Finite Group Databasebeta

← #12007111

Subgroups — #12007111

Order 1280.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3941C211yesmaximal, characteristic
2C22×#3941C211yesmaximal, characteristic
3C2×#65228C211yesmaximal, characteristic
4C5×C4⋊#95C211yesmaximal, characteristic, complemented
5C2×#64749C211yesmaximal, characteristic, complemented
6C2×#64749C211yesmaximal, characteristic, complemented
7C2×#64744C211yesmaximal, characteristic, complemented
8C23×D20C2211yescharacteristic
9C22×C5×C4⋊C4C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C42×C5C2211yescharacteristic
12C22×#685—21no—
13C22×#685—21no—
14C22×C4⋊Dic5C2211yescharacteristic
15C23×#168C2211yescharacteristic
16C23×#168C2211yescharacteristic
17C2×C5×#95—21no—
18C2×C5×#95—21no—
19C2×#3941—22no—
20C2×#3941—22no—
21C2×#3941—22no—
22C2×#3941—22no—
23C2×#3941—22no—
24C2×#3941C414yescomplemented
25#65228—22no—
26#65228—22no—
27#64749—22no—
28#64749—22no—
29#64744—22no—
30#11189—51nomaximal, Sylow
31C24×D5—21no—
32C23×C4×C5—21no—
33C23×C4×C5—21no—
34C23×C4×C5D411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C23×C4×C5C2311yescharacteristic
37C23×Dic5—21no—
38C22×D20—21no—
39C22×D20—21no—
40C22×D20—21no—
41C22×D20—21no—
42C22×D20—21no—
43C22×D20—21no—
44C22×D20—21no—
45C22×D20—21no—
46C22×D20—21no—
47C22×D20—21no—
48C22×D20—21no—
49C22×D20C2×C412yes—
50C22×D20D412yes—
51C22×D20D412yes—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4—21no—
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4—21no—
62C2×C5×C4⋊C4C2×C412yes—
63C2×C5×C4⋊C4D412yes—
64C2×C42×C5—21no—
65C2×C42×C5—21no—
66C2×C42×C5—21no—
67C2×C42×C5—21no—
68C2×C42×C5—21no—
69C2×C42×C5—21no—
70C2×#685—24no—
71C2×#685—24no—
72C2×#685—42no—
73C2×#685—42no—
74C2×#685—42no—
75C2×#685—42no—
76C2×C4⋊Dic5—21no—
77C2×C4⋊Dic5—21no—
78C2×C4⋊Dic5—21no—
79C2×C4⋊Dic5—21no—
80C2×C4⋊Dic5—21no—
81C2×C4⋊Dic5D412yes—
82C22×#168—21no—
83C22×#168—21no—
84C22×#168—21no—
85C22×#168—21no—
86C22×#168—21no—
87C22×#168—21no—
88C22×#168—21no—
89C22×#168—21no—
90C22×#168—21no—
91C22×#168—21no—
92C22×#168—21no—
93C22×#168—21no—
94C22×#168C2×C412yes—
95C22×#168D412yes—
96C5×#95—42no—
97C5×#95—42no—
98#3941—28no—
99#3941—28no—
100C22×#102—51no—
101C22×#102—51no—
102C2×#390—51no—
103C2×#340—51no—
104C2×#340—51no—
105C2×#336—51no—
106C4⋊#95D511yescharacteristic, complemented
107C24×C5C2×D411yescharacteristic
108C23×D5—22no—
109C23×D5—22no—
110C23×D5—22no—
111C23×D5—41no—
112C23×D5—41no—
113C23×D5—41no—
114C23×D5—41no—
115C23×D5—41no—
116C23×D5—41no—
117C23×D5—41no—
118C23×D5—41no—
119C23×D5—41no—
120C23×D5—41no—
121C23×D5—41no—
122C23×D5—41no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—41no—
138C22×C4×C5—41no—
139C22×C4×C5—41no—
140C22×C4×C5—41no—
141C22×C4×C5—41no—
142C22×C4×C5—41no—
143C22×C4×C5—41no—
144C22×C4×C5—41no—
145C22×C4×C5—41no—
146C22×C4×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5—41no—
