Finite Group Databasebeta

← C5×#11087 #11933807

Subgroups — C5×#11087 #11933807

Order 1280.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#99C211yesmaximal, characteristic
2C5×#2308C211yesmaximal, characteristic
3C2×C5×#386C211yesmaximal, characteristic
4C2×C5×#385C211yesmaximal, characteristic, complemented
5C2×C5×#342C211yesmaximal, characteristic, complemented
6C2×C5×#342C211yesmaximal, characteristic, complemented
7C5×C22⋊#95C211yesmaximal, characteristic, complemented
8C23×C5×D4C2211yescharacteristic
9C24×C4×C5C2211yescharacteristic
10C22×C5×C4⋊C4—21no—
11C22×C5×C22⋊C4—21no—
12C22×C5×C22⋊C4C2211yescharacteristic
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2211yescharacteristic
17C2×C5×#99—22no—
18C2×C5×#99—22no—
19C2×C5×#99C414yescomplemented
20C5×#386—22no—
21C5×#386—21no—
22C5×#386—22no—
23C5×#386—21no—
24C5×#386—22no—
25C5×#385—22no—
26C5×#385—22no—
27C5×#381—21no—
28C5×#379—21no—
29C2×C5×#95—21no—
30C2×C5×#95—21no—
31C2×C5×#95—22no—
32C5×#342—22no—
33C5×#342—22no—
34#11087C511yesmaximal, characteristic, direct product factor, Sylow
35C25×C5D411yescharacteristic
36C25×C5C2311yescharacteristic
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×D4—21no—
46C22×C5×D4—21no—
47C22×C5×D4—21no—
48C22×C5×D4—21no—
49C22×C5×D4C2×C412yes—
50C22×C5×D4Q812yes—
51C23×C4×C5—21no—
52C23×C4×C5—21no—
53C23×C4×C5—21no—
54C23×C4×C5—21no—
55C23×C4×C5—21no—
56C23×C4×C5—21no—
57C23×C4×C5—21no—
58C23×C4×C5—21no—
59C23×C4×C5—21no—
60C23×C4×C5—44no—
61C23×C4×C5D411yescharacteristic
62C23×C4×C5D411yescharacteristic
63C23×C4×C5D412yes—
64C23×C4×C5D412yes—
65C23×C4×C5D411yescharacteristic
66C2×C5×C4⋊C4—24no—
67C2×C5×C4⋊C4—44no—
68C2×C5×C22⋊C4—21no—
69C2×C5×C22⋊C4—21no—
70C2×C5×C22⋊C4—21no—
71C2×C5×C22⋊C4—21no—
72C2×C5×C22⋊C4—21no—
73C2×C5×C22⋊C4—21no—
74C2×C5×C22⋊C4—21no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—24no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4—21no—
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—21no—
88C2×C5×C22⋊C4—21no—
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—44no—
97C2×C5×C22⋊C4C2×C412yes—
98C2×C5×C22⋊C4C2×C412yes—
99C2×C5×C22⋊C4D412yes—
100C2×C5×C22⋊C4D412yes—
101C2×C5×C22⋊C4D412yes—
102C5×#99—28no—
103C5×#95—24no—
104C5×#95—24no—
105C5×#95—22no—
106C5×#95—22no—
107C5×#95—44no—
108C22×#99C2×C511yescharacteristic
109#2308C2×C511yescharacteristic
110C2×#386C2×C511yescharacteristic
111C2×#385C2×C511yescharacteristic, complemented
112C2×#342C2×C511yescharacteristic, complemented
113C2×#342C2×C511yescharacteristic, complemented
114C22⋊#95C2×C511yescharacteristic, complemented
115C24×C5—21no—
116C24×C5—21no—
117C24×C5—21no—
118C24×C5—21no—
119C24×C5—21no—
120C24×C5—21no—
121C24×C5—42no—
122C24×C5—42no—
123C24×C5—42no—
124C24×C5—42no—
125C24×C5C4⋊C412yescomplemented
126C24×C5C22×C411yescharacteristic
127C24×C5C2×D411yescharacteristic
128C24×C5C2×D411yescharacteristic
129C24×C5C2×D411yescharacteristic
