Finite Group Databasebeta

← #13044137

Subgroups — #13044137

Order 1280.

3112 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66266C211yesmaximal, characteristic, complemented
2C22×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3D5×#548C211yesmaximal, characteristic
4#10617558C211yesmaximal, characteristic, complemented
5Q8×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6#10617326C213yesmaximal, complemented
7#10617324C213yesmaximal, complemented
8#10617285C213yesmaximal, complemented
9#10617282C213yesmaximal, complemented
10#10617253C213yesmaximal, complemented
11AGL(1,𝔽5)×#121C213yesmaximal, complemented
12Q8×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
13#10617208C211yesmaximal, characteristic, complemented
14D4×C4⋊AGL(1,𝔽5)C213yesmaximal, complemented
15#10617173C213yesmaximal, complemented
16C2×D5×#41C2211yescharacteristic
17C22×Q8×D5C2211yescharacteristic
18#66266—28no—
19C2×Q8×AGL(1,𝔽5)—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×D4×AGL(1,𝔽5)C2216yes—
29C2×#4130C2213yes—
30C22×C4⋊AGL(1,𝔽5)C2213yes—
31C22×C4⋊AGL(1,𝔽5)C2213yes—
32C22×C4×AGL(1,𝔽5)C2213yes—
33C5×#548C411yescharacteristic, complemented
34#66165C411yescharacteristic, complemented
35#66151C411yescharacteristic, complemented
36#66011C413yescomplemented
37D5×#124C2213yes—
38#65967C413yescomplemented
39D5×C22⋊Q8C2213yes—
40D5×#121C2213yes—
41#65932C413yescomplemented
42#65910C411yescharacteristic, complemented
43C4×Q8×D5C2211yescharacteristic
44#65886C413yescomplemented
45C4×D4×D5C2213yes—
46(C2×AGL(1,𝔽5))⋊Q8C2213yes—
47(C2×AGL(1,𝔽5))⋊Q8C2213yes—
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#65712C2216yes—
57#65712C2213yes—
58#65712C2213yes—
59#65711C2213yes—
60#65711C2213yes—
61C4⋊C4×AGL(1,𝔽5)C2213yes—
62C4⋊C4×AGL(1,𝔽5)C2213yes—
63#65700C2213yes—
64#65700C2213yes—
65#65700C2216yes—
66#65700C2216yes—
67#65699C2211yescharacteristic
68#65699C2213yes—
69#65699C2216yes—
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#34294—51nomaximal, Sylow
77C23×AGL(1,𝔽5)C2311yescharacteristic
78C23×AGL(1,𝔽5)C2313yes—
79C23×AGL(1,𝔽5)C2316yes—
80C2×C5×#41C2×C411yescharacteristic, complemented
81C22×C5×Q8C2×C411yescharacteristic, complemented
82D5×#41—24no—
83D5×#41—24no—
84C2×#713C2×C411yescharacteristic, complemented
85C2×Q8×D5—24no—
86C2×Q8×D5—24no—
87C2×Q8×D5C2×C411yescharacteristic, complemented
88C2×Q8×D5C2×C413yescomplemented
89C2×Q8×D5C2313yes—
90C2×Q8×D5C2311yescharacteristic
91C2×#711C2×C413yescomplemented
92C2×D4×D5C2313yes—
93C2×D4×D5C2313yes—
94C2×#709C2×C413yescomplemented
