Finite Group Databasebeta

← #12005163

Subgroups — #12005163

Order 1280.

1338 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65231C211yesmaximal, characteristic
2C2×#65231C211yesmaximal, characteristic
3C2×C22⋊C4×Dic5C211yesmaximal, characteristic
4C2×C5×#342C211yesmaximal, characteristic
5C2×#64747C211yesmaximal, characteristic
6C2×#64747C211yesmaximal, characteristic
7C2×#64746C211yesmaximal, characteristic
8C24×Dic5C2211yescharacteristic
9C22×C5×C22⋊C4C2211yescharacteristic
10C22×C5×C22⋊C4C2211yescharacteristic
11C22×C5×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic5C2211yescharacteristic
13C22×C22⋊Dic5C2211yescharacteristic
14C22×C22⋊Dic5C2211yescharacteristic
15C22×#683—21no—
16C22×#683C412yescomplemented
17C22×C4×Dic5—21no—
18C2×#3963—21no—
19C2×#3963—21no—
20C2×#3963C412yescomplemented
21#65231—21no—
22#65231—21no—
23#65231—22no—
24#65231—21no—
25#65231—21no—
26#65231C414yescomplemented
27C22⋊C4×Dic5—22no—
28C22⋊C4×Dic5C414yescomplemented
29C5×#342—22no—
30#64747—22no—
31#64747—22no—
32#64746—22no—
33#10854—51nomaximal, Sylow
34C25×C5C2311yescharacteristic
35C23×C4×C5—21no—
36C23×C4×C5—21no—
37C23×C4×C5C2×C412yes—
38C23×Dic5—21no—
39C23×Dic5—21no—
40C23×Dic5—44no—
41C23×Dic5C2×C411yescharacteristic
42C23×Dic5C2×C412yes—
43C23×Dic5C2×C412yes—
44C23×Dic5C2×C412yes—
45C23×Dic5C2×C411yescharacteristic
46C23×Dic5D411yescharacteristic
47C23×Dic5D411yescharacteristic
48C23×Dic5D412yes—
49C23×Dic5D411yescharacteristic
50C23×Dic5D411yescharacteristic
51C23×Dic5Q812yes—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C5×C22⋊C4—21no—
66C2×C5×C22⋊C4C2×C412yes—
67C2×C5×C22⋊C4C2×C412yes—
68C2×C5×C22⋊C4D412yes—
69C2×C5×C22⋊C4Q812yes—
70C2×C22⋊Dic5—21no—
71C2×C22⋊Dic5—21no—
72C2×C22⋊Dic5—21no—
73C2×C22⋊Dic5—21no—
74C2×C22⋊Dic5—21no—
75C2×C22⋊Dic5—21no—
76C2×C22⋊Dic5—21no—
77C2×C22⋊Dic5—21no—
78C2×C22⋊Dic5—21no—
79C2×C22⋊Dic5—21no—
80C2×C22⋊Dic5—21no—
81C2×C22⋊Dic5—21no—
82C2×C22⋊Dic5—21no—
83C2×C22⋊Dic5—21no—
84C2×C22⋊Dic5C2×C412yes—
85C2×C22⋊Dic5C2×C412yes—
86C2×C22⋊Dic5D412yes—
87C2×C22⋊Dic5Q812yes—
88C2×#683—24no—
89C2×#683—22no—
90C2×#683—22no—
91C2×#683—44no—
92C2×#683—44no—
93C2×C4×Dic5—24no—
94C2×C4×Dic5—44no—
95#3963—24no—
96#3963—22no—
97#3963—22no—
98#3963—24no—
99C2×#380—51no—
100C2×#380—51no—
101C2×C4×C22⋊C4—51no—
102C2×#342—51no—
103C2×#342—51no—
104C2×#342—51no—
105C2×#342D511yescharacteristic
106C24×C5—42no—
107C24×C5—42no—
108C24×C5C22×C411yescharacteristic
109C24×C5C22×C411yescharacteristic
110C24×C5C22×C411yescharacteristic
111C24×C5C2×D411yescharacteristic
112C24×C5C2×D411yescharacteristic
113C24×C5C2×D411yescharacteristic
114C24×C5C2×D411yescharacteristic
115C24×C5C2×D411yescharacteristic
116C24×C5C2×Q811yescharacteristic
117C24×C5C2×Q811yescharacteristic
118C24×C5C2×Q811yescharacteristic
119C24×C5#4111yescharacteristic
120C24×C5#4111yescharacteristic
121C24×C5#4111yescharacteristic
122C24×C5#4111yescharacteristic
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—42no—
