Finite Group Databasebeta

← C5×#11067 #11933787

Subgroups — C5×#11067 #11933787

Order 1280.

1066 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#103C211yesmaximal, characteristic
2C22×C5×#103C211yesmaximal, characteristic
3C2×C5×#391C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic
5C2×C5×#340C211yesmaximal, characteristic
6C2×C5×#340C211yesmaximal, characteristic
7C2×C5×#336C211yesmaximal, characteristic
8C23×C5×Q8C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C23×C5×C8C2211yescharacteristic
11C22×C5×C4⋊C4—21no—
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C2×C5×#103—22no—
17C2×C5×#103—22no—
18C2×C5×#103—22no—
19C2×C5×#103—22no—
20C2×C5×#103—22no—
21C2×C5×#103C414yescomplemented
22C5×#391—22no—
23C5×#391—22no—
24C5×#389—22no—
25C5×#389—22no—
26C2×C5×#95—21no—
27C2×C5×#95—21no—
28C2×C5×#95—21no—
29C5×#340—22no—
30C5×#340—22no—
31C5×#336—22no—
32#11067C511yesmaximal, characteristic, direct product factor, Sylow
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×Q8—21no—
43C22×C5×Q8—21no—
44C22×C5×Q8C2×C412yes—
45C22×C5×Q8D412yes—
46C22×C5×Q8Q812yes—
47C23×C4×C5—21no—
48C23×C4×C5—21no—
49C23×C4×C5—21no—
50C23×C4×C5—21no—
51C23×C4×C5D411yescharacteristic
52C23×C4×C5D411yescharacteristic
53C23×C4×C5C2311yescharacteristic
54C22×C5×C8—21no—
55C22×C5×C8—21no—
56C22×C5×C8—21no—
57C22×C5×C8—21no—
58C22×C5×C8—21no—
59C22×C5×C8—21no—
60C22×C5×C8—21no—
61C22×C5×C8—21no—
62C22×C5×C8—21no—
63C22×C5×C8—21no—
64C22×C5×C8—21no—
65C22×C5×C8—21no—
66C22×C5×C8C2×C412yes—
67C22×C5×C8D412yes—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—24no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—42no—
83C2×C5×C4⋊C4—42no—
84C2×C5×C4⋊C4C2×C412yes—
85C2×C5×C4⋊C4D412yes—
86C2×C5×C4⋊C4D412yes—
87C2×C5×C4⋊C4D412yes—
88C2×C5×C4⋊C4D412yes—
89C2×C42×C5—21no—
90C2×C42×C5—21no—
91C2×C42×C5—21no—
92C2×C42×C5—21no—
93C2×C42×C5—21no—
94C2×C42×C5—21no—
95C5×#103—28no—
96C5×#103—28no—
97C5×#95—24no—
98C5×#95—24no—
99C5×#95—24no—
100C22×#103C2×C511yescharacteristic
101C22×#103C2×C511yescharacteristic
102C2×#391C2×C511yescharacteristic
103C2×#389C2×C511yescharacteristic
104C2×#340C2×C511yescharacteristic
105C2×#340C2×C511yescharacteristic
106C2×#336C2×C511yescharacteristic
107C24×C5C2×D411yescharacteristic
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—22no—
120C2×C5×Q8—22no—
121C2×C5×Q8—22no—
122C2×C5×Q8—22no—
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×Q8—41no—
132C2×C5×Q8—41no—
133C2×C5×Q8—41no—
134C2×C5×Q8—41no—
135C2×C5×Q8C4⋊C414yescomplemented
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—41no—
157C22×C4×C5—41no—
158C22×C4×C5—41no—
159C22×C4×C5—41no—
160C22×C4×C5—41no—
161C22×C4×C5—41no—
162C22×C4×C5—41no—
163C22×C4×C5—41no—
164C22×C4×C5—41no—
165C22×C4×C5—41no—
166C22×C4×C5—41no—
167C22×C4×C5—41no—
168C22×C4×C5—41no—
169C22×C4×C5—41no—
170C22×C4×C5—41no—
171C22×C4×C5—41no—
172C22×C4×C5—41no—
173C22×C4×C5—41no—
174C22×C4×C5—41no—
175C22×C4×C5—41no—
176C22×C4×C5SD1612yes—
177C22×C4×C5Q1612yes—
178C22×C4×C5C22×C411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×Q811yescharacteristic
186C22×C4×C5#4111yescharacteristic
187C22×C4×C5#4111yescharacteristic
188C22×C4×C5#4111yescharacteristic
189C22×C4×C5#4111yescharacteristic
190C22×C4×C5#4111yescharacteristic
191C22×C4×C5#4111yescharacteristic
192C2×C5×C8—22no—
193C2×C5×C8—22no—
194C2×C5×C8—22no—
195C2×C5×C8—22no—
196C2×C5×C8—22no—
197C2×C5×C8—22no—
198C2×C5×C8—41no—
199C2×C5×C8—41no—
200C2×C5×C8—41no—
201C2×C5×C8—41no—
