Finite Group Databasebeta

← #12006018

Subgroups — #12006018

Order 1280.

1430 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4090C211yesmaximal, characteristic
2C22×C5×#103C211yesmaximal, characteristic
3C22×#3967C211yesmaximal, characteristic
4C22×#3948C211yesmaximal, characteristic
5C22×#3942C211yesmaximal, characteristic
6C2×#64770C211yesmaximal, characteristic
7#10602356C211yesmaximal, characteristic
8C23×C5×Q8C2211yescharacteristic
9C23×Dic10C2211yescharacteristic
10C23×C5×C8C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C2×#4090—22no—
13C2×#4090—22no—
14C2×#4090—22no—
15C2×#4090—22no—
16C2×#4090—22no—
17C2×#4090C414yescomplemented
18C22×C4⋊Dic5C2211yescharacteristic
19C22×#683—22no—
20C22×C4×Dic5C2211yescharacteristic
21C23×#168C2211yescharacteristic
22C2×C5×#103—22no—
23C2×C5×#103—22no—
24C2×C5×#103—22no—
25C2×#3967—22no—
26C2×#3967—22no—
27C2×#3967—22no—
28C2×#3963—22no—
29C2×#3948—22no—
30C2×#3948—22no—
31C2×#3948—22no—
32C2×#3942—22no—
33C2×#3942—22no—
34C2×#3942—22no—
35#64770—22no—
36#11010—51nomaximal, Sylow
37C22×C5×Q8—21no—
38C22×C5×Q8—21no—
39C22×C5×Q8—21no—
40C22×C5×Q8—21no—
41C22×C5×Q8—21no—
42C22×C5×Q8—21no—
43C22×C5×Q8—21no—
44C22×C5×Q8—21no—
45C22×C5×Q8—21no—
46C22×C5×Q8—21no—
47C22×C5×Q8—21no—
48C22×C5×Q8C2×C412yes—
49C22×C5×Q8D412yes—
50C22×C5×Q8D412yes—
51C23×C4×C5—21no—
52C23×C4×C5—21no—
53C23×C4×C5C2311yescharacteristic
54C23×Dic5—21no—
55C23×Dic5—21no—
56C23×Dic5D412yes—
57C22×Dic10—21no—
58C22×Dic10—21no—
59C22×Dic10—21no—
60C22×Dic10—21no—
61C22×Dic10—21no—
62C22×Dic10—21no—
63C22×Dic10—21no—
64C22×Dic10—21no—
65C22×Dic10—21no—
66C22×Dic10—21no—
67C22×Dic10—21no—
68C22×Dic10C2×C412yes—
69C22×Dic10D412yes—
70C22×Dic10D412yes—
71C22×C5×C8—21no—
72C22×C5×C8—21no—
73C22×C5×C8—21no—
74C22×C5×C8—21no—
75C22×C5×C8—21no—
76C22×C5×C8—21no—
77C22×C5×C8D412yes—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4D412yes—
84#4090—28no—
85#4090—28no—
86#4090—28no—
87#4090—28no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5—21no—
91C2×C4⋊Dic5—21no—
92C2×C4⋊Dic5—21no—
93C2×C4⋊Dic5D412yes—
94C2×#683—28no—
95C2×#683—28no—
96C2×#683—28no—
97C2×C4×Dic5—21no—
98C2×C4×Dic5—21no—
99C2×C4×Dic5—21no—
100C2×C4×Dic5—21no—
101C2×C4×Dic5C2×C412yes—
102C2×C4×Dic5D412yes—
103C22×#168—21no—
104C22×#168—21no—
105C22×#168—21no—
106C22×#168—21no—
107C22×#168—21no—
108C22×#168—21no—
109C22×#168D412yes—
110C5×#103—28no—
111#3967—28no—
112#3963—44no—
113#3948—28no—
114#3942—28no—
115C22×C4⋊Q8—51no—
116C22×#103—51no—
117C22×#103—51no—
118C22×#103—51no—
119C22×#103D511yescharacteristic
120C2×#336—51no—
121C4⋊#95—51no—
122C24×C5C2×D411yescharacteristic
123C2×C5×Q8—22no—
124C2×C5×Q8—22no—
125C2×C5×Q8—22no—
126C2×C5×Q8—22no—
127C2×C5×Q8—22no—
128C2×C5×Q8—22no—
129C2×C5×Q8—22no—
130C2×C5×Q8—22no—
131C2×C5×Q8—22no—
132C2×C5×Q8—22no—
133C2×C5×Q8—22no—
134C2×C5×Q8—22no—
135C2×C5×Q8—22no—
136C2×C5×Q8—22no—
137C2×C5×Q8—22no—
138C2×C5×Q8—41no—
139C2×C5×Q8—41no—
140C2×C5×Q8—41no—
141C2×C5×Q8—41no—
142C2×C5×Q8—41no—
143C2×C5×Q8—41no—
144C2×C5×Q8—41no—
145C2×C5×Q8—41no—
146C2×C5×Q8—41no—
