Finite Group Databasebeta

← #12007114

Subgroups — #12007114

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×#3953C211yesmaximal, characteristic
2C22×#3953C211yesmaximal, characteristic
3C2×#65228C211yesmaximal, characteristic
4C2×C5×#336C211yesmaximal, characteristic, complemented
5C2×#64771C211yesmaximal, characteristic, complemented
6C2×#64771C211yesmaximal, characteristic, complemented
7#10602328C211yesmaximal, characteristic, complemented
8C23×D20C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C23×C5×C8C2211yescharacteristic
11C22×C42×C5C2211yescharacteristic
12C22×#685—21no—
13C22×#685—21no—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×C4⋊Dic5C2211yescharacteristic
17C2×#3963—21no—
18C2×#3963—21no—
19C2×#3953—22no—
20C2×#3953—22no—
21C2×#3953—22no—
22C2×#3953—22no—
23C2×#3953—22no—
24C2×#3953C414yescomplemented
25#65228—22no—
26#65228—22no—
27C5×#336—22no—
28#64771—22no—
29#64771—22no—
30#11189—51nomaximal, Sylow
31C24×D5—21no—
32C23×C4×C5D411yescharacteristic
33C23×C4×C5D411yescharacteristic
34C23×C4×C5C2311yescharacteristic
35C23×Dic5—21no—
36C23×Dic5—21no—
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—
52C22×C5×C8—21no—
53C22×C5×C8—21no—
54C22×C5×C8—21no—
55C22×C5×C8—21no—
56C22×C5×C8—21no—
57C22×C5×C8—21no—
58C22×C5×C8—21no—
59C22×C5×C8—21no—
60C22×C5×C8—21no—
61C22×C5×C8—21no—
62C22×C5×C8—21no—
63C22×C5×C8—21no—
64C22×C5×C8C2×C412yes—
65C22×C5×C8D412yes—
66C2×C42×C5—21no—
67C2×C42×C5—21no—
68C2×C42×C5—21no—
69C2×C42×C5—21no—
70C2×C42×C5—21no—
71C2×C42×C5—21no—
72C2×#685—24no—
73C2×#685—24no—
74C2×#685—42no—
75C2×#685—42no—
76C2×#685—42no—
77C2×#685—42no—
78C2×C4⋊Dic5—21no—
79C2×C4⋊Dic5—21no—
80C2×C4⋊Dic5—21no—
81C2×C4⋊Dic5—21no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5—21no—
91C2×C4⋊Dic5—21no—
92C2×C4⋊Dic5—21no—
93C2×C4⋊Dic5C2×C412yes—
94C2×C4⋊Dic5D412yes—
95C2×C4⋊Dic5D412yes—
96#3963—42no—
97#3963—42no—
98#3953—28no—
99#3953—28no—
100C22×#102—51no—
101C22×#102—51no—
102C2×#390—51no—
103C2×#340—51no—
104C2×#340—51no—
105C2×#336D511yescharacteristic, complemented
106C4⋊#95—51no—
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×C5D812yes—
136C22×C4×C5SD1612yes—
137C22×C4×C5C22×C411yescharacteristic
138C22×C4×C5C2×D411yescharacteristic
139C22×C4×C5C2×D411yescharacteristic
140C22×C4×C5C2×D411yescharacteristic
141C22×C4×C5C2×D411yescharacteristic
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5#4111yescharacteristic
144C22×C4×C5#4111yescharacteristic
145C22×C4×C5#4111yescharacteristic
146C22×C4×C5#4111yescharacteristic
147C22×C4×C5#4111yescharacteristic
148C22×C4×C5#4111yescharacteristic
149C22×C4×C5#4111yescharacteristic
150C22×C4×C5#4111yescharacteristic
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—41no—
155C22×Dic5—41no—
156C22×Dic5—41no—
157C22×Dic5—41no—
158C22×Dic5—41no—
159C22×Dic5—41no—
160C22×Dic5—41no—
161C22×Dic5—41no—
162C22×Dic5—41no—
163C22×Dic5—41no—
164C22×Dic5—41no—
165C22×Dic5—41no—
