Finite Group Databasebeta

← #13044106

Subgroups — #13044106

Order 1280.

2390 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#520C211yesmaximal, characteristic
2#10617558C211yesmaximal, characteristic
3#10617558C211yesmaximal, characteristic
4#10617212C211yesmaximal, characteristic, complemented
5Q8×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6#10617208C211yesmaximal, characteristic, complemented
7C4×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
8#10617182C213yesmaximal, complemented
9#10617181C213yesmaximal, complemented
10#10617176C213yesmaximal, complemented
11#10617174C213yesmaximal, complemented
12#10617130C213yesmaximal, complemented
13#10617129C213yesmaximal, complemented
14#10617104C213yesmaximal, complemented
15#10617103C213yesmaximal, complemented
16C2×D5×#41C2211yescharacteristic
17C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
18C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
19C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
20C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
21C2×#4130C2216yes—
22C5×#520C411yescharacteristic, complemented
23#66161C411yescharacteristic, complemented
24#65908C411yescharacteristic, complemented
25#65908C411yescharacteristic, complemented
26C4×Q8×D5C2211yescharacteristic
27C4×Q8×D5C2211yescharacteristic
28#65880C413yescomplemented
29#65880C413yescomplemented
30C4×D4×D5C2213yes—
31C4×D4×D5C2213yes—
32#65857C413yescomplemented
33D5×#117C2213yes—
34#65838C413yescomplemented
35C2×D5×C4⋊C4C2213yes—
36#65780C2213yes—
37#65780C2213yes—
38#65780C2213yes—
39#65780C2213yes—
40#65765C2213yes—
41#65765C2213yes—
42#65765C2216yes—
43#65764C2216yes—
44C4×C22⋊AGL(1,𝔽5)C2213yes—
45C4×C22⋊AGL(1,𝔽5)C2213yes—
46C4×C22⋊AGL(1,𝔽5)C2216yes—
47#65712C2213yes—
48#65712C2213yes—
49#65712C2213yes—
50#65712C2213yes—
51#65711C2213yes—
52#65711C2216yes—
53#65711C2213yes—
54#65711C2211yescharacteristic
55#65711C2213yes—
56C4⋊C4×AGL(1,𝔽5)C2213yes—
57C4⋊C4×AGL(1,𝔽5)C2213yes—
58C4⋊C4×AGL(1,𝔽5)C2213yes—
59C4⋊C4×AGL(1,𝔽5)C2213yes—
60#65700C2213yes—
61#65700C2213yes—
62#65700C2213yes—
63#65700C2213yes—
64#65700C2216yes—
65#65700C2216yes—
66#65689C2213yes—
67#65688C2213yes—
68C4×C4⋊AGL(1,𝔽5)C2213yes—
69C4×C4⋊AGL(1,𝔽5)C2213yes—
70C4×C4⋊AGL(1,𝔽5)C2213yes—
71C4×C4⋊AGL(1,𝔽5)C2213yes—
72#65686C2213yes—
73C42×AGL(1,𝔽5)C2213yes—
74#34263—51nomaximal, Sylow
75C2×C5×#41C2×C411yescharacteristic
76D5×#41—24no—
77D5×#41—24no—
78C2×#713C2×C411yescharacteristic
