Finite Group Databasebeta

← #12027242

Subgroups — #12027242

Order 1280.

1650 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×#65239C211yesmaximal, characteristic
4C2×#65239C211yesmaximal, characteristic
5C2×#65225C211yesmaximal, characteristic, complemented
6#10602358C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10602339C211yesmaximal, characteristic
9#10602339C211yesmaximal, characteristic
10#10602337C211yesmaximal, characteristic
11#10602328C211yesmaximal, characteristic, complemented
12#10600212C211yesmaximal, characteristic, complemented
13#10600212C211yesmaximal, characteristic, complemented
14#10600205C211yesmaximal, characteristic, complemented
15#10600200C211yesmaximal, 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#65240—24no—
53#65239—24no—
54#65239—24no—
55#65225—24no—
56#14403—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—41no—
68C23×Dic5—41no—
69C23×Dic5—41no—
70C23×Dic5—41no—
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⋊C4D414yes—
90C2×C5×C22⋊C4Q814yes—
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—22no—
99C2×C22⋊Dic5—41no—
100C2×C22⋊Dic5—41no—
101C2×C22⋊Dic5—41no—
102C2×C22⋊Dic5—41no—
103C2×C4⋊Dic5—22no—
104C2×C4⋊Dic5—22no—
105C2×C4⋊Dic5—22no—
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—41no—
115C2×C4⋊Dic5—41no—
116C2×C4⋊Dic5—41no—
117C2×C4⋊Dic5—41no—
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×Dic5—22no—
125C2×C4×Dic5—22no—
126C2×C4×Dic5—41no—
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—41no—
138#3963—41no—
139#3963—41no—
140#3963—41no—
141#3963—41no—
142#3963—41no—
143#3963—41no—
144#3963D414yes—
145C2×#388—51no—
146C2×#388D511yescharacteristic
147C2×#385—51no—
148C2×#385—51no—
149C2×#382—51no—
150#1444—51no—
151#1444—51no—
152#1442—51no—
153#1441—51no—
154#1439—51no—
155#1439—51no—
156#1436—51no—
157C4⋊#95—51no—
158C4⋊#95—51no—
159C22⋊#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×C5C2×D412yes—
174C24×C5C2×Q812yes—
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×C5C2×D412yes—
213C22×C4×C5C2×D412yes—
214C22×C4×C5C2×D412yes—
215C22×C4×C5C2×Q812yes—
216C22×C4×C5C2×Q812yes—
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—21no—
259C22×Dic5—21no—
260C22×Dic5—21no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5—21no—
264C22×Dic5—21no—
265C22×Dic5—21no—
266C22×Dic5—21no—
267C22×Dic5—21no—
268C22×Dic5—21no—
269C22×Dic5—21no—
270C22×Dic5—44no—
271C22×Dic5—44no—
272C22×Dic5—44no—
273C22×Dic5—44no—
274C22×Dic5—44no—
275C22×Dic5—44no—
276C22×Dic5—44no—
277C22×Dic5C2×D412yes—
278C22×Dic5C2×D412yes—
279C22×Dic5#4112yes—
280C22×Dic5#4112yes—
281C5×C4⋊C4—44no—
282C5×C22⋊C4—28no—
283C5×C22⋊C4—44no—
284C5×C22⋊C4C4⋊C4116yescomplemented
285C42×C5—28no—
286C22⋊Dic5—44no—
287C22⋊Dic5—44no—
288C22⋊Dic5—44no—
289C4⋊Dic5—44no—
290C4⋊Dic5—44no—
291C4⋊Dic5—44no—
292C4⋊Dic5—44no—
293C4⋊Dic5—44no—
294C4⋊Dic5—44no—
295C4⋊Dic5—44no—
296C4×Dic5—44no—
297C24×C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4C2×D511yescharacteristic
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4C2×D511yescharacteristic
310C22×C22⋊C4C2×D511yescharacteristic
311C22×C22⋊C4C2×D511yescharacteristic
312C22×C42—51no—
313C22×C42C2×D511yescharacteristic
314#388—104no—
315#388Dic518yescomplemented
316#385—104no—
317#385—104no—
318#382—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×C4⋊C414yes—
372C23×C5C23×C411yescharacteristic
373C23×C5C22×D411yescharacteristic
374C23×C5C22×D411yescharacteristic
375C23×C5C22×Q811yescharacteristic
376C23×C5C2×#4111yescharacteristic
377C23×C5C2×#4111yescharacteristic
378C23×C5C2×#4111yescharacteristic
379C23×C5H(5,𝔽2)11yescharacteristic
380C23×C5H(5,𝔽2)11yescharacteristic
381C23×C5H(5,𝔽2)11yescharacteristic
382C23×C5H(5,𝔽2)11yescharacteristic
383C23×C5H(5,𝔽2)11yescharacteristic
384C23×C52−1+411yescharacteristic
385C23×C52−1+411yescharacteristic
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×C4⋊C414yes—
427C2×C4×C5C2×C4⋊C414yes—
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—416no—
