Finite Group Databasebeta

← C5×#29744 #11952464

Subgroups — C5×#29744 #11952464

Order 1280.

1168 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#468C211yesmaximal, characteristic, complemented
2C2×C5×#407C211yesmaximal, characteristic, complemented
3C5×#2848C211yesmaximal, characteristic, complemented
4C5×#2847C211yesmaximal, characteristic
5C5×#2076C211yesmaximal, characteristic, complemented
6C5×#2075C211yesmaximal, characteristic, complemented
7C5×#2036C211yesmaximal, characteristic, complemented
8C5×#2035C211yesmaximal, characteristic, complemented
9C5×#2034C211yesmaximal, characteristic, complemented
10C5×#2033C211yesmaximal, characteristic, complemented
11C5×#2000C211yesmaximal, characteristic, complemented
12C5×#2000C211yesmaximal, characteristic, complemented
13C5×#1895C211yesmaximal, characteristic, complemented
14C5×#1894C211yesmaximal, characteristic, complemented
15C5×#1809C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic, complemented
18C22×C5×M16C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C5×#121C2211yescharacteristic
24C2×C5×#121C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C2×C5×#120—21no—
27C5×#468—24no—
28C2×C5×#107C2211yescharacteristic, complemented
29C2×C5×#107C2211yescharacteristic, complemented
30C2×C5×#106C2211yescharacteristic, complemented
31C2×C5×#103C2211yescharacteristic, complemented
32C2×C5×#103C2211yescharacteristic, complemented
33C2×C5×#103C2211yescharacteristic, complemented
34C2×C5×#102C2211yescharacteristic, complemented
35C2×C5×#102C2211yescharacteristic, complemented
36C2×C5×#102C2211yescharacteristic, complemented
37C5×#407—24no—
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×C22⋊C8C2211yescharacteristic
41C2×C5×C22⋊C8C2211yescharacteristic
42C5×#386—21no—
43C5×#386—21no—
44C5×#386—21no—
45C5×#385—21no—
46C5×#385—21no—
47C5×#385—21no—
48C5×#380C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C5×#380C2211yescharacteristic
54C5×#379—21no—
55C5×#340C2211yescharacteristic, complemented
56C5×#340C2211yescharacteristic, complemented
57C5×#340C2211yescharacteristic, complemented
58C5×#340C2211yescharacteristic, complemented
59C5×#340C2211yescharacteristic, complemented
60C5×#340C2211yescharacteristic, complemented
61#29744C511yesmaximal, characteristic, direct product factor, Sylow
62C25×C5D411yescharacteristic
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4—21no—
65C22×C5×D4—21no—
66C22×C5×D4—21no—
67C22×C5×D4C2311yescharacteristic
68C23×C4×C5—22no—
69C23×C4×C5—22no—
70C23×C4×C5—41no—
71C23×C4×C5—41no—
72C23×C4×C5—41no—
73C23×C4×C5—41no—
74C23×C4×C5D411yescharacteristic
75C23×C4×C5D411yescharacteristic
76C23×C4×C5D411yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C2×C5×SD16—22no—
81C2×C5×SD16—41no—
82C2×C5×SD16—41no—
83C2×C5×M16—22no—
84C2×C5×M16—41no—
85C2×C5×M16—41no—
86C2×C5×M16—41no—
87C2×C5×M16—41no—
88C2×C5×M16D414yescomplemented
89C22×C5×C8C2311yescharacteristic
90C22×C5×C8C2311yescharacteristic
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2311yescharacteristic
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8—41no—
96C5×C22⋊Q8—41no—
97C5×C22⋊Q8—41no—
98C5×C22⋊Q8—41no—
99C5×#121—22no—
100C5×#121—22no—
101C5×#121—41no—
102C5×#121—41no—
103C5×#121—41no—
104C5×#121—41no—
105C5×#120—44no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4—21no—
127C5×#107—22no—
128C5×#107—41no—
129C5×#106—41no—
130C5×#103—22no—
131C5×#103—41no—
132C5×#103—41no—
133C5×#102—22no—
134C5×#102—41no—
135C5×#102—41no—
136C5×C22⋊C8—22no—
137C5×C22⋊C8—22no—
138C5×C22⋊C8—22no—
139C5×C22⋊C8—22no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C5×#95—21no—
144C5×#95—21no—
145C5×#95—21no—
146C2×#468C2×C511yescharacteristic, complemented
147C2×#407C2×C511yescharacteristic, complemented
148#2848C2×C511yescharacteristic, complemented
