Finite Group Databasebeta

← #13044141

Subgroups — #13044141

Order 1280.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#547C211yesmaximal, characteristic
2#10617557C212yesmaximal, complemented
3#10617555C212yesmaximal, complemented
4#10617389C211yesmaximal, characteristic, complemented
5#10617387C211yesmaximal, characteristic, complemented
6#10617307C212yesmaximal, complemented
7#10617306C212yesmaximal, complemented
8#10617305C212yesmaximal, complemented
9AGL(1,𝔽5)×#123C212yesmaximal, complemented
10#10617287C212yesmaximal, complemented
11#10617284C212yesmaximal, complemented
12#10617254C211yesmaximal, characteristic, complemented
13#10617253C211yesmaximal, characteristic, complemented
14#10617250C211yesmaximal, characteristic, complemented
15AGL(1,𝔽5)×#121C211yesmaximal, characteristic, complemented
16#10617182C211yesmaximal, characteristic, complemented
17#10617179C211yesmaximal, characteristic, complemented
18#10617173C211yesmaximal, characteristic, complemented
19#10617172C211yesmaximal, characteristic, complemented
20#10617104C211yesmaximal, characteristic, complemented
21#10617103C211yesmaximal, characteristic, complemented
22#10617098C211yesmaximal, characteristic, complemented
23C2×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
24C2×D5×#41C2212yes—
25C2×D4×AGL(1,𝔽5)C2211yescharacteristic
26C2×D4×AGL(1,𝔽5)C2211yescharacteristic
27C2×D4×AGL(1,𝔽5)C2212yes—
28C2×D4×AGL(1,𝔽5)C2212yes—
29C2×#4130C2211yescharacteristic
30C2×#4130C2211yescharacteristic
31C2×#4130C2212yes—
32C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
33C22×C4×AGL(1,𝔽5)C2211yescharacteristic
34C22×C4×AGL(1,𝔽5)C2212yes—
35C5×#547C411yescharacteristic, complemented
36#66158C412yescomplemented
37#66060C411yescharacteristic, complemented
38D5×C4⋊Q8C2211yescharacteristic
39#65989C412yescomplemented
40#65989C412yescomplemented
41D5×#123C2212yes—
42D5×#123C2212yes—
43#65965C412yescomplemented
44D5×C22⋊Q8C2212yes—
45#65945C411yescharacteristic, complemented
46#65945C411yescharacteristic, complemented
47D5×#121C2211yescharacteristic
48D5×#121C2211yescharacteristic
49#65889C411yescharacteristic, complemented
50#65885C411yescharacteristic, complemented
51C4×D4×D5C2211yescharacteristic
52C4×D4×D5C2211yescharacteristic
53#65841C411yescharacteristic, complemented
54#65841C411yescharacteristic, complemented
55C2×D5×C4⋊C4C2211yescharacteristic
56C2×D5×C4⋊C4C2211yescharacteristic
57(C2×AGL(1,𝔽5))⋊Q8C2212yes—
58(C2×AGL(1,𝔽5))⋊Q8C2212yes—
59(C2×AGL(1,𝔽5))⋊Q8C2212yes—
60(C2×AGL(1,𝔽5))⋊Q8C2212yes—
61#65780C2211yescharacteristic
62#65780C2211yescharacteristic
63#65780C2212yes—
64#65780C2212yes—
65#65779C2211yescharacteristic
66#65779C2211yescharacteristic
67#65779C2212yes—
68#65779C2212yes—
69#65779C2212yes—
70#65779C2212yes—
71#65779C2212yes—
72#65765C2211yescharacteristic
73#65765C2211yescharacteristic
74#65765C2212yes—
75#65764C2212yes—
76#65764C2212yes—
77C4×C22⋊AGL(1,𝔽5)C2212yes—
78C4×C22⋊AGL(1,𝔽5)C2212yes—
79C4×C22⋊AGL(1,𝔽5)C2211yescharacteristic
80C4×C22⋊AGL(1,𝔽5)C2211yescharacteristic
81C4×C22⋊AGL(1,𝔽5)C2212yes—
82C4×C22⋊AGL(1,𝔽5)C2212yes—
83C4×C22⋊AGL(1,𝔽5)C2212yes—
84C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
85C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
86#65712C2211yescharacteristic
87#65712C2211yescharacteristic
88#65712C2211yescharacteristic
89#65712C2211yescharacteristic
90#65712C2212yes—
91#65711C2212yes—
92#65711C2212yes—
93#65711C2212yes—
94#65711C2212yes—
95#65711C2212yes—
96#65711C2212yes—
97#65711C2211yescharacteristic
98#65711C2211yescharacteristic
99#65711C2212yes—
100C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
101C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
102C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
103C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
104C4⋊C4×AGL(1,𝔽5)C2212yes—
105C4⋊C4×AGL(1,𝔽5)C2212yes—
106C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
107C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
108C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
109C4⋊C4×AGL(1,𝔽5)C2212yes—
110C4⋊C4×AGL(1,𝔽5)C2212yes—
111C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
112C4⋊C4×AGL(1,𝔽5)C2212yes—
113#65700C2211yescharacteristic
114#65700C2211yescharacteristic
115#65700C2212yes—
116#65700C2212yes—
117#65700C2212yes—
118#65700C2212yes—
119#65700C2212yes—
120#65700C2212yes—
121#65700C2212yes—
122#65699C2211yescharacteristic
123#65699C2211yescharacteristic
124#65699C2212yes—
125#65699C2212yes—
126C22⋊C4×AGL(1,𝔽5)C2212yes—
127C22⋊C4×AGL(1,𝔽5)C2212yes—
128C22⋊C4×AGL(1,𝔽5)C2212yes—
129C22⋊C4×AGL(1,𝔽5)C2212yes—
130C22⋊C4×AGL(1,𝔽5)C2212yes—
131#65689C2211yescharacteristic
132C4×C4⋊AGL(1,𝔽5)C2211yescharacteristic
133C4×C4⋊AGL(1,𝔽5)C2211yescharacteristic