95C22×C4×D5C2313yes—
96C22×C4×D5C2313yes—
97C22×Dic10C2×C413yescomplemented
98C2×C22⋊AGL(1,𝔽5)C2313yes—
99C2×C22⋊AGL(1,𝔽5)C2313yes—
100C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
101C2×C22⋊AGL(1,𝔽5)C2313yes—
102C2×C22⋊AGL(1,𝔽5)C2313yes—
103C2×C22⋊AGL(1,𝔽5)C2313yes—
104C2×C22⋊AGL(1,𝔽5)C2316yes—
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—
113D4×AGL(1,𝔽5)—412no—
114#4130—212no—
115C2×C4⋊AGL(1,𝔽5)—212no—
116C2×C4⋊AGL(1,𝔽5)—212no—
117C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
118C2×C4⋊AGL(1,𝔽5)C2313yes—
119C2×C4⋊AGL(1,𝔽5)C2313yes—
120C2×C4⋊AGL(1,𝔽5)C2313yes—
121C2×C4⋊AGL(1,𝔽5)C2316yes—
122C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
123C2×C4⋊AGL(1,𝔽5)C2313yes—
124C2×C4⋊AGL(1,𝔽5)C2313yes—
125C2×C4⋊AGL(1,𝔽5)C2316yes—
126C2×C4⋊AGL(1,𝔽5)C2313yes—
127C2×C4×AGL(1,𝔽5)—212no—
128C2×C4×AGL(1,𝔽5)C2313yes—
129C2×C4×AGL(1,𝔽5)C2313yes—
130C2×C4×AGL(1,𝔽5)C2313yes—
131C2×C4×AGL(1,𝔽5)C2313yes—
132C2×C4×AGL(1,𝔽5)C2313yes—
133C2×C4×AGL(1,𝔽5)C2316yes—
134C2×C4×AGL(1,𝔽5)C2313yes—
135C5×#124C2×C413yescomplemented
136C5×C22⋊Q8C2×C413yescomplemented
137C5×#121C2×C413yescomplemented
138C4×C5×Q8C2×C411yescharacteristic, complemented
139C4×C5×D4C2×C413yescomplemented
140#4093C2×C413yescomplemented
141#4092C2×C413yescomplemented
142Q8×Dic5C2×C411yescharacteristic, complemented
143#4085C2×C416yescomplemented
144#4084C2×C413yescomplemented
145#4082C2×C413yescomplemented
146D4×Dic5C2×C413yescomplemented
147#4076C2×C413yescomplemented
148C4×C22⋊D5C2×C413yescomplemented
149C4×C22⋊D5C2×C413yescomplemented
150#4070C2×C413yescomplemented
151#4043C2×C413yescomplemented
152#4042C2×C416yescomplemented
153#4041C2×C413yescomplemented
154#4039C2×C413yescomplemented
155D5×C4⋊C4C2313yes—
156D5×C4⋊C4C2313yes—
157#4033C2×C413yescomplemented
158#4031C2×C416yescomplemented
159#4031C2×C416yescomplemented
160#4030C2×C416yescomplemented
161#4027C2×C413yescomplemented
162#4027C2×C413yescomplemented
163D5×C22⋊C4C2311yescharacteristic
164D5×C22⋊C4C2313yes—
165D5×C22⋊C4C2316yes—
166#4024C2×C416yescomplemented
167#4021C2×C413yescomplemented
168C4×D20C2×C413yescomplemented
169C42×D5C2313yes—
170C4×Dic10C2×C413yescomplemented
171(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
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))⋊C4C2311yescharacteristic
180(C2×AGL(1,𝔽5))⋊C4C2313yes—
181(C2×AGL(1,𝔽5))⋊C4C2313yes—
182C2×#548—51no—
183C2×#520—51no—
184C22×C4×Q8—51no—
185#2367—53no—
186#2361—53no—
187#2360—53no—
188Q8×C4⋊C4—51no—
189D4×C4⋊C4—53no—
190#2341—51no—
191Q8×C22⋊C4—51no—
