Finite Group Databasebeta

← C5×#14519 #11937239

Subgroups — C5×#14519 #11937239

Order 1280.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#392C211yesmaximal, characteristic
2C2×C5×#390C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×C5×#386C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic, complemented
6C2×C5×#386C211yesmaximal, characteristic, complemented
7C2×C5×#385C211yesmaximal, characteristic, complemented
8C5×#1442C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1438C211yesmaximal, characteristic, complemented
13C5×#1437C211yesmaximal, characteristic, complemented
14C5×#1434C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C24×C4×C5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊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
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C5×C22⋊C4C2211yescharacteristic
36C22×C42×C5C2211yescharacteristic
37C5×#392C418yescomplemented
38C5×#390—24no—
39C5×#386—24no—
40C5×#386—24no—
41C5×#386—24no—
42C5×#386—24no—
43C5×#385—24no—
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#14519C511yesmaximal, characteristic, direct product factor, Sylow
59C25×C5C2311yescharacteristic
60C25×C5C2311yescharacteristic
61C25×C5C2311yescharacteristic
62C22×C5×D4—22no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—22no—
66C22×C5×D4—22no—
67C22×C5×D4—22no—
68C22×C5×D4—22no—
69C22×C5×D4—22no—
70C22×C5×D4—22no—
71C22×C5×D4—22no—
72C22×C5×D4—41no—
73C22×C5×D4—41no—
74C22×C5×D4—41no—
75C22×C5×D4—41no—
76C22×C5×D4—41no—
77C22×C5×D4—41no—
78C22×C5×D4—41no—
79C22×C5×D4—41no—
80C22×C5×D4C2×C414yes—
81C22×C5×D4C2×C414yescomplemented
82C22×C5×D4C2×C414yescomplemented
83C23×C4×C5—22no—
84C23×C4×C5—22no—
85C23×C4×C5—22no—
86C23×C4×C5—22no—
87C23×C4×C5—22no—
88C23×C4×C5—22no—
89C23×C4×C5—41no—
90C23×C4×C5—41no—
91C23×C4×C5—41no—
92C23×C4×C5—41no—
93C23×C4×C5—41no—
94C23×C4×C5—41no—
95C23×C4×C5—41no—
96C23×C4×C5—41no—
97C23×C4×C5C2311yescharacteristic
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C23×C4×C5C2311yescharacteristic
101C23×C4×C5C2311yescharacteristic
102C23×C4×C5C2311yescharacteristic
103C23×C4×C5C2311yescharacteristic
104C23×C4×C5C2311yescharacteristic
105C23×C4×C5C2311yescharacteristic
106C23×C4×C5C2311yescharacteristic
107C23×C4×C5C2311yescharacteristic
108C23×C4×C5C2311yescharacteristic
109C2×C5×C4⋊C4—22no—
110C2×C5×C4⋊C4—22no—
111C2×C5×C4⋊C4—22no—
112C2×C5×C4⋊C4—41no—
113C2×C5×C4⋊C4—41no—
114C2×C5×C4⋊C4—41no—
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—22no—
127C2×C5×C22⋊C4—22no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—22no—
130C2×C5×C22⋊C4—22no—
131C2×C5×C22⋊C4—41no—
132C2×C5×C22⋊C4—41no—
133C2×C5×C22⋊C4—41no—
134C2×C5×C22⋊C4—41no—
135C2×C5×C22⋊C4—41no—
136C2×C5×C22⋊C4—41no—
137C2×C5×C22⋊C4—41no—
138C2×C5×C22⋊C4—41no—
139C2×C5×C22⋊C4—41no—
140C2×C5×C22⋊C4—41no—
141C2×C5×C22⋊C4—41no—
142C2×C5×C22⋊C4—41no—
143C2×C5×C22⋊C4—41no—
144C2×C5×C22⋊C4—41no—
145C2×C5×C22⋊C4—41no—
146C2×C5×C22⋊C4—41no—
147C2×C5×C22⋊C4—41no—
