Finite Group Databasebeta

← #13044357

Subgroups — #13044357

Order 1280.

2016 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#563C211yesmaximal, characteristic
2#10617388C212yesmaximal, complemented
3#10617387C212yesmaximal, complemented
4#10617359C212yesmaximal, complemented
5#10617359C212yesmaximal, complemented
6#10617358C212yesmaximal, complemented
7#10617358C212yesmaximal, complemented
8#10617347C212yesmaximal, complemented
9#10617344C212yesmaximal, complemented
10#10617327C211yesmaximal, characteristic
11#10617324C211yesmaximal, characteristic
12#10617308C211yesmaximal, characteristic
13#10617307C211yesmaximal, characteristic
14#10617304C211yesmaximal, characteristic
15AGL(1,𝔽5)×#123C211yesmaximal, characteristic
16#10617288C212yesmaximal, complemented
17#10617285C212yesmaximal, complemented
18#10617284C212yesmaximal, complemented
19AGL(1,𝔽5)×C22⋊Q8C212yesmaximal, complemented
20C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
21C2×Q8×AGL(1,𝔽5)C2212yes—
22C2×D4×AGL(1,𝔽5)C2211yescharacteristic
23C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C22×C4×AGL(1,𝔽5)C2211yescharacteristic
25C5×#563C411yescharacteristic, complemented
26#66069C412yescomplemented
27D5×C4⋊Q8C2212yes—
28#66046C412yescomplemented
29#66046C412yescomplemented
30D5×#126C2212yes—
31D5×#126C2212yes—
32#66033C412yescomplemented
33D5×#125C2212yes—
34D5×#124C2211yescharacteristic
35#66006C411yescharacteristic, complemented
36D5×#123C2211yescharacteristic
37D5×#123C2211yescharacteristic
38#65985C411yescharacteristic, complemented
39#65985C411yescharacteristic, complemented
40#65980C412yescomplemented
41#65980C412yescomplemented
42D5×C22⋊Q8C2212yes—
43D5×C22⋊Q8C2212yes—
44(C2×AGL(1,𝔽5))⋊Q8C2211yescharacteristic
45(C2×AGL(1,𝔽5))⋊Q8C2212yes—
46(C2×AGL(1,𝔽5))⋊Q8C2212yes—
47(C2×AGL(1,𝔽5))⋊Q8C2212yes—
48(C2×AGL(1,𝔽5))⋊Q8C2212yes—
49#65780C2211yescharacteristic
50#65779C2211yescharacteristic
51#65779C2211yescharacteristic
52#65765C2212yes—
53#65764C2211yescharacteristic
54#65764C2211yescharacteristic
55C4×C22⋊AGL(1,𝔽5)C2212yes—
56#65712C2212yes—
57#65712C2212yes—
58#65712C2212yes—
59#65712C2212yes—
60#65712C2212yes—
61#65712C2212yes—
62#65712C2212yes—
63#65712C2212yes—
64#65711C2212yes—
65#65711C2212yes—
66#65711C2212yes—
67#65711C2212yes—
68#65711C2212yes—
69#65711C2212yes—
70#65711C2212yes—
71#65711C2212yes—
72#65711C2212yes—
73#65711C2212yes—
74#65711C2212yes—
75#65711C2212yes—
76#65711C2212yes—
77#65711C2212yes—
78#65711C2212yes—
79#65711C2212yes—
80C4⋊C4×AGL(1,𝔽5)C2212yes—
81C4⋊C4×AGL(1,𝔽5)C2212yes—
82C4⋊C4×AGL(1,𝔽5)C2212yes—
83C4⋊C4×AGL(1,𝔽5)C2212yes—
84C4⋊C4×AGL(1,𝔽5)C2212yes—
85C4⋊C4×AGL(1,𝔽5)C2212yes—
86C4⋊C4×AGL(1,𝔽5)C2212yes—
87C4⋊C4×AGL(1,𝔽5)C2212yes—
88#65700C2212yes—
89#65700C2212yes—
90#65700C2212yes—
91#65700C2212yes—
92#65700C2212yes—
93#65700C2212yes—
94#65700C2212yes—
95#65700C2212yes—
96#65700C2212yes—
97#65700C2212yes—
98#65699C2211yescharacteristic
99#65699C2212yes—
100#65699C2212yes—
101#65699C2212yes—
102#65699C2211yescharacteristic
103#65699C2212yes—
104C22⋊C4×AGL(1,𝔽5)C2211yescharacteristic
105C22⋊C4×AGL(1,𝔽5)C2212yes—
106C22⋊C4×AGL(1,𝔽5)C2211yescharacteristic
107C22⋊C4×AGL(1,𝔽5)C2212yes—
108C22⋊C4×AGL(1,𝔽5)C2212yes—
109C22⋊C4×AGL(1,𝔽5)C2212yes—
110#65689C2212yes—
111#65688C2211yescharacteristic
112C4×C4⋊AGL(1,𝔽5)C2212yes—
113C4×C4⋊AGL(1,𝔽5)C2212yes—
114#65686C2212yes—
115#65686C2211yescharacteristic
