Finite Group Databasebeta

← C5×#14622 #11937342

Subgroups — C5×#14622 #11937342

Order 1280.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic
2C2×C5×#386C211yesmaximal, characteristic
3C2×C5×#385C211yesmaximal, characteristic, complemented
4C5×#1445C211yesmaximal, characteristic, complemented
5C5×#1442C211yesmaximal, characteristic, complemented
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1441C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1439C211yesmaximal, characteristic, complemented
13C5×#1439C211yesmaximal, characteristic, complemented
14C5×#1438C211yesmaximal, characteristic
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
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×C5×C22⋊C4C2211yescharacteristic
33C5×#394C418yescomplemented
34C5×#386—24no—
35C5×#385—24no—
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#14622C511yesmaximal, characteristic, direct product factor, Sylow
55C25×C5C2311yescharacteristic
56C25×C5C2311yescharacteristic
57C22×C5×D4—22no—
58C22×C5×D4—22no—
59C22×C5×D4—41no—
60C22×C5×D4—41no—
61C22×C5×D4—41no—
62C22×C5×D4—41no—
63C22×C5×D4C2×C414yes—
64C23×C4×C5—41no—
65C23×C4×C5—41no—
66C23×C4×C5—41no—
67C23×C4×C5—41no—
68C23×C4×C5—41no—
69C23×C4×C5—41no—
70C23×C4×C5D414yes—
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—41no—
87C2×C5×C4⋊C4—41no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C4⋊C4C2×C414yescomplemented
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—22no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4—22no—
103C2×C5×C22⋊C4—41no—
104C2×C5×C22⋊C4—41no—
105C2×C5×C22⋊C4—41no—
106C2×C5×C22⋊C4—41no—
107C2×C5×C22⋊C4—41no—
108C2×C5×C22⋊C4—41no—
109C2×C5×C22⋊C4—41no—
110C2×C5×C22⋊C4—41no—
111C2×C5×C22⋊C4—41no—
112C2×C5×C22⋊C4—41no—
113C2×C5×C22⋊C4—41no—
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⋊C4C2×C414yes—
126C2×C5×C22⋊C4C2×C414yes—
127C2×C5×C22⋊C4C2×C414yescomplemented
128C2×C5×C22⋊C4C2×C414yescomplemented
129C5×#95—22no—
130C5×#95—22no—
131C5×#95—22no—
132C5×#95—22no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95—41no—
136C5×#95—41no—
137C5×#95—41no—
138C5×#95—41no—
139C5×#95—41no—
140C5×#95—41no—
141C5×#95—41no—
142C5×#95—41no—
143C5×#95—41no—
144C5×#95—41no—
145C5×#95—41no—
146C5×#95C2×C414yescomplemented
147C2×#394C2×C511yescharacteristic
148C2×#386C2×C511yescharacteristic
149C2×#385C2×C511yescharacteristic, complemented
150#1445C2×C511yescharacteristic, complemented
151#1442C2×C511yescharacteristic, complemented
152#1442C2×C511yescharacteristic, complemented
153#1441C2×C511yescharacteristic, complemented
154#1440C2×C511yescharacteristic, complemented
155#1440C2×C511yescharacteristic, complemented
156#1439C2×C511yescharacteristic, complemented
157#1439C2×C511yescharacteristic, complemented
158#1439C2×C511yescharacteristic, complemented
159#1439C2×C511yescharacteristic, complemented
160#1438C2×C511yescharacteristic
161C22⋊#95C2×C511yescharacteristic, complemented
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
