Finite Group Databasebeta

← #12024597

Subgroups — #12024597

Order 1280.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4033C211yesmaximal, characteristic, complemented
2C2×C5×#385C211yesmaximal, characteristic
3C2×#65499C211yesmaximal, characteristic
4C2×C4×C22⋊Dic5C211yesmaximal, characteristic
5C2×#65236C211yesmaximal, characteristic
6#10602361C211yesmaximal, characteristic, complemented
7#10602357C211yesmaximal, characteristic, complemented
8#10602357C211yesmaximal, characteristic, complemented
9#10602340C211yesmaximal, characteristic
10#10602338C211yesmaximal, characteristic
11#10602338C211yesmaximal, characteristic
12#10600217C211yesmaximal, characteristic, complemented
13#10600199C211yesmaximal, characteristic, complemented
14#10600198C211yesmaximal, characteristic, complemented
15#10600195C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C23×Dic10C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×#683C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C22×C4×Dic5C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C2×#4033—24no—
34C2×#4033—24no—
35C2×#4033—24no—
36C5×#385—24no—
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39#65499—24no—
40C4×C22⋊Dic5—24no—
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
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65236C418yescomplemented
58#14172—51nomaximal, Sylow
59C25×C5C2311yescharacteristic
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—22no—
65C23×C4×C5—41no—
66C23×C4×C5—41no—
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×Dic5C2311yescharacteristic
74C23×Dic5C2311yescharacteristic
75C23×Dic5C2311yescharacteristic
76C23×Dic5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C22×Dic10—22no—
82C22×Dic10—22no—
83C22×Dic10—22no—
84C22×Dic10—22no—
85C22×Dic10—22no—
86C22×Dic10—22no—
87C22×Dic10C2×C414yescomplemented
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4D414yes—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—41no—
99C2×C5×C22⋊C4C2×C414yes—
100C2×C22⋊Dic5—22no—
101C2×C22⋊Dic5—22no—
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—41no—
109C2×C22⋊Dic5C2×C414yes—
110C2×C22⋊Dic5C2×C414yes—
111C2×C22⋊Dic5Q814yescomplemented
112C2×#683—22no—
113C2×#683—22no—
114C2×#683—22no—
115C2×#683—22no—
116C2×#683—22no—
117C2×#683—22no—
118C2×#683—22no—
119C2×#683—41no—
120C2×#683D414yes—
121C2×C4×Dic5—22no—
122C2×C4×Dic5—22no—
123C2×C4×Dic5—22no—
124C2×C4×Dic5—22no—
125C2×C4×Dic5—22no—
126C2×C4×Dic5—22no—
127C2×C4×Dic5—22no—
128C2×C4×Dic5—22no—
129C2×C4×Dic5—22no—
130C2×C4×Dic5—41no—
131C2×C4×Dic5—41no—
132C2×C4×Dic5D414yes—
133#4033—232no—
134C5×#95—22no—
135C5×#95—22no—
136#3963—22no—
137#3963—22no—
138#3963—22no—
139#3963—22no—
140#3963—22no—
141#3963—22no—
142#3963—22no—
143#3963—22no—
144#3963—22no—
145#3963—41no—
146#3963—41no—
147#3963—41no—
148#3963—41no—
149#3963C2×C414yescomplemented
150#3963C2×C414yescomplemented
151#3963C2×C414yescomplemented
152C22×C4×Q8—51no—
153C2×#393—51no—
154C2×#385—51no—
155C2×#385D511yescharacteristic
156C2×C4×C22⋊C4—51no—
157#1446—51no—
158#1444—51no—
159#1439—51no—
160#1437—51no—
161#1437—51no—
162#1436—51no—
163#1436—51no—
164#1436—51no—
165#1436—51no—
166#1434—51no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5—21no—