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—
200C2×C5×C8—22no—
201C2×C5×C8—22no—
202C2×C5×C8—22no—
203C2×C5×C8—22no—
204C2×C5×C8—22no—
205C2×C5×C8—22no—
206C2×C5×C8—41no—
207C2×C5×C8—41no—
208C2×C5×C8—41no—
209C2×C5×C8—41no—
210C2×C5×C8—41no—
211C2×C5×C8—41no—
212C2×C5×C8—41no—
213C2×C5×C8—41no—
214C42×C5—41no—
215C42×C5—41no—
216C42×C5—41no—
217C42×C5—41no—
218#685—48no—
219#685—48no—
220C4⋊Dic5—22no—
221C4⋊Dic5—22no—
222C4⋊Dic5—22no—
223C4⋊Dic5—22no—
224C4⋊Dic5—22no—
225C4⋊Dic5—22no—
226C4⋊Dic5—41no—
227C4⋊Dic5—41no—
228C4⋊Dic5—41no—
229C4⋊Dic5—41no—
230C4⋊Dic5—41no—
231C4⋊Dic5—41no—
232C23×D4—51no—
233C23×C8C2×D511yescharacteristic
234C23×C8C2×D511yescharacteristic
235C22×C4⋊C4—51no—
236C22×C4⋊C4—51no—
237C22×C4⋊C4—51no—
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—101no—
250C2×#95—101no—
251#340—102no—
252#340—102no—
253#336—22no—
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×C5C2×C22⋊C411yescharacteristic
319C2×C4×C5#11711yescharacteristic
320C2×C4×C5#11711yescharacteristic
321C2×C4×C5C4×D411yescharacteristic
322C2×C4×C5C4×D411yescharacteristic
323C2×C4×C5C4×D411yescharacteristic
324C2×C4×C5#12011yescharacteristic
325C2×C4×C5#12111yescharacteristic
326C2×C4×C5#12111yescharacteristic
327C2×C4×C5#12111yescharacteristic
328C2×C4×C5#12111yescharacteristic
329C2×C4×C5#12111yescharacteristic
330C2×C4×C5#12311yescharacteristic
331C2×C4×C5#12311yescharacteristic
332C2×C4×C5#12311yescharacteristic
333C2×C4×C5#12311yescharacteristic
334C2×C4×C5#12311yescharacteristic
335C2×C4×C5#12311yescharacteristic
336C2×C4×C5#12311yescharacteristic
337C2×C4×C5#12311yescharacteristic
338C2×C4×C5#12311yescharacteristic
339C2×C4×C5#12411yescharacteristic
340C2×C4×C5#12411yescharacteristic
341C2×C4×C5#12411yescharacteristic
342C2×C4×C5#12611yescharacteristic
343C2×C4×C5#12611yescharacteristic
344C2×C4×C5#12611yescharacteristic
345C2×C4×C5#12611yescharacteristic
346C2×Dic5—42no—
347C2×Dic5—42no—
348C2×Dic5—42no—
349C2×Dic5—42no—
350C2×Dic5—42no—
351C2×Dic5—42no—
352C2×Dic5—42no—
353C2×Dic5—42no—
354C2×Dic5—42no—
355C2×Dic5—81no—
356C2×Dic5—81no—
357C2×Dic5—81no—
358C2×Dic5—81no—
359C2×Dic5—81no—
360C2×Dic5—81no—
361C2×Dic5—81no—
362C2×Dic5—81no—
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—
375C5×C8—42no—
376C5×C8—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—101no—
393C23×C4—101no—
394C23×C4—101no—
395C23×C4D2011yescharacteristic
396C23×C4D2011yescharacteristic
397C23×C4C22×D511yescharacteristic
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—21no—
404C22×C8—21no—
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8C4×D512yes—
411C22×C8C22⋊D512yes—
412C2×C4⋊C4—52no—
413C2×C4⋊C4—52no—
414C2×C4⋊C4—52no—
415C2×C4⋊C4—101no—
416C2×C4⋊C4—101no—
417C2×C4⋊C4—101no—
418C2×C4⋊C4—101no—
419C2×C4⋊C4—101no—
420C2×C4⋊C4—101no—
421C2×C4⋊C4—101no—
422C2×C4⋊C4—101no—
423C2×C4⋊C4—101no—
424C2×C4⋊C4—101no—
425C2×C4⋊C4—101no—
426C2×C4⋊C4—101no—
427C2×C4⋊C4—101no—
428C2×C4⋊C4—101no—
429C2×C4⋊C4—101no—
