Finite Group Databasebeta

← #72223047

Subgroups — #72223047

Order 6400.

24420 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72221019C211yesmaximal, characteristic, complemented
2#72220994C218yesmaximal, complemented
3#72220989C216yesmaximal, complemented
4#41×D5⋊AGL(1,𝔽5)C218yesmaximal, complemented
5#72220985C218yesmaximal, complemented
6#72220977C211yesmaximal, characteristic
7#72220961C214yesmaximal, complemented
8#72220956C218yesmaximal, complemented
9C2×#41×#1043C211yesmaximal, characteristic, complemented
10C2×#13107559C216yesmaximal, complemented
11#72213412C2112yesmaximal, complemented
12C2×#41×C5⋊D5C2211yescharacteristic
13C5×#66283C412yescomplemented
14#13107844C418yescomplemented
15#13107841C418yescomplemented
16#13107840C2214yes—
17#13107838C2214yes—
18D52×#41C2218yes—
19#13107835C412yescomplemented
20#13107833C2212yes—
21#13107825C416yescomplemented
22#13107821C2216yes—
23#13107815C416yescomplemented
24C2×#11717471C2216yes—
25#13107775C2218yescomplemented
26#41×#1044C2218yescomplemented
27#13107771C2212yescomplemented
28#13107767C2216yescomplemented
29C2×#11717451C2216yescomplemented
30#41×#1043C2218yescomplemented
31#41×#1043C2214yescomplemented
32#41×#1043C2214yescomplemented
33C2×Q8×#1043C2212yescomplemented
34C2×D4×#1043C2216yescomplemented
35C2×#11717438C2213yescomplemented
36C22×C4×#1043C2213yescomplemented
37#13107590C22124yescomplemented
38C2×#11717375C22124yescomplemented
39#13107576C22116yescomplemented
40#13107575C22116yescomplemented
41Q8×D5⋊AGL(1,𝔽5)C22116yescomplemented
42#13107571C22116yescomplemented
43#13107570C22148yescomplemented
44#13107569C22148yescomplemented
45#13107568C22148yescomplemented
46D4×D5⋊AGL(1,𝔽5)C22148yescomplemented
47#13107564C22124yescomplemented
48#13107563C22112yescomplemented
49#13107562C22124yescomplemented
50#13107561C22124yescomplemented
51D5⋊#4130C22124yescomplemented
52#13107559C22124yescomplemented
53#13107559C22124yescomplemented
54#13107559C22112yescomplemented
55#13107559C22112yescomplemented
56#13107559C22112yescomplemented
57#13107559C2214yescomplemented
58C2×#11717363C22112yescomplemented
59C2×C4×D5⋊AGL(1,𝔽5)C22112yescomplemented
60C2×#11717356C22112yescomplemented
61#13107542C22112yescomplemented
62C2×#11717353C22112yescomplemented
63AGL(1,𝔽5)×#585—52nomaximal
64C23×#1043C2316yes—
65C22×D5⋊AGL(1,𝔽5)C23124yes—
66C2×C52×#41C2×C411yescharacteristic, complemented
67#41×C5⋊D5C2×C414yescomplemented
