Finite Group Databasebeta

← C5×#24017 #11946737

Subgroups — C5×#24017 #11946737

Order 1280.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#537C211yesmaximal, characteristic
2C2×C5×#485C211yesmaximal, characteristic, complemented
3C2×C5×#482C211yesmaximal, characteristic, complemented
4C5×#2311C211yesmaximal, characteristic, complemented
5C5×#2036C211yesmaximal, characteristic, complemented
6C5×#2035C211yesmaximal, characteristic, complemented
7C5×#2034C211yesmaximal, characteristic, complemented
8C5×#2033C211yesmaximal, characteristic, complemented
9C5×#1874C211yesmaximal, characteristic, complemented
10C5×#1872C211yesmaximal, characteristic, complemented
11C5×#1853C211yesmaximal, characteristic, complemented
12C5×#1852C211yesmaximal, characteristic, complemented
13C5×#1788C211yesmaximal, characteristic, complemented
14C5×#1788C211yesmaximal, characteristic, complemented
15C5×#1780C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C22×C5×#41C2211yescharacteristic
18C5×#537—24no—
19C5×#537—24no—
20C2×C5×C22⋊Q8—21no—
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C5×#121—21no—
24C2×C5×#121—21no—
25C2×C5×#121—21no—
26C2×C5×#121C2211yescharacteristic
27C2×C5×#121C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C5×#485—24no—
32C5×#482—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#107C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#103C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×#102C2211yescharacteristic
44C2×C5×#102C2211yescharacteristic
45C2×C5×C22⋊C8C2211yescharacteristic
46C2×C5×C22⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C5×#391—21no—
52C5×#390—21no—
53C5×#386—21no—
54C5×#386—21no—
55C5×#380C2211yescharacteristic
56C5×#380C2211yescharacteristic
57C5×#380C2211yescharacteristic
58C5×#380C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#340C2211yescharacteristic
62C5×#340C2211yescharacteristic
63#24017C511yesmaximal, characteristic, direct product factor, Sylow
64C2×C5×#41—22no—
65C2×C5×#41—22no—
66C2×C5×#41—22no—
67C2×C5×#41—22no—
68C2×C5×#41—22no—
69C2×C5×#41—22no—
70C2×C5×#41—22no—
71C2×C5×#41—22no—
72C2×C5×#41—41no—
73C2×C5×#41—41no—
74C2×C5×#41—41no—
75C2×C5×#41—41no—
76C22×C5×Q8D411yescharacteristic
77C22×C5×Q8C2311yescharacteristic
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4D411yescharacteristic
82C22×C5×D4D411yescharacteristic
83C22×C5×D4D411yescharacteristic
84C22×C5×D4C2311yescharacteristic
85C23×C4×C5—21no—
86C23×C4×C5—21no—
87C23×C4×C5—21no—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2311yescharacteristic
93C22×C5×C8C2311yescharacteristic
94C22×C5×C8C2311yescharacteristic
95C5×C22⋊Q8—28no—
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8—22no—
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8D414yes—
100C5×#121—28no—
101C5×#121—28no—
102C5×#121—28no—
103C5×#121—22no—
104C5×#121—22no—
105C5×#121—22no—
106C5×#121D414yes—
107C5×#117—22no—
108C5×#117—22no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—22no—
113C2×C5×C4⋊C4—22no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—41no—
116C2×C5×C4⋊C4—41no—
117C2×C5×C4⋊C4C2311yescharacteristic
118C2×C5×C4⋊C4C2311yescharacteristic
119C2×C5×C4⋊C4C2311yescharacteristic
120C2×C5×C4⋊C4C2311yescharacteristic
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C4⋊C4C2311yescharacteristic
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4—21no—
127C2×C5×C22⋊C4—21no—
128C2×C5×C22⋊C4—21no—
129C2×C5×C22⋊C4—21no—
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—21no—
132C2×C42×C5—21no—
133C5×#107—22no—
134C5×#107—22no—
135C5×#106—22no—
136C5×#106—22no—
137C5×#103—22no—
138C5×#103—22no—
139C5×#103—41no—
140C5×#103—41no—
141C5×#102—22no—
142C5×#102—22no—
143C5×#102—41no—
144C5×#102—41no—
145C5×C22⋊C8—22no—
146C5×C22⋊C8—22no—
147C5×C22⋊C8—22no—
148C5×C22⋊C8—22no—
149C5×C22⋊C8—41no—
