Finite Group Databasebeta

← C5×#14218 #11936938

Subgroups — C5×#14218 #11936938

Order 1280.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#396C211yesmaximal, characteristic
2C2×C5×#387C211yesmaximal, characteristic, complemented
3C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
4C5×#1445C211yesmaximal, characteristic, complemented
5C5×#1443C211yesmaximal, characteristic, complemented
6C5×#1439C211yesmaximal, characteristic
7C5×#1437C211yesmaximal, characteristic
8C5×#1437C211yesmaximal, characteristic
9C5×#1436C211yesmaximal, characteristic, complemented
10C5×#1436C211yesmaximal, characteristic, complemented
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×C4⋊#95C211yesmaximal, characteristic, complemented
13C5×C22⋊#95C211yesmaximal, characteristic
14C5×C22⋊#95C211yesmaximal, characteristic
15C4×C5×#95C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C42×C5C2211yescharacteristic
30C22×C42×C5C2211yescharacteristic
31C5×#396C418yescomplemented
32C5×#387—24no—
33C4×C5×C22⋊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
54#14218C511yesmaximal, characteristic, direct product factor, Sylow
55C25×C5C2311yescharacteristic
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—41no—
62C23×C4×C5—41no—
63C23×C4×C5C2311yescharacteristic
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
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—41no—
82C2×C5×C4⋊C4—41no—
83C2×C5×C4⋊C4—41no—
84C2×C5×C4⋊C4—41no—
85C2×C5×C4⋊C4—41no—
86C2×C5×C4⋊C4C2×C414yescomplemented
87C2×C5×C4⋊C4C2×C414yescomplemented
88C2×C5×C4⋊C4C2×C414yescomplemented
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—41no—
98C2×C5×C22⋊C4—41no—
99C2×C5×C22⋊C4—41no—
100C2×C5×C22⋊C4—41no—
101C2×C5×C22⋊C4—41no—
102C2×C5×C22⋊C4—41no—
103C2×C5×C22⋊C4C2×C414yes—
104C2×C5×C22⋊C4C2×C414yes—
105C2×C5×C22⋊C4C2×C414yes—
106C2×C5×C22⋊C4Q814yes—
107C2×C42×C5—22no—
108C2×C42×C5—22no—
109C2×C42×C5—22no—
110C2×C42×C5—22no—
111C2×C42×C5—22no—
112C2×C42×C5—22no—
113C2×C42×C5—22no—
114C2×C42×C5—41no—
115C2×C42×C5—41no—
116C2×C42×C5—41no—
117C2×C42×C5—41no—
118C2×C42×C5—41no—
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—22no—
131C5×#95—41no—
132C5×#95—41no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95—41no—
136C5×#95—41no—
137C5×#95C2×C414yescomplemented
138C5×#95D414yes—
139C2×#396C2×C511yescharacteristic
140C2×#387C2×C511yescharacteristic, complemented
141C2×C4×C22⋊C4C2×C511yescharacteristic
142#1445C2×C511yescharacteristic, complemented
143#1443C2×C511yescharacteristic, complemented
144#1439C2×C511yescharacteristic
145#1437C2×C511yescharacteristic
146#1437C2×C511yescharacteristic
147#1436C2×C511yescharacteristic, complemented
148#1436C2×C511yescharacteristic, complemented
149#1436C2×C511yescharacteristic, complemented
150C4⋊#95C2×C511yescharacteristic, complemented
151C22⋊#95C2×C511yescharacteristic
152C22⋊#95C2×C511yescharacteristic
153C4×#95C2×C511yescharacteristic, complemented
154C24×C5—21no—
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5C22×C412yes—
167C24×C5C2×Q812yes—
168C24×C5#4112yes—
169C24×C5C2411yescharacteristic
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—28no—
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×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—44no—
252C22×C4×C5—44no—
253C22×C4×C5—44no—
254C22×C4×C5—44no—
255C22×C4×C5—44no—
256C22×C4×C5—44no—
257C22×C4×C5C22×C412yes—
258C22×C4×C5C22×C412yes—
259C22×C4×C5C22×C412yes—
260C22×C4×C5C22×C412yes—
261C22×C4×C5C22×C412yes—