149#2847C2×C511yescharacteristic
150#2076C2×C511yescharacteristic, complemented
151#2075C2×C511yescharacteristic, complemented
152#2036C2×C511yescharacteristic, complemented
153#2035C2×C511yescharacteristic, complemented
154#2034C2×C511yescharacteristic, complemented
155#2033C2×C511yescharacteristic, complemented
156#2000C2×C511yescharacteristic, complemented
157#2000C2×C511yescharacteristic, complemented
158#1895C2×C511yescharacteristic, complemented
159#1894C2×C511yescharacteristic, complemented
160#1809C2×C511yescharacteristic, complemented
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—21no—
165C24×C5—41no—
166C24×C5—41no—
167C24×C5—41no—
168C24×C5—41no—
169C24×C5C2×D411yescharacteristic
170C24×C5C2×D411yescharacteristic
171C24×C5C2×D411yescharacteristic
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8—21no—
177C2×C5×Q8—21no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4—21no—
181C2×C5×D4—21no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—42no—
185C2×C5×D4—42no—
186C2×C5×D4—42no—
187C2×C5×D4—42no—
188C2×C5×D4—42no—
189C2×C5×D4—42no—
190C2×C5×D4—42no—
191C2×C5×D4—42no—
192C2×C5×D4—42no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—41no—
220C22×C4×C5—41no—
221C22×C4×C5—41no—
222C22×C4×C5—41no—
223C22×C4×C5—41no—
224C22×C4×C5—41no—
225C22×C4×C5—44no—
226C22×C4×C5—44no—
227C22×C4×C5—44no—
228C22×C4×C5—44no—
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D412yes—
233C22×C4×C5#4112yes—
234C22×C4×C5C2411yescharacteristic
235C5×SD16—44no—
236C5×M16—44no—
237C5×M16—44no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—21no—
243C2×C5×C8—21no—
244C2×C5×C8—21no—
245C2×C5×C8—21no—
246C2×C5×C8—21no—
247C2×C5×C8—21no—
248C2×C5×C8C2×D412yes—
249C2×C5×C8C2×D412yes—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—42no—
263C5×C4⋊C4—42no—
264C5×C4⋊C4—42no—
265C5×C22⋊C4—42no—
266C5×C22⋊C4—42no—
267C5×C22⋊C4—42no—
268C5×C22⋊C4—42no—
269C5×C22⋊C4—42no—
270C5×C22⋊C4—42no—
271C5×C22⋊C4—42no—
272C5×C22⋊C4—42no—
273C5×C22⋊C4—42no—
274C5×C22⋊C4—42no—
275C5×C22⋊C4—42no—
276C5×C22⋊C4—42no—
277C24×C4C22×C511yescharacteristic
278C22×SD16C22×C511yescharacteristic, complemented
279C22×M16C22×C511yescharacteristic
280C22×M16C22×C511yescharacteristic
281C2×C22⋊Q8C22×C511yescharacteristic
282C2×C22⋊Q8C22×C511yescharacteristic
283C2×C22⋊Q8C22×C511yescharacteristic
284C2×#121C22×C511yescharacteristic
285C2×#121C22×C511yescharacteristic
286C2×#121C22×C511yescharacteristic
287C2×#120—21no—
288#468—24no—
289C2×#107C22×C511yescharacteristic, complemented
290C2×#107C22×C511yescharacteristic, complemented
291C2×#106C22×C511yescharacteristic, complemented
292C2×#103C22×C511yescharacteristic, complemented
293C2×#103C22×C511yescharacteristic, complemented
294C2×#103C22×C511yescharacteristic, complemented
295C2×#102C22×C511yescharacteristic, complemented
296C2×#102C22×C511yescharacteristic, complemented
297C2×#102C22×C511yescharacteristic, complemented
298#407—24no—
299C2×C22⋊C8C22×C511yescharacteristic
300C2×C22⋊C8C22×C511yescharacteristic
301C2×C22⋊C8C22×C511yescharacteristic
302C2×C22⋊C8C22×C511yescharacteristic
303#386—21no—
304#386—21no—
305#386—21no—
306#385—21no—
307#385—21no—
308#385—21no—
309#380C22×C511yescharacteristic
310#380C22×C511yescharacteristic
311#380C22×C511yescharacteristic
312#380C22×C511yescharacteristic
313#380C22×C511yescharacteristic
314#380C22×C511yescharacteristic
315#379—21no—
316#340C22×C511yescharacteristic, complemented
317#340C22×C511yescharacteristic, complemented
318#340C22×C511yescharacteristic, complemented
319#340C22×C511yescharacteristic, complemented
320#340C22×C511yescharacteristic, complemented
321#340C22×C511yescharacteristic, complemented
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5—21no—
334C23×C5—21no—
335C23×C5—21no—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—44no—