134#65686C2211yescharacteristic
135#34298—51nomaximal, Sylow
136C23×AGL(1,𝔽5)C2311yescharacteristic
137C23×AGL(1,𝔽5)C2312yes—
138C23×AGL(1,𝔽5)C2311yescharacteristic
139C23×AGL(1,𝔽5)C2312yes—
140C23×AGL(1,𝔽5)C2312yes—
141C2×C5×#41C2×C412yescomplemented
142D5×#41—44no—
143D5×#41—44no—
144C2×#713C2×C412yescomplemented
145C2×Q8×D5C2312yes—
146C2×#711C2×C412yescomplemented
147C2×#711C2×C412yescomplemented
148C2×#711C2×C412yescomplemented
149C2×D4×D5C2311yescharacteristic
150C2×D4×D5C2311yescharacteristic
151C2×D4×D5C2312yes—
152C2×D4×D5C2312yes—
153C2×#709C2×C412yescomplemented
154C2×#709C2×C412yescomplemented
155C2×#709C2×C412yescomplemented
156C22×C4×D5C2311yescharacteristic
157C22×C4×D5C2311yescharacteristic
158C22×C4×D5C2312yes—
159C22×C4×D5C2312yes—
160C22×C4×D5C2312yes—
161C2×C22⋊AGL(1,𝔽5)C2312yes—
162C2×C22⋊AGL(1,𝔽5)C2312yes—
163C2×C22⋊AGL(1,𝔽5)C2312yes—
164C2×C22⋊AGL(1,𝔽5)C2312yes—
165C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
166C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
167C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
168C2×C22⋊AGL(1,𝔽5)C2312yes—
169C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
170C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
171C2×C22⋊AGL(1,𝔽5)C2312yes—
172C2×C22⋊AGL(1,𝔽5)C2312yes—
173C2×C22⋊AGL(1,𝔽5)C2312yes—
174C2×C22⋊AGL(1,𝔽5)C2311yescharacteristic
175C2×C22⋊AGL(1,𝔽5)C2312yes—
176D4×AGL(1,𝔽5)—24no—
177D4×AGL(1,𝔽5)—24no—
178D4×AGL(1,𝔽5)—44no—
179D4×AGL(1,𝔽5)—44no—
180#4130—24no—
181#4130—24no—
182#4130—44no—
183C2×C4⋊AGL(1,𝔽5)—24no—
184C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
185C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
186C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
187C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
188C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
189C2×C4⋊AGL(1,𝔽5)C2312yes—
190C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
191C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
192C2×C4⋊AGL(1,𝔽5)C2312yes—
193C2×C4⋊AGL(1,𝔽5)C2312yes—
194C2×C4⋊AGL(1,𝔽5)C2312yes—
195C2×C4⋊AGL(1,𝔽5)C2312yes—
196C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
197C2×C4×AGL(1,𝔽5)—24no—
198C2×C4×AGL(1,𝔽5)—44no—
199C2×C4×AGL(1,𝔽5)C2311yescharacteristic
200C2×C4×AGL(1,𝔽5)C2311yescharacteristic
201C2×C4×AGL(1,𝔽5)C2311yescharacteristic
202C2×C4×AGL(1,𝔽5)C2311yescharacteristic
203C2×C4×AGL(1,𝔽5)C2312yes—
204C2×C4×AGL(1,𝔽5)C2311yescharacteristic
205C2×C4×AGL(1,𝔽5)C2312yes—
206C2×C4×AGL(1,𝔽5)C2312yes—
207C2×C4×AGL(1,𝔽5)C2312yes—
208C2×C4×AGL(1,𝔽5)C2312yes—
209C2×C4×AGL(1,𝔽5)C2312yes—
210C2×C4×AGL(1,𝔽5)C2312yes—
211C2×C4×AGL(1,𝔽5)C2312yes—
212C2×C4×AGL(1,𝔽5)C2312yes—
213C2×C4×AGL(1,𝔽5)C2312yes—
214C2×C4×AGL(1,𝔽5)C2311yescharacteristic
215C5×C4⋊Q8C2×C411yescharacteristic, complemented
216C5×#123C2×C412yescomplemented
217C5×#123C2×C412yescomplemented
218C5×C22⋊Q8C2×C412yescomplemented
219C5×#121C2×C411yescharacteristic
220C5×#121C2×C411yescharacteristic, complemented
221C4×C5×D4C2×C411yescharacteristic, complemented
222C4×C5×D4C2×C411yescharacteristic, complemented
223C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
224C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
225#4092C2×C412yescomplemented
226#4090C2×C412yescomplemented
227#4085C2×C412yes—
228#4085C2×C412yescomplemented
229#4084C2×C411yescharacteristic
230#4084C2×C411yescharacteristic, complemented
231#4081C2×C412yescomplemented
232#4081C2×C412yescomplemented
233D4×Dic5C2×C411yescharacteristic, complemented
234D4×Dic5C2×C411yescharacteristic, complemented
235#4076C2×C411yescharacteristic
236#4076C2×C411yescharacteristic, complemented
237#4075C2×C412yescomplemented
238#4075C2×C412yescomplemented
239C4×C22⋊D5C2×C411yescharacteristic, complemented
240C4×C22⋊D5C2×C411yescharacteristic, complemented
241C4×C22⋊D5C2×C412yescomplemented
242C2×C4⋊Dic5C2×C411yescharacteristic, complemented
243C2×C4⋊Dic5C2×C411yescharacteristic, complemented
244#4070C2×C412yescomplemented
245C2×#683C2×C412yescomplemented
246C2×#683C2×C412yescomplemented
247#4043C2×C412yescomplemented
248#4042C2×C412yescomplemented
249#4042C2×C412yescomplemented
250#4041C2×C411yescharacteristic
251#4041C2×C411yescharacteristic, complemented
252#4040C2×C412yescomplemented
253#4040C2×C412yescomplemented
254#4040C2×C412yescomplemented
255#4040C2×C412yescomplemented
256#4039C2×C411yescharacteristic, complemented
257#4039C2×C411yescharacteristic, complemented
258D5×C4⋊C4C2×C411yescharacteristic, complemented
259D5×C4⋊C4C2×C411yescharacteristic, complemented
260D5×C4⋊C4C2×C411yescharacteristic, complemented
261D5×C4⋊C4C2×C411yescharacteristic, complemented
262D5×C4⋊C4C2×C412yescomplemented
263D5×C4⋊C4C2×C412yescomplemented
264D5×C4⋊C4C2311yescharacteristic
265D5×C4⋊C4C2311yescharacteristic
