Finite Group Databasebeta

← C5×#14517 #11937237

Subgroups — C5×#14517 #11937237

Order 1280.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic
4C2×C5×#386C211yesmaximal, characteristic
5C2×C5×#385C211yesmaximal, characteristic, complemented
6C5×#1445C211yesmaximal, characteristic, complemented
7C5×#1443C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1437C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×C22⋊#95C211yesmaximal, characteristic, complemented
14C5×C22⋊#95C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#394C418yescomplemented
34C5×#388—24no—
35C5×#386—24no—
36C5×#386—24no—
37C5×#385—24no—
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#14517C511yesmaximal, characteristic, direct product factor, Sylow
57C25×C5C2311yescharacteristic
58C25×C5C2311yescharacteristic
59C22×C5×D4—22no—
60C22×C5×D4—22no—
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4—41no—
64C22×C5×D4—41no—
65C22×C5×D4C2×C414yes—
66C23×C4×C5—22no—
67C23×C4×C5—22no—
68C23×C4×C5—22no—
69C23×C4×C5—22no—
70C23×C4×C5—22no—
71C23×C4×C5—22no—
72C23×C4×C5—41no—
73C23×C4×C5—41no—
74C23×C4×C5—41no—
75C23×C4×C5—41no—
76C23×C4×C5—41no—
77C23×C4×C5—41no—
78C23×C4×C5—41no—
79C23×C4×C5—41no—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C2×C5×C4⋊C4—22no—
94C2×C5×C4⋊C4—22no—
95C2×C5×C4⋊C4—22no—
96C2×C5×C4⋊C4—22no—
97C2×C5×C4⋊C4—41no—
98C2×C5×C4⋊C4—41no—
99C2×C5×C4⋊C4—41no—
100C2×C5×C4⋊C4—41no—
101C2×C5×C4⋊C4C2×C414yescomplemented
102C2×C5×C22⋊C4—22no—
103C2×C5×C22⋊C4—22no—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—22no—
106C2×C5×C22⋊C4—22no—
107C2×C5×C22⋊C4—22no—
108C2×C5×C22⋊C4—22no—
109C2×C5×C22⋊C4—22no—
110C2×C5×C22⋊C4—22no—
111C2×C5×C22⋊C4—22no—
112C2×C5×C22⋊C4—22no—
113C2×C5×C22⋊C4—22no—
114C2×C5×C22⋊C4—41no—
115C2×C5×C22⋊C4—41no—
116C2×C5×C22⋊C4—41no—
117C2×C5×C22⋊C4—41no—
118C2×C5×C22⋊C4—41no—
119C2×C5×C22⋊C4—41no—
120C2×C5×C22⋊C4—41no—
121C2×C5×C22⋊C4—41no—
122C2×C5×C22⋊C4—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4—41no—
125C2×C5×C22⋊C4—41no—
126C2×C5×C22⋊C4C2×C414yescomplemented
127C2×C5×C22⋊C4C2×C414yescomplemented
128C2×C5×C22⋊C4C2×C414yescomplemented
129C2×C5×C22⋊C4C2×C414yescomplemented
130C2×C5×C22⋊C4D414yes—
131C2×C5×C22⋊C4D414yes—
132C2×C42×C5—22no—
133C2×C42×C5—41no—
134C2×C42×C5—41no—
135C5×#95—22no—
136C5×#95—22no—
137C5×#95—22no—
138C5×#95—22no—
139C5×#95—22no—
140C5×#95—22no—
141C5×#95—22no—
142C5×#95—22no—
143C5×#95—22no—
144C5×#95—41no—
145C5×#95—41no—
146C5×#95—41no—
147C5×#95—41no—
148C5×#95—41no—
149C5×#95—41no—
150C5×#95—41no—
151C5×#95—41no—
152C5×#95C2×C414yescomplemented
153C2×#394C2×C511yescharacteristic
154C2×#388C2×C511yescharacteristic, complemented
155C2×#386C2×C511yescharacteristic
156C2×#386C2×C511yescharacteristic
157C2×#385C2×C511yescharacteristic, complemented
158#1445C2×C511yescharacteristic, complemented
