Finite Group Databasebeta

← #12020833

Subgroups — #12020833

Order 1280.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#388C211yesmaximal, characteristic
2C2×#65240C211yesmaximal, characteristic
3C2×C22⋊C4×Dic5C211yesmaximal, characteristic
4C2×C22⋊C4×Dic5C211yesmaximal, characteristic
5C2×#65221C211yesmaximal, characteristic, complemented
6#10602357C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10602338C211yesmaximal, characteristic
9#10602338C211yesmaximal, characteristic
10#10602337C211yesmaximal, characteristic
11C4×#3963C211yesmaximal, characteristic, complemented
12#10600200C211yesmaximal, characteristic, complemented
13#10600194C211yesmaximal, characteristic, complemented
14Dic5×#95C211yesmaximal, characteristic, complemented
15Dic5×#95C211yesmaximal, characteristic, complemented
16C24×Dic5C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C22×C4×Dic5C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C5×#388C418yescomplemented
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
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
51C2×#3963C2211yescharacteristic
52#65240C418yescomplemented
53C22⋊C4×Dic5—24no—
54C22⋊C4×Dic5C418yescomplemented
55#65221—24no—
56#13816—51nomaximal, Sylow
57C25×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×Dic5—22no—
65C23×Dic5—22no—
66C23×Dic5—22no—
67C23×Dic5—22no—
68C23×Dic5—41no—
69C23×Dic5—41no—
70C23×Dic5C2×C414yes—
71C23×Dic5C2311yescharacteristic
72C23×Dic5C2311yescharacteristic
73C23×Dic5C2311yescharacteristic
74C23×Dic5C2311yescharacteristic
75C23×Dic5C2311yescharacteristic
76C23×Dic5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C2×C5×C4⋊C4—41no—
80C2×C5×C4⋊C4—41no—
81C2×C5×C4⋊C4C2×C414yescomplemented
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4—41no—
85C2×C5×C22⋊C4—41no—
86C2×C5×C22⋊C4C2×C414yes—
87C2×C5×C22⋊C4C2×C414yes—
88C2×C5×C22⋊C4C2×C414yes—
89C2×C5×C22⋊C4C2×C414yes—
90C2×C5×C22⋊C4C2×C414yes—
91C2×C42×C5—22no—
92C2×C42×C5—22no—
93C2×C42×C5C2×C414yescomplemented
94C2×C22⋊Dic5—22no—
95C2×C22⋊Dic5—22no—
96C2×C22⋊Dic5—22no—
97C2×C22⋊Dic5—22no—
98C2×C22⋊Dic5—41no—
99C2×C22⋊Dic5—41no—
100C2×C22⋊Dic5C2×C414yes—
101C2×C22⋊Dic5C2×C414yes—
102C2×C22⋊Dic5C2×C414yes—
103C2×C4⋊Dic5—41no—
104C2×C4⋊Dic5—41no—
105C2×C4⋊Dic5C2×C414yescomplemented
106C2×C4×Dic5—22no—
107C2×C4×Dic5—22no—
108C2×C4×Dic5—22no—
109C2×C4×Dic5—22no—
110C2×C4×Dic5—22no—
111C2×C4×Dic5—22no—
112C2×C4×Dic5—22no—
113C2×C4×Dic5—22no—
114C2×C4×Dic5—22no—
115C2×C4×Dic5—22no—
116C2×C4×Dic5—22no—
117C2×C4×Dic5—22no—
118C2×C4×Dic5—41no—
119C2×C4×Dic5—41no—
120C2×C4×Dic5—41no—
121C2×C4×Dic5—41no—
122C2×C4×Dic5—41no—
123C2×C4×Dic5—41no—
124C2×C4×Dic5C2×C414yes—
125C2×C4×Dic5C2×C414yes—
126C2×C4×Dic5C2×C414yescomplemented
127C5×#95C2×C414yescomplemented
128C5×#95C2×C414yescomplemented
129#3963—22no—
130#3963—22no—
131#3963—22no—
132#3963—22no—
133#3963—22no—
134#3963—22no—
135#3963—22no—
136#3963—22no—
137#3963—22no—
138#3963—41no—
139#3963—41no—
140#3963C2×C414yes—
141#3963C2×C414yes—
142#3963C2×C414yescomplemented
143#3963C2×C414yescomplemented
144#3963D414yes—
145C2×#388—51no—
146C2×#388D511yescharacteristic
147C2×C4×C22⋊C4—51no—
148C2×C4×C22⋊C4—51no—
149C2×#376—51no—
150#1437—51no—
151#1437—51no—
152#1436—51no—
153#1436—51no—
154C4⋊#95—51no—
155#1434—51no—