266D5×C4⋊C4C2312yes—
267D5×C4⋊C4C2311yescharacteristic
268D5×C4⋊C4C2312yes—
269D5×C4⋊C4C2312yes—
270D5×C4⋊C4C2311yescharacteristic
271#4034C2×C411yescharacteristic, complemented
272#4034C2×C411yescharacteristic, complemented
273#4034C2×C412yescomplemented
274#4032C2×C412yescomplemented
275#4032C2×C412yescomplemented
276#4030C2×C412yes—
277#4030C2×C412yescomplemented
278#4029C2×C412yescomplemented
279#4029C2×C412yescomplemented
280#4029C2×C412yescomplemented
281#4029C2×C412yescomplemented
282#4027C2×C411yescharacteristic, complemented
283#4027C2×C411yescharacteristic, complemented
284#4027C2×C412yescomplemented
285D5×C22⋊C4C2311yescharacteristic
286D5×C22⋊C4C2312yes—
287D5×C22⋊C4C2311yescharacteristic
288D5×C22⋊C4C2312yes—
289D5×C22⋊C4C2312yes—
290#4024C2×C412yescomplemented
291#4024C2×C412yescomplemented
292C4×D20C2×C411yescharacteristic, complemented
293C4×D20C2×C411yescharacteristic, complemented
294C42×D5C2311yescharacteristic
295#4015C2×C411yescharacteristic, complemented
296(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
297(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
298(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
299(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
300(C2×AGL(1,𝔽5))⋊C4C2312yes—
301(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
302(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
303(C2×AGL(1,𝔽5))⋊C4C2312yes—
304(C2×AGL(1,𝔽5))⋊C4C2312yes—
305(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
306(C2×AGL(1,𝔽5))⋊C4C2312yes—
307(C2×AGL(1,𝔽5))⋊C4C2312yes—
308(C2×AGL(1,𝔽5))⋊C4C2312yes—
309(C2×AGL(1,𝔽5))⋊C4C2312yes—
310(C2×AGL(1,𝔽5))⋊C4C2312yes—
311(C2×AGL(1,𝔽5))⋊C4C2312yes—
312(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
313(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
314(C2×AGL(1,𝔽5))⋊C4C2312yes—
315(C2×AGL(1,𝔽5))⋊C4C2312yes—
316(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
317(C2×AGL(1,𝔽5))⋊C4C2312yes—
318(C2×AGL(1,𝔽5))⋊C4C2312yes—
319(C2×AGL(1,𝔽5))⋊C4C2312yes—
320(C2×AGL(1,𝔽5))⋊C4C2312yes—
321(C2×AGL(1,𝔽5))⋊C4C2312yes—
322(C2×AGL(1,𝔽5))⋊C4C2312yes—
323C2×#547—51no—
324#2374—52no—
325#2369—51no—
326#2368—52no—
327#2363—51no—
328#2361—51no—
329#2359—52no—
330#2357—51no—
331#2352—51no—
332#2345—51no—
333#2344—51no—
334#2339—52no—
335#2335—52no—
336#2332—52no—
337#2331—51no—
338#2324—51no—
339C4×#123—52no—
340C4×#121—51no—
341#2297—52no—
342#2290—51no—
343#2275—51no—
344#2274—51no—
345C2×C4×C4⋊C4—51no—
346C23×D5C2411yescharacteristic
347C23×D5C2412yes—
348C23×D5C2411yescharacteristic
349C22×AGL(1,𝔽5)—22no—
350C22×AGL(1,𝔽5)—22no—
351C22×AGL(1,𝔽5)—22no—
352C22×AGL(1,𝔽5)—24no—
353C22×AGL(1,𝔽5)—22no—
354C22×AGL(1,𝔽5)—22no—
355C22×AGL(1,𝔽5)—24no—
356C22×AGL(1,𝔽5)—24no—
357C22×AGL(1,𝔽5)—24no—
358C22×AGL(1,𝔽5)—42no—
359C22×AGL(1,𝔽5)—41no—
360C22×AGL(1,𝔽5)—42no—
361C22×AGL(1,𝔽5)—42no—
362C22×AGL(1,𝔽5)—42no—
363C22×AGL(1,𝔽5)—42no—
364C22×AGL(1,𝔽5)C2411yescharacteristic
365C22×AGL(1,𝔽5)C2412yes—
366C22×AGL(1,𝔽5)C2411yescharacteristic
367C22×AGL(1,𝔽5)C2411yescharacteristic
368C22×AGL(1,𝔽5)C2411yescharacteristic
369C22×AGL(1,𝔽5)C2412yes—
370C22×AGL(1,𝔽5)C2412yes—
371C22×AGL(1,𝔽5)C2411yescharacteristic
372C22×AGL(1,𝔽5)C2411yescharacteristic
373C22×AGL(1,𝔽5)C2412yes—
374C22×AGL(1,𝔽5)C2411yescharacteristic
375C22×AGL(1,𝔽5)C2411yescharacteristic
376C5×#41—44no—
377C2×C5×Q8C22×C412yes—
378C2×C5×D4C22×C411yescharacteristic
379C2×C5×D4C22×C411yescharacteristic
380C2×C5×D4C22×C412yes—
381C2×C5×D4C22×C412yes—
382C22×C4×C5C22×C411yescharacteristic
383C22×C4×C5C22×C411yescharacteristic
384C22×C4×C5C22×C412yes—
385C22×C4×C5C22×C412yes—
386C22×C4×C5C22×C412yes—
387C2×C22⋊D5C22×C411yescharacteristic
388C2×C22⋊D5C22×C411yescharacteristic
389C2×C22⋊D5C22×C412yes—
390C2×C22⋊D5C22×C412yes—
391C2×C22⋊D5C22×C412yes—
392C2×C22⋊D5C22×C412yes—
393C2×C22⋊D5C22×C412yes—
394C22×Dic5C22×C412yes—
395C22×Dic5C22×C411yescharacteristic
396C22×Dic5C22×C411yescharacteristic
397C22×Dic5C22×C412yes—
398C22×Dic5C22×C412yes—
399#713—44no—
400Q8×D5—42no—
401Q8×D5—42no—
402#711—44no—
403#711—44no—
404#711—44no—
405D4×D5—24no—
406D4×D5—24no—
407D4×D5—22no—
408D4×D5—22no—
409D4×D5—22no—
410D4×D5—22no—
411D4×D5—42no—
412D4×D5—42no—
413#709—44no—
414#709—44no—
415#709—44no—
416C2×D20C22×C411yescharacteristic
417C2×D20C22×C412yes—
418C2×D20C22×C411yescharacteristic
419C2×D20C22×C412yes—
420C2×C4×D5—24no—
421C2×C4×D5—24no—
422C2×C4×D5—22no—
423C2×C4×D5—22no—
424C2×C4×D5—22no—
425C2×C4×D5—22no—
426C2×C4×D5—42no—
427C2×C4×D5—42no—
428C2×C4×D5—42no—
429C2×C4×D5—42no—
430C2×C4×D5C22×C412yes—
431C2×C4×D5C22×C412yes—
432C2×C4×D5C22×C411yescharacteristic
433C2×C4×D5C22×C411yescharacteristic
434C2×C4×D5C22×C411yescharacteristic
435C2×C4×D5C22×C411yescharacteristic
436C2×C4×D5C22×C412yes—