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—202no—
445#95—202no—
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#38111yescharacteristic
499C4×C5#38611yescharacteristic
500C4×C5#38811yescharacteristic
501C4×C5#38811yescharacteristic
502C4×C5#39411yescharacteristic
503C4×C5#39711yescharacteristic
504C4×C5#39711yescharacteristic
505C4×C5#39711yescharacteristic
506Dic5—82no—
507Dic5—82no—
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×D2011yescharacteristic
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—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—201no—
569C22×C4—201no—
570C22×C4—201no—
571C22×C4—201no—
572C22×C4—201no—
573C22×C4—201no—
574C22×C4—201no—
575C22×C4—201no—
576C22×C4—201no—
577C22×C4—201no—
578C22×C4—201no—
579C22×C4—201no—
580C22×C4—201no—
581C22×C4—201no—
582C22×C4—201no—
583C22×C4—201no—
584C22×C4—201no—
585C22×C4—201no—
586C22×C4#67712yes—
587C22×C4D4012yes—
588C22×C4C2×C4×D511yescharacteristic
589C22×C4#70911yescharacteristic
590C22×C4#70911yescharacteristic
591C22×C4#70911yescharacteristic
592C22×C4#70911yescharacteristic
593C22×C4D4×D511yescharacteristic
594C22×C4D4×D511yescharacteristic
595C22×C4D4×D511yescharacteristic
596C22×C4D4×D511yescharacteristic
597C22×C4#71111yescharacteristic
598C22×C4#71111yescharacteristic
599C22×C4#71311yescharacteristic
600C22×C4#71311yescharacteristic
601C22×C4C2×C22⋊D511yescharacteristic
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C4⋊C4—102no—
617C4⋊C4—102no—
618C4⋊C4—102no—
619C4⋊C4—102no—
620C4⋊C4—102no—
621C4⋊C4—102no—
622C4⋊C4—201no—
623C4⋊C4—201no—
624C4⋊C4—201no—
625C4⋊C4—201no—
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×D2011yescharacteristic
686C23#402111yescharacteristic
687C23#402811yescharacteristic
688C23#403211yescharacteristic
689C23#404111yescharacteristic
690C23#404111yescharacteristic
691C23C2×#67711yescharacteristic
692C23C2×D4011yescharacteristic
693C23#405011yescharacteristic
694C23#405011yescharacteristic
695C23#405411yescharacteristic
696C23#405411yescharacteristic
697C23#405411yescharacteristic
698C23#405511yescharacteristic
699C23#407611yescharacteristic
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—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4—202no—
731C2×C4—401no—
732C2×C4—401no—
733C2×C4—401no—
734C2×C4—401no—
735C2×C4—401no—
736C2×C4—401no—
737C2×C4—401no—
738C2×C4—401no—
739C2×C4—401no—
740C2×C4—401no—
741C2×C4—401no—
742C2×C4—401no—
743C2×C4#401811yescharacteristic
744C2×C4#402211yescharacteristic
745C2×C4D5×C22⋊C411yescharacteristic
746C2×C4#402711yescharacteristic
747C2×C4#402911yescharacteristic
748C2×C4#402911yescharacteristic
749C2×C4#402911yescharacteristic
750C2×C4#403011yescharacteristic
751C2×C4#403011yescharacteristic
752C2×C4#403011yescharacteristic
753C2×C4#403111yescharacteristic
754C2×C4#403111yescharacteristic
755C2×C4#403811yescharacteristic
756C2×C4#403911yescharacteristic
757C2×C4#404011yescharacteristic
758C2×C4#404011yescharacteristic