148C2×C5×C22⋊C4—41no—
149C2×C5×C22⋊C4C2×C414yescomplemented
150C2×C5×C22⋊C4C2×C414yescomplemented
151C2×C5×C22⋊C4C2×C414yescomplemented
152C2×C5×C22⋊C4D414yescomplemented
153C2×C5×C22⋊C4D414yescomplemented
154C2×C42×C5—22no—
155C2×C42×C5—22no—
156C2×C42×C5—41no—
157C5×#95—22no—
158C5×#95—22no—
159C5×#95—22no—
160C5×#95—22no—
161C5×#95—22no—
162C5×#95—22no—
163C5×#95—22no—
164C5×#95—22no—
165C5×#95—41no—
166C5×#95—41no—
167C5×#95—41no—
168C5×#95—41no—
169C5×#95C2×C414yescomplemented
170C5×#95D414yescomplemented
171C2×#392C2×C511yescharacteristic
172C2×#390C2×C511yescharacteristic, complemented
173C2×#386C2×C511yescharacteristic, complemented
174C2×#386C2×C511yescharacteristic, complemented
175C2×#386C2×C511yescharacteristic, complemented
176C2×#386C2×C511yescharacteristic, complemented
177C2×#385C2×C511yescharacteristic, complemented
178#1442C2×C511yescharacteristic, complemented
179#1440C2×C511yescharacteristic, complemented
180#1439C2×C511yescharacteristic, complemented
181#1439C2×C511yescharacteristic, complemented
182#1438C2×C511yescharacteristic, complemented
183#1437C2×C511yescharacteristic, complemented
184#1434C2×C511yescharacteristic, complemented
185C22⋊#95C2×C511yescharacteristic, complemented
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×C5—21no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5—21no—
202C24×C5—21no—
203C24×C5—21no—
204C24×C5—21no—
205C24×C5—21no—
206C24×C5—21no—
207C24×C5—21no—
208C24×C5—21no—
209C24×C5—21no—
210C24×C5—21no—
211C24×C5—21no—
212C24×C5—21no—
213C24×C5—21no—
214C24×C5—21no—
215C24×C5—21no—
216C24×C5—21no—
217C24×C5—21no—
218C24×C5—21no—
219C24×C5—21no—
220C24×C5—21no—
221C24×C5—21no—
222C24×C5—21no—
223C24×C5—21no—
224C24×C5C22×C412yes—
225C24×C5C22×C412yes—
226C24×C5C22×C412yes—
227C24×C5C2×D412yes—
228C24×C5C2×D412yes—
229C24×C5#4112yes—
230C24×C5#4112yes—
231C24×C5C2411yescharacteristic
232C2×C5×D4—28no—
233C2×C5×D4—28no—
234C2×C5×D4—28no—
235C2×C5×D4—28no—
236C2×C5×D4—28no—
237C2×C5×D4—44no—
238C2×C5×D4—44no—
239C2×C5×D4—44no—
240C2×C5×D4—44no—
241C2×C5×D4—44no—
242C2×C5×D4—44no—
243C2×C5×D4—44no—
244C2×C5×D4—44no—
245C2×C5×D4—44no—
246C2×C5×D4—44no—
247C2×C5×D4—44no—
248C2×C5×D4—44no—
249C2×C5×D4—44no—
250C2×C5×D4—44no—
251C2×C5×D4—44no—
252C2×C5×D4—44no—
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—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—21no—
294C22×C4×C5—21no—
295C22×C4×C5—21no—
296C22×C4×C5—21no—
297C22×C4×C5—21no—
298C22×C4×C5—21no—
299C22×C4×C5—21no—
300C22×C4×C5—21no—
301C22×C4×C5—21no—
302C22×C4×C5—21no—
303C22×C4×C5—21no—
304C22×C4×C5—21no—
305C22×C4×C5—21no—
306C22×C4×C5—21no—
307C22×C4×C5—21no—
308C22×C4×C5—21no—
309C22×C4×C5—21no—
310C22×C4×C5—21no—
311C22×C4×C5—21no—
312C22×C4×C5—21no—
313C22×C4×C5—21no—
314C22×C4×C5—21no—
315C22×C4×C5—21no—
316C22×C4×C5—21no—
317C22×C4×C5—21no—
318C22×C4×C5—21no—
319C22×C4×C5—21no—
320C22×C4×C5—21no—
321C22×C4×C5—21no—
322C22×C4×C5—21no—
323C22×C4×C5—21no—
324C22×C4×C5—21no—
325C22×C4×C5—44no—
326C22×C4×C5—44no—
