Finite Group Databasebeta

← #12007121

Subgroups — #12007121

Order 1280.

994 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3948C211yesmaximal, characteristic
2C22×#3948C211yesmaximal, characteristic
3C2×#65218C211yesmaximal, characteristic
4C2×C5×#336C211yesmaximal, characteristic
5C2×#64771C211yesmaximal, characteristic
6C2×#64771C211yesmaximal, characteristic
7#10602328C211yesmaximal, characteristic
8C23×Dic10C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C23×C5×C8C2211yescharacteristic
11C22×C42×C5C2211yescharacteristic
12C22×C4⋊Dic5C2211yescharacteristic
13C22×C4⋊Dic5C2211yescharacteristic
14C22×C4⋊Dic5C2211yescharacteristic
15C2×#3963—21no—
16C2×#3963—21no—
17C2×#3963—21no—
18C2×#3963—21no—
19C2×#3948—22no—
20C2×#3948—22no—
21C2×#3948—22no—
22C2×#3948—22no—
23C2×#3948—22no—
24C2×#3948C414yescomplemented
25#65218—22no—
26#65218—22no—
27C5×#336—22no—
28#64771—22no—
29#64771—22no—
30#11190—51nomaximal, Sylow
31C23×C4×C5D411yescharacteristic
32C23×C4×C5D411yescharacteristic
33C23×C4×C5C2311yescharacteristic
34C23×Dic5—21no—
35C23×Dic5—21no—
36C23×Dic5—21no—
37C23×Dic5—21no—
38C22×Dic10—21no—
39C22×Dic10—21no—
40C22×Dic10—21no—
41C22×Dic10—21no—
42C22×Dic10—21no—
43C22×Dic10—21no—
44C22×Dic10—21no—
45C22×Dic10—21no—
46C22×Dic10—21no—
47C22×Dic10—21no—
48C22×Dic10—21no—
49C22×Dic10C2×C412yes—
50C22×Dic10D412yes—
51C22×Dic10D412yes—
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×C4⋊Dic5—21no—
73C2×C4⋊Dic5—21no—
74C2×C4⋊Dic5—21no—
75C2×C4⋊Dic5—21no—
76C2×C4⋊Dic5—21no—
77C2×C4⋊Dic5—21no—
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⋊Dic5C2×C412yes—
88C2×C4⋊Dic5D412yes—
89C2×C4⋊Dic5D412yes—
90#3963—24no—
91#3963—24no—
92#3963—42no—
93#3963—42no—
94#3948—28no—
95#3948—28no—
96C22×#103—51no—
97C22×#103—51no—
98C2×#391—51no—
99C2×#340—51no—
100C2×#340—51no—
101C2×#336D511yescharacteristic
102C4⋊#95—51no—
103C24×C5C2×D411yescharacteristic
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5SD1612yes—
117C22×C4×C5Q1612yes—
118C22×C4×C5C22×C411yescharacteristic
119C22×C4×C5C2×D411yescharacteristic
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5C2×D411yescharacteristic
123C22×C4×C5C2×D411yescharacteristic
124C22×C4×C5#4111yescharacteristic
125C22×C4×C5#4111yescharacteristic
126C22×C4×C5#4111yescharacteristic
127C22×C4×C5#4111yescharacteristic
128C22×C4×C5#4111yescharacteristic
129C22×C4×C5#4111yescharacteristic
130C22×C4×C5#4111yescharacteristic
131C22×C4×C5#4111yescharacteristic
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—22no—
136C22×Dic5—22no—
137C22×Dic5—22no—
138C22×Dic5—41no—
139C22×Dic5—41no—
140C22×Dic5—41no—
141C22×Dic5—41no—
142C22×Dic5—41no—
143C22×Dic5—41no—
144C22×Dic5—41no—
145C22×Dic5—41no—
146C22×Dic5—41no—
147C22×Dic5—41no—
148C22×Dic5—41no—
149C22×Dic5—41no—
150C22×Dic5—41no—
151C22×Dic5—41no—
152C22×Dic5—41no—
153C22×Dic5—41no—
154C22×Dic5—41no—
155C22×Dic5—41no—
156C22×Dic5—41no—
157C22×Dic5—41no—
158C22×Dic5—41no—
159C22×Dic5—41no—
160C2×Dic10—22no—
161C2×Dic10—22no—
162C2×Dic10—22no—
163C2×Dic10—22no—
164C2×Dic10—22no—
165C2×Dic10—22no—
166C2×Dic10—22no—
167C2×Dic10—22no—
168C2×Dic10—22no—
169C2×Dic10—22no—
170C2×Dic10—22no—
171C2×Dic10—22no—