341C23×C5—44no—
342C23×C5—44no—
343C23×C5—44no—
344C23×C5—44no—
345C23×C5—44no—
346C23×C5—44no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5#12112yes—
355C23×C5AGL(1,ℤ/8)12yes—
356C23×C5#13712yes—
357C23×C5C22×D411yescharacteristic
358C5×Q8—41no—
359C5×Q8—41no—
360C5×Q8—41no—
361C5×Q8—41no—
362C5×D4—41no—
363C5×D4—41no—
364C5×D4—41no—
365C5×D4—41no—
366C5×D4—84no—
367C5×D4—84no—
368C5×D4—84no—
369C2×C4×C5—21no—
370C2×C4×C5—21no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—21no—
376C2×C4×C5—21no—
377C2×C4×C5—21no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
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#12112yes—
414C2×C4×C5C22×D411yescharacteristic
415C2×C4×C5C2×#4111yescharacteristic
416C2×C4×C5H(5,𝔽2)11yescharacteristic
417C2×C4×C5H(5,𝔽2)11yescharacteristic
418C2×C4×C5H(5,𝔽2)11yescharacteristic
419C2×C4×C5H(5,𝔽2)11yescharacteristic
420C5×C8—22no—
421C5×C8—22no—
422C5×C8—41no—
423C5×C8—41no—
424C25C5×D411yescharacteristic
425C22×Q8C23×C511yescharacteristic
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4C23×C511yescharacteristic
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—41no—
435C23×C4—41no—
436C23×C4C5×D411yescharacteristic
437C23×C4C5×D411yescharacteristic
438C23×C4C5×D411yescharacteristic
439C23×C4C23×C511yescharacteristic
440C23×C4C23×C511yescharacteristic
441C23×C4C23×C511yescharacteristic
442C2×SD16—22no—
443C2×SD16—41no—
444C2×SD16—41no—
445C2×M16—22no—
446C2×M16—41no—
447C2×M16—41no—
448C2×M16—41no—
449C2×M16—41no—
450C2×M16C5×D414yescomplemented
451C22×C8C23×C511yescharacteristic
452C22×C8C23×C511yescharacteristic
453C22×C8C23×C511yescharacteristic
454C22×C8C23×C511yescharacteristic
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—41no—
458C22⋊Q8—41no—
459C22⋊Q8—41no—
460C22⋊Q8—41no—
461#121—22no—
462#121—22no—
463#121—41no—
464#121—41no—
465#121—41no—
466#121—41no—
467#120—44no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4C23×C511yescharacteristic
472C2×C4⋊C4C23×C511yescharacteristic
473C2×C4⋊C4C23×C511yescharacteristic
474C2×C4⋊C4C23×C511yescharacteristic
475C2×C4⋊C4C23×C511yescharacteristic
476C2×C4⋊C4C23×C511yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489#107—22no—
490#107—41no—
491#106—41no—
492#103—22no—
493#103—41no—
494#103—41no—
495#102—22no—
496#102—41no—
497#102—41no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508C22×C5—22no—
509C22×C5—22no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—22no—
513C22×C5—22no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5—22no—
517C22×C5—416no—
518C22×C5—41no—
519C22×C5—41no—
520C22×C5—41no—
521C22×C5—41no—
522C22×C5—41no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5—41no—
528C22×C5—41no—
529C22×C5—41no—
530C22×C5—81no—
531C22×C5—81no—
532C22×C5—81no—
533C22×C5—81no—
534C22×C5—81no—
535C22×C5—81no—
536C22×C5—81no—
537C22×C5C2×#12111yescharacteristic
538C22×C5#53411yescharacteristic
539C22×C5#53411yescharacteristic
540C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
541C22×C5C2×#13711yescharacteristic
542C22×C5#57511yescharacteristic
543C22×C5#57511yescharacteristic
544C4×C5—22no—
545C4×C5—41no—
546C4×C5—41no—
547C4×C5—81no—
548C4×C5—81no—
549C4×C5—81no—
550C4×C5—81no—
551C4×C5—81no—
552C4×C5—81no—
553C4×C5—81no—
554C4×C5#53411yescharacteristic
555C4×C5#53511yescharacteristic
556C4×C5#53811yescharacteristic
557C4×C5#53811yescharacteristic
558C24—22no—
559C24—22no—
560C24—22no—
561C24—21no—
562C24—41no—
563C24—41no—
564C24—41no—
565C24—41no—
566C24C2×C5×D411yescharacteristic
567C24C2×C5×D411yescharacteristic
568C24C2×C5×D411yescharacteristic
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×C5×D411yescharacteristic
627C22×C4C2×C5×D411yescharacteristic
628C22×C4C2×C5×D411yescharacteristic
629C22×C4C2×C5×D412yes—
630C22×C4C5×#4112yes—
631C22×C4C24×C511yescharacteristic
632SD16—44no—
