Finite Group Databasebeta

← #12023095

Subgroups — #12023095

Order 1280.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4070C211yesmaximal, characteristic
2C22×#3963C211yesmaximal, characteristic
3C2×#65235C211yesmaximal, characteristic
4C2×C22⋊C4×Dic5C211yesmaximal, characteristic
5C2×#64935C211yesmaximal, characteristic, complemented
6C5×C22⋊#95C211yesmaximal, characteristic
7#10602337C211yesmaximal, characteristic
8#10602337C211yesmaximal, characteristic
9#10600217C211yesmaximal, characteristic, complemented
10#10600214C211yesmaximal, characteristic, complemented
11#10600204C211yesmaximal, characteristic, complemented
12#10600202C211yesmaximal, characteristic, complemented
13#10600200C211yesmaximal, characteristic, complemented
14#10600199C211yesmaximal, characteristic, complemented
15#10600197C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C24×Dic5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
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
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×#3963—24no—
39C2×#3963C2211yescharacteristic
40C2×#3963C2211yescharacteristic
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#65235—24no—
56C22⋊C4×Dic5—24no—
57#64935—24no—
58#14052—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×Dic5—22no—
74C23×Dic5—22no—
75C23×Dic5—22no—
76C23×Dic5—22no—
77C23×Dic5—22no—
78C23×Dic5—22no—
79C23×Dic5—22no—
80C23×Dic5—22no—
81C23×Dic5—22no—
82C23×Dic5—41no—
83C23×Dic5—41no—
84C23×Dic5—41no—
85C23×Dic5—41no—
86C23×Dic5Q814yescomplemented
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C22×Dic10—22no—
96C22×Dic10—22no—
97C22×Dic10—22no—
98C22×Dic10—22no—
99C22×Dic10—41no—
100C22×Dic10—41no—
101C22×Dic10C2×C414yescomplemented
102C2×C5×C22⋊C4—22no—
103C2×C5×C22⋊C4—22no—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—22no—
106C2×C5×C22⋊C4—22no—
107C2×C5×C22⋊C4Q814yescomplemented
108C2×C22⋊Dic5—22no—
109C2×C22⋊Dic5—22no—
110C2×C22⋊Dic5C2×C414yes—
111C2×C22⋊Dic5C2×C414yes—
112C2×C22⋊Dic5D414yes—
113C2×C22⋊Dic5D414yes—
114C2×C4⋊Dic5—22no—
115C2×C4⋊Dic5—22no—
116C2×C4⋊Dic5C2×C414yescomplemented
117#4070—232no—
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×#683—41no—
128C2×#683C2×C414yescomplemented
129C2×#683C2×C414yescomplemented
130C2×C4×Dic5—22no—
131C2×C4×Dic5—22no—
132C2×C4×Dic5—22no—
133C2×C4×Dic5—22no—
134C2×C4×Dic5—41no—
135C2×C4×Dic5—41no—
136C5×#95—22no—
137C5×#95—22no—
138C5×#95—41no—
139C5×#95—41no—
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—22no—
150#3963—22no—
151#3963—41no—
152#3963—41no—
153#3963—41no—
154#3963—41no—
155#3963D414yes—
156C22×C22⋊Q8—51no—
157C2×#391—51no—
158C2×#385—51no—
159C2×C4×C22⋊C4—51no—
160C22×#95—51no—
161#1446—51no—
162#1445—51no—
163#1441—51no—
164#1441—51no—
165#1436—51no—
166#1436—51no—
167C4⋊#95—51no—
168C22⋊#95—51no—
169C22⋊#95—51no—
170C22⋊#95D511yescharacteristic