130C24×C5C2×D411yescharacteristic
131C24×C5C2×D411yescharacteristic
132C24×C5C2×D411yescharacteristic
133C24×C5C2×D411yescharacteristic
134C24×C5C2×Q811yescharacteristic
135C24×C5#4111yescharacteristic
136C24×C5#4111yescharacteristic
137C24×C5#4111yescharacteristic
138C24×C5#4111yescharacteristic
139C24×C5#4111yescharacteristic
140C24×C5#4111yescharacteristic
141C2×C5×D4—22no—
142C2×C5×D4—22no—
143C2×C5×D4—22no—
144C2×C5×D4—22no—
145C2×C5×D4—22no—
146C2×C5×D4—22no—
147C2×C5×D4—22no—
148C2×C5×D4—22no—
149C2×C5×D4—22no—
150C2×C5×D4—22no—
151C2×C5×D4—22no—
152C2×C5×D4—22no—
153C2×C5×D4—41no—
154C2×C5×D4—41no—
155C2×C5×D4—41no—
156C2×C5×D4—41no—
157C2×C5×D4—41no—
158C2×C5×D4—41no—
159C2×C5×D4—41no—
160C2×C5×D4—41no—
161C2×C5×D4—41no—
162C2×C5×D4—41no—
163C2×C5×D4—41no—
164C2×C5×D4—41no—
165C2×C5×D4—41no—
166C2×C5×D4—41no—
167C2×C5×D4—41no—
168C2×C5×D4—41no—
169C22×C4×C5—24no—
170C22×C4×C5—24no—
171C22×C4×C5—24no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—22no—
195C22×C4×C5—44no—
196C22×C4×C5—44no—
197C22×C4×C5—44no—
198C22×C4×C5—44no—
199C22×C4×C5—42no—
200C22×C4×C5—42no—
201C22×C4×C5—42no—
202C22×C4×C5—42no—
203C22×C4×C5—42no—
204C22×C4×C5—41no—
205C22×C4×C5—41no—
206C22×C4×C5—41no—
207C22×C4×C5—41no—
208C22×C4×C5—42no—
209C22×C4×C5—42no—
210C22×C4×C5—42no—
211C22×C4×C5—42no—
212C22×C4×C5—42no—
213C22×C4×C5—42no—
214C22×C4×C5—42no—
215C22×C4×C5—42no—
216C22×C4×C5—41no—
217C22×C4×C5—41no—
218C22×C4×C5—41no—
219C22×C4×C5—41no—
220C22×C4×C5C4⋊C412yescomplemented
221C5×C4⋊C4—48no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—48no—
230C5×C22⋊C4—41no—
231C5×C22⋊C4—41no—
232C5×C22⋊C4—41no—
233C5×C22⋊C4—41no—
234C5×C22⋊C4—41no—
235C5×C22⋊C4—41no—
236C5×C22⋊C4—41no—
237C5×C22⋊C4—41no—
238C5×C22⋊C4—41no—
239C5×C22⋊C4—41no—
240C5×C22⋊C4—41no—
241C5×C22⋊C4—41no—
242C5×C22⋊C4—82no—
243C5×C22⋊C4—82no—
244C5×C22⋊C4C22⋊C414yescomplemented
245C23×D4C22×C511yescharacteristic
246C24×C4C22×C511yescharacteristic
247C22×C4⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4C22×C511yescharacteristic
250C22×C22⋊C4C22×C511yescharacteristic
251C22×C22⋊C4C22×C511yescharacteristic
252C22×C22⋊C4C22×C511yescharacteristic
253C22×C22⋊C4C22×C511yescharacteristic
254C2×#99—22no—
255C2×#99—22no—
256C2×#99C4×C514yescomplemented
257#386—21no—
258#386—21no—
259#386—22no—
260#386—22no—
261#386—22no—
262#385—22no—
263#385—22no—
264#381—21no—
265#379—21no—
266C2×#95—21no—
267C2×#95—21no—
268C2×#95—22no—
269#342—22no—
270#342—22no—
271C23×C5—22no—
272C23×C5—22no—
273C23×C5—22no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—22no—
278C23×C5—22no—
279C23×C5—22no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5—42no—
285C23×C5—41no—
286C23×C5—41no—
287C23×C5—41no—
288C23×C5—42no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5—42no—
292C23×C5—41no—
293C23×C5—42no—
294C23×C5—42no—
295C23×C5—42no—
296C23×C5—44no—
297C23×C5—42no—
298C23×C5—42no—
