Finite Group Databasebeta

← #13044134

Subgroups — #13044134

Order 1280.

2912 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66262C211yesmaximal, characteristic, complemented
2C22×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3D4×Q8×D5C211yesmaximal, characteristic
4Q8×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5Q8×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6#10617388C213yesmaximal, complemented
7#10617386C213yesmaximal, complemented
8#10617286C213yesmaximal, complemented
9#10617285C213yesmaximal, complemented
10#10617282C213yesmaximal, complemented
11AGL(1,𝔽5)×C22⋊Q8C213yesmaximal, complemented
12#10617212C211yesmaximal, characteristic, complemented
13#10617208C211yesmaximal, characteristic, complemented
14#10617179C213yesmaximal
15#10617173C213yesmaximal
16C22×Q8×D5C2211yescharacteristic
17C22×Q8×D5C2211yescharacteristic
18#66262—28no—
19C2×Q8×AGL(1,𝔽5)—28no—
20C2×Q8×AGL(1,𝔽5)C2213yes—
21C2×Q8×AGL(1,𝔽5)C2213yes—
22C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
23C2×Q8×AGL(1,𝔽5)C2213yes—
24C2×Q8×AGL(1,𝔽5)C2213yes—
25C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
26C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
27C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
28C2×#4130C2213yes—
29C2×#4130C2213yes—
30C22×C4⋊AGL(1,𝔽5)C2213yes—
31C22×C4×AGL(1,𝔽5)C2213yes—
32C5×D4×Q8C411yescharacteristic, complemented
33Q8×C22⋊D5C411yescharacteristic, complemented
34Q8×C22⋊D5C411yescharacteristic, complemented
35#66061C413yescomplemented
36D5×C4⋊Q8C2213yes—
37#65966C413yescomplemented
38#65966C413yescomplemented
39D5×C22⋊Q8C2213yes—
40D5×C22⋊Q8C2213yes—
41Q8×D20C411yescharacteristic, complemented
42C4×Q8×D5C2211yescharacteristic
43C4×D4×D5C2213yes—
44D4×Dic10C413yescomplemented
45(C2×AGL(1,𝔽5))⋊Q8C2213yes—
46(C2×AGL(1,𝔽5))⋊Q8C2213yes—
47(C2×AGL(1,𝔽5))⋊Q8C2213yes—
48(C2×AGL(1,𝔽5))⋊Q8C2213yes—
49#65779C2211yescharacteristic
50#65779C2213yes—
51#65765C2213yes—
52#65765C2213yes—
53C4×C22⋊AGL(1,𝔽5)C2213yes—
54C4×C22⋊AGL(1,𝔽5)C2213yes—
55#65712C2216yes—
56#65712C2213yes—
57#65712C2213yes—
58#65711C2213yes—
59#65711C2216yes—
60#65711C2216yes—
61#65711C2216yes—
62#65711C2213yes—
63C4⋊C4×AGL(1,𝔽5)C2216yes—
64C4⋊C4×AGL(1,𝔽5)C2213yes—
65C4⋊C4×AGL(1,𝔽5)C2213yes—
66#65700C2213yes—
67#65700C2213yes—
68#65700C2216yes—
69#65699C2213yes—
70#65699C2213yes—
71C22⋊C4×AGL(1,𝔽5)C2216yes—
72#65689C2213yes—
73C4×C4⋊AGL(1,𝔽5)C2213yes—
74C4×C4⋊AGL(1,𝔽5)C2213yes—
75#65686C2213yes—
