Finite Group Databasebeta

← #12022431

Subgroups — #12022431

Order 1280.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4024C211yesmaximal, characteristic
2C2×#65231C211yesmaximal, characteristic
3C2×C22⋊C4×Dic5C211yesmaximal, characteristic
4C2×C4×#683C211yesmaximal, characteristic, complemented
5C2×#64935C211yesmaximal, characteristic, complemented
6C2×#64935C211yesmaximal, characteristic, complemented
7C2×#64936C211yesmaximal, characteristic, complemented
8C5×#1437C211yesmaximal, characteristic
9#10602340C211yesmaximal, characteristic
10#10602339C211yesmaximal, characteristic
11#10602338C211yesmaximal, characteristic
12#10602328C211yesmaximal, characteristic, complemented
13#10600216C211yesmaximal, characteristic, complemented
14#10600214C211yesmaximal, characteristic, complemented
15#10600197C211yesmaximal, characteristic, complemented
16C24×Dic5C2211yescharacteristic
17C23×Dic10C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×#683C2211yescharacteristic
29C22×#683C2211yescharacteristic
30C22×#683C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C22×C4×Dic5C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C2×#4024—24no—
36C2×#4024—24no—
37C2×#4024C418yescomplemented
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54#65231—24no—
55C22⋊C4×Dic5—24no—
56C4×#683—24no—
57#64936—24no—
58#64935—24no—
59#64935—24no—
60#13997—51nomaximal, Sylow
61C25×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×Dic5—22no—
69C23×Dic5—22no—
70C23×Dic5—22no—
71C23×Dic5—22no—
72C23×Dic5—22no—
73C23×Dic5—22no—
74C23×Dic5C2×C414yes—
75C23×Dic5C2311yescharacteristic
76C23×Dic5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C22×Dic10—22no—
84C22×Dic10—22no—
85C22×Dic10—22no—
86C22×Dic10—22no—
87C22×Dic10—22no—
88C22×Dic10—22no—
89C22×Dic10C2×C414yes—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—41no—
97C2×C5×C22⋊C4C2×C414yes—
98C2×C5×C22⋊C4Q814yescomplemented
99C2×C42×C5—22no—
100C2×C42×C5—22no—
101C2×C42×C5—41no—
102C2×C22⋊Dic5—22no—
103C2×C22⋊Dic5—22no—
104C2×C22⋊Dic5—22no—
105C2×C22⋊Dic5—22no—
106C2×C22⋊Dic5—22no—
107C2×C22⋊Dic5—22no—
108C2×C22⋊Dic5—22no—
109C2×C22⋊Dic5—41no—
110C2×C22⋊Dic5C2×C414yes—
111C2×C4⋊Dic5—22no—
112C2×C4⋊Dic5—22no—
113C2×C4⋊Dic5—22no—
114C2×C4⋊Dic5—22no—
115C2×C4⋊Dic5—41no—
116C2×C4⋊Dic5C2×C414yes—
117C2×#683—22no—
118C2×#683—22no—
119C2×#683—22no—
120C2×#683—22no—
121C2×#683—22no—
122C2×#683—22no—
123C2×#683—22no—
124C2×#683—22no—
125C2×#683—22no—
126C2×#683—41no—
127C2×#683C2×C414yes—
128C2×#683C2×C414yes—
129C2×#683D414yes—
130C2×#683D414yes—
131C2×#683D414yes—
132C2×C4×Dic5—22no—
133C2×C4×Dic5—22no—
134C2×C4×Dic5—22no—
135C2×C4×Dic5—22no—
136C2×C4×Dic5—22no—
137C2×C4×Dic5—22no—
138C2×C4×Dic5—22no—
139C2×C4×Dic5—41no—
140C2×C4×Dic5D414yes—
141#4024—232no—
142C5×#95—22no—
143C5×#95—22no—
144C5×#95—22no—
145#3963—22no—
146#3963—22no—
147#3963—22no—
148#3963—22no—
149#3963—22no—
150#3963—22no—
151#3963—22no—
152#3963—22no—
153#3963—22no—
154#3963—22no—
155#3963—22no—
