Finite Group Databasebeta

← C5×#14214 #11936934

Subgroups — C5×#14214 #11936934

Order 1280.

1526 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#395C211yesmaximal, characteristic
2C2×C5×#391C211yesmaximal, characteristic
3C2×C5×#391C211yesmaximal, characteristic
4C2×C5×#387C211yesmaximal, characteristic
5C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
6C5×#1444C211yesmaximal, characteristic
7C5×#1442C211yesmaximal, characteristic
8C5×#1441C211yesmaximal, characteristic
9C5×#1436C211yesmaximal, characteristic
10C5×#1436C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic
12C5×#1436C211yesmaximal, characteristic
13C5×C4⋊#95C211yesmaximal, characteristic
14C5×#1434C211yesmaximal, characteristic
15C4×C5×#95C211yesmaximal, characteristic
16C23×C5×Q8C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C5×#395C418yescomplemented
30C5×#391—24no—
31C5×#391—24no—
32C5×#387—24no—
33C4×C5×C4⋊C4—24no—
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
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56#14214C511yesmaximal, characteristic, direct product factor, Sylow
57C22×C5×Q8—22no—
58C22×C5×Q8—22no—
59C22×C5×Q8—22no—
60C22×C5×Q8—22no—
61C22×C5×Q8—41no—
62C22×C5×Q8—41no—
63C22×C5×Q8C2×C414yes—
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C4⋊C4—41no—
96C2×C5×C4⋊C4—41no—
97C2×C5×C4⋊C4C2×C414yes—
98C2×C5×C4⋊C4C2×C414yes—
99C2×C5×C4⋊C4C2×C414yes—
100C2×C42×C5—22no—
101C2×C42×C5—22no—
102C2×C42×C5—22no—
103C2×C42×C5—22no—
104C2×C42×C5—22no—
105C2×C42×C5—22no—
106C2×C42×C5—22no—
107C2×C42×C5—22no—
108C2×C42×C5—22no—
109C2×C42×C5—22no—
110C2×C42×C5—41no—
111C2×C42×C5—41no—
112C2×C42×C5—41no—
113C2×C42×C5—41no—
114C2×C42×C5Q814yescomplemented
115C5×#95—22no—
116C5×#95—22no—
117C5×#95—22no—
118C5×#95—22no—
119C5×#95—22no—
120C5×#95—22no—
121C5×#95—22no—
122C5×#95—22no—
123C5×#95—22no—
124C5×#95—22no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—22no—
128C5×#95—22no—
129C5×#95—22no—
130C5×#95—41no—
131C5×#95C2×C414yes—
132C5×#95C2×C414yes—
133C5×#95C2×C414yes—
134C5×#95D414yes—
135C5×#95D414yes—
136C5×#95Q814yescomplemented
137C2×#395C2×C511yescharacteristic
138C2×#391C2×C511yescharacteristic
139C2×#391C2×C511yescharacteristic
140C2×#387C2×C511yescharacteristic
141C2×C4×C4⋊C4C2×C511yescharacteristic
142#1444C2×C511yescharacteristic
143#1442C2×C511yescharacteristic
144#1441C2×C511yescharacteristic
145#1436C2×C511yescharacteristic
146#1436C2×C511yescharacteristic
147#1436C2×C511yescharacteristic
148#1436C2×C511yescharacteristic
149C4⋊#95C2×C511yescharacteristic
150#1434C2×C511yescharacteristic
151C4×#95C2×C511yescharacteristic
152C24×C5C2411yescharacteristic
153C2×C5×Q8—28no—
154C2×C5×Q8—28no—
155C2×C5×Q8—44no—
156C2×C5×Q8—44no—
157C2×C5×Q8—44no—
158C2×C5×Q8—44no—
159C2×C5×Q8—44no—
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×C5—21no—
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—21no—
239C22×C4×C5—21no—
240C22×C4×C5C22×C412yes—
241C22×C4×C5C22×C412yes—
242C22×C4×C5C22×C412yes—
243C22×C4×C5C22×C412yes—
244C22×C4×C5C22×C412yes—
245C22×C4×C5C22×C412yes—
246C22×C4×C5C22×C412yes—
247C22×C4×C5C2×D412yes—
248C22×C4×C5C2×D412yes—
249C22×C4×C5C2×D412yes—
250C22×C4×C5C2×D412yes—
251C22×C4×C5C2×D412yes—
252C22×C4×C5C2×D412yes—
253C22×C4×C5C2×Q812yes—
254C22×C4×C5C2×Q812yes—
255C22×C4×C5C2×Q812yes—
256C22×C4×C5C2×Q812yes—
257C22×C4×C5C2×Q812yes—
