Finite Group Databasebeta

← #13044136

Subgroups — #13044136

Order 1280.

2984 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×#66262C211yesmaximal, characteristic, complemented
3D5×#548C211yesmaximal, characteristic
4#10617558C211yesmaximal, characteristic, complemented
5Q8×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6#10617326C213yesmaximal, complemented
7#10617324C213yesmaximal, complemented
8#10617286C213yesmaximal, complemented
9AGL(1,𝔽5)×C22⋊Q8C213yesmaximal, complemented
10#10617254C213yesmaximal, complemented
11#10617250C213yesmaximal, complemented
12Q8×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
13#10617208C211yesmaximal, characteristic, complemented
14#10617181C213yesmaximal, complemented
15#10617173C213yesmaximal, complemented
16C2×D5×#41C2211yescharacteristic
17C22×Q8×D5C2211yescharacteristic
18#41×AGL(1,𝔽5)—28no—
19#66262—28no—
20C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
21C2×Q8×AGL(1,𝔽5)C2213yes—
22C2×Q8×AGL(1,𝔽5)C2213yes—
23C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
24C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
25C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
26C2×D4×AGL(1,𝔽5)C2213yes—
27C2×D4×AGL(1,𝔽5)C2213yes—
28C2×#4130C2213yes—
29C2×#4130C2213yes—
30C2×#4130C2213yes—
31C22×C4×AGL(1,𝔽5)C2213yes—
32C5×#548C411yescharacteristic, complemented
33#66165C411yescharacteristic, complemented
34#66151C411yescharacteristic, complemented
35#66011C413yescomplemented
36D5×#124C2213yes—
37#65967C413yescomplemented
38D5×C22⋊Q8C2213yes—
39D5×#121C2213yes—
40#65932C413yescomplemented
41#65910C411yescharacteristic, complemented
42C4×Q8×D5C2211yescharacteristic
43#65886C413yescomplemented
44C4×D4×D5C2213yes—
45(C2×AGL(1,𝔽5))⋊Q8C2213yes—
46(C2×AGL(1,𝔽5))⋊Q8C2213yes—
47#65780C2216yes—
48#65780C2213yes—
49#65780C2213yes—
50#65779C2213yes—
51#65779C2213yes—
52#65765C2213yes—
53#65765C2213yes—
54C4×C22⋊AGL(1,𝔽5)C2213yes—
55C4×C22⋊AGL(1,𝔽5)C2213yes—
56#65712C2213yes—
57#65712C2213yes—
58#65711C2213yes—
59#65711C2213yes—
60C4⋊C4×AGL(1,𝔽5)C2216yes—
61C4⋊C4×AGL(1,𝔽5)C2213yes—
62C4⋊C4×AGL(1,𝔽5)C2213yes—
63#65700C2211yescharacteristic
64#65700C2213yes—
65#65700C2216yes—
66#65700C2216yes—
67#65700C2216yes—
68#65699C2213yes—
69#65699C2213yes—
70#65699C2216yes—
71C22⋊C4×AGL(1,𝔽5)C2216yes—
72#65688C2213yes—
73C4×C4⋊AGL(1,𝔽5)C2213yes—
74C4×C4⋊AGL(1,𝔽5)C2213yes—
75#65686C2213yes—
76#34293—51nomaximal, Sylow
77C23×AGL(1,𝔽5)C2313yes—
78C23×AGL(1,𝔽5)C2313yes—
79C2×C5×#41C2×C411yescharacteristic
80C22×C5×Q8C2×C411yescharacteristic, complemented
81D5×#41—24no—