156#3963—22no—
157#3963—22no—
158C22×C22⋊Q8—51no—
159C2×#391—51no—
160C2×#391—51no—
161C2×#389—51no—
162C2×#380—51no—
163C2×C4×C4⋊C4—51no—
164C2×C4×C22⋊C4—51no—
165#1445—51no—
166#1445—51no—
167#1439—51no—
168#1439—51no—
169#1437—51no—
170#1437D511yescharacteristic
171C4⋊#95—51no—
172C4⋊#95—51no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5—21no—
178C24×C5—21no—
179C24×C5—21no—
180C24×C5—21no—
181C24×C5—21no—
182C24×C5—21no—
183C24×C5—21no—
184C24×C5—21no—
185C24×C5C22×C412yes—
186C24×C5C2×Q812yes—
187C24×C5#4112yes—
188C24×C5C2411yescharacteristic
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×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5C22×C412yes—
223C22×C4×C5C22×C412yes—
224C22×C4×C5C2×D412yes—
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×Q812yes—
229C22×C4×C5C2×Q812yes—
230C22×C4×C5#4112yes—
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×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5—21no—
264C22×Dic5—21no—
265C22×Dic5—28no—
266C22×Dic5—28no—
267C22×Dic5—28no—
268C22×Dic5—21no—
269C22×Dic5—21no—
270C22×Dic5—21no—
271C22×Dic5—21no—
272C22×Dic5—21no—
273C22×Dic5—21no—
274C22×Dic5—21no—
275C22×Dic5—44no—
276C22×Dic5—44no—
277C22×Dic5—44no—
278C22×Dic5—44no—
279C22×Dic5C22×C412yes—
280C22×Dic5C22×C412yes—
281C22×Dic5C22×C412yes—
282C22×Dic5C22×C412yes—
283C22×Dic5C2×D412yes—
284C22×Dic5C2×D412yes—
285C22×Dic5C2×D412yes—
286C22×Dic5C2×D412yes—
287C22×Dic5C2×D412yes—
288C22×Dic5C2×D412yes—
289C22×Dic5C2×D412yes—
290C22×Dic5C2×D412yes—
291C22×Dic5#4112yes—
292C22×Dic5#4112yes—
293C22×Dic5#4112yes—
294C2×Dic10—28no—
295C2×Dic10—28no—
296C2×Dic10—28no—
297C2×Dic10—44no—
298C2×Dic10—44no—
299C2×Dic10—44no—
300C2×Dic10—44no—
301C5×C22⋊C4—28no—
302C5×C22⋊C4—28no—
303C5×C22⋊C4—44no—
304C42×C5—44no—
305C22⋊Dic5—28no—
306C22⋊Dic5—28no—
307C22⋊Dic5—44no—
308C4⋊Dic5—28no—
309C4⋊Dic5—44no—
310#683—28no—
311#683—28no—
312#683—44no—
313#683—44no—
314#683C22⋊C4116yescomplemented
315C4×Dic5—28no—
316C4×Dic5—44no—
317C4×Dic5—44no—
318C23×Q8—51no—
319C24×C4—51no—
320C2×C22⋊Q8—58no—
321C2×C22⋊Q8—104no—
322C2×C22⋊Q8—104no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—51no—
325C22×C4⋊C4—51no—
326C22×C4⋊C4—51no—
327C22×C4⋊C4—51no—
328C22×C4⋊C4—51no—
329C22×C4⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4C2×D511yescharacteristic
334C22×C22⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C42—51no—
337C22×C42—51no—
338C22×C42—51no—
339C22×C42C2×D511yescharacteristic
340#391—104no—
341#391—104no—
342#389—104no—
343#380—104no—
344C4×C4⋊C4—104no—
345C4×C22⋊C4—104no—
346C2×#95—51no—
347C2×#95—51no—
348C2×#95—51no—
349C2×#95—51no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C2×#95—51no—
358C2×#95—51no—
359C2×#95C2×D511yescharacteristic
360C2×#95C2×D511yescharacteristic
361C2×#95C2×D511yescharacteristic
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—41no—
381C23×C5—41no—
382C23×C5—41no—
383C23×C5—41no—
384C23×C5—41no—
385C23×C5—41no—
386C23×C5—41no—
