Finite Group Databasebeta

← #12023792

Subgroups — #12023792

Order 1280.

2006 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×#4070C211yesmaximal, characteristic
2C2×C4×C22⋊Dic5C211yesmaximal, characteristic
3C2×#64935C211yesmaximal, characteristic, complemented
4C2×#64941C211yesmaximal, characteristic, complemented
5C2×#64938C211yesmaximal, characteristic, complemented
6C5×C22⋊#95C211yesmaximal, characteristic
7#10602340C211yesmaximal, characteristic
8#10602340C211yesmaximal, characteristic
9#10602338C211yesmaximal, characteristic
10#10602338C211yesmaximal, characteristic
11#10600217C211yesmaximal, characteristic, complemented
12#10600204C211yesmaximal, characteristic, complemented
13#10600200C211yesmaximal, characteristic, complemented
14#10600198C211yesmaximal, characteristic, complemented
15#10600198C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C23×Dic10C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic5C2211yescharacteristic
21C22×C22⋊Dic5C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C4⋊Dic5C2211yescharacteristic
25C2×#4070—24no—
26C2×#4070—24no—
27C2×#4070C418yescomplemented
28C22×#683C2211yescharacteristic
29C22×#683C2211yescharacteristic
30C22×#683C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C22×C4×Dic5C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
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
55#64941—24no—
56#64938—24no—
57#64935—24no—
58#14099—51nomaximal, Sylow
59C25×C5C2311yescharacteristic
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—41no—
65C23×C4×C5—41no—
66C23×C4×C5C2×C414yes—
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—41no—
86C22×Dic10—41no—
87C22×Dic10C2×C414yes—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—41no—
93C2×C5×C22⋊C4—41no—
94C2×C22⋊Dic5—22no—
95C2×C22⋊Dic5—22no—
96C2×C22⋊Dic5—22no—
97C2×C22⋊Dic5—22no—
98C2×C22⋊Dic5—22no—
99C2×C22⋊Dic5—22no—
100C2×C22⋊Dic5—22no—
101C2×C22⋊Dic5—22no—
102C2×C22⋊Dic5—22no—
103C2×C22⋊Dic5C2×C414yes—
104C2×C22⋊Dic5C2×C414yes—
105C2×C22⋊Dic5Q814yescomplemented
106C2×C4⋊Dic5—22no—
107C2×C4⋊Dic5—22no—
108C2×C4⋊Dic5C2×C414yes—
109#4070—232no—
110C2×#683—22no—
111C2×#683—22no—
112C2×#683—22no—
113C2×#683—22no—
114C2×#683—22no—
115C2×#683—22no—
116C2×#683—22no—
117C2×#683—41no—
118C2×#683C2×C414yes—
119C2×#683C2×C414yes—
120C2×#683D414yes—
121C2×#683D414yes—
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—22no—
131C2×C4×Dic5—41no—
132C2×C4×Dic5—41no—
133C2×C4×Dic5—41no—
134C5×#95—22no—
135C5×#95—22no—
136C5×#95—22no—
137C5×#95—22no—
138#3963—22no—
139#3963—22no—
140#3963—22no—
141#3963—22no—
142#3963—22no—
143#3963—22no—
144#3963—22no—
145#3963—22no—
146#3963—22no—
147#3963—22no—
148#3963—22no—
149#3963—41no—
150#3963—41no—
151#3963D414yes—
152C22×C22⋊Q8—51no—
153C2×#391—51no—
154C2×#387—51no—
155C2×C4×C4⋊C4—51no—
156C2×C4×C22⋊C4—51no—
157#1446—51no—
158#1441—51no—
159#1439—51no—
160#1439—51no—
161#1437—51no—
162#1437—51no—
163#1436—51no—
164#1436—51no—
165#1436—51no—
166C22⋊#95D511yescharacteristic
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—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—28no—
204C22×C4×C5—28no—
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—44no—
220C22×C4×C5—44no—
221C22×C4×C5—44no—
222C22×C4×C5—44no—
223C22×C4×C5—44no—
224C22×C4×C5C22×C412yes—
225C22×C4×C5C22×C412yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×D412yes—
229C22×C4×C5#4112yes—
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×Dic5C22×C412yes—
275C22×Dic5C22×C412yes—
276C22×Dic5C22×C412yes—
277C22×Dic5C22×C412yes—
278C22×Dic5C2×D412yes—
279C22×Dic5C2×D412yes—
280C22×Dic5C2×D412yes—
281C22×Dic5C2×D412yes—
282C22×Dic5C2×D412yes—
283C22×Dic5C2×D412yes—
284C22×Dic5C2×Q812yes—
285C22×Dic5C2×Q812yes—
286C22×Dic5#4112yes—
287C22×Dic5#4112yes—
288C2×Dic10—28no—
289C2×Dic10—28no—
290C2×Dic10—44no—
291C2×Dic10—44no—
292C2×Dic10—44no—
293C2×Dic10—44no—
294C2×Dic10—44no—
295C5×C22⋊C4—44no—
296C5×C22⋊C4—44no—
297C22⋊Dic5—28no—
298C22⋊Dic5—28no—
299C22⋊Dic5—28no—
300C22⋊Dic5—28no—
301C4⋊Dic5—28no—
302#683—28no—
303#683—28no—
304#683—44no—
305#683C22⋊C4116yescomplemented
306C4×Dic5—28no—
307C4×Dic5—44no—
308C4×Dic5—44no—
309C4×Dic5—44no—
310C23×Q8—51no—
311C24×C4C2×D511yescharacteristic
