Finite Group Databasebeta

← #12022975

Subgroups — #12022975

Order 1280.

1386 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic5C211yesmaximal, characteristic
2C2×#64936C211yesmaximal, characteristic
3C2×#64938C211yesmaximal, characteristic
4C5×#1442C211yesmaximal, characteristic
5#10602360C211yesmaximal, characteristic
6#10600215C211yesmaximal, characteristic
7#10600214C211yesmaximal, characteristic
8#10600200C211yesmaximal, characteristic
9#10600200C211yesmaximal, characteristic
10#10600200C211yesmaximal, characteristic
11#10600198C211yesmaximal, characteristic
12#10600197C211yesmaximal, characteristic
13#10600197C211yesmaximal, characteristic
14#10600197C211yesmaximal, characteristic
15#10600197C211yesmaximal, characteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic5C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C22×#683C2211yescharacteristic
20C22×#683C2211yescharacteristic
21C22×#683C2211yescharacteristic
22C22×#683C2211yescharacteristic
23C22×#683C2211yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36C2×#3963C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38C2×#3963C2211yescharacteristic
39C2×#3963C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C4⋊C4×Dic5—24no—
52#64938—24no—
53#64936C418yescomplemented
54#14041—51nomaximal, Sylow
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×Dic5C2311yescharacteristic
63C23×Dic5C2311yescharacteristic
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C4⋊Dic5—22no—
74C2×C4⋊Dic5—22no—
75C2×C4⋊Dic5—41no—
76C2×C4⋊Dic5—41no—
77C2×C4⋊Dic5C2×C414yes—
78C2×C4⋊Dic5Q814yes—
79C2×#683—22no—
80C2×#683—22no—
81C2×#683—22no—
82C2×#683—22no—
83C2×#683—22no—
84C2×#683—22no—
85C2×#683—22no—
86C2×#683—22no—
87C2×#683—22no—
88C2×#683—41no—
89C2×#683—41no—
90C2×#683C2×C414yes—
91C2×#683C2×C414yes—
92C2×#683C2×C414yes—
93C2×#683Q814yes—
94C2×C4×Dic5—22no—
95C2×C4×Dic5—22no—
96C2×C4×Dic5—22no—
97C2×C4×Dic5—22no—
98C2×C4×Dic5—22no—
99C2×C4×Dic5—22no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5—22no—
102C2×C4×Dic5—22no—
103C2×C4×Dic5—41no—
104C2×C4×Dic5—41no—
105C2×C4×Dic5—41no—
106C2×C4×Dic5—41no—
107C2×C4×Dic5C2×C414yes—
108C2×C4×Dic5D414yes—
109C5×#95—22no—
110C5×#95—22no—
111C5×#95—22no—
112C5×#95—41no—
113C5×#95—41no—
114C5×#95C2×C414yes—
115#3963—22no—
116#3963—22no—
117#3963—22no—
118#3963—22no—
119#3963—22no—
120#3963—22no—
121#3963—22no—
122#3963—41no—
123#3963—41no—
124#3963—41no—
125#3963—41no—
126#3963—41no—
127#3963—41no—
128#3963—41no—
129#3963—41no—
130#3963C2×C414yes—
131C2×#389—51no—
132C2×C4×C4⋊C4—51no—
133C2×C4×C4⋊C4—51no—
134#1445—51no—
135#1445—51no—
136#1442—51no—
137#1442D511yescharacteristic
138#1436—51no—
139#1436—51no—
140#1436—51no—
141#1436—51no—
142C4⋊#95—51no—
143C4⋊#95—51no—
144C4⋊#95—51no—
145C4⋊#95—51no—
146C24×C5C2411yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5C22×C412yes—
189C22×C4×C5C22×C412yes—
190C22×C4×C5C22×C412yes—
191C22×C4×C5C2×D412yes—
192C22×C4×C5C2×Q812yes—
193C22×C4×C5C2×Q812yes—
194C22×C4×C5#4112yes—
195C22×C4×C5#4112yes—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—21no—
203C22×Dic5—21no—
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5—21no—
213C22×Dic5—21no—
214C22×Dic5—21no—
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5C22×C412yes—
238C22×Dic5C22×C412yes—
239C22×Dic5C22×C412yes—
