Finite Group Databasebeta

← C5×#14052 #11936772

Subgroups — C5×#14052 #11936772

Order 1280.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C5×#391C211yesmaximal, characteristic, complemented
3C2×C5×#385C211yesmaximal, characteristic
4C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
5C22×C5×#95C211yesmaximal, characteristic
6C5×#1446C211yesmaximal, characteristic, complemented
7C5×#1445C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1436C211yesmaximal, characteristic, complemented
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×C4⋊#95C211yesmaximal, characteristic, complemented
13C5×C22⋊#95C211yesmaximal, characteristic
14C5×C22⋊#95C211yesmaximal, characteristic
15C5×C22⋊#95C211yesmaximal, characteristic
16C23×C5×Q8C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C2×C5×C22⋊Q8—24no—
21C2×C5×C22⋊Q8—24no—
22C2×C5×C22⋊Q8C418yescomplemented
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C22×C42×C5C2211yescharacteristic
34C5×#391—24no—
35C5×#385—24no—
36C4×C5×C22⋊C4—24no—
37C2×C5×#95—24no—
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58#14052C511yesmaximal, characteristic, direct product factor, Sylow
59C25×C5C2311yescharacteristic
60C22×C5×Q8—22no—
61C22×C5×Q8—22no—
62C22×C5×Q8—22no—
63C22×C5×Q8—22no—
64C22×C5×Q8—41no—
65C22×C5×Q8—41no—
66C22×C5×Q8C2×C414yescomplemented
67C23×C4×C5—22no—
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—41no—
81C23×C4×C5—41no—
82C23×C4×C5—41no—
83C23×C4×C5—41no—
84C23×C4×C5—41no—
85C23×C4×C5—41no—
86C23×C4×C5C2×C414yes—
87C23×C4×C5Q814yescomplemented
88C23×C4×C5C2311yescharacteristic
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
102C5×C22⋊Q8—232no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4—22no—
110C2×C5×C4⋊C4—22no—
111C2×C5×C4⋊C4—22no—
112C2×C5×C4⋊C4—22no—
113C2×C5×C4⋊C4—41no—
114C2×C5×C4⋊C4—41no—
115C2×C5×C4⋊C4C2×C414yescomplemented
116C2×C5×C4⋊C4C2×C414yescomplemented
117C2×C5×C4⋊C4C2×C414yescomplemented
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⋊C4C2×C414yes—
126C2×C5×C22⋊C4C2×C414yes—
127C2×C5×C22⋊C4D414yes—
128C2×C5×C22⋊C4D414yes—
129C2×C5×C22⋊C4Q814yescomplemented
130C2×C42×C5—22no—
131C2×C42×C5—22no—
132C2×C42×C5—22no—
133C2×C42×C5—22no—
134C2×C42×C5—41no—
135C2×C42×C5—41no—
136C5×#95—22no—
137C5×#95—22no—
138C5×#95—22no—
139C5×#95—22no—
140C5×#95—22no—
141C5×#95—22no—
142C5×#95—22no—
143C5×#95—22no—
144C5×#95—22no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95—22no—
149C5×#95—41no—
150C5×#95—41no—
151C5×#95—41no—
152C5×#95—41no—
153C5×#95—41no—
154C5×#95—41no—
155C5×#95D414yes—
156C22×C22⋊Q8C2×C511yescharacteristic
157C2×#391C2×C511yescharacteristic, complemented
158C2×#385C2×C511yescharacteristic
159C2×C4×C22⋊C4C2×C511yescharacteristic
160C22×#95C2×C511yescharacteristic
161#1446C2×C511yescharacteristic, complemented
162#1445C2×C511yescharacteristic, complemented
163#1441C2×C511yescharacteristic, complemented
164#1441C2×C511yescharacteristic, complemented
165#1436C2×C511yescharacteristic, complemented
166#1436C2×C511yescharacteristic, complemented
167C4⋊#95C2×C511yescharacteristic, complemented
168C22⋊#95C2×C511yescharacteristic
169C22⋊#95C2×C511yescharacteristic
170C22⋊#95C2×C511yescharacteristic