82D5×#41—24no—
83C2×#713C2×C411yescharacteristic
84C2×Q8×D5—24no—
85C2×Q8×D5—24no—
86C2×Q8×D5C2×C411yescharacteristic, complemented
87C2×Q8×D5C2×C413yescomplemented
88C2×Q8×D5C2313yes—
89C2×Q8×D5C2311yescharacteristic
90C2×#711C2×C413yes—
91C2×D4×D5C2313yes—
92C2×D4×D5C2313yes—
93C2×#709C2×C413yes—
94C22×C4×D5C2313yes—
95C22×C4×D5C2313yes—
96C22×Dic10C2×C413yescomplemented
97C2×C22⋊AGL(1,𝔽5)C2316yes—
98C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
99C2×C22⋊AGL(1,𝔽5)C2313yes—
100C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
101C2×C22⋊AGL(1,𝔽5)C2316yes—
102C2×C22⋊AGL(1,𝔽5)C2313yes—
103C2×C22⋊AGL(1,𝔽5)C2313yes—
104C2×C22⋊AGL(1,𝔽5)C2313yes—
105Q8×AGL(1,𝔽5)—24no—
106Q8×AGL(1,𝔽5)—24no—
107Q8×AGL(1,𝔽5)—24no—
108Q8×AGL(1,𝔽5)—212no—
109Q8×AGL(1,𝔽5)—212no—
110Q8×AGL(1,𝔽5)D418yescomplemented
111D4×AGL(1,𝔽5)—212no—
112D4×AGL(1,𝔽5)—212no—
113#4130—212no—
114#4130—212no—
115#4130—212no—
116C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
117C2×C4⋊AGL(1,𝔽5)C2313yes—
118C2×C4⋊AGL(1,𝔽5)C2313yes—
119C2×C4⋊AGL(1,𝔽5)C2313yes—
120C2×C4⋊AGL(1,𝔽5)C2313yes—
121C2×C4⋊AGL(1,𝔽5)C2313yes—
122C2×C4⋊AGL(1,𝔽5)C2313yes—
123C2×C4⋊AGL(1,𝔽5)C2316yes—
124C2×C4⋊AGL(1,𝔽5)C2313yes—
125C2×C4×AGL(1,𝔽5)—212no—
126C2×C4×AGL(1,𝔽5)C2313yes—
127C2×C4×AGL(1,𝔽5)C2313yes—
128C2×C4×AGL(1,𝔽5)C2313yes—
129C2×C4×AGL(1,𝔽5)C2316yes—
130C2×C4×AGL(1,𝔽5)C2313yes—
131C2×C4×AGL(1,𝔽5)C2311yescharacteristic
132C2×C4×AGL(1,𝔽5)C2316yes—
133C2×C4×AGL(1,𝔽5)C2313yes—
134C5×#124C2×C413yescomplemented
135C5×C22⋊Q8C2×C413yescomplemented
136C5×#121C2×C413yescomplemented
137C4×C5×Q8C2×C411yescharacteristic, complemented
138C4×C5×D4C2×C413yescomplemented
139#4093C2×C413yescomplemented
140#4092C2×C413yescomplemented
141Q8×Dic5C2×C411yescharacteristic, complemented
142#4085C2×C416yescomplemented
143#4084C2×C413yescomplemented
144#4082C2×C413yescomplemented
145D4×Dic5C2×C413yescomplemented
146#4076C2×C413yescomplemented
147C4×C22⋊D5C2×C413yescomplemented
148C4×C22⋊D5C2×C413yescomplemented
149#4070C2×C413yescomplemented
150#4043C2×C413yescomplemented
151#4042C2×C416yescomplemented
152#4041C2×C413yescomplemented
153#4039C2×C413yescomplemented
154D5×C4⋊C4C2313yes—
155D5×C4⋊C4C2313yes—
156#4033C2×C413yescomplemented
157#4031C2×C416yescomplemented
158#4031C2×C416yescomplemented
159#4030C2×C416yescomplemented
160#4027C2×C413yescomplemented
161#4027C2×C413yescomplemented
162D5×C22⋊C4C2311yescharacteristic
163D5×C22⋊C4C2313yes—
164D5×C22⋊C4C2316yes—
165#4024C2×C416yescomplemented
166#4021C2×C413yescomplemented
167C4×D20C2×C413yescomplemented
168C42×D5C2313yes—