178C24×C5—21no—
179C24×C5C22×C412yes—
180C24×C5C2×Q812yes—
181C24×C5#4112yes—
182C24×C5C2411yescharacteristic
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—28no—
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—44no—
218C22×C4×C5—44no—
219C22×C4×C5—44no—
220C22×C4×C5—44no—
221C22×C4×C5—44no—
222C22×C4×C5—44no—
223C22×C4×C5C22×C412yes—
224C22×C4×C5C22×C412yes—
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×D412yes—
229C22×C4×C5C2×D412yes—
230C22×C4×C5#4112yes—
231C22×C4×C5#4112yes—
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—21no—
266C22×Dic5—21no—
267C22×Dic5—21no—
268C22×Dic5—21no—
269C22×Dic5—21no—
270C22×Dic5—21no—
271C22×Dic5—21no—
272C22×Dic5—21no—
273C22×Dic5—21no—
274C22×Dic5—21no—
275C22×Dic5C22×C412yes—
276C22×Dic5C22×C412yes—
277C22×Dic5C22×C412yes—
278C22×Dic5C22×C412yes—
279C22×Dic5C2×D412yes—
280C22×Dic5C2×D412yes—
281C22×Dic5C2×D412yes—
282C22×Dic5C2×D412yes—
283C22×Dic5C2×Q812yes—
284C22×Dic5C2×Q812yes—
285C22×Dic5#4112yes—
286C22×Dic5#4112yes—
287C22×Dic5#4112yes—
288C2×Dic10—28no—
289C2×Dic10—28no—
290C2×Dic10—28no—
291C2×Dic10—28no—
292C2×Dic10—28no—
293C2×Dic10—28no—
294C2×Dic10—28no—
295C5×C4⋊C4—28no—
296C5×C4⋊C4—44no—
297C5×C22⋊C4—28no—
298C5×C22⋊C4—44no—
299C22⋊Dic5—28no—
300C22⋊Dic5—28no—
301C22⋊Dic5—28no—
302C22⋊Dic5—44no—
303#683—28no—
304#683—28no—
305#683—44no—
306C4×Dic5—28no—
307C4×Dic5—28no—
308C4×Dic5—28no—
309C4×Dic5—44no—
310C23×Q8—51no—
311C24×C4C2×D511yescharacteristic
312C2×C4×Q8—104no—
313C2×C4×Q8—104no—
314C2×C4×Q8—104no—
315C22×C4⋊C4—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4C2×D511yescharacteristic
319C22×C4⋊C4C2×D511yescharacteristic
320C22×C22⋊C4—51no—
321C22×C22⋊C4—51no—
322C22×C22⋊C4—51no—
323C22×C22⋊C4—51no—
324C22×C22⋊C4C2×D511yescharacteristic
325C22×C22⋊C4C2×D511yescharacteristic
326C22×C42—51no—
327C22×C42—51no—
328C22×C42—51no—
329C22×C42—51no—
330#393—58no—
331#385—24no—
332#385—104no—
333C4×C22⋊C4—104no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95—51no—
346C2×#95—51no—
347C2×#95—51no—
348C2×#95—51no—
349C2×#95—51no—
350C2×#95C2×D511yescharacteristic
351C2×#95C2×D511yescharacteristic
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
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—41no—
371C23×C5—41no—
372C23×C5—41no—
373C23×C5—41no—
374C23×C5—41no—
375C23×C5—41no—
376C23×C5—41no—
377C23×C5—41no—
378C23×C5—41no—
379C23×C5—41no—
380C23×C5—41no—
381C23×C5—41no—
382C23×C5—41no—
383C23×C5—41no—
384C23×C5—41no—
385C23×C5—41no—
386C23×C5C4×Q814yescomplemented
387C23×C5C23×C411yescharacteristic
388C23×C5C22×D411yescharacteristic
389C23×C5C22×D411yescharacteristic
390C23×C5C22×D411yescharacteristic
391C23×C5C22×Q811yescharacteristic
392C23×C5C2×#4111yescharacteristic
393C23×C5C2×#4111yescharacteristic
394C23×C5C2×#4111yescharacteristic
395C23×C5C2×#4111yescharacteristic
396C23×C5C2×#4111yescharacteristic
397C23×C5C2×#4111yescharacteristic
398C23×C5H(5,𝔽2)11yescharacteristic
399C23×C5H(5,𝔽2)11yescharacteristic
400C23×C52−1+411yescharacteristic
401C23×C52−1+411yescharacteristic
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—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—416no—