159#1443C2×C511yescharacteristic, complemented
160#1441C2×C511yescharacteristic, complemented
161#1440C2×C511yescharacteristic, complemented
162#1439C2×C511yescharacteristic, complemented
163#1437C2×C511yescharacteristic, complemented
164#1436C2×C511yescharacteristic, complemented
165C22⋊#95C2×C511yescharacteristic, complemented
166C22⋊#95C2×C511yescharacteristic, complemented
167C22⋊#95C2×C511yescharacteristic, complemented
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5—21no—
178C24×C5—21no—
179C24×C5—21no—
180C24×C5—21no—
181C24×C5—21no—
182C24×C5—21no—
183C24×C5—21no—
184C24×C5—21no—
185C24×C5—21no—
186C24×C5—21no—
187C24×C5—21no—
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5—21no—
192C24×C5C22×C412yes—
193C24×C5C22×C412yes—
194C24×C5C2×D412yes—
195C24×C5C2×D412yes—
196C24×C5#4112yes—
197C24×C5#4112yes—
198C24×C5C2411yescharacteristic
199C2×C5×D4—28no—
200C2×C5×D4—28no—
201C2×C5×D4—44no—
202C2×C5×D4—44no—
203C2×C5×D4—44no—
204C2×C5×D4—44no—
205C2×C5×D4—44no—
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—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—21no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—44no—
287C22×C4×C5—44no—
288C22×C4×C5—44no—
289C22×C4×C5—44no—
290C22×C4×C5—44no—
291C22×C4×C5—44no—
292C22×C4×C5—44no—
293C22×C4×C5—44no—
294C22×C4×C5—44no—
295C22×C4×C5—44no—
296C22×C4×C5—44no—
297C22×C4×C5—44no—
298C22×C4×C5—44no—
299C22×C4×C5—44no—
300C22×C4×C5C22×C412yes—
301C22×C4×C5C22×C412yes—
302C22×C4×C5C22×C412yes—
303C22×C4×C5C22×C412yes—
304C22×C4×C5C22×C412yes—
305C22×C4×C5C2×D412yes—
306C22×C4×C5C2×D412yes—
307C22×C4×C5C2×D412yes—
308C22×C4×C5C2×D412yes—
309C22×C4×C5#4112yes—
310C22×C4×C5#4112yes—
311C5×C4⋊C4—44no—
312C5×C4⋊C4—44no—
313C5×C4⋊C4—44no—
314C5×C22⋊C4—28no—
315C5×C22⋊C4—28no—
316C5×C22⋊C4—44no—
317C5×C22⋊C4—44no—
318C5×C22⋊C4—44no—
319C5×C22⋊C4—44no—
320C5×C22⋊C4—44no—
321C5×C22⋊C4—44no—
322C5×C22⋊C4—44no—
323C5×C22⋊C4—44no—
324C42×C5—44no—
325C23×D4C22×C511yescharacteristic
326C24×C4C22×C511yescharacteristic
327C24×C4C22×C511yescharacteristic
328C22×C4⋊C4C22×C511yescharacteristic
329C22×C4⋊C4C22×C511yescharacteristic
330C22×C4⋊C4C22×C511yescharacteristic
331C22×C22⋊C4C22×C511yescharacteristic
332C22×C22⋊C4C22×C511yescharacteristic
333C22×C22⋊C4C22×C511yescharacteristic
334C22×C22⋊C4C22×C511yescharacteristic
335C22×C22⋊C4C22×C511yescharacteristic
336C22×C22⋊C4C22×C511yescharacteristic
337C22×C22⋊C4C22×C511yescharacteristic
338C22×C22⋊C4C22×C511yescharacteristic
339C22×C22⋊C4C22×C511yescharacteristic
340C22×C22⋊C4C22×C511yescharacteristic
341C22×C42C22×C511yescharacteristic
342#394C4×C518yescomplemented
343#388—24no—
344#386—24no—
345#386—24no—
346#385—24no—
347C2×#95C22×C511yescharacteristic
348C2×#95C22×C511yescharacteristic
349C2×#95C22×C511yescharacteristic
350C2×#95C22×C511yescharacteristic
351C2×#95C22×C511yescharacteristic
