Finite Group Databasebeta

← #12021925

Subgroups — #12021925

Order 1280.

1630 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic5C211yesmaximal, characteristic
2C2×#65233C212yesmaximal
3C5×C22⋊#95C211yesmaximal, characteristic
4#10602920C211yesmaximal, characteristic
5#10602340C212yesmaximal
6#10600207C212yesmaximal, complemented
7#10600198C212yesmaximal, complemented
8#10600197C211yesmaximal, characteristic, complemented
9#10600197C211yesmaximal, characteristic, complemented
10#10600194C211yesmaximal, characteristic, complemented
11Dic5×#95C211yesmaximal, characteristic, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C5×C22⋊C4C2212yes—
14C22×C22⋊Dic5C2212yes—
15C22×C22⋊Dic5C2211yescharacteristic
16C22×C22⋊Dic5C2211yescharacteristic
17C22×#683C2212yes—
18C22×#683C2212yes—
19C22×C4×Dic5C2212yes—
20C22×C4×Dic5C2211yescharacteristic
21C22×C4×Dic5C2211yescharacteristic
22C2×C5×#95C2211yescharacteristic
23C2×C5×#95C2211yescharacteristic
24C2×C5×#95C2212yes—
25C4×C22⋊Dic5C418yescomplemented
26C2×#3963C2211yescharacteristic
27C2×#3963C2212yes—
28C2×#3963C2211yescharacteristic
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36#65233—28no—
37#13948—51nomaximal, Sylow
38C25×C5C2311yescharacteristic
39C23×C4×C5—22no—
40C23×C4×C5—22no—
41C23×C4×C5—42no—
42C23×C4×C5—42no—
43C23×C4×C5C2×C414yes—
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2312yes—
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C23×Dic5C2311yescharacteristic
54C2×C5×C22⋊C4—24no—
55C2×C5×C22⋊C4—24no—
56C2×C5×C22⋊C4—42no—
57C2×C22⋊Dic5—22no—
58C2×C22⋊Dic5—22no—
59C2×C22⋊Dic5—24no—
60C2×C22⋊Dic5—24no—
61C2×C22⋊Dic5—42no—
62C2×C22⋊Dic5C2×C414yes—
63C2×C22⋊Dic5C2×C414yes—
64C2×C22⋊Dic5D414yes—
65C2×C22⋊Dic5Q814yes—
66C2×#683—24no—
67C2×#683—24no—
68C2×#683—24no—
69C2×#683—24no—
70C2×#683—42no—
71C2×#683—42no—
72C2×C4×Dic5—24no—
73C2×C4×Dic5—24no—
74C2×C4×Dic5—42no—
75C2×C4×Dic5—42no—
76C2×C4×Dic5—42no—
77C2×C4×Dic5C2×C414yes—
78C2×C4×Dic5C2×C414yes—
79C5×#95—22no—
80C5×#95—22no—
81C5×#95—42no—
82#3963—22no—
83#3963—22no—
84#3963—24no—
85#3963—24no—
86#3963—24no—
87#3963—24no—
88#3963—42no—
89#3963—42no—
90#3963C2×C414yes—
91#3963C2×C414yes—
92C2×#388—52no—
93C2×C4×C22⋊C4—51no—
94#1442—52no—
95#1439—52no—
96#1436—52no—
97C4⋊#95—51no—
98C4⋊#95—51no—
99#1434—51no—
100C22⋊#95—51no—
101C22⋊#95D511yescharacteristic
102C4×#95—51no—
103C24×C5—21no—
104C24×C5—21no—
105C24×C5—22no—
106C24×C5—22no—
107C24×C5—21no—
108C24×C5—21no—
109C24×C5—22no—
110C24×C5—22no—
111C24×C5C22×C412yes—
112C24×C5C2×D412yes—
113C24×C5C2×Q812yes—
114C24×C5C2411yescharacteristic
115C22×C4×C5—22no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—28no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—44no—
136C22×C4×C5—44no—
137C22×C4×C5—48no—
138C22×C4×C5—48no—
139C22×C4×C5C22×C412yes—