149C22×C4×C5D812yes—
150C22×C4×C5SD1612yes—
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5#4111yescharacteristic
158C22×C4×C5#4111yescharacteristic
159C22×C4×C5#4111yescharacteristic
160C22×C4×C5#4111yescharacteristic
161C22×C4×C5#4111yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C22×C4×C5#4111yescharacteristic
164C22×C4×C5#4111yescharacteristic
165C22×Dic5—22no—
166C22×Dic5—41no—
167C22×Dic5—41no—
168C22×Dic5—41no—
169C22×Dic5—41no—
170C22×Dic5—41no—
171C22×Dic5—41no—
172C2×D20—22no—
173C2×D20—22no—
174C2×D20—22no—
175C2×D20—22no—
176C2×D20—22no—
177C2×D20—22no—
178C2×D20—22no—
179C2×D20—22no—
180C2×D20—22no—
181C2×D20—22no—
182C2×D20—22no—
183C2×D20—22no—
184C2×D20—22no—
185C2×D20—22no—
186C2×D20—22no—
187C2×D20—41no—
188C2×D20—41no—
189C2×D20—41no—
190C2×D20—41no—
191C2×D20—41no—
192C2×D20—41no—
193C2×D20—41no—
194C2×D20—41no—
195C2×D20—41no—
196C2×D20—41no—
197C2×D20—41no—
198C2×D20—41no—
199C2×D20C22⋊C414yes—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—41no—
205C5×C4⋊C4—41no—
206C5×C4⋊C4—41no—
207C5×C4⋊C4—41no—
208C42×C5—41no—
209C42×C5—41no—
210C42×C5—41no—
211C42×C5—41no—
212#685—48no—
213#685—48no—
214C4⋊Dic5—22no—
215C4⋊Dic5—22no—
216C4⋊Dic5—41no—
217C4⋊Dic5—41no—
218C2×#168—22no—
219C2×#168—22no—
220C2×#168—22no—
221C2×#168—22no—
222C2×#168—22no—
223C2×#168—22no—
224C2×#168—41no—
225C2×#168—41no—
226C2×#168—41no—
227C2×#168—41no—
228C2×#168—41no—
229C2×#168—41no—
230C2×#168—41no—
231C2×#168—41no—
232C23×D4—51no—
233C23×C8—51no—
234C23×C8—51no—
235C22×C4⋊C4—51no—
236C22×C4⋊C4C2×D511yescharacteristic
237C22×C4⋊C4C2×D511yescharacteristic
238C22×C22⋊C4—101no—
239C22×C22⋊C4—101no—
240C22×C42C2×D511yescharacteristic
241C2×#102—54no—
242C2×#102—102no—
243C2×#102—102no—
244C2×#102—102no—
245C2×#102—102no—
246C2×#102—102no—
247#390—102no—
248#390—102no—
249C2×#95—21no—
250C2×#95—21no—
251#340—102no—
252#340—102no—
253#336—102no—
254C23×C5C4×D411yescharacteristic
255C23×C5#12011yescharacteristic
256C23×C5#12111yescharacteristic
257C23×C5#12111yescharacteristic
258C23×C5#12111yescharacteristic
259C23×C5#12311yescharacteristic
260C23×C5#12411yescharacteristic
261C23×C5C2×D811yescharacteristic
262C23×C5C2×SD1611yescharacteristic
263C23×C5#13511yescharacteristic
264C23×C5#13511yescharacteristic
265C23×C5AGL(1,ℤ/8)11yescharacteristic
266C23×C5AGL(1,ℤ/8)11yescharacteristic
267C23×C5AGL(1,ℤ/8)11yescharacteristic
268C23×C5#13711yescharacteristic
269C22×D5—24no—
270C22×D5—42no—
271C22×D5—42no—
272C22×D5—42no—
273C22×D5—42no—
274C22×D5—42no—
275C22×D5—42no—
276C22×D5—42no—
277C22×D5—42no—
278C22×D5—42no—
279C22×D5—42no—
280C22×D5—42no—
281C22×D5—42no—
282C22×D5—42no—
283C22×D5—42no—
284C22×D5—42no—
285C22×D5—42no—
286C22×D5—42no—
287C22×D5—42no—
288C22×D5—81no—
289C22×D5—81no—
290C22×D5—81no—
291C22×D5—81no—
292C22×D5—81no—
293C22×D5—81no—
294C22×D5—81no—
295C22×D5—81no—
296C22×D5—81no—
297C22×D5—81no—
