Finite Group Databasebeta

← #12021336

Subgroups — #12021336

Order 1280.

1342 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic5C211yesmaximal, characteristic
2C2×#65225C211yesmaximal, characteristic
3C2×C4×#683C211yesmaximal, characteristic
4C5×C4⋊#95C211yesmaximal, characteristic
5#10602356C211yesmaximal, characteristic
6#10602356C211yesmaximal, characteristic
7#10602356C211yesmaximal, characteristic
8#10600214C212yesmaximal
9#10600210C212yesmaximal
10#10600199C212yesmaximal
11#10600196C212yesmaximal
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×C4⋊Dic5C2211yescharacteristic
17C22×#683C2211yescharacteristic
18C22×#683C2211yescharacteristic
19C22×C4×Dic5C2212yes—
20C22×C4×Dic5C2211yescharacteristic
21C22×C4×Dic5C2211yescharacteristic
22C2×C5×#95C2212yes—
23C2×C5×#95C2212yes—
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C4⋊C4×Dic5—24no—
36#65225—24no—
37C4×#683C418yescomplemented
38#13885—51nomaximal, Sylow
39C23×C4×C5C2312yes—
40C23×C4×C5C2311yescharacteristic
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×Dic5C2312yes—
45C23×Dic5C2311yescharacteristic
46C23×Dic5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—22no—
52C2×C5×C4⋊C4—22no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4—22no—
55C2×C5×C4⋊C4Q814yes—
56C2×C42×C5—22no—
57C2×C42×C5—22no—
58C2×C42×C5C2×C414yes—
59C2×C4⋊Dic5—22no—
60C2×C4⋊Dic5—22no—
61C2×C4⋊Dic5—22no—
62C2×C4⋊Dic5—22no—
63C2×C4⋊Dic5—22no—
64C2×C4⋊Dic5D414yes—
65C2×#683—22no—
66C2×#683—22no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683C2×C414yes—
70C2×#683C2×C414yes—
71C2×C4×Dic5—22no—
72C2×C4×Dic5—22no—
73C2×C4×Dic5—22no—
74C2×C4×Dic5—22no—
75C2×C4×Dic5—24no—
76C2×C4×Dic5—24no—
77C2×C4×Dic5—42no—
78C2×C4×Dic5C2×C414yes—
79C2×C4×Dic5C2×C414yes—
80C5×#95—42no—
81C5×#95—42no—
82#3963—24no—
83#3963—24no—
84#3963—24no—
85#3963—24no—
86#3963—24no—
87#3963—24no—
88#3963—42no—
89#3963—42no—
90#3963—42no—
91#3963C2×C414yes—
92#3963C2×C414yes—
93C2×#382—51no—
94C2×C4×C4⋊C4—51no—
95C2×C4×C4⋊C4—51no—
96#1445—52no—
97#1443—52no—
98#1436—52no—
99C4⋊#95—51no—
100C4⋊#95—51no—
101C4⋊#95—51no—
102C4⋊#95D511yescharacteristic
103#1434—52no—
104C24×C5C2411yescharacteristic
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—22no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—22no—
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—22no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5C22×C412yes—
131C22×C4×C5C22×C412yes—
132C22×C4×C5C22×C412yes—
133C22×C4×C5C2×D412yes—
134C22×C4×C5C2×Q814yes—
135C22×C4×C5C2×Q812yes—
136C22×C4×C5#4112yes—
137C22×C4×C5#4112yes—
138C22×C4×C5#4112yes—
139C22×C4×C5#4112yes—
140C22×Dic5—21no—
141C22×Dic5—21no—
142C22×Dic5—21no—
143C22×Dic5—21no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—21no—
148C22×Dic5—21no—
149C22×Dic5—22no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—22no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—22no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5C22×C412yes—
174C22×Dic5C22×C412yes—
175C22×Dic5C22×C412yes—
176C22×Dic5C22×C412yes—
177C22×Dic5C2×D414yes—
178C22×Dic5#4112yes—
179C22×Dic5#4112yes—
