Finite Group Databasebeta

← #12020831

Subgroups — #12020831

Order 1280.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65229C211yesmaximal, characteristic
2C2×C4×#685C211yesmaximal, characteristic
3C2×#65221C211yesmaximal, characteristic, complemented
4C2×#64958C211yesmaximal, characteristic
5C2×#64955C211yesmaximal, characteristic
6C4×C5×#95C211yesmaximal, characteristic, complemented
7#10602330C211yesmaximal, characteristic
8#10602329C211yesmaximal, characteristic, complemented
9C4×#3963C211yesmaximal, characteristic, complemented
10#10600218C211yesmaximal, characteristic
11#10600201C211yesmaximal, characteristic
12#10600199C211yesmaximal, characteristic, complemented
13#10600197C211yesmaximal, characteristic, complemented
14#10600194C211yesmaximal, characteristic, complemented
15Dic5×#95C211yesmaximal, characteristic, complemented
16C23×C4×D5C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C22×#685C2211yescharacteristic
21C22×#685C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C22×C4×Dic5C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38C2×#3963C2211yescharacteristic
39C2×#3963C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51#65229C418yescomplemented
52C4×#685—24no—
53#65221—24no—
54#64958C418yescomplemented
55#64955C418yescomplemented
56#13816—51nomaximal, Sylow
57C24×D5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C23×Dic5C2311yescharacteristic
71C23×Dic5C2311yescharacteristic
72C22×C4×D5—22no—
73C22×C4×D5—22no—
74C22×C4×D5—22no—
75C22×C4×D5—22no—
76C22×C4×D5—41no—
77C22×C4×D5—41no—
78C22×C4×D5C2×C414yes—
79C2×C42×C5—22no—
80C2×C42×C5—22no—
81C2×C42×C5—22no—
82C2×C42×C5—22no—
83C2×C42×C5—22no—
84C2×C42×C5—22no—
85C2×C42×C5—41no—
86C2×C42×C5—41no—
87C2×C42×C5C2×C414yescomplemented
88C2×#685—22no—
89C2×#685—22no—
90C2×#685—22no—
91C2×#685—22no—
92C2×#685—22no—
93C2×#685—22no—
94C2×#685—41no—
95C2×#685—41no—
96C2×#685—41no—
97C2×#685—41no—
98C2×#685C2×C414yes—
99C2×#685C2×C414yes—
100C2×#685C2×C414yes—
101C2×#685C2×C414yes—
102C2×#685C2×C414yes—
103C2×#685C2×C414yes—
104C2×#685C2×C414yes—
105C2×#685C2×C414yes—
106C2×#683—41no—
107C2×#683—41no—
108C2×#683—41no—
109C2×#683—41no—
110C2×#683C2×C414yescomplemented
111C2×#683C2×C414yescomplemented
112C2×C4×Dic5—22no—
113C2×C4×Dic5—22no—
114C2×C4×Dic5—22no—
115C2×C4×Dic5—22no—
116C2×C4×Dic5—22no—
117C2×C4×Dic5—22no—
118C2×C4×Dic5—22no—
119C2×C4×Dic5—22no—
120C2×C4×Dic5—41no—
121C2×C4×Dic5—41no—
122C2×C4×Dic5—41no—
123C2×C4×Dic5—41no—
124C2×C4×Dic5C2×C414yes—
125C2×C4×Dic5C2×C414yes—
126C2×C4×Dic5C2×C414yescomplemented
127C5×#95—22no—
128C5×#95—22no—
129C5×#95C2×C414yes—
130C5×#95C2×C414yescomplemented
131#3963—22no—
132#3963—22no—
133#3963—22no—
134#3963—22no—
135#3963—22no—
136#3963—22no—
137#3963—22no—
138#3963—41no—
139#3963—41no—
140#3963C2×C414yes—
141#3963C2×C414yescomplemented
142#3963C2×C414yescomplemented
143#3963C2×C414yescomplemented
144#3963D414yes—
145C2×#388—51no—