299C23×C5—44no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—42no—
305C23×C5—42no—
306C23×C5—82no—
307C23×C5—81no—
308C23×C5—81no—
309C23×C5—82no—
310C23×C5C2×C22⋊C411yescharacteristic
311C23×C5C2×C4⋊C411yescharacteristic
312C23×C5#11711yescharacteristic
313C23×C5C4×D411yescharacteristic
314C23×C5C4×D411yescharacteristic
315C23×C5C4×D411yescharacteristic
316C23×C5C4×D411yescharacteristic
317C23×C5#12011yescharacteristic
318C23×C5#12011yescharacteristic
319C23×C5#12011yescharacteristic
320C23×C5#12111yescharacteristic
321C23×C5#12111yescharacteristic
322C23×C5#12111yescharacteristic
323C23×C5#12111yescharacteristic
324C23×C5#12111yescharacteristic
325C23×C5#12111yescharacteristic
326C23×C5#12111yescharacteristic
327C23×C5#12111yescharacteristic
328C23×C5C22⋊Q811yescharacteristic
329C23×C5C22⋊Q811yescharacteristic
330C23×C5C22⋊Q811yescharacteristic
331C23×C5C22⋊Q811yescharacteristic
332C23×C5C22⋊Q811yescharacteristic
333C23×C5C22⋊Q811yescharacteristic
334C23×C5#12311yescharacteristic
335C23×C5#12311yescharacteristic
336C23×C5#12311yescharacteristic
337C23×C5#12311yescharacteristic
338C23×C5#12311yescharacteristic
339C23×C5#12411yescharacteristic
340C23×C5#12411yescharacteristic
341C23×C5#12411yescharacteristic
342C23×C5#12611yescharacteristic
343C23×C5#12611yescharacteristic
344C23×C5#12711yescharacteristic
345C5×D4—42no—
346C5×D4—42no—
347C5×D4—42no—
348C5×D4—42no—
349C5×D4—42no—
350C5×D4—42no—
351C5×D4—42no—
352C5×D4—42no—
353C2×C4×C5—24no—
354C2×C4×C5—24no—
355C2×C4×C5—24no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—24no—
360C2×C4×C5—42no—
361C2×C4×C5—44no—
362C2×C4×C5—42no—
363C2×C4×C5—44no—
364C2×C4×C5—42no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—42no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—44no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5—44no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—44no—
382C2×C4×C5—42no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5—42no—
391C2×C4×C5—82no—
392C2×C4×C5—81no—
393C2×C4×C5—81no—
394C2×C4×C5—82no—
395C2×C4×C5—82no—
396C2×C4×C5—81no—
397C2×C4×C5—81no—
398C2×C4×C5—82no—
399C25C5×D411yescharacteristic
400C25C23×C511yescharacteristic
401C22×D4—21no—
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—21no—
405C22×D4—21no—
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4C2×C4×C512yes—
414C22×D4C5×Q812yes—
415C23×C4—21no—
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—44no—
425C23×C4C5×D411yescharacteristic
426C23×C4C5×D411yescharacteristic
427C23×C4C5×D411yescharacteristic
428C23×C4C5×D412yes—
429C23×C4C5×D412yes—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—44no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—44no—
461C2×C22⋊C4C2×C4×C512yes—
462C2×C22⋊C4C2×C4×C512yes—
463C2×C22⋊C4C5×D412yes—
464C2×C22⋊C4C5×D412yes—
465C2×C22⋊C4C5×D412yes—
466#99—28no—
467#95—24no—
468#95—24no—
469#95—22no—
470#95—22no—
471#95—44no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5—22no—
