Finite Group Databasebeta

← C5×#13999 #11936719

Subgroups — C5×#13999 #11936719

Order 1280.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 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×#386C211yesmaximal, characteristic
5C2×C5×#380C211yesmaximal, characteristic, complemented
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
7C22×C5×#95C211yesmaximal, characteristic, complemented
8C5×#1443C211yesmaximal, characteristic, complemented
9C5×#1442C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1437C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1434C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
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×C42×C5C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#388—24no—
34C5×#386—24no—
35C5×#386—24no—
36C5×#386C418yescomplemented
37C5×#380—24no—
38C4×C5×C22⋊C4—24no—
39C2×C5×#95—24no—
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
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58#13999C511yesmaximal, 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—22no—
66C22×C5×D4—22no—
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—22no—
78C23×C4×C5—22no—
79C23×C4×C5—22no—
80C23×C4×C5—22no—
81C23×C4×C5—41no—
82C23×C4×C5—41no—
83C23×C4×C5—41no—
84C23×C4×C5—41no—
85C23×C4×C5—41no—
86C23×C4×C5—41no—
87C23×C4×C5C2×C414yes—
88C23×C4×C5D414yes—
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C23×C4×C5C2311yescharacteristic
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C23×C4×C5C2311yescharacteristic
101C23×C4×C5C2311yescharacteristic
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—41no—
107C2×C5×C4⋊C4—41no—
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—41no—
126C2×C5×C22⋊C4—41no—
127C2×C5×C22⋊C4—41no—
128C2×C5×C22⋊C4—41no—
129C2×C5×C22⋊C4—41no—
130C2×C5×C22⋊C4—41no—
131C2×C5×C22⋊C4C2×C414yes—
132C2×C5×C22⋊C4C2×C414yescomplemented
133C2×C5×C22⋊C4C2×C414yescomplemented
134C2×C5×C22⋊C4D414yes—
135C2×C42×C5—22no—
136C2×C42×C5—22no—
137C2×C42×C5—22no—
138C2×C42×C5—22no—
139C2×C42×C5—41no—
140C2×C42×C5—41no—
141C5×#95—22no—
142C5×#95—22no—
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—22no—
153C5×#95—22no—
154C5×#95—41no—
155C5×#95—41no—
156C5×#95C2×C414yescomplemented
157C5×#95C2×C414yescomplemented
158C5×#95D414yescomplemented
159C2×#388C2×C511yescharacteristic, complemented
160C2×#386C2×C511yescharacteristic
161C2×#386C2×C511yescharacteristic
162C2×#386C2×C511yescharacteristic
163C2×#380C2×C511yescharacteristic, complemented
164C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
165C22×#95C2×C511yescharacteristic, complemented
166#1443C2×C511yescharacteristic, complemented
167#1442C2×C511yescharacteristic, complemented
168#1440C2×C511yescharacteristic, complemented
169#1439C2×C511yescharacteristic, complemented
170#1437C2×C511yescharacteristic, complemented
171#1436C2×C511yescharacteristic, complemented
172#1434C2×C511yescharacteristic, complemented
173C22⋊#95C2×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×C5C22×C412yes—
197C24×C5C22×C412yes—
198C24×C5C2×D412yes—
199C24×C5C2×D412yes—
200C24×C5#4112yes—