192#2326—53no—
193#2323—53no—
194C4×#121—53no—
195#2290—53no—
196#2276—51no—
197C23×D5C2413yes—
198C23×D5C2411yescharacteristic
199C22×AGL(1,𝔽5)—22no—
200C22×AGL(1,𝔽5)—22no—
201C22×AGL(1,𝔽5)—22no—
202C22×AGL(1,𝔽5)—26no—
203C22×AGL(1,𝔽5)—26no—
204C22×AGL(1,𝔽5)—212no—
205C22×AGL(1,𝔽5)—43no—
206C22×AGL(1,𝔽5)—46no—
207C22×AGL(1,𝔽5)—46no—
208C22×AGL(1,𝔽5)C2411yescharacteristic
209C22×AGL(1,𝔽5)C2413yes—
210C22×AGL(1,𝔽5)C2411yescharacteristic
211C22×AGL(1,𝔽5)C2413yes—
212C22×AGL(1,𝔽5)C2413yes—
213C22×AGL(1,𝔽5)C2411yescharacteristic
214C22×AGL(1,𝔽5)C2413yes—
215C22×AGL(1,𝔽5)C2411yescharacteristic
216C5×#41—24no—
217C2×C5×Q8—24no—
218C2×C5×Q8C22×C413yes—
219C2×C5×Q8C22×C411yescharacteristic
220C2×C5×D4C22×C413yes—
221C2×C5×D4C22×C413yes—
222C22×C4×C5C22×C413yes—
223C22×C4×C5C22×C413yes—
224C2×C22⋊D5C22×C416yes—
225C2×C22⋊D5C22×C413yes—
226C2×C22⋊D5C22×C413yes—
227C22×Dic5C22×C413yes—
228C22×Dic5C22×C413yes—
229#713—24no—
230Q8×D5—24no—
231Q8×D5—26no—
232Q8×D5—26no—
233Q8×D5—212no—
234Q8×D5C2×D414yes—
235Q8×D5#4114yes—
236#711—212no—
237D4×D5—26no—
238D4×D5—26no—
239D4×D5—26no—
240D4×D5—26no—
241#709—212no—
242C2×D20C22×C413yes—
243C2×D20C22×C413yes—
244C2×C4×D5—26no—
245C2×C4×D5—26no—
246C2×C4×D5—26no—
247C2×C4×D5—26no—
248C2×C4×D5C22×C413yes—
249C2×C4×D5C22×C413yes—
250C2×C4×D5C22×C413yes—
251C2×C4×D5C22×C413yes—
252C2×C4×D5C2413yes—
253C2×C4×D5C2413yes—
254C2×C4×D5C2411yescharacteristic
255C2×C4×D5C2411yescharacteristic
256C2×C4×D5C2413yes—
257C2×Dic10—212no—
258C2×Dic10C22×C413yes—
259C2×Dic10C22×C416yes—
260C2×Dic10C22×C413yes—
261C22⋊AGL(1,𝔽5)—26no—
262C22⋊AGL(1,𝔽5)—22no—
263C22⋊AGL(1,𝔽5)—26no—
264C22⋊AGL(1,𝔽5)—26no—
265C22⋊AGL(1,𝔽5)—26no—
266C22⋊AGL(1,𝔽5)—46no—
267C22⋊AGL(1,𝔽5)—43no—
268C4⋊AGL(1,𝔽5)—26no—
269C4⋊AGL(1,𝔽5)—212no—
270C4⋊AGL(1,𝔽5)—22no—
271C4⋊AGL(1,𝔽5)—22no—
272C4⋊AGL(1,𝔽5)—26no—
273C4⋊AGL(1,𝔽5)—26no—
274C4⋊AGL(1,𝔽5)—26no—
275C4⋊AGL(1,𝔽5)—43no—
276C4⋊AGL(1,𝔽5)—46no—
277C4⋊AGL(1,𝔽5)C2×D4112yes—
278C4×AGL(1,𝔽5)—26no—
279C4×AGL(1,𝔽5)—26no—
280C4×AGL(1,𝔽5)—26no—
281C4×AGL(1,𝔽5)—26no—
282C4×AGL(1,𝔽5)—26no—
283C4×AGL(1,𝔽5)—46no—
284C4×AGL(1,𝔽5)C2×D4112yes—
285C5×C4⋊C4C22×C413yes—
286C5×C4⋊C4C22×C413yes—
287C5×C22⋊C4C22×C411yescharacteristic
288C5×C22⋊C4C22×C413yes—
289C5×C22⋊C4C22×C416yes—
290C42×C5C22×C413yes—
291C22⋊Dic5C22×C416yes—
292C22⋊Dic5C22×C413yes—
293C22⋊Dic5C22×C411yescharacteristic
294#685C22×C411yescharacteristic
295#685C22×C413yes—
296#685C22×C416yes—
297#685C22×C416yes—
298#685C22×C413yes—
299#685C22×C411yescharacteristic
300C4⋊Dic5C22×C413yes—
301C4⋊Dic5C22×C413yes—