437C2×C4×D5C22×C412yes—
438C2×C4×D5C22×C412yes—
439C2×C4×D5C22×C412yes—
440C2×C4×D5C2412yes—
441C2×C4×D5C2412yes—
442C2×C4×D5C2412yes—
443C2×C4×D5C2411yescharacteristic
444C2×C4×D5C2411yescharacteristic
445C2×C4×D5C2411yescharacteristic
446C2×C4×D5C2411yescharacteristic
447C2×C4×D5C2411yescharacteristic
448C2×Dic10C22×C412yes—
449C2×Dic10C22×C412yes—
450C2×Dic10C22×C412yes—
451C22⋊AGL(1,𝔽5)—22no—
452C22⋊AGL(1,𝔽5)—24no—
453C22⋊AGL(1,𝔽5)—22no—
454C22⋊AGL(1,𝔽5)—22no—
455C22⋊AGL(1,𝔽5)—22no—
456C22⋊AGL(1,𝔽5)—24no—
457C22⋊AGL(1,𝔽5)—24no—
458C22⋊AGL(1,𝔽5)—24no—
459C22⋊AGL(1,𝔽5)—24no—
460C22⋊AGL(1,𝔽5)—22no—
461C22⋊AGL(1,𝔽5)—42no—
462C22⋊AGL(1,𝔽5)—42no—
463C22⋊AGL(1,𝔽5)—42no—
464C22⋊AGL(1,𝔽5)—42no—
465C22⋊AGL(1,𝔽5)—41no—
466C4⋊AGL(1,𝔽5)—24no—
467C4⋊AGL(1,𝔽5)—22no—
468C4⋊AGL(1,𝔽5)—22no—
469C4⋊AGL(1,𝔽5)—22no—
470C4⋊AGL(1,𝔽5)—22no—
471C4⋊AGL(1,𝔽5)—22no—
472C4⋊AGL(1,𝔽5)—22no—
473C4⋊AGL(1,𝔽5)—41no—
474C4⋊AGL(1,𝔽5)—42no—
475C4⋊AGL(1,𝔽5)—42no—
476C4⋊AGL(1,𝔽5)—42no—
477C4⋊AGL(1,𝔽5)—42no—
478C4⋊AGL(1,𝔽5)#4114yescomplemented
479C4×AGL(1,𝔽5)—22no—
480C4×AGL(1,𝔽5)—22no—
481C4×AGL(1,𝔽5)—24no—
482C4×AGL(1,𝔽5)—22no—
483C4×AGL(1,𝔽5)—22no—
484C4×AGL(1,𝔽5)—22no—
485C4×AGL(1,𝔽5)—42no—
486C4×AGL(1,𝔽5)—42no—
487C4×AGL(1,𝔽5)—42no—
488C4×AGL(1,𝔽5)—42no—
489C4×AGL(1,𝔽5)—42no—
490C4×AGL(1,𝔽5)—42no—
491C4×AGL(1,𝔽5)—42no—
492C4×AGL(1,𝔽5)—42no—
493C4×AGL(1,𝔽5)—42no—
494C4×AGL(1,𝔽5)#4114yescomplemented
495C5×C4⋊C4C22×C411yescharacteristic
496C5×C4⋊C4C22×C411yescharacteristic
497C5×C4⋊C4C22×C411yescharacteristic
498C5×C4⋊C4C22×C412yes—
499C5×C4⋊C4C22×C412yes—
500C5×C4⋊C4C22×C411yescharacteristic
501C5×C4⋊C4C22×C412yes—
502C5×C22⋊C4C22×C412yes—
503C5×C22⋊C4C22×C411yescharacteristic
504C5×C22⋊C4C22×C411yescharacteristic
505C5×C22⋊C4C22×C412yes—
506C5×C22⋊C4C22×C412yes—
507C42×C5C22×C411yescharacteristic
508C22⋊Dic5C22×C412yes—
509C22⋊Dic5C22×C412yes—
510C22⋊Dic5C22×C412yes—
511C22⋊Dic5C22×C411yescharacteristic
512C22⋊Dic5C22×C411yescharacteristic
513#685C22×C411yescharacteristic
514#685C22×C411yescharacteristic
515#685C22×C412yes—
516#685C22×C411yescharacteristic
517#685C22×C411yescharacteristic
518#685C22×C412yes—
519#685C22×C412yes—
520#685C22×C412yes—
521#685C22×C412yes—
522#685C22×C412yes—
523C4⋊Dic5C22×C412yes—
524C4⋊Dic5C22×C411yescharacteristic
525C4⋊Dic5C22×C411yescharacteristic
526C4⋊Dic5C22×C411yescharacteristic
527C4⋊Dic5C22×C411yescharacteristic
528C4⋊Dic5C22×C412yes—
529C4⋊Dic5C22×C412yes—
530#683C22×C411yescharacteristic
531#683C22×C411yescharacteristic
532#683C22×C412yes—
533#683C22×C412yes—
534#683C22×C412yes—
535#683C22×C412yes—
536#683C22×C412yes—
537#683C22×C412yes—
538#683C22×C412yes—
539#683C22×C412yes—
540#683C22×C412yes—
541C4×Dic5C22×C411yescharacteristic
542C4×Dic5C22×C411yescharacteristic
543C4×Dic5C22×C411yescharacteristic
544C22×#41—52no—
545#547—52no—
546#547—51no—
547#547—52no—
548#547—52no—
549#547—52no—
550#547—51no—
551#547—51no—
552#547—51no—
553#547—51no—
554#547—51no—
555#547—51no—
556#547AGL(1,𝔽5)11yescharacteristic, complemented
557C2×C4⋊Q8—51no—
558C2×#123—52no—
559C2×#123—52no—
560C2×C22⋊Q8—52no—
561C2×#121—51no—
562C2×#121—51no—
563C2×C4×D4—51no—
564C2×C4×D4—51no—
565C2×C4×D4—51no—
566C2×C4×D4—51no—
567C2×C4×D4—52no—
568C2×C4×D4—52no—
569C2×#117—51no—
570C2×#117—51no—
571C2×#117—52no—
572C22×C4⋊C4—51no—
573C22×C4⋊C4—51no—
574C22×C4⋊C4—51no—
575C22×C42—51no—
576C22×C42—52no—
577#391—52no—
578#391—52no—
579#391—52no—
580#391—52no—
581#390—52no—
582#390—51no—
583#390—51no—
584#390—52no—
585#389—51no—
586#389—51no—
587#389—51no—
588#389—52no—
589#389—51no—
590#388—52no—
591#388—52no—
592#388—52no—
593#388—52no—
594#388—51no—
595#388—52no—
596#388—52no—
597#388—52no—
598#388—51no—
599#387—52no—
600#387—52no—
601#387—51no—
602#387—52no—
603#387—52no—
604#387—52no—
605#387—52no—
606#387—52no—
607#387—51no—
608#386—52no—
609#386—52no—
610#386—51no—
611#386—52no—
612#386—52no—
613#386—51no—
614#386—52no—
615#385—52no—
616#385—52no—
617#385—51no—
618#385—51no—
619#382—51no—
620#381—52no—
621#381—52no—
622#380—51no—
623#380—52no—
624#380—51no—
625C4×C4⋊C4—51no—
626C4×C4⋊C4—51no—
627C4×C4⋊C4—52no—
628C4×C4⋊C4—52no—
629C4×C4⋊C4—51no—
630C4×C4⋊C4—51no—
631C4×C4⋊C4—51no—
632C4×C4⋊C4—51no—
633C4×C4⋊C4—51no—
634C4×C4⋊C4—52no—
635C4×C4⋊C4—51no—
636C4×C4⋊C4—51no—
637C4×C4⋊C4—52no—
638C4×C4⋊C4—52no—
639C4×C4⋊C4—51no—
640C4×C22⋊C4—52no—
641C4×C22⋊C4—52no—
642C4×C22⋊C4—52no—
643C4×C22⋊C4—52no—
644C4×C22⋊C4—51no—
645C4×C22⋊C4—51no—
646C4×C22⋊C4—52no—
647C4×C22⋊C4—52no—
648C4×C22⋊C4—52no—
649C4×C22⋊C4—52no—
650C4×C22⋊C4—52no—
651C4×C22⋊C4—52no—
652#376—51no—
653C2×#95—52no—
654C2×#95—52no—
655C23×C5C23×C412yes—
656C23×C5C23×C411yescharacteristic
657C23×C5C23×C411yescharacteristic
658C22×D5—21no—
659C22×D5—21no—
660C22×D5—21no—
661C22×D5—21no—
662C22×D5—21no—