352C2×#95C22×C511yescharacteristic
353C2×#95C22×C511yescharacteristic
354C2×#95C22×C511yescharacteristic
355C2×#95C22×C511yescharacteristic
356C2×#95C22×C511yescharacteristic
357C2×#95C22×C511yescharacteristic
358C2×#95C22×C511yescharacteristic
359C2×#95C22×C511yescharacteristic
360C2×#95C22×C511yescharacteristic
361C2×#95C22×C511yescharacteristic
362C2×#95C22×C511yescharacteristic
363C2×#95C22×C511yescharacteristic
364C2×#95C22×C511yescharacteristic
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5—22no—
395C23×C5—22no—
396C23×C5—22no—
397C23×C5—22no—
398C23×C5—22no—
399C23×C5—22no—
400C23×C5—22no—
401C23×C5—41no—
402C23×C5—41no—
403C23×C5—41no—
404C23×C5—41no—
405C23×C5—41no—
406C23×C5—41no—
407C23×C5—41no—
408C23×C5—41no—
409C23×C5—41no—
410C23×C5—41no—
411C23×C5—41no—
412C23×C5—41no—
413C23×C5—41no—
414C23×C5—41no—
415C23×C5—41no—
416C23×C5—41no—
417C23×C5—41no—
418C23×C5—41no—
419C23×C5—41no—
420C23×C5—41no—
421C23×C5—41no—
422C23×C5—41no—
423C23×C5—41no—
424C23×C5—41no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5—41no—
428C23×C5—41no—
429C23×C5—41no—
430C23×C5—41no—
431C23×C5—41no—
432C23×C5—41no—
433C23×C5C4×D414yes—
434C23×C5C4×D414yes—
435C23×C5C23×C411yescharacteristic
436C23×C5C22×D411yescharacteristic
437C23×C5C22×D411yescharacteristic
438C23×C5C2×#4111yescharacteristic
439C23×C5C2×#4111yescharacteristic
440C23×C5C2×#4111yescharacteristic
441C23×C5C2×#4111yescharacteristic
442C23×C5H(5,𝔽2)11yescharacteristic
443C23×C5H(5,𝔽2)11yescharacteristic
444C23×C5H(5,𝔽2)11yescharacteristic
445C23×C5H(5,𝔽2)11yescharacteristic
446C23×C5H(5,𝔽2)11yescharacteristic
447C23×C5H(5,𝔽2)11yescharacteristic
448C23×C52−1+411yescharacteristic
449C23×C52−1+411yescharacteristic
450C5×D4—416no—
451C2×C4×C5—22no—
452C2×C4×C5—22no—
453C2×C4×C5—22no—
454C2×C4×C5—22no—
455C2×C4×C5—22no—
456C2×C4×C5—22no—
457C2×C4×C5—22no—
458C2×C4×C5—22no—
459C2×C4×C5—22no—
460C2×C4×C5—22no—
461C2×C4×C5—22no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—22no—
466C2×C4×C5—22no—
467C2×C4×C5—22no—
468C2×C4×C5—22no—
469C2×C4×C5—22no—
470C2×C4×C5—22no—
471C2×C4×C5—22no—
472C2×C4×C5—22no—
473C2×C4×C5—22no—
474C2×C4×C5—22no—
475C2×C4×C5—22no—
476C2×C4×C5—22no—
477C2×C4×C5—22no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—22no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—416no—
485C2×C4×C5—416no—
486C2×C4×C5—41no—
487C2×C4×C5—41no—
488C2×C4×C5—41no—
489C2×C4×C5—41no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×C4×C5—41no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
500C2×C4×C5—41no—
501C2×C4×C5—41no—
502C2×C4×C5—41no—
503C2×C4×C5—41no—
504C2×C4×C5—41no—
505C2×C4×C5—41no—
506C2×C4×C5—41no—
507C2×C4×C5—41no—
508C2×C4×C5—41no—
509C2×C4×C5—41no—
510C2×C4×C5—41no—
511C2×C4×C5—41no—
512C2×C4×C5—41no—
513C2×C4×C5—41no—
514C2×C4×C5—41no—
515C2×C4×C5—41no—
516C2×C4×C5—41no—