79C2×Q8×D5C2311yescharacteristic
80C2×#711C2×C413yes—
81C2×D4×D5C2313yes—
82C2×#709C2×C413yes—
83C22×C4×D5C2313yes—
84C22×C4×D5C2316yes—
85C2×C22⋊AGL(1,𝔽5)C2313yes—
86C2×C22⋊AGL(1,𝔽5)C2313yes—
87C2×C22⋊AGL(1,𝔽5)C2316yes—
88C2×C22⋊AGL(1,𝔽5)C2313yes—
89C2×C22⋊AGL(1,𝔽5)C2313yes—
90C2×C22⋊AGL(1,𝔽5)C2316yes—
91Q8×AGL(1,𝔽5)—24no—
92Q8×AGL(1,𝔽5)—24no—
93Q8×AGL(1,𝔽5)—24no—
94Q8×AGL(1,𝔽5)—24no—
95#4130—412no—
96C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
97C2×C4⋊AGL(1,𝔽5)C2313yes—
98C2×C4⋊AGL(1,𝔽5)C2313yes—
99C2×C4⋊AGL(1,𝔽5)C2313yes—
100C2×C4⋊AGL(1,𝔽5)C2313yes—
101C2×C4⋊AGL(1,𝔽5)C2313yes—
102C2×C4⋊AGL(1,𝔽5)C2313yes—
103C2×C4⋊AGL(1,𝔽5)C2313yes—
104C2×C4⋊AGL(1,𝔽5)C2316yes—
105C2×C4×AGL(1,𝔽5)C2311yescharacteristic
106C2×C4×AGL(1,𝔽5)C2313yes—
107C2×C4×AGL(1,𝔽5)C2313yes—
108C2×C4×AGL(1,𝔽5)C2313yes—
109C2×C4×AGL(1,𝔽5)C2313yes—
110C2×C4×AGL(1,𝔽5)C2313yes—
111C2×C4×AGL(1,𝔽5)C2313yes—
112C2×C4×AGL(1,𝔽5)C2313yes—
113C2×C4×AGL(1,𝔽5)C2316yes—
114C4×C5×Q8C2×C411yescharacteristic
115C4×C5×Q8C2×C411yescharacteristic
116C4×C5×D4C2×C413yes—
117C4×C5×D4C2×C413yes—
118C5×#117C2×C413yes—
119C2×C5×C4⋊C4C2×C413yes—
120Q8×Dic5C2×C411yescharacteristic
121Q8×Dic5C2×C411yescharacteristic
122D4×Dic5C2×C413yes—
123D4×Dic5C2×C413yes—
124C4×C22⋊D5C2×C416yes—
125C4×C22⋊D5C2×C416yes—
126#4072C2×C413yes—
127C2×C4⋊Dic5C2×C413yes—
128C2×#683C2×C416yes—
129#4039C2×C413yes—
130#4039C2×C413yes—
131#4038C2×C413yes—
132#4038C2×C413yes—
133D5×C4⋊C4C2×C416yes—
134D5×C4⋊C4C2×C413yes—
135D5×C4⋊C4C2×C413yes—
136D5×C4⋊C4C2313yes—
137D5×C4⋊C4C2313yes—
138D5×C4⋊C4C2313yes—
139D5×C4⋊C4C2311yescharacteristic
140#4033C2×C413yes—
141#4033C2×C413yes—
142#4027C2×C416yes—
143#4027C2×C416yes—
144D5×C22⋊C4C2313yes—
145D5×C22⋊C4C2313yes—
146#4023C2×C413yes—
147#4023C2×C413yes—
148C4×D20C2×C413yes—
149C4×D20C2×C413yes—
150#4018C2×C413yes—
151#4018C2×C413yes—
152C42×D5C2313yes—
153C42×D5C2313yes—
154C4×Dic10C2×C413yes—
155C4×Dic10C2×C413yes—
156(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
157(C2×AGL(1,𝔽5))⋊C4C2313yes—
158(C2×AGL(1,𝔽5))⋊C4C2313yes—
159(C2×AGL(1,𝔽5))⋊C4C2313yes—
160(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
161(C2×AGL(1,𝔽5))⋊C4C2313yes—
162(C2×AGL(1,𝔽5))⋊C4C2316yes—
163(C2×AGL(1,𝔽5))⋊C4C2313yes—
164(C2×AGL(1,𝔽5))⋊C4C2313yes—
165(C2×AGL(1,𝔽5))⋊C4C2316yes—
166(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
167(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
168(C2×AGL(1,𝔽5))⋊C4C2313yes—