262C22×C4×C5C22×C412yes—
263C22×C4×C5C2×D412yes—
264C22×C4×C5C2×D412yes—
265C22×C4×C5C2×D412yes—
266C22×C4×C5C2×Q812yes—
267C22×C4×C5C2×Q812yes—
268C22×C4×C5#4112yes—
269C22×C4×C5#4112yes—
270C22×C4×C5#4112yes—
271C22×C4×C5#4112yes—
272C22×C4×C5#4112yes—
273C22×C4×C5#4112yes—
274C22×C4×C5#4112yes—
275C5×C4⋊C4—28no—
276C5×C4⋊C4—44no—
277C5×C4⋊C4—44no—
278C5×C4⋊C4—44no—
279C5×C22⋊C4—28no—
280C5×C22⋊C4—28no—
281C5×C22⋊C4—44no—
282C5×C22⋊C4—44no—
283C5×C22⋊C4—44no—
284C5×C22⋊C4—44no—
285C42×C5—44no—
286C42×C5—44no—
287C42×C5—44no—
288C42×C5—44no—
289C24×C4C22×C511yescharacteristic
290C22×C4⋊C4C22×C511yescharacteristic
291C22×C4⋊C4C22×C511yescharacteristic
292C22×C4⋊C4C22×C511yescharacteristic
293C22×C4⋊C4C22×C511yescharacteristic
294C22×C22⋊C4C22×C511yescharacteristic
295C22×C22⋊C4C22×C511yescharacteristic
296C22×C22⋊C4C22×C511yescharacteristic
297C22×C22⋊C4C22×C511yescharacteristic
298C22×C22⋊C4C22×C511yescharacteristic
299C22×C22⋊C4C22×C511yescharacteristic
300C22×C42C22×C511yescharacteristic
301C22×C42C22×C511yescharacteristic
302C22×C42C22×C511yescharacteristic
303C22×C42C22×C511yescharacteristic
304#396C4×C518yescomplemented
305#387—24no—
306C4×C22⋊C4—24no—
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
317C2×#95C22×C511yescharacteristic
318C2×#95C22×C511yescharacteristic
319C2×#95C22×C511yescharacteristic
320C2×#95C22×C511yescharacteristic
321C2×#95C22×C511yescharacteristic
322C2×#95C22×C511yescharacteristic
323C2×#95C22×C511yescharacteristic
324C2×#95C22×C511yescharacteristic
325C2×#95C22×C511yescharacteristic
326C2×#95C22×C511yescharacteristic
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5—41no—
355C23×C5—41no—
356C23×C5—41no—
357C23×C5—41no—
358C23×C5—41no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5C4×Q814yes—
362C23×C5C23×C411yescharacteristic
363C23×C5C22×D411yescharacteristic
364C23×C5C22×Q811yescharacteristic
365C23×C5C2×#4111yescharacteristic
366C23×C5C2×#4111yescharacteristic
367C23×C5C2×#4111yescharacteristic
368C23×C5C2×#4111yescharacteristic
369C23×C5C2×#4111yescharacteristic
370C23×C5C2×#4111yescharacteristic
371C23×C5C2×#4111yescharacteristic
372C23×C5C2×#4111yescharacteristic
373C23×C5H(5,𝔽2)11yescharacteristic
374C23×C5H(5,𝔽2)11yescharacteristic
375C23×C5H(5,𝔽2)11yescharacteristic
376C23×C5H(5,𝔽2)11yescharacteristic
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—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—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—416no—
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×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5—41no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—41no—
466C2×C4×C5—41no—
467C2×C4×C5—41no—
468C2×C4×C5—41no—
469C2×C4×C5—41no—
470C2×C4×C5—41no—
471C2×C4×C5—41no—
472C2×C4×C5—41no—
473C2×C4×C5C4×D414yes—
474C2×C4×C5C22⋊Q814yes—
475C2×C4×C5#12614yes—
476C25C23×C511yescharacteristic
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—41no—
483C23×C4—41no—
484C23×C4C23×C511yescharacteristic
485C23×C4C23×C511yescharacteristic
486C23×C4C23×C511yescharacteristic
487C23×C4C23×C511yescharacteristic
488C23×C4C23×C511yescharacteristic
489C23×C4C23×C511yescharacteristic
490C23×C4C23×C511yescharacteristic
491C23×C4C23×C511yescharacteristic
492C23×C4C23×C511yescharacteristic
493C23×C4C23×C511yescharacteristic
494C23×C4C23×C511yescharacteristic
495C23×C4C23×C511yescharacteristic
496C23×C4C23×C511yescharacteristic
497C23×C4C23×C511yescharacteristic
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4C2×C4×C514yescomplemented