68#41×C5⋊D5C2×C414yescomplemented
69#41×C5⋊D5C2314yes—
70#41×C5⋊D5C2314yes—
71C2×#87904C2×C411yescharacteristic, complemented
72C2×Q8×C5⋊D5C2311yescharacteristic
73C2×#87902C2×C413yescomplemented
74C2×D4×C5⋊D5C2313yes—
75C2×#87900C2×C413yescomplemented
76C22×C4×C5⋊D5C2313yes—
77C5×#4150C2×C418yescomplemented
78C5×#4149C2×C418yescomplemented
79C5×D5×#41C2×C4116yescomplemented
80C5×#4147C2×C414yescomplemented
81C5×#4144C2×C4112yescomplemented
82C2×C5×#709C2×C4112yescomplemented
83#11717495C2×C4124yescomplemented
84C2×#87886C23112yes—
85C2×#87880C2×C4112yescomplemented
86#11717485C2×C418yescomplemented
87#11717484C2318yes—
88D5×#713C2×C4116yescomplemented
89Q8×D52C2318yes—
90#11717481C2×C418yescomplemented
91#11717480C2×C4116yescomplemented
92#11717479C2×C4148yescomplemented
93#11717478C2×C4124yescomplemented
94#11717477C23124yes—
95D5×#711C2×C4148yescomplemented
96D4×D52C23124yes—
97#11717474C2×C4124yescomplemented
98#11717473C2×C4112yescomplemented
99#11717472C2×C4124yescomplemented
100#11717471C2×C4112yescomplemented
101#11717471C2×C4112yescomplemented
102#11717471C2×C4112yescomplemented
103#11717471C2×C4112yescomplemented
104#11717471C2314yes—
105#11717471C23112yes—
106#11717471C23112yes—
107#11717471C23112yes—
108D5×#709C2×C4148yescomplemented
109C2×#87877C2316yes—
110C2×C4×D52C23112yes—
111C2×#87873C2×C4112yescomplemented
112C2×#87872C2316yes—
113#11717463C2×C4112yescomplemented
114#11717462C2×C4124yescomplemented
115C2×#87871C2×C4112yescomplemented
116C2×C22⋊#1044C23112yes—
117Q8×#1044C23116yes—
118D4×#1044C23148yes—
119#11717451C2314yes—
120#11717451C23112yes—
121#11717451C23112yes—
122#11717451C23112yes—
123C2×C4⋊#1044C23112yes—
124C2×C4×#1044C23112yes—
125C2×C22⋊#1043C2316yes—
126Q8×#1043C2318yes—
127Q8×#1043C2318yes—
128D4×#1043C23124yes—
129D4×#1043C23124yes—
130#11717438C23112yes—
131#11717438C23112yes—
132C2×C4⋊#1043C2316yes—
133C2×C4×#1043C2311yescharacteristic
134C2×C4×#1043C2313yes—
135C2×C4×#1043C2316yes—
136C2×C4×#1043C23112yes—
137C2×C4×#1043C2316yes—
138C2×C4×#1043C2316yes—
139#11717377C23196yes—
140D5⋊(C22⋊AGL(1,𝔽5))C23148yes—
141#11717375C23116yes—
142#11717375C23148yes—
143#11717375C23148yes—
144#11717375C23148yes—
145C2×#87832C23124yes—
146C2×#87831C23124yes—
147#11717367C23148yes—
148C2×#87830C23124yes—
149#11717365C23148yes—
150D5⋊(C4⋊AGL(1,𝔽5))C23148yes—
151#11717363C2318yes—
152#11717363C23124yes—
153#11717363C23124yes—
154#11717363C23124yes—
