Finite Group Databasebeta

← #13044275

Subgroups — #13044275

Order 1280.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#544C211yesmaximal, characteristic
2#10617390C212yesmaximal, complemented
3#10617388C212yesmaximal, complemented
4#10617387C212yesmaximal, complemented
5#10617386C212yesmaximal, complemented
6#10617348C212yesmaximal, complemented
7#10617347C212yesmaximal, complemented
8#10617345C212yesmaximal, complemented
9#10617345C212yesmaximal, complemented
10#10617287C212yesmaximal
11#10617285C212yesmaximal
12#10617283C211yesmaximal, characteristic
13#10617283C211yesmaximal, characteristic
14AGL(1,𝔽5)×C22⋊Q8C211yesmaximal, characteristic
15AGL(1,𝔽5)×C22⋊Q8C211yesmaximal, characteristic
16#10617132C212yesmaximal
17#10617132C212yesmaximal
18#10617101C211yesmaximal, characteristic
19C2×#65711C211yesmaximal, characteristic
20C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
21C2×Q8×AGL(1,𝔽5)C2212yes—
22C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
23C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C22×C4×AGL(1,𝔽5)C2211yescharacteristic
25C5×#544C411yescharacteristic, complemented
26#66063C412yescomplemented
27#66063C412yescomplemented
28D5×C4⋊Q8C2212yes—
29D5×C4⋊Q8C2212yes—
30#66023C412yescomplemented
31#66023C412yescomplemented
32D5×#125C2212yes—
33D5×#125C2212yes—
34D5×C22⋊Q8C2211yescharacteristic
35D5×C22⋊Q8C2211yescharacteristic
36D5×C22⋊Q8C2212yes—
37#65957C411yescharacteristic, complemented
38#65957C411yescharacteristic, complemented
39#65957C412yescomplemented
40D5×#117C2212yes—
41#65853C412yescomplemented
42C2×D5×C4⋊C4C2211yescharacteristic
43#65834C411yescharacteristic, complemented
44(C2×AGL(1,𝔽5))⋊Q8C2212yes—
45(C2×AGL(1,𝔽5))⋊Q8C2212yes—
46(C2×AGL(1,𝔽5))⋊Q8C2211yescharacteristic
47(C2×AGL(1,𝔽5))⋊Q8C2212yes—
48(C2×AGL(1,𝔽5))⋊Q8C2212yes—
49(C2×AGL(1,𝔽5))⋊Q8C2212yes—
50(C2×AGL(1,𝔽5))⋊Q8C2211yescharacteristic
51#65765C2211yescharacteristic
52#65765C2211yescharacteristic
53#65764C2212yes—
54C4×C22⋊AGL(1,𝔽5)C2212yes—
55C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
56C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
57C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
58C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
59#65712C2211yescharacteristic
60#65712C2212yes—
61#65712C2212yes—
62#65712C2212yes—
63#65712C2211yescharacteristic
64#65712C2212yes—
65#65712C2212yes—
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—
80#65711C2212yes—
81#65711C2212yes—
82#65711C2212yes—
83#65711C2212yes—
84#65711C2212yes—
85#65711C2212yes—
86#65711C2212yes—
87#65711C2212yes—
88#65711C2212yes—
89#65711C2212yes—
90#65711C2212yes—
91#65711C2212yes—
92#65711C2212yes—
93#65711C2212yes—
94C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
95C4⋊C4×AGL(1,𝔽5)C2212yes—
96C4⋊C4×AGL(1,𝔽5)C2212yes—
97C4⋊C4×AGL(1,𝔽5)C2212yes—
98C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
99C4⋊C4×AGL(1,𝔽5)C2212yes—
100C4⋊C4×AGL(1,𝔽5)C2212yes—
101#65699C2212yes—
102#65699C2212yes—
103#65699C2212yes—
104#65699C2212yes—