663C22×D5—21no—
664C22×D5—22no—
665C22×D5—22no—
666C22×D5—22no—
667C22×D5—22no—
668C22×D5—21no—
669C22×D5—21no—
670C22×D5—21no—
671C22×D5—22no—
672C22×D5—21no—
673C22×D5—22no—
674C22×D5C23×C412yes—
675C22×D5C23×C411yescharacteristic
676C22×D5C23×C411yescharacteristic
677C22×D5H(5,𝔽2)12yes—
678C22×D5H(5,𝔽2)12yes—
679C22×D5C2511yescharacteristic
680C2×AGL(1,𝔽5)—28no—
681C2×AGL(1,𝔽5)—21no—
682C2×AGL(1,𝔽5)—21no—
683C2×AGL(1,𝔽5)—21no—
684C2×AGL(1,𝔽5)—22no—
685C2×AGL(1,𝔽5)—21no—
686C2×AGL(1,𝔽5)—21no—
687C2×AGL(1,𝔽5)—22no—
688C2×AGL(1,𝔽5)—21no—
689C2×AGL(1,𝔽5)—21no—
690C2×AGL(1,𝔽5)—21no—
691C2×AGL(1,𝔽5)—21no—
692C2×AGL(1,𝔽5)—22no—
693C2×AGL(1,𝔽5)—21no—
694C2×AGL(1,𝔽5)—21no—
695C2×AGL(1,𝔽5)—22no—
696C2×AGL(1,𝔽5)—22no—
697C2×AGL(1,𝔽5)—21no—
698C2×AGL(1,𝔽5)—21no—
699C2×AGL(1,𝔽5)—22no—
700C2×AGL(1,𝔽5)—22no—
701C2×AGL(1,𝔽5)—21no—
702C2×AGL(1,𝔽5)—22no—
703C2×AGL(1,𝔽5)—21no—
704C2×AGL(1,𝔽5)—21no—
705C2×AGL(1,𝔽5)—21no—
706C2×AGL(1,𝔽5)—22no—
707C2×AGL(1,𝔽5)—21no—
708C2×AGL(1,𝔽5)—22no—
709C2×AGL(1,𝔽5)—21no—
710C2×AGL(1,𝔽5)—21no—
711C2×AGL(1,𝔽5)—22no—
712C2×AGL(1,𝔽5)—21no—
713C2×AGL(1,𝔽5)—44no—
714C2×AGL(1,𝔽5)—48no—
715C2×AGL(1,𝔽5)—84no—
716C2×AGL(1,𝔽5)—84no—
717C2×AGL(1,𝔽5)C2×#4112yes—
718C2×AGL(1,𝔽5)C2×#4112yes—
719C2×AGL(1,𝔽5)C2×#4114yes—
720C2×AGL(1,𝔽5)2−1+412yes—
721C5×Q8—42no—
722C5×D4—22no—
723C5×D4—24no—
724C5×D4—22no—
725C5×D4—42no—
726C2×C4×C5—24no—
727C2×C4×C5—22no—
728C2×C4×C5—22no—
729C2×C4×C5—42no—
730C2×C4×C5—42no—
731C2×C4×C5C23×C411yescharacteristic
732C2×C4×C5C23×C411yescharacteristic
733C2×C4×C5C23×C412yes—
734C2×C4×C5C23×C412yes—
735C2×C4×C5C23×C412yes—
736C2×C4×C5C23×C411yescharacteristic
737C2×C4×C5C23×C411yescharacteristic
738C2×C4×C5C23×C411yescharacteristic
739C22⋊D5—22no—
740C22⋊D5—24no—
741C22⋊D5—22no—
742C22⋊D5—24no—
743C22⋊D5—24no—
744C22⋊D5—42no—
745C22⋊D5—42no—
746C2×Dic5—24no—
747C2×Dic5—22no—
748C2×Dic5—22no—
749C2×Dic5—42no—
750C2×Dic5—42no—
751C2×Dic5C23×C411yescharacteristic
752C2×Dic5C23×C411yescharacteristic
753C2×Dic5C23×C411yescharacteristic
754C2×Dic5C23×C411yescharacteristic
755C2×Dic5C23×C412yes—
756C2×Dic5C23×C412yes—
757C2×Dic5C23×C412yes—
758C2×Dic5C23×C411yescharacteristic
759D20—22no—
760D20—24no—
761D20—22no—
762D20—42no—
763C4×D5—24no—
764C4×D5—24no—
765C4×D5—21no—
766C4×D5—21no—
767C4×D5—21no—
768C4×D5—21no—
769C4×D5—22no—
770C4×D5—22no—
771C4×D5—22no—
772C4×D5—22no—
773C4×D5—22no—
774C4×D5—22no—
775C4×D5—21no—
776C4×D5—21no—
777C4×D5—21no—
778C4×D5—21no—
779C4×D5—22no—
780C4×D5—22no—
781C4×D5—22no—
782C4×D5—22no—
783C4×D5—42no—
784C4×D5—42no—
785C4×D5—42no—
786C4×D5—42no—
787C4×D5C2×#4112yes—
788C4×D5C2×#4112yes—
789Dic10—42no—
790Dic10—42no—
791Dic10—42no—
792C2×#41—52no—
793C2×#41—52no—
794C2×#41—52no—
795C2×#41—52no—
796C2×#41—52no—
797C2×#41—52no—
798C2×#41—52no—
799C2×#41—204no—
800C2×#41—204no—
801C2×#41C2×AGL(1,𝔽5)12yescomplemented
802C22×Q8—52no—
803C22×D4—51no—
804C22×D4—52no—
805C22×D4—51no—
806C22×D4—52no—
807C23×C4—51no—
808C23×C4—51no—
809C23×C4—52no—
810C23×C4—52no—
811C23×C4—52no—
812C23×C4—51no—
813C23×C4—52no—
814C23×C4—51no—
815C23×C4—52no—
816C23×C4—52no—
817C4⋊Q8—52no—
818C4⋊Q8—52no—
819C4⋊Q8—51no—
820C4⋊Q8—51no—
821C4⋊Q8—51no—
822C4⋊Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
823#123—52no—
824#123—52no—
825#123—52no—
826#123—52no—
827#123—52no—
828#123—52no—
829#123—52no—
830#123—52no—
831#123—52no—
832#123—52no—
833#123—52no—
834#123—52no—
835#123—52no—
836#123—52no—
837#123C2×AGL(1,𝔽5)12yescomplemented
838#123C2×AGL(1,𝔽5)12yescomplemented
839C22⋊Q8—52no—
840C22⋊Q8—52no—
841C22⋊Q8—52no—
842C22⋊Q8—52no—
843C22⋊Q8—52no—
844C22⋊Q8—52no—
845C22⋊Q8—52no—
846C22⋊Q8C2×AGL(1,𝔽5)12yescomplemented
847#121—51no—
848#121—51no—
849#121—52no—
850#121—52no—
851#121—51no—
852#121—51no—
853#121—51no—
854#121—51no—
855#121—52no—
856#121—52no—
857#121C2×AGL(1,𝔽5)11yescharacteristic
858#121C2×AGL(1,𝔽5)11yescharacteristic, complemented
859C4×D4—51no—
860C4×D4—51no—
861C4×D4—52no—
862C4×D4—51no—
863C4×D4—51no—
864C4×D4—51no—
865C4×D4—51no—
866C4×D4—52no—
867C4×D4—51no—
868C4×D4—51no—
869C4×D4—51no—
870C4×D4—51no—
871C4×D4—104no—
872C4×D4—104no—
873C4×D4—204no—
874C4×D4—204no—
875C4×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
876C4×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
877#117—104no—
878#117—104no—
879#117—204no—
880C2×C4⋊C4—51no—
881C2×C4⋊C4—52no—
882C2×C4⋊C4—52no—
883C2×C4⋊C4—51no—
884C2×C4⋊C4—51no—
885C2×C4⋊C4—51no—
886C2×C4⋊C4—51no—
887C2×C4⋊C4—51no—
888C2×C4⋊C4—52no—
889C2×C4⋊C4—52no—
890C2×C4⋊C4—52no—
891C2×C4⋊C4—52no—
892C2×C4⋊C4—51no—
893C2×C4⋊C4—51no—
894C2×C4⋊C4—51no—
895C2×C4⋊C4—51no—
896C2×C4⋊C4—51no—
897C2×C4⋊C4—52no—
898C2×C4⋊C4—51no—
899C2×C4⋊C4—52no—
900C2×C4⋊C4—51no—
901C2×C4⋊C4—51no—
902C2×C4⋊C4—51no—
903C2×C4⋊C4—51no—
904C2×C4⋊C4—51no—
905C2×C4⋊C4—52no—