156C22⋊#95—51no—
157C4×#95—51no—
158C4×#95—51no—
159C4×#95—51no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5C22×C412yes—
173C24×C5C22×C412yes—
174C24×C5C22×C412yes—
175C24×C5C2411yescharacteristic
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—21no—
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×C5C22×C412yes—
207C22×C4×C5C22×C412yes—
208C22×C4×C5C22×C412yes—
209C22×C4×C5C22×C412yes—
210C22×C4×C5C22×C412yes—
211C22×C4×C5C22×C412yes—
212C22×C4×C5C22×C412yes—
213C22×C4×C5C22×C412yes—
214C22×C4×C5C22×C412yes—
215C22×C4×C5C22×C412yes—
216C22×C4×C5C2×D412yes—
217C22×C4×C5#4112yes—
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×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—28no—
259C22×Dic5—28no—
260C22×Dic5—44no—
261C22×Dic5—44no—
262C22×Dic5—44no—
263C22×Dic5—44no—
264C22×Dic5—44no—
265C22×Dic5C22×C412yes—
266C22×Dic5C22×C412yes—
267C22×Dic5C22×C412yes—
268C22×Dic5C22×C412yes—
269C22×Dic5C22×C412yes—
270C22×Dic5C22×C412yes—
271C22×Dic5C22×C412yes—
272C22×Dic5C22×C412yes—
273C22×Dic5C2×D412yes—
274C22×Dic5C2×D412yes—
275C22×Dic5#4112yes—
276C22×Dic5#4112yes—
277C22×Dic5#4112yes—
278C22×Dic5#4112yes—
279C22×Dic5#4112yes—
280C22×Dic5#4112yes—
281C5×C4⋊C4—44no—
282C5×C22⋊C4—28no—
283C5×C22⋊C4—44no—
284C5×C22⋊C4C42116yescomplemented
285C42×C5—28no—
286C22⋊Dic5—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—44no—
289C4⋊Dic5—44no—
290C4×Dic5—28no—
291C4×Dic5—28no—
292C4×Dic5—44no—
293C4×Dic5—44no—
294C4×Dic5—44no—
295C4×Dic5—44no—
296C4×Dic5—44no—
297C24×C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4C2×D511yescharacteristic
300C22×C22⋊C4—51no—
301C22×C22⋊C4—51no—
302C22×C22⋊C4—51no—
303C22×C22⋊C4C2×D511yescharacteristic
304C22×C22⋊C4C2×D511yescharacteristic
305C22×C22⋊C4C2×D511yescharacteristic
306C22×C42—51no—
307C22×C42—51no—
308C22×C42—51no—
309C22×C42—51no—
310C22×C42—51no—
311C22×C42—51no—
312C22×C42—51no—
313C22×C42C2×D511yescharacteristic
314#388—58no—
315#388Dic518yescomplemented
316C4×C22⋊C4—58no—
317C4×C22⋊C4—104no—
318#376—104no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—51no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95C2×D511yescharacteristic
336C2×#95C2×D511yescharacteristic
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—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—41no—
356C23×C5—41no—
357C23×C5—41no—
358C23×C5—41no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5—41no—
362C23×C5—41no—
363C23×C5—41no—
364C23×C5—41no—
365C23×C5—41no—
366C23×C5—41no—
367C23×C5—41no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—41no—
371C23×C5C2×C4214yes—
372C23×C5C23×C411yescharacteristic
373C23×C5C23×C411yescharacteristic
374C23×C5C23×C411yescharacteristic
375C23×C5C22×D411yescharacteristic
376C23×C5C2×#4111yescharacteristic
377C23×C5C2×#4111yescharacteristic
378C23×C5C2×#4111yescharacteristic
379C23×C5C2×#4111yescharacteristic
380C23×C5C2×#4111yescharacteristic
381C23×C5C2×#4111yescharacteristic
382C23×C5C2×#4111yescharacteristic
383C23×C5H(5,𝔽2)11yescharacteristic
384C23×C5H(5,𝔽2)11yescharacteristic
385C23×C5H(5,𝔽2)11yescharacteristic
386C23×C52−1+411yescharacteristic
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5C2×C4214yes—
427C2×C4×C5C2×C4214yes—
428C2×C4×C5C4×D414yes—
