Finite Group Databasebeta

← #12023432

Subgroups — #12023432

Order 1280.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65499C211yesmaximal, characteristic
2C2×C4×C22⋊Dic5C211yesmaximal, characteristic
3C2×#64941C211yesmaximal, characteristic, complemented
4C5×C22⋊#95C211yesmaximal, characteristic
5#10602340C211yesmaximal, characteristic
6#10602340C211yesmaximal, characteristic
7#10602338C211yesmaximal, characteristic
8#10602338C211yesmaximal, characteristic
9#10600211C211yesmaximal, characteristic, complemented
10#10600202C211yesmaximal, characteristic, complemented
11#10600199C211yesmaximal, characteristic, complemented
12#10600198C211yesmaximal, characteristic, complemented
13#10600197C211yesmaximal, characteristic, complemented
14#10600195C211yesmaximal, characteristic, complemented
15Dic5×#95C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C22×C5×C22⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic5C2211yescharacteristic
20C22×C22⋊Dic5C2211yescharacteristic
21C22×C22⋊Dic5C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×#683C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35#65499C418yescomplemented
36C4×C22⋊Dic5—24no—
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
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#64941—24no—
54#14075—51nomaximal, Sylow
55C25×C5C2311yescharacteristic
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—41no—
59C23×C4×C5—41no—
60C23×C4×C5—41no—
61C23×C4×C5—41no—
62C23×C4×C5C2×C414yes—
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C23×Dic5C2311yescharacteristic
71C23×Dic5C2311yescharacteristic
72C23×Dic5C2311yescharacteristic
73C23×Dic5C2311yescharacteristic
74C23×Dic5C2311yescharacteristic
75C23×Dic5C2311yescharacteristic
76C23×Dic5C2311yescharacteristic
77C2×C5×C22⋊C4—22no—
78C2×C5×C22⋊C4—22no—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—41no—
82C2×C5×C22⋊C4—41no—
83C2×C22⋊Dic5—22no—
84C2×C22⋊Dic5—22no—
85C2×C22⋊Dic5—22no—
86C2×C22⋊Dic5—22no—
87C2×C22⋊Dic5—22no—
88C2×C22⋊Dic5—22no—
89C2×C22⋊Dic5—22no—
90C2×C22⋊Dic5—41no—
91C2×C22⋊Dic5—41no—
92C2×C22⋊Dic5C2×C414yes—
93C2×C22⋊Dic5C2×C414yes—
94C2×C22⋊Dic5Q814yes—
95C2×#683—22no—
96C2×#683—22no—
97C2×#683—22no—
98C2×#683—22no—
99C2×#683—22no—
100C2×#683—41no—
101C2×#683—41no—
102C2×#683—41no—
103C2×#683—41no—
104C2×#683—41no—
105C2×#683C2×C414yes—
106C2×#683C2×C414yes—
107C2×C4×Dic5—22no—
108C2×C4×Dic5—22no—
109C2×C4×Dic5—22no—
110C2×C4×Dic5—22no—
111C2×C4×Dic5—22no—
112C2×C4×Dic5—41no—
113C2×C4×Dic5—41no—
114C2×C4×Dic5—41no—
115C2×C4×Dic5—41no—
116C2×C4×Dic5—41no—
117C2×C4×Dic5—41no—
118C2×C4×Dic5D414yes—
119C5×#95—22no—
120C5×#95—22no—
121C5×#95—41no—
122C5×#95—41no—
123#3963—22no—
124#3963—22no—
125#3963—22no—
126#3963—22no—
127#3963—22no—
128#3963—22no—
129#3963—22no—
130#3963—22no—
131#3963—22no—
132#3963—22no—
133#3963—22no—
134#3963—41no—
135#3963—41no—
136#3963—41no—
137#3963C2×C414yes—
138#3963C2×C414yes—
139C2×#387—51no—
140C2×#385—51no—
141C2×C4×C22⋊C4—51no—
142#1443—51no—
143#1441—51no—
144#1439—51no—
145#1439—51no—
146#1437—51no—
147#1437—51no—
148#1436—51no—
149#1436—51no—
150C4⋊#95—51no—
151#1434—51no—
