Finite Group Databasebeta

← #13044105

Subgroups — #13044105

Order 1280.

2198 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#519C211yesmaximal, characteristic
2Q8×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3Q8×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
4#10617214C213yesmaximal, complemented
5#10617213C213yesmaximal, complemented
6#10617212C211yesmaximal, characteristic, complemented
7Q8×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
8#10617210C213yesmaximal, complemented
9#10617209C213yesmaximal, complemented
10#10617208C211yesmaximal, characteristic, complemented
11C4×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
12#10617134C213yesmaximal
13#10617133C213yesmaximal
14#10617130C213yesmaximal
15#10617129C213yesmaximal
16C22×Q8×D5C2211yescharacteristic
17C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
18C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
19C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
20C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
21C5×#519C411yescharacteristic, complemented
22#66146C411yescharacteristic, complemented
23#65906C413yescomplemented
24#65906C413yescomplemented
25#65906C411yescharacteristic, complemented
26#65906C411yescharacteristic, complemented
27C4×Q8×D5C2211yescharacteristic
28C4×Q8×D5C2213yes—
29C4×Q8×D5C2211yescharacteristic
30C4×Q8×D5C2213yes—
31D5×#117C2213yes—
32D5×#117C2213yes—
33#65850C413yescomplemented
34#65850C413yescomplemented
35(C2×AGL(1,𝔽5))⋊Q8C2213yes—
36(C2×AGL(1,𝔽5))⋊Q8C2213yes—
37(C2×AGL(1,𝔽5))⋊Q8C2213yes—
38(C2×AGL(1,𝔽5))⋊Q8C2213yes—
39#65765C2213yes—
40#65765C2213yes—
41C4×C22⋊AGL(1,𝔽5)C2213yes—
42C4×C22⋊AGL(1,𝔽5)C2213yes—
43#65712C2213yes—
44#65712C2213yes—
45#65712C2213yes—
46#65712C2213yes—
47#65711C2213yes—
48#65711C2213yes—
49#65711C2213yes—
50#65711C2213yes—
51#65711C2216yes—
52#65711C2216yes—
53C4⋊C4×AGL(1,𝔽5)C2213yes—
54C4⋊C4×AGL(1,𝔽5)C2213yes—
55C4⋊C4×AGL(1,𝔽5)C2213yes—
56C4⋊C4×AGL(1,𝔽5)C2213yes—
57#65700C2211yescharacteristic
58#65700C2213yes—
59#65700C2213yes—
60#65700C2213yes—
61#65700C2216yes—
62#65690C2216yes—
63#65689C2213yes—
64#65689C2216yes—
65#65688C2213yes—
66C4×C4⋊AGL(1,𝔽5)C2213yes—
67C4×C4⋊AGL(1,𝔽5)C2213yes—
68C4×C4⋊AGL(1,𝔽5)C2213yes—
69C4×C4⋊AGL(1,𝔽5)C2213yes—
70C4×C4⋊AGL(1,𝔽5)C2216yes—
71#65686C2213yes—
72#65686C2216yes—
73C42×AGL(1,𝔽5)C2213yes—
74#34262—51nomaximal, Sylow
