Finite Group Databasebeta

← #12007173

Subgroups — #12007173

Order 1280.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3952C211yesmaximal, characteristic
2C2×#65276C211yesmaximal, characteristic
3C2×#65276C211yesmaximal, characteristic
4C2×C5×#340C211yesmaximal, characteristic, complemented
5C2×#64771C211yesmaximal, characteristic, complemented
6C2×#64749C211yesmaximal, characteristic, complemented
7C2×#64749C211yesmaximal, characteristic, complemented
8C23×C4×D5C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×#685—21no—
13C22×#685—21no—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C23×#168C2211yescharacteristic
17C2×#3963—21no—
18C2×#3963—21no—
19C2×#3952—22no—
20C2×#3952—22no—
21C2×#3952—22no—
22#65276—22no—
23#65276—22no—
24#65276—22no—
25#65276C414yescomplemented
26C5×#340—22no—
27#64771—22no—
28#64749—22no—
29#64749—22no—
30#11200—51nomaximal, Sylow
31C24×D5D411yescharacteristic
32C23×C4×C5—21no—
33C23×C4×C5—21no—
34C23×C4×C5C2311yescharacteristic
35C23×Dic5—21no—
36C23×Dic5—21no—
37C23×Dic5D411yescharacteristic
38C22×C4×D5—21no—
39C22×C4×D5—21no—
40C22×C4×D5—21no—
41C22×C4×D5—21no—
42C22×C4×D5—21no—
43C22×C4×D5—21no—
44C22×C4×D5—21no—
45C22×C4×D5—21no—
46C22×C4×D5—21no—
47C22×C4×D5—21no—
48C22×C4×D5—21no—
49C22×C4×D5—21no—
50C22×C4×D5C2×C412yes—
51C22×C4×D5D412yes—
52C22×C5×C8—21no—
53C22×C5×C8—21no—
54C22×C5×C8—21no—
55C22×C5×C8—21no—
56C22×C5×C8—21no—
57C22×C5×C8—21no—
58C22×C5×C8D412yes—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4—21no—
62C2×C5×C4⋊C4—21no—
63C2×C5×C4⋊C4—21no—
64C2×C5×C4⋊C4—21no—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4C2×C412yes—
70C2×C5×C4⋊C4D412yes—
71C2×#685—24no—
72C2×#685—24no—
73C2×#685—42no—
74C2×#685—42no—
75C2×#685—42no—
76C2×#685—42no—
77C2×C4⋊Dic5—21no—
78C2×C4⋊Dic5—21no—
79C2×C4⋊Dic5—21no—
80C2×C4⋊Dic5—21no—
81C2×C4⋊Dic5—21no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5C2×C412yes—
88C2×C4⋊Dic5D412yes—
89C22×#168—21no—
90C22×#168—21no—
91C22×#168—21no—
92C22×#168—21no—
93C22×#168—21no—
94C22×#168—21no—
95C22×#168D412yes—
96#3963—24no—
97#3963—24no—
98#3952—28no—
99C22×C22⋊C8—51no—
100C2×#380—51no—
101C2×#380—51no—
102C2×#340—51no—
103C2×#340—51no—
104C2×#340—51no—
105C2×#340D511yescharacteristic, complemented
106C24×C5C2×D411yescharacteristic
107C23×D5—21no—
108C23×D5—21no—
109C23×D5—21no—
110C23×D5—21no—
111C23×D5—21no—
112C23×D5—21no—
113C23×D5—21no—
114C23×D5—21no—
115C23×D5—21no—
116C23×D5—21no—
117C23×D5—21no—
118C23×D5—21no—
119C23×D5C22⋊C412yes—
120C23×D5SD1612yes—
121C23×D5Q1612yes—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—41no—
125C22×C4×C5—41no—
126C22×C4×C5—41no—
127C22×C4×C5—41no—
128C22×C4×C5—41no—
129C22×C4×C5—41no—
130C22×C4×C5—41no—
131C22×C4×C5—41no—
132C22×C4×C5—41no—
133C22×C4×C5—41no—
134C22×C4×C5—41no—
135C22×C4×C5—41no—
136C22×C4×C5C22×C411yescharacteristic
137C22×C4×C5C2×D411yescharacteristic
138C22×C4×C5C2×D411yescharacteristic
139C22×C4×C5C2×D411yescharacteristic
140C22×C4×C5C2×D411yescharacteristic