152C22⋊#95D511yescharacteristic
153C4×#95—51no—
154C24×C5—21no—
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5C22×C412yes—
167C24×C5C2×Q812yes—
168C24×C5#4112yes—
169C24×C5C2411yescharacteristic
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×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—28no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—44no—
208C22×C4×C5—44no—
209C22×C4×C5—44no—
210C22×C4×C5—44no—
211C22×C4×C5—44no—
212C22×C4×C5—44no—
213C22×C4×C5C22×C412yes—
214C22×C4×C5C22×C412yes—
215C22×C4×C5C2×D412yes—
216C22×C4×C5#4112yes—
217C22×C4×C5#4112yes—
218C22×C4×C5#4112yes—
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×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—21no—
243C22×Dic5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5—21no—
249C22×Dic5—21no—
250C22×Dic5—21no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—21no—
255C22×Dic5—21no—
256C22×Dic5—21no—
257C22×Dic5—21no—
258C22×Dic5—21no—
259C22×Dic5—21no—
260C22×Dic5—21no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5C22×C412yes—
264C22×Dic5C22×C412yes—
265C22×Dic5C22×C412yes—
266C22×Dic5C22×C412yes—
267C22×Dic5C2×D412yes—
268C22×Dic5C2×D412yes—
269C22×Dic5C2×Q812yes—
270C22×Dic5C2×Q812yes—
271C22×Dic5#4112yes—
272C22×Dic5#4112yes—
273C22×Dic5#4112yes—
274C22×Dic5#4112yes—
275C5×C22⋊C4—44no—
276C5×C22⋊C4—44no—
277C22⋊Dic5—28no—
278C22⋊Dic5—28no—
279C22⋊Dic5—28no—
280C22⋊Dic5—44no—
281#683—28no—
282#683—44no—
283#683—44no—
284#683—44no—
285C4×Dic5—44no—
286C4×Dic5—44no—
287C4×Dic5—44no—
288C4×Dic5—44no—
289C24×C4C2×D511yescharacteristic
290C22×C4⋊C4—51no—
291C22×C4⋊C4—51no—
292C22×C4⋊C4—51no—
293C22×C4⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4—51no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C22⋊C4C2×D511yescharacteristic
299C22×C22⋊C4C2×D511yescharacteristic
300C22×C42—51no—
301C22×C42—51no—
302C22×C42—51no—
303C22×C42—51no—
304#387—104no—
305#385—58no—
306C4×C22⋊C4—104no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95—51no—
310C2×#95—51no—
311C2×#95—51no—
312C2×#95—51no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C2×#95C2×D511yescharacteristic
326C2×#95C2×D511yescharacteristic
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5—41no—
355C23×C5—41no—
356C23×C5—41no—
357C23×C5—41no—
358C23×C5—41no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5C4×Q814yes—
362C23×C5C23×C411yescharacteristic
363C23×C5C22×D411yescharacteristic
364C23×C5C22×Q811yescharacteristic
365C23×C5C2×#4111yescharacteristic
366C23×C5C2×#4111yescharacteristic
367C23×C5C2×#4111yescharacteristic
368C23×C5C2×#4111yescharacteristic
369C23×C5C2×#4111yescharacteristic
370C23×C5C2×#4111yescharacteristic
371C23×C5C2×#4111yescharacteristic
372C23×C5C2×#4111yescharacteristic
373C23×C5H(5,𝔽2)11yescharacteristic
374C23×C5H(5,𝔽2)11yescharacteristic
375C23×C5H(5,𝔽2)11yescharacteristic
376C23×C5H(5,𝔽2)11yescharacteristic
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—416no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—41no—
406C2×C4×C5—41no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—41no—