116#65686C2212yes—
117#34514—51nomaximal, Sylow
118C23×AGL(1,𝔽5)C2311yescharacteristic
119C23×AGL(1,𝔽5)C2311yescharacteristic
120C23×AGL(1,𝔽5)C2311yescharacteristic
121C23×AGL(1,𝔽5)C2311yescharacteristic
122C2×Q8×D5C2311yescharacteristic
123C2×Q8×D5C2312yes—
124C2×D4×D5C2311yescharacteristic
125C22×C4×D5C2311yescharacteristic
126C22×C4×D5C2311yescharacteristic
127C2×C22⋊AGL(1,𝔽5)C2312yes—
128C2×C22⋊AGL(1,𝔽5)C2312yes—
129C2×C22⋊AGL(1,𝔽5)C2312yes—
130C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
131C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
132C2×C22⋊AGL(1,𝔽5)C2312yes—
133C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
134C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
135Q8×AGL(1,𝔽5)—44no—
136Q8×AGL(1,𝔽5)—42no—
137D4×AGL(1,𝔽5)—42no—
138C2×C4⋊AGL(1,𝔽5)—42no—
139C2×C4⋊AGL(1,𝔽5)C2312yes—
140C2×C4⋊AGL(1,𝔽5)C2312yes—
141C2×C4⋊AGL(1,𝔽5)C2312yes—
142C2×C4⋊AGL(1,𝔽5)C2312yes—
143C2×C4⋊AGL(1,𝔽5)C2312yes—
144C2×C4⋊AGL(1,𝔽5)C2312yes—
145C2×C4⋊AGL(1,𝔽5)C2312yes—
146C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
147C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
148C2×C4⋊AGL(1,𝔽5)C2312yes—
149C2×C4⋊AGL(1,𝔽5)C2312yes—
150C2×C4⋊AGL(1,𝔽5)C2312yes—
151C2×C4⋊AGL(1,𝔽5)C2312yes—
152C2×C4⋊AGL(1,𝔽5)C2312yes—
153C2×C4×AGL(1,𝔽5)—42no—
154C2×C4×AGL(1,𝔽5)C2312yes—
155C2×C4×AGL(1,𝔽5)C2312yes—
156C2×C4×AGL(1,𝔽5)C2311yescharacteristic
157C2×C4×AGL(1,𝔽5)C2312yes—
158C2×C4×AGL(1,𝔽5)C2312yes—
159C2×C4×AGL(1,𝔽5)C2312yes—
160C2×C4×AGL(1,𝔽5)C2311yescharacteristic
161C2×C4×AGL(1,𝔽5)C2312yes—
162C2×C4×AGL(1,𝔽5)C2312yes—
163C2×C4×AGL(1,𝔽5)C2312yes—
164C2×C4×AGL(1,𝔽5)C2312yes—
165C2×C4×AGL(1,𝔽5)C2312yes—
166C2×C4×AGL(1,𝔽5)C2312yes—
167C2×C4×AGL(1,𝔽5)C2312yes—
168C5×C4⋊Q8C2×C412yescomplemented
169C5×#126C2×C412yescomplemented
170C5×#126C2×C412yescomplemented
171C5×#125C2×C412yescomplemented
172C5×#124C2×C411yescharacteristic
173C5×#123C2×C411yescharacteristic
174C5×#123C2×C411yescharacteristic
175C5×C22⋊Q8C2×C412yescomplemented
176C5×C22⋊Q8C2×C412yescomplemented
177#4093C2×C411yescharacteristic
178#4092C2×C412yescomplemented
179#4092C2×C412yescomplemented
180#4090C2×C412yescomplemented
181#4090C2×C412yescomplemented
182#4082C2×C411yescharacteristic
183#4081C2×C411yescharacteristic
184#4081C2×C411yescharacteristic
185#4075C2×C411yescharacteristic
186#4075C2×C411yescharacteristic
187#4070C2×C412yescomplemented
188#4070C2×C412yescomplemented
189#4044C2×C412yescomplemented
190#4044C2×C412yescomplemented
191#4044C2×C412yescomplemented
192#4044C2×C412yescomplemented
193#4044C2×C412yescomplemented
194#4044C2×C412yescomplemented
195#4043C2×C412yescomplemented
196#4043C2×C412yescomplemented
197#4042C2×C412yescomplemented
198#4042C2×C412yescomplemented
199#4042C2×C412yescomplemented
200#4042C2×C412yescomplemented
201#4040C2×C412yes—
202#4040C2×C412yes—
203D5×C4⋊C4C2312yes—
204D5×C4⋊C4C2312yes—
205D5×C4⋊C4C2312yes—
206D5×C4⋊C4C2312yes—
207D5×C4⋊C4C2312yes—
208D5×C4⋊C4C2312yes—
209D5×C4⋊C4C2312yes—
210D5×C4⋊C4C2312yes—
211#4036C2×C412yescomplemented
212#4036C2×C412yescomplemented
213#4035C2×C412yescomplemented
214#4035C2×C412yescomplemented
215#4035C2×C412yescomplemented
216#4035C2×C412yescomplemented
217#4034C2×C412yescomplemented
218#4034C2×C412yescomplemented
219#4034C2×C412yescomplemented
220#4034C2×C412yescomplemented
221#4032C2×C411yescharacteristic
222#4032C2×C411yescharacteristic