180C22×Dic5#4112yes—
181C22×Dic5#4112yes—
182C5×C4⋊C4—28no—
183C5×C4⋊C4—44no—
184C42×C5—28no—
185C4⋊Dic5—28no—
186C4⋊Dic5—44no—
187#683—28no—
188#683—28no—
189C4×Dic5—28no—
190C4×Dic5—28no—
191C4×Dic5—48no—
192C22×C4⋊C4—51no—
193C22×C4⋊C4—51no—
194C22×C4⋊C4—51no—
195C22×C4⋊C4—51no—
196C22×C4⋊C4C2×D511yescharacteristic
197C22×C4⋊C4C2×D511yescharacteristic
198C22×C42—51no—
199C22×C42—51no—
200C22×C42—52no—
201C22×C42C2×D511yescharacteristic
202#382—104no—
203C4×C4⋊C4—58no—
204C4×C4⋊C4—104no—
205C2×#95—51no—
206C2×#95—51no—
207C2×#95—52no—
208C2×#95—52no—
209C2×#95—52no—
210C2×#95—52no—
211C2×#95—52no—
212C2×#95—52no—
213C2×#95—52no—
214C2×#95—52no—
215C2×#95—52no—
216C2×#95C2×D512yes—
217C2×#95C2×D512yes—
218C23×C5C23×C411yescharacteristic
219C23×C5C22×D411yescharacteristic
220C23×C5C22×Q811yescharacteristic
221C23×C5C2×#4111yescharacteristic
222C23×C5C2×#4111yescharacteristic
223C23×C5C2×#4111yescharacteristic
224C23×C5C2×#4111yescharacteristic
225C23×C5C2×#4111yescharacteristic
226C23×C5C2×#4111yescharacteristic
227C23×C5C2×#4111yescharacteristic
228C23×C5C2×#4111yescharacteristic
229C23×C5H(5,𝔽2)11yescharacteristic
230C23×C5H(5,𝔽2)11yescharacteristic
231C23×C52−1+411yescharacteristic
232C23×C52−1+411yescharacteristic
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—24no—
240C2×C4×C5—24no—
241C2×C4×C5—24no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—42no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5#11714yes—
262C2×C4×C5C4×D414yes—
263C2×C4×C5C4×Q814yes—
264C2×C4×C5C22⋊Q814yes—
265C2×C4×C5#12314yes—
266C2×C4×C5#12514yes—
267C2×C4×C5#12614yes—
268C2×Dic5—22no—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—24no—
287C2×Dic5—24no—
288C2×Dic5—24no—
289C2×Dic5—42no—
290C2×Dic5—41no—
291C2×Dic5—41no—
292C2×Dic5—41no—
293C2×Dic5—41no—
294C2×Dic5—42no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—42no—
299C2×Dic5—41no—
300C2×Dic5—42no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5—42no—
305C2×Dic5—42no—
306C2×Dic5—42no—
307C2×Dic5—42no—
308C2×Dic5#11714yes—
309C2×Dic5#11714yes—
310C23×C4—51no—
311C23×C4—51no—
312C23×C4—51no—
313C23×C4—52no—
314C23×C4—51no—
315C23×C4—52no—
316C23×C4C22×D512yes—
317C23×C4C22×D512yes—
318C23×C4C22×D511yescharacteristic
319C23×C4C22×D511yescharacteristic
320C23×C4C22×D511yescharacteristic
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—54no—
327C2×C4⋊C4—54no—
328C2×C4⋊C4—54no—
329C2×C4⋊C4—102no—
330C2×C4⋊C4—102no—
331C2×C4⋊C4—102no—
332C2×C4⋊C4—102no—
333C2×C4⋊C4—102no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—102no—
336C2×C4⋊C4—102no—
337C2×C4⋊C4—102no—
338C2×C4⋊C4Dic1014yes—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—54no—
342C2×C42—54no—
343C2×C42—102no—
344C2×C42—102no—
345C2×C42—102no—
346C2×C42—102no—
347C2×C42—104no—
348C2×C42—104no—
349C2×C42—202no—
350C2×C42C4×D514yes—
351#95—42no—
352#95—42no—
353#95—54no—
354#95—54no—
355#95—104no—
356#95—104no—
357#95—104no—
358#95—104no—
359#95—104no—
360#95—104no—
361#95—202no—
362#95—202no—
363#95—202no—
364C22×C5C2×#11711yescharacteristic
365C22×C5C2×#11711yescharacteristic
366C22×C5C2×#11711yescharacteristic