131C22×C4×C5—42no—
132C22×C4×C5—42no—
133C22×C4×C5—42no—
134C22×C4×C5—41no—
135C22×C4×C5—41no—
136C22×C4×C5—42no—
137C22×C4×C5—42no—
138C22×Dic5—24no—
139C22×Dic5—24no—
140C22×Dic5—24no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—44no—
149C22×Dic5—44no—
150C22×Dic5—44no—
151C22×Dic5—44no—
152C22×Dic5—42no—
153C22×Dic5—42no—
154C22×Dic5—42no—
155C22×Dic5—42no—
156C22×Dic5—42no—
157C22×Dic5—42no—
158C22×Dic5—42no—
159C22×Dic5—41no—
160C22×Dic5—41no—
161C22×Dic5—42no—
162C22×Dic5—42no—
163C22×Dic5C4212yes—
164C22×Dic5C4212yes—
165C22×Dic5C22⋊C411yescharacteristic
166C22×Dic5C22⋊C411yescharacteristic
167C22×Dic5C22⋊C412yes—
168C22×Dic5C22⋊C412yes—
169C22×Dic5C22⋊C411yescharacteristic
170C22×Dic5C22⋊C412yes—
171C22×Dic5C22⋊C412yes—
172C22×Dic5C22⋊C411yescharacteristic
173C22×Dic5C4⋊C412yes—
174C22×Dic5C4⋊C412yes—
175C22×Dic5C4⋊C412yes—
176C22×Dic5C4⋊C412yes—
177C22×Dic5C4⋊C412yes—
178C22×Dic5C4⋊C412yes—
179C5×C22⋊C4—22no—
180C5×C22⋊C4—22no—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—41no—
185C5×C22⋊C4—41no—
186C5×C22⋊C4—41no—
187C5×C22⋊C4—41no—
188C5×C22⋊C4—41no—
189C5×C22⋊C4—41no—
190C5×C22⋊C4C4⋊C414yescomplemented
191C22⋊Dic5—22no—
192C22⋊Dic5—22no—
193C22⋊Dic5—22no—
194C22⋊Dic5—22no—
195C22⋊Dic5—22no—
196C22⋊Dic5—41no—
197C22⋊Dic5—41no—
198C22⋊Dic5—41no—
199C22⋊Dic5—41no—
200C22⋊Dic5—41no—
201C22⋊Dic5—41no—
202C22⋊Dic5C4⋊C414yescomplemented
203#683—44no—
204#683—48no—
205#683—44no—
206C4×Dic5—48no—
207C24×C4—51no—
208C22×C4⋊C4—52no—
209C22×C4⋊C4—101no—
210C22×C22⋊C4—51no—
211C22×C22⋊C4—51no—
212C22×C22⋊C4—51no—
213C22×C22⋊C4C2×D511yescharacteristic
214C22×C22⋊C4C2×D511yescharacteristic
215C22×C22⋊C4C2×D511yescharacteristic
216C22×C42—101no—
217#380—54no—
218#380—101no—
219#380—101no—
220#380—101no—
221#380—101no—
222#380—102no—
223C4×C22⋊C4—54no—
224C4×C22⋊C4—102no—
225C2×#95—52no—
226C2×#95—101no—
227C2×#95—101no—
228#342—22no—
229#342—102no—
230#342—102no—
231#342—102no—
232C23×C5—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5—41no—
243C23×C5—41no—
244C23×C5—42no—
245C23×C5—41no—
246C23×C5—42no—
247C23×C5—42no—
248C23×C5—41no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—42no—
253C23×C5—42no—
254C23×C5C2×C4211yescharacteristic
255C23×C5C2×C22⋊C411yescharacteristic
256C23×C5C2×C22⋊C411yescharacteristic
257C23×C5C2×C22⋊C411yescharacteristic
258C23×C5C2×C4⋊C411yescharacteristic
259C23×C5C2×C4⋊C411yescharacteristic
260C23×C5C2×C4⋊C411yescharacteristic
261C23×C5C2×C4⋊C411yescharacteristic
262C23×C5C2×C4⋊C411yescharacteristic
263C23×C5#11711yescharacteristic
264C23×C5#11711yescharacteristic
265C23×C5C4×D411yescharacteristic
266C23×C5C4×D411yescharacteristic
267C23×C5C4×D411yescharacteristic
268C23×C5C4×D411yescharacteristic
269C23×C5C4×Q811yescharacteristic
270C23×C5C4×Q811yescharacteristic
271C23×C5C4×Q811yescharacteristic
272C23×C5C4×Q811yescharacteristic
273C23×C5#12111yescharacteristic
274C23×C5#12111yescharacteristic