146C2×#388—51no—
147C2×C4×C22⋊C4—51no—
148C2×C4×C22⋊C4—51no—
149C2×#376—51no—
150#1437—51no—
151#1437—51no—
152#1436—51no—
153#1436—51no—
154C4⋊#95—51no—
155#1434—51no—
156C22⋊#95—51no—
157C4×#95—51no—
158C4×#95—51no—
159C4×#95D511yescharacteristic, complemented
160C24×C5C2411yescharacteristic
161C23×D5—21no—
162C23×D5—21no—
163C23×D5—21no—
164C23×D5—21no—
165C23×D5—21no—
166C23×D5—21no—
167C23×D5—21no—
168C23×D5—21no—
169C23×D5—21no—
170C23×D5—21no—
171C23×D5—21no—
172C23×D5—21no—
173C23×D5C22×C412yes—
174C23×D5C22×C412yes—
175C23×D5C22×C412yes—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5C22×C412yes—
211C22×C4×C5C22×C412yes—
212C22×C4×C5C22×C412yes—
213C22×C4×C5C22×C412yes—
214C22×C4×C5C22×C412yes—
215C22×C4×C5C22×C412yes—
216C22×C4×C5C22×C412yes—
217C22×C4×C5C22×C412yes—
218C22×C4×C5C22×C412yes—
219C22×C4×C5C2×D412yes—
220C22×C4×C5#4112yes—
221C22×C4×C5#4112yes—
222C22×C4×C5#4112yes—
223C22×C4×C5#4112yes—
224C22×C4×C5#4112yes—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—21no—
243C22×Dic5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5—21no—
249C22×Dic5—21no—
250C22×Dic5—21no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—21no—
255C22×Dic5—21no—
256C22×Dic5—21no—
257C22×Dic5—21no—
258C22×Dic5—21no—
259C22×Dic5—21no—
260C22×Dic5—21no—
261C22×Dic5C22×C412yes—
262C22×Dic5C22×C412yes—
263C22×Dic5C22×C412yes—
264C22×Dic5C22×C412yes—
265C22×Dic5C22×C412yes—
266C22×Dic5C22×C412yes—
267C22×Dic5C22×C412yes—
268C22×Dic5C22×C412yes—
269C22×Dic5C22×C412yes—
270C22×Dic5C2×D412yes—
271C22×Dic5C2×D412yes—
272C22×Dic5#4112yes—
273C22×Dic5#4112yes—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—44no—
277C2×C4×D5—44no—
278C2×C4×D5—44no—
279C2×C4×D5—44no—
280C2×C4×D5—44no—
281C42×C5—28no—
282C42×C5—44no—
283C42×C5—44no—
284#685—28no—
285#685—28no—
286#685—28no—
287#685—44no—
288#685—44no—
289#685C42116yescomplemented
290#683—44no—
291#683—44no—
292C4×Dic5—28no—
293C4×Dic5—28no—
294C4×Dic5—44no—
295C4×Dic5—44no—
296C4×Dic5—44no—
297C24×C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C22⋊C4—51no—
301C22×C22⋊C4—51no—
302C22×C22⋊C4—51no—
303C22×C22⋊C4—51no—
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C42—51no—
307C22×C42—51no—
308C22×C42—51no—
309C22×C42—51no—
310C22×C42—51no—
311C22×C42C2×D511yescharacteristic
312C22×C42C2×D511yescharacteristic
313C22×C42C2×D511yescharacteristic
314#388—58no—
315#388—58no—
316C4×C22⋊C4—58no—
317C4×C22⋊C4—104no—
318#376—104no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—51no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95C2×D511yescharacteristic
334C2×#95C2×D511yescharacteristic
335C2×#95C2×D511yescharacteristic
336C2×#95C2×D511yescharacteristic
337C23×C5C23×C411yescharacteristic
338C23×C5C23×C411yescharacteristic
339C23×C5C23×C411yescharacteristic
340C23×C5C22×D411yescharacteristic
341C23×C5C2×#4111yescharacteristic
342C23×C5C2×#4111yescharacteristic
343C23×C5C2×#4111yescharacteristic