517C2×C4×C5—41no—
518C2×C4×C5—41no—
519C2×C4×C5—41no—
520C2×C4×C5—41no—
521C2×C4×C5—41no—
522C2×C4×C5—41no—
523C2×C4×C5—41no—
524C2×C4×C5—41no—
525C2×C4×C5—41no—
526C2×C4×C5—41no—
527C2×C4×C5—41no—
528C2×C4×C5—41no—
529C2×C4×C5—41no—
530C2×C4×C5—41no—
531C2×C4×C5—41no—
532C2×C4×C5—41no—
533C2×C4×C5—41no—
534C2×C4×C5—41no—
535C2×C4×C5—41no—
536C2×C4×C5—41no—
537C2×C4×C5—41no—
538C2×C4×C5—41no—
539C2×C4×C5—41no—
540C2×C4×C5—41no—
541C2×C4×C5—41no—
542C2×C4×C5—41no—
543C2×C4×C5—41no—
544C25C23×C511yescharacteristic
545C25C23×C511yescharacteristic
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4C2×C4×C514yes—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—41no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4C23×C511yescharacteristic
568C23×C4C23×C511yescharacteristic
569C23×C4C23×C511yescharacteristic
570C23×C4C23×C511yescharacteristic
571C23×C4C23×C511yescharacteristic
572C23×C4C23×C511yescharacteristic
573C23×C4C23×C511yescharacteristic
574C23×C4C23×C511yescharacteristic
575C23×C4C23×C511yescharacteristic
576C23×C4C23×C511yescharacteristic
577C23×C4C23×C511yescharacteristic
578C23×C4C23×C511yescharacteristic
579C23×C4C23×C511yescharacteristic
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4C2×C4×C514yescomplemented
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4C2×C4×C514yescomplemented
614C2×C22⋊C4C2×C4×C514yescomplemented
615C2×C22⋊C4C2×C4×C514yescomplemented
616C2×C22⋊C4C2×C4×C514yescomplemented
617C2×C22⋊C4C5×D414yes—
618C2×C22⋊C4C5×D414yes—
619C2×C42—22no—
620C2×C42—41no—
621C2×C42—41no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C514yescomplemented
640C22×C5—24no—
641C22×C5—24no—
642C22×C5—24no—
643C22×C5—24no—
644C22×C5—24no—
645C22×C5—24no—
646C22×C5—42no—
647C22×C5—42no—
648C22×C5—42no—
649C22×C5—42no—
650C22×C5—42no—
651C22×C5—42no—
652C22×C5—42no—
653C22×C5—42no—
654C22×C5—42no—
655C22×C5—42no—
656C22×C5—42no—
657C22×C5—42no—
658C22×C5—42no—
659C22×C5—42no—
660C22×C5—42no—
661C22×C5—42no—
662C22×C5—42no—
663C22×C5—42no—
664C22×C5—42no—
665C22×C5—42no—
666C22×C5—42no—
667C22×C5—42no—
668C22×C5—42no—
669C22×C5—42no—
670C22×C5C2×C4×D411yescharacteristic
671C22×C5C2×C4×D411yescharacteristic
672C22×C5C4×#4111yescharacteristic
673C22×C5#51811yescharacteristic
674C22×C5#51811yescharacteristic
675C22×C5#52011yescharacteristic
676C22×C5#52011yescharacteristic
677C22×C5#53411yescharacteristic
678C22×C5#53411yescharacteristic
679C22×C5#53611yescharacteristic
680C22×C5#53711yescharacteristic
681C22×C5#53811yescharacteristic
682C22×C5#53811yescharacteristic
683C22×C5#53811yescharacteristic
684C22×C5#53911yescharacteristic
685C22×C5#53911yescharacteristic
686C22×C5#53911yescharacteristic
687C22×C5#54211yescharacteristic
688C22×C5#54211yescharacteristic
689C22×C5D4211yescharacteristic
690C22×C5#54611yescharacteristic
691C22×C5#54611yescharacteristic