223#4031C2×C412yes—
224#4031C2×C412yes—
225#4029C2×C412yes—
226#4029C2×C412yes—
227D5×C22⋊C4C2312yes—
228D5×C22⋊C4C2312yes—
229D5×C22⋊C4C2312yes—
230D5×C22⋊C4C2312yes—
231D5×C22⋊C4C2311yescharacteristic
232D5×C22⋊C4C2311yescharacteristic
233#4025C2×C412yescomplemented
234#4025C2×C412yescomplemented
235#4025C2×C412yescomplemented
236#4025C2×C412yescomplemented
237#4025C2×C412yescomplemented
238#4025C2×C412yescomplemented
239#4024C2×C412yescomplemented
240#4024C2×C412yescomplemented
241#4024C2×C412yescomplemented
242#4024C2×C412yescomplemented
243#4022C2×C412yescomplemented
244#4022C2×C412yescomplemented
245#4021C2×C411yescharacteristic
246C42×D5C2312yes—
247C42×D5C2311yescharacteristic
248#4016C2×C412yescomplemented
249#4015C2×C412yescomplemented
250(C2×AGL(1,𝔽5))⋊C4C2312yes—
251(C2×AGL(1,𝔽5))⋊C4C2312yes—
252(C2×AGL(1,𝔽5))⋊C4C2312yes—
253(C2×AGL(1,𝔽5))⋊C4C2312yes—
254(C2×AGL(1,𝔽5))⋊C4C2312yes—
255(C2×AGL(1,𝔽5))⋊C4C2312yes—
256(C2×AGL(1,𝔽5))⋊C4C2312yes—
257(C2×AGL(1,𝔽5))⋊C4C2312yes—
258(C2×AGL(1,𝔽5))⋊C4C2312yes—
259(C2×AGL(1,𝔽5))⋊C4C2312yes—
260(C2×AGL(1,𝔽5))⋊C4C2312yes—
261(C2×AGL(1,𝔽5))⋊C4C2312yes—
262(C2×AGL(1,𝔽5))⋊C4C2312yes—
263(C2×AGL(1,𝔽5))⋊C4C2312yes—
264(C2×AGL(1,𝔽5))⋊C4C2312yes—
265(C2×AGL(1,𝔽5))⋊C4C2312yes—
266(C2×AGL(1,𝔽5))⋊C4C2312yes—
267(C2×AGL(1,𝔽5))⋊C4C2312yes—
268(C2×AGL(1,𝔽5))⋊C4C2312yes—
269(C2×AGL(1,𝔽5))⋊C4C2312yes—
270(C2×AGL(1,𝔽5))⋊C4C2312yes—
271(C2×AGL(1,𝔽5))⋊C4C2312yes—
272(C2×AGL(1,𝔽5))⋊C4C2312yes—
273(C2×AGL(1,𝔽5))⋊C4C2312yes—
274(C2×AGL(1,𝔽5))⋊C4C2312yes—
275(C2×AGL(1,𝔽5))⋊C4C2312yes—
276C2×#563—51no—
277#2378—52no—
278#2376—51no—
279#2374—51no—
280#2373—52no—
281#2373—52no—
282#2372—51no—
283#2371—52no—
284#2365—52no—
285#2360—52no—
286#2334—52no—
287#2334—52no—
288#2332—52no—
289#2331—52no—
290#2330—52no—
291#2326—51no—
292#2322—51no—
293C4×C22⋊Q8—52no—
294C4×#123—51no—
295C23×D5C2411yescharacteristic
296C23×D5C2411yescharacteristic
297C22×AGL(1,𝔽5)—22no—
298C22×AGL(1,𝔽5)—24no—
299C22×AGL(1,𝔽5)—22no—
300C22×AGL(1,𝔽5)—41no—
301C22×AGL(1,𝔽5)—42no—
302C22×AGL(1,𝔽5)—41no—
303C22×AGL(1,𝔽5)—42no—
304C22×AGL(1,𝔽5)—42no—
305C22×AGL(1,𝔽5)C2412yes—
306C22×AGL(1,𝔽5)C2411yescharacteristic
307C22×AGL(1,𝔽5)C2412yes—
308C22×AGL(1,𝔽5)C2412yes—
309C22×AGL(1,𝔽5)C2412yes—
310C22×AGL(1,𝔽5)C2411yescharacteristic
311C22×AGL(1,𝔽5)C2412yes—
312C22×AGL(1,𝔽5)C2411yescharacteristic
313C22×AGL(1,𝔽5)C2411yescharacteristic
314C22×AGL(1,𝔽5)C2412yes—
315C2×C5×Q8C22×C412yes—
316C2×C5×Q8C22×C411yescharacteristic
317C2×C5×D4C22×C411yescharacteristic
318C22×C4×C5C22×C411yescharacteristic
319C22×C4×C5C22×C411yescharacteristic
320C2×C22⋊D5C22×C411yescharacteristic
321C2×C22⋊D5C22×C411yescharacteristic
322C22×Dic5C22×C411yescharacteristic
323C22×Dic5C22×C411yescharacteristic
324Q8×D5—42no—
325Q8×D5—41no—
326Q8×D5—42no—
327Q8×D5—41no—
328D4×D5—41no—
329D4×D5—41no—
330C2×D20C22×C411yescharacteristic
331C2×C4×D5—41no—
332C2×C4×D5—41no—
333C2×C4×D5—41no—
334C2×C4×D5—41no—
335C2×C4×D5C22×C412yes—
336C2×C4×D5C22×C412yes—
337C2×C4×D5C2412yes—
338C2×C4×D5C2412yes—
339C2×C4×D5C2411yescharacteristic
340C2×C4×D5C2412yes—
341C2×C4×D5C2412yes—
342C2×C4×D5C2412yes—
343C2×C4×D5C2412yes—
344C2×Dic10C22×C412yes—
345C2×Dic10C22×C412yes—
346C2×Dic10C22×C411yescharacteristic
347C2×Dic10C22×C412yes—
348C2×Dic10C22×C412yes—
349C22⋊AGL(1,𝔽5)—24no—
350C22⋊AGL(1,𝔽5)—41no—
351C22⋊AGL(1,𝔽5)—41no—
352C22⋊AGL(1,𝔽5)—42no—
353C22⋊AGL(1,𝔽5)—41no—