344C23×C5C2×#4111yescharacteristic
345C23×C5C2×#4111yescharacteristic
346C23×C5C2×#4111yescharacteristic
347C23×C5C2×#4111yescharacteristic
348C23×C5H(5,𝔽2)11yescharacteristic
349C23×C5H(5,𝔽2)11yescharacteristic
350C23×C5H(5,𝔽2)11yescharacteristic
351C23×C52−1+411yescharacteristic
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—41no—
371C22×D5—41no—
372C22×D5—41no—
373C22×D5—41no—
374C22×D5—41no—
375C22×D5—41no—
376C22×D5—41no—
377C22×D5—41no—
378C22×D5—41no—
379C22×D5—41no—
380C22×D5—41no—
381C22×D5—41no—
382C22×D5—41no—
383C22×D5—41no—
384C22×D5—41no—
385C22×D5—41no—
386C22×D5C2×C4214yes—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5C2×C4214yes—
433C2×C4×C5#11714yes—
434C2×C4×C5#11714yes—
435C2×C4×C5C4×D414yes—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—22no—
454C2×Dic5—22no—
455C2×Dic5—22no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—22no—
460C2×Dic5—22no—
461C2×Dic5—22no—
462C2×Dic5—22no—
463C2×Dic5—22no—
464C2×Dic5—22no—
465C2×Dic5—22no—
466C2×Dic5—41no—
467C2×Dic5—41no—
468C2×Dic5—41no—
469C2×Dic5—41no—
470C2×Dic5—41no—
471C2×Dic5—41no—
472C2×Dic5—41no—
473C2×Dic5—41no—
474C2×Dic5—41no—
475C2×Dic5—41no—
476C2×Dic5—41no—
477C2×Dic5—41no—
478C2×Dic5—41no—
479C2×Dic5—41no—
480C2×Dic5—41no—
481C2×Dic5—41no—
482C2×Dic5C2×C4214yes—
483C2×Dic5C4×D414yes—
484C2×Dic5C4×D414yes—
485C4×D5—416no—
486C25—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—51no—
492C23×C4—51no—
493C23×C4—51no—
494C23×C4—54no—
495C23×C4—102no—
496C23×C4—102no—
497C23×C4—102no—
498C23×C4—102no—
499C23×C4—201no—
500C23×C4—201no—
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506C23×C4C22×D511yescharacteristic
507C23×C4C22×D511yescharacteristic
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—201no—
511C2×C4⋊C4—201no—
512C2×C4⋊C4—201no—
513C2×C4⋊C4—201no—
514C2×C22⋊C4—54no—
515C2×C22⋊C4—54no—
516C2×C22⋊C4—54no—
517C2×C22⋊C4—54no—
518C2×C22⋊C4—54no—
519C2×C22⋊C4—54no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—102no—
523C2×C22⋊C4—102no—
524C2×C22⋊C4—102no—
525C2×C22⋊C4—102no—
526C2×C22⋊C4—102no—
527C2×C22⋊C4—102no—
528C2×C22⋊C4—201no—
529C2×C22⋊C4—201no—
530C2×C22⋊C4—201no—
531C2×C22⋊C4—201no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—41no—
539C2×C42—41no—
540C2×C42—54no—
541C2×C42—54no—
542C2×C42—54no—
543C2×C42—102no—
544C2×C42—102no—
545C2×C42—102no—
546C2×C42—102no—
547C2×C42—102no—
548C2×C42—102no—
549C2×C42—102no—
550C2×C42—102no—
551C2×C42—201no—
552C2×C42—201no—
553C2×C42—201no—
554C2×C42—201no—
555C2×C42C4×D514yescomplemented
556#95—22no—
557#95—22no—
558#95—54no—
559#95—54no—
560#95—54no—
561#95—54no—
562#95—54no—
563#95—102no—
564#95—102no—
565#95—102no—
566#95—102no—
567#95—102no—
568#95—102no—
569#95—102no—
570#95—201no—
571#95—201no—
572#95C4×D514yes—
573#95C4×D514yescomplemented
574C22×C5C22×C4211yescharacteristic
575C22×C5C2×#11711yescharacteristic
576C22×C5C2×#11711yescharacteristic
577C22×C5C2×C4×D411yescharacteristic
