Finite Group Databasebeta

← #12007119

Subgroups — #12007119

Order 1280.

994 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#103C211yesmaximal, characteristic
2C2×#65519C211yesmaximal, characteristic
3C22×#3967C211yesmaximal, characteristic
4C2×#64771C211yesmaximal, characteristic
5C2×#64770C211yesmaximal, characteristic
6#10602356C211yesmaximal, characteristic
7C2×#64749C211yesmaximal, characteristic
8C23×C5×Q8C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic5C2211yescharacteristic
12C22×C4⋊Dic5C2211yescharacteristic
13C22×C4×Dic5C2211yescharacteristic
14C23×#168C2211yescharacteristic
15C2×C5×#103—22no—
16C2×C5×#103—22no—
17C2×C5×#103C414yescomplemented
18#65519—22no—
19#65519—22no—
20C2×#3967—22no—
21C2×#3967—22no—
22C2×#3967—22no—
23C2×#3963—21no—
24C2×#3963—21no—
25C2×#3963—21no—
26C2×#3963—21no—
27#64771—22no—
28#64770—22no—
29#64749—22no—
30#11190—51nomaximal, Sylow
31C22×C5×Q8—21no—
32C22×C5×Q8—21no—
33C22×C5×Q8—21no—
34C22×C5×Q8—21no—
35C22×C5×Q8—21no—
36C22×C5×Q8—21no—
37C22×C5×Q8—21no—
38C22×C5×Q8—21no—
39C22×C5×Q8—21no—
40C22×C5×Q8—21no—
41C22×C5×Q8—21no—
42C22×C5×Q8C2×C412yes—
43C22×C5×Q8D412yes—
44C22×C5×Q8D412yes—
45C23×C4×C5—21no—
46C23×C4×C5—21no—
47C23×C4×C5C2311yescharacteristic
48C23×Dic5—21no—
49C23×Dic5—21no—
50C23×Dic5D411yescharacteristic
51C23×Dic5D411yescharacteristic
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×C8C2×C412yes—
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⋊C4C2×C412yes—
65C2×C4⋊Dic5—21no—
66C2×C4⋊Dic5—21no—
67C2×C4⋊Dic5—21no—
68C2×C4⋊Dic5—21no—
69C2×C4⋊Dic5—21no—
70C2×C4⋊Dic5—21no—
71C2×C4⋊Dic5—21no—
72C2×C4⋊Dic5—21no—
73C2×C4⋊Dic5—21no—
74C2×C4⋊Dic5—21no—
75C2×C4⋊Dic5D412yes—
76C2×C4⋊Dic5D412yes—
77C2×C4×Dic5—21no—
78C2×C4×Dic5—21no—
79C2×C4×Dic5—21no—
80C2×C4×Dic5—21no—
81C2×C4×Dic5—21no—
82C2×C4×Dic5—21no—
83C22×#168—21no—
84C22×#168—21no—
85C22×#168—21no—
86C22×#168—21no—
87C22×#168—21no—
88C22×#168—21no—
89C22×#168D412yes—
90C5×#103—28no—
91#3967—28no—
92#3963—24no—
93#3963—24no—
94#3963—42no—
95#3963—42no—
96C22×#103—51no—
97C22×#103D511yescharacteristic
98C2×#391—51no—
99C2×#340—51no—
100C2×#340—51no—
101C2×#336—51no—
102C4⋊#95—51no—
103C24×C5C2×D411yescharacteristic
104C2×C5×Q8—22no—
105C2×C5×Q8—22no—
106C2×C5×Q8—22no—
107C2×C5×Q8—22no—
108C2×C5×Q8—22no—
109C2×C5×Q8—22no—
110C2×C5×Q8—22no—
111C2×C5×Q8—22no—
112C2×C5×Q8—22no—
113C2×C5×Q8—22no—
114C2×C5×Q8—22no—
115C2×C5×Q8—22no—
116C2×C5×Q8—22no—
117C2×C5×Q8—22no—
118C2×C5×Q8—22no—
119C2×C5×Q8—41no—
120C2×C5×Q8—41no—
121C2×C5×Q8—41no—
122C2×C5×Q8—41no—
123C2×C5×Q8—41no—
124C2×C5×Q8—41no—
125C2×C5×Q8—41no—
126C2×C5×Q8—41no—
127C2×C5×Q8—41no—
128C2×C5×Q8—41no—
129C2×C5×Q8—41no—
130C2×C5×Q8—41no—
131C2×C5×Q8C22⋊C414yes—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—41no—
137C22×C4×C5—41no—
138C22×C4×C5—41no—
139C22×C4×C5—41no—
140C22×C4×C5—41no—
141C22×C4×C5—41no—
142C22×C4×C5—41no—
143C22×C4×C5—41no—
144C22×C4×C5—41no—
145C22×C4×C5—41no—
146C22×C4×C5C22×C411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5#4111yescharacteristic
153C22×C4×C5#4111yescharacteristic
154C22×C4×C5#4111yescharacteristic
155C22×C4×C5#4111yescharacteristic