387C23×C5—41no—
388C23×C5—41no—
389C23×C5—41no—
390C23×C5—41no—
391C23×C5—41no—
392C23×C5—41no—
393C23×C5—41no—
394C23×C5—41no—
395C23×C5—41no—
396C23×C5C4×Q814yes—
397C23×C5C23×C411yescharacteristic
398C23×C5C22×D411yescharacteristic
399C23×C5C22×D411yescharacteristic
400C23×C5C22×D411yescharacteristic
401C23×C5C22×D411yescharacteristic
402C23×C5C22×Q811yescharacteristic
403C23×C5C2×#4111yescharacteristic
404C23×C5C2×#4111yescharacteristic
405C23×C5C2×#4111yescharacteristic
406C23×C5C2×#4111yescharacteristic
407C23×C5C2×#4111yescharacteristic
408C23×C5H(5,𝔽2)11yescharacteristic
409C23×C52−1+411yescharacteristic
410C23×C52−1+411yescharacteristic
411C23×C52−1+411yescharacteristic
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—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5C2×C22⋊C414yes—
453C2×C4×C5C22⋊Q814yescomplemented
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—22no—
467C2×Dic5—22no—
468C2×Dic5—22no—
469C2×Dic5—22no—
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—22no—
473C2×Dic5—22no—
474C2×Dic5—22no—
475C2×Dic5—41no—
476C2×Dic5—41no—
477C2×Dic5—41no—
478C2×Dic5—41no—
479C2×Dic5—41no—
480C2×Dic5—41no—
481C2×Dic5—41no—
482C2×Dic5—41no—
483C2×Dic5—41no—
484C2×Dic5—41no—
485C2×Dic5—41no—
486C2×Dic5—41no—
487C2×Dic5—41no—
488C2×Dic5—41no—
489C2×Dic5—41no—
490C2×Dic5—41no—
491C2×Dic5—41no—
492C2×Dic5—41no—
493C2×Dic5—41no—
494C2×Dic5—41no—
495C2×Dic5—416no—
496C2×Dic5—41no—
497C2×Dic5—41no—
498C2×Dic5—41no—
499C2×Dic5—41no—
500C2×Dic5—41no—
501C2×Dic5—41no—
502C2×Dic5—41no—
503C2×Dic5C2×C22⋊C414yes—
504C2×Dic5C2×C22⋊C414yes—
505C2×Dic5C4×D414yes—
506C2×Dic5C4×D414yes—
507C2×Dic5#12114yes—
508C2×Dic5#12114yes—
509C2×Dic5#12414yes—
510C2×Dic5#12714yes—
511Dic10—416no—
512C25C22×D511yescharacteristic
513C22×Q8—54no—
514C22×Q8—102no—
515C22×Q8—102no—
516C22×Q8—102no—
517C22×Q8—102no—
518C22×Q8—102no—
519C22×Q8—102no—
520C23×C4—51no—
521C23×C4—51no—
522C23×C4—54no—
523C23×C4—51no—
524C23×C4—51no—
525C23×C4—51no—
526C23×C4—51no—
527C23×C4—51no—
528C23×C4—51no—
529C23×C4—102no—
530C23×C4—102no—
531C23×C4—102no—
532C23×C4—102no—
533C23×C4—102no—
534C23×C4—102no—
535C23×C4C22×D511yescharacteristic
536C23×C4C22×D511yescharacteristic
537C23×C4C22×D511yescharacteristic
538C23×C4C22×D511yescharacteristic
539C23×C4C22×D511yescharacteristic
540C23×C4C22×D511yescharacteristic
541C22⋊Q8—1032no—
542C2×C4⋊C4—54no—
543C2×C4⋊C4—54no—
544C2×C4⋊C4—54no—
545C2×C4⋊C4—54no—
546C2×C4⋊C4—54no—
547C2×C4⋊C4—54no—
548C2×C4⋊C4—102no—
549C2×C4⋊C4—102no—
550C2×C4⋊C4—102no—
551C2×C4⋊C4—102no—
552C2×C4⋊C4—102no—
553C2×C4⋊C4—102no—
554C2×C4⋊C4—102no—
555C2×C4⋊C4—102no—
556C2×C4⋊C4—102no—
557C2×C4⋊C4—102no—
558C2×C4⋊C4—102no—
559C2×C4⋊C4—102no—
560C2×C4⋊C4—102no—
561C2×C4⋊C4—201no—
562C2×C4⋊C4—201no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—54no—
571C2×C22⋊C4—102no—
572C2×C22⋊C4—102no—
573C2×C22⋊C4—102no—
574C2×C22⋊C4—102no—
575C2×C22⋊C4—102no—
576C2×C22⋊C4—102no—
577C2×C22⋊C4—102no—
578C2×C22⋊C4—201no—