578C22×C5C2×C4×D411yescharacteristic
579C22×C5C2×C4×D411yescharacteristic
580C22×C5C4×#4111yescharacteristic
581C22×C5C4×#4111yescharacteristic
582C22×C5C4×#4111yescharacteristic
583C22×C5C4×#4111yescharacteristic
584C22×C5C4×#4111yescharacteristic
585C22×C5C4×#4111yescharacteristic
586C22×C5C4×#4111yescharacteristic
587C22×C5#51811yescharacteristic
588C22×C5#51811yescharacteristic
589C22×C5#51811yescharacteristic
590C22×C5#52011yescharacteristic
591C22×C5#52011yescharacteristic
592C22×C5#52011yescharacteristic
593C22×C5#54611yescharacteristic
594C22×C5#54611yescharacteristic
595C22×C5#54711yescharacteristic
596C22×C5#55011yescharacteristic
597C22×C5#55111yescharacteristic
598C22×C5#55111yescharacteristic
599C22×C5#55111yescharacteristic
600C22×C5#55111yescharacteristic
601C22×C5#55211yescharacteristic
602C22×C5#55211yescharacteristic
603C22×C5#55311yescharacteristic
604C22×C5#55311yescharacteristic
605C22×C5#55511yescharacteristic
606C22×C5#55511yescharacteristic
607C22×C5#55511yescharacteristic
608C22×C5#55611yescharacteristic
609C2×D5—24no—
610C2×D5—24no—
611C2×D5—24no—
612C2×D5—42no—
613C2×D5—42no—
614C2×D5—42no—
615C2×D5—42no—
616C2×D5—42no—
617C2×D5—42no—
618C2×D5—42no—
619C2×D5—42no—
620C2×D5—42no—
621C2×D5—42no—
622C2×D5—42no—
623C2×D5—42no—
624C4×C5—24no—
625C4×C5—24no—
626C4×C5—24no—
627C4×C5—24no—
628C4×C5—42no—
629C4×C5—42no—
630C4×C5—42no—
631Dic5—24no—
632Dic5—24no—
633Dic5—24no—
634Dic5—42no—
635Dic5—42no—
636Dic5—42no—
637Dic5—42no—
638C24—52no—
639C24—52no—
640C24—52no—
641C24—101no—
642C24—101no—
643C24—101no—
644C24—101no—
645C24—101no—
646C24—101no—
647C24—101no—
648C24—101no—
649C24—101no—
650C24—101no—
651C24—101no—
652C24—101no—
653C24C23×D511yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—52no—
689C22×C4—52no—
690C22×C4—52no—
691C22×C4—52no—
692C22×C4—52no—
693C22×C4—52no—
694C22×C4—52no—
695C22×C4—52no—
696C22×C4—52no—
697C22×C4—52no—
698C22×C4—52no—
699C22×C4—52no—
700C22×C4—52no—
701C22×C4—108no—
702C22×C4—101no—
703C22×C4—101no—
704C22×C4—101no—
705C22×C4—101no—
706C22×C4—101no—
707C22×C4—101no—
708C22×C4—101no—
709C22×C4—101no—
710C22×C4—101no—
711C22×C4—101no—
712C22×C4—101no—
713C22×C4—101no—
714C22×C4—101no—
715C22×C4—101no—
716C22×C4—101no—
717C22×C4—101no—
718C22×C4—101no—
719C22×C4—101no—
720C22×C4—101no—
721C22×C4—101no—
722C22×C4—101no—
723C22×C4—101no—
724C22×C4—101no—
725C22×C4—101no—
726C22×C4—101no—
727C22×C4—101no—
728C22×C4—101no—
729C22×C4—101no—
730C22×C4—101no—
731C22×C4—101no—
732C22×C4—101no—
733C22×C4—101no—
734C22×C4—101no—
735C22×C4—101no—
736C22×C4—101no—
737C22×C4—101no—
738C22×C4—108no—
739C22×C4—204no—
740C22×C4—204no—
741C22×C4—204no—
742C22×C4—204no—
743C22×C4—204no—
744C22×C4C2×C4×D512yes—
745C22×C4C2×C4×D512yes—
746C22×C4C2×C4×D512yes—
747C22×C4C2×C4×D512yes—
748C22×C4C2×C4×D512yes—
749C22×C4C2×C4×D512yes—
750C22×C4C2×C4×D512yes—
751C22×C4C2×C4×D512yes—
752C22×C4C2×C4×D512yes—
753C22×C4#70912yes—