140C22×C4×C5C22×C412yes—
141C22×C4×C5#4114yes—
142C22×C4×C5#4112yes—
143C22×C4×C5#4112yes—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5C22×C412yes—
168C22×Dic5C22×C412yes—
169C22×Dic5C22×C412yes—
170C22×Dic5C22×C412yes—
171C22×Dic5C2×D412yes—
172C22×Dic5C2×D412yes—
173C22×Dic5C2×Q812yes—
174C22×Dic5C2×Q812yes—
175C22×Dic5#4114yes—
176C22×Dic5#4112yes—
177C22×Dic5#4112yes—
178C5×C22⋊C4—48no—
179C22⋊Dic5—28no—
180C22⋊Dic5—48no—
181C22⋊Dic5C4⋊C4116yescomplemented
182#683—48no—
183#683—48no—
184C4×Dic5—44no—
185C4×Dic5—44no—
186C4×Dic5—48no—
187C24×C4C2×D511yescharacteristic
188C22×C4⋊C4—52no—
189C22×C4⋊C4—52no—
190C22×C22⋊C4—51no—
191C22×C22⋊C4—51no—
192C22×C22⋊C4—52no—
193C22×C22⋊C4C2×D512yes—
194C22×C42—51no—
195C22×C42—51no—
196C22×C42—52no—
197#388—108no—
198C4×C22⋊C4—58no—
199C2×#95—51no—
200C2×#95—51no—
201C2×#95—51no—
202C2×#95—52no—
203C2×#95—51no—
204C2×#95—52no—
205C2×#95—52no—
206C2×#95—52no—
207C2×#95—52no—
208C2×#95—52no—
209C2×#95C2×D511yescharacteristic
210C2×#95C2×D511yescharacteristic
211C2×#95C2×D512yes—
212C23×C5—22no—
213C23×C5—22no—
214C23×C5—22no—
215C23×C5—22no—
216C23×C5—22no—
217C23×C5—22no—
218C23×C5—22no—
219C23×C5—22no—
220C23×C5—22no—
221C23×C5—22no—
222C23×C5—24no—
223C23×C5—24no—
224C23×C5—24no—
225C23×C5—24no—
226C23×C5—42no—
227C23×C5—42no—
228C23×C5—42no—
229C23×C5—42no—
230C23×C5—42no—
231C23×C5—42no—
232C23×C5—42no—
233C23×C5—42no—
234C23×C5C2×C4⋊C414yes—
235C23×C5C23×C411yescharacteristic
236C23×C5C22×D411yescharacteristic
237C23×C5C22×Q811yescharacteristic
238C23×C5C2×#4112yes—
239C23×C5C2×#4111yescharacteristic
240C23×C5C2×#4111yescharacteristic
241C23×C5C2×#4111yescharacteristic
242C23×C5C2×#4111yescharacteristic
243C23×C5C2×#4112yes—
244C23×C5H(5,𝔽2)12yes—
245C23×C5H(5,𝔽2)12yes—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—24no—
249C2×C4×C5—24no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—24no—
254C2×C4×C5—24no—
255C2×C4×C5—24no—
256C2×C4×C5—416no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5#11714yes—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—24no—
278C2×Dic5—24no—
279C2×Dic5—24no—
280C2×Dic5—24no—
281C2×Dic5—24no—
282C2×Dic5—24no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—24no—
287C2×Dic5—24no—
288C2×Dic5—24no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294C2×Dic5—42no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297C2×Dic5—42no—
298C2×Dic5—42no—
299C2×Dic5—42no—
300C2×Dic5—42no—
301C2×Dic5—42no—
302C2×Dic5C2×C4⋊C414yes—
303C2×Dic5C2×C4⋊C414yes—
304C2×Dic5#11714yes—
305C25C22×D511yescharacteristic
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—51no—
311C23×C4—51no—
312C23×C4—51no—
313C23×C4—52no—
314C23×C4—51no—
315C23×C4—52no—
316C23×C4C4×D514yes—
317C23×C4C22×D512yes—
318C23×C4C22×D511yescharacteristic
319C23×C4C22×D512yes—