411C2×C4×C5—41no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5C4×D414yes—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—41no—
451C2×Dic5—41no—
452C2×Dic5—41no—
453C2×Dic5—41no—
454C2×Dic5—41no—
455C2×Dic5—41no—
456C2×Dic5—41no—
457C2×Dic5—41no—
458C2×Dic5—41no—
459C2×Dic5—41no—
460C2×Dic5—41no—
461C2×Dic5—41no—
462C2×Dic5—41no—
463C2×Dic5—41no—
464C2×Dic5—41no—
465C2×Dic5—41no—
466C2×Dic5—41no—
467C2×Dic5—41no—
468C2×Dic5—41no—
469C2×Dic5—41no—
470C2×Dic5—41no—
471C2×Dic5—41no—
472C2×Dic5—41no—
473C2×Dic5—41no—
474C2×Dic5#11714yes—
475C2×Dic5C22⋊Q814yes—
476C25C22×D511yescharacteristic
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—41no—
480C23×C4—41no—
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4C4×D514yes—
492C23×C4C22×D511yescharacteristic
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C2×C4⋊C4—54no—
499C2×C4⋊C4—54no—
500C2×C4⋊C4—102no—
501C2×C4⋊C4—102no—
502C2×C4⋊C4—102no—
503C2×C4⋊C4—102no—
504C2×C4⋊C4—102no—
505C2×C4⋊C4—201no—
506C2×C4⋊C4—201no—
507C2×C4⋊C4—201no—
508C2×C4⋊C4—201no—
509C2×C4⋊C4—201no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—54no—
517C2×C22⋊C4—54no—
518C2×C22⋊C4—54no—
519C2×C22⋊C4—102no—
520C2×C22⋊C4—102no—
521C2×C22⋊C4—102no—
522C2×C22⋊C4—102no—
523C2×C22⋊C4—102no—
524C2×C22⋊C4—102no—
525C2×C22⋊C4—102no—
526C2×C22⋊C4—201no—
527C2×C22⋊C4—201no—
528C2×C42—54no—
529C2×C42—102no—
530C2×C42—102no—
531C2×C42—102no—
532C2×C42—102no—
533C2×C42—102no—
534C2×C42—201no—
535C2×C42—201no—
536C2×C42—201no—
537C2×C42—201no—
538C2×C42—201no—
539C2×C42—201no—
540#95—22no—
541#95—22no—
542#95—41no—
543#95—41no—
544#95—54no—
545#95—54no—
546#95—102no—
547#95—102no—
548#95—102no—
549#95—102no—
550#95—102no—
551#95—102no—
552#95—102no—
553#95—102no—
554#95—102no—
555#95—102no—
556#95—102no—
557#95—201no—
558#95—201no—
559#95—201no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—24no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5—42no—
575C22×C5C2×#11711yescharacteristic
576C22×C5C2×C4×D411yescharacteristic
577C22×C5C2×C4×Q811yescharacteristic
578C22×C5C4×#4111yescharacteristic
579C22×C5C4×#4111yescharacteristic
580C22×C5#51811yescharacteristic
581C22×C5#51811yescharacteristic
582C22×C5C2×C22⋊Q811yescharacteristic
583C22×C5#52511yescharacteristic
584C22×C5#52911yescharacteristic
585C22×C5#52911yescharacteristic
586C22×C5#52911yescharacteristic
587C22×C5#53211yescharacteristic
588C22×C5#53211yescharacteristic
589C22×C5#53311yescharacteristic
590C22×C5#53411yescharacteristic
591C22×C5#53511yescharacteristic
592C22×C5#53811yescharacteristic
593C22×C5#53811yescharacteristic
594C22×C5#55111yescharacteristic
595C22×C5#55111yescharacteristic
596C22×C5#55111yescharacteristic
597C22×C5#55111yescharacteristic
598C22×C5#55111yescharacteristic
599C22×C5#55311yescharacteristic
600C22×C5#55311yescharacteristic
601C22×C5#55311yescharacteristic
602C22×C5#55311yescharacteristic
603C22×C5#55311yescharacteristic
604C22×C5#55311yescharacteristic
605C22×C5#55411yescharacteristic
606C22×C5#55411yescharacteristic
607C22×C5#55411yescharacteristic
608C22×C5#55411yescharacteristic
609C22×C5#55911yescharacteristic
610C4×C5—24no—
611C4×C5—42no—
612C4×C5—42no—
613C4×C5—42no—
614C4×C5—81no—