75C22×C5×Q8C2×C411yescharacteristic
76C2×Q8×D5—24no—
77C2×Q8×D5—24no—
78C2×Q8×D5C2×C411yescharacteristic
79C2×Q8×D5C2×C413yes—
80C2×Q8×D5C2313yes—
81C2×Q8×D5C2311yescharacteristic
82C22×C4×D5C2313yes—
83C22×Dic10C2×C413yes—
84C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
85C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
86C2×C22⋊AGL(1,𝔽5)C2313yes—
87C2×C22⋊AGL(1,𝔽5)C2313yes—
88Q8×AGL(1,𝔽5)—24no—
89Q8×AGL(1,𝔽5)—24no—
90Q8×AGL(1,𝔽5)—24no—
91Q8×AGL(1,𝔽5)—24no—
92C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
93C2×C4⋊AGL(1,𝔽5)C2313yes—
94C2×C4⋊AGL(1,𝔽5)C2313yes—
95C2×C4⋊AGL(1,𝔽5)C2313yes—
96C2×C4⋊AGL(1,𝔽5)C2313yes—
97C2×C4⋊AGL(1,𝔽5)C2313yes—
98C2×C4⋊AGL(1,𝔽5)C2313yes—
99C2×C4⋊AGL(1,𝔽5)C2316yes—
100C2×C4⋊AGL(1,𝔽5)C2313yes—
101C2×C4×AGL(1,𝔽5)C2311yescharacteristic
102C2×C4×AGL(1,𝔽5)C2313yes—
103C2×C4×AGL(1,𝔽5)C2313yes—
104C2×C4×AGL(1,𝔽5)C2313yes—
105C2×C4×AGL(1,𝔽5)C2313yes—
106C2×C4×AGL(1,𝔽5)C2313yes—
107C2×C4×AGL(1,𝔽5)C2313yes—
108C2×C4×AGL(1,𝔽5)C2313yes—
109C2×C4×AGL(1,𝔽5)C2316yes—
110C4×C5×Q8C2×C413yes—
111C4×C5×Q8C2×C413yes—
112C4×C5×Q8C2×C411yescharacteristic
113C4×C5×Q8C2×C411yescharacteristic
114C5×#117C2×C413yes—
115C5×#117C2×C413yes—
116Q8×Dic5C2×C413yes—
117Q8×Dic5C2×C413yes—
118Q8×Dic5C2×C411yescharacteristic
119Q8×Dic5C2×C411yescharacteristic
120#4072C2×C413yes—
121#4072C2×C413yes—
122#4038C2×C413yes—
123#4038C2×C413yes—
124#4038C2×C413yes—
125#4038C2×C413yes—
126D5×C4⋊C4C2313yes—
127D5×C4⋊C4C2313yes—
128D5×C4⋊C4C2313yes—
129D5×C4⋊C4C2313yes—
130#4033C2×C413yes—
131#4033C2×C416yes—
132#4033C2×C413yes—
133#4033C2×C416yes—
134#4033C2×C413yes—
135#4033C2×C413yes—
136D5×C22⋊C4C2311yescharacteristic
137D5×C22⋊C4C2313yes—
138#4023C2×C413yes—
139#4023C2×C413yes—
140#4023C2×C416yes—
141#4018C2×C413yes—
142#4018C2×C413yes—
143#4018C2×C416yes—
144C42×D5C2313yes—
145C42×D5C2316yes—
146C42×D5C2313yes—
147C4×Dic10C2×C413yes—
148C4×Dic10C2×C416yes—
149C4×Dic10C2×C413yes—
150C4×Dic10C2×C416yes—
151C4×Dic10C2×C413yes—
152C4×Dic10C2×C413yes—
153(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
154(C2×AGL(1,𝔽5))⋊C4C2313yes—
155(C2×AGL(1,𝔽5))⋊C4C2313yes—
156(C2×AGL(1,𝔽5))⋊C4C2313yes—
157(C2×AGL(1,𝔽5))⋊C4C2313yes—
158(C2×AGL(1,𝔽5))⋊C4C2316yes—
159(C2×AGL(1,𝔽5))⋊C4C2316yes—
160(C2×AGL(1,𝔽5))⋊C4C2313yes—
161(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
162(C2×AGL(1,𝔽5))⋊C4C2313yes—
163(C2×AGL(1,𝔽5))⋊C4C2313yes—