327C22×C4×C5—44no—
328C22×C4×C5—44no—
329C22×C4×C5—44no—
330C22×C4×C5—44no—
331C22×C4×C5—44no—
332C22×C4×C5—44no—
333C22×C4×C5—44no—
334C22×C4×C5—44no—
335C22×C4×C5—44no—
336C22×C4×C5—44no—
337C22×C4×C5—44no—
338C22×C4×C5—44no—
339C22×C4×C5C22×C412yes—
340C22×C4×C5C22×C412yes—
341C22×C4×C5C22×C412yes—
342C22×C4×C5C22×C412yes—
343C22×C4×C5C2×D412yes—
344C22×C4×C5C2×D412yes—
345C22×C4×C5C2×D412yes—
346C22×C4×C5C2×D412yes—
347C22×C4×C5C2×D412yes—
348C22×C4×C5C2×D412yes—
349C22×C4×C5C2×D412yes—
350C22×C4×C5#4112yes—
351C5×C4⋊C4—44no—
352C5×C4⋊C4—44no—
353C5×C22⋊C4—28no—
354C5×C22⋊C4—44no—
355C5×C22⋊C4—44no—
356C5×C22⋊C4—44no—
357C5×C22⋊C4—44no—
358C5×C22⋊C4—44no—
359C5×C22⋊C4—44no—
360C5×C22⋊C4—44no—
361C5×C22⋊C4—44no—
362C5×C22⋊C4—44no—
363C5×C22⋊C4—44no—
364C5×C22⋊C4—44no—
365C5×C22⋊C4—44no—
366C42×C5—44no—
367C23×D4C22×C511yescharacteristic
368C23×D4C22×C511yescharacteristic
369C23×D4C22×C511yescharacteristic
370C24×C4C22×C511yescharacteristic
371C24×C4C22×C511yescharacteristic
372C22×C4⋊C4C22×C511yescharacteristic
373C22×C4⋊C4C22×C511yescharacteristic
374C22×C22⋊C4C22×C511yescharacteristic
375C22×C22⋊C4C22×C511yescharacteristic
376C22×C22⋊C4C22×C511yescharacteristic
377C22×C22⋊C4C22×C511yescharacteristic
378C22×C22⋊C4C22×C511yescharacteristic
379C22×C22⋊C4C22×C511yescharacteristic
380C22×C22⋊C4C22×C511yescharacteristic
381C22×C22⋊C4C22×C511yescharacteristic
382C22×C22⋊C4C22×C511yescharacteristic
383C22×C22⋊C4C22×C511yescharacteristic
384C22×C22⋊C4C22×C511yescharacteristic
385C22×C22⋊C4C22×C511yescharacteristic
386C22×C22⋊C4C22×C511yescharacteristic
387C22×C42C22×C511yescharacteristic
388#392C4×C518yescomplemented
389#390—24no—
390#386—24no—
391#386—24no—
392#386—24no—
393#386—24no—
394#385—24no—
395C2×#95C22×C511yescharacteristic
396C2×#95C22×C511yescharacteristic
397C2×#95C22×C511yescharacteristic
398C2×#95C22×C511yescharacteristic
399C2×#95C22×C511yescharacteristic
400C2×#95C22×C511yescharacteristic
401C2×#95C22×C511yescharacteristic
402C2×#95C22×C511yescharacteristic
403C2×#95C22×C511yescharacteristic
404C2×#95C22×C511yescharacteristic
405C2×#95C22×C511yescharacteristic
406C2×#95C22×C511yescharacteristic
407C2×#95C22×C511yescharacteristic
408C2×#95C22×C511yescharacteristic
409C23×C5—22no—
410C23×C5—22no—
411C23×C5—22no—
412C23×C5—22no—
413C23×C5—22no—
414C23×C5—22no—
415C23×C5—22no—
416C23×C5—22no—
417C23×C5—22no—
418C23×C5—22no—
419C23×C5—22no—
420C23×C5—22no—
421C23×C5—22no—
422C23×C5—22no—
423C23×C5—22no—
424C23×C5—22no—
425C23×C5—22no—
426C23×C5—22no—
427C23×C5—22no—
428C23×C5—22no—
429C23×C5—22no—
430C23×C5—22no—
431C23×C5—22no—
432C23×C5—22no—
433C23×C5—22no—
434C23×C5—22no—
435C23×C5—22no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5—22no—
439C23×C5—22no—
440C23×C5—22no—
441C23×C5—22no—
442C23×C5—22no—
443C23×C5—22no—
444C23×C5—22no—
445C23×C5—22no—
446C23×C5—22no—
447C23×C5—22no—
448C23×C5—22no—
449C23×C5—22no—
450C23×C5—22no—
451C23×C5—22no—
452C23×C5—41no—
453C23×C5—41no—
454C23×C5—41no—
455C23×C5—41no—
456C23×C5—41no—