354C22⋊AGL(1,𝔽5)—42no—
355C22⋊AGL(1,𝔽5)—41no—
356C22⋊AGL(1,𝔽5)—42no—
357C4⋊AGL(1,𝔽5)—24no—
358C4⋊AGL(1,𝔽5)—24no—
359C4⋊AGL(1,𝔽5)—24no—
360C4⋊AGL(1,𝔽5)—42no—
361C4⋊AGL(1,𝔽5)—42no—
362C4⋊AGL(1,𝔽5)—42no—
363C4⋊AGL(1,𝔽5)—42no—
364C4⋊AGL(1,𝔽5)—42no—
365C4⋊AGL(1,𝔽5)—42no—
366C4⋊AGL(1,𝔽5)—42no—
367C4⋊AGL(1,𝔽5)—42no—
368C4⋊AGL(1,𝔽5)—41no—
369C4⋊AGL(1,𝔽5)—42no—
370C4⋊AGL(1,𝔽5)—41no—
371C4×AGL(1,𝔽5)—24no—
372C4×AGL(1,𝔽5)—22no—
373C4×AGL(1,𝔽5)—24no—
374C4×AGL(1,𝔽5)—24no—
375C4×AGL(1,𝔽5)—42no—
376C4×AGL(1,𝔽5)—42no—
377C4×AGL(1,𝔽5)—42no—
378C4×AGL(1,𝔽5)—42no—
379C4×AGL(1,𝔽5)—42no—
380C4×AGL(1,𝔽5)—42no—
381C4×AGL(1,𝔽5)—41no—
382C4×AGL(1,𝔽5)—42no—
383C4×AGL(1,𝔽5)—42no—
384C4×AGL(1,𝔽5)—42no—
385C5×C4⋊C4C22×C412yes—
386C5×C4⋊C4C22×C412yes—
387C5×C4⋊C4C22×C412yes—
388C5×C4⋊C4C22×C412yes—
389C5×C4⋊C4C22×C412yes—
390C5×C4⋊C4C22×C412yes—
391C5×C4⋊C4C22×C412yes—
392C5×C4⋊C4C22×C412yes—
393C5×C22⋊C4C22×C412yes—
394C5×C22⋊C4C22×C412yes—
395C5×C22⋊C4C22×C412yes—
396C5×C22⋊C4C22×C412yes—
397C5×C22⋊C4C22×C411yescharacteristic
398C5×C22⋊C4C22×C411yescharacteristic
399C42×C5C22×C411yescharacteristic
400C42×C5C22×C412yes—
401C22⋊Dic5C22×C412yes—
402C22⋊Dic5C22×C412yes—
403C22⋊Dic5C22×C412yes—
404C22⋊Dic5C22×C412yes—
405C22⋊Dic5C22×C411yescharacteristic
406C22⋊Dic5C22×C411yescharacteristic
407#685C22×C412yes—
408#685C22×C412yes—
409#685C22×C412yes—
410#685C22×C412yes—
411#685C22×C412yes—
412#685C22×C412yes—
413#685C22×C412yes—
414#685C22×C412yes—
415#685C22×C412yes—
416#685C22×C412yes—
417C4⋊Dic5C22×C412yes—
418C4⋊Dic5C22×C412yes—
419C4⋊Dic5C22×C412yes—
420C4⋊Dic5C22×C412yes—
421C4⋊Dic5C22×C412yes—
422C4⋊Dic5C22×C412yes—
423C4⋊Dic5C22×C412yes—
424C4⋊Dic5C22×C412yes—
425#683C22×C412yes—
426#683C22×C412yes—
427#683C22×C412yes—
428#683C22×C412yes—
429#683C22×C412yes—
430#683C22×C412yes—
431#683C22×C412yes—
432#683C22×C412yes—
433#683C22×C412yes—
434#683C22×C412yes—
435#683C22×C412yes—
436#683C22×C412yes—
437#683C22×C412yes—
438#683C22×C412yes—
439#683C22×C412yes—
440#683C22×C412yes—
441C4×Dic5C22×C412yes—
442C4×Dic5C22×C412yes—
443C4×Dic5C22×C412yes—
444C4×Dic5C22×C412yes—
445C4×Dic5C22×C411yescharacteristic
446#563—52no—
447#563—52no—
448#563—52no—
449#563—52no—
450#563—51no—
451#563—51no—
452#563—51no—
453#563—52no—
454#563—52no—
455#563AGL(1,𝔽5)11yescharacteristic, complemented
456C2×C4⋊Q8—52no—
457C2×#126—52no—
458C2×#126—52no—
459C2×#125—52no—
460C2×#124—51no—
461C2×#123—51no—
462C2×#123—51no—
463C2×C22⋊Q8—52no—
464C2×C22⋊Q8—52no—
465C2×C4×Q8—51no—
466C2×C4×Q8—52no—
467C2×C4×D4—51no—
468C22×C4⋊C4—51no—
469C22×C42—51no—
470#391—51no—
471#391—52no—
472#391—52no—
473#391—52no—
474#391—52no—
475#390—51no—
476#389—52no—
477#389—52no—
478#389—52no—
479#389—52no—
480#389—52no—
481#389—52no—
482#389—52no—
483#389—52no—
484#388—52no—
485#388—52no—
486#388—52no—
487#388—52no—
488#388—52no—
489#388—52no—
490#388—52no—
491#388—52no—
492#388—52no—
493#388—52no—
494#387—52no—
495#387—52no—
496#387—52no—
497#387—52no—
498#387—52no—
499#387—52no—
500#387—52no—
501#387—52no—
502#387—52no—
503#387—52no—
504#387—52no—
505#387—52no—
506#387—52no—
507#387—52no—
508#387—52no—
509#387—52no—
510#386—51no—
511#386—51no—
512#385—51no—
513#385—52no—
514#385—52no—
515#385—52no—
516#385—52no—
517#385—51no—
518#384—51no—
519#382—52no—
520#381—51no—
521#381—51no—
522#380—52no—
523C4×C4⋊C4—52no—
524C4×C4⋊C4—52no—
525C4×C4⋊C4—52no—
526C4×C4⋊C4—52no—