169C4×Dic10C2×C413yescomplemented
170(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
171(C2×AGL(1,𝔽5))⋊C4C2313yes—
172(C2×AGL(1,𝔽5))⋊C4C2313yes—
173(C2×AGL(1,𝔽5))⋊C4C2313yes—
174(C2×AGL(1,𝔽5))⋊C4C2313yes—
175(C2×AGL(1,𝔽5))⋊C4C2313yes—
176(C2×AGL(1,𝔽5))⋊C4C2313yes—
177(C2×AGL(1,𝔽5))⋊C4C2316yes—
178(C2×AGL(1,𝔽5))⋊C4C2313yes—
179(C2×AGL(1,𝔽5))⋊C4C2313yes—
180(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
181C2×#548—51no—
182C2×#519—51no—
183C2×C4×#41—51no—
184#2367—53no—
185#2363—53no—
186#2362—53no—
187#2354—53no—
188Q8×C4⋊C4—51no—
189#2341—51no—
190Q8×C22⋊C4—51no—
191#2326—53no—
192#2324—53no—
193C4×C22⋊Q8—53no—
194#2290—53no—
195#2276—51no—
196C23×D5C2411yescharacteristic
197C23×D5C2413yes—
198C22×AGL(1,𝔽5)—26no—
199C22×AGL(1,𝔽5)—26no—
200C22×AGL(1,𝔽5)—26no—
201C22×AGL(1,𝔽5)—43no—
202C22×AGL(1,𝔽5)—43no—
203C22×AGL(1,𝔽5)—43no—
204C22×AGL(1,𝔽5)C2413yes—
205C22×AGL(1,𝔽5)C2411yescharacteristic
206C22×AGL(1,𝔽5)C2413yes—
207C22×AGL(1,𝔽5)C2411yescharacteristic
208C22×AGL(1,𝔽5)C2413yes—
209C22×AGL(1,𝔽5)C2413yes—
210C22×AGL(1,𝔽5)C2411yescharacteristic
211C22×AGL(1,𝔽5)C2411yescharacteristic
212C5×#41—24no—
213C2×C5×Q8—24no—
214C2×C5×Q8C22×C413yes—
215C2×C5×Q8C22×C411yescharacteristic
216C2×C5×D4C22×C413yes—
217C2×C5×D4C22×C413yes—
218C22×C4×C5C22×C413yes—
219C22×C4×C5C22×C413yes—
220C2×C22⋊D5C22×C416yes—
221C2×C22⋊D5C22×C413yes—
222C2×C22⋊D5C22×C413yes—
223C22×Dic5C22×C413yes—
224C22×Dic5C22×C413yes—
225#713—24no—
226Q8×D5—24no—
227Q8×D5—26no—
228Q8×D5—26no—
229Q8×D5—212no—
230Q8×D5C2×D414yes—
231Q8×D5#4114yes—
232#711—212no—
233D4×D5—26no—
234D4×D5—26no—
235D4×D5—43no—
236D4×D5—43no—
237#709—212no—
238C2×D20C22×C413yes—
239C2×D20C22×C413yes—
240C2×C4×D5—26no—
241C2×C4×D5—26no—
242C2×C4×D5—26no—
243C2×C4×D5—26no—
244C2×C4×D5C22×C413yes—
245C2×C4×D5C22×C413yes—
246C2×C4×D5C22×C413yes—
247C2×C4×D5C22×C413yes—
248C2×C4×D5C2411yescharacteristic
249C2×C4×D5C2413yes—
250C2×C4×D5C2413yes—
251C2×C4×D5C2411yescharacteristic
252C2×C4×D5C2413yes—
253C2×Dic10—212no—
254C2×Dic10C22×C413yes—
255C2×Dic10C22×C416yes—
256C2×Dic10C22×C413yes—
257C22⋊AGL(1,𝔽5)—26no—
258C22⋊AGL(1,𝔽5)—22no—
259C22⋊AGL(1,𝔽5)—212no—
260C22⋊AGL(1,𝔽5)—22no—
261C22⋊AGL(1,𝔽5)—43no—
262C22⋊AGL(1,𝔽5)—43no—
263C22⋊AGL(1,𝔽5)—46no—
264C22⋊AGL(1,𝔽5)—43no—
265C4⋊AGL(1,𝔽5)—26no—
266C4⋊AGL(1,𝔽5)—26no—
267C4⋊AGL(1,𝔽5)—22no—
268C4⋊AGL(1,𝔽5)—26no—
269C4⋊AGL(1,𝔽5)—26no—
270C4⋊AGL(1,𝔽5)—26no—
271C4⋊AGL(1,𝔽5)—43no—
272C4⋊AGL(1,𝔽5)—46no—
273C4⋊AGL(1,𝔽5)C2×D4112yes—
274C4×AGL(1,𝔽5)—22no—
275C4×AGL(1,𝔽5)—26no—
276C4×AGL(1,𝔽5)—212no—
277C4×AGL(1,𝔽5)—26no—
278C4×AGL(1,𝔽5)—26no—