147C2×C5×Q8—41no—
148C2×C5×Q8—41no—
149C2×C5×Q8—41no—
150C2×C5×Q8C22⋊C414yes—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—41no—
156C22×C4×C5—41no—
157C22×C4×C5—41no—
158C22×C4×C5—41no—
159C22×C4×C5—41no—
160C22×C4×C5—41no—
161C22×C4×C5—42no—
162C22×C4×C5—42no—
163C22×C4×C5C22×C411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C22×C4×C5#4111yescharacteristic
175C22×C4×C5#4111yescharacteristic
176C22×C4×C5#4111yescharacteristic
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5—41no—
186C22×Dic5—41no—
187C22×Dic5—41no—
188C22×Dic5—41no—
189C22×Dic5—41no—
190C22×Dic5—41no—
191C22×Dic5—42no—
192C22×Dic5—42no—
193C22×Dic5C22⋊C414yes—
194C22×Dic5SD1614yes—
195C22×Dic5Q1614yes—
196C2×Dic10—22no—
197C2×Dic10—22no—
198C2×Dic10—22no—
199C2×Dic10—22no—
200C2×Dic10—22no—
201C2×Dic10—22no—
202C2×Dic10—22no—
203C2×Dic10—22no—
204C2×Dic10—22no—
205C2×Dic10—22no—
206C2×Dic10—22no—
207C2×Dic10—22no—
208C2×Dic10—22no—
209C2×Dic10—22no—
210C2×Dic10—22no—
211C2×Dic10—41no—
212C2×Dic10—41no—
213C2×Dic10—41no—
214C2×Dic10—41no—
215C2×Dic10—41no—
216C2×Dic10—41no—
217C2×Dic10—41no—
218C2×Dic10—41no—
219C2×Dic10—41no—
220C2×Dic10—41no—
221C2×Dic10—41no—
222C2×Dic10—41no—
223C2×Dic10C22⋊C414yes—
224C2×C5×C8—22no—
225C2×C5×C8—22no—
226C2×C5×C8—22no—
227C2×C5×C8—41no—
228C2×C5×C8—41no—
229C2×C5×C8—41no—
230C2×C5×C8—41no—
231C5×C4⋊C4—22no—
232C5×C4⋊C4—22no—
233C5×C4⋊C4—41no—
234C5×C4⋊C4—41no—
235C4⋊Dic5—22no—
236C4⋊Dic5—22no—
237C4⋊Dic5—41no—
238C4⋊Dic5—41no—
239#683—232no—
240C4×Dic5—22no—
241C4×Dic5—22no—
242C4×Dic5—22no—
243C4×Dic5—22no—
244C2×#168—22no—
245C2×#168—22no—
246C2×#168—22no—
247C2×#168—41no—
248C2×#168—41no—
249C2×#168—41no—
250C2×#168—41no—
251C23×Q8—51no—
252C23×Q8C2×D511yescharacteristic
253C23×C8—51no—
254C23×C8C2×D511yescharacteristic
255C2×C4⋊Q8—54no—
256C2×C4⋊Q8—102no—
257C2×C4⋊Q8—102no—
258C2×C4⋊Q8—102no—
259C2×C4⋊Q8—102no—
260C2×C4⋊Q8—102no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—102no—
263C22×C4⋊C4C2×D511yescharacteristic
264C22×C42—51no—
265C2×#103—22no—
266C2×#103—22no—
267C2×#103—22no—
268C2×#103—102no—
269C2×#103—102no—
270C2×#103—102no—
271C2×#103—102no—
272C2×#103—102no—
273C2×#103—102no—
274C2×#103—102no—
275C2×#103—102no—
276C2×#103—102no—
277C2×#95—102no—
278#336—102no—
279C23×C5C2×C22⋊C411yescharacteristic
280C23×C5#12011yescharacteristic
281C23×C5#12011yescharacteristic
282C23×C5#12111yescharacteristic
283C23×C5#12111yescharacteristic
284C23×C5#12411yescharacteristic
285C23×C5#12711yescharacteristic
286C23×C5C2×SD1612yes—
287C23×C5C2×Q1612yes—
288C23×C5#13712yes—
289C23×C5#13712yes—
290C5×Q8—24no—
291C5×Q8—24no—
292C5×Q8—42no—
293C5×Q8—42no—
294C5×Q8—42no—
295C5×Q8—42no—
296C5×Q8—42no—
297C5×Q8—42no—
298C2×C4×C5—24no—
299C2×C4×C5—42no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—42no—
305C2×C4×C5—42no—
306C2×C4×C5—44no—
307C2×C4×C5—82no—
308C2×C4×C5—81no—
309C2×C4×C5—81no—
310C2×C4×C5C2×C22⋊C411yescharacteristic
311C2×C4×C5C2×C22⋊C411yescharacteristic
312C2×C4×C5C4×D411yescharacteristic
313C2×C4×C5C4×D411yescharacteristic
