Finite Group Databasebeta

← #12022743

Subgroups — #12022743

Order 1280.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#390C211yesmaximal, characteristic
2C2×#65510C211yesmaximal, characteristic
3C2×#65510C211yesmaximal, characteristic
4C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5C2×#65240C212yesmaximal, complemented
6C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10602341C212yesmaximal, complemented
9#10602339C212yesmaximal, complemented
10#10602338C212yesmaximal, complemented
11#10602328C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4C2212yes—
15C22×C5×C22⋊C4C2212yes—
16C22×C42×C5C2211yescharacteristic
17C22×C22⋊Dic5C2212yes—
18C22×C22⋊Dic5C2212yes—
19C22×C22⋊Dic5C2212yes—
20C22×C22⋊Dic5C2212yes—
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×C4⋊Dic5C2211yescharacteristic
24C22×C4⋊Dic5C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C22×C4×Dic5C2212yes—
27C22×C4×Dic5C2211yescharacteristic
28C5×#390C418yescomplemented
29#65510—24no—
30#65510—24no—
31C2×#3963C2211yescharacteristic
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C4⋊C4×Dic5—24no—
39#65240—28no—
40C4×C4⋊Dic5—24no—
41#14022—51nomaximal, Sylow
42C25×C5C2312yes—
43C22×C5×D4—22no—
44C22×C5×D4—22no—
45C22×C5×D4—22no—
46C22×C5×D4—22no—
47C22×C5×D4—22no—
48C22×C5×D4—22no—
49C22×C5×D4C2×C414yes—
50C23×C4×C5C2312yes—
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C23×C4×C5C2311yescharacteristic
54C23×Dic5C2312yes—
55C23×Dic5C2311yescharacteristic
56C23×Dic5C2312yes—
57C23×Dic5C2311yescharacteristic
58C23×Dic5C2311yescharacteristic
59C23×Dic5C2311yescharacteristic
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4C2×C414yes—
63C2×C5×C22⋊C4—24no—
64C2×C5×C22⋊C4—24no—
65C2×C5×C22⋊C4—42no—
66C2×C5×C22⋊C4—42no—
67C2×C5×C22⋊C4C2×C418yes—
68C2×C5×C22⋊C4C2×C418yes—
69C2×C42×C5—22no—
70C2×C42×C5—22no—
71C2×C42×C5C2×C414yes—
72C2×C22⋊Dic5—24no—
73C2×C22⋊Dic5—24no—
74C2×C22⋊Dic5—24no—
75C2×C22⋊Dic5—24no—
76C2×C22⋊Dic5—24no—
77C2×C22⋊Dic5—24no—
78C2×C22⋊Dic5—24no—
79C2×C22⋊Dic5—24no—
80C2×C22⋊Dic5—42no—
81C2×C22⋊Dic5—42no—
82C2×C22⋊Dic5—42no—
83C2×C22⋊Dic5—42no—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—22no—
93C2×C4⋊Dic5—22no—
94C2×C4⋊Dic5D414yes—
95C2×C4⋊Dic5D414yescomplemented
96C2×C4×Dic5—22no—
97C2×C4×Dic5—22no—
98C2×C4×Dic5—22no—
99C2×C4×Dic5—22no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5—24no—
102C2×C4×Dic5—24no—
103C2×C4×Dic5—42no—
104C2×C4×Dic5D414yes—
105#3963—24no—
106#3963—22no—
107#3963—22no—
108#3963—24no—
109#3963—24no—
110#3963—42no—
111#3963—42no—
112C2×#390—51no—
113C2×#390—51no—
114C2×#390D511yescharacteristic
115C2×#388—52no—
116C2×C4×C4⋊C4—51no—
117C2×C4×C4⋊C4—51no—
118#1440—52no—
119#1439—52no—
120#1437—52no—
121C4⋊#95—51no—
122C4⋊#95—51no—
123C24×C5—22no—
124C24×C5—22no—
125C24×C5—22no—
126C24×C5—22no—
127C24×C5—22no—
128C24×C5—22no—
129C24×C5—22no—
130C24×C5—22no—
131C24×C5—22no—
132C24×C5—22no—
133C24×C5—22no—
134C24×C5—22no—
135C24×C5—22no—
136C24×C5—22no—
137C24×C5C22×C414yes—
138C24×C5C2411yescharacteristic