169(C2×AGL(1,𝔽5))⋊C4C2313yes—
170C2×#520—51no—
171#2357—53no—
172#2354—53no—
173#2351—51no—
174Q8×C4⋊C4—51no—
175#2345—53no—
176#2344—53no—
177#2341—51no—
178#2341—51no—
179#2319—53no—
180#2314—53no—
181#2298—53no—
182#2293—53no—
183#2276—51no—
184C42×Q8—51no—
185C23×D5C2413yes—
186C22×AGL(1,𝔽5)C2413yes—
187C22×AGL(1,𝔽5)C2413yes—
188C22×AGL(1,𝔽5)C2411yescharacteristic
189C22×AGL(1,𝔽5)C2413yes—
190C22×AGL(1,𝔽5)C2413yes—
191C22×AGL(1,𝔽5)C2411yescharacteristic
192C22×AGL(1,𝔽5)C2411yescharacteristic
193C22×AGL(1,𝔽5)C2411yescharacteristic
194C5×#41—24no—
195C2×C5×Q8C22×C411yescharacteristic
196C2×C5×D4C22×C413yes—
197C22×C4×C5C22×C413yes—
198C22×C4×C5C22×C416yes—
199C2×C22⋊D5C22×C416yes—
200C22×Dic5C22×C413yes—
201C22×Dic5C22×C416yes—
202#713—24no—
203Q8×D5#4114yes—
204Q8×D5#4114yes—
205#711—212no—
206D4×D5—26no—
207D4×D5—26no—
208#709—212no—
209C2×D20C22×C413yes—
210C2×C4×D5—26no—
211C2×C4×D5—26no—
212C2×C4×D5—46no—
213C2×C4×D5—46no—
214C2×C4×D5C22×C413yes—
215C2×C4×D5C22×C413yes—
216C2×C4×D5C22×C416yes—
217C2×C4×D5C22×C416yes—
218C2×C4×D5C2413yes—
219C2×C4×D5C2411yescharacteristic
220C2×C4×D5C2413yes—
221C2×C4×D5C2411yescharacteristic
222C2×C4×D5C2411yescharacteristic
223C2×C4×D5C2413yes—
224C2×Dic10C22×C413yes—
225C22⋊AGL(1,𝔽5)—26no—
226C22⋊AGL(1,𝔽5)—26no—
227C22⋊AGL(1,𝔽5)—46no—
228C22⋊AGL(1,𝔽5)—43no—
229C22⋊AGL(1,𝔽5)—43no—
230C22⋊AGL(1,𝔽5)—46no—
231C4⋊AGL(1,𝔽5)—26no—
232C4⋊AGL(1,𝔽5)—22no—
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)—43no—
239C4⋊AGL(1,𝔽5)—46no—
240C4×AGL(1,𝔽5)—26no—
241C4×AGL(1,𝔽5)—22no—
242C4×AGL(1,𝔽5)—26no—
243C4×AGL(1,𝔽5)—26no—
244C4×AGL(1,𝔽5)—26no—
245C4×AGL(1,𝔽5)—26no—
246C4×AGL(1,𝔽5)—43no—
247C4×AGL(1,𝔽5)—43no—
248C4×AGL(1,𝔽5)—46no—
249C5×C4⋊C4C22×C413yes—
250C5×C4⋊C4C22×C413yes—
251C5×C4⋊C4C22×C413yes—
252C5×C4⋊C4C22×C411yescharacteristic
253C5×C22⋊C4C22×C413yes—
254C5×C22⋊C4C22×C413yes—
255C42×C5C22×C413yes—
256C42×C5C22×C413yes—
257C22⋊Dic5C22×C413yes—
258C22⋊Dic5C22×C413yes—
259#685C22×C413yes—
260#685C22×C413yes—
261#685C22×C413yes—
262#685C22×C413yes—
263C4⋊Dic5C22×C413yes—
264C4⋊Dic5C22×C413yes—
265C4⋊Dic5C22×C413yes—
266C4⋊Dic5C22×C411yescharacteristic
267#683C22×C416yes—
268#683C22×C416yes—
269#683C22×C411yescharacteristic
270#683C22×C411yescharacteristic
271#683C22×C413yes—
272#683C22×C413yes—
273C4×Dic5C22×C413yes—
274C4×Dic5C22×C413yes—
275C4×Dic5C22×C413yes—
276C4×Dic5C22×C413yes—
277C4×Dic5C22×C413yes—
278C4×Dic5C22×C413yes—
279C22×#41—51no—
280#520—51no—