279C4×AGL(1,𝔽5)—26no—
280C4×AGL(1,𝔽5)—46no—
281C4×AGL(1,𝔽5)C2×D4112yes—
282C5×C4⋊C4C22×C413yes—
283C5×C4⋊C4C22×C413yes—
284C5×C22⋊C4C22×C411yescharacteristic
285C5×C22⋊C4C22×C413yes—
286C5×C22⋊C4C22×C416yes—
287C42×C5C22×C413yes—
288C22⋊Dic5C22×C416yes—
289C22⋊Dic5C22×C413yes—
290C22⋊Dic5C22×C411yescharacteristic
291#685C22×C411yescharacteristic
292#685C22×C413yes—
293#685C22×C416yes—
294#685C22×C416yes—
295#685C22×C413yes—
296#685C22×C411yescharacteristic
297C4⋊Dic5C22×C413yes—
298C4⋊Dic5C22×C413yes—
299#683C22×C416yes—
300#683C22×C413yes—
301#683C22×C413yes—
302C4×Dic5C22×C413yes—
303C4×Dic5C22×C413yes—
304C4×Dic5C22×C413yes—
305C22×#41—51no—
306C23×Q8—51no—
307#548—51no—
308#548—51no—
309#548—53no—
310#548—53no—
311#548—53no—
312#548—51no—
313#548—53no—
314#548AGL(1,𝔽5)11yescharacteristic, complemented
315C2×#124—53no—
316C2×C22⋊Q8—53no—
317C2×#121—53no—
318#519—108no—
319C4×#41—108no—
320C2×C4×Q8—51no—
321C2×C4×Q8—51no—
322C2×C4×Q8—53no—
323C2×C4×Q8—51no—
324C2×C4×Q8—51no—
325C2×C4×Q8—51no—
326C2×C4×Q8—53no—
327C2×C4×D4—53no—
328C2×C4×D4—53no—
329C2×C4×D4—53no—
330C2×#117—53no—
331C2×#117—53no—
332C2×#117—53no—
333C22×C42—53no—
334#391—53no—
335#391—53no—
336#390—53no—
337#390—56no—
338#390—53no—
339#389—53no—
340#389—53no—
341#388—56no—
342#388—56no—
343#388—56no—
344#388—53no—
345#388—51no—
346#387—53no—
347#387—53no—
348#386—53no—
349#386—53no—
350#385—56no—
351#385—53no—
352#385—53no—
353#384—53no—
354#380—53no—
355#380—53no—
356C4×C4⋊C4—53no—
357C4×C4⋊C4—53no—
358C4×C4⋊C4—56no—
359C4×C4⋊C4—53no—
360C4×C4⋊C4—53no—
361C4×C22⋊C4—53no—
362C4×C22⋊C4—53no—
363C4×C22⋊C4—56no—
364#376—53no—
365C23×C5C23×C413yes—
366C23×C5C23×C411yescharacteristic
367C22×D5—21no—
368C22×D5—23no—
369C22×D5—21no—
370C22×D5—23no—
371C22×D5—21no—
372C22×D5—23no—
373C22×D5—21no—
374C22×D5—23no—
375C22×D5—23no—
376C22×D5—23no—
377C22×D5—21no—
378C22×D5—21no—
379C22×D5C23×C413yes—
380C22×D5C23×C411yescharacteristic
381C22×D5C2511yescharacteristic
382C2×AGL(1,𝔽5)—21no—
383C2×AGL(1,𝔽5)—23no—
384C2×AGL(1,𝔽5)—23no—
385C2×AGL(1,𝔽5)—21no—
386C2×AGL(1,𝔽5)—21no—
387C2×AGL(1,𝔽5)—21no—
388C2×AGL(1,𝔽5)—23no—
389C2×AGL(1,𝔽5)—21no—
390C2×AGL(1,𝔽5)—23no—
391C2×AGL(1,𝔽5)—21no—
392C2×AGL(1,𝔽5)—23no—
393C2×AGL(1,𝔽5)—21no—
394C2×AGL(1,𝔽5)—21no—
395C2×AGL(1,𝔽5)—23no—
396C2×AGL(1,𝔽5)—23no—
397C2×AGL(1,𝔽5)—23no—
398C2×AGL(1,𝔽5)—23no—
399C2×AGL(1,𝔽5)—23no—
400C2×AGL(1,𝔽5)—21no—
401C2×AGL(1,𝔽5)—21no—
402C2×AGL(1,𝔽5)—23no—
403C2×AGL(1,𝔽5)—412no—
404C2×AGL(1,𝔽5)—412no—
405C2×AGL(1,𝔽5)C22×D416yes—
406C2×AGL(1,𝔽5)C22×D412yes—
407C2×AGL(1,𝔽5)2−1+412yes—