76#34291—51nomaximal, Sylow
77C23×AGL(1,𝔽5)C2311yescharacteristic
78C23×AGL(1,𝔽5)C2313yes—
79C22×C5×Q8C2×C411yescharacteristic
80C22×C5×Q8C2×C411yescharacteristic, complemented
81C2×Q8×D5—24no—
82C2×Q8×D5—24no—
83C2×Q8×D5—24no—
84C2×Q8×D5—24no—
85C2×Q8×D5C2×C413yes—
86C2×Q8×D5C2×C411yescharacteristic
87C2×Q8×D5C2×C413yescomplemented
88C2×Q8×D5C2×C411yescharacteristic, complemented
89C2×Q8×D5C2313yes—
90C2×Q8×D5C2313yes—
91C2×Q8×D5C2311yescharacteristic
92C2×D4×D5C2311yescharacteristic
93C22×C4×D5C2313yes—
94C22×C4×D5C2313yes—
95C22×Dic10C2×C413yes—
96C22×Dic10C2×C413yescomplemented
97C2×C22⋊AGL(1,𝔽5)C2313yes—
98C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
99C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
100C2×C22⋊AGL(1,𝔽5)C2313yes—
101C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
102C2×C22⋊AGL(1,𝔽5)C2313yes—
103Q8×AGL(1,𝔽5)—24no—
104Q8×AGL(1,𝔽5)—24no—
105Q8×AGL(1,𝔽5)—24no—
106Q8×AGL(1,𝔽5)—212no—
107Q8×AGL(1,𝔽5)—212no—
108Q8×AGL(1,𝔽5)—212no—
109Q8×AGL(1,𝔽5)—212no—
110Q8×AGL(1,𝔽5)D418yescomplemented
111#4130—212no—
112#4130—212no—
113C2×C4⋊AGL(1,𝔽5)—212no—
114C2×C4⋊AGL(1,𝔽5)C2313yes—
115C2×C4⋊AGL(1,𝔽5)C2313yes—
116C2×C4⋊AGL(1,𝔽5)C2313yes—
117C2×C4⋊AGL(1,𝔽5)C2313yes—
118C2×C4⋊AGL(1,𝔽5)C2313yes—
119C2×C4⋊AGL(1,𝔽5)C2313yes—
120C2×C4⋊AGL(1,𝔽5)C2316yes—
121C2×C4⋊AGL(1,𝔽5)C2313yes—
122C2×C4⋊AGL(1,𝔽5)C2313yes—
123C2×C4×AGL(1,𝔽5)—212no—
124C2×C4×AGL(1,𝔽5)C2313yes—
125C2×C4×AGL(1,𝔽5)C2313yes—
126C2×C4×AGL(1,𝔽5)C2313yes—
127C2×C4×AGL(1,𝔽5)C2316yes—
128C2×C4×AGL(1,𝔽5)C2313yes—
129C2×C4×AGL(1,𝔽5)C2313yes—
130C2×C4×AGL(1,𝔽5)C2316yes—
131C2×C4×AGL(1,𝔽5)C2313yes—
132C5×C4⋊Q8C2×C413yescomplemented
133C5×C22⋊Q8C2×C413yes—
134C5×C22⋊Q8C2×C413yescomplemented
135C4×C5×Q8C2×C411yescharacteristic, complemented
136C4×C5×D4C2×C413yes—
137#4092C2×C413yes—
138#4092C2×C413yescomplemented
139Q8×Dic5C2×C411yescharacteristic, complemented
140#4090C2×C413yescomplemented
141#4090C2×C413yescomplemented
142D4×Dic5C2×C413yes—
143C4×C22⋊D5C2×C413yes—
144C4×C22⋊D5C2×C413yes—
145#4070C2×C413yes—
146#4070C2×C413yescomplemented
147#4043C2×C413yes—
148#4043C2×C413yescomplemented
149#4042C2×C416yes—
150#4042C2×C416yescomplemented
151#4039C2×C413yes—
152D5×C4⋊C4C2313yes—
153D5×C4⋊C4C2316yes—
154D5×C4⋊C4C2313yes—
155#4034C2×C416yescomplemented
156#4034C2×C416yescomplemented
157#4033C2×C413yescomplemented
158#4027C2×C413yes—
159#4027C2×C413yes—
160D5×C22⋊C4C2313yes—
161D5×C22⋊C4C2313yes—
162#4024C2×C416yes—
163#4024C2×C416yescomplemented