442C2×Dic5—41no—
443C2×Dic5—41no—
444C2×Dic5—41no—
445C2×Dic5—41no—
446C2×Dic5—41no—
447C2×Dic5—41no—
448C2×Dic5—41no—
449C2×Dic5—41no—
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—41no—
475C2×Dic5—41no—
476C2×Dic5—41no—
477C2×Dic5—41no—
478C2×Dic5—41no—
479C2×Dic5—41no—
480C2×Dic5—41no—
481C2×Dic5—41no—
482C2×Dic5—41no—
483C2×Dic5—41no—
484C2×Dic5—41no—
485C2×Dic5—41no—
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—102no—
496C23×C4—102no—
497C23×C4—102no—
498C23×C4—201no—
499C23×C4—201no—
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—102no—
511C2×C4⋊C4—102no—
512C2×C4⋊C4—102no—
513C2×C4⋊C4—102no—
514C2×C4⋊C4—102no—
515C2×C4⋊C4—102no—
516C2×C4⋊C4—102no—
517C2×C4⋊C4—102no—
518C2×C4⋊C4—102no—
519C2×C4⋊C4—102no—
520C2×C4⋊C4—102no—
521C2×C4⋊C4—201no—
522C2×C4⋊C4—201no—
523C2×C4⋊C4—201no—
524C2×C4⋊C4—201no—
525C2×C4⋊C4—201no—
526C2×C4⋊C4—201no—
527C2×C4⋊C4—201no—
528C2×C4⋊C4—201no—
529C2×C4⋊C4—201no—
530C2×C4⋊C4—201no—
531C2×C4⋊C4C2×Dic514yescomplemented
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—102no—
537C2×C22⋊C4—102no—
538C2×C22⋊C4—102no—
539C2×C22⋊C4—102no—
540C2×C22⋊C4—102no—
541C2×C22⋊C4—201no—
542C2×C22⋊C4—201no—
543C2×C22⋊C4—201no—
544C2×C22⋊C4—201no—
545C2×C22⋊C4Dic1014yes—
546C2×C22⋊C4D2014yes—
547C2×C22⋊C4C2×Dic514yes—
548C2×C22⋊C4C2×Dic514yes—
549C2×C22⋊C4C2×Dic514yes—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—102no—
553C2×C42—102no—
554C2×C42—201no—
555C2×C42C2×Dic514yescomplemented
556#95—54no—
557#95—102no—
558#95—102no—
559#95—102no—
560#95—102no—
561#95—102no—
562#95—102no—
563#95—102no—
564#95—102no—
565#95—201no—
566#95—201no—
567#95—201no—
568#95—201no—
569#95—201no—
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×C4⋊C411yescharacteristic
590C22×C5C2×C4×D411yescharacteristic
591C22×C5C4×#4111yescharacteristic
592C22×C5#51811yescharacteristic
593C22×C5#52011yescharacteristic
594C22×C5#52011yescharacteristic
595C22×C5#52011yescharacteristic
596C22×C5#53511yescharacteristic
597C22×C5#53511yescharacteristic
598C22×C5#53611yescharacteristic
599C22×C5#53711yescharacteristic
600C22×C5#53811yescharacteristic
601C22×C5#53911yescharacteristic
602C22×C5#54011yescharacteristic
603C22×C5#54111yescharacteristic
604C22×C5#54211yescharacteristic
605C22×C5#54211yescharacteristic
606C22×C5#54411yescharacteristic
607C22×C5#54411yescharacteristic
608C22×C5D4211yescharacteristic
609C22×C5#54611yescharacteristic
610C22×C5#54611yescharacteristic
611C22×C5#54611yescharacteristic
612C22×C5#54711yescharacteristic
613C22×C5#54711yescharacteristic
614C22×C5D4×Q811yescharacteristic
615C22×C5#55111yescharacteristic
616C22×C5#55211yescharacteristic
617C22×C5#55411yescharacteristic
618C22×C5#55411yescharacteristic
619C22×C5#55411yescharacteristic
620C22×C5H(3,𝔽4)11yescharacteristic
621C22×C5#56211yescharacteristic
622C22×C5#56211yescharacteristic
623C22×C5#56311yescharacteristic
624C4×C5—24no—
625C4×C5—24no—
626C4×C5—24no—
627C4×C5—42no—
628C4×C5—42no—
629C4×C5—42no—
630Dic5—42no—
631Dic5—42no—
632Dic5—42no—
633Dic5—42no—
634Dic5—81no—
635Dic5—81no—
636Dic5—81no—
637Dic5—81no—
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×Dic1012yes—
651C24C2×D2012yes—
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—101no—
689C22×C4—101no—
690C22×C4—101no—
691C22×C4—101no—
692C22×C4—101no—
693C22×C4—101no—
694C22×C4—101no—
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×C4—101no—
740C22×C4—204no—
741C22×C4—204no—
742C22×C4—204no—
743C22×C4—204no—
744C22×C4—204no—
745C22×C4—204no—
746C22×C4—204no—
747C22×C4C2×Dic1012yes—
748C22×C4C2×Dic1012yes—
749C22×C4C2×D2012yes—
750C22×C4C2×D2012yes—
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—
761C4⋊C4—204no—
762C4⋊C4—204no—
763C4⋊C4—204no—
764C4⋊C4—204no—
765C4⋊C4—204no—
766C4⋊C4—204no—
767C22⋊C4—28no—
768C22⋊C4—44no—
769C22⋊C4—204no—
770C22⋊C4—204no—
771C22⋊C4—204no—
772C22⋊C4C4⋊Dic5116yescomplemented
773C42—28no—
774C42—204no—
775C2×C5—44no—
776C2×C5#231711yescharacteristic
777C2×C5#232411yescharacteristic
778C2×C5#233411yescharacteristic