275C23×C5#12111yescharacteristic
276C23×C5#12111yescharacteristic
277C23×C5C22⋊Q811yescharacteristic
278C23×C5C22⋊Q811yescharacteristic
279C23×C5C22⋊Q811yescharacteristic
280C23×C5C22⋊Q811yescharacteristic
281C23×C5#12411yescharacteristic
282C23×C5#12411yescharacteristic
283C23×C5#12511yescharacteristic
284C23×C5#12511yescharacteristic
285C23×C5#12711yescharacteristic
286C23×C5C4⋊Q811yescharacteristic
287C23×C5C4⋊Q811yescharacteristic
288C23×C5C4⋊Q811yescharacteristic
289C2×C4×C5—24no—
290C2×C4×C5—42no—
291C2×C4×C5—44no—
292C2×C4×C5—42no—
293C2×C4×C5—44no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—42no—
297C2×C4×C5—42no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—82no—
301C2×C4×C5—82no—
302C2×C4×C5—82no—
303C2×C4×C5—82no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—24no—
308C2×Dic5—24no—
309C2×Dic5—24no—
310C2×Dic5—24no—
311C2×Dic5—24no—
312C2×Dic5—24no—
313C2×Dic5—24no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316C2×Dic5—42no—
317C2×Dic5—42no—
318C2×Dic5—42no—
319C2×Dic5—42no—
320C2×Dic5—42no—
321C2×Dic5—44no—
322C2×Dic5—42no—
323C2×Dic5—44no—
324C2×Dic5—42no—
325C2×Dic5—42no—
326C2×Dic5—42no—
327C2×Dic5—42no—
328C2×Dic5—42no—
329C2×Dic5—42no—
330C2×Dic5—82no—
331C2×Dic5—82no—
332C2×Dic5—82no—
333C2×Dic5—82no—
334C2×Dic5#9512yes—
335C2×Dic5#9512yes—
336C2×Dic5#9512yes—
337C2×Dic5#9512yes—
338C2×Dic5#9914yes—
339C25C22×D511yescharacteristic
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—51no—
343C23×C4—51no—
344C23×C4—51no—
345C23×C4—51no—
346C23×C4—52no—
347C23×C4—52no—
348C23×C4—51no—
349C23×C4—51no—
350C23×C4—52no—
351C23×C4—52no—
352C23×C4—52no—
353C23×C4—101no—
354C23×C4—101no—
355C23×C4—204no—
356C23×C4C4×D512yes—
357C2×C4⋊C4—102no—
358C2×C4⋊C4—102no—
359C2×C4⋊C4—104no—
360C2×C4⋊C4—204no—
361C2×C4⋊C4—204no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—52no—
377C2×C22⋊C4—52no—
378C2×C22⋊C4—52no—
379C2×C22⋊C4—52no—
380C2×C22⋊C4—101no—
381C2×C22⋊C4—101no—
382C2×C22⋊C4—101no—
383C2×C22⋊C4—101no—
384C2×C22⋊C4—101no—
385C2×C22⋊C4—101no—
386C2×C22⋊C4—101no—
387C2×C22⋊C4—101no—
388C2×C22⋊C4—101no—
389C2×C22⋊C4—101no—
390C2×C22⋊C4—101no—
391C2×C22⋊C4—101no—
392C2×C22⋊C4—101no—
393C2×C22⋊C4—101no—
394C2×C22⋊C4Dic1012yes—
395C2×C22⋊C4C4×D512yes—
396C2×C22⋊C4C4×D512yes—
397C2×C22⋊C4C22⋊D512yes—
398C2×C42—104no—
399C2×C42—204no—
400#95—102no—
401#95—102no—
402#95—104no—
403#95—104no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—22no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—21no—
411C22×C5—21no—
412C22×C5—21no—
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—22no—
423C22×C5—22no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—41no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5C2×#9511yescharacteristic
445C22×C5C4×C4⋊C411yescharacteristic
446C22×C5C4×C4⋊C411yescharacteristic
447C22×C5#38011yescharacteristic
448C22×C5#38011yescharacteristic
449C22×C5#38211yescharacteristic
450C22×C5#38411yescharacteristic