527C4×C4⋊C4—52no—
528C4×C4⋊C4—52no—
529C4×C4⋊C4—52no—
530C4×C4⋊C4—52no—
531C4×C4⋊C4—52no—
532C4×C4⋊C4—52no—
533C4×C22⋊C4—51no—
534C4×C22⋊C4—52no—
535C4×C22⋊C4—51no—
536C4×C22⋊C4—52no—
537C4×C22⋊C4—52no—
538C4×C22⋊C4—52no—
539C4×C22⋊C4—52no—
540#376—51no—
541#376—52no—
542#376—52no—
543C23×C5C23×C411yescharacteristic
544C23×C5C23×C411yescharacteristic
545C22×D5—21no—
546C22×D5—21no—
547C22×D5—22no—
548C22×D5—22no—
549C22×D5—22no—
550C22×D5—21no—
551C22×D5—21no—
552C22×D5—22no—
553C22×D5C23×C411yescharacteristic
554C22×D5C23×C411yescharacteristic
555C22×D5C2511yescharacteristic
556C2×AGL(1,𝔽5)—22no—
557C2×AGL(1,𝔽5)—22no—
558C2×AGL(1,𝔽5)—22no—
559C2×AGL(1,𝔽5)—21no—
560C2×AGL(1,𝔽5)—22no—
561C2×AGL(1,𝔽5)—21no—
562C2×AGL(1,𝔽5)—22no—
563C2×AGL(1,𝔽5)—21no—
564C2×AGL(1,𝔽5)—22no—
565C2×AGL(1,𝔽5)—22no—
566C2×AGL(1,𝔽5)—22no—
567C2×AGL(1,𝔽5)—22no—
568C2×AGL(1,𝔽5)—22no—
569C2×AGL(1,𝔽5)—22no—
570C2×AGL(1,𝔽5)—22no—
571C2×AGL(1,𝔽5)—22no—
572C2×AGL(1,𝔽5)—22no—
573C2×AGL(1,𝔽5)—22no—
574C2×AGL(1,𝔽5)—22no—
575C2×AGL(1,𝔽5)—22no—
576C2×AGL(1,𝔽5)—22no—
577C2×AGL(1,𝔽5)—22no—
578C2×AGL(1,𝔽5)—22no—
579C2×AGL(1,𝔽5)—22no—
580C2×AGL(1,𝔽5)—44no—
581C2×AGL(1,𝔽5)—44no—
582C2×AGL(1,𝔽5)—82no—
583C2×AGL(1,𝔽5)—82no—
584C2×AGL(1,𝔽5)H(5,𝔽2)12yes—
585C2×AGL(1,𝔽5)2−1+414yes—
586C5×Q8—41no—
587C5×Q8—42no—
588C5×D4—41no—
589C2×C4×C5—41no—
590C2×C4×C5—41no—
591C2×C4×C5C23×C411yescharacteristic
592C2×C4×C5C23×C412yes—
593C2×C4×C5C23×C412yes—
594C2×C4×C5C23×C412yes—
595C2×C4×C5C23×C412yes—
596C2×C4×C5C23×C412yes—
597C2×C4×C5C23×C412yes—
598C22⋊D5—41no—
599C22⋊D5—41no—
600C2×Dic5—41no—
601C2×Dic5—41no—
602C2×Dic5C23×C412yes—
603C2×Dic5C23×C412yes—
604C2×Dic5C23×C412yes—
605C2×Dic5C23×C411yescharacteristic
606C2×Dic5C23×C412yes—
607C2×Dic5C23×C412yes—
608C2×Dic5C23×C412yes—
609D20—41no—
610C4×D5—22no—
611C4×D5—21no—
612C4×D5—22no—
613C4×D5—22no—
614C4×D5—22no—
615C4×D5—22no—
616C4×D5—22no—
617C4×D5—22no—
618C4×D5—22no—
619C4×D5—22no—
620C4×D5—22no—
621C4×D5—21no—
622C4×D5—22no—
623C4×D5—22no—
624C4×D5—42no—
625C4×D5—42no—
626Dic10—41no—
627Dic10—42no—
628Dic10—42no—
629Dic10—42no—
630Dic10—42no—
631C22×Q8—52no—
632C22×Q8—51no—
633C22×D4—51no—
634C23×C4—51no—
635C23×C4—51no—
636C23×C4—51no—
637C23×C4—51no—
638C23×C4—51no—
639C23×C4—51no—
640C4⋊Q8—52no—
641C4⋊Q8—52no—
642C4⋊Q8—52no—
643C4⋊Q8—52no—
644C4⋊Q8—52no—
645C4⋊Q8—52no—
646C4⋊Q8—52no—
647C4⋊Q8C2×AGL(1,𝔽5)12yescomplemented
648#126—52no—
649#126—52no—
650#126—52no—
651#126—52no—
652#126—52no—
653#126—52no—
654#126—52no—
655#126—52no—
656#126—52no—
657#126—52no—
658#126—52no—
659#126—52no—
660#126—52no—
661#126—52no—
662#126C2×AGL(1,𝔽5)12yescomplemented
663#126C2×AGL(1,𝔽5)12yescomplemented
664#125—52no—
665#125—52no—
666#125—52no—
667#125—52no—
668#125—52no—
669#125—52no—
670#125—52no—
671#125C2×AGL(1,𝔽5)12yescomplemented
672#124—51no—
673#124—51no—
674#124—52no—
675#124—52no—
676#124—51no—
677#124C2×AGL(1,𝔽5)11yescharacteristic
678#123—51no—
679#123—51no—
680#123—51no—
681#123—51no—
682#123—52no—
683#123—52no—
684#123—52no—
685#123—52no—
686#123—51no—
687#123—51no—
688#123C2×AGL(1,𝔽5)11yescharacteristic
689#123C2×AGL(1,𝔽5)11yescharacteristic
690C22⋊Q8—52no—
691C22⋊Q8—52no—
692C22⋊Q8—52no—
693C22⋊Q8—52no—
694C22⋊Q8—52no—
695C22⋊Q8—52no—
696C22⋊Q8—52no—
697C22⋊Q8—52no—
698C22⋊Q8—52no—
699C22⋊Q8—52no—
700C22⋊Q8—52no—
701C22⋊Q8—52no—
702C22⋊Q8—52no—
703C22⋊Q8—52no—
704C22⋊Q8C2×AGL(1,𝔽5)12yescomplemented