258C22×C4×C5C2×Q812yes—
259C22×C4×C5#4112yes—
260C22×C4×C5#4112yes—
261C22×C4×C5#4112yes—
262C22×C4×C5#4112yes—
263C22×C4×C5#4112yes—
264C22×C4×C5#4112yes—
265C5×C4⋊C4—28no—
266C5×C4⋊C4—28no—
267C5×C4⋊C4—28no—
268C5×C4⋊C4—44no—
269C5×C4⋊C4—44no—
270C5×C4⋊C4—44no—
271C5×C4⋊C4—44no—
272C42×C5—28no—
273C42×C5—44no—
274C42×C5—44no—
275C42×C5—44no—
276C42×C5—44no—
277C23×Q8C22×C511yescharacteristic
278C22×C4⋊C4C22×C511yescharacteristic
279C22×C4⋊C4C22×C511yescharacteristic
280C22×C4⋊C4C22×C511yescharacteristic
281C22×C4⋊C4C22×C511yescharacteristic
282C22×C4⋊C4C22×C511yescharacteristic
283C22×C4⋊C4C22×C511yescharacteristic
284C22×C4⋊C4C22×C511yescharacteristic
285C22×C42C22×C511yescharacteristic
286C22×C42C22×C511yescharacteristic
287C22×C42C22×C511yescharacteristic
288C22×C42C22×C511yescharacteristic
289C22×C42C22×C511yescharacteristic
290#395C4×C518yescomplemented
291#391—24no—
292#391—24no—
293#387—24no—
294C4×C4⋊C4—24no—
295C2×#95C22×C511yescharacteristic
296C2×#95C22×C511yescharacteristic
297C2×#95C22×C511yescharacteristic
298C2×#95C22×C511yescharacteristic
299C2×#95C22×C511yescharacteristic
300C2×#95C22×C511yescharacteristic
301C2×#95C22×C511yescharacteristic
302C2×#95C22×C511yescharacteristic
303C2×#95C22×C511yescharacteristic
304C2×#95C22×C511yescharacteristic
305C2×#95C22×C511yescharacteristic
306C2×#95C22×C511yescharacteristic
307C2×#95C22×C511yescharacteristic
308C2×#95C22×C511yescharacteristic
309C2×#95C22×C511yescharacteristic
310C2×#95C22×C511yescharacteristic
311C2×#95C22×C511yescharacteristic
312C2×#95C22×C511yescharacteristic
313C2×#95C22×C511yescharacteristic
314C2×#95C22×C511yescharacteristic
315C2×#95C22×C511yescharacteristic
316C2×#95C22×C511yescharacteristic
317C23×C5C23×C411yescharacteristic
318C23×C5C22×D411yescharacteristic
319C23×C5C22×D411yescharacteristic
320C23×C5C22×Q811yescharacteristic
321C23×C5C22×Q811yescharacteristic
322C23×C5C2×#4111yescharacteristic
323C23×C5C2×#4111yescharacteristic
324C23×C5C2×#4111yescharacteristic
325C23×C5C2×#4111yescharacteristic
326C23×C5C2×#4111yescharacteristic
327C23×C5C2×#4111yescharacteristic
328C23×C5H(5,𝔽2)11yescharacteristic
329C23×C5H(5,𝔽2)11yescharacteristic
330C23×C52−1+411yescharacteristic
331C23×C52−1+411yescharacteristic
332C5×Q8—416no—
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—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
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—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—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5C4×D414yes—
433C2×C4×C5C4×D414yes—
434C2×C4×C5C4×Q814yes—
435C2×C4×C5C4×Q814yes—
436C2×C4×C5C22⋊Q814yes—
437C2×C4×C5C4⋊Q814yes—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—22no—
441C22×Q8—22no—
442C22×Q8—41no—
443C22×Q8—41no—
444C22×Q8C2×C4×C514yes—
445C23×C4C23×C511yescharacteristic
446C23×C4C23×C511yescharacteristic
447C23×C4C23×C511yescharacteristic
448C23×C4C23×C511yescharacteristic
449C23×C4C23×C511yescharacteristic
450C23×C4C23×C511yescharacteristic
451C23×C4C23×C511yescharacteristic
452C23×C4C23×C511yescharacteristic
453C23×C4C23×C511yescharacteristic
454C23×C4C23×C511yescharacteristic
455C23×C4C23×C511yescharacteristic
456C23×C4C23×C511yescharacteristic
457C23×C4C23×C511yescharacteristic
458C23×C4C23×C511yescharacteristic
459C23×C4C23×C511yescharacteristic