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×C5C22×C412yes—
180C24×C5C2×D412yes—
181C24×C5C2×D412yes—
182C24×C5C2×Q812yes—
183C24×C5C2×Q812yes—
184C24×C5#4112yes—
185C24×C5#4112yes—
186C24×C5C2411yescharacteristic
187C2×C5×Q8—28no—
188C2×C5×Q8—28no—
189C2×C5×Q8—44no—
190C2×C5×Q8—44no—
191C2×C5×Q8—44no—
192C2×C5×Q8—44no—
193C2×C5×Q8—44no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
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—28no—
211C22×C4×C5—28no—
212C22×C4×C5—28no—
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—28no—
262C22×C4×C5—28no—
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—44no—
278C22×C4×C5—44no—
279C22×C4×C5—44no—
280C22×C4×C5—44no—
281C22×C4×C5—44no—
282C22×C4×C5—44no—
283C22×C4×C5—44no—
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×C5—44no—
292C22×C4×C5—44no—
293C22×C4×C5C22×C412yes—
294C22×C4×C5C22×C412yes—
295C22×C4×C5C22×C412yes—
296C22×C4×C5C22×C412yes—
297C22×C4×C5C22×C412yes—
298C22×C4×C5C22×C412yes—
299C22×C4×C5C2×D412yes—
300C22×C4×C5C2×D412yes—
301C22×C4×C5C2×D412yes—
302C22×C4×C5C2×D412yes—
303C22×C4×C5C2×D412yes—
304C22×C4×C5C2×D412yes—
305C22×C4×C5C2×D412yes—
306C22×C4×C5C2×Q812yes—
307C22×C4×C5C2×Q812yes—
308C22×C4×C5C2×Q812yes—
309C22×C4×C5C2×Q812yes—
310C22×C4×C5#4112yes—
311C22×C4×C5#4112yes—
312C22×C4×C5#4112yes—
313C5×C4⋊C4—28no—
314C5×C4⋊C4—28no—
315C5×C4⋊C4—28no—
316C5×C4⋊C4—44no—
317C5×C4⋊C4—44no—
318C5×C22⋊C4—28no—
319C5×C22⋊C4—28no—
320C5×C22⋊C4—44no—
321C5×C22⋊C4C22⋊C4116yes—
322C42×C5—44no—
323C42×C5—44no—
324C23×Q8C22×C511yescharacteristic
325C24×C4C22×C511yescharacteristic
326C24×C4C22×C511yescharacteristic
327C24×C4C22×C511yescharacteristic
328C2×C22⋊Q8—24no—
329C2×C22⋊Q8—24no—
330C2×C22⋊Q8C4×C518yescomplemented
331C22×C4⋊C4C22×C511yescharacteristic
332C22×C4⋊C4C22×C511yescharacteristic
333C22×C4⋊C4C22×C511yescharacteristic
334C22×C4⋊C4C22×C511yescharacteristic
335C22×C4⋊C4C22×C511yescharacteristic
336C22×C22⋊C4C22×C511yescharacteristic
337C22×C22⋊C4C22×C511yescharacteristic
338C22×C22⋊C4C22×C511yescharacteristic
339C22×C22⋊C4C22×C511yescharacteristic
340C22×C42C22×C511yescharacteristic
341C22×C42C22×C511yescharacteristic
342#391—24no—
343#385—24no—
344C4×C22⋊C4—24no—
345C2×#95—24no—
346C2×#95C22×C511yescharacteristic
347C2×#95C22×C511yescharacteristic
348C2×#95C22×C511yescharacteristic
349C2×#95C22×C511yescharacteristic
350C2×#95C22×C511yescharacteristic
351C2×#95C22×C511yescharacteristic
352C2×#95C22×C511yescharacteristic
353C2×#95C22×C511yescharacteristic
354C2×#95C22×C511yescharacteristic
355C2×#95C22×C511yescharacteristic
356C2×#95C22×C511yescharacteristic
357C2×#95C22×C511yescharacteristic
358C2×#95C22×C511yescharacteristic
359C2×#95C22×C511yescharacteristic
360C2×#95C22×C511yescharacteristic
361C2×#95C22×C511yescharacteristic
362C2×#95C22×C511yescharacteristic
363C2×#95C22×C511yescharacteristic
364C2×#95C22×C511yescharacteristic
365C2×#95C22×C511yescharacteristic
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5C2×C22⋊C414yes—
395C23×C5C4×Q814yes—
396C23×C5C4×Q814yes—
397C23×C5C22⋊Q814yes—
398C23×C5C22⋊Q814yes—
399C23×C5#12414yes—
400C23×C5C4⋊Q814yes—
401C23×C5C23×C411yescharacteristic
402C23×C5C22×D411yescharacteristic
