Finite Group Databasebeta

← C5×#14009 #11936729

Subgroups — C5×#14009 #11936729

Order 1280.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#387C211yesmaximal, characteristic
2C2×C5×#387C211yesmaximal, characteristic
3C2×C5×#382C211yesmaximal, characteristic
4C5×#1445C211yesmaximal, characteristic
5C5×#1444C211yesmaximal, characteristic
6C5×#1443C211yesmaximal, characteristic
7C5×#1442C211yesmaximal, characteristic
8C5×#1436C211yesmaximal, characteristic
9C5×#1436C211yesmaximal, characteristic
10C5×#1436C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic
12C5×#1436C211yesmaximal, characteristic
13C5×C4⋊#95C211yesmaximal, characteristic
14C4×C5×#95C211yesmaximal, characteristic
15C4×C5×#95C211yesmaximal, characteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C5×#387—24no—
28C5×#387C418yescomplemented
29C5×#382—24no—
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54#14009C511yesmaximal, characteristic, direct product factor, Sylow
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—41no—
83C2×C5×C4⋊C4—41no—
84C2×C5×C4⋊C4—41no—
85C2×C5×C4⋊C4—41no—
86C2×C5×C4⋊C4C2×C414yes—
87C2×C5×C4⋊C4C2×C414yes—
88C2×C42×C5—22no—
89C2×C42×C5—22no—
90C2×C42×C5—22no—
91C2×C42×C5—22no—
92C2×C42×C5—22no—
93C2×C42×C5—22no—
94C2×C42×C5—22no—
95C2×C42×C5—22no—
96C2×C42×C5—22no—
97C2×C42×C5—41no—
98C2×C42×C5—41no—
99C2×C42×C5—41no—
100C2×C42×C5—41no—
101C2×C42×C5—41no—
102C2×C42×C5C2×C414yes—
103C5×#95—22no—
104C5×#95—22no—
105C5×#95—22no—
106C5×#95—22no—
107C5×#95—22no—
108C5×#95—22no—
109C5×#95—22no—
110C5×#95—22no—
111C5×#95—22no—
112C5×#95—22no—
113C5×#95—22no—
114C5×#95—22no—
115C5×#95—22no—
116C5×#95—22no—
117C5×#95—22no—
118C5×#95—41no—
119C5×#95—41no—
120C5×#95—41no—
121C5×#95C2×C414yes—
122C5×#95C2×C414yes—
123C5×#95C2×C414yes—
124C5×#95C2×C414yes—
125C5×#95D414yes—
126C5×#95Q814yes—
127C2×#387C2×C511yescharacteristic
128C2×#387C2×C511yescharacteristic
129C2×#382C2×C511yescharacteristic
130#1445C2×C511yescharacteristic
131#1444C2×C511yescharacteristic
132#1443C2×C511yescharacteristic
133#1442C2×C511yescharacteristic
134#1436C2×C511yescharacteristic
135#1436C2×C511yescharacteristic
136#1436C2×C511yescharacteristic
137#1436C2×C511yescharacteristic
138#1436C2×C511yescharacteristic
139C4⋊#95C2×C511yescharacteristic
140C4×#95C2×C511yescharacteristic
141C4×#95C2×C511yescharacteristic
142C24×C5C2411yescharacteristic
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
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—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
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—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
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—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5C22×C412yes—
228C22×C4×C5C22×C412yes—
229C22×C4×C5C22×C412yes—
230C22×C4×C5C22×C412yes—
231C22×C4×C5C22×C412yes—
232C22×C4×C5C22×C412yes—
233C22×C4×C5C22×C412yes—
234C22×C4×C5C2×D412yes—
235C22×C4×C5C2×D412yes—
236C22×C4×C5C2×D412yes—
237C22×C4×C5C2×Q812yes—
238C22×C4×C5C2×Q812yes—
239C22×C4×C5C2×Q812yes—
240C22×C4×C5#4112yes—
241C22×C4×C5#4112yes—
242C22×C4×C5#4112yes—
243C22×C4×C5#4112yes—
244C22×C4×C5#4112yes—
245C22×C4×C5#4112yes—
246C22×C4×C5#4112yes—
247C22×C4×C5#4112yes—
248C5×C4⋊C4—28no—
249C5×C4⋊C4—28no—
250C5×C4⋊C4—44no—
251C5×C4⋊C4—44no—
252C5×C4⋊C4—44no—
253C5×C4⋊C4—44no—
254C42×C5—28no—
255C42×C5—44no—
256C42×C5—44no—
257C42×C5—44no—
258C42×C5—44no—
259C22×C4⋊C4C22×C511yescharacteristic
260C22×C4⋊C4C22×C511yescharacteristic
261C22×C4⋊C4C22×C511yescharacteristic
262C22×C4⋊C4C22×C511yescharacteristic
263C22×C4⋊C4C22×C511yescharacteristic
264C22×C4⋊C4C22×C511yescharacteristic
265C22×C42C22×C511yescharacteristic
266C22×C42C22×C511yescharacteristic
267C22×C42C22×C511yescharacteristic
268C22×C42C22×C511yescharacteristic
269C22×C42C22×C511yescharacteristic
270#387—24no—
271#387C4×C518yescomplemented
272#382—24no—
273C2×#95C22×C511yescharacteristic
274C2×#95C22×C511yescharacteristic
275C2×#95C22×C511yescharacteristic