105C22⋊C4×AGL(1,𝔽5)C2212yes—
106C22⋊C4×AGL(1,𝔽5)C2212yes—
107C22⋊C4×AGL(1,𝔽5)C2212yes—
108C22⋊C4×AGL(1,𝔽5)C2212yes—
109#65690C2212yes—
110#65690C2212yes—
111#65689C2212yes—
112#65689C2212yes—
113C4×C4⋊AGL(1,𝔽5)C2212yes—
114C4×C4⋊AGL(1,𝔽5)C2212yes—
115#65686C2212yes—
116#65686C2212yes—
117#34432—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×Q8×D5C2311yescharacteristic
125C22×C4×D5C2311yescharacteristic
126C22×C4×D5C2311yescharacteristic
127C22×C4×D5C2311yescharacteristic
128C2×C22⋊AGL(1,𝔽5)C2312yes—
129C2×C22⋊AGL(1,𝔽5)C2312yes—
130Q8×AGL(1,𝔽5)—42no—
131Q8×AGL(1,𝔽5)—42no—
132Q8×AGL(1,𝔽5)—44no—
133C2×C4⋊AGL(1,𝔽5)—42no—
134C2×C4⋊AGL(1,𝔽5)C2312yes—
135C2×C4⋊AGL(1,𝔽5)C2312yes—
136C2×C4⋊AGL(1,𝔽5)C2312yes—
137C2×C4⋊AGL(1,𝔽5)C2312yes—
138C2×C4⋊AGL(1,𝔽5)C2312yes—
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)C2311yescharacteristic
144C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
145C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
146C2×C4⋊AGL(1,𝔽5)C2312yes—
147C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
148C2×C4×AGL(1,𝔽5)—42no—
149C2×C4×AGL(1,𝔽5)C2312yes—
150C2×C4×AGL(1,𝔽5)C2312yes—
151C2×C4×AGL(1,𝔽5)C2311yescharacteristic
152C2×C4×AGL(1,𝔽5)C2311yescharacteristic
153C2×C4×AGL(1,𝔽5)C2312yes—
154C2×C4×AGL(1,𝔽5)C2312yes—
155C2×C4×AGL(1,𝔽5)C2312yes—
156C2×C4×AGL(1,𝔽5)C2312yes—
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)C2311yescharacteristic
163C5×C4⋊Q8C2×C412yescomplemented
164C5×C4⋊Q8C2×C412yescomplemented
165C5×#125C2×C412yescomplemented
166C5×#125C2×C412yescomplemented
167C5×C22⋊Q8C2×C411yescharacteristic
168C5×C22⋊Q8C2×C411yescharacteristic
169C5×C22⋊Q8C2×C412yes—
170C5×#117C2×C412yes—
171C2×C5×C4⋊C4C2×C411yescharacteristic
172#4092C2×C411yescharacteristic
173#4092C2×C411yescharacteristic
174#4092C2×C412yes—
175#4090C2×C412yescomplemented
176#4090C2×C412yescomplemented
177#4090C2×C412yescomplemented
178#4090C2×C412yescomplemented
179#4072C2×C412yes—
180C2×C4⋊Dic5C2×C411yescharacteristic
181#4070C2×C411yescharacteristic
182#4070C2×C411yescharacteristic
183#4070C2×C412yes—
184C2×#683C2×C411yescharacteristic
185C2×#683C2×C411yescharacteristic
186#4043C2×C411yescharacteristic
187#4043C2×C411yescharacteristic
188#4043C2×C412yes—
189#4042C2×C412yes—
190#4042C2×C412yes—
191#4042C2×C412yes—
192#4042C2×C412yes—
193#4038C2×C412yes—
194#4038C2×C412yes—
195D5×C4⋊C4C2×C412yes—
196D5×C4⋊C4C2×C412yes—
197D5×C4⋊C4C2312yes—
198D5×C4⋊C4C2312yes—
199D5×C4⋊C4C2312yes—
200D5×C4⋊C4C2312yes—
201D5×C4⋊C4C2312yes—
202D5×C4⋊C4C2312yes—
203D5×C4⋊C4C2312yes—
204D5×C4⋊C4C2312yes—
205D5×C4⋊C4C2311yescharacteristic
206D5×C4⋊C4C2311yescharacteristic
207D5×C4⋊C4C2312yes—
208#4036C2×C412yescomplemented
209#4036C2×C412yescomplemented
210#4036C2×C412yescomplemented
211#4036C2×C412yescomplemented
212#4035C2×C412yescomplemented
213#4035C2×C412yescomplemented
214#4035C2×C412yescomplemented
215#4035C2×C412yescomplemented
216#4035C2×C412yescomplemented
217#4035C2×C412yescomplemented
218#4035C2×C412yescomplemented
219#4035C2×C412yescomplemented