281#520—51no—
282#520—51no—
283#520—53no—
284#520—53no—
285#520—53no—
286#520—53no—
287#520AGL(1,𝔽5)11yescharacteristic, complemented
288C2×C4×Q8—51no—
289C2×C4×Q8—51no—
290C2×C4×Q8—51no—
291C2×C4×Q8—51no—
292C2×C4×Q8—51no—
293C2×C4×Q8—51no—
294C2×C4×D4—53no—
295C2×C4×D4—53no—
296C2×#117—53no—
297C2×#117—56no—
298C22×C4⋊C4—53no—
299#390—53no—
300#390—53no—
301#390—53no—
302#390—53no—
303#389—53no—
304#389—53no—
305#389—53no—
306#389—53no—
307#388—56no—
308#388—56no—
309#388—53no—
310#388—53no—
311#388—53no—
312#388—53no—
313#387—53no—
314#387—56no—
315#387—53no—
316#387—53no—
317#387—51no—
318#384—53no—
319#382—53no—
320#381—56no—
321#380—53no—
322#380—53no—
323#380—56no—
324C4×C4⋊C4—53no—
325C4×C4⋊C4—53no—
326C4×C4⋊C4—53no—
327C4×C4⋊C4—53no—
328C4×C4⋊C4—53no—
329C4×C4⋊C4—53no—
330C4×C4⋊C4—53no—
331C4×C4⋊C4—53no—
332C4×C22⋊C4—53no—
333C4×C22⋊C4—53no—
334C4×C22⋊C4—56no—
335#376—53no—
336C43—53no—
337C23×C5C23×C413yes—
338C22×D5—23no—
339C22×D5—23no—
340C22×D5—23no—
341C22×D5—23no—
342C22×D5—23no—
343C22×D5—23no—
344C22×D5C23×C413yes—
345C22×D5C2511yescharacteristic
346C2×AGL(1,𝔽5)—21no—
347C2×AGL(1,𝔽5)—21no—
348C2×AGL(1,𝔽5)—21no—
349C2×AGL(1,𝔽5)—21no—
350C2×AGL(1,𝔽5)—21no—
351C2×AGL(1,𝔽5)—21no—
352C2×AGL(1,𝔽5)—23no—
353C2×AGL(1,𝔽5)—23no—
354C2×AGL(1,𝔽5)—23no—
355C2×AGL(1,𝔽5)—23no—
356C2×AGL(1,𝔽5)—23no—
357C2×AGL(1,𝔽5)—23no—
358C2×AGL(1,𝔽5)—23no—
359C2×AGL(1,𝔽5)—21no—
360C2×AGL(1,𝔽5)—23no—
361C2×AGL(1,𝔽5)—23no—
362C2×AGL(1,𝔽5)—23no—
363C2×AGL(1,𝔽5)—23no—
364C2×AGL(1,𝔽5)—21no—
365C2×AGL(1,𝔽5)—23no—
366C2×AGL(1,𝔽5)—21no—
367C2×AGL(1,𝔽5)—21no—
368C2×AGL(1,𝔽5)H(5,𝔽2)12yes—
369C2×AGL(1,𝔽5)2−1+412yes—
370C5×Q8#11714yescomplemented
371C5×D4—26no—
372C2×C4×C5—26no—
373C2×C4×C5—46no—
374C2×C4×C5C23×C411yescharacteristic
375C2×C4×C5C23×C411yescharacteristic
376C2×C4×C5C23×C413yes—
377C2×C4×C5C23×C413yes—
378C2×C4×C5C23×C411yescharacteristic
379C2×C4×C5C23×C413yes—
380C22⋊D5—212no—
381C2×Dic5—26no—
382C2×Dic5—46no—
383C2×Dic5C23×C411yescharacteristic
384C2×Dic5C23×C411yescharacteristic
385C2×Dic5C23×C413yes—
386C2×Dic5C23×C413yes—
387C2×Dic5C23×C411yescharacteristic
388C2×Dic5C23×C413yes—
389D20—26no—
390C4×D5—21no—
391C4×D5—21no—
392C4×D5—23no—
393C4×D5—23no—
394C4×D5—21no—
395C4×D5—21no—
396C4×D5—21no—
397C4×D5—23no—
398C4×D5—21no—
399C4×D5—23no—
400C4×D5—26no—
401C4×D5—26no—
402C4×D5—46no—
403C4×D5—46no—
404C4×D5C2×#4116yes—
405C4×D5C2×#4116yes—
406Dic10#117112yescomplemented
407C2×#41—51no—
408C2×#41—53no—