298C22×D5—81no—
299C22×D5—81no—
300C22×D5—81no—
301C22×D5—81no—
302C22×D5—81no—
303C22×D5—81no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—81no—
325C2×C4×C5—81no—
326C2×C4×C5—81no—
327C2×C4×C5—81no—
328C2×C4×C5—81no—
329C2×C4×C5—81no—
330C2×C4×C5—81no—
331C2×C4×C5—81no—
332C2×C4×C5C2×C22⋊C411yescharacteristic
333C2×C4×C5#11711yescharacteristic
334C2×C4×C5#11711yescharacteristic
335C2×C4×C5C4×D411yescharacteristic
336C2×C4×C5C4×D411yescharacteristic
337C2×C4×C5C4×D411yescharacteristic
338C2×C4×C5#12011yescharacteristic
339C2×C4×C5#12111yescharacteristic
340C2×C4×C5#12111yescharacteristic
341C2×C4×C5#12111yescharacteristic
342C2×C4×C5#12111yescharacteristic
343C2×C4×C5#12111yescharacteristic
344C2×C4×C5#12311yescharacteristic
345C2×C4×C5#12311yescharacteristic
346C2×C4×C5#12311yescharacteristic
347C2×C4×C5#12311yescharacteristic
348C2×C4×C5#12311yescharacteristic
349C2×C4×C5#12311yescharacteristic
350C2×C4×C5#12311yescharacteristic
351C2×C4×C5#12311yescharacteristic
352C2×C4×C5#12311yescharacteristic
353C2×C4×C5#12411yescharacteristic
354C2×C4×C5#12411yescharacteristic
355C2×C4×C5#12411yescharacteristic
356C2×C4×C5#12611yescharacteristic
357C2×C4×C5#12611yescharacteristic
358C2×C4×C5#12611yescharacteristic
359C2×C4×C5#12611yescharacteristic
360C2×Dic5—42no—
361C2×Dic5—42no—
362C2×Dic5—42no—
363C2×Dic5—81no—
364C2×Dic5—81no—
365C2×Dic5—81no—
366C2×Dic5—81no—
367D20—24no—
368D20—24no—
369D20—42no—
370D20—42no—
371D20—42no—
372D20—42no—
373D20—42no—
374D20—42no—
375#168—42no—
376#168—42no—
377C25—101no—
378C22×D4—52no—
379C22×D4—52no—
380C22×D4—52no—
381C22×D4—101no—
382C22×D4—101no—
383C22×D4—101no—
384C22×D4—101no—
385C22×D4—101no—
386C22×D4—101no—
387C22×D4—101no—
388C22×D4—101no—
389C22×D4—101no—
390C22×D4—101no—
391C22×D4—101no—
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—101no—
395C23×C4C22⋊D511yescharacteristic
396C23×C4C22⋊D511yescharacteristic
397C23×C4C22×D511yescharacteristic
398C22×C8—52no—
399C22×C8—52no—
400C22×C8—101no—
401C22×C8—101no—
402C22×C8—101no—
403C22×C8—101no—
404C22×C8—101no—
405C22×C8—101no—
406C22×C8—101no—
407C22×C8—101no—
408C22×C8—101no—
409C22×C8—101no—
410C22×C8—101no—
411C22×C8—101no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—52no—
423C2×C4⋊C4—101no—
424C2×C4⋊C4—101no—
425C2×C4⋊C4—101no—
426C2×C4⋊C4—101no—
427C2×C4⋊C4—101no—
428C2×C4⋊C4C4×D512yes—
429C2×C4⋊C4D2012yes—
430C2×C22⋊C4—104no—
431C2×C22⋊C4—104no—
432C2×C22⋊C4—202no—
433C2×C22⋊C4—202no—
434C2×C22⋊C4—202no—
435C2×C22⋊C4—202no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442#102—108no—
443#102—108no—
444#95—42no—
445#95—42no—
446C22×C5#38611yescharacteristic
447C22×C5#38811yescharacteristic
448C22×C5#38811yescharacteristic
449C22×C5#39411yescharacteristic
450C22×C5#39411yescharacteristic
451C22×C5#39411yescharacteristic
452C22×C5#39711yescharacteristic
453C22×C5C4×D811yescharacteristic
454C22×C5C4×SD1611yescharacteristic