220#4034C2×C412yescomplemented
221#4034C2×C412yescomplemented
222#4034C2×C412yescomplemented
223#4034C2×C412yescomplemented
224#4034C2×C412yescomplemented
225#4034C2×C412yescomplemented
226#4034C2×C412yescomplemented
227#4034C2×C412yescomplemented
228D5×C22⋊C4C2312yes—
229D5×C22⋊C4C2312yes—
230#4024C2×C412yes—
231#4024C2×C412yes—
232#4024C2×C412yes—
233#4024C2×C412yes—
234#4023C2×C412yes—
235#4023C2×C412yes—
236#4018C2×C412yes—
237#4018C2×C412yes—
238C42×D5C2312yes—
239C42×D5C2312yes—
240#4016C2×C412yescomplemented
241#4016C2×C412yescomplemented
242#4015C2×C412yescomplemented
243#4015C2×C412yescomplemented
244(C2×AGL(1,𝔽5))⋊C4C2312yes—
245(C2×AGL(1,𝔽5))⋊C4C2312yes—
246(C2×AGL(1,𝔽5))⋊C4C2312yes—
247(C2×AGL(1,𝔽5))⋊C4C2312yes—
248(C2×AGL(1,𝔽5))⋊C4C2312yes—
249(C2×AGL(1,𝔽5))⋊C4C2312yes—
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×#544—51no—
277#2382—52no—
278#2381—52no—
279#2371—52no—
280#2368—52no—
281#2365—52no—
282#2360—52no—
283#2343—52no—
284#2343—52no—
285#2336—52no—
286#2336—52no—
287#2331—52no—
288#2329—51no—
289#2329—51no—
290#2327—52no—
291#2313—51no—
292C4×C22⋊Q8—51no—
293C4×C22⋊Q8—51no—
294C2×#387—51no—
295C23×D5C2411yescharacteristic
296C22×AGL(1,𝔽5)—22no—
297C22×AGL(1,𝔽5)—22no—
298C22×AGL(1,𝔽5)—22no—
299C22×AGL(1,𝔽5)—22no—
300C22×AGL(1,𝔽5)—22no—
301C22×AGL(1,𝔽5)—22no—
302C22×AGL(1,𝔽5)—41no—
303C22×AGL(1,𝔽5)—41no—
304C22×AGL(1,𝔽5)—41no—
305C22×AGL(1,𝔽5)—41no—
306C22×AGL(1,𝔽5)—41no—
307C22×AGL(1,𝔽5)—41no—
308C22×AGL(1,𝔽5)C2412yes—
309C22×AGL(1,𝔽5)C2412yes—
310C22×AGL(1,𝔽5)C2412yes—
311C22×AGL(1,𝔽5)C2412yes—
312C22×AGL(1,𝔽5)C2411yescharacteristic
313C22×AGL(1,𝔽5)C2412yes—
314C22×AGL(1,𝔽5)C2411yescharacteristic
315C22×AGL(1,𝔽5)C2412yes—
316C22×AGL(1,𝔽5)C2411yescharacteristic
317C22×AGL(1,𝔽5)C2411yescharacteristic
318C2×C5×Q8C22×C411yescharacteristic
319C2×C5×Q8C22×C411yescharacteristic
320C2×C5×Q8C22×C412yes—
321C22×C4×C5C22×C411yescharacteristic
322C22×C4×C5C22×C411yescharacteristic
323C22×C4×C5C22×C411yescharacteristic
324C22×Dic5C22×C411yescharacteristic
325C22×Dic5C22×C411yescharacteristic
326C22×Dic5C22×C411yescharacteristic
327Q8×D5—41no—
328Q8×D5—41no—
329Q8×D5—42no—
330Q8×D5—42no—
331Q8×D5—41no—
332Q8×D5—41no—
333C2×C4×D5—22no—
334C2×C4×D5—22no—
335C2×C4×D5—41no—
336C2×C4×D5—41no—
337C2×C4×D5—41no—
338C2×C4×D5—41no—
339C2×C4×D5C22×C412yes—
340C2×C4×D5C22×C411yescharacteristic
341C2×C4×D5C22×C411yescharacteristic
342C2×C4×D5C22×C412yes—
343C2×C4×D5C2411yescharacteristic
344C2×C4×D5C2411yescharacteristic
345C2×C4×D5C2412yes—
346C2×C4×D5C2412yes—
347C2×C4×D5C2412yes—
348C2×C4×D5C2412yes—
349C2×C4×D5C2412yes—
350C2×C4×D5C2412yes—
351C2×Dic10C22×C412yes—
352C2×Dic10C22×C412yes—
353C2×Dic10C22×C412yes—
354C2×Dic10C22×C412yes—
355C2×Dic10C22×C411yescharacteristic
356C2×Dic10C22×C412yes—
357C2×Dic10C22×C411yescharacteristic
358C22⋊AGL(1,𝔽5)—24no—
359C22⋊AGL(1,𝔽5)—24no—
360C4⋊AGL(1,𝔽5)—24no—
361C4⋊AGL(1,𝔽5)—24no—
362C4⋊AGL(1,𝔽5)—24no—
363C4⋊AGL(1,𝔽5)—42no—
364C4⋊AGL(1,𝔽5)—42no—
365C4⋊AGL(1,𝔽5)—42no—
366C4⋊AGL(1,𝔽5)—42no—
367C4⋊AGL(1,𝔽5)—41no—