164C4×D20C2×C413yes—
165C42×D5C2313yes—
166#4015C2×C413yescomplemented
167C4×Dic10C2×C413yescomplemented
168(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
169(C2×AGL(1,𝔽5))⋊C4C2313yes—
170(C2×AGL(1,𝔽5))⋊C4C2313yes—
171(C2×AGL(1,𝔽5))⋊C4C2313yes—
172(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
173(C2×AGL(1,𝔽5))⋊C4C2313yes—
174(C2×AGL(1,𝔽5))⋊C4C2316yes—
175(C2×AGL(1,𝔽5))⋊C4C2316yes—
176(C2×AGL(1,𝔽5))⋊C4C2313yes—
177(C2×AGL(1,𝔽5))⋊C4C2313yes—
178(C2×AGL(1,𝔽5))⋊C4C2316yes—
179(C2×AGL(1,𝔽5))⋊C4C2313yes—
180(C2×AGL(1,𝔽5))⋊C4C2313yes—
181C2×D4×Q8—51no—
182C2×#519—51no—
183C22×C4×Q8—51no—
184#2365—53no—
185#2362—53no—
186#2360—53no—
187#2352—53no—
188#2351—51no—
189Q8×C22⋊C4—51no—
190Q8×C22⋊C4—51no—
191#2327—53no—
192#2323—53no—
193C4×C22⋊Q8—53no—
194#2290—53no—
195#2276—51no—
196C23×D5C2411yescharacteristic
197C23×D5C2411yescharacteristic
198C22×AGL(1,𝔽5)—22no—
199C22×AGL(1,𝔽5)—22no—
200C22×AGL(1,𝔽5)—22no—
201C22×AGL(1,𝔽5)—26no—
202C22×AGL(1,𝔽5)—26no—
203C22×AGL(1,𝔽5)—43no—
204C22×AGL(1,𝔽5)C2411yescharacteristic
205C22×AGL(1,𝔽5)C2413yes—
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
212C2×C5×Q8—24no—
213C2×C5×Q8—24no—
214C2×C5×Q8C22×C413yes—
215C2×C5×Q8C22×C413yes—
216C2×C5×Q8C22×C411yescharacteristic
217C2×C5×D4C22×C411yescharacteristic
218C22×C4×C5C22×C413yes—
219C22×C4×C5C22×C413yes—
220C2×C22⋊D5C22×C411yescharacteristic
221C2×C22⋊D5C22×C411yescharacteristic
222C22×Dic5C22×C413yes—
223C22×Dic5C22×C413yes—
224Q8×D5—24no—
225Q8×D5—24no—
226Q8×D5—26no—
227Q8×D5—26no—
228Q8×D5—26no—
229Q8×D5—26no—
230Q8×D5—212no—
231Q8×D5—212no—
232Q8×D5C2×D414yes—
233Q8×D5#4114yes—
234D4×D5—22no—
235D4×D5—22no—
236C2×D20C22×C411yescharacteristic
237C2×C4×D5—26no—
238C2×C4×D5—26no—
239C2×C4×D5—26no—
240C2×C4×D5—26no—
241C2×C4×D5C22×C413yes—
242C2×C4×D5C22×C413yes—
243C2×C4×D5C22×C413yes—
244C2×C4×D5C22×C413yes—
245C2×C4×D5C2413yes—
246C2×C4×D5C2413yes—
247C2×C4×D5C2413yes—
248C2×C4×D5C2411yescharacteristic
249C2×C4×D5C2413yes—
250C2×Dic10—212no—
251C2×Dic10—212no—
252C2×Dic10C22×C413yes—
253C2×Dic10C22×C416yes—
254C2×Dic10C22×C413yes—
255C2×Dic10C22×C416yes—
256C2×Dic10C22×C413yes—
257C22⋊AGL(1,𝔽5)—26no—
258C22⋊AGL(1,𝔽5)—22no—
259C22⋊AGL(1,𝔽5)—22no—
260C22⋊AGL(1,𝔽5)—26no—
261C22⋊AGL(1,𝔽5)—22no—
262C22⋊AGL(1,𝔽5)—43no—
263C4⋊AGL(1,𝔽5)—212no—
264C4⋊AGL(1,𝔽5)—26no—
265C4⋊AGL(1,𝔽5)—26no—
266C4⋊AGL(1,𝔽5)—26no—
267C4⋊AGL(1,𝔽5)—26no—
268C4⋊AGL(1,𝔽5)—26no—
269C4⋊AGL(1,𝔽5)—26no—
270C4⋊AGL(1,𝔽5)—43no—
271C4⋊AGL(1,𝔽5)C2×D4112yes—