139C2×C5×D4—28no—
140C2×C5×D4—28no—
141C2×C5×D4—28no—
142C2×C5×D4—44no—
143C2×C5×D4—44no—
144C2×C5×D4—44no—
145C2×C5×D4—44no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—21no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5C22×C412yes—
163C22×C4×C5C22×C414yes—
164C22×C4×C5C22×C412yes—
165C22×C4×C5C22×C412yes—
166C22×C4×C5C2×D412yes—
167C22×C4×C5C2×D412yes—
168C22×C4×C5C2×D412yes—
169C22×C4×C5#4112yes—
170C22×C4×C5#4112yes—
171C22×C4×C5#4112yes—
172C22×C4×C5#4112yes—
173C22×C4×C5#4112yes—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—22no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—22no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5C2×D412yes—
210C22×Dic5C2×D414yes—
211C22×Dic5C2×D412yes—
212C22×Dic5C2×D412yes—
213C22×Dic5C2×D412yes—
214C22×Dic5#4112yes—
215C22×Dic5#4112yes—
216C5×C4⋊C4—28no—
217C5×C22⋊C4—216no—
218C5×C22⋊C4—48no—
219C42×C5—28no—
220C22⋊Dic5—48no—
221C22⋊Dic5—48no—
222C22⋊Dic5—48no—
223C22⋊Dic5—48no—
224C4⋊Dic5—28no—
225C4⋊Dic5—28no—
226C4⋊Dic5—28no—
227C4⋊Dic5—44no—
228C4×Dic5—28no—
229C4×Dic5—48no—
230C4×Dic5—44no—
231C23×D4C2×D511yescharacteristic
232C22×C4⋊C4—51no—
233C22×C4⋊C4—51no—
234C22×C4⋊C4—51no—
235C22×C4⋊C4—51no—
236C22×C4⋊C4C2×D511yescharacteristic
237C22×C22⋊C4—52no—
238C22×C22⋊C4—52no—
239C22×C22⋊C4—52no—
240C22×C22⋊C4—52no—
241C22×C22⋊C4C2×D512yes—
242C22×C22⋊C4C2×D512yes—
243C22×C42—51no—
244C22×C42—51no—
245C22×C42—52no—
246C22×C42C2×D511yescharacteristic
247#390—104no—
248#390—104no—
249#390Dic518yescomplemented
250#388—108no—
251C4×C4⋊C4—104no—
252C4×C4⋊C4—104no—
253C2×#95—52no—
254C2×#95—52no—
255C2×#95—51no—
256C2×#95—52no—
257C2×#95—51no—
258C2×#95—52no—
259C2×#95—52no—
260C23×C5—24no—
261C23×C5—24no—
262C23×C5—24no—
263C23×C5—24no—
264C23×C5—24no—
265C23×C5—24no—
266C23×C5—24no—
267C23×C5—42no—
268C23×C5—42no—
269C23×C5—42no—
270C23×C5—42no—
271C23×C5—42no—
272C23×C5—42no—
273C23×C5—42no—
274C23×C5—42no—
275C23×C5—42no—
276C23×C5—42no—
277C23×C5—42no—
278C23×C5—42no—
279C23×C5—42no—
280C23×C5—42no—
281C23×C5—42no—
282C23×C5—42no—
283C23×C5—42no—
284C23×C5—42no—
285C23×C5—42no—
286C23×C5—42no—
287C23×C5—42no—
288C23×C5—42no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5—42no—
292C23×C5—42no—
293C23×C5—42no—
294C23×C5—42no—
295C23×C5C23×C411yescharacteristic
296C23×C5C22×D411yescharacteristic
297C23×C5C22×D411yescharacteristic
298C23×C5C22×D411yescharacteristic
299C23×C5C2×#4111yescharacteristic
300C23×C5C2×#4111yescharacteristic
301C23×C5C2×#4111yescharacteristic
302C23×C5C2×#4111yescharacteristic
303C23×C5C2×#4111yescharacteristic
304C23×C5C2×#4111yescharacteristic
305C23×C5C2×#4111yescharacteristic
306C23×C5H(5,𝔽2)11yescharacteristic
307C23×C5H(5,𝔽2)11yescharacteristic
308C23×C5H(5,𝔽2)11yescharacteristic
309C23×C52−1+411yescharacteristic
310C5×D4—416no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—24no—
319C2×C4×C5—24no—
320C2×C4×C5—22no—
321C2×C4×C5—24no—
322C2×C4×C5—22no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5#11714yes—
332C2×C4×C5C4×D414yes—