633M16—44no—
634M16—44no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8C2×C5×D412yes—
646C2×C8C2×C5×D412yes—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C2×C5—42no—
675C2×C5—42no—
676C2×C5—42no—
677C2×C5—161no—
678C2×C5#261711yescharacteristic
679C2×C5#305511yescharacteristic
680C2×C5#305611yescharacteristic
681C2×C5#319311yescharacteristic
682C2×C5#319411yescharacteristic
683C2×C5#319611yescharacteristic
684C2×C5#319711yescharacteristic
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C5×#12112yes—
718C23C5×AGL(1,ℤ/8)12yes—
719C23C5×#13712yes—
720C23C22×C5×D411yescharacteristic
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
730D4—84no—
731D4—84no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4C5×#12112yes—
777C2×C4C22×C5×D411yescharacteristic
778C2×C4C2×C5×#4111yescharacteristic
779C2×C4C5×H(5,𝔽2)11yescharacteristic
780C2×C4C5×H(5,𝔽2)11yescharacteristic
781C2×C4C5×H(5,𝔽2)11yescharacteristic
782C2×C4C5×H(5,𝔽2)11yescharacteristic
783C8—22no—
784C8—22no—
785C8—41no—
786C8—41no—
787C5#2974411yescharacteristic, direct product factor, Sylow
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C2×C5×#12111yescharacteristic
818C22C5×#53411yescharacteristic
819C22C5×#53411yescharacteristic
820C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
821C22C2×C5×#13711yescharacteristic
822C22C5×#57511yescharacteristic
823C22C5×#57511yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C5×#53411yescharacteristic
835C4C5×#53511yescharacteristic
836C4C5×#53811yescharacteristic
837C4C5×#53811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—161no—
842C2C5×#261711yescharacteristic
843C2C5×#305511yescharacteristic
844C2C5×#305611yescharacteristic
845C2C5×#319311yescharacteristic
846C2C5×#319411yescharacteristic
847C2C5×#319611yescharacteristic
848C2C5×#319711yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C24×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#468C2semidirect
2. C2×C5×#407C2semidirect
3. C5×#2848C2semidirect
5. C5×#2076C2semidirect
6. C5×#2075C2semidirect
7. C5×#2036C2semidirect
8. C5×#2035C2semidirect
9. C5×#2034C2semidirect
10. C5×#2033C2semidirect
11. C5×#2000C2semidirect
12. C5×#2000C2semidirect
13. C5×#1895C2semidirect
14. C5×#1894C2semidirect
15. C5×#1809C2semidirect
17. C22×C5×SD16C22semidirect
28. C2×C5×#107C22semidirect
29. C2×C5×#107C22semidirect
30. C2×C5×#106C22semidirect
31. C2×C5×#103C22semidirect
32. C2×C5×#103C22semidirect
33. C2×C5×#103C22semidirect
34. C2×C5×#102C22semidirect
35. C2×C5×#102C22semidirect
36. C2×C5×#102C22semidirect
55. C5×#340C22semidirect
56. C5×#340C22semidirect
57. C5×#340C22semidirect
58. C5×#340C22semidirect
59. C5×#340C22semidirect
60. C5×#340C22semidirect
61. #29744C5direct (N × H)
88. C2×C5×M16D4semidirect
146. C2×#468C2×C5semidirect
147. C2×#407C2×C5semidirect
148. #2848C2×C5semidirect
150. #2076C2×C5semidirect
151. #2075C2×C5semidirect
152. #2036C2×C5semidirect
153. #2035C2×C5semidirect
154. #2034C2×C5semidirect
155. #2033C2×C5semidirect
156. #2000C2×C5semidirect
157. #2000C2×C5semidirect
158. #1895C2×C5semidirect
159. #1894C2×C5semidirect
160. #1809C2×C5semidirect
278. C22×SD16C22×C5semidirect
289. C2×#107C22×C5semidirect
290. C2×#107C22×C5semidirect
291. C2×#106C22×C5semidirect
292. C2×#103C22×C5semidirect
293. C2×#103C22×C5semidirect
294. C2×#103C22×C5semidirect
295. C2×#102C22×C5semidirect
296. C2×#102C22×C5semidirect
297. C2×#102C22×C5semidirect
316. #340C22×C5semidirect
317. #340C22×C5semidirect
318. #340C22×C5semidirect
319. #340C22×C5semidirect
320. #340C22×C5semidirect
321. #340C22×C5semidirect
450. C2×M16C5×D4semidirect
787. C5#29744direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4682
C2×C5×#4072
C5×#28482
C5×#28472
C5×#20762
C5×#20752
C5×#20362
C5×#20352
C5×#20342
C5×#20332
C5×#20002
C5×#18952
C5×#18942
C5×#18092
#297445