408C5×Q8—26no—
409C5×Q8C4×D414yes—
410C5×D4—26no—
411C5×D4—43no—
412C2×C4×C5—26no—
413C2×C4×C5—26no—
414C2×C4×C5C23×C411yescharacteristic
415C2×C4×C5C23×C413yes—
416C2×C4×C5C23×C411yescharacteristic
417C2×C4×C5C23×C413yes—
418C2×C4×C5C23×C413yes—
419C22⋊D5—212no—
420C22⋊D5—43no—
421C22⋊D5—43no—
422C2×Dic5—26no—
423C2×Dic5—26no—
424C2×Dic5C23×C411yescharacteristic
425C2×Dic5C23×C413yes—
426C2×Dic5C23×C411yescharacteristic
427C2×Dic5C23×C413yes—
428C2×Dic5C23×C413yes—
429D20—26no—
430D20—43no—
431C4×D5—21no—
432C4×D5—23no—
433C4×D5—21no—
434C4×D5—23no—
435C4×D5—21no—
436C4×D5—23no—
437C4×D5—21no—
438C4×D5—23no—
439C4×D5—26no—
440C4×D5—26no—
441C4×D5—26no—
442C4×D5—26no—
443C4×D5C22×D416yes—
444C4×D5C2×#4116yes—
445Dic10—26no—
446Dic10—212no—
447Dic10C4×D4112yes—
448C2×#41—51no—
449C2×#41—53no—
450C2×#41—53no—
451C2×#41—104no—
452C2×#41—104no—
453C2×#41C2×AGL(1,𝔽5)11yescharacteristic
454C22×Q8—51no—
455C22×Q8—53no—
456C22×Q8—53no—
457C22×Q8—51no—
458C22×Q8—53no—
459C22×Q8—104no—
460C22×Q8—104no—
461C22×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
462C22×D4—53no—
463C22×D4—53no—
464C23×C4—53no—
465C23×C4—53no—
466C23×C4—53no—
467C23×C4—53no—
468#124—53no—
469#124—53no—
470#124—56no—
471#124—56no—
472#124—53no—
473#124C2×AGL(1,𝔽5)13yescomplemented
474C22⋊Q8—53no—
475C22⋊Q8—53no—
476C22⋊Q8—56no—
477C22⋊Q8—53no—
478C22⋊Q8—56no—
479C22⋊Q8C2×AGL(1,𝔽5)13yescomplemented
480#121—53no—
481#121—56no—
482#121—53no—
483#121—53no—
484#121—56no—
485#121C2×AGL(1,𝔽5)13yescomplemented
486C4×Q8—58no—
487C4×Q8—51no—
488C4×Q8—53no—
489C4×Q8—53no—
490C4×Q8—1012no—
491C4×Q8—1012no—
492C4×Q8—104no—
493C4×Q8—104no—
494C4×Q8—104no—
495C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
496C4×D4—53no—
497C4×D4—53no—
498C4×D4—53no—
499C4×D4—53no—
500C4×D4—53no—
501C4×D4—53no—
502C4×D4—53no—
503C4×D4—1012no—
504C4×D4—1012no—
505C4×D4C2×AGL(1,𝔽5)13yescomplemented
506#117—1012no—
507#117—1012no—
508#117—1012no—
509C2×C4⋊C4—53no—
510C2×C4⋊C4—53no—
511C2×C4⋊C4—53no—
512C2×C4⋊C4—53no—
513C2×C4⋊C4—53no—
514C2×C4⋊C4—53no—
515C2×C4⋊C4—53no—
516C2×C4⋊C4—53no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—53no—
519C2×C4⋊C4—56no—
520C2×C22⋊C4—51no—
521C2×C22⋊C4—53no—
522C2×C22⋊C4—56no—
523C2×C22⋊C4—51no—
524C2×C22⋊C4—53no—
525C2×C22⋊C4—56no—
526C2×C22⋊C4—51no—
527C2×C22⋊C4—53no—
528C2×C22⋊C4—56no—
529C2×C22⋊C4—53no—
530C2×C22⋊C4—53no—
531C2×C42—53no—
532C2×C42—53no—
533C2×C42—53no—
534C2×C42—56no—
535C2×C42—53no—
536C2×C42—53no—
537C2×C42—53no—
538C2×C42—51no—
539C2×C42—56no—
540C2×C42—1012no—
541#95—51no—
542#95—53no—
543#95—53no—
544#95—53no—