314C2×C4×C5C4×D411yescharacteristic
315C2×C4×C5C4×D411yescharacteristic
316C2×C4×C5#12011yescharacteristic
317C2×C4×C5#12011yescharacteristic
318C2×C4×C5#12011yescharacteristic
319C2×C4×C5#12011yescharacteristic
320C2×C4×C5#12011yescharacteristic
321C2×C4×C5#12011yescharacteristic
322C2×C4×C5#12111yescharacteristic
323C2×C4×C5#12111yescharacteristic
324C2×C4×C5#12111yescharacteristic
325C2×C4×C5#12111yescharacteristic
326C2×C4×C5#12111yescharacteristic
327C2×C4×C5#12111yescharacteristic
328C2×C4×C5#12111yescharacteristic
329C2×C4×C5#12111yescharacteristic
330C2×C4×C5#12111yescharacteristic
331C2×C4×C5#12111yescharacteristic
332C2×C4×C5#12311yescharacteristic
333C2×C4×C5#12311yescharacteristic
334C2×C4×C5#12311yescharacteristic
335C2×C4×C5#12311yescharacteristic
336C2×C4×C5#12411yescharacteristic
337C2×C4×C5#12711yescharacteristic
338C2×Dic5—24no—
339C2×Dic5—24no—
340C2×Dic5—24no—
341C2×Dic5—24no—
342C2×Dic5—24no—
343C2×Dic5—24no—
344C2×Dic5—24no—
345C2×Dic5—42no—
346C2×Dic5—42no—
347C2×Dic5—42no—
348C2×Dic5—42no—
349C2×Dic5—42no—
350C2×Dic5—42no—
351C2×Dic5—42no—
352C2×Dic5—44no—
353C2×Dic5—82no—
354C2×Dic5—81no—
355C2×Dic5—81no—
356C2×Dic5#10318yescomplemented
357Dic10—24no—
358Dic10—24no—
359Dic10—42no—
360Dic10—42no—
361Dic10—42no—
362Dic10—42no—
363Dic10—42no—
364Dic10—42no—
365C5×C8—42no—
366#168—42no—
367C22×Q8—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×Q8—21no—
372C22×Q8—21no—
373C22×Q8—21no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—52no—
379C22×Q8—52no—
380C22×Q8—52no—
381C22×Q8—101no—
382C22×Q8—101no—
383C22×Q8—101no—
384C22×Q8—101no—
385C22×Q8—101no—
386C22×Q8—101no—
387C22×Q8—101no—
388C22×Q8—101no—
389C22×Q8—101no—
390C22×Q8—101no—
391C22×Q8—101no—
392C22×Q8C4×D512yes—
393C22×Q8D2012yes—
394C22×Q8C22⋊D512yes—
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—52no—
398C23×C4—101no—
399C23×C4—101no—
400C23×C4C22×D511yescharacteristic
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—21no—
404C22×C8—21no—
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—52no—
408C22×C8—101no—
409C22×C8—101no—
410C22×C8—101no—
411C22×C8—101no—
412C22×C8—101no—
413C22×C8—101no—
414C22×C8C22⋊D512yes—
415C4⋊Q8—108no—
416C4⋊Q8—108no—
417C4⋊Q8—108no—
418C4⋊Q8—108no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—52no—
425C2×C4⋊C4—108no—
426C2×C4⋊C4—108no—
427C2×C4⋊C4—108no—
428C2×C4⋊C4—101no—
429C2×C4⋊C4—101no—
430C2×C4⋊C4—101no—
431C2×C4⋊C4—101no—
432C2×C4⋊C4—101no—
433C2×C4⋊C4C22⋊D512yes—
434C2×C42—52no—
435C2×C42—52no—
436C2×C42—101no—
437C2×C42—101no—
438C2×C42—101no—
439C2×C42—101no—
440#103—28no—
441#103—108no—
442#103—108no—
443#103—108no—
444#95—204no—
445C22×C5#37911yescharacteristic
446C22×C5#39011yescharacteristic
447C22×C5#39011yescharacteristic
448C22×C5#39211yescharacteristic
449C22×C5#39211yescharacteristic
450C22×C5#39411yescharacteristic
451C22×C5#39411yescharacteristic
452C22×C5C2×#10312yes—
453C22×C5#41912yes—
454C22×C5#44812yes—
455C22×C5#44812yes—
456C22×C5#45112yes—
457C22×C5#45112yes—
458C22×C5#46112yes—
459C22×C5#46112yes—
460C22×C5#46212yes—