150C5×C22⋊C8—41no—
151C5×#95—21no—
152C5×#95—21no—
153C5×#95—21no—
154C5×#95—21no—
155C2×#537C2×C511yescharacteristic
156C2×#485C2×C511yescharacteristic, complemented
157C2×#482C2×C511yescharacteristic, complemented
158#2311C2×C511yescharacteristic, complemented
159#2036C2×C511yescharacteristic, complemented
160#2035C2×C511yescharacteristic, complemented
161#2034C2×C511yescharacteristic, complemented
162#2033C2×C511yescharacteristic, complemented
163#1874C2×C511yescharacteristic, complemented
164#1872C2×C511yescharacteristic, complemented
165#1853C2×C511yescharacteristic, complemented
166#1852C2×C511yescharacteristic, complemented
167#1788C2×C511yescharacteristic, complemented
168#1788C2×C511yescharacteristic, complemented
169#1780C2×C511yescharacteristic, complemented
170C24×C5—21no—
171C24×C5C2×D411yescharacteristic
172C24×C5C2×D411yescharacteristic
173C24×C5C2×D411yescharacteristic
174C5×#41—44no—
175C5×#41—44no—
176C5×#41—44no—
177C5×#41—44no—
178C5×#41—44no—
179C5×#41—44no—
180C5×#41—44no—
181C5×#41—44no—
182C2×C5×Q8—22no—
183C2×C5×Q8—22no—
184C2×C5×Q8—21no—
185C2×C5×Q8—21no—
186C2×C5×Q8—21no—
187C2×C5×Q8—21no—
188C2×C5×Q8—21no—
189C2×C5×Q8—41no—
190C2×C5×Q8C2×D412yes—
191C2×C5×D4—24no—
192C2×C5×D4—22no—
193C2×C5×D4—22no—
194C2×C5×D4—22no—
195C2×C5×D4—22no—
196C2×C5×D4—24no—
197C2×C5×D4—24no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4—21no—
201C2×C5×D4—21no—
202C2×C5×D4—21no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—41no—
206C2×C5×D4—41no—
207C2×C5×D4—41no—
208C2×C5×D4—42no—
209C2×C5×D4—42no—
210C2×C5×D4—81no—
211C2×C5×D4—81no—
212C2×C5×D4—81no—
213C2×C5×D4—81no—
214C2×C5×D4C2×D412yes—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—24no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—24no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—42no—
239C22×C4×C5—42no—
240C22×C4×C5—42no—
241C22×C4×C5—81no—
242C22×C4×C5—81no—
243C22×C4×C5—81no—
244C22×C4×C5—81no—
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D412yes—
248C22×C4×C5C2×D412yes—
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5#4112yes—
251C22×C4×C5#4112yes—
252C22×C4×C5C2411yescharacteristic
253C2×C5×C8—21no—
254C2×C5×C8—21no—
255C2×C5×C8—21no—
256C2×C5×C8—21no—
257C2×C5×C8—21no—
258C2×C5×C8—21no—
259C2×C5×C8—21no—
260C2×C5×C8—21no—
261C2×C5×C8—21no—
262C2×C5×C8—21no—
263C2×C5×C8—21no—
264C2×C5×C8—21no—
265C5×C4⋊C4—24no—
266C5×C4⋊C4—24no—
267C5×C4⋊C4—24no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—42no—
279C5×C4⋊C4C2×D412yes—
280C5×C4⋊C4C2×D412yes—
281C5×C22⋊C4—24no—
282C5×C22⋊C4—24no—
283C5×C22⋊C4—24no—
284C5×C22⋊C4—24no—
285C5×C22⋊C4—42no—
286C5×C22⋊C4—81no—
287C5×C22⋊C4—81no—
288C5×C22⋊C4—81no—
289C5×C22⋊C4—81no—
290C42×C5—42no—
291C22×#41C22×C511yescharacteristic
292C22×#41C22×C511yescharacteristic
293#537—24no—
294#537—24no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8C22×C511yescharacteristic
297C2×C22⋊Q8C22×C511yescharacteristic
298C2×#121—21no—
299C2×#121—21no—
300C2×#121—21no—
301C2×#121C22×C511yescharacteristic
302C2×#121C22×C511yescharacteristic
303C2×#117C22×C511yescharacteristic
304C22×C4⋊C4C22×C511yescharacteristic
305C22×C4⋊C4C22×C511yescharacteristic
306#485—24no—
307#482—24no—
308C2×#107C22×C511yescharacteristic
309C2×#107C22×C511yescharacteristic
310C2×#106C22×C511yescharacteristic
311C2×#106C22×C511yescharacteristic
312C2×#103C22×C511yescharacteristic
313C2×#103C22×C511yescharacteristic
314C2×#103C22×C511yescharacteristic
315C2×#103C22×C511yescharacteristic
316C2×#102C22×C511yescharacteristic
317C2×#102C22×C511yescharacteristic
318C2×#102C22×C511yescharacteristic
319C2×#102C22×C511yescharacteristic
320C2×C22⋊C8C22×C511yescharacteristic
321C2×C22⋊C8C22×C511yescharacteristic
322C2×C22⋊C8C22×C511yescharacteristic
323C2×C22⋊C8C22×C511yescharacteristic
324C2×C22⋊C8C22×C511yescharacteristic