141C22×C4×C5C2×D411yescharacteristic
142C22×C4×C5#4111yescharacteristic
143C22×C4×C5#4111yescharacteristic
144C22×C4×C5#4111yescharacteristic
145C22×C4×C5#4111yescharacteristic
146C22×C4×C5#4111yescharacteristic
147C22×C4×C5#4111yescharacteristic
148C22×C4×C5#4111yescharacteristic
149C22×C4×C5#4111yescharacteristic
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—41no—
159C22×Dic5—41no—
160C22×Dic5—41no—
161C22×Dic5—41no—
162C22×Dic5—41no—
163C22×Dic5—41no—
164C22×Dic5—41no—
165C22×Dic5—41no—
166C22×Dic5—41no—
167C22×Dic5—41no—
168C22×Dic5—41no—
169C22×Dic5—41no—
170C22×Dic5C22⋊C412yes—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—22no—
175C2×C4×D5—22no—
176C2×C4×D5—22no—
177C2×C4×D5—22no—
178C2×C4×D5—22no—
179C2×C4×D5—22no—
180C2×C4×D5—22no—
181C2×C4×D5—22no—
182C2×C4×D5—22no—
183C2×C4×D5—41no—
184C2×C4×D5—41no—
185C2×C4×D5—41no—
186C2×C4×D5—41no—
187C2×C4×D5—41no—
188C2×C4×D5—41no—
189C2×C4×D5—41no—
190C2×C4×D5—41no—
191C2×C4×D5—41no—
192C2×C4×D5—41no—
193C2×C4×D5—41no—
194C2×C4×D5—41no—
195C2×C4×D5—41no—
196C2×C4×D5—41no—
197C2×C4×D5—41no—
198C2×C4×D5—41no—
199C2×C5×C8—22no—
200C2×C5×C8—22no—
201C2×C5×C8—22no—
202C2×C5×C8—41no—
203C2×C5×C8—41no—
204C2×C5×C8—41no—
205C2×C5×C8—41no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4—41no—
213C5×C4⋊C4—41no—
214#685—48no—
215#685—48no—
216C4⋊Dic5—22no—
217C4⋊Dic5—22no—
218C4⋊Dic5—22no—
219C4⋊Dic5—22no—
220C4⋊Dic5—41no—
221C4⋊Dic5—41no—
222C4⋊Dic5—41no—
223C4⋊Dic5—41no—
224C2×#168—22no—
225C2×#168—22no—
226C2×#168—22no—
227C2×#168—41no—
228C2×#168—41no—
229C2×#168—41no—
230C2×#168—41no—
231C24×C4—51no—
232C23×C8—51no—
233C23×C8C2×D511yescharacteristic
234C22×C4⋊C4—51no—
235C22×C4⋊C4—51no—
236C22×C4⋊C4C2×D511yescharacteristic
237C22×C4⋊C4C2×D511yescharacteristic
238C22×C22⋊C4—101no—
239C22×C22⋊C4—101no—
240C2×C22⋊C8—102no—
241C2×C22⋊C8—102no—
242C2×C22⋊C8—102no—
243#380—54no—
244#380—102no—
245#380—102no—
246#380—102no—
247C2×#95—101no—
248C2×#95—101no—
249#340—22no—
250#340—102no—
251#340—102no—
252#340—102no—
253C23×C5C2×C22⋊C411yescharacteristic
254C23×C5#12011yescharacteristic
255C23×C5#12111yescharacteristic
256C23×C5#12111yescharacteristic
257C23×C5#12311yescharacteristic
258C23×C5#12311yescharacteristic
259C23×C5#12311yescharacteristic
260C23×C5C2×SD1611yescharacteristic
261C23×C5C2×Q1611yescharacteristic
262C23×C5#13511yescharacteristic
263C23×C5#13511yescharacteristic
264C23×C5AGL(1,ℤ/8)11yescharacteristic
265C23×C5AGL(1,ℤ/8)11yescharacteristic
266C23×C5AGL(1,ℤ/8)11yescharacteristic
267C23×C5#13711yescharacteristic
268C22×D5—22no—
269C22×D5—22no—
270C22×D5—22no—
271C22×D5—22no—
272C22×D5—22no—
273C22×D5—22no—
274C22×D5—22no—
275C22×D5—22no—
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—22no—
281C22×D5—22no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5—22no—
285C22×D5—22no—
286C22×D5—41no—
287C22×D5—41no—
288C22×D5—41no—
289C22×D5—41no—
290C22×D5—41no—
291C22×D5—41no—
292C22×D5—41no—
293C22×D5—41no—
294C22×D5—41no—
295C22×D5—41no—
296C22×D5—41no—
297C22×D5—41no—