409C2×#41—53no—
410C2×#41—104no—
411C2×#41—104no—
412C2×#41C2×AGL(1,𝔽5)11yescharacteristic
413C22×Q8—51no—
414C22×D4—53no—
415C23×C4—53no—
416C23×C4—56no—
417C4×Q8—51no—
418C4×Q8—51no—
419C4×Q8—53no—
420C4×Q8—53no—
421C4×Q8—53no—
422C4×Q8—53no—
423C4×Q8—104no—
424C4×Q8—104no—
425C4×Q8—104no—
426C4×Q8—104no—
427C4×Q8C2×AGL(1,𝔽5)11yescharacteristic
428C4×Q8C2×AGL(1,𝔽5)11yescharacteristic
429C4×D4—53no—
430C4×D4—53no—
431C4×D4—56no—
432C4×D4—56no—
433C4×D4—53no—
434C4×D4—53no—
435C4×D4—56no—
436C4×D4—56no—
437C4×D4—53no—
438C4×D4—53no—
439C4×D4C2×AGL(1,𝔽5)13yes—
440C4×D4C2×AGL(1,𝔽5)13yes—
441#117—53no—
442#117—53no—
443#117—53no—
444#117—53no—
445#117—53no—
446#117—53no—
447#117—53no—
448#117—2012no—
449#117C2×AGL(1,𝔽5)13yes—
450C2×C4⋊C4—56no—
451C2×C4⋊C4—53no—
452C2×C4⋊C4—53no—
453C2×C4⋊C4—53no—
454C2×C4⋊C4—53no—
455C2×C4⋊C4—53no—
456C2×C4⋊C4—53no—
457C2×C4⋊C4—56no—
458C2×C4⋊C4—51no—
459C2×C4⋊C4—53no—
460C2×C4⋊C4—53no—
461C2×C4⋊C4—53no—
462C2×C4⋊C4—53no—
463C2×C4⋊C4—53no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—56no—
466C2×C4⋊C4—53no—
467C2×C4⋊C4—53no—
468C2×C4⋊C4C2×AGL(1,𝔽5)13yes—
469C2×C22⋊C4—53no—
470C2×C22⋊C4—53no—
471C2×C22⋊C4—53no—
472C2×C22⋊C4—53no—
473C2×C22⋊C4—56no—
474C2×C22⋊C4—53no—
475C2×C22⋊C4—56no—
476C2×C22⋊C4—53no—
477C2×C42—53no—
478C2×C42—53no—
479C2×C42—53no—
480C2×C42—53no—
481C2×C42—53no—
482C2×C42—53no—
483C2×C42—53no—
484C2×C42—51no—
485C2×C42—56no—
486C2×C42—53no—
487C2×C42—53no—
488#95—51no—
489#95—53no—
490#95—53no—
491#95—53no—
492#95—51no—
493#95—51no—
494#95—53no—
495#95—53no—
496#95—53no—
497#95—56no—
498#95—56no—
499#95—51no—
500#95—53no—
501#95—53no—
502C22×C5—23no—
503C22×C5—23no—
504C22×C5—23no—
505C22×C5C24×C411yescharacteristic
506C2×D5—23no—
507C2×D5—23no—
508C2×D5—23no—
509C2×D5—43no—
510C2×D5—43no—
511C2×D5—43no—
512C2×D5—43no—
513C2×D5C22×#4111yescharacteristic
514C2×D5C22×#4111yescharacteristic
515C2×D5C2×H(5,𝔽2)11yescharacteristic
516C2×D5C2×2−1+411yescharacteristic
517C2×D5#58511yescharacteristic
518C2×D5#58511yescharacteristic
519AGL(1,𝔽5)—22no—
520AGL(1,𝔽5)—22no—
521AGL(1,𝔽5)—41no—
522AGL(1,𝔽5)—43no—
523AGL(1,𝔽5)—43no—
524AGL(1,𝔽5)—43no—
525AGL(1,𝔽5)—41no—
526AGL(1,𝔽5)—43no—
527C4×C5—21no—
528C4×C5—23no—
529C4×C5—23no—
530C4×C5—21no—
531C4×C5—21no—
532C4×C5C2×#11716yes—
533Dic5—21no—
534Dic5—23no—
535Dic5—23no—
536Dic5—21no—
537Dic5—21no—
538Dic5C2×#11716yes—
539C24—53no—
540#41—24no—
541#41—1012no—
542#41—1012no—
543#41—104no—
544C2×Q8—54no—