155C4×D5⋊AGL(1,𝔽5)C2318yes—
156C4×D5⋊AGL(1,𝔽5)C23124yes—
157C4×D5⋊AGL(1,𝔽5)C23148yes—
158#11717356C2318yes—
159#11717356C23124yes—
160#11717356C23148yes—
161#11717355C23148yes—
162#11717354C23148yes—
163#11717353C2318yes—
164#11717353C23124yes—
165#11717353C23124yes—
166#11717353C23124yes—
167D5×#585—52no—
168AGL(1,𝔽5)×2−1+4—58no—
169AGL(1,𝔽5)×2−1+4—516no—
170AGL(1,𝔽5)×H(5,𝔽2)—516no—
171AGL(1,𝔽5)×H(5,𝔽2)—524no—
172#10619412—516no—
173#10619412—512no—
174#10619412—52no—
175C2×#41×AGL(1,𝔽5)—516no—
176C2×#41×AGL(1,𝔽5)—512no—
177C2×#41×AGL(1,𝔽5)—52no—
178C2×#41×AGL(1,𝔽5)—102no—
179C23×C5⋊D5C2413yes—
180C22×D52C24112yes—
181C22×#1044C24124yes—
182C22×#1043—412no—
183C22×#1043C2412yes—
184C22×#1043C24112yes—
185C22×#1043C2416yes—
186C22×#1043C24112yes—
187C2×D5⋊AGL(1,𝔽5)—448no—
188C2×D5⋊AGL(1,𝔽5)C24116yes—
189C2×D5⋊AGL(1,𝔽5)C24148yes—
190C52×#41C22×C414yescomplemented
191C52×#41C22×C414yescomplemented
192C2×C52×Q8C22×C411yescharacteristic, complemented
193C2×C52×D4C22×C413yescomplemented
194C22×C4×C52C22×C413yescomplemented
195C2×C22⋊(C5⋊D5)C22×C416yescomplemented
196C22×#1039C22×C413yescomplemented
197#87904C22×C414yescomplemented
198#87904C22×C414yescomplemented
199Q8×C5⋊D5C22×C414yescomplemented
200Q8×C5⋊D5C2414yes—
201#87902C22×C4112yescomplemented
202#87902C22×C4112yescomplemented
203D4×C5⋊D5C22×C4112yescomplemented
204D4×C5⋊D5C24112yes—
205#87900C22×C4112yescomplemented
206#87900C22×C4112yescomplemented
207C2×C4⋊(C5⋊D5)C22×C413yescomplemented
208C2×C4×C5⋊D5C22×C416yescomplemented
209C2×C4×C5⋊D5C22×C416yescomplemented
210C2×C4×C5⋊D5C22×C413yescomplemented
211C2×C4×C5⋊D5C22×C413yescomplemented
212C2×C4×C5⋊D5C2411yescharacteristic
213C2×C4×C5⋊D5C2413yes—
214C2×C4×C5⋊D5C2416yes—
215C2×C4×C5⋊D5C2416yes—
216C2×#6045C22×C413yescomplemented
217C2×C5×C22⋊D5C22×C4124yescomplemented
218C5×#713C22×C4116yescomplemented
219C5×Q8×D5C22×C4116yescomplemented
220C5×#711C22×C4148yescomplemented
221C5×D4×D5C22×C4148yescomplemented
222C5×#709C22×C4124yescomplemented
223C5×#709C22×C4124yescomplemented
224C5×#709C22×C4124yescomplemented
225C5×#709C22×C418yescomplemented
226C2×C5×D20C22×C4112yescomplemented
227C2×C4×C5×D5C22×C4124yescomplemented
228C2×C5×Dic10C22×C4112yescomplemented
229#87886C22×C4124yescomplemented
230#87886C22×C4124yescomplemented
231#87886C24124yes—
232#87886C2418yes—
233D5×C22⋊D5C22×C4196yescomplemented
234C2×#6039C22×C4112yescomplemented
235C2×#6038C22×C4124yescomplemented