545#95—53no—
546#95—51no—
547#95—53no—
548#95—53no—
549#95—53no—
550#95—56no—
551#95—53no—
552C22×C5—21no—
553C22×C5—23no—
554C22×C5—21no—
555C22×C5—23no—
556C22×C5—21no—
557C22×C5—23no—
558C22×C5C24×C411yescharacteristic
559C2×D5—21no—
560C2×D5—23no—
561C2×D5—21no—
562C2×D5—23no—
563C2×D5—21no—
564C2×D5—23no—
565C2×D5—43no—
566C2×D5—41no—
567C2×D5—43no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5—43no—
571C2×D5—41no—
572C2×D5—43no—
573C2×D5C23×D411yescharacteristic
574C2×D5C22×#4111yescharacteristic
575C2×D5C2×2−1+411yescharacteristic
576C2×D5#58511yescharacteristic
577C2×D5#58511yescharacteristic
578C2×D5#58511yescharacteristic
579AGL(1,𝔽5)—22no—
580AGL(1,𝔽5)—22no—
581AGL(1,𝔽5)—26no—
582AGL(1,𝔽5)—43no—
583AGL(1,𝔽5)—43no—
584AGL(1,𝔽5)—41no—
585AGL(1,𝔽5)—41no—
586AGL(1,𝔽5)—43no—
587C4×C5—23no—
588C4×C5—21no—
589C4×C5—23no—
590C4×C5—21no—
591C4×C5C2×C4×D416yes—
592Dic5—23no—
593Dic5—21no—
594Dic5—23no—
595Dic5—21no—
596Dic5C2×C4×D416yes—
597C24—53no—
598C24—51no—
599#41—24no—
600#41—1012no—
601#41—1012no—
602#41—104no—
603C2×Q8—24no—
604C2×Q8—54no—
605C2×Q8—54no—
606C2×Q8—53no—
607C2×Q8—56no—
608C2×Q8—53no—
609C2×Q8—1012no—
610C2×Q8—106no—
611C2×Q8—106no—
612C2×Q8—1012no—
613C2×Q8—104no—
614C2×Q8C22×AGL(1,𝔽5)13yes—
615C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
616C2×D4—56no—
617C2×D4—53no—
618C2×D4—53no—
619C2×D4—53no—
620C2×D4—53no—
621C2×D4—106no—
622C2×D4—106no—
623C2×D4—203no—
624C2×D4—203no—
625C2×D4C22×AGL(1,𝔽5)13yes—
626C2×D4C22×AGL(1,𝔽5)13yes—
627C22×C4—53no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—53no—
631C22×C4—53no—
632C22×C4—53no—
633C22×C4—51no—
634C22×C4—51no—
635C22×C4—53no—
636C22×C4—53no—
637C22×C4—53no—
638C22×C4—53no—
639C22×C4—53no—
640C22×C4—53no—
641C22×C4—51no—
642C22×C4—53no—
643C22×C4—51no—
644C22×C4—53no—
645C22×C4—53no—
646C22×C4—106no—
647C22×C4—106no—
648C22×C4—106no—
649C22×C4—106no—
650C22×C4—106no—
651C22×C4—106no—
652C22×C4—106no—
653C22×C4—203no—
654C22×C4—203no—
655C22×C4—203no—
656C22×C4C22×AGL(1,𝔽5)13yes—
657C22×C4C22×AGL(1,𝔽5)13yes—
658C4⋊C4—512no—
659C4⋊C4—53no—
660C4⋊C4—53no—
661C4⋊C4—53no—
662C4⋊C4—56no—
663C4⋊C4—53no—
664C4⋊C4—106no—
665C4⋊C4—106no—
666C4⋊C4—106no—
667C4⋊C4—106no—
668C4⋊C4—106no—
669C4⋊C4—102no—
670C4⋊C4—203no—
671C4⋊C4—206no—
672C4⋊C4C22×AGL(1,𝔽5)13yes—
673C4⋊C4C22×AGL(1,𝔽5)13yes—
674C22⋊C4—51no—
675C22⋊C4—53no—
676C22⋊C4—56no—
677C22⋊C4—51no—
678C22⋊C4—51no—
679C22⋊C4—53no—
680C22⋊C4—53no—
681C22⋊C4—56no—
682C22⋊C4—56no—
683C22⋊C4—102no—
684C22⋊C4—106no—
685C22⋊C4—1012no—
686C22⋊C4—102no—
687C22⋊C4—203no—