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×C5—41no—
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×C5C4×D414yes—
444C2×C4×C5#12014yes—
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—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—41no—
496C2×Dic5—41no—
497C2×Dic5—41no—
498C2×Dic5C4×D414yes—
499C2×Dic5C4×D414yes—
500C2×Dic5C22⋊Q814yes—
501Dic10—232no—
502C25C22×D511yescharacteristic
503C22×Q8—54no—
504C22×Q8—102no—
505C22×Q8—102no—
506C22×Q8—102no—
507C22×Q8—102no—
508C22×Q8—102no—
509C22×Q8—102no—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—41no—
516C23×C4—41no—
517C23×C4—51no—
518C23×C4—51no—
519C23×C4—51no—
520C23×C4—51no—
521C23×C4—51no—
522C23×C4—51no—
523C23×C4—51no—
524C23×C4—51no—
525C23×C4C22×D511yescharacteristic
526C23×C4C22×D511yescharacteristic
527C23×C4C22×D511yescharacteristic
528C23×C4C22×D511yescharacteristic
529C23×C4C22×D511yescharacteristic
530C23×C4C22×D511yescharacteristic
531C4×Q8—1032no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—54no—
538C2×C4⋊C4—102no—
539C2×C4⋊C4—102no—
540C2×C4⋊C4—102no—
541C2×C4⋊C4—102no—
542C2×C4⋊C4—102no—
543C2×C4⋊C4—102no—
544C2×C4⋊C4—102no—
545C2×C4⋊C4—201no—
546C2×C4⋊C4C22⋊D514yes—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—54no—
553C2×C22⋊C4—54no—
554C2×C22⋊C4—54no—
555C2×C22⋊C4—102no—
556C2×C22⋊C4—102no—
557C2×C22⋊C4—102no—
558C2×C22⋊C4—102no—
559C2×C22⋊C4—102no—
560C2×C22⋊C4—102no—
561C2×C22⋊C4—102no—
562C2×C22⋊C4—102no—
563C2×C22⋊C4—201no—
564C2×C22⋊C4C4×D514yes—
565C2×C42—54no—
566C2×C42—102no—
567C2×C42—102no—
568C2×C42—102no—
569C2×C42—102no—
570C2×C42—102no—
571C2×C42—102no—
572C2×C42—102no—
573C2×C42—102no—
574C2×C42—102no—
575C2×C42—201no—
576C2×C42—201no—
577#95—22no—
578#95—22no—
579#95—54no—
580#95—54no—
581#95—54no—
582#95—102no—
583#95—102no—
584#95—102no—
585#95—102no—
586#95—102no—
587#95—102no—
588#95—102no—
589#95—102no—
590#95—102no—
591#95—201no—
592#95—201no—
593#95—201no—
594#95—201no—
595C22×C5—24no—
596C22×C5—24no—
597C22×C5—24no—
598C22×C5—42no—
599C22×C5—42no—
600C22×C5—42no—
601C22×C5—42no—
602C22×C5—42no—
603C22×C5—42no—
604C22×C5—42no—
605C22×C5—42no—
606C22×C5—42no—
607C22×C5—42no—
608C22×C5—42no—
609C22×C5—42no—
610C22×C5C2×C4×D411yescharacteristic
611C22×C5C2×C4×D411yescharacteristic
612C22×C5C2×C4×D411yescharacteristic
613C22×C5C2×C4×Q811yescharacteristic
614C22×C5C4×#4111yescharacteristic
615C22×C5#52011yescharacteristic
616C22×C5#52011yescharacteristic
617C22×C5C2×#12011yescharacteristic
618C22×C5C2×C22⋊Q811yescharacteristic
619C22×C5#52511yescharacteristic
620C22×C5#52511yescharacteristic
621C22×C5#52511yescharacteristic
622C22×C5#52511yescharacteristic
623C22×C5#52911yescharacteristic
624C22×C5#53311yescharacteristic
625C22×C5#53511yescharacteristic
626C22×C5#53611yescharacteristic
627C22×C5#54211yescharacteristic
628C22×C5#54211yescharacteristic
629C22×C5#54611yescharacteristic
630C22×C5#54611yescharacteristic
631C22×C5#54611yescharacteristic
632C22×C5#54611yescharacteristic
633C22×C5#54811yescharacteristic
634C22×C5#54811yescharacteristic
635C22×C5D4×Q811yescharacteristic
636C22×C5D4×Q811yescharacteristic
637C22×C5#55211yescharacteristic
638C22×C5#55211yescharacteristic
639C22×C5#55411yescharacteristic
640C22×C5#55411yescharacteristic