368C4⋊AGL(1,𝔽5)—41no—
369C4⋊AGL(1,𝔽5)—42no—
370C4⋊AGL(1,𝔽5)—41no—
371C4⋊AGL(1,𝔽5)—41no—
372C4⋊AGL(1,𝔽5)—42no—
373C4⋊AGL(1,𝔽5)—42no—
374C4×AGL(1,𝔽5)—22no—
375C4×AGL(1,𝔽5)—22no—
376C4×AGL(1,𝔽5)—24no—
377C4×AGL(1,𝔽5)—24no—
378C4×AGL(1,𝔽5)—41no—
379C4×AGL(1,𝔽5)—41no—
380C4×AGL(1,𝔽5)—42no—
381C4×AGL(1,𝔽5)—42no—
382C4×AGL(1,𝔽5)—42no—
383C4×AGL(1,𝔽5)—42no—
384C4×AGL(1,𝔽5)—42no—
385C4×AGL(1,𝔽5)—42no—
386C4×AGL(1,𝔽5)—42no—
387C4×AGL(1,𝔽5)—42no—
388C5×C4⋊C4C22×C412yes—
389C5×C4⋊C4C22×C412yes—
390C5×C4⋊C4C22×C412yes—
391C5×C4⋊C4C22×C412yes—
392C5×C4⋊C4C22×C411yescharacteristic
393C5×C4⋊C4C22×C411yescharacteristic
394C5×C4⋊C4C22×C412yes—
395C5×C4⋊C4C22×C412yes—
396C5×C4⋊C4C22×C412yes—
397C5×C4⋊C4C22×C412yes—
398C5×C4⋊C4C22×C412yes—
399C5×C22⋊C4C22×C412yes—
400C5×C22⋊C4C22×C412yes—
401C42×C5C22×C412yes—
402C42×C5C22×C412yes—
403C22⋊Dic5C22×C412yes—
404C22⋊Dic5C22×C412yes—
405#685C22×C412yes—
406#685C22×C412yes—
407#685C22×C412yes—
408#685C22×C412yes—
409C4⋊Dic5C22×C412yes—
410C4⋊Dic5C22×C412yes—
411C4⋊Dic5C22×C412yes—
412C4⋊Dic5C22×C412yes—
413C4⋊Dic5C22×C412yes—
414C4⋊Dic5C22×C412yes—
415C4⋊Dic5C22×C412yes—
416C4⋊Dic5C22×C412yes—
417C4⋊Dic5C22×C411yescharacteristic
418C4⋊Dic5C22×C412yes—
419C4⋊Dic5C22×C411yescharacteristic
420#683C22×C412yes—
421#683C22×C412yes—
422#683C22×C412yes—
423#683C22×C412yes—
424#683C22×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—
440C4×Dic5C22×C412yes—
441C4×Dic5C22×C412yes—
442C4×Dic5C22×C412yes—
443C4×Dic5C22×C412yes—
444C4×Dic5C22×C412yes—
445C4×Dic5C22×C412yes—
446#544—52no—
447#544—52no—
448#544—52no—
449#544—52no—
450#544—51no—
451#544—51no—
452#544—52no—
453#544—52no—
454#544—51no—
455#544AGL(1,𝔽5)11yescharacteristic, complemented
456C2×C4⋊Q8—52no—
457C2×C4⋊Q8—52no—
458C2×#125—52no—
459C2×#125—52no—
460C2×C22⋊Q8—51no—
461C2×C22⋊Q8—51no—
462C2×C22⋊Q8—52no—
463C2×C4×Q8—51no—
464C2×C4×Q8—52no—
465C2×C4×Q8—51no—
466C2×#117—52no—
467C22×C4⋊C4—51no—
468C22×C4⋊C4—51no—
469C22×C42—51no—
470#391—52no—
471#391—52no—
472#391—52no—
473#391—51no—
474#391—52no—
475#391—52no—
476#391—51no—
477#389—52no—
478#389—52no—
479#389—52no—
480#389—51no—
481#389—52no—
482#389—52no—
483#389—51no—
484#387—52no—
485#387—52no—
486#387—52no—
487#387—52no—
488#387—52no—
489#387—52no—
490#387—52no—
491#387—52no—
492#387—52no—
493#387—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#387—52no—
511#387—52no—
512#385—52no—
513#385—52no—
514#385—52no—
515#385—52no—
516#383—52no—
517#383—52no—
518#382—52no—
519#382—52no—
520#381—52no—
521#380—51no—
522#380—51no—
523C4×C4⋊C4—52no—
524C4×C4⋊C4—52no—
525C4×C4⋊C4—51no—
526C4×C4⋊C4—52no—
527C4×C4⋊C4—52no—
528C4×C4⋊C4—52no—
529C4×C4⋊C4—52no—
530C4×C4⋊C4—52no—
531C4×C4⋊C4—51no—
532C4×C22⋊C4—52no—
533C4×C22⋊C4—52no—
534C4×C22⋊C4—52no—
535C4×C22⋊C4—52no—
536C4×C22⋊C4—52no—
537#376—52no—
538#376—52no—
539C2×#95—51no—
540C2×#95—51no—
541C2×#95—51no—
542C2×#95—51no—
543C23×C5C23×C411yescharacteristic
544C22×D5—21no—
545C22×D5—21no—
546C22×D5—21no—
547C22×D5—21no—
548C22×D5C23×C411yescharacteristic
549C22×D52−1+412yes—