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×C5C22×C412yes—
189C24×C5C22×C412yes—
190C24×C5C2×D412yes—
191C24×C5#4112yes—
192C24×C5C2411yescharacteristic
193C2×C5×D4—28no—
194C2×C5×D4—44no—
195C2×C5×D4—44no—
196C2×C5×D4—44no—
197C2×C5×D4—44no—
198C2×C5×D4—44no—
199C2×C5×D4—44no—
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—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—44no—
285C22×C4×C5—44no—
286C22×C4×C5—44no—
287C22×C4×C5—44no—
288C22×C4×C5—44no—
289C22×C4×C5—44no—
290C22×C4×C5—44no—
291C22×C4×C5C22×C412yes—
292C22×C4×C5C22×C412yes—
293C22×C4×C5C22×C412yes—
294C22×C4×C5C22×C412yes—
295C22×C4×C5C22×C412yes—
296C22×C4×C5C2×D412yes—
297C22×C4×C5C2×D412yes—
298C5×C4⋊C4—44no—
299C5×C4⋊C4—44no—
300C5×C4⋊C4—44no—
301C5×C4⋊C4—44no—
302C5×C22⋊C4—28no—
303C5×C22⋊C4—44no—
304C5×C22⋊C4—44no—
305C5×C22⋊C4—44no—
306C5×C22⋊C4—44no—
307C5×C22⋊C4—44no—
308C5×C22⋊C4—44no—
309C5×C22⋊C4—44no—
310C5×C22⋊C4—44no—
311C5×C22⋊C4—44no—
312C5×C22⋊C4—44no—
313C23×D4C22×C511yescharacteristic
314C24×C4C22×C511yescharacteristic
315C22×C4⋊C4C22×C511yescharacteristic
316C22×C4⋊C4C22×C511yescharacteristic
317C22×C4⋊C4C22×C511yescharacteristic
318C22×C4⋊C4C22×C511yescharacteristic
319C22×C22⋊C4C22×C511yescharacteristic
320C22×C22⋊C4C22×C511yescharacteristic
321C22×C22⋊C4C22×C511yescharacteristic
322C22×C22⋊C4C22×C511yescharacteristic
323C22×C22⋊C4C22×C511yescharacteristic
324C22×C22⋊C4C22×C511yescharacteristic
325C22×C22⋊C4C22×C511yescharacteristic
326C22×C22⋊C4C22×C511yescharacteristic
327C22×C22⋊C4C22×C511yescharacteristic
328C22×C22⋊C4C22×C511yescharacteristic
329C22×C22⋊C4C22×C511yescharacteristic
330#394C4×C518yescomplemented
331#386—24no—
332#385—24no—
333C2×#95C22×C511yescharacteristic
334C2×#95C22×C511yescharacteristic
335C2×#95C22×C511yescharacteristic
336C2×#95C22×C511yescharacteristic
337C2×#95C22×C511yescharacteristic
338C2×#95C22×C511yescharacteristic
339C2×#95C22×C511yescharacteristic
340C2×#95C22×C511yescharacteristic
341C2×#95C22×C511yescharacteristic
342C2×#95C22×C511yescharacteristic
343C2×#95C22×C511yescharacteristic
344C2×#95C22×C511yescharacteristic
345C2×#95C22×C511yescharacteristic
346C2×#95C22×C511yescharacteristic
347C2×#95C22×C511yescharacteristic
348C2×#95C22×C511yescharacteristic
349C2×#95C22×C511yescharacteristic
350C2×#95C22×C511yescharacteristic
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
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—41no—
377C23×C5—41no—
378C23×C5—41no—
379C23×C5—41no—
380C23×C5—41no—
381C23×C5—41no—
382C23×C5—41no—
383C23×C5—41no—
384C23×C5—41no—
385C23×C5—41no—
386C23×C5—41no—
387C23×C5—41no—
388C23×C5—41no—
389C23×C5—41no—
390C23×C5—41no—
391C23×C5—41no—
392C23×C5—41no—
393C23×C5—41no—
394C23×C5—41no—
395C23×C5—41no—
396C23×C5—41no—
397C23×C5—41no—
398C23×C5—41no—
399C23×C5—41no—
400C23×C5—41no—
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×C5C4×D414yes—
421C23×C5C23×C411yescharacteristic
422C23×C5C22×D411yescharacteristic