475C22×C5—22no—
476C22×C5—22no—
477C22×C5—22no—
478C22×C5—21no—
479C22×C5—21no—
480C22×C5—21no—
481C22×C5—21no—
482C22×C5—21no—
483C22×C5—21no—
484C22×C5—21no—
485C22×C5—21no—
486C22×C5—21no—
487C22×C5—21no—
488C22×C5—21no—
489C22×C5—21no—
490C22×C5—22no—
491C22×C5—22no—
492C22×C5—22no—
493C22×C5—22no—
494C22×C5—22no—
495C22×C5—22no—
496C22×C5—41no—
497C22×C5—41no—
498C22×C5—41no—
499C22×C5—41no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5—41no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5—41no—
506C22×C5—41no—
507C22×C5—41no—
508C22×C5—41no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5—44no—
513C22×C5—44no—
514C22×C5—42no—
515C22×C5—82no—
516C22×C5—82no—
517C22×C5—82no—
518C22×C5—81no—
519C22×C5—81no—
520C22×C5—82no—
521C22×C5#38011yescharacteristic
522C22×C5#38511yescharacteristic
523C22×C5#38511yescharacteristic
524C22×C5#38611yescharacteristic
525C22×C5#38811yescharacteristic
526C22×C5#38811yescharacteristic
527C22×C5#39011yescharacteristic
528C22×C5#39211yescharacteristic
529C22×C5#39311yescharacteristic
530C22×C5#39411yescharacteristic
531C22×C5#39411yescharacteristic
532C22×C5#39611yescharacteristic
533C22×C5#39611yescharacteristic
534C22×C5#39711yescharacteristic
535C22×C5#39911yescharacteristic
536C22×C5B(4,𝔽2)12yes—
537C22×C5#45812yes—
538C4×C5—44no—
539C4×C5—42no—
540C4×C5—44no—
541C4×C5—82no—
542C4×C5—82no—
543C4×C5—81no—
544C4×C5—81no—
545C4×C5—82no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24C5×C4⋊C412yescomplemented
557C24C22×C4×C511yescharacteristic
558C24C2×C5×D411yescharacteristic
559C24C2×C5×D411yescharacteristic
560C24C2×C5×D411yescharacteristic
561C24C2×C5×D411yescharacteristic
562C24C2×C5×D411yescharacteristic
563C24C2×C5×D411yescharacteristic
564C24C2×C5×D411yescharacteristic
565C24C2×C5×Q811yescharacteristic
566C24C5×#4111yescharacteristic
567C24C5×#4111yescharacteristic
568C24C5×#4111yescharacteristic
569C24C5×#4111yescharacteristic
570C24C5×#4111yescharacteristic
571C24C5×#4111yescharacteristic
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4C5×C4⋊C412yescomplemented
652C4⋊C4—48no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—48no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4C5×C22⋊C414yescomplemented
676C2×C5—21no—
677C2×C5—21no—
678C2×C5—21no—
679C2×C5—21no—
680C2×C5—21no—
681C2×C5—21no—
682C2×C5—21no—
683C2×C5—21no—
684C2×C5—21no—
685C2×C5—21no—
686C2×C5—21no—
687C2×C5—21no—
688C2×C5—82no—
689C2×C5#143911yescharacteristic
690C2×C5#186712yes—
691C2×C5#202111yescharacteristic
692C2×C5#202211yescharacteristic
693C2×C5#204412yes—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—42no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—44no—
720C23—42no—
721C23—42no—
722C23—44no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—82no—
730C23—81no—
731C23—81no—
732C23—82no—
733C23C2×C5×C22⋊C411yescharacteristic
734C23C2×C5×C4⋊C411yescharacteristic