164(C2×AGL(1,𝔽5))⋊C4C2316yes—
165(C2×AGL(1,𝔽5))⋊C4C2313yes—
166(C2×AGL(1,𝔽5))⋊C4C2316yes—
167(C2×AGL(1,𝔽5))⋊C4C2313yes—
168(C2×AGL(1,𝔽5))⋊C4C2313yes—
169C2×#519—51no—
170#2356—53no—
171#2355—53no—
172#2351—51no—
173Q8×C4⋊C4—51no—
174#2347—53no—
175#2346—53no—
176Q8×C22⋊C4—51no—
177Q8×C22⋊C4—51no—
178#2320—53no—
179#2314—53no—
180#2298—53no—
181#2295—53no—
182#2276—51no—
183C42×Q8—51no—
184C23×D5C2411yescharacteristic
185C22×AGL(1,𝔽5)C2413yes—
186C22×AGL(1,𝔽5)C2413yes—
187C22×AGL(1,𝔽5)C2411yescharacteristic
188C22×AGL(1,𝔽5)C2413yes—
189C22×AGL(1,𝔽5)C2413yes—
190C22×AGL(1,𝔽5)C2411yescharacteristic
191C22×AGL(1,𝔽5)C2411yescharacteristic
192C22×AGL(1,𝔽5)C2411yescharacteristic
193C2×C5×Q8—24no—
194C2×C5×Q8C22×C413yes—
195C2×C5×Q8C22×C411yescharacteristic
196C22×C4×C5C22×C413yes—
197C22×Dic5C22×C413yes—
198Q8×D5—24no—
199Q8×D5—26no—
200Q8×D5—26no—
201Q8×D5—212no—
202Q8×D5#4114yes—
203Q8×D5#4114yes—
204C2×C4×D5—26no—
205C2×C4×D5—26no—
206C2×C4×D5C22×C413yes—
207C2×C4×D5C22×C413yes—
208C2×C4×D5C2411yescharacteristic
209C2×C4×D5C2413yes—
210C2×C4×D5C2411yescharacteristic
211C2×C4×D5C2413yes—
212C2×C4×D5C2413yes—
213C2×C4×D5C2413yes—
214C2×Dic10—212no—
215C2×Dic10C22×C413yes—
216C2×Dic10C22×C416yes—
217C2×Dic10C22×C413yes—
218C22⋊AGL(1,𝔽5)—22no—
219C22⋊AGL(1,𝔽5)—22no—
220C22⋊AGL(1,𝔽5)—43no—
221C22⋊AGL(1,𝔽5)—43no—
222C4⋊AGL(1,𝔽5)—22no—
223C4⋊AGL(1,𝔽5)—26no—
224C4⋊AGL(1,𝔽5)—26no—
225C4⋊AGL(1,𝔽5)—26no—
226C4⋊AGL(1,𝔽5)—26no—
227C4⋊AGL(1,𝔽5)—26no—
228C4⋊AGL(1,𝔽5)—43no—
229C4⋊AGL(1,𝔽5)—46no—
230C4⋊AGL(1,𝔽5)—43no—
231C4×AGL(1,𝔽5)—22no—
232C4×AGL(1,𝔽5)—26no—
233C4×AGL(1,𝔽5)—26no—
234C4×AGL(1,𝔽5)—26no—
235C4×AGL(1,𝔽5)—26no—
236C4×AGL(1,𝔽5)—26no—
237C4×AGL(1,𝔽5)—43no—
238C4×AGL(1,𝔽5)—46no—
239C4×AGL(1,𝔽5)—43no—
240C5×C4⋊C4C22×C413yes—
241C5×C4⋊C4C22×C413yes—
242C5×C4⋊C4C22×C413yes—
243C5×C4⋊C4C22×C413yes—
244C5×C22⋊C4C22×C411yescharacteristic
245C5×C22⋊C4C22×C413yes—
246C42×C5C22×C416yes—
247C42×C5C22×C413yes—
248C42×C5C22×C413yes—
249C22⋊Dic5C22×C411yescharacteristic
250C22⋊Dic5C22×C413yes—
251#685C22×C411yescharacteristic
252#685C22×C413yes—
253#685C22×C411yescharacteristic
254#685C22×C413yes—
255C4⋊Dic5C22×C413yes—
256C4⋊Dic5C22×C413yes—
257C4⋊Dic5C22×C413yes—
258C4⋊Dic5C22×C413yes—
259#683C22×C413yes—
260#683C22×C413yes—
261#683C22×C413yes—
262#683C22×C413yes—
263#683C22×C416yes—
264#683C22×C416yes—
265C4×Dic5C22×C416yes—
266C4×Dic5C22×C416yes—