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—22no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—48no—
214C5×C4⋊C4—41no—
215C5×C4⋊C4—41no—
216C5×C4⋊C4—41no—
217C5×C4⋊C4—41no—
218C5×C4⋊C4C22⋊C414yes—
219C42×C5—41no—
220C42×C5—41no—
221C42×C5—41no—
222C42×C5—41no—
223C23×Q8C22×C511yescharacteristic
224C23×C8C22×C511yescharacteristic
225C23×C8C22×C511yescharacteristic
226C22×C4⋊C4—21no—
227C22×C4⋊C4C22×C511yescharacteristic
228C22×C4⋊C4C22×C511yescharacteristic
229C22×C4⋊C4C22×C511yescharacteristic
230C22×C42C22×C511yescharacteristic
231C2×#103—22no—
232C2×#103—22no—
233C2×#103—22no—
234C2×#103—22no—
235C2×#103—22no—
236C2×#103C4×C514yescomplemented
237#391—22no—
238#391—22no—
239#389—22no—
240#389—22no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95—21no—
244#340—22no—
245#340—22no—
246#336—22no—
247C23×C5C4×D411yescharacteristic
248C23×C5#12011yescharacteristic
249C23×C5#12011yescharacteristic
250C23×C5#12111yescharacteristic
251C23×C5#12111yescharacteristic
252C23×C5C22⋊Q811yescharacteristic
253C23×C5#12411yescharacteristic
254C23×C5C2×SD1611yescharacteristic
255C23×C5C2×Q1611yescharacteristic
256C23×C5#13511yescharacteristic
257C23×C5#13511yescharacteristic
258C23×C5AGL(1,ℤ/8)11yescharacteristic
259C23×C5#13711yescharacteristic
260C23×C5#13711yescharacteristic
261C23×C5#13711yescharacteristic
262C5×Q8—24no—
263C5×Q8—24no—
264C5×Q8—42no—
265C5×Q8—42no—
266C5×Q8—42no—
267C5×Q8—42no—
268C5×Q8—42no—
269C5×Q8—42no—
270C2×C4×C5—24no—
271C2×C4×C5—24no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5—41no—
289C2×C4×C5—42no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—81no—
305C2×C4×C5—81no—
306C2×C4×C5—81no—
307C2×C4×C5—81no—
308C2×C4×C5—81no—
309C2×C4×C5—81no—
310C2×C4×C5—81no—
311C2×C4×C5—81no—
312C2×C4×C5C2×C22⋊C411yescharacteristic
313C2×C4×C5C2×C4⋊C411yescharacteristic
314C2×C4×C5#11711yescharacteristic
315C2×C4×C5C4×D411yescharacteristic
316C2×C4×C5C4×D411yescharacteristic
317C2×C4×C5C4×D411yescharacteristic
318C2×C4×C5#12011yescharacteristic
319C2×C4×C5#12111yescharacteristic
320C2×C4×C5#12111yescharacteristic
321C2×C4×C5#12111yescharacteristic
322C2×C4×C5#12111yescharacteristic
323C2×C4×C5#12111yescharacteristic
324C2×C4×C5#12111yescharacteristic
325C2×C4×C5C22⋊Q811yescharacteristic
326C2×C4×C5C22⋊Q811yescharacteristic
327C2×C4×C5C22⋊Q811yescharacteristic
328C2×C4×C5C22⋊Q811yescharacteristic
329C2×C4×C5C22⋊Q811yescharacteristic
330C2×C4×C5#12311yescharacteristic
331C2×C4×C5#12311yescharacteristic
332C2×C4×C5#12311yescharacteristic
333C2×C4×C5#12311yescharacteristic
334C2×C4×C5#12311yescharacteristic
335C2×C4×C5#12411yescharacteristic
336C2×C4×C5#12411yescharacteristic
337C2×C4×C5#12611yescharacteristic
338C2×C4×C5#12611yescharacteristic
339C2×C4×C5#12711yescharacteristic
340C5×C8—42no—
341C5×C8—42no—
342C22×Q8—21no—
343C22×Q8—21no—
344C22×Q8—21no—
345C22×Q8—21no—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8—21no—
353C22×Q8C2×C4×C512yes—
354C22×Q8C5×D412yes—
355C22×Q8C5×Q812yes—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4C5×D411yescharacteristic
361C23×C4C5×D411yescharacteristic
362C23×C4C23×C511yescharacteristic
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8C2×C4×C512yes—
376C22×C8C5×D412yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C512yes—
394C2×C4⋊C4C5×D412yes—
395C2×C4⋊C4C5×D412yes—
396C2×C4⋊C4C5×D412yes—
397C2×C4⋊C4C5×D412yes—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404#103—28no—
405#103—28no—
406#95—24no—
407#95—24no—
408#95—24no—
409C22×C5#38511yescharacteristic
410C22×C5#38611yescharacteristic