508C2×C4⋊C4C2×C4×C514yescomplemented
509C2×C4⋊C4C2×C4×C514yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4C2×C4×C514yes—
525C2×C22⋊C4C2×C4×C514yes—
526C2×C22⋊C4C2×C4×C514yes—
527C2×C22⋊C4C5×Q814yes—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—41no—
536C2×C42—41no—
537C2×C42—41no—
538C2×C42—41no—
539C2×C42—41no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—41no—
553#95—41no—
554#95—41no—
555#95—41no—
556#95—41no—
557#95—41no—
558#95C2×C4×C514yescomplemented
559#95C5×D414yes—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—24no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5—42no—
575C22×C5C2×C4×D411yescharacteristic
576C22×C5C2×C4×Q811yescharacteristic
577C22×C5C4×#4111yescharacteristic
578C22×C5C4×#4111yescharacteristic
579C22×C5C4×#4111yescharacteristic
580C22×C5#51811yescharacteristic
581C22×C5#51811yescharacteristic
582C22×C5C2×C22⋊Q811yescharacteristic
583C22×C5#52511yescharacteristic
584C22×C5C2×#12611yescharacteristic
585C22×C5#52911yescharacteristic
586C22×C5#52911yescharacteristic
587C22×C5#52911yescharacteristic
588C22×C5#52911yescharacteristic
589C22×C5#53311yescharacteristic
590C22×C5#53811yescharacteristic
591C22×C5#53811yescharacteristic
592C22×C5#54011yescharacteristic
593C22×C5#54011yescharacteristic
594C22×C5#54611yescharacteristic
595C22×C5#54611yescharacteristic
596C22×C5#54611yescharacteristic
597C22×C5#55011yescharacteristic
598C22×C5#55111yescharacteristic
599C22×C5#55111yescharacteristic
600C22×C5#55111yescharacteristic
601C22×C5#55111yescharacteristic
602C22×C5#55311yescharacteristic
603C22×C5#55311yescharacteristic
604C22×C5#55311yescharacteristic
605C22×C5#55411yescharacteristic
606C22×C5#55411yescharacteristic
607C22×C5#55411yescharacteristic
608C22×C5#55411yescharacteristic
609C22×C5#55511yescharacteristic
610C4×C5—24no—
611C4×C5—24no—
612C4×C5—24no—
613C4×C5—42no—
614C4×C5—42no—
615C4×C5—42no—
616C4×C5—42no—
617C4×C5—42no—
618C4×C5—42no—
619C4×C5—42no—
620C4×C5—42no—
621C4×C5—42no—
622C4×C5—81no—
623C4×C5—81no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24C22×C4×C512yes—
637C24C2×C5×Q812yes—
638C24C5×#4112yes—
639C24C24×C511yescharacteristic
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—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4C22×C4×C512yes—
728C22×C4C22×C4×C512yes—
729C22×C4C22×C4×C512yes—
730C22×C4C22×C4×C512yes—
731C22×C4C22×C4×C512yes—
732C22×C4C22×C4×C512yes—
733C22×C4C2×C5×D412yes—
734C22×C4C2×C5×D412yes—
735C22×C4C2×C5×D412yes—
736C22×C4C2×C5×Q812yes—
737C22×C4C2×C5×Q812yes—
738C22×C4C5×#4112yes—
739C22×C4C5×#4112yes—
740C22×C4C5×#4112yes—
741C22×C4C5×#4112yes—
742C22×C4C5×#4112yes—
743C22×C4C5×#4112yes—
744C22×C4C5×#4112yes—
745C4⋊C4—28no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C22⋊C4—28no—
750C22⋊C4—28no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C42—44no—
756C42—44no—
757C42—44no—
758C42—44no—
759C2×C5—44no—
760C2×C5C4×C22⋊Q811yescharacteristic
761C2×C5C4×#12611yescharacteristic
762C2×C5#233311yescharacteristic
763C2×C5#236311yescharacteristic
764C2×C5#236411yescharacteristic
765C2×C5#236811yescharacteristic
766C2×C5#236811yescharacteristic
767C2×C5#245011yescharacteristic
768C2×C5#245411yescharacteristic
769C2×C5#247111yescharacteristic
770C2×C5#248011yescharacteristic
771C2×C5#249711yescharacteristic
772C2×C5#252611yescharacteristic
773C2×C5#257611yescharacteristic
774C2×C5#258711yescharacteristic
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23C4×C5×Q814yes—