457C23×C5—41no—
458C23×C5—41no—
459C23×C5—41no—
460C23×C5—41no—
461C23×C5—41no—
462C23×C5—41no—
463C23×C5—41no—
464C23×C5—41no—
465C23×C5—41no—
466C23×C5—41no—
467C23×C5—41no—
468C23×C5—41no—
469C23×C5—41no—
470C23×C5—41no—
471C23×C5—41no—
472C23×C5—41no—
473C23×C5—41no—
474C23×C5—41no—
475C23×C5—41no—
476C23×C5—41no—
477C23×C5—41no—
478C23×C5—41no—
479C23×C5—41no—
480C23×C5—41no—
481C23×C5—41no—
482C23×C5—41no—
483C23×C5—41no—
484C23×C5—41no—
485C23×C5—41no—
486C23×C5—41no—
487C23×C5—41no—
488C23×C5—41no—
489C23×C5—41no—
490C23×C5—41no—
491C23×C5—41no—
492C23×C5—41no—
493C23×C5—41no—
494C23×C5—41no—
495C23×C5—41no—
496C23×C5—41no—
497C23×C5—41no—
498C23×C5—41no—
499C23×C5—41no—
500C23×C5—41no—
501C23×C5—41no—
502C23×C5—41no—
503C23×C5—41no—
504C23×C5—41no—
505C23×C5—41no—
506C23×C5—41no—
507C23×C5—41no—
508C23×C5—41no—
509C23×C5—41no—
510C23×C5—41no—
511C23×C5—41no—
512C23×C5C4×D414yes—
513C23×C5C4×D414yes—
514C23×C5C23×C411yescharacteristic
515C23×C5C22×D411yescharacteristic
516C23×C5C22×D411yescharacteristic
517C23×C5C22×D411yescharacteristic
518C23×C5C2×#4111yescharacteristic
519C23×C5C2×#4111yescharacteristic
520C23×C5C2×#4111yescharacteristic
521C23×C5H(5,𝔽2)11yescharacteristic
522C23×C5H(5,𝔽2)11yescharacteristic
523C23×C5H(5,𝔽2)11yescharacteristic
524C23×C5H(5,𝔽2)11yescharacteristic
525C23×C5H(5,𝔽2)11yescharacteristic
526C23×C5H(5,𝔽2)11yescharacteristic
527C23×C5H(5,𝔽2)11yescharacteristic
528C23×C52−1+411yescharacteristic
529C5×D4—416no—
530C5×D4—416no—
531C5×D4—416no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—22no—
536C2×C4×C5—22no—
537C2×C4×C5—22no—
538C2×C4×C5—22no—
539C2×C4×C5—22no—
540C2×C4×C5—22no—
541C2×C4×C5—22no—
542C2×C4×C5—22no—
543C2×C4×C5—22no—
544C2×C4×C5—22no—
545C2×C4×C5—22no—
546C2×C4×C5—22no—
547C2×C4×C5—22no—
548C2×C4×C5—22no—
549C2×C4×C5—22no—
550C2×C4×C5—22no—
551C2×C4×C5—22no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—22no—
557C2×C4×C5—22no—
558C2×C4×C5—22no—
559C2×C4×C5—22no—
560C2×C4×C5—22no—
561C2×C4×C5—22no—
562C2×C4×C5—22no—
563C2×C4×C5—22no—
564C2×C4×C5—22no—
565C2×C4×C5—416no—
566C2×C4×C5—416no—
567C2×C4×C5—41no—
568C2×C4×C5—41no—
569C2×C4×C5—41no—
570C2×C4×C5—41no—
571C2×C4×C5—41no—
572C2×C4×C5—41no—
573C2×C4×C5—41no—
574C2×C4×C5—41no—
575C2×C4×C5—41no—
576C2×C4×C5—41no—
577C2×C4×C5—41no—
578C2×C4×C5—41no—
579C2×C4×C5—41no—
580C2×C4×C5—41no—
581C2×C4×C5—41no—
582C2×C4×C5—41no—
583C2×C4×C5—41no—
584C2×C4×C5—41no—
585C2×C4×C5—41no—
586C2×C4×C5—41no—
587C2×C4×C5—41no—
588C2×C4×C5—41no—
589C2×C4×C5—41no—
590C2×C4×C5—41no—
591C2×C4×C5—41no—
592C2×C4×C5—41no—
593C2×C4×C5—41no—
594C2×C4×C5—41no—
595C2×C4×C5—41no—
596C2×C4×C5—41no—
597C2×C4×C5—41no—
598C2×C4×C5—41no—
599C2×C4×C5—41no—
600C2×C4×C5—41no—
601C2×C4×C5—41no—
602C2×C4×C5—41no—
603C2×C4×C5—41no—
604C2×C4×C5—41no—
605C2×C4×C5—41no—
606C2×C4×C5—41no—
607C2×C4×C5—41no—
608C2×C4×C5—41no—
609C2×C4×C5—41no—
610C2×C4×C5—41no—
611C2×C4×C5—41no—
612C2×C4×C5—41no—
613C2×C4×C5—41no—
614C2×C4×C5—41no—
615C2×C4×C5—41no—
616C2×C4×C5—41no—