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4C2×C4×C514yes—
479C2×C4⋊C4C2×C4×C514yes—
480C2×C4⋊C4C2×C4×C514yes—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—41no—
492C2×C42—41no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42C5×Q814yescomplemented
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—41no—
512#95C2×C4×C514yes—
513#95C2×C4×C514yes—
514#95C2×C4×C514yes—
515#95C5×D414yes—
516#95C5×D414yes—
517#95C5×Q814yescomplemented
518C22×C5C2×C4×D411yescharacteristic
519C22×C5C2×C4×D411yescharacteristic
520C22×C5C2×C4×Q811yescharacteristic
521C22×C5C2×C4×Q811yescharacteristic
522C22×C5C4×#4111yescharacteristic
523C22×C5#51811yescharacteristic
524C22×C5#51911yescharacteristic
525C22×C5C2×C22⋊Q811yescharacteristic
526C22×C5#52511yescharacteristic
527C22×C5#52911yescharacteristic
528C22×C5C2×C4⋊Q811yescharacteristic
529C22×C5#53211yescharacteristic
530C22×C5#53311yescharacteristic
531C22×C5#53311yescharacteristic
532C22×C5#53311yescharacteristic
533C22×C5#54211yescharacteristic
534C22×C5#54211yescharacteristic
535C22×C5#54411yescharacteristic
536C22×C5#54411yescharacteristic
537C22×C5D4211yescharacteristic
538C22×C5#54611yescharacteristic
539C22×C5#54611yescharacteristic
540C22×C5#54711yescharacteristic
541C22×C5#54711yescharacteristic
542C22×C5#54811yescharacteristic
543C22×C5D4×Q811yescharacteristic
544C22×C5#55111yescharacteristic
545C22×C5#55111yescharacteristic
546C22×C5#55111yescharacteristic
547C22×C5#55211yescharacteristic
548C22×C5#55411yescharacteristic
549C22×C5#55411yescharacteristic
550C22×C5#55611yescharacteristic
551C22×C5#55611yescharacteristic
552C22×C5#55711yescharacteristic
553C4×C5—24no—
554C4×C5—24no—
555C4×C5—24no—
556C4×C5—24no—
557C4×C5—24no—
558C4×C5—24no—
559C4×C5—42no—
560C4×C5—42no—
561C4×C5—42no—
562C4×C5—42no—
563C4×C5—42no—
564C4×C5—42no—
565C4×C5—42no—
566C4×C5—81no—
567C4×C5—81no—
568C24C24×C511yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
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×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
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—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4C22×C4×C512yes—
657C22×C4C22×C4×C512yes—
658C22×C4C22×C4×C512yes—
659C22×C4C22×C4×C512yes—
660C22×C4C22×C4×C512yes—
661C22×C4C22×C4×C512yes—
662C22×C4C22×C4×C512yes—
663C22×C4C2×C5×D412yes—
664C22×C4C2×C5×D412yes—
665C22×C4C2×C5×D412yes—
666C22×C4C2×C5×D412yes—
667C22×C4C2×C5×D412yes—
668C22×C4C2×C5×D412yes—
669C22×C4C2×C5×Q812yes—
670C22×C4C2×C5×Q812yes—
671C22×C4C2×C5×Q812yes—
672C22×C4C2×C5×Q812yes—
673C22×C4C2×C5×Q812yes—
674C22×C4C2×C5×Q812yes—
675C22×C4C5×#4112yes—
676C22×C4C5×#4112yes—
677C22×C4C5×#4112yes—
678C22×C4C5×#4112yes—
679C22×C4C5×#4112yes—
680C22×C4C5×#4112yes—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C42—28no—
689C42—44no—
690C42—44no—
691C42—44no—
692C42—44no—
693C2×C5C4×C22⋊Q811yescharacteristic
694C2×C5C4×C4⋊Q811yescharacteristic
695C2×C5#233111yescharacteristic
696C2×C5#235811yescharacteristic
697C2×C5#236211yescharacteristic
698C2×C5#236511yescharacteristic
699C2×C5#236811yescharacteristic
700C2×C5#243811yescharacteristic
701C2×C5#244011yescharacteristic
702C2×C5#246111yescharacteristic
703C2×C5#246511yescharacteristic
704C2×C5#252011yescharacteristic
705C2×C5#252111yescharacteristic
706C2×C5#255011yescharacteristic