423C23×C5C2×#4111yescharacteristic
424C23×C5H(5,𝔽2)11yescharacteristic
425C23×C5H(5,𝔽2)11yescharacteristic
426C23×C5H(5,𝔽2)11yescharacteristic
427C23×C5H(5,𝔽2)11yescharacteristic
428C23×C5H(5,𝔽2)11yescharacteristic
429C23×C5H(5,𝔽2)11yescharacteristic
430C23×C5H(5,𝔽2)11yescharacteristic
431C23×C5H(5,𝔽2)11yescharacteristic
432C23×C5H(5,𝔽2)11yescharacteristic
433C23×C52−1+411yescharacteristic
434C23×C52−1+411yescharacteristic
435C23×C52−1+411yescharacteristic
436C5×D4—416no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5—22no—
447C2×C4×C5—22no—
448C2×C4×C5—22no—
449C2×C4×C5—22no—
450C2×C4×C5—22no—
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—416no—
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×C5—41no—
474C2×C4×C5—41no—
475C2×C4×C5—41no—
476C2×C4×C5—41no—
477C2×C4×C5—41no—
478C2×C4×C5—41no—
479C2×C4×C5—41no—
480C2×C4×C5—41no—
481C2×C4×C5—41no—
482C2×C4×C5—41no—
483C2×C4×C5—41no—
484C2×C4×C5—41no—
485C2×C4×C5—41no—
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—
529C25C23×C511yescharacteristic
530C25C23×C511yescharacteristic
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4C2×C4×C514yes—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—41no—
542C23×C4—41no—
543C23×C4—41no—
544C23×C4C5×D414yes—
545C23×C4C23×C511yescharacteristic
546C23×C4C23×C511yescharacteristic
547C23×C4C23×C511yescharacteristic
548C23×C4C23×C511yescharacteristic
549C23×C4C23×C511yescharacteristic
550C23×C4C23×C511yescharacteristic
551C23×C4C23×C511yescharacteristic
552C23×C4C23×C511yescharacteristic
553C23×C4C23×C511yescharacteristic
554C23×C4C23×C511yescharacteristic
555C23×C4C23×C511yescharacteristic
556C23×C4C23×C511yescharacteristic
557C23×C4C23×C511yescharacteristic
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4C2×C4×C514yescomplemented
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4C2×C4×C514yes—
600C2×C22⋊C4C2×C4×C514yes—
601C2×C22⋊C4C2×C4×C514yescomplemented
602C2×C22⋊C4C2×C4×C514yescomplemented
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—41no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95C2×C4×C514yescomplemented
621C22×C5—24no—
622C22×C5—24no—
623C22×C5—24no—
624C22×C5—42no—
625C22×C5—42no—
626C22×C5—42no—
627C22×C5—42no—
628C22×C5—42no—
629C22×C5—42no—
630C22×C5—42no—
631C22×C5—42no—
632C22×C5—42no—
633C22×C5—42no—
634C22×C5—42no—
635C22×C5—42no—
636C22×C5—42no—
637C22×C5—42no—
638C22×C5—42no—
639C22×C5—42no—
640C22×C5—42no—
641C22×C5—42no—
642C22×C5—42no—
643C22×C5—81no—
644C22×C5—81no—
645C22×C5—81no—
646C22×C5—81no—
647C22×C5—81no—
648C22×C5—81no—
649C22×C5—81no—
650C22×C5—81no—
651C22×C5C2×C4×D411yescharacteristic
652C22×C5#51811yescharacteristic
653C22×C5#51811yescharacteristic
654C22×C5#51811yescharacteristic
655C22×C5#52011yescharacteristic
656C22×C5#52011yescharacteristic
657C22×C5#52011yescharacteristic
658C22×C5#53411yescharacteristic
659C22×C5#53411yescharacteristic
660C22×C5#53411yescharacteristic
661C22×C5#53511yescharacteristic
662C22×C5#53611yescharacteristic