617C2×C4×C5C4×D414yes—
618C25C23×C511yescharacteristic
619C25C23×C511yescharacteristic
620C25C23×C511yescharacteristic
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4—41no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4C2×C4×C514yes—
640C22×D4C2×C4×C514yescomplemented
641C22×D4C2×C4×C514yescomplemented
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—41no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4—41no—
652C23×C4—41no—
653C23×C4—41no—
654C23×C4—41no—
655C23×C4—41no—
656C23×C4C23×C511yescharacteristic
657C23×C4C23×C511yescharacteristic
658C23×C4C23×C511yescharacteristic
659C23×C4C23×C511yescharacteristic
660C23×C4C23×C511yescharacteristic
661C23×C4C23×C511yescharacteristic
662C23×C4C23×C511yescharacteristic
663C23×C4C23×C511yescharacteristic
664C23×C4C23×C511yescharacteristic
665C23×C4C23×C511yescharacteristic
666C23×C4C23×C511yescharacteristic
667C23×C4C23×C511yescharacteristic
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4C2×C4×C514yescomplemented
709C2×C22⋊C4C2×C4×C514yescomplemented
710C2×C22⋊C4C2×C4×C514yescomplemented
711C2×C22⋊C4C5×D414yescomplemented
712C2×C22⋊C4C5×D414yescomplemented
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—41no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95C2×C4×C514yescomplemented
729#95C5×D414yescomplemented
730C22×C5—24no—
731C22×C5—24no—
732C22×C5—24no—
733C22×C5—24no—
734C22×C5—24no—
735C22×C5—24no—
736C22×C5—42no—
737C22×C5—42no—
738C22×C5—42no—
739C22×C5—42no—
740C22×C5—42no—
741C22×C5—42no—
742C22×C5—42no—
743C22×C5—42no—
744C22×C5—42no—
745C22×C5—42no—
746C22×C5—42no—
747C22×C5—42no—
748C22×C5—42no—
749C22×C5—42no—
750C22×C5—42no—
751C22×C5—42no—
752C22×C5—42no—
753C22×C5—42no—
754C22×C5—42no—
755C22×C5—42no—
756C22×C5—42no—
757C22×C5—42no—
758C22×C5—42no—
759C22×C5—42no—
760C22×C5—42no—
761C22×C5—42no—
762C22×C5—42no—
763C22×C5—42no—
764C22×C5—42no—
765C22×C5—42no—
766C22×C5—42no—
767C22×C5—81no—
768C22×C5—81no—
769C22×C5—81no—
770C22×C5—81no—
771C22×C5—81no—
772C22×C5—81no—
773C22×C5—81no—
774C22×C5—81no—
775C22×C5C2×C4×D411yescharacteristic
776C22×C5C2×C4×D411yescharacteristic
777C22×C5C2×C4×D411yescharacteristic
778C22×C5#51811yescharacteristic
779C22×C5#51811yescharacteristic
780C22×C5#51811yescharacteristic
781C22×C5#52011yescharacteristic
782C22×C5#53411yescharacteristic
783C22×C5#53411yescharacteristic
784C22×C5#53511yescharacteristic
785C22×C5#53511yescharacteristic
786C22×C5#53511yescharacteristic
787C22×C5#53711yescharacteristic
788C22×C5#53811yescharacteristic
789C22×C5#53811yescharacteristic
790C22×C5#53811yescharacteristic
791C22×C5#53911yescharacteristic
792C22×C5#54011yescharacteristic
793C22×C5#54011yescharacteristic
794C22×C5D4211yescharacteristic
795C22×C5D4211yescharacteristic
796C22×C5D4211yescharacteristic
797C22×C5#54611yescharacteristic
798C22×C5#54611yescharacteristic
799C22×C5#54611yescharacteristic
800C22×C5#54611yescharacteristic
801C22×C5#54711yescharacteristic
802C22×C5#54811yescharacteristic
