Finite Group Databasebeta

← #12024939

Subgroups — #12024939

Order 1280.

1578 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic5C211yesmaximal, characteristic
2C2×#65242C211yesmaximal, characteristic
3C2×#65233C211yesmaximal, characteristic
4C5×C22⋊#95C211yesmaximal, characteristic
5#10602920C211yesmaximal, characteristic
6#10602342C211yesmaximal, characteristic
7#10602338C211yesmaximal, characteristic
8#10600210C211yesmaximal, characteristic, complemented
9#10600210C211yesmaximal, characteristic, complemented
10#10600200C211yesmaximal, characteristic, complemented
11#10600200C211yesmaximal, characteristic, complemented
12#10600199C211yesmaximal, characteristic, complemented
13#10600199C211yesmaximal, characteristic, complemented
14#10600196C211yesmaximal, 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×C4⋊Dic5C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2211yescharacteristic
33C4×C22⋊Dic5—24no—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
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#65242C418yescomplemented
53#65233—24no—
54#14197—51nomaximal, Sylow
55C25×C5C2311yescharacteristic
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—41no—
62C23×C4×C5—41no—
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—41no—
80C2×C5×C22⋊C4—41no—
81C2×C5×C22⋊C4—41no—
82C2×C5×C22⋊C4C2×C414yes—
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—22no—
91C2×C22⋊Dic5—41no—
92C2×C22⋊Dic5C2×C414yes—
93C2×C22⋊Dic5C2×C414yes—
94C2×C22⋊Dic5D414yes—
95C2×C4⋊Dic5—41no—
96C2×C4⋊Dic5—41no—
97C2×C4⋊Dic5C2×C414yescomplemented
98C2×#683—22no—
99C2×#683—22no—
100C2×#683—22no—
101C2×C4×Dic5—22no—
102C2×C4×Dic5—22no—
103C2×C4×Dic5—22no—
104C2×C4×Dic5—22no—
105C2×C4×Dic5—22no—
106C2×C4×Dic5—22no—
107C2×C4×Dic5—22no—
108C2×C4×Dic5—41no—
109C2×C4×Dic5—41no—
110C2×C4×Dic5—41no—
111C2×C4×Dic5—41no—
112C2×C4×Dic5—41no—
113C5×#95—22no—
114C5×#95—22no—
115C5×#95—22no—
116C5×#95—41no—
117#3963—22no—
118#3963—22no—
119#3963—22no—
120#3963—22no—
121#3963—22no—
122#3963—22no—
123#3963—22no—
124#3963—22no—
125#3963—22no—
126#3963—22no—
127#3963—22no—
128#3963—41no—
129#3963—41no—
130#3963—41no—
131#3963—41no—
132#3963C2×C414yescomplemented
133#3963C2×C414yescomplemented
134#3963C2×C414yescomplemented
135C2×#397—51no—
136C2×#388—51no—
137C2×C4×C22⋊C4—51no—
138#1443—51no—
139#1443—51no—
140#1440—51no—
141#1437—51no—
142#1436—51no—
143#1436—51no—
144#1436—51no—
145#1436—51no—
146#1434—51no—
147C22⋊#95—51no—
148C22⋊#95D511yescharacteristic
149C4×#95—51no—
150C24×C5—21no—
151C24×C5—21no—
152C24×C5—21no—
153C24×C5—21no—
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×C5C22×C412yes—
163C24×C5C2×D412yes—
164C24×C5#4112yes—
165C24×C5C2411yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—28no—
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—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—44no—
203C22×C4×C5—44no—
204C22×C4×C5—44no—
205C22×C4×C5—44no—
206C22×C4×C5—44no—
207C22×C4×C5—44no—
208C22×C4×C5C22×C412yes—
209C22×C4×C5C22×C412yes—
210C22×C4×C5#4112yes—
211C22×C4×C5#4112yes—
212C22×C4×C5#4112yes—
213C22×C4×C5#4112yes—
214C22×C4×C5#4112yes—
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
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×Dic5C22×C412yes—
263C22×Dic5C22×C412yes—
264C22×Dic5C22×C412yes—
265C22×Dic5C22×C412yes—
266C22×Dic5C2×D412yes—
267C22×Dic5C2×D412yes—