461C22×C5#46212yes—
462C22×C5#48712yes—
463C22×C5#49112yes—
464C22×C5#49211yescharacteristic
465C22×C5#49411yescharacteristic
466C22×C5#49711yescharacteristic
467C22×C5#49711yescharacteristic
468C4×C5—44no—
469C4×C5—82no—
470C4×C5#38611yescharacteristic
471C4×C5#38611yescharacteristic
472C4×C5#38611yescharacteristic
473C4×C5#38611yescharacteristic
474C4×C5#39211yescharacteristic
475C4×C5#39211yescharacteristic
476C4×C5#39411yescharacteristic
477C4×C5#39411yescharacteristic
478Dic5—28no—
479Dic5—44no—
480Dic5—82no—
481C24D4×D511yescharacteristic
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—54no—
510C2×Q8—102no—
511C2×Q8—102no—
512C2×Q8—102no—
513C2×Q8—102no—
514C2×Q8—102no—
515C2×Q8—102no—
516C2×Q8—102no—
517C2×Q8—102no—
518C2×Q8—102no—
519C2×Q8—102no—
520C2×Q8—102no—
521C2×Q8—102no—
522C2×Q8—102no—
523C2×Q8—102no—
524C2×Q8—102no—
525C2×Q8—201no—
526C2×Q8—201no—
527C2×Q8—201no—
528C2×Q8—201no—
529C2×Q8—201no—
530C2×Q8—201no—
531C2×Q8—201no—
532C2×Q8—201no—
533C2×Q8—201no—
534C2×Q8—201no—
535C2×Q8—201no—
536C2×Q8—201no—
537C2×Q8#68514yes—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—54no—
551C22×C4—54no—
552C22×C4—54no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—201no—
562C22×C4—201no—
563C22×C4—201no—
564C22×C4—201no—
565C22×C4—201no—
566C22×C4—202no—
567C22×C4—202no—
568C22×C4—201no—
569C22×C4C2×C4×D511yescharacteristic
570C22×C4C2×D2011yescharacteristic
571C22×C4#70911yescharacteristic
572C22×C4#70911yescharacteristic
573C22×C4D4×D511yescharacteristic
574C22×C4D4×D511yescharacteristic
575C22×C4D4×D511yescharacteristic
576C22×C4D4×D511yescharacteristic
577C22×C4D4×D511yescharacteristic
578C22×C4#71111yescharacteristic
579C22×C4#71111yescharacteristic
580C22×C4C2×C22⋊D511yescharacteristic
581C22×C4C2×C22⋊D511yescharacteristic
582C22×C4C2×C22⋊D511yescharacteristic
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—102no—
591C2×C8—102no—
592C2×C8—102no—
593C2×C8—201no—
594C2×C8—201no—
595C2×C8—201no—
596C2×C8—201no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—1032no—
602C4⋊C4—102no—
603C4⋊C4—102no—
604C4⋊C4—201no—
605C4⋊C4—201no—
606C42—102no—
607C42—102no—
608C42—102no—
609C42—102no—
610C2×C5#143811yescharacteristic
611C2×C5#178712yes—
612C2×C5#195611yescharacteristic
613C2×C5#196011yescharacteristic
614C2×C5#198112yes—
615C2×C5#201311yescharacteristic
616C2×C5#201311yescharacteristic
617C2×C5#201611yescharacteristic
618C2×C5#201611yescharacteristic
619C2×C5#204312yes—
620C2×C5#204312yes—
621C23D5×C22⋊C411yescharacteristic
622C23#402811yescharacteristic
623C23#403011yescharacteristic
624C23#403111yescharacteristic
625C23D5×SD1612yes—
626C23#406112yes—
627C23D5×Q1612yes—
628C23#406412yes—
629C23#408311yescharacteristic
630C23#408511yescharacteristic
631C23#408611yescharacteristic
632Q8—24no—
633Q8—24no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—104no—
641Q8—104no—
642Q8—202no—
643Q8—202no—
644Q8—202no—
645Q8—202no—
646Q8—202no—
647Q8—202no—
648C2×C4—24no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—44no—
656C2×C4—42no—
657C2×C4—58no—
658C2×C4—81no—