240C22×Dic5C22×C412yes—
241C22×Dic5C2×D412yes—
242C22×Dic5C2×D412yes—
243C22×Dic5C2×Q812yes—
244C22×Dic5C2×Q812yes—
245C22×Dic5C2×Q812yes—
246C22×Dic5C2×Q812yes—
247C22×Dic5#4112yes—
248C22×Dic5#4112yes—
249C22×Dic5#4112yes—
250C22×Dic5#4112yes—
251C22×Dic5#4112yes—
252C5×C4⋊C4—28no—
253C4⋊Dic5—28no—
254C4⋊Dic5—44no—
255#683—28no—
256#683—28no—
257#683—28no—
258#683—44no—
259#683—44no—
260C4×Dic5—28no—
261C4×Dic5—28no—
262C4×Dic5—44no—
263C4×Dic5—44no—
264C4×Dic5—44no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4—51no—
268C22×C4⋊C4—51no—
269C22×C4⋊C4—51no—
270C22×C4⋊C4—51no—
271C22×C4⋊C4—51no—
272C22×C4⋊C4C2×D511yescharacteristic
273C22×C42—51no—
274C22×C42—51no—
275C22×C42—51no—
276C22×C42—51no—
277C22×C42—51no—
278#389—58no—
279C4×C4⋊C4—104no—
280C4×C4⋊C4—104no—
281C2×#95—51no—
282C2×#95—51no—
283C2×#95—51no—
284C2×#95—51no—
285C2×#95—51no—
286C2×#95—51no—
287C2×#95—51no—
288C2×#95—51no—
289C2×#95—51no—
290C2×#95—51no—
291C2×#95—51no—
292C2×#95—51no—
293C2×#95—51no—
294C2×#95—51no—
295C2×#95—51no—
296C2×#95—51no—
297C2×#95C2×D511yescharacteristic
298C2×#95C2×D511yescharacteristic
299C2×#95C2×D511yescharacteristic
300C2×#95C2×D511yescharacteristic
301C2×#95C2×D511yescharacteristic
302C2×#95C2×D511yescharacteristic
303C23×C5C23×C411yescharacteristic
304C23×C5C22×D411yescharacteristic
305C23×C5C22×Q811yescharacteristic
306C23×C5C22×Q811yescharacteristic
307C23×C5C2×#4111yescharacteristic
308C23×C5C2×#4111yescharacteristic
309C23×C5C2×#4111yescharacteristic
310C23×C5C2×#4111yescharacteristic
311C23×C5C2×#4111yescharacteristic
312C23×C5C2×#4111yescharacteristic
313C23×C5C2×#4111yescharacteristic
314C23×C5H(5,𝔽2)11yescharacteristic
315C23×C5H(5,𝔽2)11yescharacteristic
316C23×C5H(5,𝔽2)11yescharacteristic
317C23×C52−1+411yescharacteristic
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5C4×Q814yes—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—41no—
389C2×Dic5—41no—
390C2×Dic5—41no—
391C2×Dic5—41no—
392C2×Dic5—41no—
393C2×Dic5—41no—
394C2×Dic5—41no—
395C2×Dic5—41no—
396C2×Dic5—41no—
397C2×Dic5—41no—
398C2×Dic5—41no—
399C2×Dic5—41no—
400C2×Dic5—41no—
401C2×Dic5—41no—
402C2×Dic5—41no—
403C2×Dic5—41no—
404C2×Dic5—41no—
405C2×Dic5—41no—
406C2×Dic5—41no—
407C2×Dic5—41no—
408C2×Dic5—41no—
409C2×Dic5—41no—
410C2×Dic5—41no—
411C2×Dic5—41no—
412C2×Dic5—41no—
413C2×Dic5—41no—
414C2×Dic5—41no—
415C2×Dic5#11714yes—
416C2×Dic5C4×D414yes—
417C2×Dic5C4×Q814yes—
418C2×Dic5C22⋊Q814yes—
419C2×Dic5C22⋊Q814yes—
420C2×Dic5#12314yes—
421C2×Dic5#12514yes—
422C2×Dic5#12614yes—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—102no—
448C2×C4⋊C4—102no—
449C2×C4⋊C4—102no—
450C2×C4⋊C4—102no—
451C2×C4⋊C4—102no—
452C2×C4⋊C4—102no—
453C2×C4⋊C4—102no—
454C2×C4⋊C4—102no—
455C2×C4⋊C4—102no—
456C2×C4⋊C4—102no—
457C2×C4⋊C4—102no—
458C2×C4⋊C4—201no—
459C2×C4⋊C4—201no—
460C2×C4⋊C4—201no—
461C2×C4⋊C4—201no—
462C2×C42—54no—
463C2×C42—54no—
464C2×C42—102no—
465C2×C42—102no—
466C2×C42—102no—
467C2×C42—102no—
468C2×C42—102no—
469C2×C42—102no—
470C2×C42—102no—
471C2×C42—102no—
472C2×C42—102no—
473C2×C42—201no—
474C2×C42—201no—
475C2×C42—201no—
476C2×C42—201no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—41no—
481#95—41no—
482#95—54no—
483#95—102no—
484#95—102no—
485#95—102no—
486#95—102no—
487#95—102no—
488#95—102no—
489#95—102no—
490#95—201no—