759C2×C4#404011yescharacteristic
760C2×C4#404011yescharacteristic
761C2×C4#404011yescharacteristic
762C2×C4#404411yescharacteristic
763C2×C4#404411yescharacteristic
764C2×C4#404411yescharacteristic
765C2×C4C4×C22⋊D511yescharacteristic
766C2×C4#407511yescharacteristic
767C2×C4#408311yescharacteristic
768C2×C4#408411yescharacteristic
769C2×C4#408511yescharacteristic
770C2×C4#409311yescharacteristic
771C8—42no—
772C8—42no—
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#6495411yescharacteristic
790C22#6495911yescharacteristic
791C22#6496111yescharacteristic
792C22#6496311yescharacteristic
793C22C4×#67711yescharacteristic
794C22C4×D4011yescharacteristic
795C22#6498311yescharacteristic
796C22#6498611yescharacteristic
797C22#6499911yescharacteristic
798C22#6500011yescharacteristic
799C22#6500211yescharacteristic
800C22#6500311yescharacteristic
801C22#6502011yescharacteristic
802C22#6502111yescharacteristic
803C22#6502211yescharacteristic
804C22#6502311yescharacteristic
805C22#6502411yescharacteristic
806C22#6502511yescharacteristic
807C22#6502611yescharacteristic
808C22#6502611yescharacteristic
809C22#6513011yescharacteristic
810C22#6513211yescharacteristic
811C22#6513211yescharacteristic
812C22#6513311yescharacteristic
813C22#6513311yescharacteristic
814C22#6513311yescharacteristic
815C22#6513411yescharacteristic
816C22#6513711yescharacteristic
817C22#6522911yescharacteristic
818C22#6525011yescharacteristic
819C22#6528011yescharacteristic
820C22#6540311yescharacteristic
821C22#6540411yescharacteristic
822C22#6542311yescharacteristic
823C22#6542411yescharacteristic
824C4—42no—
825C4—42no—
826C4—402no—
827C4—402no—
828C4—402no—
829C4#6495311yescharacteristic
830C4#6495811yescharacteristic
831C4#6496411yescharacteristic
832C4#6496411yescharacteristic
833C4#6524511yescharacteristic
834C4#6524811yescharacteristic
835C4#6527911yescharacteristic
836C4#6528211yescharacteristic
837C2—404no—
838C2#1059941811yescharacteristic
839C2#1059941911yescharacteristic
840C2#1059942211yescharacteristic
841C2#1059942311yescharacteristic
842C2#1059942811yescharacteristic
843C2#1059943011yescharacteristic
844C2#1059946511yescharacteristic
845C2#1059946611yescharacteristic
846C2#1060022211yescharacteristic
847C2#1060056111yescharacteristic
848C2#1060061111yescharacteristic
849C2#1060072711yescharacteristic
850C2#1060072811yescharacteristic
851C2#1060127411yescharacteristic
852C2#1060127511yescharacteristic
subgroupG/H
centerC24C2×D20
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#336C2
socleC24×C5C2×D4
prime radicalC23×D20C22
cosocleC23×C4×C5C23
hypercenterC2×#336D5
hypocenterC5#11189
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×C5×#336C2semidirect
5. C2×#64771C2semidirect
6. C2×#64771C2semidirect
7. #10602328C2semidirect
24. C2×#3953C4semidirect
105. C2×#336D5semidirect
773. C5#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#39532
C2×#652282
C2×C5×#3362
C2×#647712
#106023282
#111895