411C22×C5#38811yescharacteristic
412C22×C5#39211yescharacteristic
413C22×C5#39311yescharacteristic
414C22×C5#39411yescharacteristic
415C22×C5#39611yescharacteristic
416C22×C5C4×SD1611yescharacteristic
417C22×C5C4×Q1611yescharacteristic
418C22×C5#44011yescharacteristic
419C22×C5#44111yescharacteristic
420C22×C5#44811yescharacteristic
421C22×C5#44911yescharacteristic
422C22×C5#45011yescharacteristic
423C22×C5#45111yescharacteristic
424C22×C5#45111yescharacteristic
425C22×C5#45211yescharacteristic
426C22×C5#45211yescharacteristic
427C22×C5#45211yescharacteristic
428C22×C5#46111yescharacteristic
429C22×C5#46211yescharacteristic
430C22×C5#46311yescharacteristic
431C22×C5#46411yescharacteristic
432C22×C5#46511yescharacteristic
433C22×C5#46711yescharacteristic
434C22×C5#46811yescharacteristic
435C22×C5#47011yescharacteristic
436C22×C5#47511yescharacteristic
437C22×C5#47711yescharacteristic
438C22×C5#47911yescharacteristic
439C22×C5#47911yescharacteristic
440C22×C5#48711yescharacteristic
441C22×C5#48811yescharacteristic
442C22×C5#48911yescharacteristic
443C22×C5#49111yescharacteristic
444C4×C5—44no—
445C4×C5—44no—
446C4×C5—42no—
447C4×C5—42no—
448C4×C5—82no—
449C4×C5—82no—
450C4×C5#38011yescharacteristic
451C4×C5#38511yescharacteristic
452C4×C5#38811yescharacteristic
453C4×C5#39011yescharacteristic
454C4×C5#39411yescharacteristic
455C4×C5#39611yescharacteristic
456C4×C5#39711yescharacteristic
457C4×C5#39911yescharacteristic
458C24C2×C5×D411yescharacteristic
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—41no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8C5×C4⋊C414yescomplemented
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4C5×SD1612yes—
528C22×C4C5×Q1612yes—
529C22×C4C22×C4×C511yescharacteristic
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C2×C5×D411yescharacteristic
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C2×C5×D411yescharacteristic
534C22×C4C2×C5×D411yescharacteristic
535C22×C4C2×C5×D411yescharacteristic
536C22×C4C2×C5×Q811yescharacteristic
537C22×C4C5×#4111yescharacteristic
538C22×C4C5×#4111yescharacteristic
539C22×C4C5×#4111yescharacteristic
540C22×C4C5×#4111yescharacteristic
541C22×C4C5×#4111yescharacteristic
542C22×C4C5×#4111yescharacteristic
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—48no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4C5×C22⋊C414yes—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C2×C5#143911yescharacteristic
575C2×C5#186311yescharacteristic
576C2×C5#186511yescharacteristic
577C2×C5#187711yescharacteristic
578C2×C5#187811yescharacteristic
579C2×C5#193311yescharacteristic
580C2×C5#193511yescharacteristic
581C2×C5#200011yescharacteristic
582C2×C5#200111yescharacteristic
583C2×C5#202411yescharacteristic
584C2×C5#202611yescharacteristic
585C2×C5#204211yescharacteristic
586C2×C5#204311yescharacteristic
587C2×C5#206611yescharacteristic
588C2×C5#206811yescharacteristic
589C23C4×C5×D411yescharacteristic
590C23C5×#12011yescharacteristic
591C23C5×#12011yescharacteristic
592C23C5×#12111yescharacteristic
593C23C5×#12111yescharacteristic
594C23C5×C22⋊Q811yescharacteristic
595C23C5×#12411yescharacteristic
596C23C2×C5×SD1611yescharacteristic
597C23C2×C5×Q1611yescharacteristic
598C23C5×#13511yescharacteristic
599C23C5×#13511yescharacteristic
600C23C5×AGL(1,ℤ/8)11yescharacteristic
601C23C5×#13711yescharacteristic
602C23C5×#13711yescharacteristic
603C23C5×#13711yescharacteristic
604Q8—24no—
605Q8—24no—
606Q8—42no—
607Q8—42no—
608Q8—42no—
609Q8—42no—