272C4×AGL(1,𝔽5)—26no—
273C4×AGL(1,𝔽5)—26no—
274C4×AGL(1,𝔽5)—212no—
275C4×AGL(1,𝔽5)—26no—
276C4×AGL(1,𝔽5)—26no—
277C4×AGL(1,𝔽5)—26no—
278C4×AGL(1,𝔽5)—46no—
279C4×AGL(1,𝔽5)C2×D4112yes—
280C5×C4⋊C4C22×C413yes—
281C5×C4⋊C4C22×C413yes—
282C5×C4⋊C4C22×C416yes—
283C5×C22⋊C4C22×C413yes—
284C5×C22⋊C4C22×C413yes—
285C42×C5C22×C413yes—
286C22⋊Dic5C22×C413yes—
287C22⋊Dic5C22×C413yes—
288#685C22×C413yes—
289#685C22×C413yes—
290#685C22×C413yes—
291#685C22×C413yes—
292C4⋊Dic5C22×C413yes—
293C4⋊Dic5C22×C413yes—
294C4⋊Dic5C22×C416yes—
295#683C22×C416yes—
296#683C22×C416yes—
297#683C22×C416yes—
298#683C22×C413yes—
299#683C22×C413yes—
300C4×Dic5C22×C413yes—
301C4×Dic5C22×C413yes—
302C4×Dic5C22×C413yes—
303C23×Q8—51no—
304C23×Q8—51no—
305D4×Q8—51no—
306D4×Q8—51no—
307D4×Q8—53no—
308D4×Q8—53no—
309D4×Q8—53no—
310D4×Q8—51no—
311D4×Q8—53no—
312D4×Q8AGL(1,𝔽5)11yescharacteristic, complemented
313C2×C4⋊Q8—53no—
314C2×C22⋊Q8—53no—
315C2×C22⋊Q8—53no—
316#519—108no—
317C2×C4×Q8—51no—
318C2×C4×Q8—51no—
319C2×C4×Q8—53no—
320C2×C4×Q8—53no—
321C2×C4×Q8—51no—
322C2×C4×Q8—51no—
323C2×C4×Q8—51no—
324C2×C4×Q8—53no—
325C2×C4×Q8—53no—
326C2×C4×Q8—108no—
327C2×C4×D4—53no—
328C2×#117—53no—
329C2×#117—53no—
330C22×C4⋊C4—53no—
331C22×C42—53no—
332#391—53no—
333#391—53no—
334#391—53no—
335#391—53no—
336#389—53no—
337#389—56no—
338#389—53no—
339#388—53no—
340#388—56no—
341#388—53no—
342#387—56no—
343#387—53no—
344#387—56no—
345#387—56no—
346#387—53no—
347#386—53no—
348#386—51no—
349#385—53no—
350#385—53no—
351#382—53no—
352#380—53no—
353#380—53no—
354C4×C4⋊C4—53no—
355C4×C4⋊C4—53no—
356C4×C4⋊C4—53no—
357C4×C4⋊C4—53no—
358C4×C4⋊C4—56no—
359C4×C22⋊C4—53no—
360C4×C22⋊C4—53no—
361C4×C22⋊C4—56no—
362#376—53no—
363C23×C5C23×C411yescharacteristic
364C23×C5C23×C411yescharacteristic
365C22×D5—21no—
366C22×D5—21no—
367C22×D5—21no—
368C22×D5—21no—
369C22×D5—21no—
370C22×D5—21no—
371C22×D5—21no—
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—21no—
375C22×D5C23×C411yescharacteristic
376C22×D5C23×C411yescharacteristic
377C22×D52−1+412yes—
378C22×D52−1+412yes—
379C22×D5C2511yescharacteristic
380C2×AGL(1,𝔽5)—28no—
381C2×AGL(1,𝔽5)—21no—
382C2×AGL(1,𝔽5)—21no—
383C2×AGL(1,𝔽5)—21no—
384C2×AGL(1,𝔽5)—21no—
385C2×AGL(1,𝔽5)—23no—
386C2×AGL(1,𝔽5)—23no—
387C2×AGL(1,𝔽5)—23no—
388C2×AGL(1,𝔽5)—21no—
389C2×AGL(1,𝔽5)—23no—
390C2×AGL(1,𝔽5)—21no—
391C2×AGL(1,𝔽5)—23no—
392C2×AGL(1,𝔽5)—23no—
393C2×AGL(1,𝔽5)—23no—
394C2×AGL(1,𝔽5)—21no—
395C2×AGL(1,𝔽5)—23no—
396C2×AGL(1,𝔽5)—21no—