579C2×C22⋊C4Dic1014yescomplemented
580C2×C22⋊C4C4×D514yes—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—41no—
584C2×C42—54no—
585C2×C42—102no—
586C2×C42—102no—
587C2×C42—102no—
588C2×C42—102no—
589C2×C42—102no—
590C2×C42—102no—
591C2×C42—102no—
592C2×C42—201no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—102no—
597#95—102no—
598#95—102no—
599#95—102no—
600#95—102no—
601#95—102no—
602#95—102no—
603#95—102no—
604#95—102no—
605#95—102no—
606#95—102no—
607#95—102no—
608#95—102no—
609C22×C5—24no—
610C22×C5—24no—
611C22×C5—24no—
612C22×C5—42no—
613C22×C5—42no—
614C22×C5—42no—
615C22×C5—42no—
616C22×C5—42no—
617C22×C5—42no—
618C22×C5—42no—
619C22×C5—42no—
620C22×C5—42no—
621C22×C5—42no—
622C22×C5—42no—
623C22×C5—42no—
624C22×C5C22×C22⋊C411yescharacteristic
625C22×C5C2×C4×D411yescharacteristic
626C22×C5C2×C4×D411yescharacteristic
627C22×C5C2×C4×Q811yescharacteristic
628C22×C5C4×#4111yescharacteristic
629C22×C5#51911yescharacteristic
630C22×C5#52011yescharacteristic
631C22×C5C2×#12111yescharacteristic
632C22×C5C2×#12111yescharacteristic
633C22×C5C2×C22⋊Q811yescharacteristic
634C22×C5#52511yescharacteristic
635C22×C5C2×#12411yescharacteristic
636C22×C5#52911yescharacteristic
637C22×C5C2×#12711yescharacteristic
638C22×C5#53311yescharacteristic
639C22×C5#53611yescharacteristic
640C22×C5#53711yescharacteristic
641C22×C5#54111yescharacteristic
642C22×C5#54211yescharacteristic
643C22×C5#54611yescharacteristic
644C22×C5#54611yescharacteristic
645C22×C5#54611yescharacteristic
646C22×C5#54711yescharacteristic
647C22×C5#54711yescharacteristic
648C22×C5#54711yescharacteristic
649C22×C5#54811yescharacteristic
650C22×C5#54811yescharacteristic
651C22×C5#54811yescharacteristic
652C22×C5D4×Q811yescharacteristic
653C22×C5D4×Q811yescharacteristic
654C22×C5D4×Q811yescharacteristic
655C22×C5#55211yescharacteristic
656C22×C5#55211yescharacteristic
657C22×C5#55411yescharacteristic
658C22×C5#55611yescharacteristic
659C4×C5—24no—
660C4×C5—24no—
661C4×C5—42no—
662C4×C5—42no—
663C4×C5—42no—
664C4×C5—81no—
665Dic5—24no—
666Dic5—42no—
667Dic5—42no—
668Dic5—42no—
669Dic5—42no—
670Dic5—42no—
671Dic5—81no—
672Dic5#39018yes—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24C2×Dic1012yes—
686C24C2×C4×D512yes—
687C24#70912yes—
688C24C23×D511yescharacteristic
689C2×Q8—108no—
690C2×Q8—108no—
691C2×Q8—108no—
692C2×Q8—204no—
693C2×Q8—204no—
694C2×Q8—204no—
695C2×Q8—204no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—52no—
730C22×C4—52no—
731C22×C4—52no—
732C22×C4—52no—
733C22×C4—52no—
734C22×C4—52no—
735C22×C4—52no—
736C22×C4—52no—
737C22×C4—52no—
738C22×C4—52no—
739C22×C4—52no—
740C22×C4—52no—
741C22×C4—52no—
742C22×C4—52no—
743C22×C4—52no—
744C22×C4—108no—
745C22×C4—108no—
746C22×C4—108no—
747C22×C4—101no—
748C22×C4—101no—
749C22×C4—101no—
750C22×C4—101no—
751C22×C4—101no—
752C22×C4—101no—
753C22×C4—101no—
754C22×C4—101no—
755C22×C4—101no—
756C22×C4—101no—
757C22×C4—101no—
758C22×C4—101no—
759C22×C4—101no—
760C22×C4—101no—