615C4×C5—81no—
616Dic5—24no—
617Dic5—24no—
618Dic5—42no—
619Dic5—42no—
620Dic5—42no—
621Dic5—42no—
622Dic5—42no—
623Dic5—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24C2×C4×D512yes—
637C24#71112yes—
638C24Q8×D512yes—
639C24C23×D511yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—28no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—52no—
684C22×C4—52no—
685C22×C4—52no—
686C22×C4—52no—
687C22×C4—52no—
688C22×C4—52no—
689C22×C4—52no—
690C22×C4—52no—
691C22×C4—52no—
692C22×C4—52no—
693C22×C4—52no—
694C22×C4—52no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4—101no—
698C22×C4—101no—
699C22×C4—101no—
700C22×C4—101no—
701C22×C4—101no—
702C22×C4—101no—
703C22×C4—101no—
704C22×C4—101no—
705C22×C4—101no—
706C22×C4—101no—
707C22×C4—101no—
708C22×C4—101no—
709C22×C4—101no—
710C22×C4—101no—
711C22×C4—101no—
712C22×C4—101no—
713C22×C4—101no—
714C22×C4—101no—
715C22×C4—101no—
716C22×C4—101no—
717C22×C4—101no—
718C22×C4—101no—
719C22×C4—101no—
720C22×C4—101no—
721C22×C4—101no—
722C22×C4—101no—
723C22×C4—101no—
724C22×C4—101no—
725C22×C4—101no—
726C22×C4—101no—
727C22×C4—101no—
728C22×C4—101no—
729C22×C4—101no—
730C22×C4—101no—
731C22×C4—101no—
732C22×C4—101no—
733C22×C4—101no—
734C22×C4—101no—
735C22×C4—101no—
736C22×C4—101no—
737C22×C4—101no—
738C22×C4—101no—
739C22×C4C2×C4×D512yes—
740C22×C4C2×C4×D512yes—
741C22×C4#70912yes—
742C22×C4#70912yes—
743C22×C4D4×D512yes—
744C22×C4#71112yes—
745C4⋊C4—108no—
746C4⋊C4—204no—
747C4⋊C4—204no—
748C4⋊C4—204no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C22⋊C4—108no—
752C22⋊C4—108no—
753C22⋊C4—108no—
754C22⋊C4—204no—
755C42—204no—
756C42—204no—
757C42—204no—
758C42—204no—
759C2×C5—44no—
760C2×C5#229311yescharacteristic
761C2×C5C4×C22⋊Q811yescharacteristic
762C2×C5#232111yescharacteristic
763C2×C5#234511yescharacteristic
764C2×C5#235311yescharacteristic
765C2×C5#236811yescharacteristic
766C2×C5#237411yescharacteristic
767C2×C5#256411yescharacteristic
768C2×C5#256611yescharacteristic
769C2×C5#257611yescharacteristic
770C2×C5#257811yescharacteristic
771C2×C5#258711yescharacteristic
772C2×C5#258911yescharacteristic
773C2×C5#260211yescharacteristic
774C2×C5#260311yescharacteristic
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23#403314yes—
810C23C22×C4×D511yescharacteristic
811C23C2×#70911yescharacteristic
812C23C2×#70911yescharacteristic
813C23C2×D4×D511yescharacteristic
814C23C2×#71111yescharacteristic
815C23C2×#71111yescharacteristic
816C23#414411yescharacteristic
817C23#414411yescharacteristic
818C23#414411yescharacteristic
819C23#414411yescharacteristic
820C23C2×Q8×D511yescharacteristic
821C23D5×#4111yescharacteristic
822C23D5×#4111yescharacteristic
823C23D5×#4111yescharacteristic
824C23D5×#4111yescharacteristic
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—416no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—54no—
868C2×C4—54no—
869C2×C4—102no—
870C2×C4—102no—
871C2×C4—102no—
872C2×C4—102no—
873C2×C4—102no—
874C2×C4—102no—
875C2×C4—102no—
876C2×C4—102no—
877C2×C4—102no—
878C2×C4—102no—
879C2×C4—102no—
880C2×C4—102no—
881C2×C4—102no—
882C2×C4—102no—
883C2×C4—102no—
884C2×C4—102no—