312C2×C22⋊Q8—58no—
313C2×C22⋊Q8—104no—
314C2×C22⋊Q8—104no—
315C22×C4⋊C4—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
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#391—104no—
331#387—104no—
332C4×C4⋊C4—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×#95C2×D511yescharacteristic
349C2×#95C2×D511yescharacteristic
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×Q814yes—
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—416no—
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×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×C5C2×C22⋊C414yes—
444C2×C4×C5C4×D414yes—
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—22no—
476C2×Dic5—22no—
477C2×Dic5—22no—
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×Dic5C2×C22⋊C414yes—
499C2×Dic5C2×C22⋊C414yes—
500C2×Dic5C22⋊Q814yescomplemented
501Dic10—416no—
502C25C22×D511yescharacteristic
503C22×Q8—54no—
504C22×Q8—102no—
505C22×Q8—102no—
506C22×Q8—102no—
507C22×Q8—102no—
508C22×Q8—201no—
509C22×Q8—201no—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4—51no—
517C23×C4—51no—
518C23×C4—51no—
519C23×C4—51no—
520C23×C4—51no—
521C23×C4—51no—
522C23×C4—51no—
523C23×C4—51no—
524C23×C4C4×D514yes—
525C23×C4C22×D511yescharacteristic
526C23×C4C22×D511yescharacteristic
527C23×C4C22×D511yescharacteristic
528C23×C4C22×D511yescharacteristic
529C23×C4C22×D511yescharacteristic
530C23×C4C22×D511yescharacteristic
531C22⋊Q8—1032no—
532C2×C4⋊C4—54no—
533C2×C4⋊C4—54no—
534C2×C4⋊C4—54no—
535C2×C4⋊C4—54no—
536C2×C4⋊C4—54no—
537C2×C4⋊C4—102no—
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—102no—
546C2×C4⋊C4—201no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—54no—
554C2×C22⋊C4—54no—
555C2×C22⋊C4—54no—
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—102no—
564C2×C22⋊C4—102no—
565C2×C42—102no—
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—201no—
575C2×C42—201no—
576C2×C42—201no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
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—102no—
592#95—102no—
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×C5C22×C22⋊C411yescharacteristic
611C22×C5C2×C4×D411yescharacteristic
612C22×C5C2×C4×Q811yescharacteristic
613C22×C5C4×#4111yescharacteristic
614C22×C5C4×#4111yescharacteristic
615C22×C5#51811yescharacteristic
616C22×C5#51911yescharacteristic
617C22×C5C2×C22⋊Q811yescharacteristic
618C22×C5#52511yescharacteristic
619C22×C5#52511yescharacteristic
620C22×C5#52511yescharacteristic
621C22×C5#52911yescharacteristic
622C22×C5#53211yescharacteristic
623C22×C5#53211yescharacteristic
624C22×C5#53311yescharacteristic
625C22×C5#53911yescharacteristic
626C22×C5#53911yescharacteristic
627C22×C5#54211yescharacteristic
628C22×C5#54211yescharacteristic
629C22×C5D4211yescharacteristic
630C22×C5D4211yescharacteristic
631C22×C5#54611yescharacteristic
632C22×C5#54611yescharacteristic
633C22×C5#54711yescharacteristic
634C22×C5#54811yescharacteristic
635C22×C5#54811yescharacteristic
636C22×C5#54811yescharacteristic
637C22×C5D4×Q811yescharacteristic
638C22×C5D4×Q811yescharacteristic
639C22×C5#55111yescharacteristic
640C22×C5#55111yescharacteristic
641C22×C5#55211yescharacteristic
642C22×C5#55411yescharacteristic
643C22×C5#55411yescharacteristic
644C22×C5#55611yescharacteristic
645C4×C5—24no—
646C4×C5—24no—
647C4×C5—42no—
648C4×C5—42no—
649C4×C5—81no—
650C4×C5—81no—
651Dic5—24no—
652Dic5—24no—
653Dic5—24no—
654Dic5—42no—
655Dic5—42no—
656Dic5—42no—
657Dic5—42no—
658Dic5—42no—
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—204no—
678C2×Q8—204no—
679C2×Q8—204no—
680C2×Q8—204no—
681C2×Q8—204no—
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—21no—
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—28no—
703C22×C4—28no—
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—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
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—52no—
736C22×C4—52no—
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×C4—101no—
779C22×C4C2×C4×D512yes—
780C22×C4C2×C4×D512yes—
781C22×C4#70912yes—
782C22×C4#70912yes—
783C22×C4D4×D512yes—
784C22×C4D4×D512yes—
785C22×C4D4×D512yes—
786C22×C4#71112yes—
787C4⋊C4—516no—
788C4⋊C4—108no—
789C4⋊C4—108no—
790C4⋊C4—108no—
