Finite Group Databasebeta

← #12021550

Subgroups — #12021550

Order 1280.

2366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic
2C2×C5×#389C211yesmaximal, characteristic, complemented
3C2×#65276C211yesmaximal, characteristic
4C2×#65276C212yesmaximal
5C2×#65274C211yesmaximal, characteristic, complemented
6C2×C4×#685C211yesmaximal, characteristic
7#10602359C212yesmaximal, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602328C211yesmaximal, characteristic, complemented
10#10600218C212yesmaximal
11#10600203C212yesmaximal, complemented
12C23×C4×D5C2212yes—
13C23×C4×D5C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×#685C2212yes—
19C22×#685C2211yescharacteristic
20C22×#685C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2212yes—
23C22×C4⋊Dic5C2211yescharacteristic
24C22×#683C2212yes—
25C22×C4×Dic5C2211yescharacteristic
26C2×D5×C4⋊C4—24no—
27C2×D5×C4⋊C4—24no—
28C2×D5×C4⋊C4C418yescomplemented
29C5×#389—24no—
30C2×C5×#95C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39#65276—28no—
40#65276—24no—
41#65274—24no—
42C4×#685—24no—
43#13907—51nomaximal, Sylow
44C24×D5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2312yes—
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2312yes—
52C23×Dic5C2311yescharacteristic
53C23×Dic5C2311yescharacteristic
54C23×Dic5C2311yescharacteristic
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5—24no—
60C22×C4×D5—24no—
61C22×C4×D5—24no—
62C22×C4×D5—24no—
63C22×C4×D5—42no—
64C22×C4×D5—42no—
65C22×C4×D5C2×C418yes—
66C22×C4×D5C2×C414yes—
67C22×C4×D5D414yes—
68C22×C4×D5Q814yes—
69C2×C5×C4⋊C4—24no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—24no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—42no—
75C2×C5×C4⋊C4C2×C414yes—
76C2×C5×C4⋊C4D414yes—
77C2×C5×C4⋊C4D414yes—
78C2×C42×C5—22no—
79C2×C42×C5—22no—
80C2×C42×C5—22no—
81C2×#685—22no—
82C2×#685—22no—
83C2×#685—22no—
84C2×#685—22no—
85C2×#685—24no—
86C2×#685—24no—
87C2×#685—24no—
88C2×#685D414yes—
89C2×#685Q814yes—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—24no—
93C2×C4⋊Dic5—22no—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5—22no—
96C2×C4⋊Dic5—24no—
97C2×C4⋊Dic5—42no—
98C2×C4⋊Dic5C2×C414yes—
99C2×#683—24no—
100C2×#683—24no—
101C2×#683C2×C418yes—
102C2×C4×Dic5—22no—
103C2×C4×Dic5—22no—
104C2×C4×Dic5—22no—
105D5×C4⋊C4—232no—
106C5×#95—24no—
107#3963—24no—
108#3963—24no—
109#3963—22no—
110#3963—22no—
111#3963—24no—
112#3963—24no—
113#3963—42no—
114#3963—42no—
115C23×C4⋊C4—51no—
116C2×#389—51no—
117C2×#389D511yescharacteristic, complemented
118C2×#380—52no—
119C2×#380—51no—
120C2×C4×C22⋊C4—51no—
121#1441—52no—
122#1441—52no—
123C4⋊#95—51no—
124C4⋊#95—51no—
125C22⋊#95—52no—
126C24×C5C2411yescharacteristic
127C23×D5—21no—
128C23×D5—21no—
129C23×D5—21no—
130C23×D5—21no—
131C23×D5—21no—
132C23×D5—21no—
133C23×D5—21no—
134C23×D5—21no—
135C23×D5C22×C412yes—
136C23×D5C2×D412yes—
137C23×D5C2×D412yes—
138C23×D5C2×Q812yes—
139C23×D5C2×Q812yes—
140C23×D5#4112yes—
141C23×D5#4112yes—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
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—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5C22×C414yes—