302#683C22×C416yes—
303#683C22×C413yes—
304#683C22×C413yes—
305C4×Dic5C22×C413yes—
306C4×Dic5C22×C413yes—
307C4×Dic5C22×C413yes—
308C22×#41—51no—
309C23×Q8—51no—
310#548—51no—
311#548—51no—
312#548—53no—
313#548—53no—
314#548—53no—
315#548—51no—
316#548—53no—
317#548AGL(1,𝔽5)11yescharacteristic, complemented
318C2×#124—53no—
319C2×C22⋊Q8—53no—
320C2×#121—53no—
321#520—108no—
322C2×C4×Q8—51no—
323C2×C4×Q8—51no—
324C2×C4×Q8—53no—
325C2×C4×Q8—51no—
326C2×C4×Q8—51no—
327C2×C4×Q8—51no—
328C2×C4×Q8—53no—
329C2×C4×Q8—108no—
330C2×C4×D4—53no—
331C2×C4×D4—53no—
332C2×C4×D4—53no—
333C2×C4×D4—56no—
334C2×#117—53no—
335C22×C4⋊C4—53no—
336C22×C4⋊C4—53no—
337C22×C42—53no—
338#391—53no—
339#391—53no—
340#390—53no—
341#390—53no—
342#389—56no—
343#389—53no—
344#389—53no—
345#388—56no—
346#388—56no—
347#388—53no—
348#388—53no—
349#387—53no—
350#387—53no—
351#386—53no—
352#386—53no—
353#385—56no—
354#385—56no—
355#385—53no—
356#385—51no—
357#384—53no—
358#380—53no—
359#380—53no—
360C4×C4⋊C4—53no—
361C4×C4⋊C4—53no—
362C4×C4⋊C4—53no—
363C4×C4⋊C4—53no—
364C4×C22⋊C4—53no—
365C4×C22⋊C4—53no—
366C4×C22⋊C4—56no—
367#376—53no—
368C23×C5C23×C413yes—
369C23×C5C23×C411yescharacteristic
370C22×D5—21no—
371C22×D5—21no—
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—23no—
375C22×D5—23no—
376C22×D5—23no—
377C22×D5—23no—
378C22×D5—23no—
379C22×D5—23no—
380C22×D5C23×C413yes—
381C22×D5C23×C411yescharacteristic
382C22×D5H(5,𝔽2)12yes—
383C22×D52−1+412yes—
384C22×D5C2511yescharacteristic
385C2×AGL(1,𝔽5)—28no—
386C2×AGL(1,𝔽5)—21no—
387C2×AGL(1,𝔽5)—23no—
388C2×AGL(1,𝔽5)—21no—
389C2×AGL(1,𝔽5)—21no—
390C2×AGL(1,𝔽5)—21no—
391C2×AGL(1,𝔽5)—23no—
392C2×AGL(1,𝔽5)—21no—
393C2×AGL(1,𝔽5)—23no—
394C2×AGL(1,𝔽5)—23no—
395C2×AGL(1,𝔽5)—21no—
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)—21no—
403C2×AGL(1,𝔽5)—23no—
404C2×AGL(1,𝔽5)—23no—
405C2×AGL(1,𝔽5)—23no—
406C2×AGL(1,𝔽5)—21no—
407C2×AGL(1,𝔽5)—412no—
408C2×AGL(1,𝔽5)—812no—
409C2×AGL(1,𝔽5)C22×D412yes—
410C2×AGL(1,𝔽5)C22×D416yes—
411C2×AGL(1,𝔽5)2−1+412yes—
412C5×Q8—26no—
413C5×Q8C4×D414yescomplemented
414C5×D4—26no—
415C5×D4—26no—
416C2×C4×C5—26no—
417C2×C4×C5—26no—
418C2×C4×C5C23×C411yescharacteristic
419C2×C4×C5C23×C413yes—
420C2×C4×C5C23×C411yescharacteristic
421C2×C4×C5C23×C413yes—
422C2×C4×C5C23×C413yes—
423C22⋊D5—26no—
424C22⋊D5—26no—
425C22⋊D5—212no—
426C2×Dic5—26no—
427C2×Dic5—26no—
428C2×Dic5C23×C411yescharacteristic
429C2×Dic5C23×C413yes—
430C2×Dic5C23×C411yescharacteristic
431C2×Dic5C23×C413yes—
432C2×Dic5C23×C413yes—
433D20—26no—
434D20—26no—
435C4×D5—23no—