268C22×Dic5#4112yes—
269C22×Dic5#4112yes—
270C22×Dic5#4112yes—
271C5×C22⋊C4—44no—
272C5×C22⋊C4—44no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—28no—
276C22⋊Dic5—44no—
277C4⋊Dic5—44no—
278#683—44no—
279C4×Dic5—44no—
280C4×Dic5—44no—
281C4×Dic5—44no—
282C4×Dic5—44no—
283C24×C4C2×D511yescharacteristic
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C22⋊C4—51no—
287C22×C22⋊C4—51no—
288C22×C22⋊C4—51no—
289C22×C22⋊C4—51no—
290C22×C22⋊C4C2×D511yescharacteristic
291C22×C22⋊C4C2×D511yescharacteristic
292C22×C42—51no—
293C22×C42—51no—
294C22×C42—51no—
295C22×C42—51no—
296#397—58no—
297#388—104no—
298C4×C22⋊C4—104no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95—51no—
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×#95C2×D511yescharacteristic
318C2×#95C2×D511yescharacteristic
319C2×#95C2×D511yescharacteristic
320C2×#95C2×D511yescharacteristic
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
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—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
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×C5C4×D414yes—
356C23×C5C23×C411yescharacteristic
357C23×C5C22×D411yescharacteristic
358C23×C5C2×#4111yescharacteristic
359C23×C5C2×#4111yescharacteristic
360C23×C5C2×#4111yescharacteristic
361C23×C5C2×#4111yescharacteristic
362C23×C5C2×#4111yescharacteristic
363C23×C5C2×#4111yescharacteristic
364C23×C5C2×#4111yescharacteristic
365C23×C5C2×#4111yescharacteristic
366C23×C5C2×#4111yescharacteristic
367C23×C5H(5,𝔽2)11yescharacteristic
368C23×C5H(5,𝔽2)11yescharacteristic
369C23×C5H(5,𝔽2)11yescharacteristic
370C23×C52−1+411yescharacteristic
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
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—416no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
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#12614yes—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
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—41no—
439C2×Dic5—41no—
440C2×Dic5—41no—
441C2×Dic5—41no—
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#12314yes—
470C25C22×D511yescharacteristic
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—41no—
477C23×C4—41no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4C22×D511yescharacteristic
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D511yescharacteristic
490C23×C4C22×D511yescharacteristic
491C23×C4C22×D511yescharacteristic
492C2×C4⋊C4—54no—
493C2×C4⋊C4—102no—
494C2×C4⋊C4—102no—
495C2×C4⋊C4—102no—
496C2×C4⋊C4—201no—
497C2×C4⋊C4—201no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—102no—
507C2×C22⋊C4—102no—
508C2×C22⋊C4—102no—
509C2×C22⋊C4—102no—
510C2×C22⋊C4—102no—
511C2×C22⋊C4—102no—
512C2×C22⋊C4—102no—
513C2×C22⋊C4—102no—
514C2×C22⋊C4—201no—
515C2×C22⋊C4C4×D514yes—
516C2×C42—102no—
517C2×C42—102no—
518C2×C42—102no—
519C2×C42—102no—
520C2×C42—102no—
521C2×C42—102no—
522C2×C42—102no—
523C2×C42—201no—
524C2×C42—201no—
525C2×C42—201no—
526C2×C42—201no—
527C2×C42—201no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—41no—
532#95—54no—
533#95—54no—
534#95—54no—
535#95—102no—
536#95—102no—
537#95—102no—
538#95—102no—
539#95—102no—
540#95—102no—
541#95—102no—
542#95—102no—
543#95—102no—
544#95—102no—
545#95—102no—
546#95—201no—
547#95—201no—
548#95—201no—
549#95—201no—
550C22×C5—24no—
551C22×C5—24no—
552C22×C5—24no—