906C2×C4⋊C4—52no—
907C2×C4⋊C4—52no—
908C2×C4⋊C4—52no—
909C2×C4⋊C4—51no—
910C2×C4⋊C4—104no—
911C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
912C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
913C2×C22⋊C4—51no—
914C2×C22⋊C4—52no—
915C2×C22⋊C4—51no—
916C2×C22⋊C4—52no—
917C2×C22⋊C4—52no—
918C2×C22⋊C4—51no—
919C2×C22⋊C4—52no—
920C2×C22⋊C4—51no—
921C2×C22⋊C4—52no—
922C2×C22⋊C4—51no—
923C2×C22⋊C4—51no—
924C2×C22⋊C4—52no—
925C2×C22⋊C4—52no—
926C2×C22⋊C4—52no—
927C2×C22⋊C4—51no—
928C2×C22⋊C4—52no—
929C2×C22⋊C4—52no—
930C2×C22⋊C4—51no—
931C2×C22⋊C4—52no—
932C2×C22⋊C4—52no—
933C2×C42—51no—
934C2×C42—51no—
935C2×C42—52no—
936C2×C42—51no—
937C2×C42—51no—
938C2×C42—51no—
939C2×C42—51no—
940C2×C42—51no—
941C2×C42—52no—
942C2×C42—52no—
943C2×C42—52no—
944C2×C42—52no—
945C2×C42—52no—
946C2×C42—52no—
947C2×C42—52no—
948C2×C42—52no—
949C2×C42—52no—
950C2×C42—104no—
951C2×C42—204no—
952#95—51no—
953#95—52no—
954#95—52no—
955#95—52no—
956#95—52no—
957#95—52no—
958#95—52no—
959#95—51no—
960#95—51no—
961#95—51no—
962#95—51no—
963#95—52no—
964#95—51no—
965#95—52no—
966#95—52no—
967#95—52no—
968#95—52no—
969#95—52no—
970#95—52no—
971#95—52no—
972#95—52no—
973#95—51no—
974#95—51no—
975#95—52no—
976#95—51no—
977#95—51no—
978#95—52no—
979C22×C5—21no—
980C22×C5—21no—
981C22×C5—21no—
982C22×C5—22no—
983C22×C5—21no—
984C22×C5—22no—
985C22×C5—21no—
986C22×C5—22no—
987C22×C5#51812yes—
988C22×C5C24×C411yescharacteristic
989C2×D5—21no—
990C2×D5—21no—
991C2×D5—22no—
992C2×D5—22no—
993C2×D5—22no—
994C2×D5—22no—
995C2×D5—21no—
996C2×D5—22no—
997C2×D5—21no—
998C2×D5—22no—
999C2×D5—21no—
1000C2×D5—22no—
1001C2×D5—41no—
1002C2×D5—42no—
1003C2×D5—42no—
1004C2×D5—41no—
1005C2×D5—42no—
1006C2×D5—41no—
1007C2×D5—41no—
1008C2×D5—42no—
1009C2×D5#51812yes—
1010C2×D5C22×#4111yescharacteristic
1011C2×D5C22×#4111yescharacteristic
1012C2×D5C2×H(5,𝔽2)11yescharacteristic
1013C2×D5C2×H(5,𝔽2)11yescharacteristic
1014C2×D5C2×2−1+411yescharacteristic
1015C2×D5#58511yescharacteristic
1016AGL(1,𝔽5)—22no—
1017AGL(1,𝔽5)—22no—
1018AGL(1,𝔽5)—22no—
1019AGL(1,𝔽5)—24no—
1020AGL(1,𝔽5)—41no—
1021AGL(1,𝔽5)—41no—
1022AGL(1,𝔽5)—41no—
1023AGL(1,𝔽5)—42no—
1024AGL(1,𝔽5)—42no—
1025AGL(1,𝔽5)—41no—
1026AGL(1,𝔽5)—42no—
1027AGL(1,𝔽5)—41no—
1028C4×C5—21no—
1029C4×C5—21no—
1030C4×C5—21no—
1031C4×C5—22no—
1032C4×C5—22no—
1033C4×C5—22no—
1034C4×C5—21no—
1035C4×C5C4×#4112yes—
1036Dic5—21no—
1037Dic5—21no—
1038Dic5—21no—
1039Dic5—22no—
1040Dic5—22no—
1041Dic5—22no—
1042Dic5—21no—
1043Dic5C4×#4112yes—
1044C24—51no—
1045C24—52no—
1046C24—51no—
1047#41—44no—
1048#41—204no—
1049#41—204no—
1050#41—204no—
1051#41—204no—
1052#41—204no—
1053#41—204no—
1054#41—204no—
1055C2×Q8—52no—
1056C2×Q8—52no—
1057C2×Q8—52no—
1058C2×Q8—202no—
1059C2×Q8—202no—
1060C2×Q8C22×AGL(1,𝔽5)12yes—
1061C2×D4—52no—
1062C2×D4—51no—
1063C2×D4—51no—
1064C2×D4—52no—
1065C2×D4—52no—
1066C2×D4—52no—
1067C2×D4—52no—
1068C2×D4—51no—
1069C2×D4—51no—
1070C2×D4—52no—
1071C2×D4—52no—
1072C2×D4—102no—
1073C2×D4—102no—
1074C2×D4—104no—
1075C2×D4—104no—
1076C2×D4—102no—
1077C2×D4—102no—
1078C2×D4—202no—
1079C2×D4—202no—
1080C2×D4C22×AGL(1,𝔽5)11yescharacteristic
1081C2×D4C22×AGL(1,𝔽5)11yescharacteristic
1082C2×D4C22×AGL(1,𝔽5)12yes—
1083C2×D4C22×AGL(1,𝔽5)12yes—
1084C22×C4—51no—
1085C22×C4—51no—
1086C22×C4—51no—
1087C22×C4—51no—
1088C22×C4—52no—
1089C22×C4—51no—
1090C22×C4—51no—
1091C22×C4—52no—
1092C22×C4—52no—
1093C22×C4—52no—
1094C22×C4—51no—
1095C22×C4—52no—
1096C22×C4—51no—
1097C22×C4—51no—
1098C22×C4—51no—
1099C22×C4—52no—
1100C22×C4—52no—
1101C22×C4—51no—
1102C22×C4—51no—
1103C22×C4—51no—
1104C22×C4—51no—
1105C22×C4—52no—
1106C22×C4—52no—
1107C22×C4—52no—
1108C22×C4—52no—
1109C22×C4—52no—
1110C22×C4—52no—
1111C22×C4—51no—
1112C22×C4—51no—
1113C22×C4—51no—
1114C22×C4—52no—
1115C22×C4—51no—
1116C22×C4—52no—
1117C22×C4—52no—
1118C22×C4—51no—
1119C22×C4—102no—
1120C22×C4—102no—
1121C22×C4—102no—
1122C22×C4—102no—
1123C22×C4—104no—
1124C22×C4—104no—
1125C22×C4—102no—
1126C22×C4—102no—
1127C22×C4—102no—
1128C22×C4—104no—
1129C22×C4—104no—
1130C22×C4—104no—
1131C22×C4—102no—
1132C22×C4—104no—
1133C22×C4—102no—
1134C22×C4—202no—
1135C22×C4—202no—
1136C22×C4—202no—
1137C22×C4—202no—
1138C22×C4—202no—
1139C22×C4—201no—
1140C22×C4—202no—
1141C22×C4—202no—
1142C22×C4—202no—
1143C22×C4—202no—
1144C22×C4C22×AGL(1,𝔽5)11yescharacteristic
1145C22×C4C22×AGL(1,𝔽5)11yescharacteristic
1146C22×C4C22×AGL(1,𝔽5)12yes—
1147C22×C4C22×AGL(1,𝔽5)12yes—
1148C22×C4C22×AGL(1,𝔽5)12yes—
1149C4⋊C4—54no—
1150C4⋊C4—52no—
1151C4⋊C4—51no—
1152C4⋊C4—52no—
1153C4⋊C4—52no—
1154C4⋊C4—51no—
1155C4⋊C4—51no—
1156C4⋊C4—52no—
1157C4⋊C4—52no—
1158C4⋊C4—52no—
1159C4⋊C4—52no—
1160C4⋊C4—52no—
1161C4⋊C4—52no—
1162C4⋊C4—51no—
1163C4⋊C4—51no—
1164C4⋊C4—51no—
1165C4⋊C4—52no—
1166C4⋊C4—52no—