885C2×C4—102no—
886C2×C4—102no—
887C2×C4—102no—
888C2×C4—102no—
889C2×C4—102no—
890C2×C4—102no—
891C2×C4—102no—
892C2×C4—102no—
893C2×C4—102no—
894C2×C4—102no—
895C2×C4—102no—
896C2×C4—102no—
897C2×C4—102no—
898C2×C4—102no—
899C2×C4—201no—
900C2×C4—201no—
901C2×C4—201no—
902C2×C4—201no—
903C2×C4—201no—
904C2×C4—201no—
905C2×C4—201no—
906C2×C4—201no—
907C2×C4—201no—
908C2×C4—201no—
909C2×C4—201no—
910C2×C4—201no—
911C2×C4—201no—
912C2×C4—201no—
913C2×C4—201no—
914C2×C4—201no—
915C2×C4—201no—
916C2×C4—201no—
917C2×C4—201no—
918C2×C4—201no—
919C2×C4—201no—
920C2×C4—201no—
921C2×C4—201no—
922C2×C4—201no—
923C2×C4#402714yes—
924C5#1407511yescharacteristic, complemented, Sylow
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C4×#70911yescharacteristic
941C22C2×#402711yescharacteristic
942C22#6582011yescharacteristic
943C22#6582011yescharacteristic
944C22#6582911yescharacteristic
945C22#6582911yescharacteristic
946C22C2×#403311yescharacteristic
947C22#6584511yescharacteristic
948C22#6584511yescharacteristic
949C22D5×#11711yescharacteristic
950C22#6585611yescharacteristic
951C22#6587211yescharacteristic
952C22#6587211yescharacteristic
953C22#6587411yescharacteristic
954C22#6588211yescharacteristic
955C22#6588211yescharacteristic
956C22#6589011yescharacteristic
957C22#6589211yescharacteristic
958C22#6589311yescharacteristic
959C22#6592311yescharacteristic
960C22#6592611yescharacteristic
961C22#6592711yescharacteristic
962C22#6592711yescharacteristic
963C22#6593411yescharacteristic
964C22#6593511yescharacteristic
965C22#6593511yescharacteristic
966C22#6594011yescharacteristic
967C22#6595611yescharacteristic
968C22D5×C22⋊Q811yescharacteristic
969C22#6597011yescharacteristic
970C22#6597011yescharacteristic
971C22#6599311yescharacteristic
972C22#6599311yescharacteristic
973C22#6599511yescharacteristic
974C22#6599511yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—104no—
982C4—104no—
983C4—202no—
984C4—202no—
985C4—202no—
986C4—202no—
987C4—202no—
988C4—202no—
989C2—44no—
990C2#1060507011yescharacteristic
991C2#1060517011yescharacteristic
992C2#1060520911yescharacteristic
993C2#1060555211yescharacteristic
994C2#1060559711yescharacteristic
995C2#1060561111yescharacteristic
996C2#1060585411yescharacteristic
997C2#1060620811yescharacteristic
998C2#1060622111yescharacteristic
999C2#1060622311yescharacteristic
1000C2#1060634611yescharacteristic
1001C2#1060649711yescharacteristic
1002C2#1060649911yescharacteristic
1003C2#1060650911yescharacteristic
1004C2#1060663511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22⋊#95D5
hypocenterC5#14075
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#64941C2semidirect
9. #10600211C2semidirect
10. #10600202C2semidirect
11. #10600199C2semidirect
12. #10600198C2semidirect
13. #10600197C2semidirect
14. #10600195C2semidirect
15. Dic5×#95C2semidirect
35. #65499C4semidirect
924. C5#14075semidirect

Maximal subgroups

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

subgroupindex
C2×#654992
C2×C4×C22⋊Dic52
C2×#649412
C5×C22⋊#952
#106023402
#106023382
#106002112
#106002022
#106001992
#106001982
#106001972
#106001952
Dic5×#952
#140755