Finite Group Databasebeta

← C5×#13988 #11936708

Subgroups — C5×#13988 #11936708

Order 1280.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#388C211yesmaximal, characteristic, complemented
2C2×C5×#386C211yesmaximal, characteristic
3C2×C5×#386C211yesmaximal, characteristic
4C2×C5×#385C211yesmaximal, characteristic, complemented
5C2×C5×#380C211yesmaximal, characteristic, complemented
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
7C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
8C5×#1442C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1438C211yesmaximal, characteristic
12C5×#1437C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×#1434C211yesmaximal, 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
33C22×C42×C5C2211yescharacteristic
34C22×C42×C5C2211yescharacteristic
35C5×#388—24no—
36C5×#386—24no—
37C5×#386C418yescomplemented
38C5×#385—24no—
39C5×#380—24no—
40C4×C5×C22⋊C4—24no—
41C4×C5×C22⋊C4—24no—
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
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58#13988C511yesmaximal, characteristic, direct product factor, Sylow
59C25×C5C2311yescharacteristic
60C25×C5C2311yescharacteristic
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—41no—
66C22×C5×D4—41no—
67C22×C5×D4C2×C414yes—
68C23×C4×C5—22no—
69C23×C4×C5—22no—
70C23×C4×C5—22no—
71C23×C4×C5—22no—
72C23×C4×C5—22no—
73C23×C4×C5—22no—
74C23×C4×C5—22no—
75C23×C4×C5—22no—
76C23×C4×C5—22no—
77C23×C4×C5—41no—
78C23×C4×C5—41no—
79C23×C4×C5—41no—
80C23×C4×C5—41no—
81C23×C4×C5C2×C414yescomplemented
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
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C2×C5×C4⋊C4—22no—
96C2×C5×C4⋊C4—22no—
97C2×C5×C4⋊C4—22no—
98C2×C5×C4⋊C4—22no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—41no—
103C2×C5×C4⋊C4—41no—
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—22no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4—22no—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—41no—
127C2×C5×C22⋊C4—41no—
128C2×C5×C22⋊C4—41no—
129C2×C5×C22⋊C4—41no—
130C2×C5×C22⋊C4C2×C414yes—
131C2×C5×C22⋊C4C2×C414yes—
132C2×C5×C22⋊C4C2×C414yescomplemented
133C2×C5×C22⋊C4D414yes—
134C2×C42×C5—22no—
135C2×C42×C5—22no—
136C2×C42×C5—22no—
137C2×C42×C5—22no—
138C2×C42×C5—22no—
139C2×C42×C5—22no—
140C2×C42×C5—41no—
141C2×C42×C5—41no—
142C2×C42×C5—41no—
143C5×#95—22no—
144C5×#95—22no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95—22no—
149C5×#95—22no—
150C5×#95—22no—
151C5×#95—22no—
152C5×#95—41no—
153C5×#95—41no—
154C5×#95—41no—
155C5×#95C2×C414yescomplemented
156C5×#95C2×C414yescomplemented
157C5×#95D414yescomplemented
158C5×#95D414yescomplemented
159C2×#388C2×C511yescharacteristic, complemented
160C2×#386C2×C511yescharacteristic
161C2×#386C2×C511yescharacteristic
162C2×#385C2×C511yescharacteristic, complemented
163C2×#380C2×C511yescharacteristic, complemented
164C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
165C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
166#1442C2×C511yescharacteristic, complemented
167#1440C2×C511yescharacteristic, complemented
168#1439C2×C511yescharacteristic, complemented
169#1438C2×C511yescharacteristic
170#1437C2×C511yescharacteristic, complemented
171#1436C2×C511yescharacteristic, complemented