663C22×C5#53711yescharacteristic
664C22×C5#53811yescharacteristic
665C22×C5#53811yescharacteristic
666C22×C5#53811yescharacteristic
667C22×C5#53911yescharacteristic
668C22×C5#53911yescharacteristic
669C22×C5#53911yescharacteristic
670C22×C5#56011yescharacteristic
671C22×C5#56011yescharacteristic
672C22×C5#56011yescharacteristic
673C22×C5#56011yescharacteristic
674C22×C5#56011yescharacteristic
675C22×C5H(3,𝔽4)11yescharacteristic
676C22×C5#56211yescharacteristic
677C22×C5#56211yescharacteristic
678C22×C5#56211yescharacteristic
679C22×C5#56211yescharacteristic
680C22×C5#56211yescharacteristic
681C22×C5#56211yescharacteristic
682C22×C5#56211yescharacteristic
683C22×C5#56211yescharacteristic
684C22×C5#56311yescharacteristic
685C22×C5#56311yescharacteristic
686C4×C5—42no—
687C4×C5—42no—
688C4×C5—42no—
689C4×C5—42no—
690C4×C5—42no—
691C4×C5—42no—
692C4×C5—42no—
693C4×C5—81no—
694C4×C5—81no—
695C4×C5—81no—
696C4×C5—81no—
697C4×C5—81no—
698C4×C5—81no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24C22×C4×C512yes—
726C24C22×C4×C512yes—
727C24C2×C5×D412yes—
728C24C5×#4112yes—
729C24C24×C511yescharacteristic
730C2×D4—28no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
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—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4C22×C4×C512yes—
829C22×C4C22×C4×C512yes—
830C22×C4C22×C4×C512yes—
831C22×C4C22×C4×C512yes—
832C22×C4C22×C4×C512yes—
833C22×C4C2×C5×D412yes—
834C22×C4C2×C5×D412yes—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C22⋊C4—28no—
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—
850C2×C5—44no—
851C2×C5—82no—
852C2×C5#232111yescharacteristic
853C2×C5#232211yescharacteristic
854C2×C5#232511yescharacteristic
855C2×C5#237611yescharacteristic
856C2×C5#237711yescharacteristic
857C2×C5#237711yescharacteristic
858C2×C5#237911yescharacteristic
859C2×C5#281211yescharacteristic
860C2×C5#281311yescharacteristic
861C2×C5#281411yescharacteristic
862C2×C5#281611yescharacteristic
863C2×C5#282411yescharacteristic
864C2×C5#282611yescharacteristic
865C2×C5#282711yescharacteristic
866C2×C5#282711yescharacteristic
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23C4×C5×D414yes—
937C23C23×C4×C511yescharacteristic
938C23C22×C5×D411yescharacteristic
939C23C2×C5×#4111yescharacteristic
940C23C5×H(5,𝔽2)11yescharacteristic
941C23C5×H(5,𝔽2)11yescharacteristic
942C23C5×H(5,𝔽2)11yescharacteristic
943C23C5×H(5,𝔽2)11yescharacteristic
944C23C5×H(5,𝔽2)11yescharacteristic
945C23C5×H(5,𝔽2)11yescharacteristic
946C23C5×H(5,𝔽2)11yescharacteristic
947C23C5×H(5,𝔽2)11yescharacteristic
948C23C5×H(5,𝔽2)11yescharacteristic
949C23C5×2−1+411yescharacteristic
950C23C5×2−1+411yescharacteristic
951C23C5×2−1+411yescharacteristic
952D4—416no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—416no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
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—
1045C5#1462211yescharacteristic, direct product factor, Sylow
