D5semidirect
619. C5#20720semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#7092
C2×#650092
C5×#18172
#106023242
#106007492
#105994562
#105994552
#105993942
#105993932
#105993922
#207205