692C22×C5#54611yescharacteristic
693C22×C5#54611yescharacteristic
694C22×C5#54611yescharacteristic
695C22×C5#54711yescharacteristic
696C22×C5#55111yescharacteristic
697C22×C5#55111yescharacteristic
698C22×C5#55211yescharacteristic
699C22×C5#55311yescharacteristic
700C22×C5#55311yescharacteristic
701C22×C5#56011yescharacteristic
702C22×C5#56011yescharacteristic
703C22×C5#56211yescharacteristic
704C22×C5#56211yescharacteristic
705C4×C5—42no—
706C4×C5—42no—
707C4×C5—42no—
708C4×C5—42no—
709C4×C5—42no—
710C4×C5—42no—
711C4×C5—42no—
712C4×C5—42no—
713C4×C5—42no—
714C4×C5—42no—
715C4×C5—42no—
716C4×C5—81no—
717C4×C5—81no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24C22×C4×C512yes—
743C24C22×C4×C512yes—
744C24C2×C5×D412yes—
745C24C2×C5×D412yes—
746C24C5×#4112yes—
747C24C5×#4112yes—
748C24C24×C511yescharacteristic
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4C22×C4×C512yes—
851C22×C4C22×C4×C512yes—
852C22×C4C22×C4×C512yes—
853C22×C4C22×C4×C512yes—
854C22×C4C22×C4×C512yes—
855C22×C4C2×C5×D412yes—
856C22×C4C2×C5×D412yes—
857C22×C4C2×C5×D412yes—
858C22×C4C2×C5×D412yes—
859C22×C4C5×#4112yes—
860C22×C4C5×#4112yes—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C42—44no—
875C2×C5—44no—
876C2×C5—44no—
877C2×C5#232211yescharacteristic
878C2×C5#232511yescharacteristic
879C2×C5#233711yescharacteristic
880C2×C5#235811yescharacteristic
881C2×C5#235911yescharacteristic
882C2×C5#236411yescharacteristic
883C2×C5#237711yescharacteristic
884C2×C5#266811yescharacteristic
885C2×C5#267211yescharacteristic
886C2×C5#268711yescharacteristic
887C2×C5#269111yescharacteristic
888C2×C5#269711yescharacteristic
889C2×C5#270811yescharacteristic
890C2×C5#274611yescharacteristic
891C2×C5#275011yescharacteristic
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23C4×C5×D414yes—
961C23C4×C5×D414yes—
962C23C23×C4×C511yescharacteristic
963C23C22×C5×D411yescharacteristic
964C23C22×C5×D411yescharacteristic
965C23C2×C5×#4111yescharacteristic
966C23C2×C5×#4111yescharacteristic
967C23C2×C5×#4111yescharacteristic
968C23C2×C5×#4111yescharacteristic
969C23C5×H(5,𝔽2)11yescharacteristic
970C23C5×H(5,𝔽2)11yescharacteristic
971C23C5×H(5,𝔽2)11yescharacteristic
972C23C5×H(5,𝔽2)11yescharacteristic
973C23C5×H(5,𝔽2)11yescharacteristic
974C23C5×H(5,𝔽2)11yescharacteristic
975C23C5×2−1+411yescharacteristic
976C23C5×2−1+411yescharacteristic
977D4—416no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—416no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C5#1451711yescharacteristic, direct product factor, Sylow
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22C2×C4×C5×D411yescharacteristic
1103C22C2×C4×C5×D411yescharacteristic
1104C22C4×C5×#4111yescharacteristic
1105C22C5×#51811yescharacteristic
1106C22C5×#51811yescharacteristic
1107C22C5×#52011yescharacteristic
1108C22C5×#52011yescharacteristic