166C22×C4×C5C22×C412yes—
167C22×C4×C5C2×D414yes—
168C22×C4×C5C2×D412yes—
169C22×C4×C5C2×D412yes—
170C22×C4×C5C2×D412yes—
171C22×C4×C5C2×D414yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×Q812yes—
174C22×C4×C5C2×Q812yes—
175C22×C4×C5#4112yes—
176C22×C4×C5#4112yes—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—21no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—22no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5C22×C414yes—
207C22×Dic5C22×C412yes—
208C22×Dic5C2×D412yes—
209C22×Dic5C2×D412yes—
210C22×Dic5C2×Q812yes—
211C22×Dic5C2×Q812yes—
212C2×C4×D5—28no—
213C2×C4×D5—28no—
214C2×C4×D5—28no—
215C2×C4×D5—28no—
216C2×C4×D5—28no—
217C2×C4×D5—28no—
218C2×C4×D5—216no—
219C2×C4×D5—216no—
220C2×C4×D5—48no—
221C2×C4×D5—48no—
222C2×C4×D5—48no—
223C2×C4×D5—48no—
224C2×C4×D5—48no—
225C2×C4×D5C4⋊C4116yescomplemented
226C5×C4⋊C4—48no—
227C5×C4⋊C4—44no—
228C5×C4⋊C4C22⋊C4116yescomplemented
229C42×C5—44no—
230#685—28no—
231#685—28no—
232#685—48no—
233C4⋊Dic5—28no—
234C4⋊Dic5—48no—
235C4⋊Dic5—44no—
236#683—216no—
237C4×Dic5—44no—
238C24×C4—51no—
239C24×C4—52no—
240C22×C4⋊C4—52no—
241C22×C4⋊C4—51no—
242C22×C4⋊C4—58no—
243C22×C4⋊C4—51no—
244C22×C4⋊C4—52no—
245C22×C4⋊C4—104no—
246C22×C4⋊C4—104no—
247C22×C4⋊C4C2×D511yescharacteristic
248C22×C4⋊C4C2×D512yes—
249C22×C4⋊C4C2×D511yescharacteristic
250C22×C22⋊C4—51no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—52no—
253C22×C42—51no—
254C22×C42C2×D511yescharacteristic
255#389—24no—
256#389—104no—
257#380—108no—
258#380—104no—
259C4×C22⋊C4—104no—
260C2×#95—52no—
261C2×#95—52no—
262C2×#95—52no—
263C2×#95—51no—
264C2×#95—51no—
265C2×#95—52no—
266C2×#95—52no—
267C2×#95—52no—
268C2×#95C2×D512yes—
269C23×C5C23×C411yescharacteristic
270C23×C5C22×D411yescharacteristic
271C23×C5C22×D411yescharacteristic
272C23×C5C22×D411yescharacteristic
273C23×C5C22×D411yescharacteristic
274C23×C5C22×Q811yescharacteristic
275C23×C5C22×Q811yescharacteristic
276C23×C5C2×#4111yescharacteristic
277C23×C5C2×#4111yescharacteristic
278C23×C5C2×#4111yescharacteristic
279C23×C5C2×#4111yescharacteristic
280C23×C5H(5,𝔽2)11yescharacteristic
281C23×C5H(5,𝔽2)11yescharacteristic
282C23×C52−1+411yescharacteristic
283C23×C52−1+411yescharacteristic
284C22×D5—22no—
285C22×D5—22no—
286C22×D5—22no—
287C22×D5—22no—
288C22×D5—22no—
289C22×D5—22no—
290C22×D5—22no—
291C22×D5—22no—
292C22×D5—22no—
293C22×D5—22no—
294C22×D5—22no—
295C22×D5—22no—
296C22×D5—22no—
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—22no—
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5—22no—
308C22×D5—22no—
309C22×D5—22no—
310C22×D5—22no—
311C22×D5—22no—
312C22×D5C2×C4⋊C414yes—
313C22×D5C4×D414yes—
314C22×D5C4×Q814yes—
315C22×D5#12114yes—
316C22×D5C22⋊Q814yes—
317C22×D5#12514yes—
318C22×D5C4⋊Q814yes—
319C2×C4×C5—24no—
320C2×C4×C5—24no—
321C2×C4×C5—24no—
322C2×C4×C5—24no—
323C2×C4×C5—24no—
324C2×C4×C5—24no—
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—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5C2×C22⋊C418yes—
347C2×C4×C5C2×C22⋊C414yes—
348C2×C4×C5C2×C4⋊C414yes—
349C2×C4×C5#11714yes—
350C2×C4×C5#12114yes—
351C2×C4×C5#12114yes—
352C2×C4×C5C22⋊Q814yes—