754C22×C4#70912yes—
755C22×C4#70912yes—
756C22×C4#70912yes—
757C22×C4D4×D512yes—
758C22×C4#71112yes—
759C4⋊C4—204no—
760C4⋊C4—204no—
761C22⋊C4—516no—
762C22⋊C4—108no—
763C22⋊C4—108no—
764C22⋊C4—108no—
765C22⋊C4—204no—
766C22⋊C4—204no—
767C42—28no—
768C42—44no—
769C42—44no—
770C42—108no—
771C42—108no—
772C42—204no—
773C42—204no—
774C42—204no—
775C2×C5C4×#11711yescharacteristic
776C2×C5C42×D411yescharacteristic
777C2×C5#227511yescharacteristic
778C2×C5#234211yescharacteristic
779C2×C5#234611yescharacteristic
780C2×C5#235311yescharacteristic
781C2×C5#235411yescharacteristic
782C2×C5#235911yescharacteristic
783C2×C5#235911yescharacteristic
784C2×C5#236311yescharacteristic
785C2×C5#236311yescharacteristic
786C2×C5#237211yescharacteristic
787C2×C5#237211yescharacteristic
788C2×C5#237311yescharacteristic
789C2×C5#237311yescharacteristic
790D5—44no—
791C23—54no—
792C23—102no—
793C23—102no—
794C23—102no—
795C23—102no—
796C23—102no—
797C23—102no—
798C23—102no—
799C23—102no—
800C23—102no—
801C23—102no—
802C23—102no—
803C23—102no—
804C23—102no—
805C23—102no—
806C23—102no—
807C23—102no—
808C23—102no—
809C23—102no—
810C23—201no—
811C23—201no—
812C23—201no—
813C23—201no—
814C23—201no—
815C23—201no—
816C23—201no—
817C23—201no—
818C23—201no—
819C23—201no—
820C23—201no—
821C23—201no—
822C23—201no—
823C23—201no—
824C23—201no—
825C23—201no—
826C23C22×C4×D511yescharacteristic
827C23C22×C4×D511yescharacteristic
828C23C22×C4×D511yescharacteristic
829C23C2×#70911yescharacteristic
830C23C2×#70911yescharacteristic
831C23C2×#70911yescharacteristic
832C23C2×#70911yescharacteristic
833C23C2×D4×D511yescharacteristic
834C23C2×#71111yescharacteristic
835C23#414411yescharacteristic
836C23#414711yescharacteristic
837C23D5×#4111yescharacteristic
838C23D5×#4111yescharacteristic
839C23#414911yescharacteristic
840C23#414911yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—54no—
887C2×C4—54no—
888C2×C4—54no—
889C2×C4—102no—
890C2×C4—102no—
891C2×C4—102no—
892C2×C4—102no—
893C2×C4—102no—
894C2×C4—102no—
895C2×C4—102no—
896C2×C4—102no—
897C2×C4—102no—
898C2×C4—102no—
899C2×C4—102no—
900C2×C4—102no—
901C2×C4—102no—
902C2×C4—102no—
903C2×C4—102no—
904C2×C4—102no—
905C2×C4—102no—
906C2×C4—102no—
907C2×C4—102no—
908C2×C4—102no—
909C2×C4—102no—
910C2×C4—102no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—102no—
916C2×C4—102no—
917C2×C4—102no—
918C2×C4—102no—
919C2×C4—2016no—
920C2×C4—201no—
921C2×C4—201no—
922C2×C4—201no—
923C2×C4—201no—
924C2×C4—201no—
925C2×C4—201no—
926C2×C4—201no—
927C2×C4—201no—
928C2×C4—201no—
929C2×C4—201no—
930C2×C4—201no—
931C2×C4—201no—
932C2×C4—201no—
933C2×C4—201no—
934C2×C4—201no—
935C2×C4—201no—
936C2×C4C42×D514yes—
937C2×C4#401814yes—
938C2×C4#401814yes—
939C2×C4#402714yes—
940C5#1381611yescharacteristic, complemented, Sylow
941C22—104no—
942C22—104no—
943C22—104no—
944C22—202no—
945C22—202no—
946C22—202no—
947C22—202no—
948C22—202no—
949C22—202no—
950C22—202no—