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—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—22no—
454C2×Dic5—22no—
455C2×Dic5—22no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—22no—
460C2×Dic5—22no—
461C2×Dic5—22no—
462C2×Dic5—22no—
463C2×Dic5—22no—
464C2×Dic5—22no—
465C2×Dic5—416no—
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—41no—
475C2×Dic5—41no—
476C2×Dic5—41no—
477C2×Dic5—41no—
478C2×Dic5—41no—
479C2×Dic5—41no—
480C2×Dic5—41no—
481C2×Dic5—41no—
482C2×Dic5#11714yes—
483C2×Dic5#11714yes—
484C2×Dic5C4×D414yes—
485C2×Dic5C4×D414yes—
486C25C22×D511yescharacteristic
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—51no—
492C23×C4—51no—
493C23×C4—51no—
494C23×C4—51no—
495C23×C4—54no—
496C23×C4—102no—
497C23×C4—102no—
498C23×C4—102no—
499C23×C4—102no—
500C23×C4—201no—
501C23×C4—201no—
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506C23×C4C22×D511yescharacteristic
507C23×C4C22×D511yescharacteristic
508C2×C4⋊C4—41no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—201no—
512C2×C4⋊C4—201no—
513C2×C4⋊C4C2×Dic514yescomplemented
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—54no—
519C2×C22⋊C4—54no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—102no—
522C2×C22⋊C4—102no—
523C2×C22⋊C4—102no—
524C2×C22⋊C4—102no—
525C2×C22⋊C4—201no—
526C2×C22⋊C4—201no—
527C2×C22⋊C4C4×D514yes—
528C2×C22⋊C4C4×D514yes—
529C2×C22⋊C4C2×Dic514yes—
530C2×C22⋊C4C2×Dic514yes—
531C2×C22⋊C4C2×Dic514yes—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—54no—
535C2×C42—54no—
536C2×C42—54no—
537C2×C42—102no—
538C2×C42—102no—
539C2×C42—102no—
540C2×C42—102no—
541C2×C42—102no—
542C2×C42—102no—
543C2×C42—102no—
544C2×C42—102no—
545C2×C42—102no—
546C2×C42—102no—
547C2×C42—102no—
548C2×C42—102no—
549C2×C42—201no—
550C2×C42—201no—
551C2×C42—201no—
552C2×C42—201no—
553C2×C42—201no—
554C2×C42—201no—
555C2×C42C2×Dic514yescomplemented
556#95—54no—
557#95—54no—
558#95—54no—
559#95—54no—
560#95—54no—
561#95—102no—
562#95—102no—
563#95—102no—
564#95—102no—
565#95—102no—
566#95—102no—
567#95—102no—
568#95—102no—
569#95—102no—
570#95—201no—
571#95—201no—
572#95C2×Dic514yescomplemented
573#95C2×Dic514yescomplemented
574C22×C5—24no—
575C22×C5—24no—
576C22×C5—24no—
577C22×C5—42no—
578C22×C5—42no—
579C22×C5—42no—
580C22×C5—42no—
581C22×C5—42no—
582C22×C5—42no—
583C22×C5—42no—
584C22×C5—42no—
585C22×C5—42no—
586C22×C5—42no—
587C22×C5—42no—
588C22×C5—42no—
589C22×C5C22×C4211yescharacteristic
590C22×C5C2×#11711yescharacteristic
591C22×C5C2×#11711yescharacteristic
592C22×C5C2×C4×D411yescharacteristic
593C22×C5C2×C4×D411yescharacteristic
594C22×C5C2×C4×D411yescharacteristic
595C22×C5C4×#4111yescharacteristic
596C22×C5C4×#4111yescharacteristic
597C22×C5C4×#4111yescharacteristic
598C22×C5C4×#4111yescharacteristic
599C22×C5C4×#4111yescharacteristic
600C22×C5C4×#4111yescharacteristic
601C22×C5C4×#4111yescharacteristic
602C22×C5#51811yescharacteristic
603C22×C5#51811yescharacteristic
604C22×C5#51811yescharacteristic
605C22×C5#52011yescharacteristic
606C22×C5#52011yescharacteristic
607C22×C5#52011yescharacteristic
608C22×C5#54611yescharacteristic
609C22×C5#54611yescharacteristic
610C22×C5#54711yescharacteristic
611C22×C5#55011yescharacteristic
612C22×C5#55111yescharacteristic
613C22×C5#55111yescharacteristic
614C22×C5#55111yescharacteristic
615C22×C5#55111yescharacteristic