333C2×C4×C5C4×D414yes—
334C2×C4×C5C4×D414yes—
335C2×C4×C5#12114yes—
336C2×C4×C5#12314yes—
337C2×C4×C5#12414yes—
338C2×C4×C5#12614yes—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—24no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—24no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—24no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—41no—
358C2×Dic5—41no—
359C2×Dic5—42no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—42no—
363C2×Dic5—41no—
364C2×Dic5—41no—
365C2×Dic5—41no—
366C2×Dic5—41no—
367C2×Dic5—42no—
368C2×Dic5—41no—
369C2×Dic5—41no—
370C2×Dic5—41no—
371C2×Dic5—41no—
372C2×Dic5—42no—
373C2×Dic5—42no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5—42no—
377C2×Dic5—42no—
378C2×Dic5—42no—
379C2×Dic5—42no—
380C2×Dic5#12114yes—
381C25C22×D512yes—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4C2×Dic514yes—
389C23×C4—51no—
390C23×C4—51no—
391C23×C4—51no—
392C23×C4—52no—
393C23×C4—51no—
394C23×C4—52no—
395C23×C4C22×D512yes—
396C23×C4C22×D511yescharacteristic
397C23×C4C22×D511yescharacteristic
398C23×C4C22×D511yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—54no—
402C2×C4⋊C4—54no—
403C2×C4⋊C4—102no—
404C2×C4⋊C4—102no—
405C2×C4⋊C4—102no—
406C2×C4⋊C4—102no—
407C2×C4⋊C4—102no—
408C2×C4⋊C4—102no—
409C2×C4⋊C4—102no—
410C2×C4⋊C4—102no—
411C2×C4⋊C4—102no—
412C2×C4⋊C4—102no—
413C2×C4⋊C4C2×Dic514yes—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—104no—
419C2×C22⋊C4—104no—
420C2×C22⋊C4—104no—
421C2×C22⋊C4—104no—
422C2×C22⋊C4—104no—
423C2×C22⋊C4—104no—
424C2×C22⋊C4—104no—
425C2×C22⋊C4—104no—
426C2×C22⋊C4—202no—
427C2×C22⋊C4—202no—
428C2×C22⋊C4—202no—
429C2×C22⋊C4—202no—
430C2×C22⋊C4C2×Dic518yes—
431C2×C22⋊C4C2×Dic518yes—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—54no—
435C2×C42—102no—
436C2×C42—102no—
437C2×C42—104no—
438C2×C42—104no—
439C2×C42—102no—
440C2×C42—102no—
441C2×C42—102no—
442C2×C42—202no—
443C2×C42C2×Dic514yes—
444#95—102no—
445#95—102no—
446#95—104no—
447#95—104no—
448#95—104no—
449#95—202no—
450#95—202no—
451C22×C5—44no—
452C22×C5—44no—
453C22×C5—44no—
454C22×C5—44no—
455C22×C5—44no—
456C22×C5—44no—
457C22×C5—44no—
458C22×C5—82no—
459C22×C5—82no—
460C22×C5—82no—
461C22×C5—82no—
462C22×C5—82no—
463C22×C5—82no—
464C22×C5—82no—
465C22×C5—82no—
466C22×C5C2×#11711yescharacteristic
467C22×C5C2×C4×D411yescharacteristic
468C22×C5C2×C4×D411yescharacteristic
469C22×C5C2×C4×D411yescharacteristic
470C22×C5C4×#4111yescharacteristic
471C22×C5#51811yescharacteristic
472C22×C5#52011yescharacteristic
473C22×C5C2×#12111yescharacteristic
474C22×C5C2×#12111yescharacteristic
475C22×C5C2×#12311yescharacteristic
476C22×C5#52511yescharacteristic
477C22×C5C2×#12411yescharacteristic
478C22×C5C2×#12611yescharacteristic
479C22×C5#52911yescharacteristic
480C22×C5#53211yescharacteristic
481C22×C5#53511yescharacteristic
482C22×C5#53711yescharacteristic
483C22×C5#54011yescharacteristic
484C22×C5#54211yescharacteristic
485C22×C5D4211yescharacteristic
486C22×C5#54611yescharacteristic
487C22×C5#54711yescharacteristic