201C24×C5#4112yes—
202C24×C5#4112yes—
203C24×C5#4112yes—
204C24×C5C2411yescharacteristic
205C2×C5×D4—28no—
206C2×C5×D4—28no—
207C2×C5×D4—28no—
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—28no—
221C22×C4×C5—28no—
222C22×C4×C5—28no—
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—28no—
278C22×C4×C5—28no—
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—21no—
290C22×C4×C5—21no—
291C22×C4×C5—21no—
292C22×C4×C5—21no—
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×C5—44no—
301C22×C4×C5—44no—
302C22×C4×C5—44no—
303C22×C4×C5—44no—
304C22×C4×C5—44no—
305C22×C4×C5—44no—
306C22×C4×C5—44no—
307C22×C4×C5—44no—
308C22×C4×C5—44no—
309C22×C4×C5C22×C412yes—
310C22×C4×C5C22×C412yes—
311C22×C4×C5C22×C412yes—
312C22×C4×C5C22×C412yes—
313C22×C4×C5C22×C412yes—
314C22×C4×C5C2×D412yes—
315C22×C4×C5C2×D412yes—
316C22×C4×C5C2×D412yes—
317C22×C4×C5C2×D412yes—
318C22×C4×C5C2×D412yes—
319C22×C4×C5C2×D412yes—
320C22×C4×C5C2×D412yes—
321C22×C4×C5#4112yes—
322C22×C4×C5#4112yes—
323C22×C4×C5#4112yes—
324C5×C4⋊C4—44no—
325C5×C4⋊C4—44no—
326C5×C22⋊C4—28no—
327C5×C22⋊C4—28no—
328C5×C22⋊C4—28no—
329C5×C22⋊C4—44no—
330C5×C22⋊C4—44no—
331C5×C22⋊C4—44no—
332C5×C22⋊C4—44no—
333C5×C22⋊C4—44no—
334C5×C22⋊C4—44no—
335C42×C5—44no—
336C42×C5—44no—
337C23×D4C22×C511yescharacteristic
338C24×C4C22×C511yescharacteristic
339C24×C4C22×C511yescharacteristic
340C24×C4C22×C511yescharacteristic
341C22×C4⋊C4C22×C511yescharacteristic
342C22×C4⋊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×C22⋊C4C22×C511yescharacteristic
350C22×C22⋊C4C22×C511yescharacteristic
351C22×C22⋊C4C22×C511yescharacteristic
352C22×C42C22×C511yescharacteristic
353C22×C42C22×C511yescharacteristic
354#388—24no—
355#386—24no—
356#386—24no—
357#386C4×C518yescomplemented
358#380—24no—
359C4×C22⋊C4—24no—
360C2×#95—24no—
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
375C2×#95C22×C511yescharacteristic
376C2×#95C22×C511yescharacteristic
377C2×#95C22×C511yescharacteristic
378C2×#95C22×C511yescharacteristic
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—22no—
412C23×C5—22no—
413C23×C5—22no—
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#11714yes—
443C23×C5C4×D414yes—
444C23×C5C4×D414yes—
445C23×C5#12114yes—
446C23×C5#12314yes—
447C23×C5#12414yes—
448C23×C5#12614yes—
449C23×C5C23×C411yescharacteristic
450C23×C5C22×D411yescharacteristic
451C23×C5C22×D411yescharacteristic
452C23×C5C22×D411yescharacteristic
453C23×C5C2×#4111yescharacteristic
454C23×C5C2×#4111yescharacteristic
455C23×C5C2×#4111yescharacteristic
456C23×C5C2×#4111yescharacteristic
457C23×C5C2×#4111yescharacteristic
458C23×C5C2×#4111yescharacteristic
459C23×C5C2×#4111yescharacteristic
460C23×C5H(5,𝔽2)11yescharacteristic
461C23×C5H(5,𝔽2)11yescharacteristic
462C23×C5H(5,𝔽2)11yescharacteristic
463C23×C52−1+411yescharacteristic
464C5×D4—416no—
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—22no—
504C2×C4×C5—416no—
505C2×C4×C5—416no—
506C2×C4×C5—416no—
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×C5—41no—
552C2×C4×C5—41no—
553C2×C4×C5—41no—
554C2×C4×C5—41no—
555C2×C4×C5—41no—