298C22×D5—41no—
299C22×D5—41no—
300C22×D5—41no—
301C22×D5—41no—
302C22×D5#10314yes—
303C2×C4×C5—42no—
304C2×C4×C5—42no—
305C2×C4×C5—42no—
306C2×C4×C5—42no—
307C2×C4×C5—42no—
308C2×C4×C5—42no—
309C2×C4×C5—81no—
310C2×C4×C5—81no—
311C2×C4×C5—81no—
312C2×C4×C5—81no—
313C2×C4×C5—81no—
314C2×C4×C5—81no—
315C2×C4×C5—81no—
316C2×C4×C5—81no—
317C2×C4×C5#11711yescharacteristic
318C2×C4×C5#11711yescharacteristic
319C2×C4×C5C4×D411yescharacteristic
320C2×C4×C5C4×D411yescharacteristic
321C2×C4×C5C4×D411yescharacteristic
322C2×C4×C5C4×D411yescharacteristic
323C2×C4×C5#12011yescharacteristic
324C2×C4×C5#12111yescharacteristic
325C2×C4×C5#12111yescharacteristic
326C2×C4×C5#12111yescharacteristic
327C2×C4×C5#12111yescharacteristic
328C2×C4×C5#12111yescharacteristic
329C2×C4×C5#12111yescharacteristic
330C2×C4×C5#12311yescharacteristic
331C2×C4×C5#12311yescharacteristic
332C2×C4×C5#12311yescharacteristic
333C2×C4×C5#12311yescharacteristic
334C2×C4×C5#12311yescharacteristic
335C2×C4×C5#12311yescharacteristic
336C2×C4×C5#12311yescharacteristic
337C2×C4×C5#12411yescharacteristic
338C2×C4×C5#12411yescharacteristic
339C2×C4×C5#12411yescharacteristic
340C2×C4×C5#12411yescharacteristic
341C2×C4×C5#12611yescharacteristic
342C2×C4×C5#12611yescharacteristic
343C2×C4×C5#12611yescharacteristic
344C2×C4×C5#12611yescharacteristic
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—41no—
349C2×Dic5—41no—
350C2×Dic5—41no—
351C2×Dic5—41no—
352C2×Dic5—42no—
353C2×Dic5—42no—
354C2×Dic5—42no—
355C2×Dic5—42no—
356C2×Dic5—42no—
357C2×Dic5—42no—
358C2×Dic5—81no—
359C2×Dic5—81no—
360C2×Dic5—81no—
361C2×Dic5—81no—
362C2×Dic5—81no—
363C2×Dic5—81no—
364C2×Dic5—81no—
365C2×Dic5—81no—
366C4×D5—42no—
367C4×D5—42no—
368C4×D5—42no—
369C4×D5—42no—
370C4×D5—42no—
371C4×D5—42no—
372C4×D5—42no—
373C4×D5—42no—
374C5×C8—42no—
375#168—42no—
376C25—51no—
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—51no—
380C23×C4—52no—
381C23×C4—52no—
382C23×C4—101no—
383C23×C4—101no—
384C23×C4—101no—
385C23×C4—101no—
386C23×C4—101no—
387C23×C4—101no—
388C23×C4—101no—
389C23×C4—101no—
390C23×C4—101no—
391C23×C4—101no—
392C23×C4—101no—
393C23×C4—101no—
394C23×C4—101no—
395C23×C4—101no—
396C23×C4C22×D511yescharacteristic
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—52no—
404C22×C8—101no—
405C22×C8—101no—
406C22×C8—101no—
407C22×C8—101no—
408C22×C8—101no—
409C22×C8—101no—
410C22×C8D2012yes—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—52no—
422C2×C4⋊C4—52no—
423C2×C4⋊C4—101no—
424C2×C4⋊C4—101no—
425C2×C4⋊C4—101no—
426C2×C4⋊C4—101no—
427C2×C4⋊C4—101no—
428C2×C4⋊C4—101no—
429C2×C4⋊C4—101no—
430C2×C4⋊C4—101no—
431C2×C4⋊C4—101no—
432C2×C4⋊C4—101no—
433C2×C4⋊C4C4×D512yes—
434C2×C4⋊C4C22⋊D512yes—
435C2×C22⋊C4—104no—
436C2×C22⋊C4—104no—
437C2×C22⋊C4—202no—
438C2×C22⋊C4—202no—
439C2×C22⋊C4—202no—
440C2×C22⋊C4—202no—
441C22⋊C8—108no—
442#95—104no—
443#95—104no—
444C22×C5#38111yescharacteristic
445C22×C5#38611yescharacteristic
446C22×C5#38611yescharacteristic
447C22×C5#39411yescharacteristic