705C22⋊Q8C2×AGL(1,𝔽5)12yescomplemented
706C4×Q8—204no—
707C4×Q8—202no—
708C4×D4—202no—
709C2×C4⋊C4—52no—
710C2×C4⋊C4—52no—
711C2×C4⋊C4—52no—
712C2×C4⋊C4—52no—
713C2×C4⋊C4—52no—
714C2×C4⋊C4—52no—
715C2×C4⋊C4—52no—
716C2×C4⋊C4—52no—
717C2×C4⋊C4—52no—
718C2×C4⋊C4—52no—
719C2×C4⋊C4—52no—
720C2×C4⋊C4—52no—
721C2×C4⋊C4—51no—
722C2×C4⋊C4—52no—
723C2×C4⋊C4—51no—
724C2×C4⋊C4—52no—
725C2×C4⋊C4—52no—
726C2×C4⋊C4—52no—
727C2×C4⋊C4—52no—
728C2×C4⋊C4—52no—
729C2×C4⋊C4—52no—
730C2×C4⋊C4—52no—
731C2×C4⋊C4—202no—
732C2×C22⋊C4—52no—
733C2×C22⋊C4—52no—
734C2×C22⋊C4—52no—
735C2×C22⋊C4—52no—
736C2×C22⋊C4—51no—
737C2×C22⋊C4—51no—
738C2×C22⋊C4—52no—
739C2×C22⋊C4—51no—
740C2×C22⋊C4—51no—
741C2×C22⋊C4—52no—
742C2×C22⋊C4—52no—
743C2×C22⋊C4—51no—
744C2×C22⋊C4—51no—
745C2×C22⋊C4—52no—
746C2×C42—51no—
747C2×C42—52no—
748C2×C42—51no—
749C2×C42—52no—
750C2×C42—52no—
751C2×C42—52no—
752C2×C42—52no—
753C2×C42—52no—
754C2×C42—52no—
755C2×C42—52no—
756C2×C42—52no—
757C2×C42—51no—
758C2×C42—52no—
759C2×C42—52no—
760C2×C42—52no—
761C2×C42—52no—
762C2×C42—202no—
763#95—52no—
764#95—52no—
765#95—52no—
766#95—52no—
767#95—52no—
768#95—52no—
769#95—52no—
770#95—52no—
771#95—52no—
772#95—52no—
773#95—52no—
774#95—52no—
775#95—52no—
776#95—52no—
777#95—52no—
778#95—52no—
779#95—52no—
780#95—52no—
781#95—52no—
782#95—52no—
783#95—52no—
784#95—52no—
785#95—52no—
786#95—52no—
787#95—52no—
788#95—52no—
789C22×C5—21no—
790C22×C5—21no—
791C22×C5—22no—
792C22×C5—22no—
793C22×C5C24×C411yescharacteristic
794C2×D5—21no—
795C2×D5—21no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—41no—
799C2×D5—41no—
800C2×D5—41no—
801C2×D5—41no—
802C2×D5—42no—
803C2×D5—42no—
804C2×D5C2×H(5,𝔽2)11yescharacteristic
805C2×D5C2×2−1+412yes—
806C2×D5#58512yes—
807C2×D5#58511yescharacteristic
808AGL(1,𝔽5)—22no—
809AGL(1,𝔽5)—24no—
810AGL(1,𝔽5)—42no—
811AGL(1,𝔽5)—41no—
812AGL(1,𝔽5)—42no—
813AGL(1,𝔽5)—41no—
814AGL(1,𝔽5)—41no—
815AGL(1,𝔽5)—42no—
816AGL(1,𝔽5)—42no—
817AGL(1,𝔽5)—42no—
818C4×C5—22no—
819C4×C5—22no—
820C4×C5—22no—
821C4×C5—21no—
822C4×C5—22no—
823C4×C5—22no—
824C4×C5—22no—
825Dic5—22no—
826Dic5—22no—
827Dic5—22no—
828Dic5—21no—
829Dic5—22no—
830Dic5—22no—
831Dic5—22no—
832C24—51no—
833C24—51no—
834C2×Q8—52no—
835C2×Q8—52no—
836C2×Q8—52no—
837C2×Q8—51no—
838C2×Q8—52no—
839C2×Q8—202no—
840C2×Q8—201no—
841C2×Q8—202no—
842C2×Q8—201no—
843C2×Q8C22×AGL(1,𝔽5)12yes—
844C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
845C2×D4—51no—
846C2×D4—51no—
847C2×D4—51no—
848C2×D4—201no—
849C2×D4—201no—
850C2×D4C22×AGL(1,𝔽5)11yescharacteristic
851C22×C4—52no—
852C22×C4—51no—
853C22×C4—51no—
854C22×C4—51no—
855C22×C4—52no—
856C22×C4—52no—
857C22×C4—52no—
858C22×C4—52no—
859C22×C4—51no—
860C22×C4—52no—
861C22×C4—52no—
862C22×C4—52no—
863C22×C4—52no—
864C22×C4—51no—
865C22×C4—52no—
866C22×C4—52no—
867C22×C4—52no—
868C22×C4—51no—
869C22×C4—52no—
870C22×C4—51no—
871C22×C4—52no—
872C22×C4—102no—
873C22×C4—104no—
874C22×C4—102no—
875C22×C4—201no—
876C22×C4—201no—
877C22×C4—201no—
878C22×C4—201no—
879C22×C4—201no—
880C22×C4—202no—
881C22×C4—201no—
882C22×C4—202no—
883C22×C4—202no—
884C22×C4C22×AGL(1,𝔽5)11yescharacteristic
885C22×C4C22×AGL(1,𝔽5)11yescharacteristic
886C4⋊C4—52no—
887C4⋊C4—52no—
888C4⋊C4—52no—
889C4⋊C4—52no—
890C4⋊C4—52no—
891C4⋊C4—52no—
892C4⋊C4—52no—
893C4⋊C4—52no—
894C4⋊C4—52no—
895C4⋊C4—52no—
896C4⋊C4—52no—
897C4⋊C4—52no—
898C4⋊C4—52no—
899C4⋊C4—52no—