156C22×C4×C5#4111yescharacteristic
157C22×C4×C5#4111yescharacteristic
158C22×C4×C5#4111yescharacteristic
159C22×C4×C5#4111yescharacteristic
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—41no—
175C22×Dic5—41no—
176C22×Dic5—41no—
177C22×Dic5—41no—
178C22×Dic5—41no—
179C22×Dic5—41no—
180C22×Dic5—41no—
181C22×Dic5—41no—
182C22×Dic5—41no—
183C22×Dic5—41no—
184C22×Dic5—41no—
185C22×Dic5—41no—
186C22×Dic5SD1612yes—
187C22×Dic5Q1612yes—
188C2×C5×C8—22no—
189C2×C5×C8—22no—
190C2×C5×C8—22no—
191C2×C5×C8—41no—
192C2×C5×C8—41no—
193C2×C5×C8—41no—
194C2×C5×C8—41no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—41no—
198C5×C4⋊C4—41no—
199C4⋊Dic5—22no—
200C4⋊Dic5—22no—
201C4⋊Dic5—22no—
202C4⋊Dic5—22no—
203C4⋊Dic5—41no—
204C4⋊Dic5—41no—
205C4⋊Dic5—41no—
206C4⋊Dic5—41no—
207C4×Dic5—41no—
208C4×Dic5—41no—
209C4×Dic5—41no—
210C4×Dic5—41no—
211C2×#168—22no—
212C2×#168—22no—
213C2×#168—22no—
214C2×#168—41no—
215C2×#168—41no—
216C2×#168—41no—
217C2×#168—41no—
218C23×Q8C2×D511yescharacteristic
219C23×C8—51no—
220C23×C8C2×D511yescharacteristic
221C22×C4⋊C4—51no—
222C22×C4⋊C4—51no—
223C22×C4⋊C4C2×D511yescharacteristic
224C22×C42—51no—
225C2×#103—22no—
226C2×#103—22no—
227C2×#103—102no—
228C2×#103—102no—
229C2×#103—102no—
230C2×#103Dic514yescomplemented
231#391—102no—
232#391—102no—
233C2×#95—101no—
234C2×#95—101no—
235C2×#95—101no—
236C2×#95—101no—
237#340—102no—
238#340—102no—
239#336—102no—
240C23×C5C4×D411yescharacteristic
241C23×C5#12011yescharacteristic
242C23×C5#12111yescharacteristic
243C23×C5#12111yescharacteristic
244C23×C5#12111yescharacteristic
245C23×C5#12311yescharacteristic
246C23×C5#12411yescharacteristic
247C23×C5C2×SD1611yescharacteristic
248C23×C5C2×Q1611yescharacteristic
249C23×C5#13511yescharacteristic
250C23×C5#13511yescharacteristic
251C23×C5AGL(1,ℤ/8)11yescharacteristic
252C23×C5#13711yescharacteristic
253C23×C5#13711yescharacteristic
254C23×C5#13711yescharacteristic
255C5×Q8—24no—
256C5×Q8—24no—
257C5×Q8—42no—
258C5×Q8—42no—
259C5×Q8—42no—
260C5×Q8—42no—
261C5×Q8—42no—
262C5×Q8—42no—
263C2×C4×C5—24no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—81no—
274C2×C4×C5—81no—
275C2×C4×C5—81no—
276C2×C4×C5—81no—
277C2×C4×C5C2×C22⋊C411yescharacteristic
278C2×C4×C5#11711yescharacteristic
279C2×C4×C5#11711yescharacteristic
280C2×C4×C5C4×D411yescharacteristic
281C2×C4×C5C4×D411yescharacteristic
282C2×C4×C5C4×D411yescharacteristic
283C2×C4×C5#12011yescharacteristic
284C2×C4×C5#12111yescharacteristic
285C2×C4×C5#12111yescharacteristic
286C2×C4×C5#12111yescharacteristic
287C2×C4×C5#12111yescharacteristic
288C2×C4×C5#12111yescharacteristic
289C2×C4×C5#12311yescharacteristic
290C2×C4×C5#12311yescharacteristic
291C2×C4×C5#12311yescharacteristic
292C2×C4×C5#12311yescharacteristic
293C2×C4×C5#12311yescharacteristic
294C2×C4×C5#12311yescharacteristic
295C2×C4×C5#12311yescharacteristic
296C2×C4×C5#12311yescharacteristic
297C2×C4×C5#12311yescharacteristic
298C2×C4×C5#12411yescharacteristic
299C2×C4×C5#12411yescharacteristic
300C2×C4×C5#12411yescharacteristic
301C2×C4×C5#12611yescharacteristic
302C2×C4×C5#12611yescharacteristic
303C2×C4×C5#12611yescharacteristic