367C22×C5C2×C4×D411yescharacteristic
368C22×C5C2×C4×Q811yescharacteristic
369C22×C5#52011yescharacteristic
370C22×C5#52011yescharacteristic
371C22×C5C2×C22⋊Q811yescharacteristic
372C22×C5C2×#12311yescharacteristic
373C22×C5C2×#12511yescharacteristic
374C22×C5C2×#12611yescharacteristic
375C22×C5#52911yescharacteristic
376C22×C5#52911yescharacteristic
377C22×C5#52911yescharacteristic
378C22×C5#52911yescharacteristic
379C22×C5#54011yescharacteristic
380C22×C5#54111yescharacteristic
381C22×C5#54211yescharacteristic
382C22×C5#54211yescharacteristic
383C22×C5#54611yescharacteristic
384C22×C5#54711yescharacteristic
385C22×C5#54811yescharacteristic
386C22×C5#55011yescharacteristic
387C22×C5#55211yescharacteristic
388C22×C5#55311yescharacteristic
389C22×C5#55411yescharacteristic
390C22×C5#55411yescharacteristic
391C22×C5#55511yescharacteristic
392C22×C5#55611yescharacteristic
393C22×C5#55611yescharacteristic
394C22×C5#55611yescharacteristic
395C22×C5#55711yescharacteristic
396C22×C5#55711yescharacteristic
397C22×C5#55911yescharacteristic
398C22×C5#55911yescharacteristic
399C4×C5—42no—
400C4×C5—42no—
401C4×C5—44no—
402C4×C5—82no—
403C4×C5#38718yes—
404Dic5—24no—
405Dic5—24no—
406Dic5—42no—
407Dic5—42no—
408Dic5—44no—
409Dic5—82no—
410C24C23×D511yescharacteristic
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—52no—
439C22×C4—52no—
440C22×C4—52no—
441C22×C4—52no—
442C22×C4—52no—
443C22×C4—52no—
444C22×C4—54no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—102no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—101no—
460C22×C4—102no—
461C22×C4—101no—
462C22×C4—102no—
463C22×C4—101no—
464C22×C4—101no—
465C22×C4—101no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—101no—
470C22×C4—101no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—102no—
477C22×C4—102no—
478C22×C4C2×Dic1014yes—
479C22×C4C2×Dic1012yes—
480C22×C4C2×C4×D512yes—
481C22×C4C2×C4×D512yes—
482C22×C4C2×C4×D512yes—
483C22×C4#70912yes—
484C22×C4D4×D512yes—
485C22×C4#71112yes—
486C22×C4#71112yes—
487C22×C4#71312yes—
488C4⋊C4—28no—
489C4⋊C4—44no—
490C4⋊C4—108no—
491C4⋊C4—108no—
492C4⋊C4—108no—
493C4⋊C4—204no—
494C42—28no—
495C42—108no—
496C42—108no—
497C42—208no—
498C2×C5#228311yescharacteristic
499C2×C5C2×#38711yescharacteristic
500C2×C5#231411yescharacteristic
501C2×C5#235211yescharacteristic
502C2×C5#235411yescharacteristic
503C2×C5#235511yescharacteristic
504C2×C5#235511yescharacteristic
505C2×C5#244711yescharacteristic
506C2×C5#244811yescharacteristic
507C2×C5#245311yescharacteristic
508C2×C5#245411yescharacteristic
509C2×C5#250811yescharacteristic
510C2×C5#250911yescharacteristic
511C2×C5#251311yescharacteristic
512C2×C5#251411yescharacteristic
513C23C22×Dic1011yescharacteristic
514C23C22×C4×D511yescharacteristic
515C23C2×#70911yescharacteristic
516C23C2×D4×D511yescharacteristic
517C23C2×#71111yescharacteristic
518C23C2×#71111yescharacteristic
519C23#414411yescharacteristic
520C23#414411yescharacteristic
521C23C2×#71311yescharacteristic
522C23#414711yescharacteristic
523C23#414711yescharacteristic
524C23D5×#4111yescharacteristic
525C23D5×#4111yescharacteristic