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×D412yes—
181C24×C5C2×D412yes—
182C24×C5C2×Q812yes—
183C24×C5C2×Q812yes—
184C24×C5#4112yes—
185C24×C5#4112yes—
186C24×C5C2411yescharacteristic
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—28no—
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×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—44no—
226C22×C4×C5—44no—
227C22×C4×C5—44no—
228C22×C4×C5—44no—
229C22×C4×C5—44no—
230C22×C4×C5C22×C412yes—
231C22×C4×C5C22×C412yes—
232C22×C4×C5C2×D412yes—
233C22×C4×C5C2×Q812yes—
234C22×C4×C5C2×Q812yes—
235C22×C4×C5#4112yes—
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—28no—
249C22×Dic5—28no—
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×Dic5—21no—
276C22×Dic5—21no—
277C22×Dic5—21no—
278C22×Dic5—21no—
279C22×Dic5—21no—
280C22×Dic5—28no—
281C22×Dic5—44no—
282C22×Dic5—44no—
283C22×Dic5—44no—
284C22×Dic5—44no—
285C22×Dic5—44no—
286C22×Dic5—44no—
287C22×Dic5—44no—
288C22×Dic5—44no—
289C22×Dic5—44no—
290C22×Dic5—44no—
291C22×Dic5—44no—
292C22×Dic5C22×C412yes—
293C22×Dic5C22×C412yes—
294C22×Dic5C22×C412yes—
295C22×Dic5C22×C412yes—
296C22×Dic5C2×D412yes—
297C22×Dic5C2×D412yes—
298C22×Dic5C2×D412yes—
299C22×Dic5C2×D412yes—
300C22×Dic5C2×D412yes—
301C22×Dic5C2×D412yes—
302C22×Dic5C2×Q812yes—
303C22×Dic5C2×Q812yes—
304C22×Dic5#4112yes—
305C22×Dic5#4112yes—
306C2×Dic10—28no—
307C2×Dic10—28no—
308C2×Dic10—44no—
309C2×Dic10—44no—
310C2×Dic10—44no—
311C2×Dic10—44no—
312C2×Dic10—44no—
313C5×C22⋊C4—28no—
314C5×C22⋊C4—44no—
315C22⋊Dic5—28no—
316C22⋊Dic5C22⋊C4116yes—
317C4⋊Dic5—28no—
318#683—28no—
319#683—28no—
320#683—44no—
321#683—44no—
322C4×Dic5—44no—
323C4×Dic5—44no—
324C23×Q8—51no—
325C24×C4—51no—
326C24×C4—51no—
327C24×C4C2×D511yescharacteristic
328C2×C22⋊Q8—58no—
329C2×C22⋊Q8—104no—
330C2×C22⋊Q8—104no—
331C22×C4⋊C4—51no—
332C22×C4⋊C4—51no—
333C22×C4⋊C4—51no—
334C22×C4⋊C4—51no—
335C22×C4⋊C4—51no—
336C22×C22⋊C4—51no—
337C22×C22⋊C4—51no—
338C22×C22⋊C4C2×D511yescharacteristic
339C22×C22⋊C4C2×D511yescharacteristic
340C22×C42—51no—
341C22×C42—51no—
342#391—104no—
343#385—104no—
344C4×C22⋊C4—104no—
345C2×#95—51no—
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×#95—51no—
360C2×#95—51no—
361C2×#95—104no—
362C2×#95C2×D511yescharacteristic
363C2×#95C2×D511yescharacteristic
364C2×#95C2×D511yescharacteristic
365C2×#95C2×D511yescharacteristic
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—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5C2×C22⋊C414yes—
395C23×C5C4×Q814yes—
396C23×C5C4×Q814yes—
397C23×C5C22⋊Q814yes—
398C23×C5C22⋊Q814yes—
399C23×C5#12414yes—
400C23×C5C4⋊Q814yes—
401C23×C5C23×C411yescharacteristic
402C23×C5C22×D411yescharacteristic
403C23×C5C22×D411yescharacteristic
404C23×C5C22×D411yescharacteristic
405C23×C5C22×Q811yescharacteristic
406C23×C5C22×Q811yescharacteristic