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×C4×C5×D411yescharacteristic
1077C22C5×#51811yescharacteristic
1078C22C5×#51811yescharacteristic
1079C22C5×#51811yescharacteristic
1080C22C5×#52011yescharacteristic
1081C22C5×#52011yescharacteristic
1082C22C5×#52011yescharacteristic
1083C22C5×#53411yescharacteristic
1084C22C5×#53411yescharacteristic
1085C22C5×#53411yescharacteristic
1086C22C5×#53511yescharacteristic
1087C22C5×#53611yescharacteristic
1088C22C5×#53711yescharacteristic
1089C22C5×#53811yescharacteristic
1090C22C5×#53811yescharacteristic
1091C22C5×#53811yescharacteristic
1092C22C5×#53911yescharacteristic
1093C22C5×#53911yescharacteristic
1094C22C5×#53911yescharacteristic
1095C22C5×#56011yescharacteristic
1096C22C5×#56011yescharacteristic
1097C22C5×#56011yescharacteristic
1098C22C5×#56011yescharacteristic
1099C22C5×#56011yescharacteristic
1100C22C5×H(3,𝔽4)11yescharacteristic
1101C22C5×#56211yescharacteristic
1102C22C5×#56211yescharacteristic
1103C22C5×#56211yescharacteristic
1104C22C5×#56211yescharacteristic
1105C22C5×#56211yescharacteristic
1106C22C5×#56211yescharacteristic
1107C22C5×#56211yescharacteristic
1108C22C5×#56211yescharacteristic
1109C22C5×#56311yescharacteristic
1110C22C5×#56311yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C2—44no—
1125C2—82no—
1126C2C5×#232111yescharacteristic
1127C2C5×#232211yescharacteristic
1128C2C5×#232511yescharacteristic
1129C2C5×#237611yescharacteristic
1130C2C5×#237711yescharacteristic
1131C2C5×#237711yescharacteristic
1132C2C5×#237911yescharacteristic
1133C2C5×#281211yescharacteristic
1134C2C5×#281311yescharacteristic
1135C2C5×#281411yescharacteristic
1136C2C5×#281611yescharacteristic
1137C2C5×#282411yescharacteristic
1138C2C5×#282611yescharacteristic
1139C2C5×#282711yescharacteristic
1140C2C5×#282711yescharacteristic
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
3. C2×C5×#385C2semidirect
4. C5×#1445C2semidirect
5. C5×#1442C2semidirect
6. C5×#1442C2semidirect
7. C5×#1441C2semidirect
8. C5×#1440C2semidirect
9. C5×#1440C2semidirect
10. C5×#1439C2semidirect
11. C5×#1439C2semidirect
12. C5×#1439C2semidirect
13. C5×#1439C2semidirect
15. C5×C22⋊#95C2semidirect
33. C5×#394C4semidirect
54. #14622C5direct (N × H)
95. C2×C5×C4⋊C4C2×C4semidirect
127. C2×C5×C22⋊C4C2×C4semidirect
128. C2×C5×C22⋊C4C2×C4semidirect
146. C5×#95C2×C4semidirect
149. C2×#385C2×C5semidirect
150. #1445C2×C5semidirect
151. #1442C2×C5semidirect
152. #1442C2×C5semidirect
153. #1441C2×C5semidirect
154. #1440C2×C5semidirect
155. #1440C2×C5semidirect
156. #1439C2×C5semidirect
157. #1439C2×C5semidirect
158. #1439C2×C5semidirect
159. #1439C2×C5semidirect
161. C22⋊#95C2×C5semidirect
330. #394C4×C5semidirect
569. C2×C4⋊C4C2×C4×C5semidirect
601. C2×C22⋊C4C2×C4×C5semidirect
602. C2×C22⋊C4C2×C4×C5semidirect
620. #95C2×C4×C5semidirect
1045. C5#14622direct (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×#3862
C2×C5×#3852
C5×#14452
C5×#14422
C5×#14412
C5×#14402
C5×#14392
C5×#14382
C5×C22⋊#952
#146225