491#95—201no—
492#95—201no—
493#95—201no—
494#95—201no—
495#95—201no—
496#95—201no—
497#95—201no—
498#95C4×D514yes—
499C22×C5C2×#11711yescharacteristic
500C22×C5C2×C4×D411yescharacteristic
501C22×C5C2×C4×Q811yescharacteristic
502C22×C5C2×C4×Q811yescharacteristic
503C22×C5C4×#4111yescharacteristic
504C22×C5#51811yescharacteristic
505C22×C5#52011yescharacteristic
506C22×C5C2×C22⋊Q811yescharacteristic
507C22×C5C2×C22⋊Q811yescharacteristic
508C22×C5C2×#12311yescharacteristic
509C22×C5#52511yescharacteristic
510C22×C5C2×#12511yescharacteristic
511C22×C5C2×#12611yescharacteristic
512C22×C5#52911yescharacteristic
513C22×C5#53311yescharacteristic
514C22×C5#53511yescharacteristic
515C22×C5#53711yescharacteristic
516C22×C5#54011yescharacteristic
517C22×C5#54211yescharacteristic
518C22×C5#55211yescharacteristic
519C22×C5#55311yescharacteristic
520C22×C5#55311yescharacteristic
521C22×C5#55311yescharacteristic
522C22×C5#55411yescharacteristic
523C22×C5#55411yescharacteristic
524C22×C5#55411yescharacteristic
525C22×C5#55411yescharacteristic
526C22×C5#55511yescharacteristic
527C22×C5#55611yescharacteristic
528C22×C5#55711yescharacteristic
529C22×C5#55711yescharacteristic
530C22×C5Q8211yescharacteristic
531C22×C5#55911yescharacteristic
532C22×C5#55911yescharacteristic
533C22×C5#55911yescharacteristic
534C4×C5—24no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5—81no—
541Dic5—24no—
542Dic5—42no—
543Dic5—42no—
544Dic5—42no—
545Dic5—42no—
546Dic5—42no—
547Dic5—81no—
548Dic5#38718yes—
549C24C23×D511yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
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—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—52no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—52no—
598C22×C4—52no—
599C22×C4—52no—
600C22×C4—52no—
601C22×C4—52no—
602C22×C4—52no—
603C22×C4—52no—
604C22×C4—52no—
605C22×C4—52no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—101no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4—101no—
628C22×C4—101no—
629C22×C4—101no—
630C22×C4—101no—
631C22×C4—101no—
632C22×C4—101no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—101no—
636C22×C4—101no—
637C22×C4—101no—
638C22×C4—101no—
639C22×C4—101no—
640C22×C4—101no—
641C22×C4—101no—
642C22×C4—101no—
643C22×C4—101no—
644C22×C4—101no—
645C22×C4—101no—
646C22×C4—101no—
647C22×C4C2×C4×D512yes—
648C22×C4C2×C4×D512yes—
649C22×C4C2×C4×D512yes—
650C22×C4D4×D512yes—
651C22×C4#71112yes—
652C22×C4#71112yes—
653C22×C4Q8×D512yes—
654C22×C4Q8×D512yes—
655C4⋊C4—28no—
656C4⋊C4—108no—
657C4⋊C4—108no—
658C4⋊C4—108no—
659C4⋊C4—108no—
660C4⋊C4—204no—
661C4⋊C4—204no—
662C4⋊C4—204no—
663C42—108no—
664C42—108no—
665C42—204no—
666C42—204no—
667C42—204no—
668C2×C5C2×#38711yescharacteristic
669C2×C5C4×C22⋊Q811yescharacteristic
670C2×C5#232411yescharacteristic
671C2×C5#235511yescharacteristic
672C2×C5#235711yescharacteristic
673C2×C5#236911yescharacteristic
674C2×C5#237011yescharacteristic
675C2×C5#248511yescharacteristic
676C2×C5#248711yescharacteristic
677C2×C5#250711yescharacteristic
678C2×C5#250911yescharacteristic
679C2×C5#251111yescharacteristic
680C2×C5#251311yescharacteristic
681C2×C5#258011yescharacteristic
682C2×C5#258211yescharacteristic
683C23C22×C4×D511yescharacteristic
684C23C2×D4×D511yescharacteristic
685C23C2×#71111yescharacteristic
