Finite Group Databasebeta

← C5×#11066 #11933786

Subgroups — C5×#11066 #11933786

Order 1280.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#102C211yesmaximal, characteristic
2C22×C5×#102C211yesmaximal, characteristic
3C2×C5×#390C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic, complemented
5C2×C5×#340C211yesmaximal, characteristic, complemented
6C2×C5×#340C211yesmaximal, characteristic, complemented
7C2×C5×#336C211yesmaximal, characteristic, complemented
8C23×C5×D4C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C23×C5×C8C2211yescharacteristic
11C22×C5×C4⋊C4—21no—
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4—21no—
16C22×C5×C22⋊C4—21no—
17C22×C42×C5C2211yescharacteristic
18C2×C5×#102—22no—
19C2×C5×#102—22no—
20C2×C5×#102—22no—
21C2×C5×#102—22no—
22C2×C5×#102—22no—
23C2×C5×#102C414yescomplemented
24C5×#390—22no—
25C5×#390—22no—
26C5×#389—22no—
27C5×#389—22no—
28C2×C5×#95—21no—
29C5×#340—22no—
30C5×#340—22no—
31C5×#336—22no—
32#11066C511yesmaximal, characteristic, direct product factor, Sylow
33C25×C5—21no—
34C22×C5×D4—21no—
35C22×C5×D4—21no—
36C22×C5×D4—21no—
37C22×C5×D4—21no—
38C22×C5×D4—21no—
39C22×C5×D4—21no—
40C22×C5×D4—21no—
41C22×C5×D4—21no—
42C22×C5×D4—21no—
43C22×C5×D4—21no—
44C22×C5×D4—21no—
45C22×C5×D4C2×C412yes—
46C22×C5×D4D412yes—
47C22×C5×D4Q812yes—
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×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—24no—
91C2×C5×C22⋊C4—42no—
92C2×C5×C22⋊C4—42no—
93C2×C5×C22⋊C4—42no—
94C2×C5×C22⋊C4—42no—
95C2×C42×C5—21no—
96C2×C42×C5—21no—
97C2×C42×C5—21no—
98C2×C42×C5—21no—
99C2×C42×C5—21no—
100C2×C42×C5—21no—
101C5×#102—28no—
102C5×#102—28no—
103C5×#95—24no—
104C22×#102C2×C511yescharacteristic
105C22×#102C2×C511yescharacteristic
106C2×#390C2×C511yescharacteristic
107C2×#389C2×C511yescharacteristic, complemented
108C2×#340C2×C511yescharacteristic, complemented
109C2×#340C2×C511yescharacteristic, complemented
110C2×#336C2×C511yescharacteristic, complemented
111C24×C5—22no—
112C24×C5—22no—
113C24×C5—22no—
114C24×C5—41no—
115C24×C5—41no—
116C24×C5—41no—
117C24×C5—41no—
118C24×C5—41no—
119C24×C5—41no—
120C24×C5—41no—
121C24×C5—41no—
122C24×C5—41no—
123C24×C5—41no—
124C24×C5—41no—
125C24×C5—41no—
126C24×C5C2×D411yescharacteristic
127C2×C5×D4—22no—
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4—22no—
131C2×C5×D4—22no—
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—22no—
136C2×C5×D4—22no—
137C2×C5×D4—22no—
138C2×C5×D4—22no—
139C2×C5×D4—22no—
140C2×C5×D4—22no—
141C2×C5×D4—22no—
142C2×C5×D4—41no—
143C2×C5×D4—41no—
144C2×C5×D4—41no—
145C2×C5×D4—41no—
146C2×C5×D4—41no—
147C2×C5×D4—41no—
148C2×C5×D4—41no—
149C2×C5×D4—41no—
150C2×C5×D4—41no—
151C2×C5×D4—41no—
152C2×C5×D4—41no—
153C2×C5×D4—41no—
154C2×C5×D4C4⋊C414yescomplemented
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—22no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—41no—
173C22×C4×C5—41no—
174C22×C4×C5—41no—
175C22×C4×C5—41no—
176C22×C4×C5—41no—
177C22×C4×C5—41no—
178C22×C4×C5—41no—
179C22×C4×C5—41no—
180C22×C4×C5—41no—
181C22×C4×C5—41no—
182C22×C4×C5—41no—
183C22×C4×C5—41no—
184C22×C4×C5—41no—
185C22×C4×C5—41no—
186C22×C4×C5—41no—