900C4⋊C4—52no—
901C4⋊C4—52no—
902C4⋊C4—52no—
903C4⋊C4—52no—
904C4⋊C4—52no—
905C4⋊C4—52no—
906C4⋊C4—52no—
907C4⋊C4—52no—
908C4⋊C4—52no—
909C4⋊C4—52no—
910C4⋊C4—104no—
911C4⋊C4—104no—
912C4⋊C4—104no—
913C4⋊C4—202no—
914C4⋊C4—201no—
915C4⋊C4—202no—
916C4⋊C4—201no—
917C4⋊C4—202no—
918C4⋊C4—202no—
919C4⋊C4—202no—
920C4⋊C4—202no—
921C4⋊C4—202no—
922C4⋊C4—202no—
923C4⋊C4—202no—
924C4⋊C4C22×AGL(1,𝔽5)12yes—
925C4⋊C4C22×AGL(1,𝔽5)12yes—
926C4⋊C4C22×AGL(1,𝔽5)12yes—
927C4⋊C4C22×AGL(1,𝔽5)12yes—
928C4⋊C4C22×AGL(1,𝔽5)12yes—
929C4⋊C4C22×AGL(1,𝔽5)12yes—
930C4⋊C4C22×AGL(1,𝔽5)12yes—
931C4⋊C4C22×AGL(1,𝔽5)12yes—
932C22⋊C4—52no—
933C22⋊C4—52no—
934C22⋊C4—52no—
935C22⋊C4—52no—
936C22⋊C4—51no—
937C22⋊C4—51no—
938C22⋊C4—52no—
939C22⋊C4—52no—
940C22⋊C4—52no—
941C22⋊C4—52no—
942C22⋊C4—52no—
943C22⋊C4—52no—
944C22⋊C4—52no—
945C22⋊C4—52no—
946C22⋊C4—52no—
947C22⋊C4—52no—
948C22⋊C4—104no—
949C22⋊C4—201no—
950C22⋊C4—201no—
951C22⋊C4—202no—
952C22⋊C4—201no—
953C22⋊C4—202no—
954C22⋊C4—202no—
955C22⋊C4—201no—
956C22⋊C4C22×AGL(1,𝔽5)12yes—
957C22⋊C4C22×AGL(1,𝔽5)12yes—
958C22⋊C4C22×AGL(1,𝔽5)12yes—
959C22⋊C4C22×AGL(1,𝔽5)12yes—
960C22⋊C4C22×AGL(1,𝔽5)11yescharacteristic
961C22⋊C4C22×AGL(1,𝔽5)11yescharacteristic
962C42—51no—
963C42—52no—
964C42—52no—
965C42—52no—
966C42—52no—
967C42—104no—
968C42—102no—
969C42—104no—
970C42—104no—
971C42—202no—
972C42—202no—
973C42—202no—
974C42—202no—
975C42—202no—
976C42—202no—
977C42—202no—
978C42—202no—
979C42—202no—
980C42—201no—
981C42C22×AGL(1,𝔽5)11yescharacteristic
982C42C22×AGL(1,𝔽5)12yes—
983C2×C5—41no—
984C2×C5—41no—
985C2×C5C4×H(5,𝔽2)11yescharacteristic
986C2×C5C4×2−1+412yes—
987D5—41no—
988D5—41no—
989D5#353311yescharacteristic
990D5#353811yescharacteristic
991D5#356512yes—
992C23—51no—
993C23—51no—
994C23—51no—
995C23—102no—
996C23—102no—
997C23—101no—
998C23—101no—
999C23—102no—
1000C23—101no—
1001C23—101no—
1002C23—102no—
1003C23C23×AGL(1,𝔽5)11yescharacteristic
1004C23C23×AGL(1,𝔽5)11yescharacteristic
1005Q8—42no—
1006Q8—41no—
1007Q8—202no—
1008Q8—202no—
1009Q8—201no—
1010Q8—202no—
1011Q8—202no—
1012D4—41no—
1013D4—201no—
1014D4—201no—
1015D4—201no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—52no—
1019C2×C4—54no—
1020C2×C4—52no—
1021C2×C4—52no—
1022C2×C4—52no—
1023C2×C4—52no—
1024C2×C4—51no—
1025C2×C4—52no—
1026C2×C4—52no—
1027C2×C4—102no—
1028C2×C4—101no—
1029C2×C4—102no—
1030C2×C4—102no—
1031C2×C4—102no—
1032C2×C4—102no—
1033C2×C4—102no—
1034C2×C4—102no—
1035C2×C4—102no—
1036C2×C4—102no—
1037C2×C4—101no—
1038C2×C4—102no—
1039C2×C4—102no—
1040C2×C4—102no—
1041C2×C4—102no—
1042C2×C4—102no—
1043C2×C4—102no—
1044C2×C4—101no—
1045C2×C4—102no—
1046C2×C4—102no—
1047C2×C4—101no—
1048C2×C4—102no—
1049C2×C4—102no—
1050C2×C4—102no—
1051C2×C4—102no—
1052C2×C4—102no—
1053C2×C4—102no—
1054C2×C4—102no—
1055C2×C4—102no—
1056C2×C4—102no—
1057C2×C4—102no—
1058C2×C4—102no—
1059C2×C4—101no—
1060C2×C4—102no—
1061C2×C4—102no—
1062C2×C4—102no—
1063C2×C4—102no—
1064C2×C4—102no—
1065C2×C4—202no—
1066C2×C4—202no—
1067C2×C4—201no—
1068C2×C4—201no—
1069C2×C4—204no—
1070C2×C4—204no—
1071C2×C4—402no—
1072C2×C4—402no—
1073C2×C4C23×AGL(1,𝔽5)12yes—
1074C2×C4C23×AGL(1,𝔽5)12yes—
1075C2×C4C23×AGL(1,𝔽5)12yes—
1076C2×C4C23×AGL(1,𝔽5)12yes—
1077C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1078C2×C4C23×AGL(1,𝔽5)12yes—
1079C2×C4C23×AGL(1,𝔽5)12yes—
1080C5#3451411yescharacteristic, complemented, Sylow