688C22⋊C4—206no—
689C22⋊C4—203no—
690C22⋊C4—203no—
691C22⋊C4C22×AGL(1,𝔽5)11yescharacteristic
692C22⋊C4C22×AGL(1,𝔽5)13yes—
693C22⋊C4C22×AGL(1,𝔽5)16yes—
694C42—512no—
695C42—53no—
696C42—53no—
697C42—53no—
698C42—102no—
699C42—106no—
700C42—106no—
701C42—106no—
702C42—1012no—
703C42—106no—
704C42—206no—
705C42C22×AGL(1,𝔽5)13yes—
706C2×C5—43no—
707C2×C5—41no—
708C2×C5C22×C4×D411yescharacteristic
709C2×C5#342811yescharacteristic
710C2×C5C4×2−1+411yescharacteristic
711D5—41no—
712D5—43no—
713D5#348711yescharacteristic
714D5#348911yescharacteristic
715D5#351811yescharacteristic
716D5#352411yescharacteristic
717C23—51no—
718C23—53no—
719C23—51no—
720C23—101no—
721C23—103no—
722C23—101no—
723C23—101no—
724C23—103no—
725C23—103no—
726C23—103no—
727C23—101no—
728C23—103no—
729C23—103no—
730C23—101no—
731C23—101no—
732C23C23×AGL(1,𝔽5)13yes—
733C23C23×AGL(1,𝔽5)11yescharacteristic
734Q8—26no—
735Q8—512no—
736Q8—1012no—
737Q8—106no—
738Q8D4×AGL(1,𝔽5)14yes—
739D4—26no—
740D4—43no—
741D4—1012no—
742D4—106no—
743D4—203no—
744D4—203no—
745D4—203no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—53no—
749C2×C4—56no—
750C2×C4—56no—
751C2×C4—52no—
752C2×C4—56no—
753C2×C4—52no—
754C2×C4—51no—
755C2×C4—53no—
756C2×C4—53no—
757C2×C4—51no—
758C2×C4—106no—
759C2×C4—106no—
760C2×C4—101no—
761C2×C4—103no—
762C2×C4—103no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—103no—
766C2×C4—101no—
767C2×C4—103no—
768C2×C4—106no—
769C2×C4—106no—
770C2×C4—101no—
771C2×C4—103no—
772C2×C4—103no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—106no—
777C2×C4—106no—
778C2×C4—101no—
779C2×C4—103no—
780C2×C4—101no—
781C2×C4—103no—
782C2×C4—103no—
783C2×C4—103no—
784C2×C4—101no—
785C2×C4—101no—
786C2×C4—101no—
787C2×C4—103no—
788C2×C4—103no—
789C2×C4—103no—
790C2×C4—103no—
791C2×C4—101no—
792C2×C4—103no—
793C2×C4—2012no—
794C2×C4—2012no—
795C2×C4C23×AGL(1,𝔽5)11yescharacteristic
796C2×C4C23×AGL(1,𝔽5)13yes—
797C2×C4C23×AGL(1,𝔽5)13yes—
798C2×C4C23×AGL(1,𝔽5)11yescharacteristic
799C2×C4C23×AGL(1,𝔽5)13yes—
800C5#3429311yescharacteristic, complemented, Sylow
801C22—21no—
802C22—23no—
803C22—21no—
804C22—23no—
805C22—21no—
806C22—23no—
807C22—51no—
808C22—51no—
809C22—51no—
810C22—51no—
811C22—51no—
812C22—51no—
813C22—101no—
814C22—103no—
815C22—101no—
816C22—103no—
817C22—103no—
818C22—101no—
819C22—203no—
820C22—203no—
821C22—201no—
822C22—201no—
823C22—201no—
824C22—203no—
825C22—201no—
826C22—203no—
827C22C24×AGL(1,𝔽5)11yescharacteristic
828C4—21no—
829C4—23no—
830C4—23no—
831C4—21no—
832C4—56no—
833C4—102no—
834C4—102no—
835C4—106no—
836C4—101no—