803C22×C5#55111yescharacteristic
804C22×C5#55111yescharacteristic
805C22×C5#55311yescharacteristic
806C22×C5#56011yescharacteristic
807C22×C5#56011yescharacteristic
808C22×C5#56211yescharacteristic
809C22×C5#56211yescharacteristic
810C4×C5—24no—
811C4×C5—42no—
812C4×C5—42no—
813C4×C5—42no—
814C4×C5—42no—
815C4×C5—42no—
816C4×C5—42no—
817C4×C5—42no—
818C4×C5—42no—
819C4×C5—42no—
820C4×C5—81no—
821C4×C5—81no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24C22×C4×C512yes—
861C24C22×C4×C512yes—
862C24C22×C4×C512yes—
863C24C2×C5×D412yes—
864C24C2×C5×D412yes—
865C24C5×#4112yes—
866C24C5×#4112yes—
867C24C24×C511yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—28no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4C22×C4×C512yes—
976C22×C4C22×C4×C512yes—
977C22×C4C22×C4×C512yes—
978C22×C4C22×C4×C512yes—
979C22×C4C2×C5×D412yes—
980C22×C4C2×C5×D412yes—
981C22×C4C2×C5×D412yes—
982C22×C4C2×C5×D412yes—
983C22×C4C2×C5×D412yes—
984C22×C4C2×C5×D412yes—
985C22×C4C2×C5×D412yes—
986C22×C4C5×#4112yes—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C22⋊C4—28no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C42—44no—
1003C2×C5—44no—
1004C2×C5—44no—
1005C2×C5—82no—
1006C2×C5#232111yescharacteristic
1007C2×C5#232511yescharacteristic
1008C2×C5#232811yescharacteristic
1009C2×C5#235811yescharacteristic
1010C2×C5#235811yescharacteristic
1011C2×C5#236111yescharacteristic
1012C2×C5#237711yescharacteristic
1013C2×C5#266911yescharacteristic
1014C2×C5#267111yescharacteristic
1015C2×C5#267611yescharacteristic
1016C2×C5#267811yescharacteristic
1017C2×C5#268811yescharacteristic
1018C2×C5#269611yescharacteristic
1019C2×C5#270611yescharacteristic
1020C2×C5#274911yescharacteristic
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23C4×C5×D414yes—
1125C23C4×C5×D414yes—
1126C23C23×C4×C511yescharacteristic
1127C23C22×C5×D411yescharacteristic
1128C23C22×C5×D411yescharacteristic
1129C23C22×C5×D411yescharacteristic
1130C23C2×C5×#4111yescharacteristic
1131C23C2×C5×#4111yescharacteristic
1132C23C2×C5×#4111yescharacteristic
1133C23C5×H(5,𝔽2)11yescharacteristic
1134C23C5×H(5,𝔽2)11yescharacteristic
1135C23C5×H(5,𝔽2)11yescharacteristic
1136C23C5×H(5,𝔽2)11yescharacteristic
1137C23C5×H(5,𝔽2)11yescharacteristic
1138C23C5×H(5,𝔽2)11yescharacteristic
1139C23C5×H(5,𝔽2)11yescharacteristic
1140C23C5×2−1+411yescharacteristic
1141D4—416no—
1142D4—416no—
1143D4—416no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—416no—
1178C2×C4—416no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4C4×C5×D414yes—
1230C5#1451911yescharacteristic, direct product factor, Sylow
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×C4×C5×D411yescharacteristic
1277C22C2×C4×C5×D411yescharacteristic
1278C22C2×C4×C5×D411yescharacteristic
1279C22C5×#51811yescharacteristic
1280C22C5×#51811yescharacteristic
1281C22C5×#51811yescharacteristic
1282C22C5×#52011yescharacteristic
1283C22C5×#53411yescharacteristic
1284C22C5×#53411yescharacteristic
1285C22C5×#53511yescharacteristic
1286C22C5×#53511yescharacteristic