187C22×C4×C5—41no—
188C22×C4×C5D812yes—
189C22×C4×C5SD1612yes—
190C22×C4×C5C22×C411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×Q811yescharacteristic
198C22×C4×C5#4111yescharacteristic
199C22×C4×C5#4111yescharacteristic
200C22×C4×C5#4111yescharacteristic
201C22×C4×C5#4111yescharacteristic
202C22×C4×C5#4111yescharacteristic
203C22×C4×C5#4111yescharacteristic
204C2×C5×C8—22no—
205C2×C5×C8—22no—
206C2×C5×C8—22no—
207C2×C5×C8—22no—
208C2×C5×C8—22no—
209C2×C5×C8—22no—
210C2×C5×C8—41no—
211C2×C5×C8—41no—
212C2×C5×C8—41no—
213C2×C5×C8—41no—
214C2×C5×C8—41no—
215C2×C5×C8—41no—
216C2×C5×C8—41no—
217C2×C5×C8—41no—
218C5×C4⋊C4—22no—
219C5×C4⋊C4—22no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—22no—
223C5×C4⋊C4—22no—
224C5×C4⋊C4—22no—
225C5×C4⋊C4—48no—
226C5×C4⋊C4—41no—
227C5×C4⋊C4—41no—
228C5×C4⋊C4—41no—
229C5×C4⋊C4—41no—
230C5×C4⋊C4C22⋊C414yescomplemented
231C5×C22⋊C4—48no—
232C5×C22⋊C4—48no—
233C42×C5—41no—
234C42×C5—41no—
235C42×C5—41no—
236C42×C5—41no—
237C23×D4C22×C511yescharacteristic
238C23×C8C22×C511yescharacteristic
239C23×C8C22×C511yescharacteristic
240C22×C4⋊C4—21no—
241C22×C4⋊C4C22×C511yescharacteristic
242C22×C4⋊C4C22×C511yescharacteristic
243C22×C4⋊C4C22×C511yescharacteristic
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C42C22×C511yescharacteristic
247C2×#102—22no—
248C2×#102—22no—
249C2×#102—22no—
250C2×#102—22no—
251C2×#102—22no—
252C2×#102C4×C514yescomplemented
253#390—22no—
254#390—22no—
255#389—22no—
256#389—22no—
257C2×#95—21no—
258#340—22no—
259#340—22no—
260#336—22no—
261C23×C5—24no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5—42no—
265C23×C5—42no—
266C23×C5—42no—
267C23×C5—42no—
268C23×C5—42no—
269C23×C5—42no—
270C23×C5—42no—
271C23×C5—42no—
272C23×C5—42no—
273C23×C5—42no—
274C23×C5—42no—
275C23×C5—42no—
276C23×C5—42no—
277C23×C5—42no—
278C23×C5—42no—
279C23×C5—42no—
280C23×C5—81no—
281C23×C5—81no—
282C23×C5—81no—
283C23×C5—81no—
284C23×C5—81no—
285C23×C5—81no—
286C23×C5—81no—
287C23×C5—81no—
288C23×C5—81no—
289C23×C5—81no—
290C23×C5—81no—
291C23×C5—81no—
292C23×C5—81no—
293C23×C5—81no—
294C23×C5—81no—
295C23×C5—81no—
296C23×C5C4×D411yescharacteristic
297C23×C5#12011yescharacteristic
298C23×C5#12011yescharacteristic
299C23×C5#12111yescharacteristic
300C23×C5#12111yescharacteristic
301C23×C5C22⋊Q811yescharacteristic
302C23×C5#12411yescharacteristic
303C23×C5C2×D811yescharacteristic
304C23×C5C2×SD1611yescharacteristic
305C23×C5#13511yescharacteristic
306C23×C5#13511yescharacteristic
307C23×C5AGL(1,ℤ/8)11yescharacteristic
308C23×C5AGL(1,ℤ/8)11yescharacteristic
309C23×C5AGL(1,ℤ/8)11yescharacteristic
310C23×C5#13711yescharacteristic
311C5×D4—24no—
312C5×D4—24no—
313C5×D4—42no—
314C5×D4—42no—
315C5×D4—42no—
316C5×D4—42no—
317C5×D4—42no—
318C5×D4—42no—
319C2×C4×C5—24no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—42no—
335C2×C4×C5—41no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5—81no—
347C2×C4×C5—81no—
348C2×C4×C5—81no—
349C2×C4×C5—81no—
350C2×C4×C5—81no—
351C2×C4×C5—81no—
352C2×C4×C5—81no—
353C2×C4×C5—81no—
354C2×C4×C5C2×C22⋊C411yescharacteristic
355C2×C4×C5C2×C4⋊C411yescharacteristic
356C2×C4×C5#11711yescharacteristic
357C2×C4×C5C4×D411yescharacteristic