451C22×C5#38911yescharacteristic
452C22×C5#38911yescharacteristic
453C22×C5#38911yescharacteristic
454C22×C5#38911yescharacteristic
455C22×C5#39011yescharacteristic
456C22×C5#39011yescharacteristic
457C22×C5#39111yescharacteristic
458C22×C5#39111yescharacteristic
459C22×C5C2×#9912yes—
460C22×C5#41012yes—
461C4×C5—44no—
462C4×C5—82no—
463C4×C5—82no—
464Dic5—22no—
465Dic5—22no—
466Dic5—22no—
467Dic5—44no—
468Dic5—82no—
469Dic5—82no—
470Dic5#34214yescomplemented
471C24—42no—
472C24—42no—
473C24C2×Dic1011yescharacteristic
474C24C2×C4×D511yescharacteristic
475C24C2×C4×D511yescharacteristic
476C24C2×C4×D511yescharacteristic
477C24#70911yescharacteristic
478C24#70911yescharacteristic
479C24D4×D511yescharacteristic
480C24D4×D511yescharacteristic
481C24D4×D511yescharacteristic
482C24D4×D511yescharacteristic
483C24#71111yescharacteristic
484C24#71111yescharacteristic
485C24Q8×D511yescharacteristic
486C24Q8×D511yescharacteristic
487C24C2×C22⋊D511yescharacteristic
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—51no—
504C22×C4—52no—
505C22×C4—52no—
506C22×C4—52no—
507C22×C4—51no—
508C22×C4—51no—
509C22×C4—51no—
510C22×C4—52no—
511C22×C4—52no—
512C22×C4—52no—
513C22×C4—52no—
514C22×C4—52no—
515C22×C4—52no—
516C22×C4—52no—
517C22×C4—52no—
518C22×C4—52no—
519C22×C4—104no—
520C22×C4—104no—
521C22×C4—104no—
522C22×C4—102no—
523C22×C4—102no—
524C22×C4—102no—
525C22×C4—102no—
526C22×C4—102no—
527C22×C4—102no—
528C22×C4—102no—
529C22×C4—204no—
530C22×C4—204no—
531C22×C4—204no—
532C22×C4—204no—
533C22×C4—202no—
534C22×C4—202no—
535C22×C4—202no—
536C22×C4—202no—
537C22×C4—202no—
538C22×C4—202no—
539C22×C4—202no—
540C22×C4—201no—
541C22×C4—201no—
542C22×C4—202no—
543C22×C4—202no—
544C4⋊C4—204no—
545C4⋊C4—208no—
546C4⋊C4—204no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—54no—
559C22⋊C4—102no—
560C22⋊C4—102no—
561C22⋊C4—102no—
562C22⋊C4—102no—
563C22⋊C4—102no—
564C22⋊C4—201no—
565C22⋊C4—201no—
566C22⋊C4—201no—
567C22⋊C4—201no—
568C22⋊C4—201no—
569C22⋊C4—201no—
570C22⋊C4#68314yescomplemented
571C42—208no—
572C2×C5—21no—
573C2×C5—21no—
574C2×C5—21no—
575C2×C5—21no—
576C2×C5—21no—
577C2×C5—21no—
578C2×C5—21no—
579C2×C5—21no—
580C2×C5—21no—
581C2×C5—21no—
582C2×C5—21no—
583C2×C5—21no—
584C2×C5C4⋊#9511yescharacteristic
585C2×C5C2×#34211yescharacteristic
586C2×C5#174011yescharacteristic
587C2×C5#196412yes—
588C2×C5#199612yes—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—42no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23C4×Dic1011yescharacteristic
612C23C4×Dic1011yescharacteristic
613C23C42×D511yescharacteristic
614C23#401811yescharacteristic
615C23#402311yescharacteristic
616C23#402411yescharacteristic
617C23#402411yescharacteristic
618C23D5×C22⋊C411yescharacteristic
619C23D5×C22⋊C411yescharacteristic
620C23D5×C22⋊C411yescharacteristic
621C23#402711yescharacteristic
622C23#402711yescharacteristic
623C23#403011yescharacteristic
624C23#403011yescharacteristic