810C23C23×C4×C511yescharacteristic
811C23C22×C5×D411yescharacteristic
812C23C22×C5×Q811yescharacteristic
813C23C2×C5×#4111yescharacteristic
814C23C2×C5×#4111yescharacteristic
815C23C2×C5×#4111yescharacteristic
816C23C2×C5×#4111yescharacteristic
817C23C2×C5×#4111yescharacteristic
818C23C2×C5×#4111yescharacteristic
819C23C2×C5×#4111yescharacteristic
820C23C2×C5×#4111yescharacteristic
821C23C5×H(5,𝔽2)11yescharacteristic
822C23C5×H(5,𝔽2)11yescharacteristic
823C23C5×H(5,𝔽2)11yescharacteristic
824C23C5×H(5,𝔽2)11yescharacteristic
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—416no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4C4×C5×D414yes—
922C2×C4C5×C22⋊Q814yes—
923C2×C4C5×#12614yes—
924C5#1421811yescharacteristic, direct product factor, Sylow
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C2×C4×C5×D411yescharacteristic
941C22C2×C4×C5×Q811yescharacteristic
942C22C4×C5×#4111yescharacteristic
943C22C4×C5×#4111yescharacteristic
944C22C4×C5×#4111yescharacteristic
945C22C5×#51811yescharacteristic
946C22C5×#51811yescharacteristic
947C22C2×C5×C22⋊Q811yescharacteristic
948C22C5×#52511yescharacteristic
949C22C2×C5×#12611yescharacteristic
950C22C5×#52911yescharacteristic
951C22C5×#52911yescharacteristic
952C22C5×#52911yescharacteristic
953C22C5×#52911yescharacteristic
954C22C5×#53311yescharacteristic
955C22C5×#53811yescharacteristic
956C22C5×#53811yescharacteristic
957C22C5×#54011yescharacteristic
958C22C5×#54011yescharacteristic
959C22C5×#54611yescharacteristic
960C22C5×#54611yescharacteristic
961C22C5×#54611yescharacteristic
962C22C5×#55011yescharacteristic
963C22C5×#55111yescharacteristic
964C22C5×#55111yescharacteristic
965C22C5×#55111yescharacteristic
966C22C5×#55111yescharacteristic
967C22C5×#55311yescharacteristic
968C22C5×#55311yescharacteristic
969C22C5×#55311yescharacteristic
970C22C5×#55411yescharacteristic
971C22C5×#55411yescharacteristic
972C22C5×#55411yescharacteristic
973C22C5×#55411yescharacteristic
974C22C5×#55511yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C4×C5×C22⋊Q811yescharacteristic
991C2C4×C5×#12611yescharacteristic
992C2C5×#233311yescharacteristic
993C2C5×#236311yescharacteristic
994C2C5×#236411yescharacteristic
995C2C5×#236811yescharacteristic
996C2C5×#236811yescharacteristic
997C2C5×#245011yescharacteristic
998C2C5×#245411yescharacteristic
999C2C5×#247111yescharacteristic
1000C2C5×#248011yescharacteristic
1001C2C5×#249711yescharacteristic
1002C2C5×#252611yescharacteristic
1003C2C5×#257611yescharacteristic
1004C2C5×#258711yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#387C2semidirect
4. C5×#1445C2semidirect
5. C5×#1443C2semidirect
9. C5×#1436C2semidirect
10. C5×#1436C2semidirect
11. C5×#1436C2semidirect
12. C5×C4⋊#95C2semidirect
15. C4×C5×#95C2semidirect
31. C5×#396C4semidirect
54. #14218C5direct (N × H)
86. C2×C5×C4⋊C4C2×C4semidirect
87. C2×C5×C4⋊C4C2×C4semidirect
88. C2×C5×C4⋊C4C2×C4semidirect
137. C5×#95C2×C4semidirect
140. C2×#387C2×C5semidirect
142. #1445C2×C5semidirect
143. #1443C2×C5semidirect
147. #1436C2×C5semidirect
148. #1436C2×C5semidirect
149. #1436C2×C5semidirect
150. C4⋊#95C2×C5semidirect
153. C4×#95C2×C5semidirect
304. #396C4×C5semidirect
507. C2×C4⋊C4C2×C4×C5semidirect
508. C2×C4⋊C4C2×C4×C5semidirect
509. C2×C4⋊C4C2×C4×C5semidirect
558. #95C2×C4×C5semidirect
924. C5#14218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3962
C2×C5×#3872
C2×C4×C5×C22⋊C42
C5×#14452
C5×#14432
C5×#14392
C5×#14372
C5×#14362
C5×C4⋊#952
C5×C22⋊#952
C4×C5×#952
#142185