172#1436C2×C511yescharacteristic, complemented
173#1434C2×C511yescharacteristic, complemented
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×C5—21no—
193C24×C5—21no—
194C24×C5—21no—
195C24×C5—21no—
196C24×C5—21no—
197C24×C5—21no—
198C24×C5C22×C412yes—
199C24×C5C22×C412yes—
200C24×C5C2×D412yes—
201C24×C5#4112yes—
202C24×C5#4112yes—
203C24×C5#4112yes—
204C24×C5C2411yescharacteristic
205C2×C5×D4—28no—
206C2×C5×D4—28no—
207C2×C5×D4—44no—
208C2×C5×D4—44no—
209C2×C5×D4—44no—
210C2×C5×D4—44no—
211C2×C5×D4—44no—
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—28no—
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—28no—
274C22×C4×C5—28no—
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—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
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×C5C2×D412yes—
310C22×C4×C5C2×D412yes—
311C22×C4×C5C2×D412yes—
312C22×C4×C5C2×D412yes—
313C22×C4×C5#4112yes—
314C22×C4×C5#4112yes—
315C22×C4×C5#4112yes—
316C22×C4×C5#4112yes—
317C5×C4⋊C4—44no—
318C5×C4⋊C4—44no—
319C5×C4⋊C4—44no—
320C5×C22⋊C4—28no—
321C5×C22⋊C4—28no—
322C5×C22⋊C4—28no—
323C5×C22⋊C4—28no—
324C5×C22⋊C4—28no—
325C5×C22⋊C4—28no—
326C5×C22⋊C4—44no—
327C5×C22⋊C4—44no—
328C5×C22⋊C4—44no—
329C5×C22⋊C4—44no—
330C42×C5—44no—
331C42×C5—44no—
332C42×C5—44no—
333C23×D4C22×C511yescharacteristic
334C24×C4C22×C511yescharacteristic
335C24×C4C22×C511yescharacteristic
336C22×C4⋊C4C22×C511yescharacteristic
337C22×C4⋊C4C22×C511yescharacteristic
338C22×C4⋊C4C22×C511yescharacteristic
339C22×C22⋊C4C22×C511yescharacteristic
340C22×C22⋊C4C22×C511yescharacteristic
341C22×C22⋊C4C22×C511yescharacteristic
342C22×C22⋊C4C22×C511yescharacteristic
343C22×C22⋊C4C22×C511yescharacteristic
344C22×C22⋊C4C22×C511yescharacteristic
345C22×C22⋊C4C22×C511yescharacteristic
346C22×C22⋊C4C22×C511yescharacteristic
347C22×C22⋊C4C22×C511yescharacteristic
348C22×C22⋊C4C22×C511yescharacteristic
349C22×C42C22×C511yescharacteristic
350C22×C42C22×C511yescharacteristic
351C22×C42C22×C511yescharacteristic
352#388—24no—
353#386—24no—
354#386C4×C518yescomplemented
355#385—24no—
356#380—24no—
357C4×C22⋊C4—24no—
358C4×C22⋊C4—24no—
359C2×#95C22×C511yescharacteristic
360C2×#95C22×C511yescharacteristic
361C2×#95C22×C511yescharacteristic
362C2×#95C22×C511yescharacteristic
363C2×#95C22×C511yescharacteristic
364C2×#95C22×C511yescharacteristic
365C2×#95C22×C511yescharacteristic
366C2×#95C22×C511yescharacteristic
367C2×#95C22×C511yescharacteristic
368C2×#95C22×C511yescharacteristic
369C2×#95C22×C511yescharacteristic
370C2×#95C22×C511yescharacteristic
371C2×#95C22×C511yescharacteristic
372C2×#95C22×C511yescharacteristic
373C2×#95C22×C511yescharacteristic
374C2×#95C22×C511yescharacteristic
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—22no—
402C23×C5—22no—
403C23×C5—22no—
404C23×C5—22no—
405C23×C5—22no—
406C23×C5—22no—
407C23×C5—22no—
408C23×C5—22no—
409C23×C5—22no—
410C23×C5—22no—
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×C5—41no—
434C23×C5—41no—
435C23×C5—41no—
436C23×C5—41no—
437C23×C5—41no—
438C23×C5—41no—
439C23×C5—41no—
440C23×C5—41no—
441C23×C5—41no—
442C23×C5—41no—
443C23×C5#11714yes—
444C23×C5C4×D414yes—
445C23×C5C23×C411yescharacteristic
446C23×C5C22×D411yescharacteristic