320C23×C4C22×D511yescharacteristic
321C2×C4⋊C4—104no—
322C2×C4⋊C4—104no—
323C2×C4⋊C4—104no—
324C2×C4⋊C4—104no—
325C2×C4⋊C4—202no—
326C2×C4⋊C4—202no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—54no—
331C2×C22⋊C4—54no—
332C2×C22⋊C4—54no—
333C2×C22⋊C4—54no—
334C2×C22⋊C4—102no—
335C2×C22⋊C4—102no—
336C2×C22⋊C4—104no—
337C2×C22⋊C4—104no—
338C2×C22⋊C4—202no—
339C2×C42—54no—
340C2×C42—54no—
341C2×C42—104no—
342C2×C42—104no—
343C2×C42—202no—
344C2×C42—202no—
345C2×C42—202no—
346#95—22no—
347#95—22no—
348#95—42no—
349#95—54no—
350#95—54no—
351#95—104no—
352#95—104no—
353#95—104no—
354#95—104no—
355#95—102no—
356#95—102no—
357#95—202no—
358#95—202no—
359C22×C5—24no—
360C22×C5—24no—
361C22×C5—24no—
362C22×C5—42no—
363C22×C5—44no—
364C22×C5—44no—
365C22×C5—42no—
366C22×C5—42no—
367C22×C5—42no—
368C22×C5—44no—
369C22×C5—44no—
370C22×C5C22×C4⋊C411yescharacteristic
371C22×C5C2×#11711yescharacteristic
372C22×C5C2×#11711yescharacteristic
373C22×C5C4×#4111yescharacteristic
374C22×C5C4×#4111yescharacteristic
375C22×C5#51811yescharacteristic
376C22×C5#51811yescharacteristic
377C22×C5#52912yes—
378C22×C5#52912yes—
379C22×C5#53211yescharacteristic
380C22×C5#53211yescharacteristic
381C22×C5#53311yescharacteristic
382C22×C5#53311yescharacteristic
383C22×C5#53812yes—
384C22×C5#53812yes—
385C22×C5#54612yes—
386C22×C5#54612yes—
387C22×C5#55112yes—
388C22×C5#55312yes—
389C22×C5#55312yes—
390C22×C5#55412yes—
391C22×C5#55412yes—
392C22×C5#55912yes—
393C4×C5—24no—
394C4×C5—42no—
395C4×C5—44no—
396C4×C5—82no—
397Dic5—24no—
398Dic5—24no—
399Dic5—24no—
400Dic5—42no—
401Dic5—44no—
402Dic5—82no—
403C24—22no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24C2×C4×D512yes—
412C24D4×D512yes—
413C24Q8×D512yes—
414C24C23×D511yescharacteristic
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—28no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—48no—
438C22×C4—48no—
439C22×C4—52no—
440C22×C4—52no—
441C22×C4—52no—
442C22×C4—52no—
443C22×C4—52no—
444C22×C4—52no—
445C22×C4—52no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—54no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—101no—
465C22×C4—101no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4C2×C4×D512yes—
474C22×C4C2×C4×D512yes—
475C22×C4#70914yes—
476C22×C4#71112yes—
477C22×C4#71112yes—
478C4⋊C4—208no—
479C4⋊C4—208no—
480C22⋊C4—48no—
481C22⋊C4—516no—
482C22⋊C4—108no—
483C22⋊C4—208no—
484C42—204no—
485C42—204no—
486C42—208no—
487C2×C5—44no—
488C2×C5#228511yescharacteristic
489C2×C5#229811yescharacteristic
490C2×C5#231211yescharacteristic
491C2×C5#234911yescharacteristic
492C2×C5#234911yescharacteristic
493C2×C5#235311yescharacteristic
494C2×C5#235711yescharacteristic
495C2×C5#255712yes—
496C2×C5#255912yes—
497C2×C5#258712yes—