550C22×D52−1+412yes—
551C22×D5C2511yescharacteristic
552C2×AGL(1,𝔽5)—21no—
553C2×AGL(1,𝔽5)—21no—
554C2×AGL(1,𝔽5)—21no—
555C2×AGL(1,𝔽5)—21no—
556C2×AGL(1,𝔽5)—22no—
557C2×AGL(1,𝔽5)—21no—
558C2×AGL(1,𝔽5)—22no—
559C2×AGL(1,𝔽5)—21no—
560C2×AGL(1,𝔽5)—22no—
561C2×AGL(1,𝔽5)—22no—
562C2×AGL(1,𝔽5)—22no—
563C2×AGL(1,𝔽5)—22no—
564C2×AGL(1,𝔽5)—22no—
565C2×AGL(1,𝔽5)—22no—
566C2×AGL(1,𝔽5)—22no—
567C2×AGL(1,𝔽5)—21no—
568C2×AGL(1,𝔽5)—22no—
569C2×AGL(1,𝔽5)—21no—
570C2×AGL(1,𝔽5)—21no—
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)—21no—
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+412yes—
586C5×Q8—41no—
587C5×Q8—42no—
588C5×Q8—41no—
589C2×C4×C5—22no—
590C2×C4×C5—41no—
591C2×C4×C5—41no—
592C2×C4×C5C23×C412yes—
593C2×C4×C5C23×C412yes—
594C2×C4×C5C23×C412yes—
595C2×C4×C5C23×C412yes—
596C2×C4×C5C23×C412yes—
597C2×C4×C5C23×C411yescharacteristic
598C2×C4×C5C23×C411yescharacteristic
599C2×C4×C5C23×C412yes—
600C2×Dic5—22no—
601C2×Dic5—41no—
602C2×Dic5—41no—
603C2×Dic5C23×C412yes—
604C2×Dic5C23×C412yes—
605C2×Dic5C23×C412yes—
606C2×Dic5C23×C412yes—
607C2×Dic5C23×C412yes—
608C2×Dic5C23×C411yescharacteristic
609C2×Dic5C23×C411yescharacteristic
610C2×Dic5C23×C412yes—
611C4×D5—24no—
612C4×D5—21no—
613C4×D5—21no—
614C4×D5—22no—
615C4×D5—22no—
616C4×D5—22no—
617C4×D5—22no—
618C4×D5—22no—
619C4×D5—22no—
620C4×D5—22no—
621C4×D5—22no—
622C4×D5—22no—
623C4×D5—22no—
624C4×D5—22no—
625C4×D5—21no—
626C4×D5—21no—
627C4×D5—22no—
628C4×D5—41no—
629C4×D5—41no—
630C4×D5—42no—
631Dic10—41no—
632Dic10—42no—
633Dic10—41no—
634Dic10—42no—
635Dic10—42no—
636Dic10—42no—
637Dic10—42no—
638C22×Q8—51no—
639C22×Q8—52no—
640C22×Q8—51no—
641C23×C4—51no—
642C23×C4—51no—
643C23×C4—51no—
644C23×C4—51no—
645C23×C4—51no—
646C23×C4—51no—
647C23×C4—51no—
648C4⋊Q8—52no—
649C4⋊Q8—52no—
650C4⋊Q8—52no—
651C4⋊Q8—52no—
652C4⋊Q8—52no—
653C4⋊Q8—52no—
654C4⋊Q8—52no—
655C4⋊Q8—52no—
656C4⋊Q8—52no—
657C4⋊Q8—52no—
658C4⋊Q8—52no—
659C4⋊Q8—52no—
660C4⋊Q8—52no—
661C4⋊Q8—52no—
662C4⋊Q8C2×AGL(1,𝔽5)12yescomplemented
663C4⋊Q8C2×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#125—52no—
672#125—52no—
673#125—52no—
674#125—52no—
675#125—52no—
676#125—52no—
677#125—52no—
678#125C2×AGL(1,𝔽5)12yescomplemented
679#125C2×AGL(1,𝔽5)12yescomplemented
680C22⋊Q8—51no—
681C22⋊Q8—51no—
682C22⋊Q8—52no—
683C22⋊Q8—51no—
684C22⋊Q8—51no—
685C22⋊Q8—52no—
686C22⋊Q8—52no—
687C22⋊Q8—52no—
688C22⋊Q8—52no—
689C22⋊Q8—52no—
690C22⋊Q8—51no—
691C22⋊Q8—51no—
692C22⋊Q8—52no—
693C22⋊Q8—52no—
694C22⋊Q8—52no—
695C22⋊Q8—52no—
696C22⋊Q8—52no—
697C22⋊Q8C2×AGL(1,𝔽5)11yescharacteristic
698C22⋊Q8C2×AGL(1,𝔽5)11yescharacteristic
699C22⋊Q8C2×AGL(1,𝔽5)12yes—
700C4×Q8—202no—
701C4×Q8—202no—
702C4×Q8—204no—
703#117—52no—
704#117—52no—
705#117—52no—
706#117—52no—
707#117—52no—
708#117—52no—
709#117—52no—
710#117C2×AGL(1,𝔽5)12yes—
711C2×C4⋊C4—51no—
712C2×C4⋊C4—51no—
713C2×C4⋊C4—51no—
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—51no—
721C2×C4⋊C4—51no—
722C2×C4⋊C4—52no—
723C2×C4⋊C4—52no—
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—51no—