267C4×Dic5C22×C413yes—
268C4×Dic5C22×C413yes—
269C4×Dic5C22×C413yes—
270C4×Dic5C22×C413yes—
271C4×Dic5C22×C416yes—
272C4×Dic5C22×C413yes—
273C4×Dic5C22×C413yes—
274C23×Q8—51no—
275#519—51no—
276#519—53no—
277#519—53no—
278#519—51no—
279#519—51no—
280#519—53no—
281#519—53no—
282#519AGL(1,𝔽5)11yescharacteristic, complemented
283C2×C4×Q8—53no—
284C2×C4×Q8—51no—
285C2×C4×Q8—53no—
286C2×C4×Q8—51no—
287C2×C4×Q8—51no—
288C2×C4×Q8—51no—
289C2×C4×Q8—51no—
290C2×C4×Q8—51no—
291C2×#117—53no—
292C2×#117—53no—
293#391—53no—
294#391—53no—
295#391—53no—
296#391—53no—
297#389—53no—
298#389—53no—
299#389—53no—
300#389—53no—
301#388—53no—
302#388—56no—
303#388—53no—
304#388—53no—
305#388—51no—
306#387—56no—
307#387—56no—
308#387—53no—
309#387—53no—
310#387—53no—
311#387—53no—
312#384—53no—
313#383—56no—
314#382—53no—
315#382—56no—
316#380—53no—
317#380—53no—
318C4×C4⋊C4—53no—
319C4×C4⋊C4—53no—
320C4×C4⋊C4—53no—
321C4×C4⋊C4—53no—
322C4×C4⋊C4—56no—
323C4×C4⋊C4—53no—
324C4×C4⋊C4—53no—
325C4×C4⋊C4—53no—
326C4×C4⋊C4—53no—
327C4×C22⋊C4—53no—
328C4×C22⋊C4—53no—
329#376—53no—
330#376—56no—
331C43—53no—
332C23×C5C23×C411yescharacteristic
333C22×D5—21no—
334C22×D5—21no—
335C22×D5—21no—
336C22×D5—21no—
337C22×D5—21no—
338C22×D5—21no—
339C22×D5C23×C411yescharacteristic
340C22×D5C2511yescharacteristic
341C2×AGL(1,𝔽5)—21no—
342C2×AGL(1,𝔽5)—21no—
343C2×AGL(1,𝔽5)—21no—
344C2×AGL(1,𝔽5)—21no—
345C2×AGL(1,𝔽5)—21no—
346C2×AGL(1,𝔽5)—21no—
347C2×AGL(1,𝔽5)—23no—
348C2×AGL(1,𝔽5)—23no—
349C2×AGL(1,𝔽5)—23no—
350C2×AGL(1,𝔽5)—23no—
351C2×AGL(1,𝔽5)—23no—
352C2×AGL(1,𝔽5)—23no—
353C2×AGL(1,𝔽5)—21no—
354C2×AGL(1,𝔽5)—21no—
355C2×AGL(1,𝔽5)—21no—
356C2×AGL(1,𝔽5)—23no—
357C2×AGL(1,𝔽5)—23no—
358C2×AGL(1,𝔽5)—23no—
359C2×AGL(1,𝔽5)—23no—
360C2×AGL(1,𝔽5)—23no—
361C2×AGL(1,𝔽5)—21no—
362C2×AGL(1,𝔽5)—23no—
363C2×AGL(1,𝔽5)2−1+412yes—
364C2×AGL(1,𝔽5)2−1+412yes—
365C5×Q8—26no—
366C5×Q8#11714yes—
367C2×C4×C5—26no—
368C2×C4×C5C23×C413yes—
369C2×C4×C5C23×C411yescharacteristic
370C2×C4×C5C23×C413yes—
371C2×C4×C5C23×C411yescharacteristic
372C2×C4×C5C23×C413yes—
373C2×C4×C5C23×C413yes—
374C2×Dic5—26no—
375C2×Dic5C23×C413yes—
376C2×Dic5C23×C411yescharacteristic
377C2×Dic5C23×C413yes—
378C2×Dic5C23×C411yescharacteristic
379C2×Dic5C23×C413yes—
380C2×Dic5C23×C413yes—
381C4×D5—23no—
382C4×D5—23no—
383C4×D5—21no—
384C4×D5—23no—
385C4×D5—23no—
386C4×D5—21no—
387C4×D5—23no—
388C4×D5—21no—
389C4×D5—21no—