616C22×C5#55211yescharacteristic
617C22×C5#55211yescharacteristic
618C22×C5#55311yescharacteristic
619C22×C5#55311yescharacteristic
620C22×C5#55511yescharacteristic
621C22×C5#55511yescharacteristic
622C22×C5#55511yescharacteristic
623C22×C5#55611yescharacteristic
624C4×C5—24no—
625C4×C5—24no—
626C4×C5—24no—
627C4×C5—42no—
628C4×C5—42no—
629C4×C5—42no—
630Dic5—24no—
631Dic5—24no—
632Dic5—24no—
633Dic5—24no—
634Dic5—42no—
635Dic5—42no—
636Dic5—42no—
637Dic5—42no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24C2×C4×D512yes—
651C24C2×C4×D512yes—
652C24C22×Dic512yes—
653C24C23×D511yescharacteristic
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—21no—
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—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
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—52no—
696C22×C4—52no—
697C22×C4—52no—
698C22×C4—52no—
699C22×C4—52no—
700C22×C4—108no—
701C22×C4—108no—
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×C4—101no—
740C22×C4—101no—
741C22×C4—101no—
742C22×C4—204no—
743C22×C4—204no—
744C22×C4—204no—
745C22×C4—204no—
746C22×C4—204no—
747C22×C4C2×C4×D512yes—
748C22×C4C2×C4×D512yes—
749C22×C4C2×C4×D512yes—
750C22×C4C2×C4×D512yes—
751C22×C4D4×D512yes—
752C22×C4#71112yes—
753C22×C4C22×Dic512yes—
754C22×C4C22×Dic512yes—
755C22×C4C22×Dic512yes—
756C22×C4C22×Dic512yes—
757C22×C4C22×Dic512yes—
758C22×C4C22×Dic512yes—
759C4⋊C4—44no—
760C4⋊C4—204no—
761C22⋊C4—28no—
762C22⋊C4—44no—
763C22⋊C4—108no—
764C22⋊C4—108no—
765C22⋊C4—204no—
766C22⋊C4C4×Dic5116yescomplemented
767C42—28no—
768C42—108no—
769C42—108no—
770C42—204no—
771C42—204no—
772C42—204no—
773C42—204no—
774C42—204no—
775C2×C5—44no—
776C2×C5C4×#11711yescharacteristic
777C2×C5C42×D411yescharacteristic
778C2×C5#227511yescharacteristic
779C2×C5#234211yescharacteristic
780C2×C5#234611yescharacteristic
781C2×C5#235311yescharacteristic
782C2×C5#235411yescharacteristic
783C2×C5#235911yescharacteristic
784C2×C5#235911yescharacteristic
785C2×C5#236311yescharacteristic
786C2×C5#236311yescharacteristic
787C2×C5#237211yescharacteristic
788C2×C5#237211yescharacteristic
789C2×C5#237311yescharacteristic
790C2×C5#237311yescharacteristic
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C2×C4×Dic514yes—
826C23C22×C4×D511yescharacteristic
827C23C22×C4×D511yescharacteristic
828C23C2×D4×D511yescharacteristic
829C23C2×#71111yescharacteristic
830C23#414411yescharacteristic
831C23#414411yescharacteristic
832C23D5×#4111yescharacteristic
833C23D5×#4111yescharacteristic
834C23D5×#4111yescharacteristic
835C23D5×#4111yescharacteristic
836C23D5×#4111yescharacteristic
837C23D5×#4111yescharacteristic
838C23#414911yescharacteristic
839C23#415011yescharacteristic
840C23C23×Dic511yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—54no—
881C2×C4—54no—
882C2×C4—54no—
883C2×C4—54no—
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—102no—
900C2×C4—102no—
901C2×C4—102no—
902C2×C4—102no—
903C2×C4—102no—
904C2×C4—102no—
905C2×C4—102no—
906C2×C4—102no—
907C2×C4—102no—
908C2×C4—102no—
909C2×C4—102no—
910C2×C4—102no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—102no—
916C2×C4—102no—
917C2×C4—102no—
918C2×C4—102no—
919C2×C4—102no—
920C2×C4—2016no—
921C2×C4—201no—
922C2×C4—201no—
923C2×C4—201no—
924C2×C4—201no—