397C2×AGL(1,𝔽5)—21no—
398C2×AGL(1,𝔽5)—23no—
399C2×AGL(1,𝔽5)—23no—
400C2×AGL(1,𝔽5)—21no—
401C2×AGL(1,𝔽5)—23no—
402C2×AGL(1,𝔽5)—412no—
403C2×AGL(1,𝔽5)C22×D412yes—
404C2×AGL(1,𝔽5)C22×D416yes—
405C2×AGL(1,𝔽5)2−1+412yes—
406C5×Q8—26no—
407C5×Q8—26no—
408C5×Q8C4×D414yes—
409C5×D4—22no—
410C2×C4×C5—26no—
411C2×C4×C5—26no—
412C2×C4×C5C23×C411yescharacteristic
413C2×C4×C5C23×C413yes—
414C2×C4×C5C23×C413yes—
415C2×C4×C5C23×C413yes—
416C2×C4×C5C23×C413yes—
417C22⋊D5—22no—
418C22⋊D5—22no—
419C2×Dic5—26no—
420C2×Dic5—26no—
421C2×Dic5C23×C411yescharacteristic
422C2×Dic5C23×C413yes—
423C2×Dic5C23×C413yes—
424C2×Dic5C23×C413yes—
425C2×Dic5C23×C413yes—
426D20—22no—
427C4×D5—23no—
428C4×D5—23no—
429C4×D5—23no—
430C4×D5—23no—
431C4×D5—23no—
432C4×D5—21no—
433C4×D5—21no—
434C4×D5—23no—
435C4×D5—26no—
436C4×D5—26no—
437C4×D5—26no—
438C4×D5—26no—
439C4×D5C22×D416yes—
440C4×D5C2×#4116yes—
441Dic10—26no—
442Dic10—26no—
443Dic10—212no—
444Dic10—212no—
445Dic10C4×D4112yes—
446C22×Q8—51no—
447C22×Q8—53no—
448C22×Q8—53no—
449C22×Q8—53no—
450C22×Q8—51no—
451C22×Q8—53no—
452C22×Q8—51no—
453C22×Q8—53no—
454C22×Q8—53no—
455C22×Q8—104no—
456C22×Q8—104no—
457C22×Q8—104no—
458C22×Q8—104no—
459C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
460C22×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
461C22×D4—51no—
462C23×C4—53no—
463C23×C4—53no—
464C23×C4—51no—
465C23×C4—53no—
466C4⋊Q8—53no—
467C4⋊Q8—53no—
468C4⋊Q8—56no—
469C4⋊Q8—56no—
470C4⋊Q8—53no—
471C4⋊Q8C2×AGL(1,𝔽5)13yescomplemented
472C22⋊Q8—53no—
473C22⋊Q8—53no—
474C22⋊Q8—53no—
475C22⋊Q8—53no—
476C22⋊Q8—56no—
477C22⋊Q8—56no—
478C22⋊Q8—53no—
479C22⋊Q8—53no—
480C22⋊Q8—56no—
481C22⋊Q8—56no—
482C22⋊Q8C2×AGL(1,𝔽5)13yes—
483C22⋊Q8C2×AGL(1,𝔽5)13yescomplemented
484C4×Q8—58no—
485C4×Q8—51no—
486C4×Q8—53no—
487C4×Q8—53no—
488C4×Q8—1012no—
489C4×Q8—1012no—
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×D4C2×AGL(1,𝔽5)13yes—
504#117—1012no—
505#117—1012no—
506C2×C4⋊C4—53no—
507C2×C4⋊C4—53no—
508C2×C4⋊C4—53no—
509C2×C4⋊C4—56no—
510C2×C4⋊C4—53no—
511C2×C4⋊C4—56no—
512C2×C4⋊C4—53no—
513C2×C4⋊C4—53no—
514C2×C4⋊C4—53no—
515C2×C4⋊C4—53no—
516C2×C4⋊C4—53no—
517C2×C4⋊C4—53no—
518C2×C4⋊C4—1012no—
519C2×C22⋊C4—53no—
520C2×C22⋊C4—53no—
521C2×C22⋊C4—51no—
522C2×C22⋊C4—53no—
523C2×C22⋊C4—53no—
524C2×C22⋊C4—51no—
525C2×C22⋊C4—51no—
526C2×C22⋊C4—53no—
527C2×C42—53no—
528C2×C42—53no—
529C2×C42—56no—
530C2×C42—53no—
531C2×C42—53no—
532C2×C42—53no—
533C2×C42—53no—
534C2×C42—53no—
535C2×C42—56no—