403C23×C5C22×D411yescharacteristic
404C23×C5C22×D411yescharacteristic
405C23×C5C22×Q811yescharacteristic
406C23×C5C22×Q811yescharacteristic
407C23×C5C2×#4111yescharacteristic
408C23×C5C2×#4111yescharacteristic
409C23×C5C2×#4111yescharacteristic
410C23×C5C2×#4111yescharacteristic
411C23×C5C2×#4111yescharacteristic
412C23×C5H(5,𝔽2)11yescharacteristic
413C23×C5H(5,𝔽2)11yescharacteristic
414C23×C5H(5,𝔽2)11yescharacteristic
415C23×C52−1+411yescharacteristic
416C5×Q8—416no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
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—22no—
459C2×C4×C5—22no—
460C2×C4×C5—22no—
461C2×C4×C5—22no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—416no—
466C2×C4×C5—416no—
467C2×C4×C5—416no—
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×C5C2×C22⋊C414yes—
515C2×C4×C5C2×C22⋊C414yes—
516C2×C4×C5C4×D414yes—
517C2×C4×C5C22⋊Q814yescomplemented
518C25C23×C511yescharacteristic
519C22×Q8—22no—
520C22×Q8—22no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—41no—
524C22×Q8—41no—
525C22×Q8C2×C4×C514yescomplemented
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—22no—
530C23×C4—22no—
531C23×C4—22no—
532C23×C4—22no—
533C23×C4—22no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—22no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—41no—
542C23×C4—41no—
543C23×C4—41no—
544C23×C4—41no—
545C23×C4C2×C4×C514yes—
546C23×C4C5×Q814yescomplemented
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
558C23×C4C23×C511yescharacteristic
559C23×C4C23×C511yescharacteristic
560C23×C4C23×C511yescharacteristic
561C22⋊Q8—232no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4C2×C4×C514yescomplemented
575C2×C4⋊C4C2×C4×C514yescomplemented
576C2×C4⋊C4C2×C4×C514yescomplemented
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4C2×C4×C514yes—
585C2×C22⋊C4C2×C4×C514yes—
586C2×C22⋊C4C5×D414yes—
587C2×C22⋊C4C5×D414yes—
588C2×C22⋊C4C5×Q814yescomplemented
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—41no—
594C2×C42—41no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95C5×D414yes—
615C22×C5—24no—
616C22×C5—24no—
617C22×C5—24no—
618C22×C5—24no—
619C22×C5—24no—
620C22×C5—24no—
621C22×C5—24no—
622C22×C5—24no—
623C22×C5—24no—
624C22×C5—24no—
625C22×C5—24no—
626C22×C5—24no—
627C22×C5—24no—
628C22×C5—24no—
629C22×C5#39118yescomplemented
630C22×C5C22×C22⋊C411yescharacteristic
631C22×C5C2×C4×D411yescharacteristic
632C22×C5C2×C4×Q811yescharacteristic
633C22×C5C2×C4×Q811yescharacteristic
634C22×C5C4×#4111yescharacteristic
635C22×C5#51811yescharacteristic
636C22×C5#52011yescharacteristic
637C22×C5C2×C22⋊Q811yescharacteristic
638C22×C5C2×C22⋊Q811yescharacteristic
639C22×C5C2×C22⋊Q811yescharacteristic
640C22×C5#52511yescharacteristic
641C22×C5C2×#12411yescharacteristic
642C22×C5#52911yescharacteristic
643C22×C5C2×C4⋊Q811yescharacteristic
644C22×C5#53311yescharacteristic
645C22×C5#53811yescharacteristic
646C22×C5#53911yescharacteristic
647C22×C5#54311yescharacteristic
648C22×C5#54411yescharacteristic
649C22×C5D4211yescharacteristic
650C22×C5D4211yescharacteristic
651C22×C5#54611yescharacteristic
652C22×C5#54611yescharacteristic
653C22×C5#54611yescharacteristic
654C22×C5#54611yescharacteristic