447C23×C5C22×D411yescharacteristic
448C23×C5C22×D411yescharacteristic
449C23×C5C2×#4111yescharacteristic
450C23×C5C2×#4111yescharacteristic
451C23×C5C2×#4111yescharacteristic
452C23×C5C2×#4111yescharacteristic
453C23×C5C2×#4111yescharacteristic
454C23×C5C2×#4111yescharacteristic
455C23×C5C2×#4111yescharacteristic
456C23×C5H(5,𝔽2)11yescharacteristic
457C23×C5H(5,𝔽2)11yescharacteristic
458C23×C5H(5,𝔽2)11yescharacteristic
459C23×C52−1+411yescharacteristic
460C5×D4—416no—
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—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—22no—
490C2×C4×C5—22no—
491C2×C4×C5—22no—
492C2×C4×C5—22no—
493C2×C4×C5—22no—
494C2×C4×C5—22no—
495C2×C4×C5—22no—
496C2×C4×C5—22no—
497C2×C4×C5—22no—
498C2×C4×C5—22no—
499C2×C4×C5—22no—
500C2×C4×C5—22no—
501C2×C4×C5—22no—
502C2×C4×C5—22no—
503C2×C4×C5—416no—
504C2×C4×C5—416no—
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—
544C2×C4×C5—41no—
545C2×C4×C5—41no—
546C2×C4×C5—41no—
547C2×C4×C5—41no—
548C2×C4×C5—41no—
549C2×C4×C5—41no—
550C2×C4×C5—41no—
551C2×C4×C5C4×D414yes—
552C2×C4×C5C4×D414yes—
553C2×C4×C5#12114yes—
554C25C23×C511yescharacteristic
555C25C23×C511yescharacteristic
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4C2×C4×C514yes—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4—41no—
576C23×C4C2×C4×C514yescomplemented
577C23×C4C23×C511yescharacteristic
578C23×C4C23×C511yescharacteristic
579C23×C4C23×C511yescharacteristic
580C23×C4C23×C511yescharacteristic
581C23×C4C23×C511yescharacteristic
582C23×C4C23×C511yescharacteristic
583C23×C4C23×C511yescharacteristic
584C23×C4C23×C511yescharacteristic
585C23×C4C23×C511yescharacteristic
586C23×C4C23×C511yescharacteristic
587C23×C4C23×C511yescharacteristic
588C23×C4C23×C511yescharacteristic
589C23×C4C23×C511yescharacteristic
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4C2×C4×C514yes—
626C2×C22⋊C4C2×C4×C514yes—
627C2×C22⋊C4C2×C4×C514yescomplemented
628C2×C22⋊C4C5×D414yes—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42—41no—
637C2×C42—41no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95C2×C4×C514yescomplemented
651#95C2×C4×C514yescomplemented
652#95C5×D414yescomplemented
653#95C5×D414yescomplemented
654C22×C5—24no—
655C22×C5—24no—
656C22×C5—24no—
657C22×C5—24no—
658C22×C5—24no—
659C22×C5—24no—
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×C5—42no—
671C22×C5—42no—
672C22×C5—42no—
673C22×C5—42no—
674C22×C5—42no—
675C22×C5—42no—
676C22×C5—42no—
677C22×C5—42no—
678C22×C5—42no—
679C22×C5—42no—
680C22×C5—42no—
681C22×C5—42no—
682C22×C5—42no—
683C22×C5—42no—
684C22×C5C2×#11711yescharacteristic
685C22×C5C2×C4×D411yescharacteristic
686C22×C5C2×C4×D411yescharacteristic
687C22×C5C2×C4×D411yescharacteristic
688C22×C5C4×#4111yescharacteristic
689C22×C5#51811yescharacteristic
690C22×C5#52011yescharacteristic
691C22×C5C2×#12111yescharacteristic
692C22×C5#52511yescharacteristic
693C22×C5#52511yescharacteristic
694C22×C5#52511yescharacteristic
695C22×C5#52911yescharacteristic
696C22×C5#52911yescharacteristic
697C22×C5#52911yescharacteristic
698C22×C5#53211yescharacteristic
699C22×C5#53811yescharacteristic
700C22×C5#53911yescharacteristic
701C22×C5#54011yescharacteristic
702C22×C5#54211yescharacteristic
703C22×C5D4211yescharacteristic