536C2×C42—1012no—
537#95—51no—
538#95—53no—
539#95—53no—
540#95—53no—
541#95—53no—
542#95—56no—
543#95—56no—
544#95—53no—
545#95—53no—
546#95—53no—
547#95—51no—
548#95—56no—
549#95—53no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—21no—
553C22×C5—21no—
554C22×C5—21no—
555C22×C5#51912yescomplemented
556C22×C5C24×C411yescharacteristic
557C2×D5—21no—
558C2×D5—21no—
559C2×D5—22no—
560C2×D5—22no—
561C2×D5—22no—
562C2×D5—22no—
563C2×D5—21no—
564C2×D5—21no—
565C2×D5—21no—
566C2×D5—41no—
567C2×D5—41no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5#51912yescomplemented
571C2×D5C23×D411yescharacteristic
572C2×D5C22×#4111yescharacteristic
573C2×D5C2×2−1+411yescharacteristic
574C2×D5C2×2−1+411yescharacteristic
575C2×D5C2×2−1+411yescharacteristic
576C2×D5#58511yescharacteristic
577AGL(1,𝔽5)—22no—
578AGL(1,𝔽5)—22no—
579AGL(1,𝔽5)—26no—
580AGL(1,𝔽5)—43no—
581AGL(1,𝔽5)—41no—
582AGL(1,𝔽5)—43no—
583AGL(1,𝔽5)—43no—
584AGL(1,𝔽5)—41no—
585C4×C5—23no—
586C4×C5—23no—
587C4×C5—21no—
588C4×C5—23no—
589C4×C5C2×C4×D416yes—
590Dic5—23no—
591Dic5—23no—
592Dic5—21no—
593Dic5—23no—
594Dic5C2×C4×D416yes—
595C24—51no—
596C24—51no—
597C2×Q8—24no—
598C2×Q8—24no—
599C2×Q8—54no—
600C2×Q8—54no—
601C2×Q8—53no—
602C2×Q8—56no—
603C2×Q8—56no—
604C2×Q8—53no—
605C2×Q8—53no—
606C2×Q8—1012no—
607C2×Q8—1012no—
608C2×Q8—106no—
609C2×Q8—106no—
610C2×Q8—106no—
611C2×Q8—106no—
612C2×Q8—1012no—
613C2×Q8—1012no—
614C2×Q8—104no—
615C2×Q8—104no—
616C2×Q8C22×AGL(1,𝔽5)13yes—
617C2×Q8C22×AGL(1,𝔽5)13yes—
618C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
619C2×D4—51no—
620C2×D4—51no—
621C2×D4—51no—
622C2×D4—102no—
623C2×D4—102no—
624C2×D4C22×AGL(1,𝔽5)11yescharacteristic
625C22×C4—53no—
626C22×C4—51no—
627C22×C4—51no—
628C22×C4—53no—
629C22×C4—53no—
630C22×C4—53no—
631C22×C4—51no—
632C22×C4—53no—
633C22×C4—53no—
634C22×C4—53no—
635C22×C4—53no—
636C22×C4—53no—
637C22×C4—53no—
638C22×C4—53no—
639C22×C4—51no—
640C22×C4—53no—
641C22×C4—53no—
642C22×C4—53no—
643C22×C4—51no—
644C22×C4—106no—
645C22×C4—106no—
646C22×C4—106no—
647C22×C4—106no—
648C22×C4—102no—
649C22×C4—102no—
650C22×C4—106no—
651C22×C4—102no—
652C22×C4—106no—
653C22×C4—203no—
654C22×C4C22×AGL(1,𝔽5)13yes—
655C22×C4C22×AGL(1,𝔽5)13yes—
656C4⋊C4—512no—
657C4⋊C4—53no—
658C4⋊C4—53no—
659C4⋊C4—53no—
660C4⋊C4—56no—
661C4⋊C4—53no—
662C4⋊C4—56no—
663C4⋊C4—56no—
664C4⋊C4—56no—
665C4⋊C4—106no—
666C4⋊C4—1012no—
667C4⋊C4—106no—
668C4⋊C4—106no—
669C4⋊C4—106no—
670C4⋊C4—106no—
671C4⋊C4—106no—