488C22×C5#54811yescharacteristic
489C22×C5#55011yescharacteristic
490C22×C5#55011yescharacteristic
491C22×C5#55011yescharacteristic
492C22×C5#55311yescharacteristic
493C22×C5#55311yescharacteristic
494C22×C5#55511yescharacteristic
495C22×C5#55611yescharacteristic
496C22×C5#55611yescharacteristic
497C22×C5#55911yescharacteristic
498C22×C5#55911yescharacteristic
499C22×C5#55911yescharacteristic
500C22×C5#55911yescharacteristic
501C4×C5—24no—
502C4×C5—42no—
503C4×C5—44no—
504C4×C5#38818yescomplemented
505Dic5—24no—
506Dic5—42no—
507Dic5—42no—
508Dic5—42no—
509Dic5—44no—
510Dic5—82no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24C22×Dic514yes—
526C24C23×D511yescharacteristic
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—54no—
556C22×C4—52no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—102no—
565C22×C4—101no—
566C22×C4—102no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—102no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—102no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—102no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—102no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4#70912yes—
593C22×C4#70912yes—
594C22×C4D4×D512yes—
595C22×C4D4×D512yes—
596C22×C4D4×D512yes—
597C22×C4#71112yes—
598C22×C4#71112yes—
599C22×C4#71112yes—
600C22×C4C22×Dic512yes—
601C22×C4C22×Dic514yes—
602C22×C4C22×Dic512yes—
603C22×C4C22×Dic512yes—
604C4⋊C4—28no—
605C4⋊C4—108no—
606C4⋊C4—108no—
607C4⋊C4—108no—
608C4⋊C4—204no—
609C22⋊C4—216no—
610C22⋊C4—48no—
611C22⋊C4—208no—
612C22⋊C4—208no—
613C22⋊C4—208no—
614C22⋊C4—208no—
615C42—28no—
616C42—108no—
617C42—208no—
618C42—204no—
619C2×C5—84no—
620C2×C5C2×#38811yescharacteristic
621C2×C5C4×#12111yescharacteristic
622C2×C5#232411yescharacteristic
623C2×C5#235411yescharacteristic
624C2×C5#235711yescharacteristic
625C2×C5#236611yescharacteristic
626C2×C5#236711yescharacteristic
627C2×C5#241411yescharacteristic
628C2×C5#241611yescharacteristic
629C2×C5#244511yescharacteristic
630C2×C5#244811yescharacteristic
631C2×C5#251211yescharacteristic
632C2×C5#251311yescharacteristic
633C2×C5#254811yescharacteristic
634C2×C5#259211yescharacteristic
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23C2×#70911yescharacteristic
671C23C2×#70911yescharacteristic
672C23C2×D4×D511yescharacteristic
673C23C2×D4×D511yescharacteristic
674C23C2×D4×D511yescharacteristic
675C23C2×#71111yescharacteristic
676C23C2×#71111yescharacteristic
677C23C2×#71111yescharacteristic
678C23#414411yescharacteristic
679C23#414411yescharacteristic
680C23D5×#4111yescharacteristic
681C23D5×#4111yescharacteristic
682C23#414911yescharacteristic
683C23#415011yescharacteristic
684C23C23×Dic511yescharacteristic
685D4—416no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—54no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—104no—
714C2×C4—102no—
715C2×C4—104no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—104no—
725C2×C4—201no—
726C2×C4—201no—
727C2×C4—201no—
728C2×C4—201no—
729C2×C4—202no—
730C2×C4—201no—
731C2×C4—201no—