556C2×C4×C5—41no—
557C2×C4×C5C4×D414yes—
558C2×C4×C5#12114yes—
559C25C23×C511yescharacteristic
560C25C23×C511yescharacteristic
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—22no—
567C22×D4C2×C4×C514yes—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4—41no—
586C23×C4—41no—
587C23×C4C2×C4×C514yes—
588C23×C4C5×D414yes—
589C23×C4C23×C511yescharacteristic
590C23×C4C23×C511yescharacteristic
591C23×C4C23×C511yescharacteristic
592C23×C4C23×C511yescharacteristic
593C23×C4C23×C511yescharacteristic
594C23×C4C23×C511yescharacteristic
595C23×C4C23×C511yescharacteristic
596C23×C4C23×C511yescharacteristic
597C23×C4C23×C511yescharacteristic
598C23×C4C23×C511yescharacteristic
599C23×C4C23×C511yescharacteristic
600C23×C4C23×C511yescharacteristic
601C23×C4C23×C511yescharacteristic
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
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—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4—41no—
629C2×C22⋊C4—41no—
630C2×C22⋊C4—41no—
631C2×C22⋊C4C2×C4×C514yes—
632C2×C22⋊C4C2×C4×C514yescomplemented
633C2×C22⋊C4C2×C4×C514yescomplemented
634C2×C22⋊C4C5×D414yes—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—41no—
640C2×C42—41no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—41no—
655#95—41no—
656#95C2×C4×C514yescomplemented
657#95C2×C4×C514yescomplemented
658#95C5×D414yescomplemented
659C22×C5—24no—
660C22×C5—24no—
661C22×C5—24no—
662C22×C5—24no—
663C22×C5—24no—
664C22×C5—24no—
665C22×C5—24no—
666C22×C5—24no—
667C22×C5—24no—
668C22×C5—24no—
669C22×C5—24no—
670C22×C5—24no—
671C22×C5—24no—
672C22×C5—24no—
673C22×C5—42no—
674C22×C5—42no—
675C22×C5—42no—
676C22×C5—42no—
677C22×C5—42no—
678C22×C5—42no—
679C22×C5—42no—
680C22×C5—81no—
681C22×C5—81no—
682C22×C5—81no—
683C22×C5—81no—
684C22×C5—81no—
685C22×C5—81no—
686C22×C5—81no—
687C22×C5—81no—
688C22×C5#38818yescomplemented
689C22×C5C2×#11711yescharacteristic
690C22×C5C2×C4×D411yescharacteristic
691C22×C5C2×C4×D411yescharacteristic
692C22×C5C2×C4×D411yescharacteristic
693C22×C5C4×#4111yescharacteristic
694C22×C5#51811yescharacteristic
695C22×C5#52011yescharacteristic
696C22×C5C2×#12111yescharacteristic
697C22×C5C2×#12111yescharacteristic
698C22×C5C2×#12311yescharacteristic
699C22×C5#52511yescharacteristic
700C22×C5C2×#12411yescharacteristic
701C22×C5C2×#12611yescharacteristic
702C22×C5#52911yescharacteristic
703C22×C5#53211yescharacteristic
704C22×C5#53411yescharacteristic
705C22×C5#53711yescharacteristic
706C22×C5#53811yescharacteristic
707C22×C5#53911yescharacteristic
708C22×C5D4211yescharacteristic
709C22×C5#54611yescharacteristic
710C22×C5#54611yescharacteristic
711C22×C5#54611yescharacteristic
712C22×C5#54611yescharacteristic
713C22×C5#54711yescharacteristic
714C22×C5#54811yescharacteristic
715C22×C5#55111yescharacteristic
716C22×C5#55111yescharacteristic
717C22×C5#55111yescharacteristic
718C22×C5#55111yescharacteristic
719C22×C5#55211yescharacteristic
720C22×C5#55211yescharacteristic
721C22×C5#55311yescharacteristic
722C22×C5#55311yescharacteristic
723C22×C5#55311yescharacteristic
724C4×C5—24no—
725C4×C5—24no—
726C4×C5—42no—