436C4×D5—21no—
437C4×D5—21no—
438C4×D5—23no—
439C4×D5—23no—
440C4×D5—21no—
441C4×D5—23no—
442C4×D5—21no—
443C4×D5—26no—
444C4×D5—26no—
445C4×D5—26no—
446C4×D5—26no—
447C4×D5C22×D416yes—
448C4×D5C2×#4116yes—
449Dic10—26no—
450Dic10—212no—
451Dic10C4×D4112yescomplemented
452C2×#41—51no—
453C2×#41—53no—
454C2×#41—53no—
455C2×#41—104no—
456C2×#41—104no—
457C2×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
458C22×Q8—51no—
459C22×Q8—53no—
460C22×Q8—53no—
461C22×Q8—51no—
462C22×Q8—53no—
463C22×Q8—104no—
464C22×Q8—104no—
465C22×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
466C22×D4—53no—
467C22×D4—53no—
468C23×C4—53no—
469C23×C4—53no—
470C23×C4—51no—
471C23×C4—53no—
472C23×C4—56no—
473#124—53no—
474#124—53no—
475#124—56no—
476#124—56no—
477#124—53no—
478#124C2×AGL(1,𝔽5)13yescomplemented
479C22⋊Q8—53no—
480C22⋊Q8—53no—
481C22⋊Q8—56no—
482C22⋊Q8—53no—
483C22⋊Q8—56no—
484C22⋊Q8C2×AGL(1,𝔽5)13yescomplemented
485#121—53no—
486#121—56no—
487#121—53no—
488#121—53no—
489#121—56no—
490#121C2×AGL(1,𝔽5)13yescomplemented
491C4×Q8—58no—
492C4×Q8—51no—
493C4×Q8—53no—
494C4×Q8—53no—
495C4×Q8—1012no—
496C4×Q8—1012no—
497C4×Q8—104no—
498C4×Q8—104no—
499C4×Q8—104no—
500C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
501C4×D4—53no—
502C4×D4—53no—
503C4×D4—53no—
504C4×D4—53no—
505C4×D4—53no—
506C4×D4—53no—
507C4×D4—53no—
508C4×D4—1012no—
509C4×D4—1012no—
510C4×D4—2012no—
511C4×D4C2×AGL(1,𝔽5)13yescomplemented
512#117—1012no—
513C2×C4⋊C4—53no—
514C2×C4⋊C4—53no—
515C2×C4⋊C4—53no—
516C2×C4⋊C4—53no—
517C2×C4⋊C4—53no—
518C2×C4⋊C4—53no—
519C2×C4⋊C4—56no—
520C2×C4⋊C4—51no—
521C2×C4⋊C4—53no—
522C2×C4⋊C4—51no—
523C2×C4⋊C4—56no—
524C2×C4⋊C4—53no—
525C2×C4⋊C4—1012no—
526C2×C4⋊C4—1012no—
527C2×C22⋊C4—51no—
528C2×C22⋊C4—53no—
529C2×C22⋊C4—56no—
530C2×C22⋊C4—53no—
531C2×C22⋊C4—53no—
532C2×C22⋊C4—53no—
533C2×C22⋊C4—51no—
534C2×C22⋊C4—53no—
535C2×C22⋊C4—56no—
536C2×C22⋊C4—53no—
537C2×C42—53no—
538C2×C42—53no—
539C2×C42—53no—
540C2×C42—53no—
541C2×C42—53no—
542C2×C42—53no—
543C2×C42—53no—
544C2×C42—56no—
545C2×C42—1012no—
546#95—51no—
547#95—53no—
548#95—53no—
549#95—53no—
550#95—51no—
551#95—53no—
552#95—53no—
553#95—56no—
554#95—53no—
555#95—53no—
556#95—53no—
557C22×C5—21no—
558C22×C5—21no—
559C22×C5—23no—
560C22×C5—23no—
561C22×C5—23no—
562C22×C5#52012yescomplemented
563C22×C5C24×C411yescharacteristic
564C2×D5—21no—
565C2×D5—21no—
566C2×D5—22no—
567C2×D5—22no—
568C2×D5—22no—
569C2×D5—22no—
570C2×D5—23no—
571C2×D5—23no—
572C2×D5—23no—
573C2×D5—43no—
574C2×D5—43no—
575C2×D5—43no—
576C2×D5—43no—