304C2×C4×C5#12611yescharacteristic
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—42no—
320C2×Dic5—42no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C2×Dic5—42no—
324C2×Dic5—42no—
325C2×Dic5—81no—
326C2×Dic5—81no—
327C2×Dic5—81no—
328C2×Dic5—81no—
329C2×Dic5—81no—
330C2×Dic5—81no—
331C2×Dic5—81no—
332C2×Dic5—81no—
333C5×C8—42no—
334#168—42no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8—21no—
341C22×Q8—21no—
342C22×Q8—21no—
343C22×Q8—21no—
344C22×Q8—21no—
345C22×Q8—21no—
346C22×Q8C2×Dic512yes—
347C22×Q8C22⋊D512yes—
348C22×Q8C22⋊D512yes—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—51no—
352C23×C4—51no—
353C23×C4—101no—
354C23×C4—101no—
355C23×C4C22×D511yescharacteristic
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—52no—
363C22×C8—101no—
364C22×C8—101no—
365C22×C8—101no—
366C22×C8—101no—
367C22×C8—101no—
368C22×C8—101no—
369C22×C8C2×Dic512yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—52no—
376C2×C4⋊C4—52no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—101no—
379C2×C4⋊C4—101no—
380C2×C4⋊C4—101no—
381C2×C4⋊C4—101no—
382C2×C4⋊C4—101no—
383C2×C4⋊C4—101no—
384C2×C4⋊C4—101no—
385C2×C4⋊C4—101no—
386C2×C4⋊C4—101no—
387C2×C4⋊C4C2×Dic512yes—
388C2×C42—101no—
389C2×C42—101no—
390C2×C42—101no—
391C2×C42—101no—
392C2×C42—101no—
393C2×C42—101no—
394#103—28no—
395#103—108no—
396#95—104no—
397#95—104no—
398#95—202no—
399#95—202no—
400C22×C5#38611yescharacteristic
401C22×C5#38811yescharacteristic
402C22×C5#38811yescharacteristic
403C22×C5#39411yescharacteristic
404C22×C5#39411yescharacteristic
405C22×C5#39411yescharacteristic
406C22×C5#39711yescharacteristic
407C22×C5C4×SD1611yescharacteristic
408C22×C5C4×Q1611yescharacteristic
409C22×C5#44011yescharacteristic
410C22×C5#44111yescharacteristic
411C22×C5#44811yescharacteristic
412C22×C5#44911yescharacteristic
413C22×C5#45111yescharacteristic
414C22×C5#45211yescharacteristic
415C22×C5#46011yescharacteristic
416C22×C5#46111yescharacteristic
417C22×C5#46211yescharacteristic
418C22×C5#46211yescharacteristic
419C22×C5#46311yescharacteristic
420C22×C5#46411yescharacteristic
421C22×C5#46411yescharacteristic
422C22×C5#46411yescharacteristic
423C22×C5#46511yescharacteristic
424C22×C5#46711yescharacteristic
425C22×C5#46811yescharacteristic
426C22×C5#47011yescharacteristic
427C22×C5#48311yescharacteristic
428C22×C5#48411yescharacteristic
429C22×C5#48511yescharacteristic
430C22×C5#48511yescharacteristic
431C22×C5#48711yescharacteristic
432C22×C5#48811yescharacteristic
433C22×C5#48911yescharacteristic
434C22×C5#49111yescharacteristic
435C4×C5—44no—
436C4×C5—82no—
437C4×C5#38111yescharacteristic
438C4×C5#38611yescharacteristic
439C4×C5#38811yescharacteristic
440C4×C5#38811yescharacteristic
441C4×C5#39411yescharacteristic
442C4×C5#39711yescharacteristic
443C4×C5#39711yescharacteristic
444C4×C5#39711yescharacteristic
445Dic5—42no—
446Dic5—42no—
447Dic5—82no—
448Dic5—82no—
449C24D4×D511yescharacteristic
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—41no—
473C2×Q8—41no—
474C2×Q8—41no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8C22⋊Dic514yes—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—52no—