276C2×#95C22×C511yescharacteristic
277C2×#95C22×C511yescharacteristic
278C2×#95C22×C511yescharacteristic
279C2×#95C22×C511yescharacteristic
280C2×#95C22×C511yescharacteristic
281C2×#95C22×C511yescharacteristic
282C2×#95C22×C511yescharacteristic
283C2×#95C22×C511yescharacteristic
284C2×#95C22×C511yescharacteristic
285C2×#95C22×C511yescharacteristic
286C2×#95C22×C511yescharacteristic
287C2×#95C22×C511yescharacteristic
288C2×#95C22×C511yescharacteristic
289C2×#95C22×C511yescharacteristic
290C2×#95C22×C511yescharacteristic
291C2×#95C22×C511yescharacteristic
292C2×#95C22×C511yescharacteristic
293C2×#95C22×C511yescharacteristic
294C2×#95C22×C511yescharacteristic
295C2×#95C22×C511yescharacteristic
296C2×#95C22×C511yescharacteristic
297C23×C5C23×C411yescharacteristic
298C23×C5C22×D411yescharacteristic
299C23×C5C22×Q811yescharacteristic
300C23×C5C2×#4111yescharacteristic
301C23×C5C2×#4111yescharacteristic
302C23×C5C2×#4111yescharacteristic
303C23×C5C2×#4111yescharacteristic
304C23×C5C2×#4111yescharacteristic
305C23×C5C2×#4111yescharacteristic
306C23×C5C2×#4111yescharacteristic
307C23×C5C2×#4111yescharacteristic
308C23×C5H(5,𝔽2)11yescharacteristic
309C23×C5H(5,𝔽2)11yescharacteristic
310C23×C52−1+411yescharacteristic
311C23×C52−1+411yescharacteristic
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
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—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
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#11714yes—
414C2×C4×C5C4×D414yes—
415C2×C4×C5C4×Q814yes—
416C2×C4×C5#12514yes—
417C23×C4C23×C511yescharacteristic
418C23×C4C23×C511yescharacteristic
419C23×C4C23×C511yescharacteristic
420C23×C4C23×C511yescharacteristic
421C23×C4C23×C511yescharacteristic
422C23×C4C23×C511yescharacteristic
423C23×C4C23×C511yescharacteristic
424C23×C4C23×C511yescharacteristic
425C23×C4C23×C511yescharacteristic
426C23×C4C23×C511yescharacteristic
427C23×C4C23×C511yescharacteristic
428C23×C4C23×C511yescharacteristic
429C23×C4C23×C511yescharacteristic
430C23×C4C23×C511yescharacteristic
431C23×C4C23×C511yescharacteristic
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4C2×C4×C514yes—
449C2×C4⋊C4C2×C4×C514yes—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—41no—
460C2×C42—41no—
461C2×C42—41no—
462C2×C42—41no—
463C2×C42—41no—
464C2×C42C2×C4×C514yes—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—41no—
481#95—41no—
482#95—41no—
483#95C2×C4×C514yes—
484#95C2×C4×C514yes—
485#95C2×C4×C514yes—
486#95C2×C4×C514yes—
487#95C5×D414yes—
488#95C5×Q814yes—
489C22×C5C2×#11711yescharacteristic
490C22×C5C2×C4×D411yescharacteristic
491C22×C5C2×C4×Q811yescharacteristic
492C22×C5C4×#4111yescharacteristic
493C22×C5C4×#4111yescharacteristic
494C22×C5#52011yescharacteristic
495C22×C5#52011yescharacteristic
496C22×C5C2×#12511yescharacteristic
497C22×C5#52911yescharacteristic
498C22×C5#52911yescharacteristic
499C22×C5#52911yescharacteristic
500C22×C5#52911yescharacteristic
501C22×C5#53211yescharacteristic
502C22×C5#53211yescharacteristic
503C22×C5#53311yescharacteristic
504C22×C5#53811yescharacteristic
505C22×C5#53911yescharacteristic
506C22×C5#54111yescharacteristic
507C22×C5#54211yescharacteristic
508C22×C5#54611yescharacteristic
509C22×C5#54611yescharacteristic
510C22×C5#54711yescharacteristic
511C22×C5D4×Q811yescharacteristic
512C22×C5#55111yescharacteristic
513C22×C5#55111yescharacteristic
514C22×C5#55111yescharacteristic
515C22×C5#55211yescharacteristic
516C22×C5#55211yescharacteristic
517C22×C5#55211yescharacteristic
518C22×C5#55211yescharacteristic
519C22×C5#55411yescharacteristic
520C22×C5#55411yescharacteristic
521C22×C5#55611yescharacteristic
522C22×C5#55711yescharacteristic
523C22×C5#55911yescharacteristic
524C4×C5—24no—
525C4×C5—24no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—42no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5—81no—
538C4×C5—81no—
539C24C24×C511yescharacteristic
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