358C2×C4×C5C4×D411yescharacteristic
359C2×C4×C5C4×D411yescharacteristic
360C2×C4×C5#12011yescharacteristic
361C2×C4×C5#12111yescharacteristic
362C2×C4×C5#12111yescharacteristic
363C2×C4×C5#12111yescharacteristic
364C2×C4×C5#12111yescharacteristic
365C2×C4×C5#12111yescharacteristic
366C2×C4×C5#12111yescharacteristic
367C2×C4×C5C22⋊Q811yescharacteristic
368C2×C4×C5C22⋊Q811yescharacteristic
369C2×C4×C5C22⋊Q811yescharacteristic
370C2×C4×C5C22⋊Q811yescharacteristic
371C2×C4×C5C22⋊Q811yescharacteristic
372C2×C4×C5#12311yescharacteristic
373C2×C4×C5#12311yescharacteristic
374C2×C4×C5#12311yescharacteristic
375C2×C4×C5#12311yescharacteristic
376C2×C4×C5#12311yescharacteristic
377C2×C4×C5#12411yescharacteristic
378C2×C4×C5#12411yescharacteristic
379C2×C4×C5#12611yescharacteristic
380C2×C4×C5#12611yescharacteristic
381C2×C4×C5#12711yescharacteristic
382C5×C8—42no—
383C5×C8—42no—
384C25—21no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4C2×C4×C512yes—
397C22×D4C5×D412yes—
398C22×D4C5×Q812yes—
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C5×D411yescharacteristic
403C23×C4C5×D411yescharacteristic
404C23×C4C23×C511yescharacteristic
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8—21no—
411C22×C8—21no—
412C22×C8—21no—
413C22×C8—21no—
414C22×C8—21no—
415C22×C8—21no—
416C22×C8—21no—
417C22×C8C2×C4×C512yes—
418C22×C8C5×D412yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4C2×C4×C512yes—
436C2×C4⋊C4C5×D412yes—
437C2×C4⋊C4C5×D412yes—
438C2×C4⋊C4C5×D412yes—
439C2×C4⋊C4C5×D412yes—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452#102—28no—
453#102—28no—
454#95—24no—
455C22×C5—44no—
456C22×C5—44no—
457C22×C5—44no—
458C22×C5—82no—
459C22×C5—82no—
460C22×C5—82no—
461C22×C5—82no—
462C22×C5—82no—
463C22×C5—82no—
464C22×C5—82no—
465C22×C5—82no—
466C22×C5—82no—
467C22×C5—82no—
468C22×C5—82no—
469C22×C5—82no—
470C22×C5#38511yescharacteristic
471C22×C5#38611yescharacteristic
472C22×C5#38811yescharacteristic
473C22×C5#39211yescharacteristic
474C22×C5#39311yescharacteristic
475C22×C5#39411yescharacteristic
476C22×C5#39611yescharacteristic
477C22×C5C4×D811yescharacteristic
478C22×C5C4×SD1611yescharacteristic
479C22×C5#44011yescharacteristic
480C22×C5#44211yescharacteristic
481C22×C5#44711yescharacteristic
482C22×C5#44711yescharacteristic
483C22×C5#44811yescharacteristic
484C22×C5#44911yescharacteristic
485C22×C5#44911yescharacteristic
486C22×C5#44911yescharacteristic
487C22×C5#45011yescharacteristic
488C22×C5#45211yescharacteristic
489C22×C5#45911yescharacteristic
490C22×C5#46011yescharacteristic
491C22×C5#46311yescharacteristic
492C22×C5#46411yescharacteristic
493C22×C5#46511yescharacteristic
494C22×C5#46611yescharacteristic
495C22×C5#46811yescharacteristic
496C22×C5#46911yescharacteristic
497C22×C5#47411yescharacteristic
498C22×C5#47611yescharacteristic
499C22×C5#47811yescharacteristic
500C22×C5#47811yescharacteristic
501C22×C5#48611yescharacteristic
502C22×C5#48811yescharacteristic
503C22×C5#48911yescharacteristic
504C22×C5#49011yescharacteristic
505C4×C5—44no—
506C4×C5—42no—
507C4×C5—42no—
508C4×C5—82no—
509C4×C5—82no—
510C4×C5#38011yescharacteristic
511C4×C5#38511yescharacteristic