448C22×C5#39411yescharacteristic
449C22×C5#39711yescharacteristic
450C22×C5#39711yescharacteristic
451C22×C5C2×#10311yescharacteristic
452C22×C5#41611yescharacteristic
453C22×C5#41711yescharacteristic
454C22×C5#41811yescharacteristic
455C22×C5#44911yescharacteristic
456C22×C5#44911yescharacteristic
457C22×C5#45011yescharacteristic
458C22×C5#45111yescharacteristic
459C22×C5#46511yescharacteristic
460C22×C5#46511yescharacteristic
461C22×C5#46711yescharacteristic
462C22×C5#46711yescharacteristic
463C22×C5#46811yescharacteristic
464C22×C5#46811yescharacteristic
465C22×C5#46911yescharacteristic
466C22×C5#46911yescharacteristic
467C22×C5#48111yescharacteristic
468C22×C5#48111yescharacteristic
469C22×C5#48211yescharacteristic
470C22×C5#48211yescharacteristic
471C22×C5#48211yescharacteristic
472C22×C5#48211yescharacteristic
473C22×C5#48311yescharacteristic
474C22×C5#48411yescharacteristic
475C22×C5#48411yescharacteristic
476C22×C5#48411yescharacteristic
477C22×C5#48511yescharacteristic
478C22×C5#48511yescharacteristic
479C2×D5—24no—
480C2×D5—24no—
481C2×D5—24no—
482C2×D5—42no—
483C2×D5—42no—
484C2×D5—42no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5—42no—
488C2×D5—42no—
489C2×D5—42no—
490C2×D5—42no—
491C2×D5—42no—
492C2×D5—42no—
493C2×D5—42no—
494C4×C5—82no—
495C4×C5—82no—
496C4×C5#38811yescharacteristic
497C4×C5#38811yescharacteristic
498C4×C5#38811yescharacteristic
499C4×C5#38811yescharacteristic
500C4×C5#39411yescharacteristic
501C4×C5#39411yescharacteristic
502C4×C5#39711yescharacteristic
503C4×C5#39711yescharacteristic
504Dic5—42no—
505Dic5—82no—
506Dic5—82no—
507C24—52no—
508C24—52no—
509C24—52no—
510C24—101no—
511C24—101no—
512C24—101no—
513C24—101no—
514C24—101no—
515C24—101no—
516C24—101no—
517C24—101no—
518C24—101no—
519C24—101no—
520C24—101no—
521C24—101no—
522C24D4×D511yescharacteristic
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—52no—
538C22×C4—101no—
539C22×C4—101no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544C22×C4—102no—
545C22×C4—102no—
546C22×C4—102no—
547C22×C4—102no—
548C22×C4—102no—
549C22×C4—102no—
550C22×C4—102no—
551C22×C4—102no—
552C22×C4—102no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—201no—
559C22×C4—201no—
560C22×C4—201no—
561C22×C4—201no—
562C22×C4—201no—
563C22×C4—201no—
564C22×C4—201no—
565C22×C4—201no—
566C22×C4—201no—
567C22×C4—201no—
568C22×C4—201no—
569C22×C4—201no—
570C22×C4—201no—
571C22×C4—201no—
572C22×C4—201no—
573C22×C4—201no—
574C22×C4—201no—
575C22×C4—201no—
576C22×C4—201no—
577C22×C4—201no—
578C22×C4—201no—
579C22×C4—201no—
580C22×C4—201no—
581C22×C4—201no—
582C22×C4—201no—
583C22×C4—201no—
584C22×C4—201no—
585C22×C4—201no—
586C22×C4C2×C4×D511yescharacteristic
587C22×C4C2×D2011yescharacteristic
588C22×C4#70911yescharacteristic
589C22×C4#70911yescharacteristic
590C22×C4#70911yescharacteristic
591C22×C4#70911yescharacteristic
592C22×C4D4×D511yescharacteristic
593C22×C4D4×D511yescharacteristic
594C22×C4D4×D511yescharacteristic
595C22×C4#71111yescharacteristic