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—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4C22×C4×C512yes—
625C22×C4C22×C4×C512yes—
626C22×C4C22×C4×C512yes—
627C22×C4C22×C4×C512yes—
628C22×C4C22×C4×C512yes—
629C22×C4C22×C4×C512yes—
630C22×C4C22×C4×C512yes—
631C22×C4C2×C5×D412yes—
632C22×C4C2×C5×D412yes—
633C22×C4C2×C5×D412yes—
634C22×C4C2×C5×Q812yes—
635C22×C4C2×C5×Q812yes—
636C22×C4C2×C5×Q812yes—
637C22×C4C5×#4112yes—
638C22×C4C5×#4112yes—
639C22×C4C5×#4112yes—
640C22×C4C5×#4112yes—
641C22×C4C5×#4112yes—
642C22×C4C5×#4112yes—
643C22×C4C5×#4112yes—
644C22×C4C5×#4112yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C42—28no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—44no—
656C2×C5#229311yescharacteristic
657C2×C5C4×#12511yescharacteristic
658C2×C5#233411yescharacteristic
659C2×C5#234311yescharacteristic
660C2×C5#235511yescharacteristic
661C2×C5#235911yescharacteristic
662C2×C5#236011yescharacteristic
663C2×C5#250511yescharacteristic
664C2×C5#250611yescharacteristic
665C2×C5#251711yescharacteristic
666C2×C5#252011yescharacteristic
667C2×C5#252111yescharacteristic
668C2×C5#252811yescharacteristic
669C2×C5#255611yescharacteristic
670C2×C5#255711yescharacteristic
671C23C23×C4×C511yescharacteristic
672C23C22×C5×D411yescharacteristic
673C23C22×C5×Q811yescharacteristic
674C23C2×C5×#4111yescharacteristic
675C23C2×C5×#4111yescharacteristic
676C23C2×C5×#4111yescharacteristic
677C23C2×C5×#4111yescharacteristic
678C23C2×C5×#4111yescharacteristic
679C23C2×C5×#4111yescharacteristic
680C23C2×C5×#4111yescharacteristic
681C23C2×C5×#4111yescharacteristic
682C23C5×H(5,𝔽2)11yescharacteristic
683C23C5×H(5,𝔽2)11yescharacteristic
684C23C5×2−1+411yescharacteristic
685C23C5×2−1+411yescharacteristic
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
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×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×C4C5×#11714yes—
788C2×C4C4×C5×D414yes—
789C2×C4C4×C5×Q814yes—
790C2×C4C5×#12514yes—
791C5#1400911yescharacteristic, direct product factor, Sylow
792C22C2×C5×#11711yescharacteristic
793C22C2×C4×C5×D411yescharacteristic
794C22C2×C4×C5×Q811yescharacteristic
795C22C4×C5×#4111yescharacteristic
796C22C4×C5×#4111yescharacteristic
797C22C5×#52011yescharacteristic
798C22C5×#52011yescharacteristic
799C22C2×C5×#12511yescharacteristic
800C22C5×#52911yescharacteristic
801C22C5×#52911yescharacteristic
802C22C5×#52911yescharacteristic
803C22C5×#52911yescharacteristic
804C22C5×#53211yescharacteristic
805C22C5×#53211yescharacteristic
806C22C5×#53311yescharacteristic
807C22C5×#53811yescharacteristic
808C22C5×#53911yescharacteristic
809C22C5×#54111yescharacteristic
810C22C5×#54211yescharacteristic
811C22C5×#54611yescharacteristic
812C22C5×#54611yescharacteristic
813C22C5×#54711yescharacteristic
814C22C5×D4×Q811yescharacteristic
815C22C5×#55111yescharacteristic
816C22C5×#55111yescharacteristic
817C22C5×#55111yescharacteristic
818C22C5×#55211yescharacteristic
819C22C5×#55211yescharacteristic
820C22C5×#55211yescharacteristic
821C22C5×#55211yescharacteristic
822C22C5×#55411yescharacteristic
823C22C5×#55411yescharacteristic
824C22C5×#55611yescharacteristic
825C22C5×#55711yescharacteristic
826C22C5×#55911yescharacteristic
827C4—24no—
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C2C5×#229311yescharacteristic
843C2C4×C5×#12511yescharacteristic
844C2C5×#233411yescharacteristic
845C2C5×#234311yescharacteristic
846C2C5×#235511yescharacteristic
847C2C5×#235911yescharacteristic
848C2C5×#236011yescharacteristic
849C2C5×#250511yescharacteristic
850C2C5×#250611yescharacteristic
851C2C5×#251711yescharacteristic
852C2C5×#252011yescharacteristic
853C2C5×#252111yescharacteristic
854C2C5×#252811yescharacteristic
855C2C5×#255611yescharacteristic
856C2C5×#255711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
28. C5×#387C4semidirect
54. #14009C5direct (N × H)
271. #387C4×C5semidirect
791. C5#14009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3872
C2×C5×#3822
C5×#14452
C5×#14442
C5×#14432
C5×#14422
C5×#14362
C5×C4⋊#952
C4×C5×#952
#140095