577C2×D5#52012yescomplemented
578C2×D5C23×D411yescharacteristic
579C2×D5C22×#4111yescharacteristic
580C2×D5C2×H(5,𝔽2)11yescharacteristic
581C2×D5C2×2−1+411yescharacteristic
582C2×D5C2×2−1+411yescharacteristic
583C2×D5#58511yescharacteristic
584AGL(1,𝔽5)—22no—
585AGL(1,𝔽5)—22no—
586AGL(1,𝔽5)—26no—
587AGL(1,𝔽5)—41no—
588AGL(1,𝔽5)—43no—
589AGL(1,𝔽5)—43no—
590AGL(1,𝔽5)—41no—
591AGL(1,𝔽5)—43no—
592C4×C5—23no—
593C4×C5—21no—
594C4×C5—23no—
595C4×C5—21no—
596C4×C5C2×C4×D416yes—
597Dic5—23no—
598Dic5—21no—
599Dic5—23no—
600Dic5—21no—
601Dic5C2×C4×D416yes—
602C24—51no—
603C24—53no—
604#41—24no—
605#41—1012no—
606#41—1012no—
607#41—104no—
608C2×Q8—24no—
609C2×Q8—54no—
610C2×Q8—54no—
611C2×Q8—53no—
612C2×Q8—56no—
613C2×Q8—53no—
614C2×Q8—1012no—
615C2×Q8—106no—
616C2×Q8—106no—
617C2×Q8—1012no—
618C2×Q8—104no—
619C2×Q8C22×AGL(1,𝔽5)13yes—
620C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
621C2×D4—53no—
622C2×D4—53no—
623C2×D4—56no—
624C2×D4—53no—
625C2×D4—53no—
626C2×D4—106no—
627C2×D4—106no—
628C2×D4—106no—
629C2×D4—106no—
630C2×D4C22×AGL(1,𝔽5)13yes—
631C2×D4C22×AGL(1,𝔽5)13yes—
632C22×C4—53no—
633C22×C4—51no—
634C22×C4—51no—
635C22×C4—53no—
636C22×C4—53no—
637C22×C4—53no—
638C22×C4—51no—
639C22×C4—53no—
640C22×C4—53no—
641C22×C4—51no—
642C22×C4—53no—
643C22×C4—53no—
644C22×C4—53no—
645C22×C4—53no—
646C22×C4—51no—
647C22×C4—51no—
648C22×C4—53no—
649C22×C4—53no—
650C22×C4—53no—
651C22×C4—106no—
652C22×C4—106no—
653C22×C4—106no—
654C22×C4—106no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—106no—
658C22×C4—1012no—
659C22×C4—102no—
660C22×C4—106no—
661C22×C4—203no—
662C22×C4—206no—
663C22×C4—206no—
664C22×C4C22×AGL(1,𝔽5)13yes—
665C22×C4C22×AGL(1,𝔽5)13yes—
666C4⋊C4—512no—
667C4⋊C4—53no—
668C4⋊C4—53no—
669C4⋊C4—53no—
670C4⋊C4—56no—
671C4⋊C4—53no—
672C4⋊C4—106no—
673C4⋊C4—106no—
674C4⋊C4—106no—
675C4⋊C4—1012no—
676C4⋊C4—102no—
677C4⋊C4—106no—
678C4⋊C4—102no—
679C4⋊C4—206no—
680C4⋊C4—203no—
681C4⋊C4C22×AGL(1,𝔽5)13yes—
682C4⋊C4C22×AGL(1,𝔽5)13yes—
683C22⋊C4—51no—
684C22⋊C4—53no—
685C22⋊C4—56no—
686C22⋊C4—51no—
687C22⋊C4—51no—
688C22⋊C4—53no—
689C22⋊C4—53no—
690C22⋊C4—56no—
691C22⋊C4—56no—
692C22⋊C4—106no—
693C22⋊C4—106no—
694C22⋊C4—106no—
695C22⋊C4—106no—
696C22⋊C4—102no—
697C22⋊C4—206no—
698C22⋊C4—203no—
699C22⋊C4C22×AGL(1,𝔽5)11yescharacteristic
700C22⋊C4C22×AGL(1,𝔽5)13yes—
701C22⋊C4C22×AGL(1,𝔽5)16yes—
702C42—512no—
703C42—53no—
704C42—53no—
705C42—53no—
706C42—106no—
707C42—106no—
708C42—106no—
709C42—106no—
710C42—106no—
711C42—206no—
712C42C22×AGL(1,𝔽5)13yes—
713C2×C5—22no—