172C2×Dic10—22no—
173C2×Dic10—22no—
174C2×Dic10—22no—
175C2×Dic10—41no—
176C2×Dic10—41no—
177C2×Dic10—41no—
178C2×Dic10—41no—
179C2×Dic10—41no—
180C2×Dic10—41no—
181C2×Dic10—41no—
182C2×Dic10—41no—
183C2×Dic10—41no—
184C2×Dic10—41no—
185C2×Dic10—41no—
186C2×Dic10—41no—
187C2×Dic10C22⋊C414yes—
188C2×C5×C8—22no—
189C2×C5×C8—22no—
190C2×C5×C8—22no—
191C2×C5×C8—22no—
192C2×C5×C8—22no—
193C2×C5×C8—22no—
194C2×C5×C8—41no—
195C2×C5×C8—41no—
196C2×C5×C8—41no—
197C2×C5×C8—41no—
198C2×C5×C8—41no—
199C2×C5×C8—41no—
200C2×C5×C8—41no—
201C2×C5×C8—41no—
202C42×C5—41no—
203C42×C5—41no—
204C42×C5—41no—
205C42×C5—41no—
206C4⋊Dic5—22no—
207C4⋊Dic5—22no—
208C4⋊Dic5—22no—
209C4⋊Dic5—22no—
210C4⋊Dic5—22no—
211C4⋊Dic5—22no—
212C4⋊Dic5—41no—
213C4⋊Dic5—41no—
214C4⋊Dic5—41no—
215C4⋊Dic5—41no—
216C4⋊Dic5—41no—
217C4⋊Dic5—41no—
218C23×Q8—51no—
219C23×C8C2×D511yescharacteristic
220C23×C8C2×D511yescharacteristic
221C22×C4⋊C4—51no—
222C22×C4⋊C4—51no—
223C22×C4⋊C4—51no—
224C22×C42C2×D511yescharacteristic
225C2×#103—54no—
226C2×#103—102no—
227C2×#103—102no—
228C2×#103—102no—
229C2×#103—102no—
230C2×#103—102no—
231#391—102no—
232#391—102no—
233C2×#95—101no—
234C2×#95—101no—
235C2×#95—101no—
236C2×#95—101no—
237#340—102no—
238#340—102no—
239#336—22no—
240C23×C5C4×D411yescharacteristic
241C23×C5#12011yescharacteristic
242C23×C5#12111yescharacteristic
243C23×C5#12111yescharacteristic
244C23×C5#12111yescharacteristic
245C23×C5#12311yescharacteristic
246C23×C5#12411yescharacteristic
247C23×C5C2×SD1611yescharacteristic
248C23×C5C2×Q1611yescharacteristic
249C23×C5#13511yescharacteristic
250C23×C5#13511yescharacteristic
251C23×C5AGL(1,ℤ/8)11yescharacteristic
252C23×C5#13711yescharacteristic
253C23×C5#13711yescharacteristic
254C23×C5#13711yescharacteristic
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5C2×C22⋊C411yescharacteristic
270C2×C4×C5#11711yescharacteristic
271C2×C4×C5#11711yescharacteristic
272C2×C4×C5C4×D411yescharacteristic
273C2×C4×C5C4×D411yescharacteristic
274C2×C4×C5C4×D411yescharacteristic
275C2×C4×C5#12011yescharacteristic
276C2×C4×C5#12111yescharacteristic
277C2×C4×C5#12111yescharacteristic
278C2×C4×C5#12111yescharacteristic
279C2×C4×C5#12111yescharacteristic
280C2×C4×C5#12111yescharacteristic
281C2×C4×C5#12311yescharacteristic
282C2×C4×C5#12311yescharacteristic
283C2×C4×C5#12311yescharacteristic
284C2×C4×C5#12311yescharacteristic
285C2×C4×C5#12311yescharacteristic
286C2×C4×C5#12311yescharacteristic
287C2×C4×C5#12311yescharacteristic
288C2×C4×C5#12311yescharacteristic
289C2×C4×C5#12311yescharacteristic
290C2×C4×C5#12411yescharacteristic
291C2×C4×C5#12411yescharacteristic
292C2×C4×C5#12411yescharacteristic
293C2×C4×C5#12611yescharacteristic
294C2×C4×C5#12611yescharacteristic
295C2×C4×C5#12611yescharacteristic
296C2×C4×C5#12611yescharacteristic
297C2×Dic5—24no—
298C2×Dic5—42no—
299C2×Dic5—42no—
300C2×Dic5—42no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5—42no—
305C2×Dic5—42no—
306C2×Dic5—42no—
307C2×Dic5—42no—
308C2×Dic5—42no—
309C2×Dic5—42no—
310C2×Dic5—42no—
311C2×Dic5—42no—
312C2×Dic5—42no—
313C2×Dic5—81no—
314C2×Dic5—81no—
315C2×Dic5—81no—
316C2×Dic5—81no—
317C2×Dic5—81no—
318C2×Dic5—81no—
319C2×Dic5—81no—