732C2×C4—202no—
733C2×C4—201no—
734C2×C4—201no—
735C2×C4—202no—
736C2×C4—201no—
737C2×C4—201no—
738C2×C4—202no—
739C2×C4—201no—
740C2×C4—201no—
741C2×C4—202no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—202no—
747C2×C4—202no—
748C2×C4#402514yes—
749C2×C4#402914yes—
750C2×C4#403014yes—
751C2×C4#403114yes—
752C2×C4#407214yes—
753C2×C4D4×Dic514yes—
754C2×C4D4×Dic514yes—
755C2×C4D4×Dic514yes—
756C5#1402211yescharacteristic, complemented, Sylow
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×#402511yescharacteristic
773C22C2×#402911yescharacteristic
774C22C2×#403011yescharacteristic
775C22C2×#403111yescharacteristic
776C22#6587611yescharacteristic
777C22#6588511yescharacteristic
778C22#6588711yescharacteristic
779C22#6589211yescharacteristic
780C22#6589211yescharacteristic
781C22#6589311yescharacteristic
782C22#6589311yescharacteristic
783C22#6589711yescharacteristic
784C22#6593011yescharacteristic
785C22#6593411yescharacteristic
786C22#6593711yescharacteristic
787C22D5×#12111yescharacteristic
788C22#6594011yescharacteristic
789C22#6594111yescharacteristic
790C22#6594211yescharacteristic
791C22#6595311yescharacteristic
792C22#6600511yescharacteristic
793C22#6601011yescharacteristic
794C22#6601111yescharacteristic
795C22#6601511yescharacteristic
796C22#6604711yescharacteristic
797C22#6605111yescharacteristic
798C22#6605211yescharacteristic
799C22#6605211yescharacteristic
800C22C2×#407211yescharacteristic
801C22C2×D4×Dic511yescharacteristic
802C22C2×D4×Dic511yescharacteristic
803C22C2×D4×Dic511yescharacteristic
804C22#6613211yescharacteristic
805C22#41×Dic511yescharacteristic
806C22#6616111yescharacteristic
807C4—24no—
808C4—42no—
809C4—44no—
810C4—104no—
811C4—202no—
812C4—202no—
813C4—202no—
814C4—204no—
815C4—402no—
816C4#6524018yescomplemented
817C2—84no—
818C2#1060804911yescharacteristic
819C2#1060805211yescharacteristic
820C2#1060807011yescharacteristic
821C2#1060807311yescharacteristic
822C2#1060808411yescharacteristic
823C2#1060809611yescharacteristic
824C2#1060816911yescharacteristic
825C2#1060817011yescharacteristic
826C2C2×#6524011yescharacteristic
827C2#1061406811yescharacteristic
828C2#1061406911yescharacteristic
829C2Dic5×#12111yescharacteristic
830C2#1061436411yescharacteristic
831C2#1061468611yescharacteristic
832C2#1061490411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#390C2
socle, cosocleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC2×#390D5
hypocenterC5#14022
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic5C2semidirect
5. C2×#65240C2semidirect
6. C2×C4×C4⋊Dic5C2semidirect
7. #10602356C2semidirect
8. #10602341C2semidirect
9. #10602339C2semidirect
10. #10602338C2semidirect
11. #10602328C2semidirect
28. C5×#390C4semidirect
95. C2×C4⋊Dic5D4semidirect
249. #390Dic5semidirect
504. C4×C5#388semidirect
756. C5#14022semidirect
816. C4#65240semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3902
C2×#655102
C2×C4⋊C4×Dic52
C2×#652402
C2×C4×C4⋊Dic52
#106023562
#106023412
#106023392
#106023382
#106023282
#140225