704C22×C5D4211yescharacteristic
705C22×C5#54611yescharacteristic
706C22×C5#54611yescharacteristic
707C22×C5#54611yescharacteristic
708C22×C5#54611yescharacteristic
709C22×C5#54611yescharacteristic
710C22×C5#54711yescharacteristic
711C22×C5#54811yescharacteristic
712C22×C5#54811yescharacteristic
713C22×C5#55111yescharacteristic
714C22×C5#55111yescharacteristic
715C22×C5#55111yescharacteristic
716C22×C5#55211yescharacteristic
717C22×C5#55311yescharacteristic
718C22×C5#55311yescharacteristic
719C4×C5—24no—
720C4×C5—24no—
721C4×C5—24no—
722C4×C5—42no—
723C4×C5—42no—
724C4×C5—42no—
725C4×C5—42no—
726C4×C5—42no—
727C4×C5—42no—
728C4×C5—42no—
729C4×C5—42no—
730C4×C5—81no—
731C4×C5—81no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24C22×C4×C512yes—
757C24C22×C4×C512yes—
758C24C2×C5×D412yes—
759C24C5×#4112yes—
760C24C5×#4112yes—
761C24C5×#4112yes—
762C24C24×C511yescharacteristic
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
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—28no—
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—28no—
832C22×C4—28no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4C22×C4×C512yes—
859C22×C4C22×C4×C512yes—
860C22×C4C22×C4×C512yes—
861C22×C4C22×C4×C512yes—
862C22×C4C22×C4×C512yes—
863C22×C4C2×C5×D412yes—
864C22×C4C2×C5×D412yes—
865C22×C4C2×C5×D412yes—
866C22×C4C2×C5×D412yes—
867C22×C4C2×C5×D412yes—
868C22×C4C2×C5×D412yes—
869C22×C4C2×C5×D412yes—
870C22×C4C2×C5×D412yes—
871C22×C4C5×#4112yes—
872C22×C4C5×#4112yes—
873C22×C4C5×#4112yes—
874C22×C4C5×#4112yes—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C42—44no—
889C42—44no—
890C42—44no—
891C2×C5—44no—
892C2×C5—44no—
893C2×C5#229011yescharacteristic
894C2×C5C4×#12111yescharacteristic
895C2×C5#233511yescharacteristic
896C2×C5#234211yescharacteristic
897C2×C5#235211yescharacteristic
898C2×C5#235811yescharacteristic
899C2×C5#236111yescharacteristic
900C2×C5#242411yescharacteristic
901C2×C5#242711yescharacteristic
902C2×C5#245711yescharacteristic
903C2×C5#246311yescharacteristic
904C2×C5#246411yescharacteristic
905C2×C5#247711yescharacteristic
906C2×C5#255311yescharacteristic
907C2×C5#257811yescharacteristic
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—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
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—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23C5×#11714yes—
977C23C4×C5×D414yes—
978C23C23×C4×C511yescharacteristic
979C23C22×C5×D411yescharacteristic
980C23C22×C5×D411yescharacteristic
981C23C22×C5×D411yescharacteristic
982C23C2×C5×#4111yescharacteristic
983C23C2×C5×#4111yescharacteristic
984C23C2×C5×#4111yescharacteristic
985C23C2×C5×#4111yescharacteristic
986C23C2×C5×#4111yescharacteristic
987C23C2×C5×#4111yescharacteristic
988C23C2×C5×#4111yescharacteristic
989C23C5×H(5,𝔽2)11yescharacteristic
990C23C5×H(5,𝔽2)11yescharacteristic
991C23C5×H(5,𝔽2)11yescharacteristic
992C23C5×2−1+411yescharacteristic
993D4—416no—
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—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—416no—
1037C2×C4—416no—
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—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4C4×C5×D414yes—
1085C2×C4C4×C5×D414yes—
1086C2×C4C5×#12114yes—