732C2×C4⋊C4—51no—
733C2×C4⋊C4—52no—
734C2×C4⋊C4—52no—
735C2×C4⋊C4—51no—
736C2×C4⋊C4—51no—
737C2×C4⋊C4—52no—
738C2×C4⋊C4—52no—
739C2×C4⋊C4—52no—
740C2×C4⋊C4—52no—
741C2×C4⋊C4—202no—
742C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
743C2×C22⋊C4—52no—
744C2×C22⋊C4—52no—
745C2×C22⋊C4—52no—
746C2×C22⋊C4—52no—
747C2×C42—52no—
748C2×C42—52no—
749C2×C42—52no—
750C2×C42—51no—
751C2×C42—51no—
752C2×C42—52no—
753C2×C42—52no—
754C2×C42—52no—
755C2×C42—52no—
756C2×C42—52no—
757C2×C42—52no—
758C2×C42—52no—
759C2×C42—52no—
760C2×C42—52no—
761C2×C42—51no—
762C2×C42—51no—
763C2×C42—202no—
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—
789#95—52no—
790#95—52no—
791#95—52no—
792#95—52no—
793#95—52no—
794#95—52no—
795#95—52no—
796C22×C5—21no—
797C22×C5—21no—
798C22×C5#51912yes—
799C22×C5C24×C411yescharacteristic
800C2×D5—21no—
801C2×D5—21no—
802C2×D5—22no—
803C2×D5—22no—
804C2×D5—22no—
805C2×D5—22no—
806C2×D5#51912yes—
807C2×D5C2×H(5,𝔽2)11yescharacteristic
808C2×D5C2×2−1+411yescharacteristic
809C2×D5C2×2−1+411yescharacteristic
810C2×D5C2×2−1+411yescharacteristic
811C2×D5#58511yescharacteristic
812C2×D5#58511yescharacteristic
813AGL(1,𝔽5)—22no—
814AGL(1,𝔽5)—22no—
815AGL(1,𝔽5)—42no—
816AGL(1,𝔽5)—41no—
817AGL(1,𝔽5)—42no—
818AGL(1,𝔽5)—42no—
819AGL(1,𝔽5)—41no—
820AGL(1,𝔽5)—42no—
821AGL(1,𝔽5)—42no—
822AGL(1,𝔽5)—42no—
823C4×C5—22no—
824C4×C5—22no—
825C4×C5—22no—
826C4×C5—21no—
827C4×C5—21no—
828C4×C5—22no—
829C4×C5—22no—
830C4×C5—22no—
831Dic5—22no—
832Dic5—22no—
833Dic5—22no—
834Dic5—21no—
835Dic5—21no—
836Dic5—22no—
837Dic5—22no—
838Dic5—22no—
839C24—51no—
840C2×Q8—51no—
841C2×Q8—51no—
842C2×Q8—52no—
843C2×Q8—52no—
844C2×Q8—52no—
845C2×Q8—52no—
846C2×Q8—52no—
847C2×Q8—201no—
848C2×Q8—201no—
849C2×Q8—202no—
850C2×Q8—202no—
851C2×Q8—201no—
852C2×Q8—201no—
853C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
854C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
855C2×Q8C22×AGL(1,𝔽5)12yes—
856C22×C4—51no—
857C22×C4—51no—
858C22×C4—51no—
859C22×C4—51no—
860C22×C4—51no—
861C22×C4—52no—
862C22×C4—52no—
863C22×C4—52no—
864C22×C4—52no—
865C22×C4—52no—
866C22×C4—51no—
867C22×C4—51no—
868C22×C4—52no—
869C22×C4—52no—
870C22×C4—52no—
871C22×C4—51no—
872C22×C4—51no—
873C22×C4—52no—
874C22×C4—51no—
875C22×C4—52no—
876C22×C4—52no—
877C22×C4—52no—
878C22×C4—51no—
879C22×C4—52no—
880C22×C4—52no—
881C22×C4—102no—
882C22×C4—102no—
883C22×C4—102no—
884C22×C4—102no—
885C22×C4—102no—
886C22×C4—102no—
887C22×C4—102no—
888C22×C4—102no—
889C22×C4—201no—
890C22×C4—201no—
891C22×C4—201no—
892C22×C4—201no—
893C22×C4—201no—
894C22×C4—201no—
895C22×C4—201no—
896C22×C4—201no—
897C22×C4—201no—
898C22×C4—201no—
899C22×C4C22×AGL(1,𝔽5)11yescharacteristic
900C22×C4C22×AGL(1,𝔽5)11yescharacteristic
901C22×C4C22×AGL(1,𝔽5)11yescharacteristic
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—52no—
911C4⋊C4—52no—
912C4⋊C4—52no—
913C4⋊C4—52no—
914C4⋊C4—52no—
915C4⋊C4—52no—
916C4⋊C4—52no—
917C4⋊C4—52no—
918C4⋊C4—51no—
919C4⋊C4—51no—
920C4⋊C4—52no—
921C4⋊C4—52no—
922C4⋊C4—52no—