455C22×C5#44011yescharacteristic
456C22×C5#44211yescharacteristic
457C22×C5#44711yescharacteristic
458C22×C5#44911yescharacteristic
459C22×C5#45011yescharacteristic
460C22×C5#45211yescharacteristic
461C22×C5#45911yescharacteristic
462C22×C5#45911yescharacteristic
463C22×C5#46011yescharacteristic
464C22×C5#46111yescharacteristic
465C22×C5#46311yescharacteristic
466C22×C5#46311yescharacteristic
467C22×C5#46311yescharacteristic
468C22×C5#46411yescharacteristic
469C22×C5#46511yescharacteristic
470C22×C5#46611yescharacteristic
471C22×C5#46811yescharacteristic
472C22×C5#46911yescharacteristic
473C22×C5#48011yescharacteristic
474C22×C5#48111yescharacteristic
475C22×C5#48211yescharacteristic
476C22×C5#48211yescharacteristic
477C22×C5#48611yescharacteristic
478C22×C5#48811yescharacteristic
479C22×C5#48911yescharacteristic
480C22×C5#49011yescharacteristic
481C2×D5—44no—
482C2×D5—44no—
483C2×D5—44no—
484C2×D5—82no—
485C2×D5—82no—
486C2×D5—82no—
487C2×D5—82no—
488C2×D5—82no—
489C2×D5—82no—
490C2×D5—82no—
491C2×D5—82no—
492C2×D5—82no—
493C2×D5—82no—
494C2×D5—82no—
495C2×D5—82no—
496C4×C5—42no—
497C4×C5—42no—
498C4×C5—82no—
499C4×C5—82no—
500C4×C5#38111yescharacteristic
501C4×C5#38611yescharacteristic
502C4×C5#38811yescharacteristic
503C4×C5#38811yescharacteristic
504C4×C5#39411yescharacteristic
505C4×C5#39711yescharacteristic
506C4×C5#39711yescharacteristic
507C4×C5#39711yescharacteristic
508Dic5—82no—
509C24—102no—
510C24—102no—
511C24—102no—
512C24—201no—
513C24—201no—
514C24—201no—
515C24—201no—
516C24—201no—
517C24—201no—
518C24—201no—
519C24—201no—
520C24—201no—
521C24—201no—
522C24—201no—
523C24—201no—
524C24C2×C22⋊D511yescharacteristic
525C2×D4—54no—
526C2×D4—102no—
527C2×D4—102no—
528C2×D4—102no—
529C2×D4—102no—
530C2×D4—102no—
531C2×D4—102no—
532C2×D4—102no—
533C2×D4—102no—
534C2×D4—102no—
535C2×D4—102no—
536C2×D4—102no—
537C2×D4—102no—
538C2×D4—102no—
539C2×D4—102no—
540C2×D4—102no—
541C2×D4—201no—
542C2×D4—201no—
543C2×D4—201no—
544C2×D4—201no—
545C2×D4—201no—
546C2×D4—201no—
547C2×D4—201no—
548C2×D4—201no—
549C2×D4—201no—
550C2×D4—201no—
551C2×D4—201no—
552C2×D4—201no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—102no—
580C22×C4—201no—
581C22×C4—201no—
582C22×C4—201no—
583C22×C4—201no—
584C22×C4—201no—
585C22×C4—201no—
586C22×C4#68612yes—
587C22×C4#68812yes—
588C22×C4C2×C4×D511yescharacteristic
589C22×C4C2×D2011yescharacteristic
590C22×C4#70911yescharacteristic
591C22×C4#70911yescharacteristic
592C22×C4#70911yescharacteristic
593C22×C4#70911yescharacteristic
594C22×C4D4×D511yescharacteristic
595C22×C4D4×D511yescharacteristic
596C22×C4D4×D511yescharacteristic
597C22×C4D4×D511yescharacteristic
598C22×C4#71111yescharacteristic
599C22×C4#71111yescharacteristic
600C22×C4#71311yescharacteristic
601C22×C4#71311yescharacteristic
602C2×C8—102no—
603C2×C8—102no—
604C2×C8—102no—
605C2×C8—102no—
606C2×C8—102no—