761C22×C4—101no—
762C22×C4—101no—
763C22×C4—101no—
764C22×C4—101no—
765C22×C4—101no—
766C22×C4—101no—
767C22×C4—101no—
768C22×C4—101no—
769C22×C4—101no—
770C22×C4—101no—
771C22×C4—101no—
772C22×C4—101no—
773C22×C4—101no—
774C22×C4—101no—
775C22×C4—101no—
776C22×C4—101no—
777C22×C4—101no—
778C22×C4—101no—
779C22×C4—101no—
780C22×C4—101no—
781C22×C4—101no—
782C22×C4—101no—
783C22×C4—101no—
784C22×C4—101no—
785C22×C4—101no—
786C22×C4—101no—
787C22×C4—101no—
788C22×C4—204no—
789C22×C4—204no—
790C22×C4—204no—
791C22×C4—204no—
792C22×C4C2×Dic1012yes—
793C22×C4C2×Dic1012yes—
794C22×C4C2×C4×D512yes—
795C22×C4C2×C4×D512yes—
796C22×C4D4×D512yes—
797C22×C4D4×D512yes—
798C22×C4D4×D512yes—
799C22×C4D4×D512yes—
800C22×C4#71112yes—
801C4⋊C4—516no—
802C4⋊C4—108no—
803C4⋊C4—108no—
804C4⋊C4—108no—
805C4⋊C4—204no—
806C4⋊C4—204no—
807C4⋊C4—204no—
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—44no—
811C22⋊C4—108no—
812C22⋊C4—108no—
813C22⋊C4—204no—
814C42—44no—
815C42—108no—
816C42—204no—
817C42—204no—
818C2×C5—44no—
819C2×C5C2×#39011yescharacteristic
820C2×C5C4×C22⋊Q811yescharacteristic
821C2×C5#232311yescharacteristic
822C2×C5#233911yescharacteristic
823C2×C5Q8×C22⋊C411yescharacteristic
824C2×C5#236011yescharacteristic
825C2×C5#236211yescharacteristic
826C2×C5#241511yescharacteristic
827C2×C5#241711yescharacteristic
828C2×C5#242711yescharacteristic
829C2×C5#242911yescharacteristic
830C2×C5#248911yescharacteristic
831C2×C5#249211yescharacteristic
832C2×C5#254011yescharacteristic
833C2×C5#254211yescharacteristic
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23C4×Dic1014yes—
869C23C22×Dic1011yescharacteristic
870C23C22×C4×D511yescharacteristic
871C23C2×#70911yescharacteristic
872C23C2×D4×D511yescharacteristic
873C23C2×D4×D511yescharacteristic
874C23C2×D4×D511yescharacteristic
875C23C2×D4×D511yescharacteristic
876C23C2×#71111yescharacteristic
877C23#414411yescharacteristic
878C23D5×#4111yescharacteristic
879C23D5×#4111yescharacteristic
880C23D5×#4111yescharacteristic
881C23#415011yescharacteristic
882C23#415011yescharacteristic
883C23#415011yescharacteristic
884Q8—2016no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—54no—
926C2×C4—54no—
927C2×C4—54no—
928C2×C4—54no—
929C2×C4—54no—
930C2×C4—54no—
931C2×C4—54no—
932C2×C4—54no—
933C2×C4—102no—
934C2×C4—102no—
935C2×C4—102no—
936C2×C4—102no—
937C2×C4—102no—
938C2×C4—102no—
939C2×C4—102no—
940C2×C4—102no—
941C2×C4—102no—
942C2×C4—102no—
943C2×C4—102no—
944C2×C4—102no—
945C2×C4—102no—
946C2×C4—102no—
947C2×C4—102no—
948C2×C4—102no—
949C2×C4—102no—
950C2×C4—102no—
951C2×C4—102no—
952C2×C4—102no—
953C2×C4—102no—
954C2×C4—2016no—
955C2×C4—201no—
956C2×C4—201no—
957C2×C4—201no—
958C2×C4—201no—
959C2×C4—201no—
960C2×C4—201no—
961C2×C4—201no—
962C2×C4—201no—
963C2×C4—201no—
964C2×C4—201no—
965C2×C4—201no—
966C2×C4—201no—
967C2×C4—201no—
968C2×C4—201no—
969C2×C4—201no—
970C2×C4—201no—
971C2×C4—201no—
972C2×C4—201no—
973C2×C4—201no—
974C2×C4—201no—
975C2×C4—201no—
976C2×C4—201no—