407C23×C5C2×#4111yescharacteristic
408C23×C5C2×#4111yescharacteristic
409C23×C5C2×#4111yescharacteristic
410C23×C5C2×#4111yescharacteristic
411C23×C5C2×#4111yescharacteristic
412C23×C5H(5,𝔽2)11yescharacteristic
413C23×C5H(5,𝔽2)11yescharacteristic
414C23×C5H(5,𝔽2)11yescharacteristic
415C23×C52−1+411yescharacteristic
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—416no—
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×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×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5C4×D414yes—
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—22no—
479C2×Dic5—22no—
480C2×Dic5—22no—
481C2×Dic5—22no—
482C2×Dic5—22no—
483C2×Dic5—22no—
484C2×Dic5—22no—
485C2×Dic5—22no—
486C2×Dic5—22no—
487C2×Dic5—22no—
488C2×Dic5—22no—
489C2×Dic5—22no—
490C2×Dic5—22no—
491C2×Dic5—22no—
492C2×Dic5—416no—
493C2×Dic5—416no—
494C2×Dic5—41no—
495C2×Dic5—41no—
496C2×Dic5—41no—
497C2×Dic5—41no—
498C2×Dic5—41no—
499C2×Dic5—41no—
500C2×Dic5—41no—
501C2×Dic5—41no—
502C2×Dic5—41no—
503C2×Dic5—41no—
504C2×Dic5—41no—
505C2×Dic5—41no—
506C2×Dic5—41no—
507C2×Dic5—41no—
508C2×Dic5—41no—
509C2×Dic5—41no—
510C2×Dic5—41no—
511C2×Dic5—41no—
512C2×Dic5—41no—
513C2×Dic5—41no—
514C2×Dic5C2×C22⋊C414yes—
515C2×Dic5C2×C22⋊C414yes—
516C2×Dic5C22⋊Q814yescomplemented
517Dic10—416no—
518C25C22×D511yescharacteristic
519C22×Q8—54no—
520C22×Q8—102no—
521C22×Q8—102no—
522C22×Q8—102no—
523C22×Q8—102no—
524C22×Q8—201no—
525C22×Q8—201no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—22no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4—51no—
533C23×C4—51no—
534C23×C4—51no—
535C23×C4—51no—
536C23×C4—51no—
537C23×C4—51no—
538C23×C4—51no—
539C23×C4—51no—
540C23×C4—54no—
541C23×C4—102no—
542C23×C4—102no—
543C23×C4—102no—
544C23×C4—102no—
545C23×C4—102no—
546C23×C4—102no—
547C23×C4—102no—
548C23×C4—102no—
549C23×C4—102no—
550C23×C4—201no—
551C23×C4—201no—
552C23×C4—201no—
553C23×C4—201no—
554C23×C4C4×D514yes—
555C23×C4C22×D511yescharacteristic
556C23×C4C22×D511yescharacteristic
557C23×C4C22×D511yescharacteristic
558C23×C4C22×D511yescharacteristic
559C23×C4C22×D511yescharacteristic
560C23×C4C22×D511yescharacteristic
561C22⋊Q8—1032no—
562C2×C4⋊C4—54no—
563C2×C4⋊C4—54no—
564C2×C4⋊C4—54no—
565C2×C4⋊C4—102no—
566C2×C4⋊C4—102no—
567C2×C4⋊C4—102no—
568C2×C4⋊C4—102no—
569C2×C4⋊C4—102no—
570C2×C4⋊C4—102no—
571C2×C4⋊C4—102no—
572C2×C4⋊C4—102no—
573C2×C4⋊C4—102no—
574C2×C4⋊C4—102no—
575C2×C4⋊C4—201no—
576C2×C4⋊C4—201no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—54no—
583C2×C22⋊C4—54no—
584C2×C22⋊C4—54no—
585C2×C22⋊C4—54no—
586C2×C22⋊C4—102no—
587C2×C22⋊C4—102no—
588C2×C22⋊C4Dic1014yescomplemented
589C2×C42—102no—
590C2×C42—102no—
591C2×C42—102no—
592C2×C42—102no—
593C2×C42—201no—
594C2×C42—201no—
595#95—22no—
596#95—22no—
597#95—41no—
598#95—41no—
599#95—54no—
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—