791C4⋊C4—204no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—108no—
795C22⋊C4—108no—
796C22⋊C4—108no—
797C22⋊C4—108no—
798C42—108no—
799C42—204no—
800C42—204no—
801C42—204no—
802C2×C5—44no—
803C2×C5#229711yescharacteristic
804C2×C5C4×C22⋊Q811yescharacteristic
805C2×C5#233211yescharacteristic
806C2×C5D4×C22⋊C411yescharacteristic
807C2×C5Q8×C22⋊C411yescharacteristic
808C2×C5#236211yescharacteristic
809C2×C5#236811yescharacteristic
810C2×C5#244911yescharacteristic
811C2×C5#245211yescharacteristic
812C2×C5#246111yescharacteristic
813C2×C5#246311yescharacteristic
814C2×C5#246511yescharacteristic
815C2×C5#247711yescharacteristic
816C2×C5#255611yescharacteristic
817C2×C5#256011yescharacteristic
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#403314yes—
853C23C22×C4×D511yescharacteristic
854C23C2×#70911yescharacteristic
855C23C2×#70911yescharacteristic
856C23C2×D4×D511yescharacteristic
857C23C2×D4×D511yescharacteristic
858C23C2×D4×D511yescharacteristic
859C23C2×#71111yescharacteristic
860C23C2×#71111yescharacteristic
861C23#414411yescharacteristic
862C23#414411yescharacteristic
863C23C2×Q8×D511yescharacteristic
864C23D5×#4111yescharacteristic
865C23D5×#4111yescharacteristic
866C23#415011yescharacteristic
867C23#415011yescharacteristic
868Q8—2016no—
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—416no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
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—102no—
944C2×C4—102no—
945C2×C4—102no—
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×C4D5×C22⋊C414yes—
967C2×C4#402714yes—
968C5#1409911yescharacteristic, 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—
984C22C4×#70911yescharacteristic
985C22C2×D5×C22⋊C411yescharacteristic
986C22C2×#402711yescharacteristic
987C22#6582011yescharacteristic
988C22#6582911yescharacteristic
989C22#6582911yescharacteristic
990C22C2×#403311yescharacteristic
991C22#6584511yescharacteristic
992C22#6584511yescharacteristic
993C22#6585011yescharacteristic
994C22#6585611yescharacteristic
995C22#6587511yescharacteristic
996C22#6587611yescharacteristic
997C22#6588111yescharacteristic
998C22#6588111yescharacteristic
999C22#6588211yescharacteristic
1000C22#6588211yescharacteristic
1001C22#6588511yescharacteristic
1002C22#6588611yescharacteristic
1003C22#6592411yescharacteristic
1004C22#6592411yescharacteristic
1005C22#6592511yescharacteristic
1006C22#6592511yescharacteristic
1007C22#6593211yescharacteristic
1008C22#6593211yescharacteristic
1009C22#6593411yescharacteristic
1010C22#6594011yescharacteristic
1011C22#6595611yescharacteristic
1012C22D5×C22⋊Q811yescharacteristic
1013C22#6596611yescharacteristic
1014C22#6596611yescharacteristic
1015C22#6599411yescharacteristic
1016C22#6599411yescharacteristic
1017C22#6599611yescharacteristic
1018C22#6599611yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—81no—
1024C4—81no—
1025C4—104no—
1026C4—104no—
1027C4—104no—
1028C4—202no—
1029C4—202no—
1030C4—202no—
1031C4—202no—
1032C4—202no—
1033C2—44no—
1034C2#1060507011yescharacteristic
1035C2#1060519911yescharacteristic
1036C2#1060529411yescharacteristic
1037C2#1060558111yescharacteristic
1038C2#1060559711yescharacteristic
1039C2#1060560711yescharacteristic
1040C2#1060578811yescharacteristic
1041C2#1060615611yescharacteristic
1042C2#1060616411yescharacteristic
1043C2#1060620511yescharacteristic
1044C2#1060634011yescharacteristic
1045C2#1060644911yescharacteristic
1046C2#1060646311yescharacteristic
1047C2#1060649311yescharacteristic
1048C2#1060663111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22⋊#95D5
hypocenterC5#14099
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#64935C2semidirect
4. C2×#64941C2semidirect
5. C2×#64938C2semidirect
11. #10600217C2semidirect
12. #10600204C2semidirect
13. #10600200C2semidirect
14. #10600198C2semidirect
15. #10600198C2semidirect
27. C2×#4070C4semidirect
105. C2×C22⋊Dic5Q8semidirect
305. #683C22⋊C4semidirect
500. C2×Dic5C22⋊Q8semidirect
968. C5#14099semidirect

Maximal subgroups

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

subgroupindex
C22×#40702
C2×C4×C22⋊Dic52
C2×#649352
C2×#649412
C2×#649382
C5×C22⋊#952
#106023402
#106023382
#106002172
#106002042
#106002002
#106001982
#140995