610Q8—42no—
611Q8—42no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4C2×C5×C22⋊C411yescharacteristic
655C2×C4C2×C5×C4⋊C411yescharacteristic
656C2×C4C5×#11711yescharacteristic
657C2×C4C4×C5×D411yescharacteristic
658C2×C4C4×C5×D411yescharacteristic
659C2×C4C4×C5×D411yescharacteristic
660C2×C4C5×#12011yescharacteristic
661C2×C4C5×#12111yescharacteristic
662C2×C4C5×#12111yescharacteristic
663C2×C4C5×#12111yescharacteristic
664C2×C4C5×#12111yescharacteristic
665C2×C4C5×#12111yescharacteristic
666C2×C4C5×#12111yescharacteristic
667C2×C4C5×C22⋊Q811yescharacteristic
668C2×C4C5×C22⋊Q811yescharacteristic
669C2×C4C5×C22⋊Q811yescharacteristic
670C2×C4C5×C22⋊Q811yescharacteristic
671C2×C4C5×C22⋊Q811yescharacteristic
672C2×C4C5×#12311yescharacteristic
673C2×C4C5×#12311yescharacteristic
674C2×C4C5×#12311yescharacteristic
675C2×C4C5×#12311yescharacteristic
676C2×C4C5×#12311yescharacteristic
677C2×C4C5×#12411yescharacteristic
678C2×C4C5×#12411yescharacteristic
679C2×C4C5×#12611yescharacteristic
680C2×C4C5×#12611yescharacteristic
681C2×C4C5×#12711yescharacteristic
682C8—42no—
683C8—42no—
684C5#1106711yescharacteristic, direct product factor, Sylow
685C22C5×#38511yescharacteristic
686C22C5×#38611yescharacteristic
687C22C5×#38811yescharacteristic
688C22C5×#39211yescharacteristic
689C22C5×#39311yescharacteristic
690C22C5×#39411yescharacteristic
691C22C5×#39611yescharacteristic
692C22C4×C5×SD1611yescharacteristic
693C22C4×C5×Q1611yescharacteristic
694C22C5×#44011yescharacteristic
695C22C5×#44111yescharacteristic
696C22C5×#44811yescharacteristic
697C22C5×#44911yescharacteristic
698C22C5×#45011yescharacteristic
699C22C5×#45111yescharacteristic
700C22C5×#45111yescharacteristic
701C22C5×#45211yescharacteristic
702C22C5×#45211yescharacteristic
703C22C5×#45211yescharacteristic
704C22C5×#46111yescharacteristic
705C22C5×#46211yescharacteristic
706C22C5×#46311yescharacteristic
707C22C5×#46411yescharacteristic
708C22C5×#46511yescharacteristic
709C22C5×#46711yescharacteristic
710C22C5×#46811yescharacteristic
711C22C5×#47011yescharacteristic
712C22C5×#47511yescharacteristic
713C22C5×#47711yescharacteristic
714C22C5×#47911yescharacteristic
715C22C5×#47911yescharacteristic
716C22C5×#48711yescharacteristic
717C22C5×#48811yescharacteristic
718C22C5×#48911yescharacteristic
719C22C5×#49111yescharacteristic
720C4—44no—
721C4—44no—
722C4—42no—
723C4—42no—
724C4—82no—
725C4—82no—
726C4C5×#38011yescharacteristic
727C4C5×#38511yescharacteristic
728C4C5×#38811yescharacteristic
729C4C5×#39011yescharacteristic
730C4C5×#39411yescharacteristic
731C4C5×#39611yescharacteristic
732C4C5×#39711yescharacteristic
733C4C5×#39911yescharacteristic
734C2C5×#143911yescharacteristic
735C2C5×#186311yescharacteristic
736C2C5×#186511yescharacteristic
737C2C5×#187711yescharacteristic
738C2C5×#187811yescharacteristic
739C2C5×#193311yescharacteristic
740C2C5×#193511yescharacteristic
741C2C5×#200011yescharacteristic
742C2C5×#200111yescharacteristic
743C2C5×#202411yescharacteristic
744C2C5×#202611yescharacteristic
745C2C5×#204211yescharacteristic
746C2C5×#204311yescharacteristic
747C2C5×#206611yescharacteristic
748C2C5×#206811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C5C2×D4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
21. C2×C5×#103C4semidirect
32. #11067C5direct (N × H)
135. C2×C5×Q8C4⋊C4semidirect
236. C2×#103C4×C5semidirect
486. C2×Q8C5×C4⋊C4semidirect
684. C5#11067direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1032
C2×C5×#3912
C2×C5×#3892
C2×C5×#3402
C2×C5×#3362
#110675