545C2×Q8—54no—
546C2×Q8—53no—
547C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
548C2×D4—56no—
549C2×D4—53no—
550C2×D4—106no—
551C2×D4—106no—
552C2×D4C22×AGL(1,𝔽5)13yes—
553C22×C4—53no—
554C22×C4—51no—
555C22×C4—51no—
556C22×C4—53no—
557C22×C4—56no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—53no—
561C22×C4—51no—
562C22×C4—53no—
563C22×C4—53no—
564C22×C4—53no—
565C22×C4—56no—
566C22×C4—56no—
567C22×C4—51no—
568C22×C4—51no—
569C22×C4—53no—
570C22×C4—53no—
571C22×C4—53no—
572C22×C4—53no—
573C22×C4—106no—
574C22×C4—106no—
575C22×C4—206no—
576C22×C4—206no—
577C22×C4C22×AGL(1,𝔽5)13yes—
578C22×C4C22×AGL(1,𝔽5)16yes—
579C4⋊C4—53no—
580C4⋊C4—53no—
581C4⋊C4—53no—
582C4⋊C4—56no—
583C4⋊C4—56no—
584C4⋊C4—53no—
585C4⋊C4—53no—
586C4⋊C4—51no—
587C4⋊C4—51no—
588C4⋊C4—51no—
589C4⋊C4—106no—
590C4⋊C4—106no—
591C4⋊C4—106no—
592C4⋊C4—106no—
593C4⋊C4—106no—
594C4⋊C4—102no—
595C4⋊C4—206no—
596C4⋊C4—203no—
597C4⋊C4—203no—
598C4⋊C4C22×AGL(1,𝔽5)13yes—
599C4⋊C4C22×AGL(1,𝔽5)13yes—
600C4⋊C4C22×AGL(1,𝔽5)13yes—
601C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
602C22⋊C4—53no—
603C22⋊C4—53no—
604C22⋊C4—53no—
605C22⋊C4—53no—
606C22⋊C4—53no—
607C22⋊C4—53no—
608C22⋊C4—106no—
609C22⋊C4—106no—
610C22⋊C4—206no—
611C22⋊C4—206no—
612C22⋊C4—203no—
613C22⋊C4—203no—
614C22⋊C4C22×AGL(1,𝔽5)13yes—
615C22⋊C4C22×AGL(1,𝔽5)13yes—
616C42—53no—
617C42—53no—
618C42—53no—
619C42—53no—
620C42—53no—
621C42—53no—
622C42—106no—
623C42—106no—
624C42—106no—
625C42—106no—
626C42—106no—
627C42—102no—
628C42—206no—
629C42—203no—
630C42—203no—
631C42C22×AGL(1,𝔽5)13yes—
632C42C22×AGL(1,𝔽5)13yes—
633C2×C5—43no—
634C2×C5C22×#11711yescharacteristic
635C2×C5C4×H(5,𝔽2)11yescharacteristic
636C2×C5C4×2−1+411yescharacteristic
637D5—43no—
638D5#351611yescharacteristic
639D5#351711yescharacteristic
640D5#352211yescharacteristic
641D5#352411yescharacteristic
642C23—51no—
643C23—53no—
644C23—103no—
645C23—103no—
646C23—103no—
647C23—103no—
648C23—103no—
649C23—103no—
650C23C23×AGL(1,𝔽5)13yes—
651Q8—512no—
652Q8#413014yescomplemented
653D4—26no—
654D4—1012no—
655D4—106no—
656C2×C4—26no—
657C2×C4—46no—
658C2×C4—53no—
659C2×C4—56no—
660C2×C4—56no—
661C2×C4—52no—
662C2×C4—52no—
663C2×C4—51no—
664C2×C4—51no—
665C2×C4—53no—
666C2×C4—53no—
667C2×C4—51no—
668C2×C4—106no—
669C2×C4—103no—
670C2×C4—101no—
671C2×C4—101no—
672C2×C4—103no—
673C2×C4—103no—
674C2×C4—101no—
675C2×C4—101no—
676C2×C4—103no—
677C2×C4—101no—
678C2×C4—101no—