236C2×#6037C22×C4112yescomplemented
237C2×#6036C24112yes—
238#87880C22×C4124yescomplemented
239#87880C22×C418yescomplemented
240#87880C22×C4124yescomplemented
241#87880C22×C4124yescomplemented
242#87879C22×C4196yescomplemented
243C2×D5×Dic5C22×C4124yescomplemented
244#87877C22×C4112yescomplemented
245#87877C22×C4112yescomplemented
246#87877C2414yes—
247#87877C24112yes—
248D5×D20C22×C4148yescomplemented
249C4×D52C22×C4124yescomplemented
250C4×D52C22×C4124yescomplemented
251C4×D52C2418yes—
252C4×D52C24124yes—
253#87874C22×C4148yescomplemented
254#87873C22×C418yescomplemented
255#87873C22×C4124yescomplemented
256#87873C22×C4124yescomplemented
257#87873C22×C4124yescomplemented
258#87872C22×C4112yescomplemented
259#87872C22×C4112yescomplemented
260#87872C2414yes—
261#87872C24112yes—
262#87871C22×C418yescomplemented
263#87871C22×C4124yescomplemented
264#87871C22×C4124yescomplemented
265#87871C22×C4124yescomplemented
266#87870C22×C4148yescomplemented
267D5×Dic10C22×C4148yescomplemented
268C22⋊#1044C24124yes—
269C22⋊#1044C2418yes—
270C4⋊#1044C2418yes—
271C4⋊#1044C24124yes—
272C4×#1044C2418yes—
273C4×#1044C24124yes—
274C22⋊#1043C24124yes—
275C4⋊#1043C24124yes—
276C4×#1043C2412yes—
277C4×#1043C2411yescharacteristic
278C4×#1043C2411yescharacteristic
279C4×#1043C2416yes—
280C4×#1043C2416yes—
281C4×#1043C24112yes—
282C4×#1043C24112yes—
283#87832C24148yes—
284#87832C24116yes—
285#87831C24148yes—
286#87831C24116yes—
287#87830C24148yes—
288#87830C24116yes—
289C5×#585—52no—
290#66287—58no—
291#66287—54no—
292D5×2−1+4—58no—
293D5×2−1+4—54no—
294#66285—58no—
295#66285—512no—
296D5×H(5,𝔽2)—58no—
297D5×H(5,𝔽2)—512no—
298#66283—516no—
299#66283—512no—
300#66283AGL(1,𝔽5)12yescomplemented
301C2×D5×#41—52no—
302C2×D5×#41—516no—
303C2×D5×#41—512no—
304C2×D5×#41—102no—
305#66266—516no—
306#66266—548no—
307#66266—548no—
308#66266—596no—
309#66266—532no—
310#41×AGL(1,𝔽5)—58no—
311#41×AGL(1,𝔽5)—524no—
312#41×AGL(1,𝔽5)—58no—
313#41×AGL(1,𝔽5)—58no—
314#41×AGL(1,𝔽5)—516no—
315#41×AGL(1,𝔽5)—524no—
316#41×AGL(1,𝔽5)—524no—
317#41×AGL(1,𝔽5)—548no—
318#41×AGL(1,𝔽5)—516no—
319#41×AGL(1,𝔽5)—548no—
320#41×AGL(1,𝔽5)—548no—
321#41×AGL(1,𝔽5)—596no—
322#41×AGL(1,𝔽5)—532no—
323#41×AGL(1,𝔽5)—108no—
324#41×AGL(1,𝔽5)—108no—
325#41×AGL(1,𝔽5)—1016no—
326#66262—54no—
327#66262—524no—
328#66262—532no—
329C2×Q8×AGL(1,𝔽5)—54no—
330C2×Q8×AGL(1,𝔽5)—524no—
331C2×Q8×AGL(1,𝔽5)—532no—
332C2×Q8×AGL(1,𝔽5)—104no—
333#66258—512no—
334#66258—524no—