609#95—102no—
610#95—102no—
611#95—201no—
612#95—201no—
613#95—201no—
614#95—201no—
615C22×C5—24no—
616C22×C5—24no—
617C22×C5—24no—
618C22×C5—24no—
619C22×C5—24no—
620C22×C5—24no—
621C22×C5—24no—
622C22×C5—24no—
623C22×C5—24no—
624C22×C5—24no—
625C22×C5—24no—
626C22×C5—24no—
627C22×C5—24no—
628C22×C5—24no—
629C22×C5#39118yescomplemented
630C22×C5C22×C22⋊C411yescharacteristic
631C22×C5C2×C4×D411yescharacteristic
632C22×C5C2×C4×Q811yescharacteristic
633C22×C5C2×C4×Q811yescharacteristic
634C22×C5C4×#4111yescharacteristic
635C22×C5#51811yescharacteristic
636C22×C5#52011yescharacteristic
637C22×C5C2×C22⋊Q811yescharacteristic
638C22×C5C2×C22⋊Q811yescharacteristic
639C22×C5C2×C22⋊Q811yescharacteristic
640C22×C5#52511yescharacteristic
641C22×C5C2×#12411yescharacteristic
642C22×C5#52911yescharacteristic
643C22×C5C2×C4⋊Q811yescharacteristic
644C22×C5#53311yescharacteristic
645C22×C5#53811yescharacteristic
646C22×C5#53911yescharacteristic
647C22×C5#54311yescharacteristic
648C22×C5#54411yescharacteristic
649C22×C5D4211yescharacteristic
650C22×C5D4211yescharacteristic
651C22×C5#54611yescharacteristic
652C22×C5#54611yescharacteristic
653C22×C5#54611yescharacteristic
654C22×C5#54611yescharacteristic
655C22×C5#54611yescharacteristic
656C22×C5#54711yescharacteristic
657C22×C5#54711yescharacteristic
658C22×C5D4×Q811yescharacteristic
659C22×C5#55111yescharacteristic
660C22×C5#55111yescharacteristic
661C22×C5#55211yescharacteristic
662C22×C5#55411yescharacteristic
663C22×C5#55411yescharacteristic
664C22×C5#55411yescharacteristic
665C4×C5—24no—
666C4×C5—42no—
667C4×C5—42no—
668C4×C5—42no—
669C4×C5—81no—
670C4×C5—81no—
671Dic5—24no—
672Dic5—24no—
673Dic5—24no—
674Dic5—42no—
675Dic5—42no—
676Dic5—42no—
677Dic5—42no—
678Dic5—42no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×Dic1012yes—
688C24C2×C4×D512yes—
689C24#70912yes—
690C24D4×D512yes—
691C24D4×D512yes—
692C24#71112yes—
693C24Q8×D512yes—
694C24C23×D511yescharacteristic
695C2×Q8—108no—
696C2×Q8—108no—
697C2×Q8—204no—
698C2×Q8—204no—
699C2×Q8—204no—
700C2×Q8—204no—
701C2×Q8—204no—
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—28no—
725C22×C4—28no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—52no—
746C22×C4—52no—
747C22×C4—52no—
748C22×C4—52no—
749C22×C4—52no—
750C22×C4—52no—
751C22×C4—52no—
752C22×C4—52no—
753C22×C4—52no—
754C22×C4—52no—
755C22×C4—52no—
756C22×C4—52no—
757C22×C4—52no—
758C22×C4—52no—
759C22×C4—108no—
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—108no—
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—101no—
789C22×C4—101no—
790C22×C4—101no—
791C22×C4—101no—
792C22×C4—101no—
793C22×C4—101no—
794C22×C4—101no—
795C22×C4—101no—
796C22×C4—101no—
797C22×C4—101no—
798C22×C4—101no—
799C22×C4—101no—
800C22×C4—101no—
801C22×C4—101no—
802C22×C4—101no—
803C22×C4—108no—
804C22×C4—204no—