607C2×C8—102no—
608C2×C8—201no—
609C2×C8—201no—
610C2×C8—201no—
611C2×C8—201no—
612C2×C8—201no—
613C2×C8—201no—
614C2×C8—201no—
615C2×C8—201no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—102no—
625C4⋊C4—102no—
626C4⋊C4—201no—
627C4⋊C4—201no—
628C22⋊C4—208no—
629C22⋊C4—208no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C2×C5#144011yescharacteristic
635C2×C5#187711yescharacteristic
636C2×C5#187911yescharacteristic
637C2×C5#192511yescharacteristic
638C2×C5#192611yescharacteristic
639C2×C5#193411yescharacteristic
640C2×C5#193611yescharacteristic
641C2×C5#203311yescharacteristic
642C2×C5#203411yescharacteristic
643C2×C5#204111yescharacteristic
644C2×C5#204211yescharacteristic
645C2×C5#205411yescharacteristic
646C2×C5#205511yescharacteristic
647C2×C5#207111yescharacteristic
648C2×C5#207311yescharacteristic
649D5—84no—
650C23—104no—
651C23—202no—
652C23—202no—
653C23—202no—
654C23—202no—
655C23—202no—
656C23—202no—
657C23—202no—
658C23—202no—
659C23—202no—
660C23—202no—
661C23—202no—
662C23—202no—
663C23—202no—
664C23—202no—
665C23—202no—
666C23—202no—
667C23—202no—
668C23—202no—
669C23—401no—
670C23—401no—
671C23—401no—
672C23—401no—
673C23—401no—
674C23—401no—
675C23—401no—
676C23—401no—
677C23—401no—
678C23—401no—
679C23—401no—
680C23—401no—
681C23—401no—
682C23—401no—
683C23—401no—
684C23—401no—
685C23C4×C22⋊D511yescharacteristic
686C23#407511yescharacteristic
687C23#407611yescharacteristic
688C23C2×#68611yescharacteristic
689C23#407811yescharacteristic
690C23#408311yescharacteristic
691C23#408411yescharacteristic
692C23#408511yescharacteristic
693C23C2×#68811yescharacteristic
694C23#408811yescharacteristic
695C23#409311yescharacteristic
696C23#409511yescharacteristic
697C23#409511yescharacteristic
698C23#409611yescharacteristic
699C23#409611yescharacteristic
700D4—104no—
701D4—104no—
702D4—202no—
703D4—202no—
704D4—202no—
705D4—202no—
706D4—202no—
707D4—202no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—202no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—401no—
740C2×C4—401no—
741C2×C4—401no—
742C2×C4—401no—
743C2×C4#401811yescharacteristic
744C2×C4C4×D2011yescharacteristic
745C2×C4#402111yescharacteristic
746C2×C4#402211yescharacteristic
747C2×C4D5×C22⋊C411yescharacteristic
748C2×C4#402711yescharacteristic
749C2×C4#402811yescharacteristic
750C2×C4#402911yescharacteristic
751C2×C4#402911yescharacteristic
752C2×C4#402911yescharacteristic
753C2×C4#403011yescharacteristic
754C2×C4#403011yescharacteristic
755C2×C4#403011yescharacteristic
756C2×C4#403111yescharacteristic
757C2×C4#403111yescharacteristic
758C2×C4#403211yescharacteristic
759C2×C4#403811yescharacteristic
760C2×C4#403911yescharacteristic
761C2×C4#404011yescharacteristic
762C2×C4#404011yescharacteristic
763C2×C4#404011yescharacteristic
764C2×C4#404011yescharacteristic
765C2×C4#404011yescharacteristic
766C2×C4#404111yescharacteristic