335#66258—596no—
336#66258—548no—
337C2×D4×AGL(1,𝔽5)—512no—
338C2×D4×AGL(1,𝔽5)—524no—
339C2×D4×AGL(1,𝔽5)—596no—
340C2×D4×AGL(1,𝔽5)—548no—
341C2×D4×AGL(1,𝔽5)—1012no—
342C2×#4130—56no—
343C2×#4130—512no—
344C2×#4130—524no—
345C2×#4130—548no—
346C2×#4130—106no—
347C22×C4×AGL(1,𝔽5)—56no—
348C22×C4×AGL(1,𝔽5)—524no—
349C22×C4×AGL(1,𝔽5)—106no—
350C4×#585—251noSylow
351C23×C52C23×C413yes—
352C22×C5⋊D5—46no—
353C22×C5⋊D5C23×C416yes—
354C22×C5⋊D5C23×C413yes—
355C22×C5⋊D5C2516yes—
356C22×C5⋊D5C2511yescharacteristic
357C22×C5×D5C23×C4124yes—
358C2×D52—424no—
359C2×D52C23×C4124yes—
360C2×D52C2518yes—
361C2×#1044—424no—
362C2×#1044C25116yes—
363C2×#1043—24no—
364C2×#1043—224no—
365C2×#1043—412no—
366C2×#1043—46no—
367C2×#1043C25112yes—
368C2×#1043C2512yes—
369C2×#1043C2512yes—
370D5⋊AGL(1,𝔽5)—232no—
371D5⋊AGL(1,𝔽5)—448no—
372C52×Q8C23×C414yes—
373C52×D4C23×C4112yes—
374C2×C4×C52C23×C416yes—
375C2×C4×C52C23×C416yes—
376C2×C4×C52C23×C413yes—
377C2×C4×C52C23×C411yescharacteristic
378C22⋊(C5⋊D5)C23×C4124yes—
379C2×#1039C23×C416yes—
380C2×#1039C23×C413yes—
381C2×#1039C23×C411yescharacteristic
382C2×#1039C23×C416yes—
383C4⋊(C5⋊D5)C23×C4112yes—
384C4×C5⋊D5C23×C411yescharacteristic
385C4×C5⋊D5C23×C416yes—
386C4×C5⋊D5C23×C416yes—
387C4×C5⋊D5C23×C416yes—
388C4×C5⋊D5C23×C416yes—
389C4×C5⋊D5C23×C411yescharacteristic
390C4×C5⋊D5C23×C416yes—
391C4×C5⋊D5C2511yescharacteristic
392C4×C5⋊D5C2511yescharacteristic
393C4×C5⋊D5C2516yes—
394#6045C23×C4112yes—
395C5×C22⋊D5C23×C4148yes—
396C5×C22⋊D5C23×C4116yes—
397C2×C5×Dic5C23×C4124yes—
398C5×D20C23×C4124yes—
399C5×D20C23×C418yes—
400C4×C5×D5C23×C4148yes—
401C4×C5×D5C23×C4116yes—
402C5×Dic10C23×C4124yes—
403C5×Dic10C23×C418yes—
404#6039C23×C4124yes—
405#6039C23×C418yes—
406#6038C23×C4116yes—
407#6038C23×C4148yes—
408#6037C23×C4124yes—
409#6037C23×C418yes—
410#6036C23×C4124yes—
411#6036C2518yes—
412D5×Dic5C23×C4148yes—
413D5×Dic5C23×C4116yes—
414C23×AGL(1,𝔽5)—548no—
415C23×AGL(1,𝔽5)—512no—
416C23×AGL(1,𝔽5)—1012no—
417C5×2−1+4—58no—
418C5×2−1+4—54no—
419C5×H(5,𝔽2)—58no—
420C5×H(5,𝔽2)—512no—
421C2×C5×#41—22no—
422C2×C5×#41—516no—
423C2×C5×#41—512no—
424C2×C5×#41C2×AGL(1,𝔽5)12yescomplemented
425#4150—516no—
426#4150—548no—
427#4150—524no—
428#4150—524no—
429#4150C2×AGL(1,𝔽5)18yescomplemented
430#4149—516no—
431#4149—548no—
432#4149—524no—
433#4149—524no—
434#4149C2×AGL(1,𝔽5)18yescomplemented
435D5×#41—58no—
436D5×#41—58no—
437D5×#41—58no—
438D5×#41—58no—