493C22×C4—52no—
494C22×C4—101no—
495C22×C4—101no—
496C22×C4—101no—
497C22×C4—101no—
498C22×C4—101no—
499C22×C4—101no—
500C22×C4—101no—
501C22×C4—101no—
502C22×C4—101no—
503C22×C4—101no—
504C22×C4—101no—
505C22×C4—101no—
506C22×C4—102no—
507C22×C4—102no—
508C22×C4—201no—
509C22×C4—201no—
510C22×C4—201no—
511C22×C4—201no—
512C22×C4—201no—
513C22×C4—201no—
514C22×C4—201no—
515C22×C4—201no—
516C22×C4—201no—
517C22×C4—201no—
518C22×C4—201no—
519C22×C4—201no—
520C22×C4#70911yescharacteristic
521C22×C4#70911yescharacteristic
522C22×C4#70911yescharacteristic
523C22×C4#70911yescharacteristic
524C22×C4D4×D511yescharacteristic
525C22×C4D4×D511yescharacteristic
526C22×C4D4×D511yescharacteristic
527C22×C4#71111yescharacteristic
528C22×C4#71111yescharacteristic
529C22×C4#71111yescharacteristic
530C22×C4#71111yescharacteristic
531C22×C4C22×Dic511yescharacteristic
532C22×C4C2×C22⋊D511yescharacteristic
533C22×C4C2×C22⋊D511yescharacteristic
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—102no—
542C2×C8—102no—
543C2×C8—102no—
544C2×C8—201no—
545C2×C8—201no—
546C2×C8—201no—
547C2×C8—201no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—102no—
553C4⋊C4—102no—
554C4⋊C4—102no—
555C4⋊C4—102no—
556C4⋊C4—201no—
557C4⋊C4—201no—
558C4⋊C4—201no—
559C4⋊C4—201no—
560C42—201no—
561C42—201no—
562C42—201no—
563C42—201no—
564C2×C5#144011yescharacteristic
565C2×C5#187811yescharacteristic
566C2×C5#188011yescharacteristic
567C2×C5#192711yescharacteristic
568C2×C5#192811yescharacteristic
569C2×C5#193311yescharacteristic
570C2×C5#193511yescharacteristic
571C2×C5#203511yescharacteristic
572C2×C5#203611yescharacteristic
573C2×C5#204211yescharacteristic
574C2×C5#204311yescharacteristic
575C2×C5#205511yescharacteristic
576C2×C5#205611yescharacteristic
577C2×C5#207211yescharacteristic
578C2×C5#207411yescharacteristic
579C23#402911yescharacteristic
580C23#403011yescharacteristic
581C23#403011yescharacteristic
582C23#403111yescharacteristic
583C23D5×SD1611yescharacteristic
584C23#406011yescharacteristic
585C23#406111yescharacteristic
586C23#406211yescharacteristic
587C23D5×Q1611yescharacteristic
588C23#406411yescharacteristic
589C23#406411yescharacteristic
590C23#406511yescharacteristic
591C23D4×Dic511yescharacteristic
592C23#408311yescharacteristic
593C23#408511yescharacteristic
594Q8—24no—
595Q8—24no—
596Q8—42no—
597Q8—42no—
598Q8—42no—
599Q8—42no—
600Q8—42no—
601Q8—42no—
602C2×C4—24no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—201no—
623C2×C4—201no—
624C2×C4—201no—
625C2×C4—201no—
626C2×C4—201no—
627C2×C4—201no—
628C2×C4—201no—
629C2×C4—201no—
630C2×C4—202no—
631C2×C4—202no—
632C2×C4—202no—
633C2×C4—202no—
634C2×C4—202no—
635C2×C4—202no—
636C2×C4—401no—
637C2×C4—401no—
638C2×C4—401no—
639C2×C4—401no—
640C2×C4—401no—
641C2×C4—401no—
642C2×C4—401no—
643C2×C4—401no—
644C2×C4#402511yescharacteristic
645C2×C4#402511yescharacteristic
646C2×C4#402511yescharacteristic
647C2×C4#402511yescharacteristic
648C2×C4#402911yescharacteristic
649C2×C4#402911yescharacteristic
650C2×C4#402911yescharacteristic
651C2×C4#403011yescharacteristic
652C2×C4#403011yescharacteristic