353C2×C4×C5C22⋊Q814yes—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—24no—
361C2×Dic5—24no—
362C2×Dic5—24no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—41no—
370C2×Dic5—41no—
371C2×Dic5—41no—
372C2×Dic5—41no—
373C2×Dic5—42no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5—42no—
377C2×Dic5—41no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—42no—
382C2×Dic5—42no—
383C2×Dic5—42no—
384C2×Dic5—42no—
385C2×Dic5—42no—
386C2×Dic5—42no—
387C2×Dic5—42no—
388C2×Dic5C2×C4⋊C414yes—
389C4×D5—232no—
390C4×D5—432no—
391C25—51no—
392C23×C4—51no—
393C23×C4—54no—
394C23×C4—54no—
395C23×C4—54no—
396C23×C4—51no—
397C23×C4—51no—
398C23×C4—52no—
399C23×C4—58no—
400C23×C4—52no—
401C23×C4—104no—
402C23×C4—104no—
403C23×C4—102no—
404C23×C4—102no—
405C23×C4—102no—
406C23×C4—102no—
407C23×C4—104no—
408C23×C4—104no—
409C23×C4—202no—
410C23×C4—202no—
411C23×C4C22×D512yes—
412C23×C4C22×D511yescharacteristic
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D512yes—
415C23×C4C22×D511yescharacteristic
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—58no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—104no—
425C2×C4⋊C4—102no—
426C2×C4⋊C4—104no—
427C2×C4⋊C4—102no—
428C2×C4⋊C4—1032no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—102no—
433C2×C4⋊C4—102no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4C4×D514yes—
436C2×C4⋊C4D2014yes—
437C2×C4⋊C4C22⋊D514yes—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—54no—
440C2×C22⋊C4—102no—
441C2×C22⋊C4—102no—
442C2×C22⋊C4—102no—
443C2×C22⋊C4—102no—
444C2×C22⋊C4—104no—
445C2×C22⋊C4—104no—
446C2×C22⋊C4—104no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—102no—
451C2×C42—102no—
452C2×C42—102no—
453#95—24no—
454#95—102no—
455#95—102no—
456#95—104no—
457#95—104no—
458#95—104no—
459#95—104no—
460#95—202no—
461#95—202no—
462C22×C5C22×C22⋊C411yescharacteristic
463C22×C5C22×C4⋊C411yescharacteristic
464C22×C5C2×#11711yescharacteristic
465C22×C5C2×C4×D411yescharacteristic
466C22×C5C2×C4×Q811yescharacteristic
467C22×C5#51811yescharacteristic
468C22×C5#51911yescharacteristic
469C22×C5C2×#12111yescharacteristic
470C22×C5C2×#12111yescharacteristic
471C22×C5C2×#12111yescharacteristic
472C22×C5C2×C22⋊Q811yescharacteristic
473C22×C5C2×C22⋊Q811yescharacteristic
474C22×C5C2×C22⋊Q811yescharacteristic
475C22×C5C2×#12511yescharacteristic
476C22×C5C2×C4⋊Q811yescharacteristic
477C22×C5#53711yescharacteristic
478C22×C5#53711yescharacteristic
479C22×C5#54411yescharacteristic
480C22×C5#54411yescharacteristic
481C22×C5D4211yescharacteristic
482C22×C5D4211yescharacteristic
483C22×C5#54611yescharacteristic
484C22×C5#54611yescharacteristic
485C22×C5#54711yescharacteristic
486C22×C5#54711yescharacteristic
487C22×C5#54811yescharacteristic
488C22×C5#54811yescharacteristic
489C22×C5D4×Q811yescharacteristic
490C22×C5D4×Q811yescharacteristic
491C22×C5#55211yescharacteristic
492C22×C5#55211yescharacteristic
493C22×C5#55311yescharacteristic
494C22×C5#55311yescharacteristic
495C22×C5#55411yescharacteristic
496C22×C5#55411yescharacteristic
497C2×D5—24no—
498C2×D5—24no—
499C2×D5—24no—
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—24no—
503C2×D5—24no—
504C2×D5—24no—
505C2×D5—24no—