805C22×C4—204no—
806C22×C4—204no—
807C22×C4—204no—
808C22×C4—204no—
809C22×C4—204no—
810C22×C4—204no—
811C22×C4—204no—
812C22×C4—204no—
813C22×C4—204no—
814C22×C4—204no—
815C22×C4C2×Dic1012yes—
816C22×C4C2×Dic1012yes—
817C22×C4C2×C4×D512yes—
818C22×C4C2×C4×D512yes—
819C22×C4D4×D512yes—
820C22×C4#71112yes—
821C4⋊C4—108no—
822C4⋊C4—108no—
823C4⋊C4—108no—
824C4⋊C4—204no—
825C4⋊C4—204no—
826C22⋊C4—28no—
827C22⋊C4—44no—
828C22⋊C4—516no—
829C22⋊C4—108no—
830C42—204no—
831C42—204no—
832C2×C5—28no—
833C2×C5C2×#39111yescharacteristic
834C2×C5C4×C22⋊Q811yescharacteristic
835C2×C5#232911yescharacteristic
836C2×C5D4×C22⋊C411yescharacteristic
837C2×C5#233911yescharacteristic
838C2×C5#236011yescharacteristic
839C2×C5#236811yescharacteristic
840C2×C5#243711yescharacteristic
841C2×C5#243811yescharacteristic
842C2×C5#244011yescharacteristic
843C2×C5#244911yescharacteristic
844C2×C5#245011yescharacteristic
845C2×C5#247211yescharacteristic
846C2×C5#248811yescharacteristic
847C2×C5#254911yescharacteristic
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23C4×Dic1014yes—
877C23#402414yes—
878C23D5×C22⋊C414yes—
879C23#403114yes—
880C23#403314yes—
881C23#403414yes—
882C23#404214yes—
883C23C22×Dic1011yescharacteristic
884C23C22×C4×D511yescharacteristic
885C23C2×#70911yescharacteristic
886C23C2×D4×D511yescharacteristic
887C23C2×D4×D511yescharacteristic
888C23C2×D4×D511yescharacteristic
889C23C2×#71111yescharacteristic
890C23C2×#71111yescharacteristic
891C23#414411yescharacteristic
892C23#414411yescharacteristic
893C23C2×Q8×D511yescharacteristic
894C23D5×#4111yescharacteristic
895C23D5×#4111yescharacteristic
896C23#414911yescharacteristic
897C23#415011yescharacteristic
898Q8—2016no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—416no—
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—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—54no—
942C2×C4—54no—
943C2×C4—54no—
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—102no—
955C2×C4—102no—
956C2×C4—102no—
957C2×C4—102no—
958C2×C4—102no—
959C2×C4—102no—
960C2×C4—102no—
961C2×C4—102no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—102no—
965C2×C4—102no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—102no—
969C2×C4—102no—
970C2×C4—102no—
971C2×C4—102no—
972C2×C4—102no—
973C2×C4—102no—
974C2×C4—102no—
975C2×C4—102no—
976C2×C4—102no—
977C2×C4—2016no—
978C2×C4—2016no—
979C2×C4—201no—
980C2×C4—201no—
981C2×C4—201no—
982C2×C4—201no—
983C2×C4—201no—
984C2×C4—201no—
985C2×C4—201no—
986C2×C4—201no—
987C2×C4—201no—
988C2×C4—201no—
989C2×C4—201no—
990C2×C4—201no—
991C2×C4—201no—
992C2×C4—201no—
993C2×C4—201no—
994C2×C4—201no—
995C2×C4—201no—
996C2×C4—201no—
997C2×C4—201no—
998C2×C4—201no—
999C2×C4#402714yes—
1000C5#1405211yescharacteristic, complemented, Sylow
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#6493518yescomplemented