653C2×C4#403111yescharacteristic
654C2×C4#403111yescharacteristic
655C2×C4#403111yescharacteristic
656C2×C4#407211yescharacteristic
657C2×C4#407211yescharacteristic
658C2×C4#407511yescharacteristic
659C2×C4#407511yescharacteristic
660C2×C4#407511yescharacteristic
661C2×C4#407511yescharacteristic
662C2×C4D4×Dic511yescharacteristic
663C2×C4D4×Dic511yescharacteristic
664C2×C4D4×Dic511yescharacteristic
665C2×C4#408111yescharacteristic
666C2×C4#408111yescharacteristic
667C2×C4#408311yescharacteristic
668C2×C4#408511yescharacteristic
669C2×C4#408511yescharacteristic
670C2×C4#408511yescharacteristic
671C2×C4C2×C22⋊Dic511yescharacteristic
672C8—42no—
673C8—202no—
674C5#1119011yescharacteristic, complemented, Sylow
675C22#6508111yescharacteristic
676C22#6508211yescharacteristic
677C22#6508411yescharacteristic
678C22#6508611yescharacteristic
679C22#6508711yescharacteristic
680C22#6508911yescharacteristic
681C22#6509411yescharacteristic
682C22#6509611yescharacteristic
683C22#6509811yescharacteristic
684C22#6510111yescharacteristic
685C22#6510211yescharacteristic
686C22#6510311yescharacteristic
687C22#6510411yescharacteristic
688C22#6510511yescharacteristic
689C22#6510711yescharacteristic
690C22#6510811yescharacteristic
691C22#6524011yescharacteristic
692C22#6524011yescharacteristic
693C22#6524111yescharacteristic
694C22#6524811yescharacteristic
695C22#6524811yescharacteristic
696C22#6524811yescharacteristic
697C22SD16×Dic511yescharacteristic
698C22#6545211yescharacteristic
699C22#6545311yescharacteristic
700C22#6545511yescharacteristic
701C22#6545911yescharacteristic
702C22#6546111yescharacteristic
703C22#6547111yescharacteristic
704C22Q16×Dic511yescharacteristic
705C22#6547311yescharacteristic
706C22#6547411yescharacteristic
707C22#6547511yescharacteristic
708C22#6547611yescharacteristic
709C22#6550911yescharacteristic
710C4—44no—
711C4—82no—
712C4—202no—
713C4—202no—
714C4—402no—
715C4—402no—
716C4#6524011yescharacteristic
717C4#6524011yescharacteristic
718C4#6524111yescharacteristic
719C4#6524111yescharacteristic
720C4#6524111yescharacteristic
721C4#6524811yescharacteristic
722C4#6550011yescharacteristic
723C4#6550911yescharacteristic
724C2#1060101611yescharacteristic
725C2#1060101711yescharacteristic
726C2#1060102611yescharacteristic
727C2#1060102711yescharacteristic
728C2#1060104611yescharacteristic
729C2#1060104811yescharacteristic
730C2#1060106711yescharacteristic
731C2#1060106811yescharacteristic
732C2#1060107211yescharacteristic
733C2#1060107311yescharacteristic
734C2#1060107711yescharacteristic
735C2#1060107811yescharacteristic
736C2#1060234111yescharacteristic
737C2#1060284111yescharacteristic
738C2#1060285811yescharacteristic
subgroupG/H
centerC24D4×D5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC22×C5×#103C2
socle, prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC22×#103D5
hypocenterC5#11190
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
17. C2×C5×#103C4semidirect
230. C2×#103Dic5semidirect
674. C5#11190semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#1032
C2×#655192
C22×#39672
C2×#647712
C2×#647702
#106023562
C2×#647492
#111905