923C4⋊C4—52no—
924C4⋊C4—52no—
925C4⋊C4—52no—
926C4⋊C4—52no—
927C4⋊C4—52no—
928C4⋊C4—52no—
929C4⋊C4—52no—
930C4⋊C4—52no—
931C4⋊C4—52no—
932C4⋊C4—52no—
933C4⋊C4—104no—
934C4⋊C4—104no—
935C4⋊C4—104no—
936C4⋊C4—202no—
937C4⋊C4—201no—
938C4⋊C4—201no—
939C4⋊C4—202no—
940C4⋊C4—202no—
941C4⋊C4—202no—
942C4⋊C4—202no—
943C4⋊C4—202no—
944C4⋊C4—201no—
945C4⋊C4—201no—
946C4⋊C4—202no—
947C4⋊C4C22×AGL(1,𝔽5)12yes—
948C4⋊C4C22×AGL(1,𝔽5)12yes—
949C4⋊C4C22×AGL(1,𝔽5)12yes—
950C4⋊C4C22×AGL(1,𝔽5)12yes—
951C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
952C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
953C4⋊C4C22×AGL(1,𝔽5)12yes—
954C4⋊C4C22×AGL(1,𝔽5)12yes—
955C4⋊C4C22×AGL(1,𝔽5)12yes—
956C4⋊C4C22×AGL(1,𝔽5)12yes—
957C4⋊C4C22×AGL(1,𝔽5)12yes—
958C22⋊C4—52no—
959C22⋊C4—52no—
960C22⋊C4—52no—
961C22⋊C4—52no—
962C22⋊C4—52no—
963C22⋊C4—52no—
964C22⋊C4—104no—
965C22⋊C4—104no—
966C22⋊C4C22×AGL(1,𝔽5)12yes—
967C22⋊C4C22×AGL(1,𝔽5)12yes—
968C42—52no—
969C42—52no—
970C42—52no—
971C42—52no—
972C42—52no—
973C42—52no—
974C42—102no—
975C42—102no—
976C42—104no—
977C42—104no—
978C42—201no—
979C42—201no—
980C42—202no—
981C42—202no—
982C42—202no—
983C42—202no—
984C42—202no—
985C42—202no—
986C42—202no—
987C42—202no—
988C42C22×AGL(1,𝔽5)12yes—
989C42C22×AGL(1,𝔽5)12yes—
990C2×C5—22no—
991C2×C5C2×#51911yescharacteristic
992C2×C5C4×H(5,𝔽2)11yescharacteristic
993C2×C5C4×2−1+411yescharacteristic
994D5—22no—
995D5#353511yescharacteristic
996D5#353811yescharacteristic
997D5#356311yescharacteristic
998D5#356411yescharacteristic
999C23—51no—
1000C23—52no—
1001C23—52no—
1002C23—51no—
1003C23—101no—
1004C23—101no—
1005C23—101no—
1006C23—101no—
1007C23C23×AGL(1,𝔽5)11yescharacteristic
1008Q8—41no—
1009Q8—41no—
1010Q8—42no—
1011Q8—201no—
1012Q8—201no—
1013Q8—202no—
1014Q8—202no—
1015Q8—202no—
1016Q8—202no—
1017Q8—202no—
1018C2×C4—22no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—52no—
1022C2×C4—52no—
1023C2×C4—52no—
1024C2×C4—52no—
1025C2×C4—52no—
1026C2×C4—52no—
1027C2×C4—52no—
1028C2×C4—51no—
1029C2×C4—51no—
1030C2×C4—52no—
1031C2×C4—101no—
1032C2×C4—101no—
1033C2×C4—102no—
1034C2×C4—102no—
1035C2×C4—102no—
1036C2×C4—102no—
1037C2×C4—102no—
1038C2×C4—102no—
1039C2×C4—102no—
1040C2×C4—102no—
1041C2×C4—102no—
1042C2×C4—101no—
1043C2×C4—101no—
1044C2×C4—102no—
1045C2×C4—102no—
1046C2×C4—102no—
1047C2×C4—104no—
1048C2×C4—101no—
1049C2×C4—101no—
1050C2×C4—101no—
1051C2×C4—101no—
1052C2×C4—102no—
1053C2×C4—102no—
1054C2×C4—101no—
1055C2×C4—102no—
1056C2×C4—102no—
1057C2×C4—101no—
1058C2×C4—102no—
1059C2×C4—102no—
1060C2×C4—102no—
1061C2×C4—102no—
1062C2×C4—102no—
1063C2×C4—102no—
1064C2×C4—102no—
1065C2×C4—102no—
1066C2×C4—102no—
1067C2×C4—102no—
1068C2×C4—102no—
1069C2×C4—102no—
1070C2×C4—102no—
1071C2×C4—101no—
1072C2×C4—101no—
1073C2×C4—101no—
1074C2×C4—101no—
1075C2×C4—102no—
1076C2×C4—102no—
1077C2×C4—201no—
1078C2×C4—201no—
1079C2×C4—202no—
1080C2×C4—201no—
1081C2×C4—201no—
1082C2×C4—204no—
1083C2×C4—204no—
1084C2×C4—402no—
1085C2×C4—402no—
1086C2×C4C23×AGL(1,𝔽5)12yes—
1087C2×C4C23×AGL(1,𝔽5)12yes—