837C4—103no—
838C4—103no—
839C4—101no—
840C4—203no—
841C4—201no—
842C4—203no—
843C4—203no—
844C4—201no—
845C4C2×D4×AGL(1,𝔽5)16yes—
846C2—41no—
847C2—43no—
848C2—51no—
849C2—51no—
850C2—51no—
851C2—51no—
852C2—201no—
853C2—203no—
854C2C22×D4×AGL(1,𝔽5)11yescharacteristic
855C2#1061941211yescharacteristic
856C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#548C4
prime radicalD5×#548C2
cosocleC22×D5C25
hypercenter#548AGL(1,𝔽5)
hypocenterC5#34293
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×AGL(1,𝔽5)C2semidirect
2. C2×#66262C2semidirect
4. #10617558C2semidirect
5. Q8×C22⋊AGL(1,𝔽5)C2semidirect
6. #10617326C2semidirect
7. #10617324C2semidirect
8. #10617286C2semidirect
9. AGL(1,𝔽5)×C22⋊Q8C2semidirect
10. #10617254C2semidirect
11. #10617250C2semidirect
12. Q8×C4⋊AGL(1,𝔽5)C2semidirect
13. #10617208C2semidirect
14. #10617181C2semidirect
15. #10617173C2semidirect
32. C5×#548C4semidirect
33. #66165C4semidirect
34. #66151C4semidirect
35. #66011C4semidirect
37. #65967C4semidirect
40. #65932C4semidirect
41. #65910C4semidirect
43. #65886C4semidirect
80. C22×C5×Q8C2×C4semidirect
86. C2×Q8×D5C2×C4semidirect
87. C2×Q8×D5C2×C4semidirect
96. C22×Dic10C2×C4semidirect
110. Q8×AGL(1,𝔽5)D4semidirect
134. C5×#124C2×C4semidirect
135. C5×C22⋊Q8C2×C4semidirect
136. C5×#121C2×C4semidirect
137. C4×C5×Q8C2×C4semidirect
138. C4×C5×D4C2×C4semidirect
139. #4093C2×C4semidirect
140. #4092C2×C4semidirect
141. Q8×Dic5C2×C4semidirect
142. #4085C2×C4semidirect
143. #4084C2×C4semidirect
144. #4082C2×C4semidirect
145. D4×Dic5C2×C4semidirect
146. #4076C2×C4semidirect
147. C4×C22⋊D5C2×C4semidirect
148. C4×C22⋊D5C2×C4semidirect
149. #4070C2×C4semidirect
150. #4043C2×C4semidirect
151. #4042C2×C4semidirect
152. #4041C2×C4semidirect
153. #4039C2×C4semidirect
156. #4033C2×C4semidirect
157. #4031C2×C4semidirect
158. #4031C2×C4semidirect
159. #4030C2×C4semidirect
160. #4027C2×C4semidirect
161. #4027C2×C4semidirect
165. #4024C2×C4semidirect
166. #4021C2×C4semidirect
167. C4×D20C2×C4semidirect
169. C4×Dic10C2×C4semidirect
314. #548AGL(1,𝔽5)semidirect
461. C22×Q8C2×AGL(1,𝔽5)semidirect
473. #124C2×AGL(1,𝔽5)semidirect
479. C22⋊Q8C2×AGL(1,𝔽5)semidirect
485. #121C2×AGL(1,𝔽5)semidirect
495. C4×Q8C2×AGL(1,𝔽5)semidirect
505. C4×D4C2×AGL(1,𝔽5)semidirect
800. C5#34293semidirect

Maximal subgroups

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

subgroupindex
C2×#41×AGL(1,𝔽5)2
C2×#662622
D5×#5482
#106175582
Q8×C22⋊AGL(1,𝔽5)2
#106173262
#106173242
#106172862
AGL(1,𝔽5)×C22⋊Q82
#106172542
#106172502
Q8×C4⋊AGL(1,𝔽5)2
#106172082
#106171812
#106171732
#342935