686C23C2×#71111yescharacteristic
687C23#414411yescharacteristic
688C23C2×Q8×D511yescharacteristic
689C23C2×Q8×D511yescharacteristic
690C23D5×#4111yescharacteristic
691C23D5×#4111yescharacteristic
692C23D5×#4111yescharacteristic
693C23D5×#4111yescharacteristic
694C23D5×#4111yescharacteristic
695C23#414911yescharacteristic
696C23#414911yescharacteristic
697C23#415011yescharacteristic
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—54no—
747C2×C4—54no—
748C2×C4—54no—
749C2×C4—54no—
750C2×C4—54no—
751C2×C4—54no—
752C2×C4—54no—
753C2×C4—54no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—201no—
776C2×C4—201no—
777C2×C4—201no—
778C2×C4—201no—
779C2×C4—201no—
780C2×C4—201no—
781C2×C4—201no—
782C2×C4—201no—
783C2×C4—201no—
784C2×C4—201no—
785C2×C4—201no—
786C2×C4—201no—
787C2×C4—201no—
788C2×C4—201no—
789C2×C4—201no—
790C2×C4—201no—
791C2×C4—201no—
792C2×C4—201no—
793C2×C4—201no—
794C2×C4—201no—
795C2×C4—201no—
796C2×C4—201no—
797C2×C4—201no—
798C2×C4—201no—
799C2×C4—201no—
800C2×C4—201no—
801C2×C4—201no—
802C2×C4#403314yes—
803C5#1404111yescharacteristic, complemented, Sylow
804C22C2×#403311yescharacteristic
805C22D5×#11711yescharacteristic
806C22#6585711yescharacteristic
807C22C4×#71111yescharacteristic
808C22C4×D4×D511yescharacteristic
809C22#6587911yescharacteristic
810C22C4×Q8×D511yescharacteristic
811C22#6592011yescharacteristic
812C22#6593111yescharacteristic
813C22#6593511yescharacteristic
814C22#6595011yescharacteristic
815C22#6595611yescharacteristic
816C22D5×C22⋊Q811yescharacteristic
817C22D5×C22⋊Q811yescharacteristic
818C22#6596911yescharacteristic
819C22#6596911yescharacteristic
820C22#6598311yescharacteristic
821C22#6598411yescharacteristic
822C22D5×#12311yescharacteristic
823C22#6599711yescharacteristic
824C22#6599811yescharacteristic
825C22#6600511yescharacteristic
826C22#6600811yescharacteristic
827C22#6601511yescharacteristic
828C22#6601511yescharacteristic
829C22#6601911yescharacteristic
830C22#6601911yescharacteristic
831C22D5×#12511yescharacteristic
832C22#6602411yescharacteristic
833C22#6602411yescharacteristic
834C22D5×#12611yescharacteristic
835C22#6604311yescharacteristic
836C22#6604311yescharacteristic
837C22#6604411yescharacteristic
838C22#6605611yescharacteristic
839C4—24no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—58no—
846C4—81no—
847C4—104no—
848C4—202no—
849C4—202no—
850C4—202no—
851C4—202no—
852C4—202no—
853C4—401no—
854C2#1060588911yescharacteristic
855C2#1060611211yescharacteristic
856C2#1060670011yescharacteristic
857C2D5×#38711yescharacteristic
858C2#1060719211yescharacteristic
859C2#1060720711yescharacteristic
860C2#1060771811yescharacteristic
861C2#1060853311yescharacteristic
862C2#1060866411yescharacteristic
863C2#1060922611yescharacteristic
864C2#1060949811yescharacteristic
865C2#1060952711yescharacteristic
866C2#1060987711yescharacteristic
867C2#1060988711yescharacteristic
868C2#1060988811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1442C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1442D5
hypocenterC5#14041
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
53. #64936C4semidirect
803. C5#14041semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic52
C2×#649362
C2×#649382
C5×#14422
#106023602
#106002152
#106002142
#106002002
#106001982
#106001972
#140415