325C2×C22⋊C8C22×C511yescharacteristic
326#391—21no—
327#390—21no—
328#386—21no—
329#386—21no—
330#380C22×C511yescharacteristic
331#380C22×C511yescharacteristic
332#380C22×C511yescharacteristic
333#380C22×C511yescharacteristic
334#340C22×C511yescharacteristic
335#340C22×C511yescharacteristic
336#340C22×C511yescharacteristic
337#340C22×C511yescharacteristic
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—21no—
341C23×C5—21no—
342C23×C5—21no—
343C23×C5—21no—
344C23×C5—21no—
345C23×C5—21no—
346C23×C5—21no—
347C23×C5—21no—
348C23×C5—21no—
349C23×C5—21no—
350C23×C5—21no—
351C23×C5—22no—
352C23×C5—21no—
353C23×C5—21no—
354C23×C5—21no—
355C23×C5—21no—
356C23×C5—21no—
357C23×C5—21no—
358C23×C5—41no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5—41no—
362C23×C5—41no—
363C23×C5—41no—
364C23×C5#12012yes—
365C23×C5#12312yes—
366C23×C5C22×D411yescharacteristic
367C5×Q8—22no—
368C5×Q8—22no—
369C5×Q8—44no—
370C5×Q8—41no—
371C5×Q8—41no—
372C5×D4—22no—
373C5×D4—22no—
374C5×D4—44no—
375C5×D4—44no—
376C5×D4—44no—
377C5×D4—48no—
378C5×D4—41no—
379C5×D4—41no—
380C5×D4—84no—
381C5×D4—84no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—48no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—41no—
406C2×C4×C5—41no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—41no—
411C2×C4×C5—41no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—84no—
424C2×C4×C5—84no—
425C2×C4×C5#12012yes—
426C2×C4×C5#12312yes—
427C2×C4×C5C22×D411yescharacteristic
428C2×C4×C5C22×D411yescharacteristic
429C2×C4×C5C2×#4111yescharacteristic
430C2×C4×C5C2×#4111yescharacteristic
431C2×C4×C5H(5,𝔽2)11yescharacteristic
432C2×C4×C5H(5,𝔽2)11yescharacteristic
433C5×C8—41no—
434C5×C8—41no—
435C5×C8—41no—
436C5×C8—41no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C5×D411yescharacteristic
450C22×Q8C23×C511yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C5×D411yescharacteristic
455C22×D4C5×D411yescharacteristic
456C22×D4C5×D411yescharacteristic
457C22×D4C23×C511yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C23×C511yescharacteristic
462C23×C4C23×C511yescharacteristic
463C23×C4C23×C511yescharacteristic
464C22×C8C23×C511yescharacteristic
465C22×C8C23×C511yescharacteristic
466C22×C8C23×C511yescharacteristic
467C22×C8C23×C511yescharacteristic
468C22⋊Q8—28no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8C5×D414yes—
473#121—28no—
474#121—28no—
475#121—28no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121C5×D414yes—
480#117—22no—
481#117—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4C23×C511yescharacteristic
491C2×C4⋊C4C23×C511yescharacteristic
492C2×C4⋊C4C23×C511yescharacteristic
493C2×C4⋊C4C23×C511yescharacteristic
494C2×C4⋊C4C23×C511yescharacteristic
495C2×C4⋊C4C23×C511yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C42—21no—
506#107—22no—
507#107—22no—
508#106—22no—
509#106—22no—
510#103—22no—
511#103—22no—
512#103—41no—
513#103—41no—
514#102—22no—
515#102—22no—
516#102—41no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8—41no—
523C22⋊C8—41no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528C22×C5—22no—
529C22×C5—22no—
530C22×C5—22no—
531C22×C5—22no—
532C22×C5—22no—
533C22×C5—22no—
534C22×C5—41no—
535C22×C5—41no—
536C22×C5—41no—
537C22×C5—41no—
538C22×C5—41no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5—42no—
545C22×C5—41no—
546C22×C5—41no—
547C22×C5—41no—
548C22×C5—41no—
549C22×C5—42no—
550C22×C5—41no—
551C22×C5—42no—
552C22×C5—81no—
553C22×C5—81no—
554C22×C5—81no—
555C22×C5—81no—
556C22×C5C2×#12011yescharacteristic
557C22×C5C2×#12311yescharacteristic
558C22×C5#53411yescharacteristic
559C22×C5#57611yescharacteristic
560C22×C5#57711yescharacteristic
561C22×C5#57711yescharacteristic
562C22×C5#57811yescharacteristic
563C4×C5—22no—
564C4×C5—22no—
565C4×C5—41no—
566C4×C5—42no—
567C4×C5—42no—