506C2×D5—24no—
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—24no—
511C2×D5#38918yescomplemented
512C4×C5—28no—
513C4×C5—42no—
514C4×C5—42no—
515C4×C5—82no—
516C4×C5#38018yescomplemented
517Dic5—24no—
518Dic5—44no—
519Dic5—42no—
520Dic5—42no—
521Dic5—82no—
522C24—52no—
523C24—52no—
524C24—52no—
525C24—52no—
526C24—52no—
527C24—52no—
528C24—52no—
529C24—101no—
530C24—101no—
531C24—101no—
532C24—101no—
533C24—101no—
534C24—101no—
535C24—101no—
536C24—101no—
537C24C23×D511yescharacteristic
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—516no—
565C22×C4—54no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—1016no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—108no—
574C22×C4—108no—
575C22×C4—108no—
576C22×C4—108no—
577C22×C4—108no—
578C22×C4—108no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—102no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—102no—
597C22×C4—1016no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—208no—
606C22×C4—208no—
607C22×C4—208no—
608C22×C4—208no—
609C22×C4—208no—
610C22×C4C2×C4×D514yes—
611C22×C4C2×C4×D512yes—
612C22×C4C2×D2014yes—
613C22×C4C2×D2012yes—
614C22×C4D4×D512yes—
615C22×C4D4×D512yes—
616C22×C4#71112yes—
617C22×C4Q8×D512yes—
618C22×C4Q8×D512yes—
619C22×C4#71312yes—
620C22×C4C2×C22⋊D514yes—
621C22×C4C2×C22⋊D512yes—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—1016no—
625C4⋊C4—108no—
626C4⋊C4—208no—
627C4⋊C4—204no—
628C4⋊C4#685116yescomplemented
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—208no—
632C42—44no—
633C42—204no—
634C2×C5C2×#38011yescharacteristic
635C2×C5C2×#38911yescharacteristic
636C2×C5#231611yescharacteristic
637C2×C5D4×C22⋊C411yescharacteristic
638C2×C5Q8×C22⋊C411yescharacteristic
639C2×C5#234411yescharacteristic
640C2×C5#234511yescharacteristic
641C2×C5#241611yescharacteristic
642C2×C5#241611yescharacteristic
643C2×C5#241711yescharacteristic
644C2×C5#241711yescharacteristic
645C2×C5#244011yescharacteristic
646C2×C5#244011yescharacteristic
647C2×C5#244211yescharacteristic
648C2×C5#244211yescharacteristic
649D5—28no—
650C23—54no—
651C23—54no—
652C23—54no—
653C23—54no—
654C23—54no—
655C23—54no—
656C23—54no—
657C23—102no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—102no—
679C23—102no—
680C23—102no—
681C23—102no—
682C23—102no—
683C23—102no—
684C23—102no—
685C23C22×C4×D511yescharacteristic
686C23C22×D2011yescharacteristic
687C23C2×D4×D511yescharacteristic
688C23C2×D4×D511yescharacteristic
689C23C2×#71111yescharacteristic
690C23#414411yescharacteristic
691C23C2×Q8×D511yescharacteristic
692C23C2×Q8×D511yescharacteristic
693C23C2×#71311yescharacteristic
694C23#414711yescharacteristic
695C23D5×#4111yescharacteristic
696C23D5×#4111yescharacteristic
697C23#414911yescharacteristic
698C23#415011yescharacteristic
699C23C22×C22⋊D511yescharacteristic
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—54no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—1032no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—104no—
738C2×C4—104no—
739C2×C4—104no—
740C2×C4—102no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—102no—
744C2×C4—2032no—
745C2×C4—201no—
746C2×C4—201no—
747C2×C4—202no—