439D5×#41—516no—
440D5×#41—516no—
441D5×#41—548no—
442D5×#41—548no—
443D5×#41—524no—
444D5×#41—524no—
445D5×#41—524no—
446D5×#41—524no—
447D5×#41—524no—
448D5×#41—58no—
449D5×#41—524no—
450D5×#41—524no—
451D5×#41—548no—
452D5×#41—108no—
453D5×#41—108no—
454D5×#41—108no—
455D5×#41—108no—
456D5×#41C2×AGL(1,𝔽5)116yescomplemented
457#4147—516no—
458#4147—516no—
459#4147—524no—
460#4147C2×AGL(1,𝔽5)14yescomplemented
461C2×#713—52no—
462C2×#713—516no—
463C2×#713—512no—
464C2×#713—102no—
465C2×Q8×D5—52no—
466C2×Q8×D5—516no—
467C2×Q8×D5—512no—
468C2×Q8×D5—102no—
469#4144—548no—
470#4144—548no—
471#4144—548no—
472#4144—524no—
473#4144C2×AGL(1,𝔽5)112yescomplemented
474C2×#711—56no—
475C2×#711—524no—
476C2×#711—548no—
477C2×#711—512no—
478C2×#711—106no—
479C2×D4×D5—56no—
480C2×D4×D5—524no—
481C2×D4×D5—548no—
482C2×D4×D5—512no—
483C2×D4×D5—106no—
484C2×#709—56no—
485C2×#709—548no—
486C2×#709—524no—
487C2×#709—106no—
488C2×#709C2×AGL(1,𝔽5)112yescomplemented
489C22×C4×D5—56no—
490C22×C4×D5—524no—
491C22×C4×D5—106no—
492C2×C22⋊AGL(1,𝔽5)—596no—
493C2×C22⋊AGL(1,𝔽5)—512no—
494C2×C22⋊AGL(1,𝔽5)—524no—
495C2×C22⋊AGL(1,𝔽5)—548no—
496C2×C22⋊AGL(1,𝔽5)—1012no—
497Q8×AGL(1,𝔽5)—516no—
498Q8×AGL(1,𝔽5)—516no—
499Q8×AGL(1,𝔽5)—532no—
500Q8×AGL(1,𝔽5)—516no—
501Q8×AGL(1,𝔽5)—548no—
502Q8×AGL(1,𝔽5)—548no—
503Q8×AGL(1,𝔽5)—548no—
504Q8×AGL(1,𝔽5)—596no—
505Q8×AGL(1,𝔽5)—1016no—
506Q8×AGL(1,𝔽5)—1016no—
507D4×AGL(1,𝔽5)—5192no—
508D4×AGL(1,𝔽5)—548no—
509D4×AGL(1,𝔽5)—548no—
510D4×AGL(1,𝔽5)—596no—
511D4×AGL(1,𝔽5)—516no—
512D4×AGL(1,𝔽5)—548no—
513D4×AGL(1,𝔽5)—596no—
514D4×AGL(1,𝔽5)—532no—
515D4×AGL(1,𝔽5)—548no—
516D4×AGL(1,𝔽5)—548no—
517D4×AGL(1,𝔽5)—596no—
518D4×AGL(1,𝔽5)—596no—
519D4×AGL(1,𝔽5)—596no—
520D4×AGL(1,𝔽5)—1048no—
521D4×AGL(1,𝔽5)—1048no—
522#4130—524no—
523#4130—524no—
524#4130—58no—
525#4130—524no—
526#4130—524no—
527#4130—524no—
528#4130—516no—
529#4130—548no—
530#4130—596no—
531#4130—596no—
532#4130—596no—
533#4130—1024no—
534#4130—1024no—
535C2×C4⋊AGL(1,𝔽5)—512no—
536C2×C4⋊AGL(1,𝔽5)—524no—
537C2×C4⋊AGL(1,𝔽5)—596no—
538C2×C4⋊AGL(1,𝔽5)—548no—
539C2×C4⋊AGL(1,𝔽5)—1012no—
540C2×C4×AGL(1,𝔽5)—52no—
541C2×C4×AGL(1,𝔽5)—512no—
542C2×C4×AGL(1,𝔽5)—56no—
543C2×C4×AGL(1,𝔽5)—512no—
544C2×C4×AGL(1,𝔽5)—512no—
545C2×C4×AGL(1,𝔽5)—524no—
546C2×C4×AGL(1,𝔽5)—524no—
547C2×C4×AGL(1,𝔽5)—516no—
548C2×C4×AGL(1,𝔽5)—548no—
549C2×C4×AGL(1,𝔽5)—596no—
550C2×C4×AGL(1,𝔽5)—548no—
551C2×C4×AGL(1,𝔽5)—102no—
552C2×C4×AGL(1,𝔽5)—106no—