568C4×C5—42no—
569C4×C5—81no—
570C4×C5—81no—
571C4×C5—81no—
572C4×C5—81no—
573C4×C5#54611yescharacteristic
574C4×C5#54611yescharacteristic
575C4×C5#54611yescharacteristic
576C4×C5#54611yescharacteristic
577C24—21no—
578C24C2×C5×D411yescharacteristic
579C24C2×C5×D411yescharacteristic
580C24C2×C5×D411yescharacteristic
581#41—44no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—41no—
597C2×Q8C2×C5×D412yes—
598C2×D4—24no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×C5×D412yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—81no—
649C22×C4—81no—
650C22×C4—81no—
651C22×C4—81no—
652C22×C4C2×C5×D411yescharacteristic
653C22×C4C2×C5×D411yescharacteristic
654C22×C4C2×C5×D412yes—
655C22×C4C2×C5×D412yes—
656C22×C4C2×C5×D411yescharacteristic
657C22×C4C5×#4112yes—
658C22×C4C5×#4112yes—
659C22×C4C24×C511yescharacteristic
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—42no—
686C4⋊C4C2×C5×D412yes—
687C4⋊C4C2×C5×D412yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—42no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—42no—
698C2×C5—42no—
699C2×C5—42no—
700C2×C5—81no—
701C2×C5—82no—
702C2×C5#240511yescharacteristic
703C2×C5#301211yescharacteristic
704C2×C5#301311yescharacteristic
705C2×C5#309811yescharacteristic
706C2×C5#309911yescharacteristic
707C2×C5#319811yescharacteristic
708C2×C5#320111yescharacteristic
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23C5×#12012yes—
736C23C5×#12312yes—
737C23C22×C5×D411yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—44no—
741Q8—41no—
742Q8—41no—
743D4—22no—
744D4—22no—
745D4—44no—
746D4—44no—
747D4—44no—
748D4—48no—
749D4—41no—
750D4—41no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—84no—
795C2×C4—84no—
796C2×C4C5×#12012yes—
797C2×C4C5×#12312yes—
798C2×C4C22×C5×D411yescharacteristic
799C2×C4C22×C5×D411yescharacteristic
800C2×C4C2×C5×#4111yescharacteristic
801C2×C4C2×C5×#4111yescharacteristic
802C2×C4C5×H(5,𝔽2)11yescharacteristic
803C2×C4C5×H(5,𝔽2)11yescharacteristic
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C5#2401711yescharacteristic, direct product factor, Sylow
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×C5×#12011yescharacteristic
838C22C2×C5×#12311yescharacteristic
839C22C5×#53411yescharacteristic
840C22C5×#57611yescharacteristic
841C22C5×#57711yescharacteristic
842C22C5×#57711yescharacteristic
843C22C5×#57811yescharacteristic
844C4—22no—
845C4—22no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C5×#54611yescharacteristic
855C4C5×#54611yescharacteristic
856C4C5×#54611yescharacteristic
857C4C5×#54611yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C5×#240511yescharacteristic
863C2C5×#301211yescharacteristic
864C2C5×#301311yescharacteristic
865C2C5×#309811yescharacteristic
866C2C5×#309911yescharacteristic
867C2C5×#319811yescharacteristic
868C2C5×#320111yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#485C2semidirect
3. C2×C5×#482C2semidirect
4. C5×#2311C2semidirect
5. C5×#2036C2semidirect
6. C5×#2035C2semidirect
7. C5×#2034C2semidirect
8. C5×#2033C2semidirect
9. C5×#1874C2semidirect
10. C5×#1872C2semidirect
11. C5×#1853C2semidirect
12. C5×#1852C2semidirect
13. C5×#1788C2semidirect
14. C5×#1788C2semidirect
15. C5×#1780C2semidirect
63. #24017C5direct (N × H)
156. C2×#485C2×C5semidirect
157. C2×#482C2×C5semidirect
158. #2311C2×C5semidirect
159. #2036C2×C5semidirect
160. #2035C2×C5semidirect
161. #2034C2×C5semidirect
162. #2033C2×C5semidirect
163. #1874C2×C5semidirect
164. #1872C2×C5semidirect
165. #1853C2×C5semidirect
166. #1852C2×C5semidirect
167. #1788C2×C5semidirect
168. #1788C2×C5semidirect
169. #1780C2×C5semidirect
808. C5#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5372
C2×C5×#4852
C2×C5×#4822
C5×#23112
C5×#20362
C5×#20352
C5×#20342
C5×#20332
C5×#18742
C5×#18722
C5×#18532
C5×#18522
C5×#17882
C5×#17802
#240175