748C2×C4—202no—
749C2×C4—202no—
750C2×C4—201no—
751C2×C4—202no—
752C2×C4—201no—
753C2×C4—201no—
754C2×C4—201no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—202no—
763C2×C4—202no—
764C2×C4D5×C4⋊C414yes—
765C2×C4#403814yes—
766C2×C4#404114yes—
767C2×C4#404314yes—
768C2×C4C2×#68518yes—
769C2×C4C2×#68514yes—
770C2×C4#408414yes—
771C2×C4#409214yes—
772C5#1390711yescharacteristic, complemented, Sylow
773C22—58no—
774C22—104no—
775C22—104no—
776C22—104no—
777C22—104no—
778C22—104no—
779C22—104no—
780C22—104no—
781C22—104no—
782C22—104no—
783C22—104no—
784C22—104no—
785C22—104no—
786C22—104no—
787C22—104no—
788C22C2×D5×C4⋊C411yescharacteristic
789C22C2×#403811yescharacteristic
790C22C2×#404111yescharacteristic
791C22C2×#404311yescharacteristic
792C22C4×D4×D511yescharacteristic
793C22#6587911yescharacteristic
794C22D4×D2011yescharacteristic
795C22#6588811yescharacteristic
796C22C4×Q8×D511yescharacteristic
797C22#6590611yescharacteristic
798C22Q8×D2011yescharacteristic
799C22#6591011yescharacteristic
800C22D5×#12111yescharacteristic
801C22#6594211yescharacteristic
802C22#6594511yescharacteristic
803C22#6594811yescharacteristic
804C22D5×C22⋊Q811yescharacteristic
805C22#6596311yescharacteristic
806C22#6596911yescharacteristic
807C22#6597311yescharacteristic
808C22D5×#12511yescharacteristic
809C22#6602311yescharacteristic
810C22#6602811yescharacteristic
811C22#6602911yescharacteristic
812C22D5×C4⋊Q811yescharacteristic
813C22#6606011yescharacteristic
814C22#6606311yescharacteristic
815C22#6606411yescharacteristic
816C22C22×#68511yescharacteristic
817C22C2×#408411yescharacteristic
818C22D4×C22⋊D511yescharacteristic
819C22C2×#409211yescharacteristic
820C22Q8×C22⋊D511yescharacteristic
821C22#6616311yescharacteristic
822C22#6616511yescharacteristic
823C4—28no—
824C4—42no—
825C4—42no—
826C4—82no—
827C4—104no—
828C4—202no—
829C4—202no—
830C4—204no—
831C4—402no—
832C4#6527618yescomplemented
833C2—108no—
834C2#1060773011yescharacteristic
835C2#1060773411yescharacteristic
836C2D5×#38911yescharacteristic
837C2#1060792611yescharacteristic
838C2#1060793111yescharacteristic
839C2#1060793211yescharacteristic
840C2#1060794211yescharacteristic
841C2#1060794311yescharacteristic
842C2C2×#6527611yescharacteristic
843C2D4×#68511yescharacteristic
844C2Q8×#68511yescharacteristic
845C2#1061437211yescharacteristic
846C2#1061448311yescharacteristic
847C2#1061475911yescharacteristic
848C2#1061496411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#389C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#389D5
hypocenterC5#13907
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×C5×#389C2semidirect
5. C2×#65274C2semidirect
7. #10602359C2semidirect
8. #10602356C2semidirect
9. #10602328C2semidirect
11. #10600203C2semidirect
28. C2×D5×C4⋊C4C4semidirect
117. C2×#389D5semidirect
225. C2×C4×D5C4⋊C4semidirect
228. C5×C4⋊C4C22⋊C4semidirect
511. C2×D5#389semidirect
516. C4×C5#380semidirect
628. C4⋊C4#685semidirect
772. C5#13907semidirect
832. C4#65276semidirect

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C2×C5×#3892
C2×#652762
C2×#652742
C2×C4×#6852
#106023592
#106023562
#106023282
#106002182
#106002032
#139075