1016C22C2×C4×Dic1011yescharacteristic
1017C22C2×#402411yescharacteristic
1018C22C2×D5×C22⋊C411yescharacteristic
1019C22C2×#402711yescharacteristic
1020C22#6582011yescharacteristic
1021C22C2×#403111yescharacteristic
1022C22C2×#403311yescharacteristic
1023C22C2×#403411yescharacteristic
1024C22C2×#404211yescharacteristic
1025C22#6585611yescharacteristic
1026C22#6585711yescharacteristic
1027C22D4×Dic1011yescharacteristic
1028C22#6587311yescharacteristic
1029C22#6587311yescharacteristic
1030C22#6587511yescharacteristic
1031C22#6587711yescharacteristic
1032C22#6588411yescharacteristic
1033C22#6589011yescharacteristic
1034C22#6589011yescharacteristic
1035C22#6592411yescharacteristic
1036C22#6592411yescharacteristic
1037C22#6592511yescharacteristic
1038C22#6592511yescharacteristic
1039C22#6593411yescharacteristic
1040C22#6593611yescharacteristic
1041C22#6594011yescharacteristic
1042C22#6595111yescharacteristic
1043C22#6595611yescharacteristic
1044C22#6595711yescharacteristic
1045C22D5×C22⋊Q811yescharacteristic
1046C22#6596811yescharacteristic
1047C22#6598811yescharacteristic
1048C22#6598811yescharacteristic
1049C22#6598911yescharacteristic
1050C22#6598911yescharacteristic
1051C4—24no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—81no—
1056C4—81no—
1057C4—104no—
1058C4—104no—
1059C4—104no—
1060C4—202no—
1061C4—202no—
1062C4—202no—
1063C4—202no—
1064C4—202no—
1065C2—28no—
1066C2C2×#6493511yescharacteristic
1067C2#1060519611yescharacteristic
1068C2#1060520411yescharacteristic
1069C2#1060558111yescharacteristic
1070C2#1060559711yescharacteristic
1071C2#1060560511yescharacteristic
1072C2#1060585211yescharacteristic
1073C2#1060614511yescharacteristic
1074C2#1060614711yescharacteristic
1075C2#1060620311yescharacteristic
1076C2#1060633811yescharacteristic
1077C2#1060644011yescharacteristic
1078C2#1060644211yescharacteristic
1079C2#1060645911yescharacteristic
1080C2#1060647111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22⋊#95D5
hypocenterC5#14052
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
5. C2×#64935C2semidirect
9. #10600217C2semidirect
10. #10600214C2semidirect
11. #10600204C2semidirect
12. #10600202C2semidirect
13. #10600200C2semidirect
14. #10600199C2semidirect
15. #10600197C2semidirect
27. C2×#4070C4semidirect
86. C23×Dic5Q8semidirect
101. C22×Dic10C2×C4semidirect
107. C2×C5×C22⋊C4Q8semidirect
116. C2×C4⋊Dic5C2×C4semidirect
128. C2×#683C2×C4semidirect
129. C2×#683C2×C4semidirect
516. C2×Dic5C22⋊Q8semidirect
588. C2×C22⋊C4Dic10semidirect
629. C22×C5#391semidirect
1000. C5#14052semidirect
1015. C22#64935semidirect

Maximal subgroups

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

subgroupindex
C22×#40702
C22×#39632
C2×#652352
C2×C22⋊C4×Dic52
C2×#649352
C5×C22⋊#952
#106023372
#106002172
#106002142
#106002042
#106002022
#106002002
#106001992
#106001972
#140525