1087C5#1398811yescharacteristic, direct product factor, Sylow
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22C2×C5×#11711yescharacteristic
1119C22C2×C4×C5×D411yescharacteristic
1120C22C2×C4×C5×D411yescharacteristic
1121C22C2×C4×C5×D411yescharacteristic
1122C22C4×C5×#4111yescharacteristic
1123C22C5×#51811yescharacteristic
1124C22C5×#52011yescharacteristic
1125C22C2×C5×#12111yescharacteristic
1126C22C5×#52511yescharacteristic
1127C22C5×#52511yescharacteristic
1128C22C5×#52511yescharacteristic
1129C22C5×#52911yescharacteristic
1130C22C5×#52911yescharacteristic
1131C22C5×#52911yescharacteristic
1132C22C5×#53211yescharacteristic
1133C22C5×#53811yescharacteristic
1134C22C5×#53911yescharacteristic
1135C22C5×#54011yescharacteristic
1136C22C5×#54211yescharacteristic
1137C22C5×D4211yescharacteristic
1138C22C5×D4211yescharacteristic
1139C22C5×#54611yescharacteristic
1140C22C5×#54611yescharacteristic
1141C22C5×#54611yescharacteristic
1142C22C5×#54611yescharacteristic
1143C22C5×#54611yescharacteristic
1144C22C5×#54711yescharacteristic
1145C22C5×#54811yescharacteristic
1146C22C5×#54811yescharacteristic
1147C22C5×#55111yescharacteristic
1148C22C5×#55111yescharacteristic
1149C22C5×#55111yescharacteristic
1150C22C5×#55211yescharacteristic
1151C22C5×#55311yescharacteristic
1152C22C5×#55311yescharacteristic
1153C4—24no—
1154C4—24no—
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C2—44no—
1167C2—44no—
1168C2C5×#229011yescharacteristic
1169C2C4×C5×#12111yescharacteristic
1170C2C5×#233511yescharacteristic
1171C2C5×#234211yescharacteristic
1172C2C5×#235211yescharacteristic
1173C2C5×#235811yescharacteristic
1174C2C5×#236111yescharacteristic
1175C2C5×#242411yescharacteristic
1176C2C5×#242711yescharacteristic
1177C2C5×#245711yescharacteristic
1178C2C5×#246311yescharacteristic
1179C2C5×#246411yescharacteristic
1180C2C5×#247711yescharacteristic
1181C2C5×#255311yescharacteristic
1182C2C5×#257811yescharacteristic
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
1. C2×C5×#388C2semidirect
4. C2×C5×#385C2semidirect
5. C2×C5×#380C2semidirect
6. C2×C4×C5×C22⋊C4C2semidirect
7. C2×C4×C5×C22⋊C4C2semidirect
8. C5×#1442C2semidirect
9. C5×#1440C2semidirect
10. C5×#1439C2semidirect
12. C5×#1437C2semidirect
13. C5×#1436C2semidirect
14. C5×#1436C2semidirect
15. C5×#1434C2semidirect
37. C5×#386C4semidirect
58. #13988C5direct (N × H)
81. C23×C4×C5C2×C4semidirect
132. C2×C5×C22⋊C4C2×C4semidirect
155. C5×#95C2×C4semidirect
156. C5×#95C2×C4semidirect
157. C5×#95D4semidirect
158. C5×#95D4semidirect
159. C2×#388C2×C5semidirect
162. C2×#385C2×C5semidirect
163. C2×#380C2×C5semidirect
164. C2×C4×C22⋊C4C2×C5semidirect
165. C2×C4×C22⋊C4C2×C5semidirect
166. #1442C2×C5semidirect
167. #1440C2×C5semidirect
168. #1439C2×C5semidirect
170. #1437C2×C5semidirect
171. #1436C2×C5semidirect
172. #1436C2×C5semidirect
173. #1434C2×C5semidirect
354. #386C4×C5semidirect
576. C23×C4C2×C4×C5semidirect
627. C2×C22⋊C4C2×C4×C5semidirect
650. #95C2×C4×C5semidirect
651. #95C2×C4×C5semidirect
652. #95C5×D4semidirect
653. #95C5×D4semidirect
1087. C5#13988direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3882
C2×C5×#3862
C2×C5×#3852
C2×C5×#3802
C2×C4×C5×C22⋊C42
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
C5×#14342
#139885