512C4×C5#38811yescharacteristic
513C4×C5#39011yescharacteristic
514C4×C5#39411yescharacteristic
515C4×C5#39611yescharacteristic
516C4×C5#39711yescharacteristic
517C4×C5#39911yescharacteristic
518C24—22no—
519C24—22no—
520C24—22no—
521C24—41no—
522C24—41no—
523C24—41no—
524C24—41no—
525C24—41no—
526C24—41no—
527C24—41no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24C2×C5×D411yescharacteristic
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4C5×C4⋊C414yescomplemented
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C5×D812yes—
596C22×C4C5×SD1612yes—
597C22×C4C22×C4×C511yescharacteristic
598C22×C4C2×C5×D411yescharacteristic
599C22×C4C2×C5×D411yescharacteristic
600C22×C4C2×C5×D411yescharacteristic
601C22×C4C2×C5×D411yescharacteristic
602C22×C4C2×C5×D411yescharacteristic
603C22×C4C2×C5×D411yescharacteristic
604C22×C4C2×C5×Q811yescharacteristic
605C22×C4C5×#4111yescharacteristic
606C22×C4C5×#4111yescharacteristic
607C22×C4C5×#4111yescharacteristic
608C22×C4C5×#4111yescharacteristic
609C22×C4C5×#4111yescharacteristic
610C22×C4C5×#4111yescharacteristic
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—48no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4C5×C22⋊C414yescomplemented
638C22⋊C4—48no—
639C22⋊C4—48no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C2×C5—84no—
645C2×C5#143911yescharacteristic
646C2×C5#186211yescharacteristic
647C2×C5#186411yescharacteristic
648C2×C5#187911yescharacteristic
649C2×C5#188011yescharacteristic
650C2×C5#193411yescharacteristic
651C2×C5#193611yescharacteristic
652C2×C5#199911yescharacteristic
653C2×C5#200011yescharacteristic
654C2×C5#202311yescharacteristic
655C2×C5#202511yescharacteristic
656C2×C5#204111yescharacteristic
657C2×C5#204211yescharacteristic
658C2×C5#206511yescharacteristic
659C2×C5#206711yescharacteristic
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23C4×C5×D411yescharacteristic
696C23C5×#12011yescharacteristic
697C23C5×#12011yescharacteristic
698C23C5×#12111yescharacteristic
699C23C5×#12111yescharacteristic
700C23C5×C22⋊Q811yescharacteristic
701C23C5×#12411yescharacteristic
702C23C2×C5×D811yescharacteristic
703C23C2×C5×SD1611yescharacteristic
704C23C5×#13511yescharacteristic
705C23C5×#13511yescharacteristic
706C23C5×AGL(1,ℤ/8)11yescharacteristic
707C23C5×AGL(1,ℤ/8)11yescharacteristic
708C23C5×AGL(1,ℤ/8)11yescharacteristic
709C23C5×#13711yescharacteristic
710D4—24no—
711D4—24no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4C2×C5×C22⋊C411yescharacteristic
754C2×C4C2×C5×C4⋊C411yescharacteristic
755C2×C4C5×#11711yescharacteristic
756C2×C4C4×C5×D411yescharacteristic
757C2×C4C4×C5×D411yescharacteristic
758C2×C4C4×C5×D411yescharacteristic
759C2×C4C5×#12011yescharacteristic
760C2×C4C5×#12111yescharacteristic
761C2×C4C5×#12111yescharacteristic
762C2×C4C5×#12111yescharacteristic
763C2×C4C5×#12111yescharacteristic
764C2×C4C5×#12111yescharacteristic
765C2×C4C5×#12111yescharacteristic
766C2×C4C5×C22⋊Q811yescharacteristic
767C2×C4C5×C22⋊Q811yescharacteristic
768C2×C4C5×C22⋊Q811yescharacteristic
769C2×C4C5×C22⋊Q811yescharacteristic
770C2×C4C5×C22⋊Q811yescharacteristic
771C2×C4C5×#12311yescharacteristic
772C2×C4C5×#12311yescharacteristic