655C22×C5#54611yescharacteristic
656C22×C5#54711yescharacteristic
657C22×C5#54711yescharacteristic
658C22×C5D4×Q811yescharacteristic
659C22×C5#55111yescharacteristic
660C22×C5#55111yescharacteristic
661C22×C5#55211yescharacteristic
662C22×C5#55411yescharacteristic
663C22×C5#55411yescharacteristic
664C22×C5#55411yescharacteristic
665C4×C5—24no—
666C4×C5—24no—
667C4×C5—24no—
668C4×C5—24no—
669C4×C5—42no—
670C4×C5—42no—
671C4×C5—42no—
672C4×C5—42no—
673C4×C5—42no—
674C4×C5—42no—
675C4×C5—42no—
676C4×C5—42no—
677C4×C5—81no—
678C4×C5—81no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C22×C4×C512yes—
688C24C2×C5×D412yes—
689C24C2×C5×D412yes—
690C24C2×C5×Q812yes—
691C24C2×C5×Q812yes—
692C24C5×#4112yes—
693C24C5×#4112yes—
694C24C24×C511yescharacteristic
695C2×Q8—28no—
696C2×Q8—28no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
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—28no—
770C22×C4—28no—
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—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4C22×C4×C512yes—
802C22×C4C22×C4×C512yes—
803C22×C4C22×C4×C512yes—
804C22×C4C22×C4×C512yes—
805C22×C4C22×C4×C512yes—
806C22×C4C22×C4×C512yes—
807C22×C4C2×C5×D412yes—
808C22×C4C2×C5×D412yes—
809C22×C4C2×C5×D412yes—
810C22×C4C2×C5×D412yes—
811C22×C4C2×C5×D412yes—
812C22×C4C2×C5×D412yes—
813C22×C4C2×C5×D412yes—
814C22×C4C2×C5×Q812yes—
815C22×C4C2×C5×Q812yes—
816C22×C4C2×C5×Q812yes—
817C22×C4C2×C5×Q812yes—
818C22×C4C5×#4112yes—
819C22×C4C5×#4112yes—
820C22×C4C5×#4112yes—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—44no—
829C22⋊C4C5×C22⋊C4116yes—
830C42—44no—
831C42—44no—
832C2×C5—28no—
833C2×C5C2×#39111yescharacteristic
834C2×C5C4×C22⋊Q811yescharacteristic
835C2×C5#232911yescharacteristic
836C2×C5D4×C22⋊C411yescharacteristic
837C2×C5#233911yescharacteristic
838C2×C5#236011yescharacteristic
839C2×C5#236811yescharacteristic
840C2×C5#243711yescharacteristic
841C2×C5#243811yescharacteristic
842C2×C5#244011yescharacteristic
843C2×C5#244911yescharacteristic
844C2×C5#245011yescharacteristic
845C2×C5#247211yescharacteristic
846C2×C5#248811yescharacteristic
847C2×C5#254911yescharacteristic
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23C2×C5×C22⋊C414yes—
877C23C4×C5×Q814yes—
878C23C4×C5×Q814yes—
879C23C5×C22⋊Q814yes—
880C23C5×C22⋊Q814yes—
881C23C5×#12414yes—
882C23C5×C4⋊Q814yes—
883C23C23×C4×C511yescharacteristic
884C23C22×C5×D411yescharacteristic
885C23C22×C5×D411yescharacteristic
886C23C22×C5×D411yescharacteristic
887C23C22×C5×Q811yescharacteristic
888C23C22×C5×Q811yescharacteristic
889C23C2×C5×#4111yescharacteristic
890C23C2×C5×#4111yescharacteristic
891C23C2×C5×#4111yescharacteristic
892C23C2×C5×#4111yescharacteristic
893C23C2×C5×#4111yescharacteristic
894C23C5×H(5,𝔽2)11yescharacteristic
895C23C5×H(5,𝔽2)11yescharacteristic
896C23C5×H(5,𝔽2)11yescharacteristic
897C23C5×2−1+411yescharacteristic
898Q8—416no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—416no—
948C2×C4—416no—
949C2×C4—416no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
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×C4C2×C5×C22⋊C414yes—
997C2×C4C2×C5×C22⋊C414yes—
998C2×C4C4×C5×D414yes—
999C2×C4C5×C22⋊Q814yescomplemented