320C2×Dic5—81no—
321C2×Dic5—81no—
322C2×Dic5—81no—
323C2×Dic5—81no—
324C2×Dic5—81no—
325Dic10—24no—
326Dic10—24no—
327Dic10—42no—
328Dic10—42no—
329Dic10—42no—
330Dic10—42no—
331Dic10—42no—
332Dic10—42no—
333C5×C8—42no—
334C5×C8—42no—
335C22×Q8—52no—
336C22×Q8—52no—
337C22×Q8—52no—
338C22×Q8—101no—
339C22×Q8—101no—
340C22×Q8—101no—
341C22×Q8—101no—
342C22×Q8—101no—
343C22×Q8—101no—
344C22×Q8—101no—
345C22×Q8—101no—
346C22×Q8—101no—
347C22×Q8—101no—
348C22×Q8—101no—
349C23×C4—101no—
350C23×C4—101no—
351C23×C4—101no—
352C23×C4—101no—
353C23×C4D2011yescharacteristic
354C23×C4D2011yescharacteristic
355C23×C4C22×D511yescharacteristic
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8C4×D512yes—
369C22×C8C22⋊D512yes—
370C2×C4⋊C4—52no—
371C2×C4⋊C4—52no—
372C2×C4⋊C4—52no—
373C2×C4⋊C4—101no—
374C2×C4⋊C4—101no—
375C2×C4⋊C4—101no—
376C2×C4⋊C4—101no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—101no—
379C2×C4⋊C4—101no—
380C2×C4⋊C4—101no—
381C2×C4⋊C4—101no—
382C2×C4⋊C4—101no—
383C2×C4⋊C4—101no—
384C2×C4⋊C4—101no—
385C2×C4⋊C4—101no—
386C2×C4⋊C4—101no—
387C2×C4⋊C4—101no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394#103—108no—
395#103—108no—
396#95—104no—
397#95—104no—
398#95—202no—
399#95—202no—
400C22×C5#38611yescharacteristic
401C22×C5#38811yescharacteristic
402C22×C5#38811yescharacteristic
403C22×C5#39411yescharacteristic
404C22×C5#39411yescharacteristic
405C22×C5#39411yescharacteristic
406C22×C5#39711yescharacteristic
407C22×C5C4×SD1611yescharacteristic
408C22×C5C4×Q1611yescharacteristic
409C22×C5#44011yescharacteristic
410C22×C5#44111yescharacteristic
411C22×C5#44811yescharacteristic
412C22×C5#44911yescharacteristic
413C22×C5#45111yescharacteristic
414C22×C5#45211yescharacteristic
415C22×C5#46011yescharacteristic
416C22×C5#46111yescharacteristic
417C22×C5#46211yescharacteristic
418C22×C5#46211yescharacteristic
419C22×C5#46311yescharacteristic
420C22×C5#46411yescharacteristic
421C22×C5#46411yescharacteristic
422C22×C5#46411yescharacteristic
423C22×C5#46511yescharacteristic
424C22×C5#46711yescharacteristic
425C22×C5#46811yescharacteristic
426C22×C5#47011yescharacteristic
427C22×C5#48311yescharacteristic
428C22×C5#48411yescharacteristic
429C22×C5#48511yescharacteristic
430C22×C5#48511yescharacteristic
431C22×C5#48711yescharacteristic
432C22×C5#48811yescharacteristic
433C22×C5#48911yescharacteristic
434C22×C5#49111yescharacteristic
435C4×C5—42no—
436C4×C5—42no—
437C4×C5#38111yescharacteristic
438C4×C5#38611yescharacteristic
439C4×C5#38811yescharacteristic
440C4×C5#38811yescharacteristic
441C4×C5#39411yescharacteristic
442C4×C5#39711yescharacteristic
443C4×C5#39711yescharacteristic
444C4×C5#39711yescharacteristic
445Dic5—44no—
446Dic5—82no—
447Dic5—82no—
448Dic5—82no—
449C24C2×D2011yescharacteristic
450C2×Q8—54no—
451C2×Q8—102no—
452C2×Q8—102no—
453C2×Q8—102no—
454C2×Q8—102no—
455C2×Q8—102no—
456C2×Q8—102no—
457C2×Q8—102no—
458C2×Q8—102no—
459C2×Q8—102no—
460C2×Q8—102no—
461C2×Q8—102no—
462C2×Q8—102no—
463C2×Q8—102no—
464C2×Q8—102no—
465C2×Q8—102no—
466C2×Q8—201no—
467C2×Q8—201no—
468C2×Q8—201no—
469C2×Q8—201no—
470C2×Q8—201no—
471C2×Q8—201no—
472C2×Q8—201no—
473C2×Q8—201no—
474C2×Q8—201no—