1088C2×C4C23×AGL(1,𝔽5)12yes—
1089C2×C4C23×AGL(1,𝔽5)12yes—
1090C2×C4C23×AGL(1,𝔽5)12yes—
1091C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1092C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1093C2×C4C23×AGL(1,𝔽5)12yes—
1094C5#3443211yescharacteristic, complemented, Sylow
1095C22—21no—
1096C22—21no—
1097C22—51no—
1098C22—51no—
1099C22—51no—
1100C22—51no—
1101C22—51no—
1102C22—51no—
1103C22—52no—
1104C22—102no—
1105C22—102no—
1106C22—102no—
1107C22—102no—
1108C22—101no—
1109C22—101no—
1110C22#6626212yes—
1111C22C24×AGL(1,𝔽5)11yescharacteristic
1112C4—22no—
1113C4—21no—
1114C4—21no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—102no—
1121C4—102no—
1122C4—102no—
1123C4—101no—
1124C4—101no—
1125C4—102no—
1126C4—102no—
1127C4—102no—
1128C4—102no—
1129C4—102no—
1130C4—201no—
1131C4—201no—
1132C4—202no—
1133C4—202no—
1134C4—202no—
1135C4—202no—
1136C4—202no—
1137C4—202no—
1138C2—22no—
1139C2—51no—
1140C2—51no—
1141C2—51no—
1142C2—51no—
1143C2—102no—
1144C2C2×#6626211yescharacteristic
1145C2AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic
1146C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#544C4
prime radicalC23×D5C24
cosocleC22×D5C25
hypercenter#544AGL(1,𝔽5)
hypocenterC5#34432
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #10617390C2semidirect
3. #10617388C2semidirect
4. #10617387C2semidirect
5. #10617386C2semidirect
6. #10617348C2semidirect
7. #10617347C2semidirect
8. #10617345C2semidirect
9. #10617345C2semidirect
25. C5×#544C4semidirect
26. #66063C4semidirect
27. #66063C4semidirect
30. #66023C4semidirect
31. #66023C4semidirect
37. #65957C4semidirect
38. #65957C4semidirect
39. #65957C4semidirect
41. #65853C4semidirect
43. #65834C4semidirect
163. C5×C4⋊Q8C2×C4semidirect
164. C5×C4⋊Q8C2×C4semidirect
165. C5×#125C2×C4semidirect
166. C5×#125C2×C4semidirect
175. #4090C2×C4semidirect
176. #4090C2×C4semidirect
177. #4090C2×C4semidirect
178. #4090C2×C4semidirect
208. #4036C2×C4semidirect
209. #4036C2×C4semidirect
210. #4036C2×C4semidirect
211. #4036C2×C4semidirect
212. #4035C2×C4semidirect
213. #4035C2×C4semidirect
214. #4035C2×C4semidirect
215. #4035C2×C4semidirect
216. #4035C2×C4semidirect
217. #4035C2×C4semidirect
218. #4035C2×C4semidirect
219. #4035C2×C4semidirect
220. #4034C2×C4semidirect
221. #4034C2×C4semidirect
222. #4034C2×C4semidirect
223. #4034C2×C4semidirect
224. #4034C2×C4semidirect
225. #4034C2×C4semidirect
226. #4034C2×C4semidirect
227. #4034C2×C4semidirect
240. #4016C2×C4semidirect
241. #4016C2×C4semidirect
242. #4015C2×C4semidirect
243. #4015C2×C4semidirect
455. #544AGL(1,𝔽5)semidirect
662. C4⋊Q8C2×AGL(1,𝔽5)semidirect
663. C4⋊Q8C2×AGL(1,𝔽5)semidirect
678. #125C2×AGL(1,𝔽5)semidirect
679. #125C2×AGL(1,𝔽5)semidirect
1094. C5#34432semidirect

Maximal subgroups

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

subgroupindex
D5×#5442
#106173902
#106173882
#106173872
#106173862
#106173482
#106173472
#106173452
#106172872
#106172852
#106172832
AGL(1,𝔽5)×C22⋊Q82
#106171322
#106171012
C2×#657112
#344325