679C2×C4—106no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—106no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—103no—
688C2×C4—103no—
689C2×C4—103no—
690C2×C4—103no—
691C2×C4—103no—
692C2×C4—103no—
693C2×C4—103no—
694C2×C4—103no—
695C2×C4—103no—
696C2×C4—103no—
697C2×C4—103no—
698C2×C4—101no—
699C2×C4—101no—
700C2×C4—103no—
701C2×C4—101no—
702C2×C4—101no—
703C2×C4—206no—
704C2×C4—206no—
705C2×C4—206no—
706C2×C4C23×AGL(1,𝔽5)11yescharacteristic
707C2×C4C23×AGL(1,𝔽5)11yescharacteristic
708C2×C4C23×AGL(1,𝔽5)13yes—
709C2×C4C23×AGL(1,𝔽5)13yes—
710C2×C4C23×AGL(1,𝔽5)11yescharacteristic
711C2×C4C23×AGL(1,𝔽5)13yes—
712C5#3426311yescharacteristic, complemented, Sylow
713C22—23no—
714C22—23no—
715C22—23no—
716C22—51no—
717C22—51no—
718C22—51no—
719C22—51no—
720C22—51no—
721C22—51no—
722C22—103no—
723C22—103no—
724C22—103no—
725C22—203no—
726C22—203no—
727C22—203no—
728C22—203no—
729C22C24×AGL(1,𝔽5)11yescharacteristic
730C4—21no—
731C4—23no—
732C4—23no—
733C4—21no—
734C4—21no—
735C4—56no—
736C4—102no—
737C4—102no—
738C4—101no—
739C4—103no—
740C4—103no—
741C4—101no—
742C4—101no—
743C4—203no—
744C4—201no—
745C4—203no—
746C4—203no—
747C4—201no—
748C4—203no—
749C4C2×#413016yes—
750C2—43no—
751C2—51no—
752C2—51no—
753C2—51no—
754C2—51no—
755C2—203no—
756C2C22×#413011yescharacteristic
757C2AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic
758C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#520C4
prime radicalC2×D5×#41C22
cosocleC22×D5C25
hypercenter#520AGL(1,𝔽5)
hypocenterC5#34263
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
4. #10617212C2semidirect
5. Q8×C4⋊AGL(1,𝔽5)C2semidirect
6. #10617208C2semidirect
7. C4×Q8×AGL(1,𝔽5)C2semidirect
8. #10617182C2semidirect
9. #10617181C2semidirect
10. #10617176C2semidirect
11. #10617174C2semidirect
12. #10617130C2semidirect
13. #10617129C2semidirect
14. #10617104C2semidirect
15. #10617103C2semidirect
22. C5×#520C4semidirect
23. #66161C4semidirect
24. #65908C4semidirect
25. #65908C4semidirect
28. #65880C4semidirect
29. #65880C4semidirect
32. #65857C4semidirect
34. #65838C4semidirect
287. #520AGL(1,𝔽5)semidirect
370. C5×Q8#117semidirect
406. Dic10#117semidirect
652. Q8#4130semidirect
712. C5#34263semidirect

Maximal subgroups

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

subgroupindex
D5×#5202
#106175582
#106172122
Q8×C4⋊AGL(1,𝔽5)2
#106172082
C4×Q8×AGL(1,𝔽5)2
#106171822
#106171812
#106171762
#106171742
#106171302
#106171292
#106171042
#106171032
#342635