1000C5#1405211yescharacteristic, direct product factor, Sylow
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22C5×#39118yescomplemented
1016C22C22×C5×C22⋊C411yescharacteristic
1017C22C2×C4×C5×D411yescharacteristic
1018C22C2×C4×C5×Q811yescharacteristic
1019C22C2×C4×C5×Q811yescharacteristic
1020C22C4×C5×#4111yescharacteristic
1021C22C5×#51811yescharacteristic
1022C22C5×#52011yescharacteristic
1023C22C2×C5×C22⋊Q811yescharacteristic
1024C22C2×C5×C22⋊Q811yescharacteristic
1025C22C2×C5×C22⋊Q811yescharacteristic
1026C22C5×#52511yescharacteristic
1027C22C2×C5×#12411yescharacteristic
1028C22C5×#52911yescharacteristic
1029C22C2×C5×C4⋊Q811yescharacteristic
1030C22C5×#53311yescharacteristic
1031C22C5×#53811yescharacteristic
1032C22C5×#53911yescharacteristic
1033C22C5×#54311yescharacteristic
1034C22C5×#54411yescharacteristic
1035C22C5×D4211yescharacteristic
1036C22C5×D4211yescharacteristic
1037C22C5×#54611yescharacteristic
1038C22C5×#54611yescharacteristic
1039C22C5×#54611yescharacteristic
1040C22C5×#54611yescharacteristic
1041C22C5×#54611yescharacteristic
1042C22C5×#54711yescharacteristic
1043C22C5×#54711yescharacteristic
1044C22C5×D4×Q811yescharacteristic
1045C22C5×#55111yescharacteristic
1046C22C5×#55111yescharacteristic
1047C22C5×#55211yescharacteristic
1048C22C5×#55411yescharacteristic
1049C22C5×#55411yescharacteristic
1050C22C5×#55411yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—24no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—81no—
1065C2—28no—
1066C2C2×C5×#39111yescharacteristic
1067C2C4×C5×C22⋊Q811yescharacteristic
1068C2C5×#232911yescharacteristic
1069C2C5×D4×C22⋊C411yescharacteristic
1070C2C5×#233911yescharacteristic
1071C2C5×#236011yescharacteristic
1072C2C5×#236811yescharacteristic
1073C2C5×#243711yescharacteristic
1074C2C5×#243811yescharacteristic
1075C2C5×#244011yescharacteristic
1076C2C5×#244911yescharacteristic
1077C2C5×#245011yescharacteristic
1078C2C5×#247211yescharacteristic
1079C2C5×#248811yescharacteristic
1080C2C5×#254911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#391C2semidirect
6. C5×#1446C2semidirect
7. C5×#1445C2semidirect
8. C5×#1441C2semidirect
9. C5×#1441C2semidirect
10. C5×#1436C2semidirect
11. C5×#1436C2semidirect
12. C5×C4⋊#95C2semidirect
22. C2×C5×C22⋊Q8C4semidirect
58. #14052C5direct (N × H)
66. C22×C5×Q8C2×C4semidirect
87. C23×C4×C5Q8semidirect
115. C2×C5×C4⋊C4C2×C4semidirect
116. C2×C5×C4⋊C4C2×C4semidirect
117. C2×C5×C4⋊C4C2×C4semidirect
129. C2×C5×C22⋊C4Q8semidirect
157. C2×#391C2×C5semidirect
161. #1446C2×C5semidirect
162. #1445C2×C5semidirect
163. #1441C2×C5semidirect
164. #1441C2×C5semidirect
165. #1436C2×C5semidirect
166. #1436C2×C5semidirect
167. C4⋊#95C2×C5semidirect
330. C2×C22⋊Q8C4×C5semidirect
517. C2×C4×C5C22⋊Q8semidirect
525. C22×Q8C2×C4×C5semidirect
546. C23×C4C5×Q8semidirect
574. C2×C4⋊C4C2×C4×C5semidirect
575. C2×C4⋊C4C2×C4×C5semidirect
576. C2×C4⋊C4C2×C4×C5semidirect
588. C2×C22⋊C4C5×Q8semidirect
629. C22×C5#391semidirect
999. C2×C4C5×C22⋊Q8semidirect
1000. C5#14052direct (N × H)
1015. C22C5×#391semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C2×C5×#3912
C2×C5×#3852
C2×C4×C5×C22⋊C42
C22×C5×#952
C5×#14462
C5×#14452
C5×#14412
C5×#14362
C5×C4⋊#952
C5×C22⋊#952
#140525