390C4×D5—23no—
391C4×D5—26no—
392C4×D5—26no—
393C4×D5C2×#4116yes—
394C4×D5C2×#4116yes—
395Dic10—26no—
396Dic10—212no—
397Dic10#117112yes—
398C22×Q8—51no—
399C22×Q8—53no—
400C22×Q8—53no—
401C22×Q8—51no—
402C22×Q8—53no—
403C22×Q8—104no—
404C22×Q8—104no—
405C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
406C23×C4—53no—
407C4×Q8—53no—
408C4×Q8—53no—
409C4×Q8—51no—
410C4×Q8—51no—
411C4×Q8—53no—
412C4×Q8—53no—
413C4×Q8—56no—
414C4×Q8—53no—
415C4×Q8—56no—
416C4×Q8—53no—
417C4×Q8—53no—
418C4×Q8—53no—
419C4×Q8—56no—
420C4×Q8—53no—
421C4×Q8—56no—
422C4×Q8—53no—
423C4×Q8—104no—
424C4×Q8—104no—
425C4×Q8—104no—
426C4×Q8—104no—
427C4×Q8C2×AGL(1,𝔽5)13yes—
428C4×Q8C2×AGL(1,𝔽5)13yes—
429C4×Q8C2×AGL(1,𝔽5)11yescharacteristic
430C4×Q8C2×AGL(1,𝔽5)11yescharacteristic
431#117—53no—
432#117—53no—
433#117—53no—
434#117—53no—
435#117—53no—
436#117—53no—
437#117—53no—
438#117—53no—
439#117—56no—
440#117—53no—
441#117—53no—
442#117—56no—
443#117C2×AGL(1,𝔽5)13yes—
444#117C2×AGL(1,𝔽5)13yes—
445C2×C4⋊C4—53no—
446C2×C4⋊C4—53no—
447C2×C4⋊C4—53no—
448C2×C4⋊C4—53no—
449C2×C4⋊C4—53no—
450C2×C4⋊C4—53no—
451C2×C4⋊C4—53no—
452C2×C4⋊C4—53no—
453C2×C4⋊C4—51no—
454C2×C4⋊C4—53no—
455C2×C4⋊C4—53no—
456C2×C4⋊C4—56no—
457C2×C4⋊C4—53no—
458C2×C22⋊C4—51no—
459C2×C22⋊C4—53no—
460C2×C22⋊C4—51no—
461C2×C22⋊C4—51no—
462C2×C22⋊C4—53no—
463C2×C22⋊C4—53no—
464C2×C42—53no—
465C2×C42—56no—
466C2×C42—53no—
467C2×C42—53no—
468C2×C42—53no—
469C2×C42—53no—
470C2×C42—53no—
471C2×C42—51no—
472C2×C42—53no—
473C2×C42—53no—
474C2×C42—53no—
475C2×C42—56no—
476#95—51no—
477#95—53no—
478#95—53no—
479#95—53no—
480#95—53no—
481#95—53no—
482#95—56no—
483#95—56no—
484#95—53no—
485#95—53no—
486#95—53no—
487#95—56no—
488#95—51no—
489#95—56no—
490#95—53no—
491#95—53no—
492C22×C5—21no—
493C22×C5—21no—
494C22×C5—21no—
495C22×C5C24×C411yescharacteristic
496C2×D5—21no—
497C2×D5—21no—
498C2×D5—21no—
499C2×D5—41no—
500C2×D5—41no—
501C2×D5—41no—
502C2×D5—41no—
503C2×D5C22×#4111yescharacteristic
504C2×D5C22×#4111yescharacteristic
505C2×D5C2×2−1+411yescharacteristic
506C2×D5C2×2−1+411yescharacteristic
507C2×D5#58511yescharacteristic
508C2×D5#58511yescharacteristic
509AGL(1,𝔽5)—22no—
510AGL(1,𝔽5)—22no—
511AGL(1,𝔽5)—43no—
512AGL(1,𝔽5)—41no—
513AGL(1,𝔽5)—43no—
514AGL(1,𝔽5)—41no—
515AGL(1,𝔽5)—43no—
516AGL(1,𝔽5)—43no—
517C4×C5—23no—
518C4×C5—21no—
519C4×C5—23no—
520C4×C5—23no—
521C4×C5—21no—
522C4×C5C2×#11716yes—