1167C4⋊C4—52no—
1168C4⋊C4—102no—
1169C4⋊C4—104no—
1170C4⋊C4—102no—
1171C4⋊C4—102no—
1172C4⋊C4—102no—
1173C4⋊C4—102no—
1174C4⋊C4—102no—
1175C4⋊C4—202no—
1176C4⋊C4—202no—
1177C4⋊C4—202no—
1178C4⋊C4—202no—
1179C4⋊C4—201no—
1180C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
1181C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
1182C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
1183C4⋊C4C22×AGL(1,𝔽5)12yes—
1184C4⋊C4C22×AGL(1,𝔽5)12yes—
1185C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
1186C4⋊C4C22×AGL(1,𝔽5)12yes—
1187C22⋊C4—51no—
1188C22⋊C4—51no—
1189C22⋊C4—52no—
1190C22⋊C4—52no—
1191C22⋊C4—52no—
1192C22⋊C4—51no—
1193C22⋊C4—51no—
1194C22⋊C4—52no—
1195C22⋊C4—51no—
1196C22⋊C4—51no—
1197C22⋊C4—52no—
1198C22⋊C4—52no—
1199C22⋊C4—52no—
1200C22⋊C4—52no—
1201C22⋊C4—52no—
1202C22⋊C4—102no—
1203C22⋊C4—102no—
1204C22⋊C4—104no—
1205C22⋊C4—104no—
1206C22⋊C4—104no—
1207C22⋊C4—104no—
1208C22⋊C4—102no—
1209C22⋊C4—102no—
1210C22⋊C4—104no—
1211C22⋊C4—102no—
1212C22⋊C4—202no—
1213C22⋊C4—202no—
1214C22⋊C4—202no—
1215C22⋊C4—202no—
1216C22⋊C4—201no—
1217C22⋊C4C22×AGL(1,𝔽5)11yescharacteristic
1218C22⋊C4C22×AGL(1,𝔽5)11yescharacteristic
1219C22⋊C4C22×AGL(1,𝔽5)12yes—
1220C22⋊C4C22×AGL(1,𝔽5)12yes—
1221C22⋊C4C22×AGL(1,𝔽5)12yes—
1222C42—54no—
1223C42—51no—
1224C42—51no—
1225C42—51no—
1226C42—102no—
1227C42—102no—
1228C42—102no—
1229C42—102no—
1230C42—104no—
1231C42—102no—
1232C42—202no—
1233C42—202no—
1234C42—202no—
1235C42—202no—
1236C42—202no—
1237C42—202no—
1238C42—202no—
1239C42—202no—
1240C42—202no—
1241C42C22×AGL(1,𝔽5)11yescharacteristic
1242C2×C5—22no—
1243C2×C5—42no—
1244C2×C5—41no—
1245C2×C5C2×C4×#4111yescharacteristic
1246C2×C5C2×#51811yescharacteristic
1247C2×C5C4×2−1+411yescharacteristic
1248D5—22no—
1249D5—41no—
1250D5—42no—
1251D5#349211yescharacteristic
1252D5#349411yescharacteristic
1253D5#351311yescharacteristic
1254D5#352211yescharacteristic
1255C23—51no—
1256C23—52no—
1257C23—52no—
1258C23—51no—
1259C23—52no—
1260C23—51no—
1261C23—101no—
1262C23—101no—
1263C23—101no—
1264C23—101no—
1265C23—101no—
1266C23—101no—
1267C23—102no—
1268C23—102no—
1269C23—101no—
1270C23—102no—
1271C23—101no—
1272C23—102no—
1273C23—102no—
1274C23—102no—
1275C23—101no—
1276C23—101no—
1277C23C23×AGL(1,𝔽5)12yes—
1278C23C23×AGL(1,𝔽5)11yescharacteristic
1279C23C23×AGL(1,𝔽5)11yescharacteristic
1280Q8—42no—
1281Q8—202no—
1282Q8—202no—
1283Q8—202no—
1284D4—22no—
1285D4—24no—
1286D4—22no—
1287D4—42no—
1288D4—102no—
1289D4—104no—
1290D4—104no—
1291D4—102no—
1292D4—104no—
1293D4—102no—
1294D4—104no—
1295D4—102no—
1296D4—202no—
1297D4—202no—
1298D4—202no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—42no—
1303C2×C4—42no—
1304C2×C4—51no—
1305C2×C4—52no—
1306C2×C4—52no—
1307C2×C4—52no—
1308C2×C4—52no—
1309C2×C4—54no—
1310C2×C4—52no—
1311C2×C4—51no—
1312C2×C4—51no—
1313C2×C4—51no—
1314C2×C4—51no—
1315C2×C4—52no—
1316C2×C4—52no—
1317C2×C4—52no—
1318C2×C4—102no—
1319C2×C4—102no—
1320C2×C4—101no—
1321C2×C4—101no—
1322C2×C4—101no—
1323C2×C4—102no—
1324C2×C4—102no—
1325C2×C4—102no—
1326C2×C4—102no—
1327C2×C4—102no—
1328C2×C4—101no—
1329C2×C4—101no—
1330C2×C4—101no—
1331C2×C4—102no—
1332C2×C4—104no—
1333C2×C4—104no—
1334C2×C4—101no—
1335C2×C4—101no—
1336C2×C4—102no—
1337C2×C4—102no—
1338C2×C4—101no—
1339C2×C4—101no—
1340C2×C4—101no—
1341C2×C4—102no—
1342C2×C4—101no—
1343C2×C4—102no—
1344C2×C4—101no—
1345C2×C4—101no—
1346C2×C4—108no—
1347C2×C4—104no—
1348C2×C4—102no—
1349C2×C4—102no—
1350C2×C4—101no—
1351C2×C4—101no—
1352C2×C4—101no—
1353C2×C4—102no—
1354C2×C4—101no—
1355C2×C4—101no—
1356C2×C4—101no—
1357C2×C4—102no—
1358C2×C4—101no—
1359C2×C4—101no—
1360C2×C4—102no—
1361C2×C4—102no—
1362C2×C4—102no—
1363C2×C4—102no—
1364C2×C4—101no—
1365C2×C4—101no—
1366C2×C4—102no—
1367C2×C4—101no—
1368C2×C4—101no—
1369C2×C4—102no—
1370C2×C4—101no—
1371C2×C4—101no—
1372C2×C4—102no—
1373C2×C4—101no—
1374C2×C4—202no—
1375C2×C4—202no—
1376C2×C4—202no—
1377C2×C4—202no—
1378C2×C4—202no—
1379C2×C4—202no—
1380C2×C4—204no—
1381C2×C4—208no—
1382C2×C4—404no—
1383C2×C4—404no—
1384C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1385C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1386C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1387C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1388C2×C4C23×AGL(1,𝔽5)12yes—
1389C2×C4C23×AGL(1,𝔽5)12yes—
1390C2×C4C23×AGL(1,𝔽5)12yes—
1391C2×C4C23×AGL(1,𝔽5)11yescharacteristic
1392C5#3429811yescharacteristic, complemented, Sylow
1393C22—21no—
1394C22—21no—
1395C22—21no—
1396C22—22no—
1397C22—21no—
1398C22—22no—
1399C22—21no—
1400C22—22no—
1401C22—51no—
1402C22—51no—
1403C22—51no—
1404C22—51no—
1405C22—51no—
1406C22—51no—
1407C22—52no—
1408C22—102no—
1409C22—102no—
1410C22—102no—
1411C22—102no—
1412C22—101no—
1413C22—101no—