714C2×C5—43no—
715C2×C5C22×C4×D411yescharacteristic
716C2×C5C2×#52011yescharacteristic
717C2×C5C4×2−1+411yescharacteristic
718D5—22no—
719D5—43no—
720D5#348611yescharacteristic
721D5#348811yescharacteristic
722D5#351611yescharacteristic
723D5#352211yescharacteristic
724C23—51no—
725C23—52no—
726C23—52no—
727C23—51no—
728C23—53no—
729C23—101no—
730C23—101no—
731C23—101no—
732C23—101no—
733C23—103no—
734C23—103no—
735C23—103no—
736C23—103no—
737C23—103no—
738C23—103no—
739C23C23×AGL(1,𝔽5)13yes—
740C23C23×AGL(1,𝔽5)11yescharacteristic
741Q8—26no—
742Q8—512no—
743Q8—1012no—
744Q8—106no—
745Q8D4×AGL(1,𝔽5)14yescomplemented
746D4—26no—
747D4—26no—
748D4—106no—
749D4—1012no—
750D4—106no—
751D4—106no—
752D4—106no—
753C2×C4—26no—
754C2×C4—26no—
755C2×C4—53no—
756C2×C4—56no—
757C2×C4—56no—
758C2×C4—52no—
759C2×C4—56no—
760C2×C4—52no—
761C2×C4—51no—
762C2×C4—53no—
763C2×C4—53no—
764C2×C4—51no—
765C2×C4—106no—
766C2×C4—106no—
767C2×C4—103no—
768C2×C4—103no—
769C2×C4—101no—
770C2×C4—101no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—103no—
774C2×C4—103no—
775C2×C4—106no—
776C2×C4—106no—
777C2×C4—101no—
778C2×C4—103no—
779C2×C4—101no—
780C2×C4—101no—
781C2×C4—101no—
782C2×C4—103no—
783C2×C4—108no—
784C2×C4—106no—
785C2×C4—106no—
786C2×C4—101no—
787C2×C4—101no—
788C2×C4—103no—
789C2×C4—103no—
790C2×C4—103no—
791C2×C4—103no—
792C2×C4—103no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—103no—
796C2×C4—101no—
797C2×C4—103no—
798C2×C4—103no—
799C2×C4—101no—
800C2×C4—103no—
801C2×C4—2012no—
802C2×C4—4012no—
803C2×C4C23×AGL(1,𝔽5)11yescharacteristic
804C2×C4C23×AGL(1,𝔽5)13yes—
805C2×C4C23×AGL(1,𝔽5)13yes—
806C2×C4C23×AGL(1,𝔽5)11yescharacteristic
807C2×C4C23×AGL(1,𝔽5)13yes—
808C5#3429411yescharacteristic, complemented, Sylow
809C22—21no—
810C22—21no—
811C22—23no—
812C22—23no—
813C22—23no—
814C22—51no—
815C22—51no—
816C22—51no—
817C22—51no—
818C22—51no—
819C22—51no—
820C22—52no—
821C22—102no—
822C22—102no—
823C22—102no—
824C22—102no—
825C22—101no—
826C22—101no—
827C22—103no—
828C22—103no—
829C22—103no—
830C22—203no—
831C22—203no—
832C22—203no—
833C22—203no—
834C22#6626612yescomplemented
835C22C24×AGL(1,𝔽5)11yescharacteristic
836C4—21no—
837C4—23no—
838C4—23no—
839C4—21no—
840C4—56no—
841C4—102no—
842C4—102no—
843C4—106no—
844C4—101no—
845C4—103no—
846C4—103no—
847C4—101no—
848C4—203no—
849C4—203no—
850C4—201no—
851C4—203no—
852C4—201no—
853C4C2×D4×AGL(1,𝔽5)16yes—
854C2—22no—
855C2—43no—
856C2—51no—
857C2—51no—
858C2—51no—
859C2—51no—
860C2—102no—
861C2—203no—
862C2C22×D4×AGL(1,𝔽5)11yescharacteristic