553C22×C5—42no—
554C22×C5—42no—
555C22×C5—42no—
556C22×C5—42no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5C2×C4×D411yescharacteristic
566C22×C5C4×#4111yescharacteristic
567C22×C5C4×#4111yescharacteristic
568C22×C5C4×#4111yescharacteristic
569C22×C5C4×#4111yescharacteristic
570C22×C5#51811yescharacteristic
571C22×C5#52011yescharacteristic
572C22×C5C2×#12311yescharacteristic
573C22×C5#52511yescharacteristic
574C22×C5C2×#12611yescharacteristic
575C22×C5#52911yescharacteristic
576C22×C5#52911yescharacteristic
577C22×C5#52911yescharacteristic
578C22×C5#52911yescharacteristic
579C22×C5#52911yescharacteristic
580C22×C5#53811yescharacteristic
581C22×C5#53811yescharacteristic
582C22×C5#54211yescharacteristic
583C22×C5#54211yescharacteristic
584C22×C5#54611yescharacteristic
585C22×C5#54611yescharacteristic
586C22×C5#54611yescharacteristic
587C22×C5#54711yescharacteristic
588C22×C5#55111yescharacteristic
589C22×C5#55111yescharacteristic
590C22×C5#55111yescharacteristic
591C22×C5#55211yescharacteristic
592C22×C5#55211yescharacteristic
593C22×C5#55311yescharacteristic
594C22×C5#55311yescharacteristic
595C22×C5#55311yescharacteristic
596C22×C5#55311yescharacteristic
597C22×C5#55311yescharacteristic
598C22×C5#55611yescharacteristic
599C22×C5#55911yescharacteristic
600C4×C5—24no—
601C4×C5—42no—
602C4×C5—42no—
603C4×C5—42no—
604C4×C5—42no—
605C4×C5—81no—
606Dic5—24no—
607Dic5—42no—
608Dic5—42no—
609Dic5—42no—
610Dic5—42no—
611Dic5—42no—
612Dic5—42no—
613Dic5—81no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C2×C4×D512yes—
627C24D4×D512yes—
628C24#71312yes—
629C24C23×D511yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—28no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
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—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—52no—
677C22×C4—52no—
678C22×C4—52no—
679C22×C4—52no—
680C22×C4—52no—
681C22×C4—101no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4—101no—
686C22×C4—101no—
687C22×C4—101no—
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×C4C2×C4×D512yes—
729C22×C4C2×C4×D512yes—
730C22×C4#70912yes—
731C22×C4#70912yes—
732C22×C4#71112yes—
733C22×C4#71112yes—
734C22×C4#71112yes—
735C4⋊C4—204no—
736C4⋊C4—204no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C22⋊C4—108no—
740C22⋊C4—108no—
741C22⋊C4—108no—
742C22⋊C4—204no—
743C42—204no—
744C42—204no—
745C42—204no—
746C42—204no—
747C2×C5—44no—
748C2×C5C4×#12311yescharacteristic
749C2×C5C4×#12611yescharacteristic
750C2×C5#233711yescharacteristic
751C2×C5#235911yescharacteristic
752C2×C5#236411yescharacteristic
753C2×C5#237311yescharacteristic
754C2×C5#237411yescharacteristic
755C2×C5#244411yescharacteristic
756C2×C5#244711yescharacteristic
757C2×C5#247011yescharacteristic
758C2×C5#248011yescharacteristic
759C2×C5#249411yescharacteristic
760C2×C5#253011yescharacteristic
761C2×C5#257811yescharacteristic
762C2×C5#259511yescharacteristic
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23#403914yes—
798C23C22×C4×D511yescharacteristic
799C23C2×#70911yescharacteristic
800C23C2×#70911yescharacteristic
801C23C2×D4×D511yescharacteristic
802C23C2×#71111yescharacteristic
803C23C2×#71111yescharacteristic
804C23C2×#71111yescharacteristic
805C23#414411yescharacteristic
806C23#414411yescharacteristic
807C23#414411yescharacteristic
808C23C2×#71311yescharacteristic