596C22×C4#71111yescharacteristic
597C22×C4#71311yescharacteristic
598C22×C4#71311yescharacteristic
599C22×C4C2×C22⋊D511yescharacteristic
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—102no—
608C2×C8—102no—
609C2×C8—102no—
610C2×C8—201no—
611C2×C8—201no—
612C2×C8—201no—
613C2×C8—201no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—102no—
623C4⋊C4—102no—
624C4⋊C4—102no—
625C4⋊C4—102no—
626C4⋊C4—201no—
627C4⋊C4—201no—
628C4⋊C4—201no—
629C4⋊C4—201no—
630C22⋊C4—208no—
631C22⋊C4—208no—
632C2×C5#144011yescharacteristic
633C2×C5#182411yescharacteristic
634C2×C5#182511yescharacteristic
635C2×C5#187211yescharacteristic
636C2×C5#187511yescharacteristic
637C2×C5#189211yescharacteristic
638C2×C5#189511yescharacteristic
639C2×C5#203411yescharacteristic
640C2×C5#203411yescharacteristic
641C2×C5#203611yescharacteristic
642C2×C5#203611yescharacteristic
643C2×C5#207611yescharacteristic
644C2×C5#207611yescharacteristic
645C2×C5#207711yescharacteristic
646C2×C5#207711yescharacteristic
647D5—44no—
648C23—54no—
649C23—102no—
650C23—102no—
651C23—102no—
652C23—102no—
653C23—102no—
654C23—102no—
655C23—102no—
656C23—102no—
657C23—102no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—201no—
668C23—201no—
669C23—201no—
670C23—201no—
671C23—201no—
672C23—201no—
673C23—201no—
674C23—201no—
675C23—201no—
676C23—201no—
677C23—201no—
678C23—201no—
679C23—201no—
680C23—201no—
681C23—201no—
682C23—201no—
683C23D5×C22⋊C411yescharacteristic
684C23#402911yescharacteristic
685C23#402911yescharacteristic
686C23#403011yescharacteristic
687C23#404011yescharacteristic
688C23#404111yescharacteristic
689C23#405711yescharacteristic
690C23#405811yescharacteristic
691C23D5×SD1611yescharacteristic
692C23#406011yescharacteristic
693C23#406011yescharacteristic
694C23#406211yescharacteristic
695C23D5×Q1611yescharacteristic
696C23#406411yescharacteristic
697C23#408311yescharacteristic
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—201no—
716C2×C4—201no—
717C2×C4—201no—
718C2×C4—201no—
719C2×C4—202no—
720C2×C4—202no—
721C2×C4—202no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4—202no—
731C2×C4—202no—
732C2×C4—202no—
733C2×C4—401no—
734C2×C4—401no—
735C2×C4—401no—
736C2×C4—401no—
737C2×C4—401no—
738C2×C4—401no—
739C2×C4—401no—
740C2×C4—401no—
741C2×C4#401811yescharacteristic
742C2×C4C4×D2011yescharacteristic
743C2×C4#402111yescharacteristic
744C2×C4#402211yescharacteristic
745C2×C4#402711yescharacteristic
746C2×C4#402811yescharacteristic
747C2×C4#402911yescharacteristic
748C2×C4#403011yescharacteristic
749C2×C4#403011yescharacteristic
750C2×C4#403111yescharacteristic
751C2×C4#403111yescharacteristic
752C2×C4#403211yescharacteristic
753C2×C4#403811yescharacteristic
754C2×C4#403911yescharacteristic
755C2×C4#404011yescharacteristic
756C2×C4#404011yescharacteristic
757C2×C4#404011yescharacteristic
758C2×C4#404011yescharacteristic
759C2×C4#404111yescharacteristic
760C2×C4#404411yescharacteristic
761C2×C4#404411yescharacteristic
762C2×C4#404411yescharacteristic