672C4⋊C4—203no—
673C4⋊C4C22×AGL(1,𝔽5)13yes—
674C4⋊C4C22×AGL(1,𝔽5)13yes—
675C4⋊C4C22×AGL(1,𝔽5)16yes—
676C22⋊C4—53no—
677C22⋊C4—53no—
678C22⋊C4—53no—
679C22⋊C4—53no—
680C22⋊C4—53no—
681C22⋊C4—53no—
682C22⋊C4—102no—
683C22⋊C4—106no—
684C22⋊C4—102no—
685C22⋊C4—106no—
686C22⋊C4—102no—
687C22⋊C4—203no—
688C22⋊C4C22×AGL(1,𝔽5)13yes—
689C22⋊C4C22×AGL(1,𝔽5)13yes—
690C42—512no—
691C42—53no—
692C42—53no—
693C42—53no—
694C42—106no—
695C42—106no—
696C42—106no—
697C42—106no—
698C42—1012no—
699C42—106no—
700C42—206no—
701C42C22×AGL(1,𝔽5)13yes—
702C2×C5—22no—
703C2×C5—41no—
704C2×C5C22×C4×D411yescharacteristic
705C2×C5C2×#51911yescharacteristic
706C2×C5C4×2−1+411yescharacteristic
707D5—22no—
708D5—41no—
709D5#348611yescharacteristic
710D5#348911yescharacteristic
711D5#351611yescharacteristic
712D5#352311yescharacteristic
713C23—51no—
714C23—52no—
715C23—52no—
716C23—51no—
717C23—51no—
718C23—101no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23—101no—
723C23—101no—
724C23—101no—
725C23—101no—
726C23—101no—
727C23—101no—
728C23C23×AGL(1,𝔽5)11yescharacteristic
729C23C23×AGL(1,𝔽5)11yescharacteristic
730Q8—26no—
731Q8—26no—
732Q8—512no—
733Q8—1012no—
734Q8—1012no—
735Q8—106no—
736Q8—106no—
737Q8D4×AGL(1,𝔽5)14yes—
738D4—22no—
739D4—102no—
740D4—102no—
741D4—102no—
742C2×C4—26no—
743C2×C4—26no—
744C2×C4—53no—
745C2×C4—56no—
746C2×C4—56no—
747C2×C4—52no—
748C2×C4—56no—
749C2×C4—52no—
750C2×C4—51no—
751C2×C4—53no—
752C2×C4—53no—
753C2×C4—53no—
754C2×C4—106no—
755C2×C4—106no—
756C2×C4—103no—
757C2×C4—103no—
758C2×C4—103no—
759C2×C4—103no—
760C2×C4—103no—
761C2×C4—103no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—106no—
765C2×C4—106no—
766C2×C4—101no—
767C2×C4—103no—
768C2×C4—101no—
769C2×C4—101no—
770C2×C4—101no—
771C2×C4—103no—
772C2×C4—108no—
773C2×C4—106no—
774C2×C4—106no—
775C2×C4—103no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—103no—
779C2×C4—103no—
780C2×C4—103no—
781C2×C4—101no—
782C2×C4—103no—
783C2×C4—103no—
784C2×C4—101no—
785C2×C4—101no—
786C2×C4—103no—
787C2×C4—103no—
788C2×C4—101no—
789C2×C4—103no—
790C2×C4—2012no—
791C2×C4C23×AGL(1,𝔽5)11yescharacteristic
792C2×C4C23×AGL(1,𝔽5)13yes—
793C2×C4C23×AGL(1,𝔽5)13yes—
794C2×C4C23×AGL(1,𝔽5)13yes—
795C2×C4C23×AGL(1,𝔽5)13yes—
796C5#3429111yescharacteristic, complemented, Sylow
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—51no—
803C22—51no—
804C22—51no—
805C22—51no—
806C22—51no—
807C22—51no—
808C22—52no—
809C22—102no—
810C22—102no—
811C22—102no—
812C22—102no—