526C23D5×#4111yescharacteristic
527C23D5×#4111yescharacteristic
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
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—54no—
557C2×C4—54no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—102no—
563C2×C4—102no—
564C2×C4—102no—
565C2×C4—102no—
566C2×C4—102no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—102no—
574C2×C4—102no—
575C2×C4—104no—
576C2×C4—102no—
577C2×C4—104no—
578C2×C4—104no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4—202no—
584C2×C4—202no—
585C2×C4—202no—
586C2×C4—201no—
587C2×C4—201no—
588C2×C4—201no—
589C2×C4—201no—
590C2×C4—202no—
591C2×C4—202no—
592C2×C4—202no—
593C2×C4—202no—
594C2×C4—202no—
595C2×C4—202no—
596C2×C4—202no—
597C2×C4—202no—
598C2×C4C4×Dic1014yes—
599C2×C4#402414yes—
600C2×C4#402514yes—
601C2×C4#402714yes—
602C2×C4#403614yes—
603C2×C4#403814yes—
604C2×C4#404014yes—
605C5#1388511yescharacteristic, complemented, Sylow
606C22C2×C4×Dic1011yescharacteristic
607C22C2×#402411yescharacteristic
608C22C2×#402511yescharacteristic
609C22C2×#402711yescharacteristic
610C22C2×#403611yescharacteristic
611C22C2×#403811yescharacteristic
612C22#6583811yescharacteristic
613C22#6583811yescharacteristic
614C22C2×#404011yescharacteristic
615C22D5×#11711yescharacteristic
616C22D5×#11711yescharacteristic
617C22#6587311yescharacteristic
618C22#6587311yescharacteristic
619C22#6589311yescharacteristic
620C22#6589311yescharacteristic
621C22#6590211yescharacteristic
622C22#6590211yescharacteristic
623C22#6590311yescharacteristic
624C22#6590311yescharacteristic
625C22#6593311yescharacteristic
626C22#6594611yescharacteristic
627C22#6594811yescharacteristic
628C22#6595011yescharacteristic
629C22#6596511yescharacteristic
630C22#6596711yescharacteristic
631C22#6597311yescharacteristic
632C22#6597511yescharacteristic
633C22#6601411yescharacteristic
634C22#6601411yescharacteristic
635C22#6602511yescharacteristic
636C22#6602511yescharacteristic
637C22#6605311yescharacteristic
638C22#6606511yescharacteristic
639C22#6606711yescharacteristic
640C22#6606711yescharacteristic
641C4—42no—
642C4—42no—
643C4—44no—
644C4—82no—
645C4—104no—
646C4—104no—
647C4—202no—
648C4—202no—
649C4—204no—
650C4—402no—
651C4#6494418yes—
652C2C2×#6494411yescharacteristic
653C2#1060537311yescharacteristic
654C2#1060537311yescharacteristic
655C2#1060561611yescharacteristic
656C2#1060574311yescharacteristic
657C2#1060587811yescharacteristic
658C2#1060608911yescharacteristic
659C2#1060773711yescharacteristic
660C2#1060773811yescharacteristic
661C2#1060776811yescharacteristic
662C2#1060777211yescharacteristic
663C2#1060805511yescharacteristic
664C2#1060807111yescharacteristic
665C2#1060824211yescharacteristic
666C2#1060825511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, prime radical, cosocleC24×C5C24
hypercenterC4⋊#95D5
hypocenterC5#13885
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
37. C4×#683C4semidirect
605. C5#13885semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic52
C2×#652252
C2×C4×#6832
C5×C4⋊#952
#106023562
#106002142
#106002102
#106001992
#106001962
#138855