727C4×C5—42no—
728C4×C5—42no—
729C4×C5—42no—
730C4×C5—42no—
731C4×C5—42no—
732C4×C5—42no—
733C4×C5—42no—
734C4×C5—42no—
735C4×C5—81no—
736C4×C5—81no—
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—
756C24—21no—
757C24—21no—
758C24—21no—
759C24C22×C4×C512yes—
760C24C22×C4×C512yes—
761C24C2×C5×D412yes—
762C24C2×C5×D412yes—
763C24C5×#4112yes—
764C24C5×#4112yes—
765C24C5×#4112yes—
766C24C5×#4112yes—
767C24C24×C511yescharacteristic
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
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—28no—
784C22×C4—28no—
785C22×C4—28no—
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—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—28no—
841C22×C4—28no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4C22×C4×C512yes—
873C22×C4C22×C4×C512yes—
874C22×C4C22×C4×C512yes—
875C22×C4C22×C4×C512yes—
876C22×C4C22×C4×C512yes—
877C22×C4C2×C5×D412yes—
878C22×C4C2×C5×D412yes—
879C22×C4C2×C5×D412yes—
880C22×C4C2×C5×D412yes—
881C22×C4C2×C5×D412yes—
882C22×C4C2×C5×D412yes—
883C22×C4C2×C5×D412yes—
884C22×C4C5×#4112yes—
885C22×C4C5×#4112yes—
886C22×C4C5×#4112yes—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—44no—
899C42—44no—
900C2×C5—28no—
901C2×C5—82no—
902C2×C5C2×#38811yescharacteristic
903C2×C5C4×#12111yescharacteristic
904C2×C5#232511yescharacteristic
905C2×C5#235211yescharacteristic
906C2×C5#235311yescharacteristic
907C2×C5#235811yescharacteristic
908C2×C5#235911yescharacteristic
909C2×C5#241211yescharacteristic
910C2×C5#241611yescharacteristic
911C2×C5#247211yescharacteristic
912C2×C5#248111yescharacteristic
913C2×C5#248811yescharacteristic
914C2×C5#249811yescharacteristic
915C2×C5#251011yescharacteristic
916C2×C5#254311yescharacteristic
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—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
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—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C5×#11714yes—
981C23C4×C5×D414yes—
982C23C4×C5×D414yes—
983C23C5×#12114yes—
984C23C5×#12314yes—
985C23C5×#12414yes—
986C23C5×#12614yes—
987C23C23×C4×C511yescharacteristic
988C23C22×C5×D411yescharacteristic
989C23C22×C5×D411yescharacteristic
990C23C22×C5×D411yescharacteristic
991C23C2×C5×#4111yescharacteristic
992C23C2×C5×#4111yescharacteristic
993C23C2×C5×#4111yescharacteristic
994C23C2×C5×#4111yescharacteristic
995C23C2×C5×#4111yescharacteristic
996C23C2×C5×#4111yescharacteristic
997C23C2×C5×#4111yescharacteristic
998C23C5×H(5,𝔽2)11yescharacteristic
999C23C5×H(5,𝔽2)11yescharacteristic
1000C23C5×H(5,𝔽2)11yescharacteristic
1001C23C5×2−1+411yescharacteristic
1002D4—416no—
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—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—416no—
1043C2×C4—416no—
1044C2×C4—416no—
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×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4C4×C5×D414yes—
1096C2×C4C5×#12114yes—
1097C5#1399911yescharacteristic, direct product factor, Sylow
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22C5×#38818yescomplemented
1128C22C2×C5×#11711yescharacteristic