813C22—101no—
814C22—101no—
815C22—101no—
816C22—101no—
817C22—101no—
818C22—201no—
819C22—201no—
820C22—201no—
821C22—201no—
822C22#6626212yescomplemented
823C22C24×AGL(1,𝔽5)11yescharacteristic
824C4—23no—
825C4—23no—
826C4—21no—
827C4—23no—
828C4—56no—
829C4—102no—
830C4—102no—
831C4—106no—
832C4—103no—
833C4—103no—
834C4—101no—
835C4—103no—
836C4—203no—
837C4—201no—
838C4—203no—
839C4—203no—
840C4—201no—
841C4C2×D4×AGL(1,𝔽5)16yes—
842C2—22no—
843C2—41no—
844C2—51no—
845C2—51no—
846C2—51no—
847C2—51no—
848C2—102no—
849C2—201no—
850C2C22×D4×AGL(1,𝔽5)11yescharacteristic
851C2C2×#6626211yescharacteristic
852C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×D4×Q8C4
prime radicalC2×D4×D5C23
cosocleC22×D5C25
hypercenterD4×Q8AGL(1,𝔽5)
hypocenterC5#34291
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#66262C2semidirect
2. C22×Q8×AGL(1,𝔽5)C2semidirect
4. Q8×C22⋊AGL(1,𝔽5)C2semidirect
5. Q8×C22⋊AGL(1,𝔽5)C2semidirect
6. #10617388C2semidirect
7. #10617386C2semidirect
8. #10617286C2semidirect
9. #10617285C2semidirect
10. #10617282C2semidirect
11. AGL(1,𝔽5)×C22⋊Q8C2semidirect
12. #10617212C2semidirect
13. #10617208C2semidirect
32. C5×D4×Q8C4semidirect
33. Q8×C22⋊D5C4semidirect
34. Q8×C22⋊D5C4semidirect
35. #66061C4semidirect
37. #65966C4semidirect
38. #65966C4semidirect
41. Q8×D20C4semidirect
44. D4×Dic10C4semidirect
80. C22×C5×Q8C2×C4semidirect
87. C2×Q8×D5C2×C4semidirect
88. C2×Q8×D5C2×C4semidirect
96. C22×Dic10C2×C4semidirect
110. Q8×AGL(1,𝔽5)D4semidirect
132. C5×C4⋊Q8C2×C4semidirect
134. C5×C22⋊Q8C2×C4semidirect
135. C4×C5×Q8C2×C4semidirect
138. #4092C2×C4semidirect
139. Q8×Dic5C2×C4semidirect
140. #4090C2×C4semidirect
141. #4090C2×C4semidirect
146. #4070C2×C4semidirect
148. #4043C2×C4semidirect
150. #4042C2×C4semidirect
155. #4034C2×C4semidirect
156. #4034C2×C4semidirect
157. #4033C2×C4semidirect
163. #4024C2×C4semidirect
166. #4015C2×C4semidirect
167. C4×Dic10C2×C4semidirect
312. D4×Q8AGL(1,𝔽5)semidirect
460. C22×Q8C2×AGL(1,𝔽5)semidirect
471. C4⋊Q8C2×AGL(1,𝔽5)semidirect
483. C22⋊Q8C2×AGL(1,𝔽5)semidirect
495. C4×Q8C2×AGL(1,𝔽5)semidirect
555. C22×C5#519semidirect
570. C2×D5#519semidirect
796. C5#34291semidirect
822. C22#66262semidirect

Maximal subgroups

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

subgroupindex
C2×#662622
C22×Q8×AGL(1,𝔽5)2
D4×Q8×D52
Q8×C22⋊AGL(1,𝔽5)2
#106173882
#106173862
#106172862
#106172852
#106172822
AGL(1,𝔽5)×C22⋊Q82
#106172122
#106172082
#106171792
#106171732
#342915