1287C22C5×#53511yescharacteristic
1288C22C5×#53711yescharacteristic
1289C22C5×#53811yescharacteristic
1290C22C5×#53811yescharacteristic
1291C22C5×#53811yescharacteristic
1292C22C5×#53911yescharacteristic
1293C22C5×#54011yescharacteristic
1294C22C5×#54011yescharacteristic
1295C22C5×D4211yescharacteristic
1296C22C5×D4211yescharacteristic
1297C22C5×D4211yescharacteristic
1298C22C5×#54611yescharacteristic
1299C22C5×#54611yescharacteristic
1300C22C5×#54611yescharacteristic
1301C22C5×#54611yescharacteristic
1302C22C5×#54711yescharacteristic
1303C22C5×#54811yescharacteristic
1304C22C5×#55111yescharacteristic
1305C22C5×#55111yescharacteristic
1306C22C5×#55311yescharacteristic
1307C22C5×#56011yescharacteristic
1308C22C5×#56011yescharacteristic
1309C22C5×#56211yescharacteristic
1310C22C5×#56211yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2C5×#232111yescharacteristic
1327C2C5×#232511yescharacteristic
1328C2C5×#232811yescharacteristic
1329C2C5×#235811yescharacteristic
1330C2C5×#235811yescharacteristic
1331C2C5×#236111yescharacteristic
1332C2C5×#237711yescharacteristic
1333C2C5×#266911yescharacteristic
1334C2C5×#267111yescharacteristic
1335C2C5×#267611yescharacteristic
1336C2C5×#267811yescharacteristic
1337C2C5×#268811yescharacteristic
1338C2C5×#269611yescharacteristic
1339C2C5×#270611yescharacteristic
1340C2C5×#274911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC2×C5×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#390C2semidirect
3. C2×C5×#386C2semidirect
4. C2×C5×#386C2semidirect
5. C2×C5×#386C2semidirect
6. C2×C5×#386C2semidirect
7. C2×C5×#385C2semidirect
8. C5×#1442C2semidirect
9. C5×#1440C2semidirect
10. C5×#1439C2semidirect
11. C5×#1439C2semidirect
12. C5×#1438C2semidirect
13. C5×#1437C2semidirect
14. C5×#1434C2semidirect
15. C5×C22⋊#95C2semidirect
37. C5×#392C4semidirect
58. #14519C5direct (N × H)
81. C22×C5×D4C2×C4semidirect
82. C22×C5×D4C2×C4semidirect
149. C2×C5×C22⋊C4C2×C4semidirect
150. C2×C5×C22⋊C4C2×C4semidirect
151. C2×C5×C22⋊C4C2×C4semidirect
152. C2×C5×C22⋊C4D4semidirect
153. C2×C5×C22⋊C4D4semidirect
169. C5×#95C2×C4semidirect
170. C5×#95D4semidirect
172. C2×#390C2×C5semidirect
173. C2×#386C2×C5semidirect
174. C2×#386C2×C5semidirect
175. C2×#386C2×C5semidirect
176. C2×#386C2×C5semidirect
177. C2×#385C2×C5semidirect
178. #1442C2×C5semidirect
179. #1440C2×C5semidirect
180. #1439C2×C5semidirect
181. #1439C2×C5semidirect
182. #1438C2×C5semidirect
183. #1437C2×C5semidirect
184. #1434C2×C5semidirect
185. C22⋊#95C2×C5semidirect
388. #392C4×C5semidirect
640. C22×D4C2×C4×C5semidirect
641. C22×D4C2×C4×C5semidirect
708. C2×C22⋊C4C2×C4×C5semidirect
709. C2×C22⋊C4C2×C4×C5semidirect
710. C2×C22⋊C4C2×C4×C5semidirect
711. C2×C22⋊C4C5×D4semidirect
712. C2×C22⋊C4C5×D4semidirect
728. #95C2×C4×C5semidirect
729. #95C5×D4semidirect
1230. C5#14519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3922
C2×C5×#3902
C2×C5×#3862
C2×C5×#3852
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14342
C5×C22⋊#952
#145195