977C2×C4—201no—
978C2×C4—201no—
979C2×C4—201no—
980C2×C4—201no—
981C2×C4—201no—
982C2×C4#402414yescomplemented
983C2×C4D5×C22⋊C414yes—
984C5#1399711yescharacteristic, complemented, Sylow
985C22—24no—
986C22—24no—
987C22—24no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22C2×C4×Dic1011yescharacteristic
1001C22C2×#402411yescharacteristic
1002C22C2×D5×C22⋊C411yescharacteristic
1003C22#6582411yescharacteristic
1004C22#6585011yescharacteristic
1005C22#6585111yescharacteristic
1006C22#6586511yescharacteristic
1007C22C4×#71111yescharacteristic
1008C22D4×Dic1011yescharacteristic
1009C22D4×Dic1011yescharacteristic
1010C22D4×Dic1011yescharacteristic
1011C22#6587211yescharacteristic
1012C22#6587311yescharacteristic
1013C22C4×D4×D511yescharacteristic
1014C22C4×D4×D511yescharacteristic
1015C22#6588011yescharacteristic
1016C22#6588111yescharacteristic
1017C22#6588611yescharacteristic
1018C22#6588611yescharacteristic
1019C22#6592511yescharacteristic
1020C22#6593111yescharacteristic
1021C22D5×#12111yescharacteristic
1022C22D5×#12111yescharacteristic
1023C22#6594411yescharacteristic
1024C22#6594511yescharacteristic
1025C22#6594511yescharacteristic
1026C22#6598411yescharacteristic
1027C22#6598911yescharacteristic
1028C22#6599611yescharacteristic
1029C22D5×#12411yescharacteristic
1030C22#6600911yescharacteristic
1031C22#6601111yescharacteristic
1032C22#6603511yescharacteristic
1033C22#6603611yescharacteristic
1034C22D5×#12711yescharacteristic
1035C4—24no—
1036C4—24no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—58no—
1041C4—81no—
1042C4—104no—
1043C4—202no—
1044C4—202no—
1045C4—202no—
1046C4—202no—
1047C4—202no—
1048C4—401no—
1049C2—44no—
1050C2C4×#402411yescharacteristic
1051C2C22⋊C4×Dic1011yescharacteristic
1052C2#1060519711yescharacteristic
1053C2#1060640311yescharacteristic
1054C2#1060642411yescharacteristic
1055C2#1060642811yescharacteristic
1056C2#1060719011yescharacteristic
1057C2#1060720911yescharacteristic
1058C2#1060722711yescharacteristic
1059C2#1060723111yescharacteristic
1060C2#1060727511yescharacteristic
1061C2#1060727811yescharacteristic
1062C2#1060807811yescharacteristic
1063C2#1060808011yescharacteristic
1064C2D5×#39011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1437C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenter#1437D5
hypocenterC5#13997
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C4×#683C2semidirect
5. C2×#64935C2semidirect
6. C2×#64935C2semidirect
7. C2×#64936C2semidirect
12. #10602328C2semidirect
13. #10600216C2semidirect
14. #10600214C2semidirect
15. #10600197C2semidirect
37. C2×#4024C4semidirect
98. C2×C5×C22⋊C4Q8semidirect
314. #683C22⋊C4semidirect
453. C2×C4×C5C22⋊Q8semidirect
579. C2×C22⋊C4Dic10semidirect
982. C2×C4#4024semidirect
984. C5#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#40242
C2×#652312
C2×C22⋊C4×Dic52
C2×C4×#6832
C2×#649352
C2×#649362
C5×#14372
#106023402
#106023392
#106023382
#106023282
#106002162
#106002142
#106001972
#139975