1414C22—101no—
1415C22—102no—
1416C22—101no—
1417C22—102no—
1418C22—102no—
1419C22—101no—
1420C22—202no—
1421C22—202no—
1422C22—201no—
1423C22—201no—
1424C22—202no—
1425C22—201no—
1426C22—201no—
1427C22—202no—
1428C22#6625812yes—
1429C22C24×AGL(1,𝔽5)11yescharacteristic
1430C4—22no—
1431C4—22no—
1432C4—21no—
1433C4—22no—
1434C4—21no—
1435C4—21no—
1436C4—21no—
1437C4—52no—
1438C4—102no—
1439C4—102no—
1440C4—102no—
1441C4—104no—
1442C4—102no—
1443C4—102no—
1444C4—101no—
1445C4—102no—
1446C4—101no—
1447C4—101no—
1448C4—101no—
1449C4—202no—
1450C4—201no—
1451C4—201no—
1452C4—202no—
1453C4—201no—
1454C4—201no—
1455C4—201no—
1456C4—202no—
1457C4#41×AGL(1,𝔽5)12yes—
1458C2—22no—
1459C2—41no—
1460C2—42no—
1461C2—51no—
1462C2—51no—
1463C2—51no—
1464C2—51no—
1465C2—102no—
1466C2—201no—
1467C2—202no—
1468C2C2×#6625811yescharacteristic
1469C2C2×#41×AGL(1,𝔽5)11yescharacteristic
1470C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#547C4
prime radicalD5×#547C2
cosocleC22×D5C25
hypercenter#547AGL(1,𝔽5)
hypocenterC5#34298
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #10617557C2semidirect
3. #10617555C2semidirect
4. #10617389C2semidirect
5. #10617387C2semidirect
6. #10617307C2semidirect
7. #10617306C2semidirect
8. #10617305C2semidirect
9. AGL(1,𝔽5)×#123C2semidirect
10. #10617287C2semidirect
11. #10617284C2semidirect
12. #10617254C2semidirect
13. #10617253C2semidirect
14. #10617250C2semidirect
15. AGL(1,𝔽5)×#121C2semidirect
16. #10617182C2semidirect
17. #10617179C2semidirect
18. #10617173C2semidirect
19. #10617172C2semidirect
20. #10617104C2semidirect
21. #10617103C2semidirect
22. #10617098C2semidirect
23. C2×C4⋊C4×AGL(1,𝔽5)C2semidirect
35. C5×#547C4semidirect
36. #66158C4semidirect
37. #66060C4semidirect
39. #65989C4semidirect
40. #65989C4semidirect
43. #65965C4semidirect
45. #65945C4semidirect
46. #65945C4semidirect
49. #65889C4semidirect
50. #65885C4semidirect
53. #65841C4semidirect
54. #65841C4semidirect
141. C2×C5×#41C2×C4semidirect
144. C2×#713C2×C4semidirect
146. C2×#711C2×C4semidirect
147. C2×#711C2×C4semidirect
148. C2×#711C2×C4semidirect
153. C2×#709C2×C4semidirect
154. C2×#709C2×C4semidirect
155. C2×#709C2×C4semidirect
215. C5×C4⋊Q8C2×C4semidirect
216. C5×#123C2×C4semidirect
217. C5×#123C2×C4semidirect
218. C5×C22⋊Q8C2×C4semidirect
220. C5×#121C2×C4semidirect
221. C4×C5×D4C2×C4semidirect
222. C4×C5×D4C2×C4semidirect
223. C2×C5×C4⋊C4C2×C4semidirect
224. C2×C5×C4⋊C4C2×C4semidirect
225. #4092C2×C4semidirect
226. #4090C2×C4semidirect
228. #4085C2×C4semidirect
230. #4084C2×C4semidirect
231. #4081C2×C4semidirect
232. #4081C2×C4semidirect
233. D4×Dic5C2×C4semidirect
234. D4×Dic5C2×C4semidirect
236. #4076C2×C4semidirect
237. #4075C2×C4semidirect
238. #4075C2×C4semidirect
239. C4×C22⋊D5C2×C4semidirect
240. C4×C22⋊D5C2×C4semidirect
241. C4×C22⋊D5C2×C4semidirect
242. C2×C4⋊Dic5C2×C4semidirect
243. C2×C4⋊Dic5C2×C4semidirect
244. #4070C2×C4semidirect
245. C2×#683C2×C4semidirect
246. C2×#683C2×C4semidirect
247. #4043C2×C4semidirect
248. #4042C2×C4semidirect
249. #4042C2×C4semidirect
251. #4041C2×C4semidirect
252. #4040C2×C4semidirect
253. #4040C2×C4semidirect
254. #4040C2×C4semidirect
255. #4040C2×C4semidirect
256. #4039C2×C4semidirect
257. #4039C2×C4semidirect
258. D5×C4⋊C4C2×C4semidirect
259. D5×C4⋊C4C2×C4semidirect
260. D5×C4⋊C4C2×C4semidirect
261. D5×C4⋊C4C2×C4semidirect
262. D5×C4⋊C4C2×C4semidirect
263. D5×C4⋊C4C2×C4semidirect
271. #4034C2×C4semidirect
272. #4034C2×C4semidirect
273. #4034C2×C4semidirect
274. #4032C2×C4semidirect
275. #4032C2×C4semidirect
277. #4030C2×C4semidirect
278. #4029C2×C4semidirect
279. #4029C2×C4semidirect
280. #4029C2×C4semidirect
281. #4029C2×C4semidirect
282. #4027C2×C4semidirect
283. #4027C2×C4semidirect
284. #4027C2×C4semidirect
290. #4024C2×C4semidirect
291. #4024C2×C4semidirect
292. C4×D20C2×C4semidirect
293. C4×D20C2×C4semidirect
295. #4015C2×C4semidirect
478. C4⋊AGL(1,𝔽5)#41semidirect
494. C4×AGL(1,𝔽5)#41semidirect
556. #547AGL(1,𝔽5)semidirect
801. C2×#41C2×AGL(1,𝔽5)semidirect
822. C4⋊Q8C2×AGL(1,𝔽5)semidirect
837. #123C2×AGL(1,𝔽5)semidirect
838. #123C2×AGL(1,𝔽5)semidirect
846. C22⋊Q8C2×AGL(1,𝔽5)semidirect
858. #121C2×AGL(1,𝔽5)semidirect
875. C4×D4C2×AGL(1,𝔽5)semidirect
876. C4×D4C2×AGL(1,𝔽5)semidirect
911. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
912. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
1392. C5#34298semidirect

Maximal subgroups

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

subgroupindex
D5×#5472
#106175572
#106175552
#106173892
#106173872
#106173072
#106173062
#106173052
AGL(1,𝔽5)×#1232
#106172872
#106172842
#106172542
#106172532
#106172502
AGL(1,𝔽5)×#1212
#106171822
#106171792
#106171732
#106171722
#106171042
#106171032
#106170982
C2×C4⋊C4×AGL(1,𝔽5)2
#342985