707C2×C5#260511yescharacteristic
708C23C23×C4×C511yescharacteristic
709C23C22×C5×D411yescharacteristic
710C23C22×C5×D411yescharacteristic
711C23C22×C5×Q811yescharacteristic
712C23C22×C5×Q811yescharacteristic
713C23C2×C5×#4111yescharacteristic
714C23C2×C5×#4111yescharacteristic
715C23C2×C5×#4111yescharacteristic
716C23C2×C5×#4111yescharacteristic
717C23C2×C5×#4111yescharacteristic
718C23C2×C5×#4111yescharacteristic
719C23C5×H(5,𝔽2)11yescharacteristic
720C23C5×H(5,𝔽2)11yescharacteristic
721C23C5×2−1+411yescharacteristic
722C23C5×2−1+411yescharacteristic
723Q8—416no—
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—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
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—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
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—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4C4×C5×D414yes—
824C2×C4C4×C5×D414yes—
825C2×C4C4×C5×Q814yes—
826C2×C4C4×C5×Q814yes—
827C2×C4C5×C22⋊Q814yes—
828C2×C4C5×C4⋊Q814yes—
829C5#1421411yescharacteristic, direct product factor, Sylow
830C22C2×C4×C5×D411yescharacteristic
831C22C2×C4×C5×D411yescharacteristic
832C22C2×C4×C5×Q811yescharacteristic
833C22C2×C4×C5×Q811yescharacteristic
834C22C4×C5×#4111yescharacteristic
835C22C5×#51811yescharacteristic
836C22C5×#51911yescharacteristic
837C22C2×C5×C22⋊Q811yescharacteristic
838C22C5×#52511yescharacteristic
839C22C5×#52911yescharacteristic
840C22C2×C5×C4⋊Q811yescharacteristic
841C22C5×#53211yescharacteristic
842C22C5×#53311yescharacteristic
843C22C5×#53311yescharacteristic
844C22C5×#53311yescharacteristic
845C22C5×#54211yescharacteristic
846C22C5×#54211yescharacteristic
847C22C5×#54411yescharacteristic
848C22C5×#54411yescharacteristic
849C22C5×D4211yescharacteristic
850C22C5×#54611yescharacteristic
851C22C5×#54611yescharacteristic
852C22C5×#54711yescharacteristic
853C22C5×#54711yescharacteristic
854C22C5×#54811yescharacteristic
855C22C5×D4×Q811yescharacteristic
856C22C5×#55111yescharacteristic
857C22C5×#55111yescharacteristic
858C22C5×#55111yescharacteristic
859C22C5×#55211yescharacteristic
860C22C5×#55411yescharacteristic
861C22C5×#55411yescharacteristic
862C22C5×#55611yescharacteristic
863C22C5×#55611yescharacteristic
864C22C5×#55711yescharacteristic
865C4—24no—
866C4—24no—
867C4—24no—
868C4—24no—
869C4—24no—
870C4—24no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—81no—
879C4—81no—
880C2C4×C5×C22⋊Q811yescharacteristic
881C2C4×C5×C4⋊Q811yescharacteristic
882C2C5×#233111yescharacteristic
883C2C5×#235811yescharacteristic
884C2C5×#236211yescharacteristic
885C2C5×#236511yescharacteristic
886C2C5×#236811yescharacteristic
887C2C5×#243811yescharacteristic
888C2C5×#244011yescharacteristic
889C2C5×#246111yescharacteristic
890C2C5×#246511yescharacteristic
891C2C5×#252011yescharacteristic
892C2C5×#252111yescharacteristic
893C2C5×#255011yescharacteristic
894C2C5×#260511yescharacteristic
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
29. C5×#395C4semidirect
56. #14214C5direct (N × H)
114. C2×C42×C5Q8semidirect
136. C5×#95Q8semidirect
290. #395C4×C5semidirect
495. C2×C42C5×Q8semidirect
517. #95C5×Q8semidirect
829. C5#14214direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3952
C2×C5×#3912
C2×C5×#3872
C2×C4×C5×C4⋊C42
C5×#14442
C5×#14422
C5×#14412
C5×#14362
C5×C4⋊#952
C5×#14342
C4×C5×#952
#142145