625C23#403111yescharacteristic
626C23#403111yescharacteristic
627C23#403311yescharacteristic
628C23#403311yescharacteristic
629C23#403411yescharacteristic
630C23#403411yescharacteristic
631C23#403511yescharacteristic
632C23#403511yescharacteristic
633C23D5×C4⋊C411yescharacteristic
634C23D5×C4⋊C411yescharacteristic
635C23D5×C4⋊C411yescharacteristic
636C23D5×C4⋊C411yescharacteristic
637C23#404211yescharacteristic
638C23#404211yescharacteristic
639C23C2×#68311yescharacteristic
640C23C4×C22⋊D511yescharacteristic
641C23C4×C22⋊D511yescharacteristic
642C23#408511yescharacteristic
643C23#408511yescharacteristic
644C23#408611yescharacteristic
645C23#409011yescharacteristic
646C2×C4—24no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—54no—
658C2×C4—52no—
659C2×C4—52no—
660C2×C4—52no—
661C2×C4—52no—
662C2×C4—82no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4—82no—
666C2×C4—104no—
667C2×C4—104no—
668C2×C4—104no—
669C2×C4—104no—
670C2×C4—104no—
671C2×C4—104no—
672C2×C4—102no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—104no—
676C2×C4—202no—
677C2×C4—202no—
678C2×C4—202no—
679C2×C4—202no—
680C2×C4—202no—
681C2×C4—202no—
682C2×C4—202no—
683C2×C4—202no—
684C2×C4—204no—
685C2×C4—204no—
686C2×C4—202no—
687C2×C4—202no—
688C2×C4—202no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—202no—
692C2×C4—402no—
693C2×C4—402no—
694C2×C4—402no—
695C2×C4—402no—
696C5#1085411yescharacteristic, complemented, Sylow
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#6493511yescharacteristic
738C22#6493511yescharacteristic
739C22#6493611yescharacteristic
740C22#6493611yescharacteristic
741C22#6493811yescharacteristic
742C22#6493911yescharacteristic
743C22D5×#9511yescharacteristic
744C22#6495611yescharacteristic
745C22#6502912yes—
746C22D5×#9912yes—
747C22C4×#68311yescharacteristic
748C22#6523111yescharacteristic
749C22#6524611yescharacteristic
750C22#6524611yescharacteristic
751C22#6526111yescharacteristic
752C22#6526111yescharacteristic
753C22#6526511yescharacteristic
754C4—44no—
755C4—54no—
756C4—82no—
757C4—82no—
758C4—102no—
759C4—102no—
760C4—102no—
761C4—204no—
762C4—402no—
763C4—402no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2#1059974411yescharacteristic
777C2#1059974812yes—
778C2D5×#34211yescharacteristic
779C2#1060019711yescharacteristic
780C2#1060082312yes—
subgroupG/H
centerC23D5×C22⋊C4
commutatorC23×C5C2×C42
FrattiniC25C22×D5
FittingC2×C5×#342C2
socleC23×C5C2×C22⋊C4
prime radical, cosocleC25×C5C23
hypercenterC2×#342D5
hypocenterC5#10854
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
16. C22×#683C4semidirect
20. C2×#3963C4semidirect
26. #65231C4semidirect
28. C22⋊C4×Dic5C4semidirect
190. C5×C22⋊C4C4⋊C4semidirect
202. C22⋊Dic5C4⋊C4semidirect
470. Dic5#342semidirect
570. C22⋊C4#683semidirect
696. C5#10854semidirect

Maximal subgroups

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

subgroupindex
C2×#652312
C2×C22⋊C4×Dic52
C2×C5×#3422
C2×#647472
C2×#647462
#108545