475C2×Q8—201no—
476C2×Q8—201no—
477C2×Q8—201no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4—102no—
493C22×C4—102no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—201no—
497C22×C4—201no—
498C22×C4—201no—
499C22×C4—201no—
500C22×C4—201no—
501C22×C4—201no—
502C22×C4—201no—
503C22×C4—201no—
504C22×C4—201no—
505C22×C4—201no—
506C22×C4—201no—
507C22×C4—201no—
508C22×C4—201no—
509C22×C4—201no—
510C22×C4—201no—
511C22×C4—201no—
512C22×C4—201no—
513C22×C4—201no—
514C22×C4—201no—
515C22×C4—201no—
516C22×C4—201no—
517C22×C4—201no—
518C22×C4#67712yes—
519C22×C4Dic2012yes—
520C22×C4C2×C4×D511yescharacteristic
521C22×C4#70911yescharacteristic
522C22×C4#70911yescharacteristic
523C22×C4#70911yescharacteristic
524C22×C4#70911yescharacteristic
525C22×C4D4×D511yescharacteristic
526C22×C4D4×D511yescharacteristic
527C22×C4D4×D511yescharacteristic
528C22×C4D4×D511yescharacteristic
529C22×C4#71111yescharacteristic
530C22×C4#71111yescharacteristic
531C22×C4#71311yescharacteristic
532C22×C4#71311yescharacteristic
533C22×C4C2×C22⋊D511yescharacteristic
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C4⋊C4—102no—
549C4⋊C4—102no—
550C4⋊C4—102no—
551C4⋊C4—102no—
552C4⋊C4—102no—
553C4⋊C4—102no—
554C4⋊C4—201no—
555C4⋊C4—201no—
556C4⋊C4—201no—
557C4⋊C4—201no—
558C4⋊C4—201no—
559C4⋊C4—201no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C2×C5#144011yescharacteristic
565C2×C5#187811yescharacteristic
566C2×C5#188011yescharacteristic
567C2×C5#192711yescharacteristic
568C2×C5#192811yescharacteristic
569C2×C5#193311yescharacteristic
570C2×C5#193511yescharacteristic
571C2×C5#203511yescharacteristic
572C2×C5#203611yescharacteristic
573C2×C5#204211yescharacteristic
574C2×C5#204311yescharacteristic
575C2×C5#205511yescharacteristic
576C2×C5#205611yescharacteristic
577C2×C5#207211yescharacteristic
578C2×C5#207411yescharacteristic
579C23C4×D2011yescharacteristic
580C23#402111yescharacteristic
581C23#402811yescharacteristic
582C23#403211yescharacteristic
583C23#404111yescharacteristic
584C23#404111yescharacteristic
585C23C2×#67711yescharacteristic
586C23#405011yescharacteristic
587C23#405011yescharacteristic
588C23C2×Dic2011yescharacteristic
589C23#405411yescharacteristic
590C23#405511yescharacteristic
591C23#405511yescharacteristic
592C23#405511yescharacteristic
593C23#407611yescharacteristic
594Q8—104no—
595Q8—104no—
596Q8—202no—
597Q8—202no—
598Q8—202no—
599Q8—202no—
600Q8—202no—
601Q8—202no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—104no—
617C2×C4—202no—
618C2×C4—202no—
619C2×C4—202no—
620C2×C4—202no—
621C2×C4—202no—
622C2×C4—202no—
623C2×C4—202no—
624C2×C4—202no—
625C2×C4—202no—
626C2×C4—202no—
627C2×C4—202no—
628C2×C4—202no—
629C2×C4—202no—
630C2×C4—202no—
631C2×C4—202no—
632C2×C4—401no—
633C2×C4—401no—
634C2×C4—401no—
635C2×C4—401no—
636C2×C4—401no—
637C2×C4—401no—
638C2×C4—401no—
639C2×C4—401no—
640C2×C4—401no—
641C2×C4—401no—
642C2×C4—401no—
643C2×C4—401no—
644C2×C4#401811yescharacteristic
645C2×C4#402211yescharacteristic
646C2×C4D5×C22⋊C411yescharacteristic
647C2×C4#402711yescharacteristic
648C2×C4#402911yescharacteristic
649C2×C4#402911yescharacteristic
650C2×C4#402911yescharacteristic