523Dic5—23no—
524Dic5—21no—
525Dic5—23no—
526Dic5—23no—
527Dic5—21no—
528Dic5C2×#11716yes—
529C24—51no—
530C2×Q8—24no—
531C2×Q8—54no—
532C2×Q8—54no—
533C2×Q8—53no—
534C2×Q8—56no—
535C2×Q8—53no—
536C2×Q8—1012no—
537C2×Q8—106no—
538C2×Q8—106no—
539C2×Q8—1012no—
540C2×Q8—104no—
541C2×Q8C22×AGL(1,𝔽5)13yes—
542C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
543C22×C4—53no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—53no—
547C22×C4—53no—
548C22×C4—51no—
549C22×C4—53no—
550C22×C4—53no—
551C22×C4—51no—
552C22×C4—53no—
553C22×C4—53no—
554C22×C4—51no—
555C22×C4—51no—
556C22×C4—53no—
557C22×C4—53no—
558C22×C4—53no—
559C22×C4—53no—
560C22×C4—106no—
561C22×C4—106no—
562C22×C4C22×AGL(1,𝔽5)13yes—
563C4⋊C4—56no—
564C4⋊C4—56no—
565C4⋊C4—53no—
566C4⋊C4—53no—
567C4⋊C4—53no—
568C4⋊C4—53no—
569C4⋊C4—53no—
570C4⋊C4—53no—
571C4⋊C4—53no—
572C4⋊C4—53no—
573C4⋊C4—106no—
574C4⋊C4—106no—
575C4⋊C4—106no—
576C4⋊C4—106no—
577C4⋊C4—102no—
578C4⋊C4—106no—
579C4⋊C4—203no—
580C4⋊C4—203no—
581C4⋊C4—206no—
582C4⋊C4C22×AGL(1,𝔽5)13yes—
583C4⋊C4C22×AGL(1,𝔽5)13yes—
584C4⋊C4C22×AGL(1,𝔽5)13yes—
585C4⋊C4C22×AGL(1,𝔽5)13yes—
586C22⋊C4—51no—
587C22⋊C4—53no—
588C22⋊C4—51no—
589C22⋊C4—53no—
590C22⋊C4—51no—
591C22⋊C4—53no—
592C22⋊C4—102no—
593C22⋊C4—102no—
594C22⋊C4—203no—
595C22⋊C4—203no—
596C22⋊C4C22×AGL(1,𝔽5)11yescharacteristic
597C22⋊C4C22×AGL(1,𝔽5)13yes—
598C42—53no—
599C42—53no—
600C42—53no—
601C42—53no—
602C42—56no—
603C42—53no—
604C42—53no—
605C42—56no—
606C42—56no—
607C42—106no—
608C42—106no—
609C42—106no—
610C42—106no—
611C42—106no—
612C42—102no—
613C42—203no—
614C42—206no—
615C42—203no—
616C42C22×AGL(1,𝔽5)16yes—
617C42C22×AGL(1,𝔽5)13yes—
618C42C22×AGL(1,𝔽5)13yes—
619C2×C5—41no—
620C2×C5C22×#11711yescharacteristic
621C2×C5C4×2−1+411yescharacteristic
622C2×C5C4×2−1+411yescharacteristic
623D5—41no—
624D5#351611yescharacteristic
625D5#351811yescharacteristic
626D5#352311yescharacteristic
627D5#352411yescharacteristic
628C23—51no—
629C23—51no—
630C23—101no—
631C23—101no—
632C23—101no—
633C23—101no—
634C23—101no—
635C23—101no—
636C23C23×AGL(1,𝔽5)11yescharacteristic
637Q8—26no—
638Q8—512no—
639Q8—1012no—
640Q8—106no—
641Q8#413014yes—
642C2×C4—26no—
643C2×C4—53no—
644C2×C4—56no—
645C2×C4—56no—
646C2×C4—52no—
647C2×C4—52no—
648C2×C4—51no—
649C2×C4—53no—
650C2×C4—51no—
651C2×C4—53no—
652C2×C4—53no—
653C2×C4—106no—
654C2×C4—101no—
655C2×C4—103no—