641C22×C5#55611yescharacteristic
642C22×C5#55611yescharacteristic
643C22×C5#55911yescharacteristic
644C22×C5#55911yescharacteristic
645C4×C5—24no—
646C4×C5—24no—
647C4×C5—42no—
648C4×C5—42no—
649C4×C5—42no—
650C4×C5—81no—
651Dic5—24no—
652Dic5—24no—
653Dic5—24no—
654Dic5—42no—
655Dic5—42no—
656Dic5—42no—
657Dic5—42no—
658Dic5—81no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24C2×C4×D512yes—
672C24#71112yes—
673C24Q8×D512yes—
674C24C23×D511yescharacteristic
675C2×Q8—108no—
676C2×Q8—108no—
677C2×Q8—108no—
678C2×Q8—108no—
679C2×Q8—108no—
680C2×Q8—108no—
681C2×Q8—108no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—28no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
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—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—52no—
723C22×C4—52no—
724C22×C4—52no—
725C22×C4—52no—
726C22×C4—52no—
727C22×C4—52no—
728C22×C4—52no—
729C22×C4—52no—
730C22×C4—52no—
731C22×C4—52no—
732C22×C4—52no—
733C22×C4—52no—
734C22×C4—52no—
735C22×C4—101no—
736C22×C4—101no—
737C22×C4—101no—
738C22×C4—101no—
739C22×C4—101no—
740C22×C4—101no—
741C22×C4—101no—
742C22×C4—101no—
743C22×C4—101no—
744C22×C4—101no—
745C22×C4—101no—
746C22×C4—101no—
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×C4C2×C4×D512yes—
779C22×C4C2×C4×D512yes—
780C22×C4#70912yes—
781C22×C4D4×D512yes—
782C22×C4D4×D512yes—
783C22×C4#71112yes—
784C22×C4C2×C22⋊D512yes—
785C22×C4C2×C22⋊D512yes—
786C22×C4C2×C22⋊D512yes—
787C4⋊C4—28no—
788C4⋊C4—44no—
789C4⋊C4—108no—
790C4⋊C4—108no—
791C4⋊C4—204no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—108no—
795C22⋊C4—108no—
796C22⋊C4—108no—
797C22⋊C4—204no—
798C42—108no—
799C42—108no—
800C42—108no—
801C42—204no—
802C2×C5—44no—
803C2×C5C4×#12011yescharacteristic
804C2×C5C4×C22⋊Q811yescharacteristic
805C2×C5#232611yescharacteristic
806C2×C5#236011yescharacteristic
807C2×C5#236011yescharacteristic
808C2×C5#236711yescharacteristic
809C2×C5#236711yescharacteristic
810C2×C5#240411yescharacteristic
811C2×C5#240911yescharacteristic
812C2×C5#245811yescharacteristic
813C2×C5#245811yescharacteristic
814C2×C5#246511yescharacteristic
815C2×C5#246511yescharacteristic
816C2×C5#258011yescharacteristic
817C2×C5#259911yescharacteristic
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23#403314yescomplemented
853C23C22×C4×D511yescharacteristic
854C23C2×#70911yescharacteristic
855C23C2×D4×D511yescharacteristic
856C23C2×D4×D511yescharacteristic
857C23C2×#71111yescharacteristic
858C23C2×#71111yescharacteristic
859C23#414411yescharacteristic
860C23#414411yescharacteristic
861C23C2×Q8×D511yescharacteristic
862C23#414711yescharacteristic
863C23D5×#4111yescharacteristic
864C23D5×#4111yescharacteristic
865C23D5×#4111yescharacteristic
866C23#415011yescharacteristic
867C23C22×C22⋊D511yescharacteristic
868Q8—1032no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—416no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—54no—
911C2×C4—54no—
912C2×C4—54no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—102no—
916C2×C4—102no—
917C2×C4—102no—
918C2×C4—102no—
919C2×C4—102no—
920C2×C4—102no—
921C2×C4—102no—
922C2×C4—102no—
923C2×C4—102no—
924C2×C4—102no—
925C2×C4—102no—
926C2×C4—102no—
927C2×C4—102no—