925C2×C4—201no—
926C2×C4—201no—
927C2×C4—201no—
928C2×C4—201no—
929C2×C4—201no—
930C2×C4—201no—
931C2×C4—201no—
932C2×C4—201no—
933C2×C4—201no—
934C2×C4—201no—
935C2×C4—201no—
936C2×C4—201no—
937C2×C4C2×C4×Dic514yes—
938C2×C4C2×C4×Dic514yes—
939C2×C4D4×Dic514yes—
940C5#1381611yescharacteristic, complemented, Sylow
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22D5×#11711yescharacteristic
957C22D5×#11711yescharacteristic
958C22#6585611yescharacteristic
959C22#6585611yescharacteristic
960C22C4×#71111yescharacteristic
961C22C4×#71111yescharacteristic
962C22C4×D4×D511yescharacteristic
963C22C4×D4×D511yescharacteristic
964C22#6587911yescharacteristic
965C22#6587911yescharacteristic
966C22#6588011yescharacteristic
967C22#6588011yescharacteristic
968C22#6593311yescharacteristic
969C22#6594611yescharacteristic
970C22#6594811yescharacteristic
971C22#6595011yescharacteristic
972C22#6598411yescharacteristic
973C22#6598811yescharacteristic
974C22#6598911yescharacteristic
975C22#6599211yescharacteristic
976C22#6600411yescharacteristic
977C22#6600411yescharacteristic
978C22#6601311yescharacteristic
979C22#6601311yescharacteristic
980C22#6603611yescharacteristic
981C22#6603911yescharacteristic
982C22#6604211yescharacteristic
983C22#6604311yescharacteristic
984C22C22×C4×Dic511yescharacteristic
985C22C2×D4×Dic511yescharacteristic
986C22#6613211yescharacteristic
987C22#41×Dic511yescharacteristic
988C22#41×Dic511yescharacteristic
989C22#41×Dic511yescharacteristic
990C22#6616111yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—104no—
998C4—104no—
999C4—104no—
1000C4—104no—
1001C4—202no—
1002C4—202no—
1003C4—202no—
1004C4—202no—
1005C2—44no—
1006C2#1060720411yescharacteristic
1007C2#1060720611yescharacteristic
1008C2#1060721111yescharacteristic
1009C2#1060721411yescharacteristic
1010C2#1060721611yescharacteristic
1011C2#1060756311yescharacteristic
1012C2#1060756611yescharacteristic
1013C2#1060756811yescharacteristic
1014C2Dic5×#11711yescharacteristic
1015C2C4×D4×Dic511yescharacteristic
1016C2#1061404811yescharacteristic
1017C2#1061436811yescharacteristic
1018C2#1061456911yescharacteristic
1019C2#1061468711yescharacteristic
1020C2#1061480611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC2×C5×#388C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#388D5
hypocenterC5#13816
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. C2×#65221C2semidirect
6. #10602357C2semidirect
7. #10602356C2semidirect
11. C4×#3963C2semidirect
12. #10600200C2semidirect
13. #10600194C2semidirect
14. Dic5×#95C2semidirect
15. Dic5×#95C2semidirect
33. C5×#388C4semidirect
52. #65240C4semidirect
54. C22⋊C4×Dic5C4semidirect
81. C2×C5×C4⋊C4C2×C4semidirect
93. C2×C42×C5C2×C4semidirect
105. C2×C4⋊Dic5C2×C4semidirect
126. C2×C4×Dic5C2×C4semidirect
127. C5×#95C2×C4semidirect
128. C5×#95C2×C4semidirect
142. #3963C2×C4semidirect
143. #3963C2×C4semidirect
284. C5×C22⋊C4C42semidirect
315. #388Dic5semidirect
513. C2×C4⋊C4C2×Dic5semidirect
555. C2×C42C2×Dic5semidirect
572. #95C2×Dic5semidirect
573. #95C2×Dic5semidirect
766. C22⋊C4C4×Dic5semidirect
940. C5#13816semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3882
C2×#652402
C2×C22⋊C4×Dic52
C2×#652212
#106023572
#106023562
#106023382
#106023372
C4×#39632
#106002002
#106001942
Dic5×#952
#138165