779C2×C5D4×C4⋊C411yescharacteristic
780C2×C5#234911yescharacteristic
781C2×C5#235911yescharacteristic
782C2×C5#237911yescharacteristic
783C2×C5#267011yescharacteristic
784C2×C5#267211yescharacteristic
785C2×C5#269811yescharacteristic
786C2×C5#270411yescharacteristic
787C2×C5#270611yescharacteristic
788C2×C5#272011yescharacteristic
789C2×C5#276311yescharacteristic
790C2×C5#276811yescharacteristic
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×Dic1011yescharacteristic
827C23C22×D2011yescharacteristic
828C23C2×D4×D511yescharacteristic
829C23C2×#71111yescharacteristic
830C23#414411yescharacteristic
831C23#414411yescharacteristic
832C23D5×#4111yescharacteristic
833C23D5×#4111yescharacteristic
834C23#414911yescharacteristic
835C23#414911yescharacteristic
836C23#414911yescharacteristic
837C23#415011yescharacteristic
838C23#415011yescharacteristic
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—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—2016no—
893C2×C4—201no—
894C2×C4—201no—
895C2×C4—201no—
896C2×C4—201no—
897C2×C4—201no—
898C2×C4—201no—
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—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#1440311yescharacteristic, 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—
956C22#6585311yescharacteristic
957C22#6585311yescharacteristic
958C22#6585911yescharacteristic
959C22#6586011yescharacteristic
960C22D4×Dic1011yescharacteristic
961C22#6587311yescharacteristic
962C22#6587311yescharacteristic
963C22#6587711yescharacteristic
964C22D4×D2011yescharacteristic
965C22#6588811yescharacteristic
966C22#6588811yescharacteristic
967C22#6588911yescharacteristic
968C22#6593711yescharacteristic
969C22#6594111yescharacteristic
970C22#6594211yescharacteristic
971C22#6595311yescharacteristic
972C22#6598411yescharacteristic
973C22#6598811yescharacteristic
974C22#6598911yescharacteristic
975C22#6599211yescharacteristic
976C22#6600611yescharacteristic
977C22#6601711yescharacteristic
978C22#6601811yescharacteristic
979C22#6601811yescharacteristic
980C22#6603511yescharacteristic
981C22#6603811yescharacteristic
982C22#6604111yescharacteristic
983C22#6604411yescharacteristic
984C22C22×C4⋊Dic511yescharacteristic
985C22C2×D4×Dic511yescharacteristic
986C22#6613211yescharacteristic
987C22#41×Dic511yescharacteristic
988C22#6616111yescharacteristic
989C22#6616111yescharacteristic
990C22#6616111yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—202no—
998C4—202no—
999C4—202no—
1000C4—202no—
1001C4—401no—
1002C4—401no—
1003C4—401no—
1004C4—401no—
1005C2—44no—
1006C2#1060739611yescharacteristic
1007C2#1060740911yescharacteristic
1008C2#1060741511yescharacteristic
1009C2#1060741811yescharacteristic
1010C2#1060742811yescharacteristic
1011C2#1060747911yescharacteristic
1012C2#1060748311yescharacteristic
1013C2#1060764411yescharacteristic
1014C2#1061396411yescharacteristic
1015C2D4×C4⋊Dic511yescharacteristic
1016C2#1061406411yescharacteristic
1017C2#1061436411yescharacteristic
1018C2#1061456911yescharacteristic
1019C2#1061468811yescharacteristic
1020C2#1061480511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#388C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#388D5
hypocenterC5#14403
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. C2×#65225C2semidirect
6. #10602358C2semidirect
7. #10602356C2semidirect
11. #10602328C2semidirect
12. #10600212C2semidirect
13. #10600212C2semidirect
14. #10600205C2semidirect
15. #10600200C2semidirect
33. C5×#388C4semidirect
81. C2×C5×C4⋊C4C2×C4semidirect
93. C2×C42×C5C2×C4semidirect
127. C5×#95C2×C4semidirect
128. C5×#95C2×C4semidirect
284. C5×C22⋊C4C4⋊C4semidirect
315. #388Dic5semidirect
531. C2×C4⋊C4C2×Dic5semidirect
555. C2×C42C2×Dic5semidirect
572. #95C2×Dic5semidirect
573. #95C2×Dic5semidirect
772. C22⋊C4C4⋊Dic5semidirect
940. C5#14403semidirect

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×#652392
C2×#652252
#106023582
#106023562
#106023392
#106023372
#106023282
#106002122
#106002052
#106002002
#144035