951C22—202no—
952C22—202no—
953C22—202no—
954C22—202no—
955C22—202no—
956C22C2×C42×D511yescharacteristic
957C22C2×#401811yescharacteristic
958C22C2×#401811yescharacteristic
959C22C4×#70911yescharacteristic
960C22C4×#70911yescharacteristic
961C22C4×#70911yescharacteristic
962C22C4×#70911yescharacteristic
963C22C2×#402711yescharacteristic
964C22#6582411yescharacteristic
965C22#6582911yescharacteristic
966C22#6583811yescharacteristic
967C22#6584111yescharacteristic
968C22#6584711yescharacteristic
969C22#6585511yescharacteristic
970C22#6585611yescharacteristic
971C22#6586111yescharacteristic
972C22#6586111yescharacteristic
973C22#6586611yescharacteristic
974C22#6586611yescharacteristic
975C22C4×#71111yescharacteristic
976C22C4×#71111yescharacteristic
977C22#6587411yescharacteristic
978C22C4×D4×D511yescharacteristic
979C22C4×D4×D511yescharacteristic
980C22#6587911yescharacteristic
981C22#6587911yescharacteristic
982C22#6588411yescharacteristic
983C22#6588711yescharacteristic
984C22#6589011yescharacteristic
985C22#6589711yescharacteristic
986C22#6589911yescharacteristic
987C22#6590211yescharacteristic
988C22#6590811yescharacteristic
989C22#6590811yescharacteristic
990C22#6591511yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—104no—
999C4—104no—
1000C4—104no—
1001C4—202no—
1002C4—202no—
1003C4—202no—
1004C4—202no—
1005C2—204no—
1006C2C4×#401811yescharacteristic
1007C2#1060506811yescharacteristic
1008C2#1060512611yescharacteristic
1009C2C4×#402711yescharacteristic
1010C2#1060519311yescharacteristic
1011C2#1060520011yescharacteristic
1012C2#1060520111yescharacteristic
1013C2#1060520611yescharacteristic
1014C2#1060530511yescharacteristic
1015C2#1060536411yescharacteristic
1016C2#1060537011yescharacteristic
1017C2#1060539511yescharacteristic
1018C2#1060539711yescharacteristic
1019C2#1060548211yescharacteristic
1020C2#1060550311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC4×C5×#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4×#95D5
hypocenterC5#13816
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×#65221C2semidirect
6. C4×C5×#95C2semidirect
8. #10602329C2semidirect
9. C4×#3963C2semidirect
12. #10600199C2semidirect
13. #10600197C2semidirect
14. #10600194C2semidirect
15. Dic5×#95C2semidirect
51. #65229C4semidirect
54. #64958C4semidirect
55. #64955C4semidirect
87. C2×C42×C5C2×C4semidirect
110. C2×#683C2×C4semidirect
111. C2×#683C2×C4semidirect
126. C2×C4×Dic5C2×C4semidirect
130. C5×#95C2×C4semidirect
141. #3963C2×C4semidirect
142. #3963C2×C4semidirect
143. #3963C2×C4semidirect
159. C4×#95D5semidirect
289. #685C42semidirect
555. C2×C42C4×D5semidirect
573. #95C4×D5semidirect
940. C5#13816semidirect

Maximal subgroups

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

subgroupindex
C2×#652292
C2×C4×#6852
C2×#652212
C2×#649582
C2×#649552
C4×C5×#952
#106023302
#106023292
C4×#39632
#106002182
#106002012
#106001992
#106001972
#106001942
Dic5×#952
#138165