498C2×C5#258912yes—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—24no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23D5×C4⋊C414yes—
522C23C22×C4×D511yescharacteristic
523C23C2×#70912yes—
524C23C2×D4×D511yescharacteristic
525C23C2×#71111yescharacteristic
526C23C2×#71111yescharacteristic
527C23#414412yes—
528C23#414412yes—
529C23C2×Q8×D511yescharacteristic
530C23D5×#4111yescharacteristic
531C23D5×#4111yescharacteristic
532C23D5×#4112yes—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—416no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—54no—
558C2×C4—54no—
559C2×C4—54no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—102no—
563C2×C4—102no—
564C2×C4—102no—
565C2×C4—104no—
566C2×C4—104no—
567C2×C4—102no—
568C2×C4—104no—
569C2×C4—104no—
570C2×C4—104no—
571C2×C4—104no—
572C2×C4—102no—
573C2×C4—102no—
574C2×C4—102no—
575C2×C4—104no—
576C2×C4—104no—
577C2×C4—104no—
578C2×C4—202no—
579C2×C4—202no—
580C2×C4—202no—
581C2×C4—202no—
582C2×C4—202no—
583C2×C4—202no—
584C2×C4—202no—
585C2×C4—202no—
586C2×C4—202no—
587C2×C4—202no—
588C2×C4—202no—
589C2×C4—202no—
590C2×C4—202no—
591C2×C4#402314yes—
592C5#1394811yescharacteristic, complemented, Sylow
593C22—24no—
594C22—24no—
595C22—24no—
596C22—42no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22C4×#70911yescharacteristic
605C22C2×#402311yescharacteristic
606C22#6582011yescharacteristic
607C22#6582011yescharacteristic
608C22#6582412yes—
609C22C2×D5×C4⋊C411yescharacteristic
610C22#6584512yes—
611C22D5×#11711yescharacteristic
612C22#6585611yescharacteristic
613C22#6587212yes—
614C22#6589012yes—
615C22#6589112yes—
616C22#6589212yes—
617C22#6592712yes—
618C22#6592712yes—
619C22#6593011yescharacteristic
620C22#6593011yescharacteristic
621C22#6594412yes—
622C22#6595611yescharacteristic
623C22#6595611yescharacteristic
624C22#6597012yes—
625C22#6599512yes—
626C22#6599812yes—
627C4—24no—
628C4—44no—
629C4—42no—
630C4—82no—
631C4—104no—
632C4—104no—
633C4—104no—
634C4—204no—
635C4—202no—
636C4—402no—
637C2—44no—
638C2#1060510011yescharacteristic
639C2#1060517111yescharacteristic
640C2#1060530711yescharacteristic
641C2#1060555111yescharacteristic
642C2#1060559511yescharacteristic
643C2#1060574211yescharacteristic
644C2#1060579211yescharacteristic
645C2#1060622112yes—
646C2#1060622412yes—
647C2#1060648912yes—
648C2#1060649212yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22⋊#95D5
hypocenterC5#13948
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. #10600207C2semidirect
7. #10600198C2semidirect
8. #10600197C2semidirect
9. #10600197C2semidirect
10. #10600194C2semidirect
11. Dic5×#95C2semidirect
25. C4×C22⋊Dic5C4semidirect
181. C22⋊Dic5C4⋊C4semidirect
592. C5#13948semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic52
C2×#652332
C5×C22⋊#952
#106029202
#106023402
#106002072
#106001982
#106001972
#106001942
Dic5×#952
#139485