763C2×C4C4×C22⋊D511yescharacteristic
764C2×C4#407511yescharacteristic
765C2×C4#407611yescharacteristic
766C2×C4#408411yescharacteristic
767C2×C4#408511yescharacteristic
768C2×C4#409311yescharacteristic
769C8—42no—
770C8—202no—
771C5#1120011yescharacteristic, complemented, Sylow
772C22—104no—
773C22—104no—
774C22—104no—
775C22—202no—
776C22—202no—
777C22—202no—
778C22—202no—
779C22—202no—
780C22—202no—
781C22—202no—
782C22—202no—
783C22—202no—
784C22—202no—
785C22—202no—
786C22—202no—
787C22#6495311yescharacteristic
788C22#6495411yescharacteristic
789C22#6496311yescharacteristic
790C22#6496411yescharacteristic
791C22#6505911yescharacteristic
792C22#6506111yescharacteristic
793C22#6506611yescharacteristic
794C22#6506711yescharacteristic
795C22#6506811yescharacteristic
796C22#6507111yescharacteristic
797C22#6507311yescharacteristic
798C22#6507311yescharacteristic
799C22D5×#10311yescharacteristic
800C22#6509211yescharacteristic
801C22#6509411yescharacteristic
802C22#6509811yescharacteristic
803C22#6509811yescharacteristic
804C22#6510111yescharacteristic
805C22#6510211yescharacteristic
806C22#6510411yescharacteristic
807C22#6515211yescharacteristic
808C22#6515311yescharacteristic
809C22#6515411yescharacteristic
810C22#6515511yescharacteristic
811C22#6517311yescharacteristic
812C22#6517511yescharacteristic
813C22#6517611yescharacteristic
814C22#6517711yescharacteristic
815C22#6524511yescharacteristic
816C22#6524811yescharacteristic
817C22#6528011yescharacteristic
818C22#6544711yescharacteristic
819C22#6545811yescharacteristic
820C22#6546111yescharacteristic
821C22#6547511yescharacteristic
822C4—82no—
823C4—82no—
824C4—202no—
825C4—402no—
826C4—402no—
827C4#6495811yescharacteristic
828C4#6495911yescharacteristic
829C4#6496111yescharacteristic
830C4#6496411yescharacteristic
831C4#6522911yescharacteristic
832C4#6525011yescharacteristic
833C4#6527911yescharacteristic
834C4#6528211yescharacteristic
835C2—204no—
836C2#1059962411yescharacteristic
837C2#1059962511yescharacteristic
838C2#1059966511yescharacteristic
839C2#1059966611yescharacteristic
840C2#1059967511yescharacteristic
841C2#1059967811yescharacteristic
842C2#1059968311yescharacteristic
843C2#1059968411yescharacteristic
844C2#1060022211yescharacteristic
845C2#1060099411yescharacteristic
846C2#1060100011yescharacteristic
847C2#1060106111yescharacteristic
848C2#1060106811yescharacteristic
849C2#1060137411yescharacteristic
850C2#1060142811yescharacteristic
subgroupG/H
centerC24D4×D5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#340C2
socleC24×C5C2×D4
prime radicalC24×D5D4
cosocleC23×C4×C5C23
hypercenterC2×#340D5
hypocenterC5#11200
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×C5×#340C2semidirect
5. C2×#64771C2semidirect
6. C2×#64749C2semidirect
7. C2×#64749C2semidirect
25. #65276C4semidirect
105. C2×#340D5semidirect
771. C5#11200semidirect

Maximal subgroups

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

subgroupindex
C22×#39522
C2×#652762
C2×C5×#3402
C2×#647712
C2×#647492
#112005