735C23C5×#11711yescharacteristic
736C23C4×C5×D411yescharacteristic
737C23C4×C5×D411yescharacteristic
738C23C4×C5×D411yescharacteristic
739C23C4×C5×D411yescharacteristic
740C23C5×#12011yescharacteristic
741C23C5×#12011yescharacteristic
742C23C5×#12011yescharacteristic
743C23C5×#12111yescharacteristic
744C23C5×#12111yescharacteristic
745C23C5×#12111yescharacteristic
746C23C5×#12111yescharacteristic
747C23C5×#12111yescharacteristic
748C23C5×#12111yescharacteristic
749C23C5×#12111yescharacteristic
750C23C5×#12111yescharacteristic
751C23C5×C22⋊Q811yescharacteristic
752C23C5×C22⋊Q811yescharacteristic
753C23C5×C22⋊Q811yescharacteristic
754C23C5×C22⋊Q811yescharacteristic
755C23C5×C22⋊Q811yescharacteristic
756C23C5×C22⋊Q811yescharacteristic
757C23C5×#12311yescharacteristic
758C23C5×#12311yescharacteristic
759C23C5×#12311yescharacteristic
760C23C5×#12311yescharacteristic
761C23C5×#12311yescharacteristic
762C23C5×#12411yescharacteristic
763C23C5×#12411yescharacteristic
764C23C5×#12411yescharacteristic
765C23C5×#12611yescharacteristic
766C23C5×#12611yescharacteristic
767C23C5×#12711yescharacteristic
768D4—42no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—82no—
822C5#1108711yescharacteristic, direct product factor, Sylow
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—81no—
870C22—81no—
871C22—82no—
872C22C5×#38011yescharacteristic
873C22C5×#38511yescharacteristic
874C22C5×#38511yescharacteristic
875C22C5×#38611yescharacteristic
876C22C5×#38811yescharacteristic
877C22C5×#38811yescharacteristic
878C22C5×#39011yescharacteristic
879C22C5×#39211yescharacteristic
880C22C5×#39311yescharacteristic
881C22C5×#39411yescharacteristic
882C22C5×#39411yescharacteristic
883C22C5×#39611yescharacteristic
884C22C5×#39611yescharacteristic
885C22C5×#39711yescharacteristic
886C22C5×#39911yescharacteristic
887C22C5×B(4,𝔽2)12yes—
888C22C5×#45812yes—
889C4—44no—
890C4—44no—
891C4—42no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4—82no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—82no—
910C2C5×#143911yescharacteristic
911C2C5×#186712yes—
912C2C5×#202111yescharacteristic
913C2C5×#202211yescharacteristic
914C2C5×#204412yes—
subgroupG/H
center, socleC23×C5#120
commutatorC24C22×C4×C5
Frattini, cosocleC25C23×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C5×#385C2semidirect
5. C2×C5×#342C2semidirect
6. C2×C5×#342C2semidirect
7. C5×C22⋊#95C2semidirect
19. C2×C5×#99C4semidirect
34. #11087C5direct (N × H)
111. C2×#385C2×C5semidirect
112. C2×#342C2×C5semidirect
113. C2×#342C2×C5semidirect
114. C22⋊#95C2×C5semidirect
125. C24×C5C4⋊C4semidirect
220. C22×C4×C5C4⋊C4semidirect
244. C5×C22⋊C4C22⋊C4semidirect
256. C2×#99C4×C5semidirect
556. C24C5×C4⋊C4semidirect
651. C22×C4C5×C4⋊C4semidirect
675. C22⋊C4C5×C22⋊C4semidirect
822. C5#11087direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#992
C5×#23082
C2×C5×#3862
C2×C5×#3852
C2×C5×#3422
C5×C22⋊#952
#110875