767C2×C4#404111yescharacteristic
768C2×C4#404411yescharacteristic
769C2×C4#404411yescharacteristic
770C2×C4#404411yescharacteristic
771C8—202no—
772C8—202no—
773C5#1118911yescharacteristic, complemented, Sylow
774C22—204no—
775C22—204no—
776C22—204no—
777C22—402no—
778C22—402no—
779C22—402no—
780C22—402no—
781C22—402no—
782C22—402no—
783C22—402no—
784C22—402no—
785C22—402no—
786C22—402no—
787C22—402no—
788C22—402no—
789C22#6522911yescharacteristic
790C22#6524511yescharacteristic
791C22#6524811yescharacteristic
792C22#6525011yescharacteristic
793C22#6525611yescharacteristic
794C22#6525711yescharacteristic
795C22#6527911yescharacteristic
796C22#6528011yescharacteristic
797C22#6528211yescharacteristic
798C22#6529211yescharacteristic
799C22#6529211yescharacteristic
800C22C4×#68611yescharacteristic
801C22#6530311yescharacteristic
802C22#6530411yescharacteristic
803C22#6530511yescharacteristic
804C22C4×#68811yescharacteristic
805C22#6531511yescharacteristic
806C22#6531611yescharacteristic
807C22#6531711yescharacteristic
808C22#6532511yescharacteristic
809C22#6532611yescharacteristic
810C22#6532711yescharacteristic
811C22#6532811yescharacteristic
812C22#6533511yescharacteristic
813C22#6533611yescharacteristic
814C22#6533711yescharacteristic
815C22#6533811yescharacteristic
816C22#6534611yescharacteristic
817C22#6534611yescharacteristic
818C22#6535611yescharacteristic
819C22#6535711yescharacteristic
820C22#6536111yescharacteristic
821C22#6537211yescharacteristic
822C22#6537711yescharacteristic
823C22#6537811yescharacteristic
824C4—42no—
825C4—42no—
826C4—82no—
827C4—82no—
828C4—402no—
829C4#6495311yescharacteristic
830C4#6495411yescharacteristic
831C4#6495811yescharacteristic
832C4#6495911yescharacteristic
833C4#6496111yescharacteristic
834C4#6496311yescharacteristic
835C4#6496411yescharacteristic
836C4#6496411yescharacteristic
837C2—404no—
838C2#1060022211yescharacteristic
839C2#1060025511yescharacteristic
840C2#1060025611yescharacteristic
841C2#1060031611yescharacteristic
842C2#1060031711yescharacteristic
843C2#1060035011yescharacteristic
844C2#1060037811yescharacteristic
845C2#1060040811yescharacteristic
846C2#1060041011yescharacteristic
847C2#1060042011yescharacteristic
848C2#1060042111yescharacteristic
849C2#1060044311yescharacteristic
850C2#1060045011yescharacteristic
851C2#1060047311yescharacteristic
852C2#1060048011yescharacteristic
subgroupG/H
centerC24C2×C22⋊D5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×C4⋊#95C2
socleC24×C5C2×D4
prime radicalC23×D20C22
cosocleC23×C4×C5C23
hypercenterC4⋊#95D5
hypocenterC5#11189
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C5×C4⋊#95C2semidirect
5. C2×#64749C2semidirect
6. C2×#64749C2semidirect
7. C2×#64744C2semidirect
24. C2×#3941C4semidirect
106. C4⋊#95D5semidirect
773. C5#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#39412
C2×#652282
C5×C4⋊#952
C2×#647492
C2×#647442
#111895