651C2×C4#403011yescharacteristic
652C2×C4#403011yescharacteristic
653C2×C4#403011yescharacteristic
654C2×C4#403111yescharacteristic
655C2×C4#403111yescharacteristic
656C2×C4#403811yescharacteristic
657C2×C4#403911yescharacteristic
658C2×C4#404011yescharacteristic
659C2×C4#404011yescharacteristic
660C2×C4#404011yescharacteristic
661C2×C4#404011yescharacteristic
662C2×C4#404011yescharacteristic
663C2×C4#404411yescharacteristic
664C2×C4#404411yescharacteristic
665C2×C4#404411yescharacteristic
666C2×C4C4×C22⋊D511yescharacteristic
667C2×C4#407511yescharacteristic
668C2×C4#408311yescharacteristic
669C2×C4#408411yescharacteristic
670C2×C4#408511yescharacteristic
671C2×C4#409311yescharacteristic
672C8—42no—
673C8—42no—
674C5#1119011yescharacteristic, complemented, Sylow
675C22#6495411yescharacteristic
676C22#6495911yescharacteristic
677C22#6496111yescharacteristic
678C22#6496311yescharacteristic
679C22#6497011yescharacteristic
680C22C4×#67711yescharacteristic
681C22#6498611yescharacteristic
682C22C4×Dic2011yescharacteristic
683C22#6499211yescharacteristic
684C22#6499911yescharacteristic
685C22#6500311yescharacteristic
686C22#6500511yescharacteristic
687C22#6501011yescharacteristic
688C22#6501111yescharacteristic
689C22#6501211yescharacteristic
690C22#6501211yescharacteristic
691C22#6502211yescharacteristic
692C22#6502311yescharacteristic
693C22#6502711yescharacteristic
694C22#6502811yescharacteristic
695C22#6513011yescharacteristic
696C22#6513311yescharacteristic
697C22#6513411yescharacteristic
698C22#6513411yescharacteristic
699C22#6513411yescharacteristic
700C22#6513711yescharacteristic
701C22#6513811yescharacteristic
702C22#6513811yescharacteristic
703C22#6522911yescharacteristic
704C22#6525011yescharacteristic
705C22#6528011yescharacteristic
706C22#6540311yescharacteristic
707C22#6540511yescharacteristic
708C22#6542311yescharacteristic
709C22#6542611yescharacteristic
710C4—42no—
711C4—42no—
712C4—204no—
713C4—402no—
714C4—402no—
715C4—402no—
716C4#6495311yescharacteristic
717C4#6495811yescharacteristic
718C4#6496411yescharacteristic
719C4#6496411yescharacteristic
720C4#6524511yescharacteristic
721C4#6524811yescharacteristic
722C4#6527911yescharacteristic
723C4#6528211yescharacteristic
724C2#1059942011yescharacteristic
725C2#1059942111yescharacteristic
726C2#1059942311yescharacteristic
727C2#1059942411yescharacteristic
728C2#1059942911yescharacteristic
729C2#1059943111yescharacteristic
730C2#1059947811yescharacteristic
731C2#1059947911yescharacteristic
732C2#1060022211yescharacteristic
733C2#1060056011yescharacteristic
734C2#1060061011yescharacteristic
735C2#1060072911yescharacteristic
736C2#1060073011yescharacteristic
737C2#1060127511yescharacteristic
738C2#1060128011yescharacteristic
subgroupG/H
centerC24C2×D20
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#336C2
socle, prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#336D5
hypocenterC5#11190
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
24. C2×#3948C4semidirect
674. C5#11190semidirect

Maximal subgroups

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

subgroupindex
C22×#39482
C2×#652182
C2×C5×#3362
C2×#647712
#106023282
#111905