1081C22—21no—
1082C22—21no—
1083C22—22no—
1084C22—22no—
1085C22—51no—
1086C22—51no—
1087C22—52no—
1088C22—52no—
1089C22—101no—
1090C22—101no—
1091C22—102no—
1092C22—102no—
1093C22—201no—
1094C22—201no—
1095C22—201no—
1096C22—201no—
1097C22—202no—
1098C22—202no—
1099C22C24×AGL(1,𝔽5)11yescharacteristic
1100C4—22no—
1101C4—22no—
1102C4—21no—
1103C4—22no—
1104C4—22no—
1105C4—22no—
1106C4—22no—
1107C4—102no—
1108C4—104no—
1109C4—102no—
1110C4—102no—
1111C4—101no—
1112C4—102no—
1113C4—102no—
1114C4—102no—
1115C4—102no—
1116C4—201no—
1117C4—202no—
1118C4—201no—
1119C4—201no—
1120C4—202no—
1121C4—202no—
1122C4—202no—
1123C4—202no—
1124C2—41no—
1125C2—41no—
1126C2—51no—
1127C2—51no—
1128C2—52no—
1129C2—201no—
1130C2—201no—
1131C2AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic
1132C2AGL(1,𝔽5)×2−1+412yes—
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#563C4
prime radicalC2×D4×D5C23
cosocleC22×D5C25
hypercenter#563AGL(1,𝔽5)
hypocenterC5#34514
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #10617388C2semidirect
3. #10617387C2semidirect
4. #10617359C2semidirect
5. #10617359C2semidirect
6. #10617358C2semidirect
7. #10617358C2semidirect
8. #10617347C2semidirect
9. #10617344C2semidirect
16. #10617288C2semidirect
17. #10617285C2semidirect
18. #10617284C2semidirect
19. AGL(1,𝔽5)×C22⋊Q8C2semidirect
25. C5×#563C4semidirect
26. #66069C4semidirect
28. #66046C4semidirect
29. #66046C4semidirect
32. #66033C4semidirect
35. #66006C4semidirect
38. #65985C4semidirect
39. #65985C4semidirect
40. #65980C4semidirect
41. #65980C4semidirect
168. C5×C4⋊Q8C2×C4semidirect
169. C5×#126C2×C4semidirect
170. C5×#126C2×C4semidirect
171. C5×#125C2×C4semidirect
175. C5×C22⋊Q8C2×C4semidirect
176. C5×C22⋊Q8C2×C4semidirect
178. #4092C2×C4semidirect
179. #4092C2×C4semidirect
180. #4090C2×C4semidirect
181. #4090C2×C4semidirect
187. #4070C2×C4semidirect
188. #4070C2×C4semidirect
189. #4044C2×C4semidirect
190. #4044C2×C4semidirect
191. #4044C2×C4semidirect
192. #4044C2×C4semidirect
193. #4044C2×C4semidirect
194. #4044C2×C4semidirect
195. #4043C2×C4semidirect
196. #4043C2×C4semidirect
197. #4042C2×C4semidirect
198. #4042C2×C4semidirect
199. #4042C2×C4semidirect
200. #4042C2×C4semidirect
211. #4036C2×C4semidirect
212. #4036C2×C4semidirect
213. #4035C2×C4semidirect
214. #4035C2×C4semidirect
215. #4035C2×C4semidirect
216. #4035C2×C4semidirect
217. #4034C2×C4semidirect
218. #4034C2×C4semidirect
219. #4034C2×C4semidirect
220. #4034C2×C4semidirect
233. #4025C2×C4semidirect
234. #4025C2×C4semidirect
235. #4025C2×C4semidirect
236. #4025C2×C4semidirect
237. #4025C2×C4semidirect
238. #4025C2×C4semidirect
239. #4024C2×C4semidirect
240. #4024C2×C4semidirect
241. #4024C2×C4semidirect
242. #4024C2×C4semidirect
243. #4022C2×C4semidirect
244. #4022C2×C4semidirect
248. #4016C2×C4semidirect
249. #4015C2×C4semidirect
455. #563AGL(1,𝔽5)semidirect
647. C4⋊Q8C2×AGL(1,𝔽5)semidirect
662. #126C2×AGL(1,𝔽5)semidirect
663. #126C2×AGL(1,𝔽5)semidirect
671. #125C2×AGL(1,𝔽5)semidirect
704. C22⋊Q8C2×AGL(1,𝔽5)semidirect
705. C22⋊Q8C2×AGL(1,𝔽5)semidirect
1080. C5#34514semidirect

Maximal subgroups

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

subgroupindex
D5×#5632
#106173882
#106173872
#106173592
#106173582
#106173472
#106173442
#106173272
#106173242
#106173082
#106173072
#106173042
AGL(1,𝔽5)×#1232
#106172882
#106172852
#106172842
AGL(1,𝔽5)×C22⋊Q82
#345145