773C2×C4C5×#12311yescharacteristic
774C2×C4C5×#12311yescharacteristic
775C2×C4C5×#12311yescharacteristic
776C2×C4C5×#12411yescharacteristic
777C2×C4C5×#12411yescharacteristic
778C2×C4C5×#12611yescharacteristic
779C2×C4C5×#12611yescharacteristic
780C2×C4C5×#12711yescharacteristic
781C8—42no—
782C8—42no—
783C5#1106611yescharacteristic, direct product factor, Sylow
784C22—44no—
785C22—44no—
786C22—44no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22C5×#38511yescharacteristic
800C22C5×#38611yescharacteristic
801C22C5×#38811yescharacteristic
802C22C5×#39211yescharacteristic
803C22C5×#39311yescharacteristic
804C22C5×#39411yescharacteristic
805C22C5×#39611yescharacteristic
806C22C4×C5×D811yescharacteristic
807C22C4×C5×SD1611yescharacteristic
808C22C5×#44011yescharacteristic
809C22C5×#44211yescharacteristic
810C22C5×#44711yescharacteristic
811C22C5×#44711yescharacteristic
812C22C5×#44811yescharacteristic
813C22C5×#44911yescharacteristic
814C22C5×#44911yescharacteristic
815C22C5×#44911yescharacteristic
816C22C5×#45011yescharacteristic
817C22C5×#45211yescharacteristic
818C22C5×#45911yescharacteristic
819C22C5×#46011yescharacteristic
820C22C5×#46311yescharacteristic
821C22C5×#46411yescharacteristic
822C22C5×#46511yescharacteristic
823C22C5×#46611yescharacteristic
824C22C5×#46811yescharacteristic
825C22C5×#46911yescharacteristic
826C22C5×#47411yescharacteristic
827C22C5×#47611yescharacteristic
828C22C5×#47811yescharacteristic
829C22C5×#47811yescharacteristic
830C22C5×#48611yescharacteristic
831C22C5×#48811yescharacteristic
832C22C5×#48911yescharacteristic
833C22C5×#49011yescharacteristic
834C4—44no—
835C4—42no—
836C4—42no—
837C4—82no—
838C4—82no—
839C4C5×#38011yescharacteristic
840C4C5×#38511yescharacteristic
841C4C5×#38811yescharacteristic
842C4C5×#39011yescharacteristic
843C4C5×#39411yescharacteristic
844C4C5×#39611yescharacteristic
845C4C5×#39711yescharacteristic
846C4C5×#39911yescharacteristic
847C2—84no—
848C2C5×#143911yescharacteristic
849C2C5×#186211yescharacteristic
850C2C5×#186411yescharacteristic
851C2C5×#187911yescharacteristic
852C2C5×#188011yescharacteristic
853C2C5×#193411yescharacteristic
854C2C5×#193611yescharacteristic
855C2C5×#199911yescharacteristic
856C2C5×#200011yescharacteristic
857C2C5×#202311yescharacteristic
858C2C5×#202511yescharacteristic
859C2C5×#204111yescharacteristic
860C2C5×#204211yescharacteristic
861C2C5×#206511yescharacteristic
862C2C5×#206711yescharacteristic
subgroupG/H
center, socleC24×C5C2×D4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC23×C5×D4C22
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
4. C2×C5×#389C2semidirect
5. C2×C5×#340C2semidirect
6. C2×C5×#340C2semidirect
7. C2×C5×#336C2semidirect
23. C2×C5×#102C4semidirect
32. #11066C5direct (N × H)
107. C2×#389C2×C5semidirect
108. C2×#340C2×C5semidirect
109. C2×#340C2×C5semidirect
110. C2×#336C2×C5semidirect
154. C2×C5×D4C4⋊C4semidirect
230. C5×C4⋊C4C22⋊C4semidirect
252. C2×#102C4×C5semidirect
561. C2×D4C5×C4⋊C4semidirect
637. C4⋊C4C5×C22⋊C4semidirect
783. C5#11066direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1022
C2×C5×#3902
C2×C5×#3892
C2×C5×#3402
C2×C5×#3362
#110665