1129C22C2×C4×C5×D411yescharacteristic
1130C22C2×C4×C5×D411yescharacteristic
1131C22C2×C4×C5×D411yescharacteristic
1132C22C4×C5×#4111yescharacteristic
1133C22C5×#51811yescharacteristic
1134C22C5×#52011yescharacteristic
1135C22C2×C5×#12111yescharacteristic
1136C22C2×C5×#12111yescharacteristic
1137C22C2×C5×#12311yescharacteristic
1138C22C5×#52511yescharacteristic
1139C22C2×C5×#12411yescharacteristic
1140C22C2×C5×#12611yescharacteristic
1141C22C5×#52911yescharacteristic
1142C22C5×#53211yescharacteristic
1143C22C5×#53411yescharacteristic
1144C22C5×#53711yescharacteristic
1145C22C5×#53811yescharacteristic
1146C22C5×#53911yescharacteristic
1147C22C5×D4211yescharacteristic
1148C22C5×#54611yescharacteristic
1149C22C5×#54611yescharacteristic
1150C22C5×#54611yescharacteristic
1151C22C5×#54611yescharacteristic
1152C22C5×#54711yescharacteristic
1153C22C5×#54811yescharacteristic
1154C22C5×#55111yescharacteristic
1155C22C5×#55111yescharacteristic
1156C22C5×#55111yescharacteristic
1157C22C5×#55111yescharacteristic
1158C22C5×#55211yescharacteristic
1159C22C5×#55211yescharacteristic
1160C22C5×#55311yescharacteristic
1161C22C5×#55311yescharacteristic
1162C22C5×#55311yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—81no—
1175C4—81no—
1176C2—28no—
1177C2—82no—
1178C2C2×C5×#38811yescharacteristic
1179C2C4×C5×#12111yescharacteristic
1180C2C5×#232511yescharacteristic
1181C2C5×#235211yescharacteristic
1182C2C5×#235311yescharacteristic
1183C2C5×#235811yescharacteristic
1184C2C5×#235911yescharacteristic
1185C2C5×#241211yescharacteristic
1186C2C5×#241611yescharacteristic
1187C2C5×#247211yescharacteristic
1188C2C5×#248111yescharacteristic
1189C2C5×#248811yescharacteristic
1190C2C5×#249811yescharacteristic
1191C2C5×#251011yescharacteristic
1192C2C5×#254311yescharacteristic
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
5. C2×C5×#380C2semidirect
6. C2×C4×C5×C22⋊C4C2semidirect
7. C22×C5×#95C2semidirect
8. C5×#1443C2semidirect
9. C5×#1442C2semidirect
10. C5×#1440C2semidirect
11. C5×#1439C2semidirect
12. C5×#1437C2semidirect
13. C5×#1436C2semidirect
14. C5×#1434C2semidirect
15. C5×C22⋊#95C2semidirect
36. C5×#386C4semidirect
58. #13999C5direct (N × H)
132. C2×C5×C22⋊C4C2×C4semidirect
133. C2×C5×C22⋊C4C2×C4semidirect
156. C5×#95C2×C4semidirect
157. C5×#95C2×C4semidirect
158. C5×#95D4semidirect
159. C2×#388C2×C5semidirect
163. C2×#380C2×C5semidirect
164. C2×C4×C22⋊C4C2×C5semidirect
165. C22×#95C2×C5semidirect
166. #1443C2×C5semidirect
167. #1442C2×C5semidirect
168. #1440C2×C5semidirect
169. #1439C2×C5semidirect
170. #1437C2×C5semidirect
171. #1436C2×C5semidirect
172. #1434C2×C5semidirect
173. C22⋊#95C2×C5semidirect
357. #386C4×C5semidirect
632. C2×C22⋊C4C2×C4×C5semidirect
633. C2×C22⋊C4C2×C4×C5semidirect
656. #95C2×C4×C5semidirect
657. #95C2×C4×C5semidirect
658. #95C5×D4semidirect
688. C22×C5#388semidirect
1097. C5#13999direct (N × H)
1127. C22C5×#388semidirect

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×#3802
C2×C4×C5×C22⋊C42
C22×C5×#952
C5×#14432
C5×#14422
C5×#14402
C5×#14392
C5×#14372
C5×#14362
C5×#14342
C5×C22⋊#952
#139995