928C2×C4—102no—
929C2×C4—102no—
930C2×C4—102no—
931C2×C4—102no—
932C2×C4—102no—
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—201no—
944C2×C4—201no—
945C2×C4—201no—
946C2×C4—201no—
947C2×C4—201no—
948C2×C4—201no—
949C2×C4—201no—
950C2×C4—201no—
951C2×C4—201no—
952C2×C4—201no—
953C2×C4—201no—
954C2×C4—201no—
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×C4C4×C22⋊D514yes—
967C2×C4#408314yes—
968C5#1417211yescharacteristic, complemented, Sylow
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C2×#403311yescharacteristic
985C22#6583811yescharacteristic
986C22#6584511yescharacteristic
987C22#6584711yescharacteristic
988C22C4×#71111yescharacteristic
989C22#6587611yescharacteristic
990C22C4×D4×D511yescharacteristic
991C22C4×D4×D511yescharacteristic
992C22#6588011yescharacteristic
993C22#6588111yescharacteristic
994C22#6588111yescharacteristic
995C22#6589311yescharacteristic
996C22#6592011yescharacteristic
997C22#6592511yescharacteristic
998C22#6592511yescharacteristic
999C22#6592611yescharacteristic
1000C22#6595611yescharacteristic
1001C22D5×C22⋊Q811yescharacteristic
1002C22#6596211yescharacteristic
1003C22#6596611yescharacteristic
1004C22#6596711yescharacteristic
1005C22#6597011yescharacteristic
1006C22#6597411yescharacteristic
1007C22#6597511yescharacteristic
1008C22#6598311yescharacteristic
1009C22#6598411yescharacteristic
1010C22#6599611yescharacteristic
1011C22#6599811yescharacteristic
1012C22C2×C4×C22⋊D511yescharacteristic
1013C22C2×#408311yescharacteristic
1014C22#6614011yescharacteristic
1015C22#6614011yescharacteristic
1016C22Q8×C22⋊D511yescharacteristic
1017C22#6616211yescharacteristic
1018C22#6616511yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—104no—
1026C4—104no—
1027C4—104no—
1028C4—202no—
1029C4—202no—
1030C4—202no—
1031C4—202no—
1032C4—401no—
1033C2—44no—
1034C2#1060611211yescharacteristic
1035C2#1060611711yescharacteristic
1036C2#1060612711yescharacteristic
1037C2#1060612911yescharacteristic
1038C2#1060615911yescharacteristic
1039C2#1060616411yescharacteristic
1040C2#1060621811yescharacteristic
1041C2#1060622811yescharacteristic
1042C2#1061389311yescharacteristic
1043C2#1061407511yescharacteristic
1044C2C4×#408311yescharacteristic
1045C2#1061431211yescharacteristic
1046C2#1061448211yescharacteristic
1047C2#1061449911yescharacteristic
1048C2#1061458211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#385C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#385D5
hypocenterC5#14172
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#4033C2semidirect
6. #10602361C2semidirect
7. #10602357C2semidirect
8. #10602357C2semidirect
12. #10600217C2semidirect
13. #10600199C2semidirect
14. #10600198C2semidirect
15. #10600195C2semidirect
57. #65236C4semidirect
87. C22×Dic10C2×C4semidirect
111. C2×C22⋊Dic5Q8semidirect
149. #3963C2×C4semidirect
150. #3963C2×C4semidirect
151. #3963C2×C4semidirect
386. C23×C5C4×Q8semidirect
852. C23#4033semidirect
968. C5#14172semidirect

Maximal subgroups

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

subgroupindex
C22×#40332
C2×C5×#3852
C2×#654992
C2×C4×C22⋊Dic52
C2×#652362
#106023612
#106023572
#106023402
#106023382
#106002172
#106001992
#106001982
#106001952
#141725