659C2×C4—82no—
660C2×C4—81no—
661C2×C4—104no—
662C2×C4—104no—
663C2×C4—104no—
664C2×C4—104no—
665C2×C4—104no—
666C2×C4—104no—
667C2×C4—104no—
668C2×C4—202no—
669C2×C4—202no—
670C2×C4—202no—
671C2×C4—202no—
672C2×C4—202no—
673C2×C4—202no—
674C2×C4—204no—
675C2×C4—202no—
676C2×C4—402no—
677C2×C4—401no—
678C2×C4—401no—
679C2×C4D5×C22⋊C411yescharacteristic
680C2×C4#402711yescharacteristic
681C2×C4#402711yescharacteristic
682C2×C4#402811yescharacteristic
683C2×C4#402811yescharacteristic
684C2×C4#402911yescharacteristic
685C2×C4#402911yescharacteristic
686C2×C4#403011yescharacteristic
687C2×C4#403011yescharacteristic
688C2×C4#403011yescharacteristic
689C2×C4#403111yescharacteristic
690C2×C4#403211yescharacteristic
691C2×C4C2×#68511yescharacteristic
692C2×C4C4×C22⋊D511yescharacteristic
693C2×C4C4×C22⋊D511yescharacteristic
694C2×C4#407511yescharacteristic
695C2×C4#407611yescharacteristic
696C2×C4#407611yescharacteristic
697C2×C4#408311yescharacteristic
698C2×C4#408311yescharacteristic
699C2×C4#408311yescharacteristic
700C2×C4#408411yescharacteristic
701C2×C4#408411yescharacteristic
702C2×C4#408511yescharacteristic
703C2×C4#408511yescharacteristic
704C2×C4#408511yescharacteristic
705C2×C4#408611yescharacteristic
706C2×C4#409911yescharacteristic
707C8—42no—
708C8—202no—
709C5#1101011yescharacteristic, complemented, Sylow
710C22#6508112yes—
711C22#6508212yes—
712C22#6508612yes—
713C22D5×#10312yes—
714C22#6509112yes—
715C22#6509512yes—
716C22#6509712yes—
717C22#6510712yes—
718C22#6524411yescharacteristic
719C22#6524611yescharacteristic
720C22#6524611yescharacteristic
721C22#6524811yescharacteristic
722C22#6524911yescharacteristic
723C22#6525011yescharacteristic
724C22#6545112yes—
725C22#6545611yescharacteristic
726C22#6545912yes—
727C22#6546411yescharacteristic
728C22#6547011yescharacteristic
729C22#6547112yes—
730C22#6547512yes—
731C22#6547911yescharacteristic
732C22#6551211yescharacteristic
733C4—44no—
734C4—82no—
735C4—108no—
736C4—204no—
737C4—402no—
738C4#6524511yescharacteristic
739C4#6524511yescharacteristic
740C4#6524711yescharacteristic
741C4#6524811yescharacteristic
742C4#6524911yescharacteristic
743C4#6525011yescharacteristic
744C4#6550211yescharacteristic
745C4#6551211yescharacteristic
746C2#1060101811yescharacteristic
747C2#1060102111yescharacteristic
748C2#1060102212yes—
749C2#1060103912yes—
750C2#1060105912yes—
751C2#1060107511yescharacteristic
752C2#1060107611yescharacteristic
753C2#1060107712yes—
754C2#1060234311yescharacteristic
755C2#1060285011yescharacteristic
756C2#1060286611yescharacteristic
subgroupG/H
centerC24D4×D5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC22×C5×#103C2
socle, prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC22×#103D5
hypocenterC5#11010
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
17. C2×#4090C4semidirect
356. C2×Dic5#103semidirect
709. C5#11010semidirect

Maximal subgroups

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

subgroupindex
C22×#40902
C22×C5×#1032
C22×#39672
C22×#39482
C22×#39422
C2×#647702
#106023562
#110105