656C2×C4—103no—
657C2×C4—101no—
658C2×C4—103no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—103no—
662C2×C4—103no—
663C2×C4—103no—
664C2×C4—106no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—101no—
668C2×C4—101no—
669C2×C4—106no—
670C2×C4—101no—
671C2×C4—101no—
672C2×C4—103no—
673C2×C4—103no—
674C2×C4—103no—
675C2×C4—103no—
676C2×C4—103no—
677C2×C4—103no—
678C2×C4—103no—
679C2×C4—103no—
680C2×C4—103no—
681C2×C4—103no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—103no—
685C2×C4—101no—
686C2×C4—103no—
687C2×C4—101no—
688C2×C4C23×AGL(1,𝔽5)11yescharacteristic
689C2×C4C23×AGL(1,𝔽5)13yes—
690C2×C4C23×AGL(1,𝔽5)11yescharacteristic
691C2×C4C23×AGL(1,𝔽5)13yes—
692C2×C4C23×AGL(1,𝔽5)13yes—
693C2×C4C23×AGL(1,𝔽5)13yes—
694C5#3426211yescharacteristic, complemented, Sylow
695C22—21no—
696C22—21no—
697C22—21no—
698C22—51no—
699C22—51no—
700C22—51no—
701C22—51no—
702C22—51no—
703C22—51no—
704C22—101no—
705C22—101no—
706C22—101no—
707C22—201no—
708C22—201no—
709C22—201no—
710C22—201no—
711C22C24×AGL(1,𝔽5)11yescharacteristic
712C4—23no—
713C4—23no—
714C4—21no—
715C4—21no—
716C4—23no—
717C4—56no—
718C4—102no—
719C4—102no—
720C4—103no—
721C4—103no—
722C4—101no—
723C4—101no—
724C4—103no—
725C4—203no—
726C4—201no—
727C4—203no—
728C4—203no—
729C4—201no—
730C4—203no—
731C4C2×#413016yes—
732C2—41no—
733C2—51no—
734C2—51no—
735C2—51no—
736C2—51no—
737C2—201no—
738C2C22×#413011yescharacteristic
739C2AGL(1,𝔽5)×2−1+411yescharacteristic
740C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#519C4
prime radicalC23×D5C24
cosocleC22×D5C25
hypercenter#519AGL(1,𝔽5)
hypocenterC5#34262
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
4. #10617214C2semidirect
5. #10617213C2semidirect
6. #10617212C2semidirect
7. Q8×C4⋊AGL(1,𝔽5)C2semidirect
8. #10617210C2semidirect
9. #10617209C2semidirect
10. #10617208C2semidirect
11. C4×Q8×AGL(1,𝔽5)C2semidirect
21. C5×#519C4semidirect
22. #66146C4semidirect
23. #65906C4semidirect
24. #65906C4semidirect
25. #65906C4semidirect
26. #65906C4semidirect
33. #65850C4semidirect
34. #65850C4semidirect
282. #519AGL(1,𝔽5)semidirect
694. C5#34262semidirect

Maximal subgroups

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

subgroupindex
D5×#5192
Q8×C22⋊AGL(1,𝔽5)2
#106172142
#106172132
#106172122
Q8×C4⋊AGL(1,𝔽5)2
#106172102
#106172092
#106172082
C4×Q8×AGL(1,𝔽5)2
#106171342
#106171332
#106171302
#106171292
#342625