1109C22C5×#53411yescharacteristic
1110C22C5×#53411yescharacteristic
1111C22C5×#53611yescharacteristic
1112C22C5×#53711yescharacteristic
1113C22C5×#53811yescharacteristic
1114C22C5×#53811yescharacteristic
1115C22C5×#53811yescharacteristic
1116C22C5×#53911yescharacteristic
1117C22C5×#53911yescharacteristic
1118C22C5×#53911yescharacteristic
1119C22C5×#54211yescharacteristic
1120C22C5×#54211yescharacteristic
1121C22C5×D4211yescharacteristic
1122C22C5×#54611yescharacteristic
1123C22C5×#54611yescharacteristic
1124C22C5×#54611yescharacteristic
1125C22C5×#54611yescharacteristic
1126C22C5×#54611yescharacteristic
1127C22C5×#54711yescharacteristic
1128C22C5×#55111yescharacteristic
1129C22C5×#55111yescharacteristic
1130C22C5×#55211yescharacteristic
1131C22C5×#55311yescharacteristic
1132C22C5×#55311yescharacteristic
1133C22C5×#56011yescharacteristic
1134C22C5×#56011yescharacteristic
1135C22C5×#56211yescharacteristic
1136C22C5×#56211yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C2—44no—
1151C2—44no—
1152C2C5×#232211yescharacteristic
1153C2C5×#232511yescharacteristic
1154C2C5×#233711yescharacteristic
1155C2C5×#235811yescharacteristic
1156C2C5×#235911yescharacteristic
1157C2C5×#236411yescharacteristic
1158C2C5×#237711yescharacteristic
1159C2C5×#266811yescharacteristic
1160C2C5×#267211yescharacteristic
1161C2C5×#268711yescharacteristic
1162C2C5×#269111yescharacteristic
1163C2C5×#269711yescharacteristic
1164C2C5×#270811yescharacteristic
1165C2C5×#274611yescharacteristic
1166C2C5×#275011yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#388C2semidirect
5. C2×C5×#385C2semidirect
6. C5×#1445C2semidirect
7. C5×#1443C2semidirect
8. C5×#1441C2semidirect
9. C5×#1440C2semidirect
10. C5×#1439C2semidirect
11. C5×#1437C2semidirect
12. C5×#1436C2semidirect
13. C5×C22⋊#95C2semidirect
14. C5×C22⋊#95C2semidirect
15. C5×C22⋊#95C2semidirect
33. C5×#394C4semidirect
56. #14517C5direct (N × H)
101. C2×C5×C4⋊C4C2×C4semidirect
126. C2×C5×C22⋊C4C2×C4semidirect
127. C2×C5×C22⋊C4C2×C4semidirect
128. C2×C5×C22⋊C4C2×C4semidirect
129. C2×C5×C22⋊C4C2×C4semidirect
152. C5×#95C2×C4semidirect
154. C2×#388C2×C5semidirect
157. C2×#385C2×C5semidirect
158. #1445C2×C5semidirect
159. #1443C2×C5semidirect
160. #1441C2×C5semidirect
161. #1440C2×C5semidirect
162. #1439C2×C5semidirect
163. #1437C2×C5semidirect
164. #1436C2×C5semidirect
165. C22⋊#95C2×C5semidirect
166. C22⋊#95C2×C5semidirect
167. C22⋊#95C2×C5semidirect
342. #394C4×C5semidirect
588. C2×C4⋊C4C2×C4×C5semidirect
613. C2×C22⋊C4C2×C4×C5semidirect
614. C2×C22⋊C4C2×C4×C5semidirect
615. C2×C22⋊C4C2×C4×C5semidirect
616. C2×C22⋊C4C2×C4×C5semidirect
639. #95C2×C4×C5semidirect
1071. C5#14517direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3942
C2×C5×#3882
C2×C5×#3862
C2×C5×#3852
C5×#14452
C5×#14432
C5×#14412
C5×#14402
C5×#14392
C5×#14372
C5×#14362
C5×C22⋊#952
#145175