809C23D5×#4111yescharacteristic
810C23D5×#4111yescharacteristic
811C23D5×#4111yescharacteristic
812C23#415011yescharacteristic
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—416no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
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—54no—
856C2×C4—102no—
857C2×C4—102no—
858C2×C4—102no—
859C2×C4—102no—
860C2×C4—102no—
861C2×C4—102no—
862C2×C4—102no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—102no—
867C2×C4—102no—
868C2×C4—102no—
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—201no—
881C2×C4—201no—
882C2×C4—201no—
883C2×C4—201no—
884C2×C4—201no—
885C2×C4—201no—
886C2×C4—201no—
887C2×C4—201no—
888C2×C4—201no—
889C2×C4—201no—
890C2×C4—201no—
891C2×C4—201no—
892C2×C4—201no—
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#402514yes—
912C5#1419711yescharacteristic, complemented, Sylow
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C4×#70911yescharacteristic
929C22C2×#402511yescharacteristic
930C22#6582011yescharacteristic
931C22#6582411yescharacteristic
932C22#6582411yescharacteristic
933C22#6582911yescharacteristic
934C22C2×#403911yescharacteristic
935C22#6584811yescharacteristic
936C22#6584811yescharacteristic
937C22#6586211yescharacteristic
938C22#6586711yescharacteristic
939C22C4×#71111yescharacteristic
940C22C4×#71111yescharacteristic
941C22C4×#71111yescharacteristic
942C22#6587211yescharacteristic
943C22#6587511yescharacteristic
944C22#6588011yescharacteristic
945C22#6589111yescharacteristic
946C22#6589211yescharacteristic
947C22#6592011yescharacteristic
948C22#6592111yescharacteristic
949C22#6592511yescharacteristic
950C22#6592711yescharacteristic
951C22#6593711yescharacteristic
952C22#6594711yescharacteristic
953C22#6594811yescharacteristic
954C22#6594811yescharacteristic
955C22#6595811yescharacteristic
956C22#6595811yescharacteristic
957C22#6597111yescharacteristic
958C22#6597611yescharacteristic
959C22D5×#12311yescharacteristic
960C22#6598911yescharacteristic
961C22#6599611yescharacteristic
962C22#6599811yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—104no—
970C4—202no—
971C4—202no—
972C4—202no—
973C4—202no—
974C4—202no—
975C4—202no—
976C4—401no—
977C2—44no—
978C2#1060506911yescharacteristic
979C2C4×#402511yescharacteristic
980C2#1060520711yescharacteristic
981C2#1060556111yescharacteristic
982C2#1060565011yescharacteristic
983C2#1060567911yescharacteristic
984C2#1060579911yescharacteristic
985C2#1060611111yescharacteristic
986C2#1060612611yescharacteristic
987C2#1060620211yescharacteristic
988C2#1060622511yescharacteristic
989C2#1060640211yescharacteristic
990C2#1060641211yescharacteristic
991C2#1060645411yescharacteristic
992C2#1060662811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22⋊#95D5
hypocenterC5#14197
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
8. #10600210C2semidirect
9. #10600210C2semidirect
10. #10600200C2semidirect
11. #10600200C2semidirect
12. #10600199C2semidirect
13. #10600199C2semidirect
14. #10600196C2semidirect
15. Dic5×#95C2semidirect
52. #65242C4semidirect
97. C2×C4⋊Dic5C2×C4semidirect
132. #3963C2×C4semidirect
133. #3963C2×C4semidirect
134. #3963C2×C4semidirect
912. C5#14197semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic52
C2×#652422
C2×#652332
C5×C22⋊#952
#106029202
#106023422
#106023382
#106002102
#106002002
#106001992
#106001962
Dic5×#952
#141975