863C2C2×#6626611yescharacteristic
864C2AGL(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#34294
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#66266C2semidirect
2. C22×Q8×AGL(1,𝔽5)C2semidirect
4. #10617558C2semidirect
5. Q8×C22⋊AGL(1,𝔽5)C2semidirect
6. #10617326C2semidirect
7. #10617324C2semidirect
8. #10617285C2semidirect
9. #10617282C2semidirect
10. #10617253C2semidirect
11. AGL(1,𝔽5)×#121C2semidirect
12. Q8×C4⋊AGL(1,𝔽5)C2semidirect
13. #10617208C2semidirect
14. D4×C4⋊AGL(1,𝔽5)C2semidirect
15. #10617173C2semidirect
33. C5×#548C4semidirect
34. #66165C4semidirect
35. #66151C4semidirect
36. #66011C4semidirect
38. #65967C4semidirect
41. #65932C4semidirect
42. #65910C4semidirect
44. #65886C4semidirect
80. C2×C5×#41C2×C4semidirect
81. C22×C5×Q8C2×C4semidirect
84. C2×#713C2×C4semidirect
87. C2×Q8×D5C2×C4semidirect
88. C2×Q8×D5C2×C4semidirect
91. C2×#711C2×C4semidirect
94. C2×#709C2×C4semidirect
97. C22×Dic10C2×C4semidirect
110. Q8×AGL(1,𝔽5)D4semidirect
135. C5×#124C2×C4semidirect
136. C5×C22⋊Q8C2×C4semidirect
137. C5×#121C2×C4semidirect
138. C4×C5×Q8C2×C4semidirect
139. C4×C5×D4C2×C4semidirect
140. #4093C2×C4semidirect
141. #4092C2×C4semidirect
142. Q8×Dic5C2×C4semidirect
143. #4085C2×C4semidirect
144. #4084C2×C4semidirect
145. #4082C2×C4semidirect
146. D4×Dic5C2×C4semidirect
147. #4076C2×C4semidirect
148. C4×C22⋊D5C2×C4semidirect
149. C4×C22⋊D5C2×C4semidirect
150. #4070C2×C4semidirect
151. #4043C2×C4semidirect
152. #4042C2×C4semidirect
153. #4041C2×C4semidirect
154. #4039C2×C4semidirect
157. #4033C2×C4semidirect
158. #4031C2×C4semidirect
159. #4031C2×C4semidirect
160. #4030C2×C4semidirect
161. #4027C2×C4semidirect
162. #4027C2×C4semidirect
166. #4024C2×C4semidirect
167. #4021C2×C4semidirect
168. C4×D20C2×C4semidirect
170. C4×Dic10C2×C4semidirect
317. #548AGL(1,𝔽5)semidirect
413. C5×Q8C4×D4semidirect
451. Dic10C4×D4semidirect
457. C2×#41C2×AGL(1,𝔽5)semidirect
465. C22×Q8C2×AGL(1,𝔽5)semidirect
478. #124C2×AGL(1,𝔽5)semidirect
484. C22⋊Q8C2×AGL(1,𝔽5)semidirect
490. #121C2×AGL(1,𝔽5)semidirect
500. C4×Q8C2×AGL(1,𝔽5)semidirect
511. C4×D4C2×AGL(1,𝔽5)semidirect
562. C22×C5#520semidirect
577. C2×D5#520semidirect
745. Q8D4×AGL(1,𝔽5)semidirect
808. C5#34294semidirect
834. C22#66266semidirect

Maximal subgroups

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

subgroupindex
C2×#662662
C22×Q8×AGL(1,𝔽5)2
D5×#5482
#106175582
Q8×C22⋊AGL(1,𝔽5)2
#106173262
#106173242
#106172852
#106172822
#106172532
AGL(1,𝔽5)×#1212
Q8×C4⋊AGL(1,𝔽5)2
#106172082
D4×C4⋊AGL(1,𝔽5)2
#106171732
#342945