553C2×C4×AGL(1,𝔽5)—1012no—
554C2×C4×AGL(1,𝔽5)—1012no—
555C2×C4×AGL(1,𝔽5)—1024no—
556C2×C4×AGL(1,𝔽5)—1012no—
557C2×#585—251no—
558C4×2−1+4—258no—
559C4×2−1+4—254no—
560C4×H(5,𝔽2)—258no—
561C4×H(5,𝔽2)—2512no—
562#3428—251no—
563#3428—258no—
564#3428—256no—
565C2×C4×#41—251no—
566C2×C4×#41—256no—
567C2×C4×#41—258no—
568C22×C52—43no—
569C22×C52C24×C416yes—
570C22×C52C24×C411yescharacteristic
571C2×C5⋊D5—22no—
572C2×C5⋊D5—212no—
573C2×C5⋊D5—46no—
574C2×C5⋊D5—43no—
575C2×C5⋊D5C24×C416yes—
576C2×C5⋊D5C24×C411yescharacteristic
577C2×C5⋊D5C2611yescharacteristic
578C2×C5×D5—424no—
579C2×C5×D5C24×C4116yes—
580D52—216no—
581D52—424no—
582#1044—216no—
583#1043—22no—
584#1043—212no—
585#1043#58514yescomplemented
586C4×C52C24×C411yescharacteristic
587C4×C52C24×C416yes—
588C4×C52C24×C411yescharacteristic
589#1039C24×C411yescharacteristic
590#1039C24×C416yes—
591#1039C24×C411yescharacteristic
592C5×Dic5C24×C4116yes—
593C23×D5—56no—
594C23×D5—524no—
595C23×D5—106no—
596C22×AGL(1,𝔽5)—532no—
597C22×AGL(1,𝔽5)—54no—
598C22×AGL(1,𝔽5)—524no—
599C22×AGL(1,𝔽5)—596no—
600C22×AGL(1,𝔽5)—512no—
601C22×AGL(1,𝔽5)—524no—
602C22×AGL(1,𝔽5)—548no—
603C22×AGL(1,𝔽5)—104no—
604C22×AGL(1,𝔽5)—1012no—
605C22×AGL(1,𝔽5)—1024no—
606C22×AGL(1,𝔽5)—1024no—
607C22×AGL(1,𝔽5)—2096no—
608C22×AGL(1,𝔽5)—2024no—
609C22×AGL(1,𝔽5)—2048no—
610C5×#41—28no—
611C5×#41—28no—
612C5×#41—516no—
613C5×#41—548no—
614C5×#41—58no—
615C5×#41—524no—
616C5×#41—524no—
617C5×#41—524no—
618C5×#41C22×AGL(1,𝔽5)18yescomplemented
619C5×#41C22×AGL(1,𝔽5)18yescomplemented
620C2×C5×Q8—22no—
621C2×C5×Q8—516no—
622C2×C5×Q8—512no—
623C2×C5×Q8C22×AGL(1,𝔽5)12yescomplemented
624C2×C5×D4—26no—
625C2×C5×D4—524no—
626C2×C5×D4—548no—
627C2×C5×D4—512no—
628C2×C5×D4C22×AGL(1,𝔽5)16yescomplemented
629C22×C4×C5—26no—
630C22×C4×C5—524no—
631C22×C4×C5C22×AGL(1,𝔽5)16yescomplemented
632C2×C22⋊D5—512no—
633C2×C22⋊D5—524no—
634C2×C22⋊D5—596no—
635C2×C22⋊D5—524no—
636C2×C22⋊D5—1012no—
637C2×C22⋊D5C22×AGL(1,𝔽5)124yescomplemented
638C22×Dic5—56no—
639C22×Dic5—524no—
640C22×Dic5—106no—
641#713—58no—
642#713—58no—
643#713—524no—
644#713—58no—
645#713—524no—
646#713—524no—
647#713—548no—
648#713—108no—
649#713—108no—
650#713C22×AGL(1,𝔽5)116yescomplemented
651Q8×D5—58no—
652Q8×D5—58no—
653Q8×D5—548no—
654Q8×D5—524no—
655Q8×D5—58no—
656Q8×D5—524no—
657Q8×D5—524no—
658Q8×D5—108no—
659Q8×D5—108no—
660Q8×D5C22×AGL(1,𝔽5)116yescomplemented
661#711—524no—
662#711—524no—
663#711—548no—
664#711—516no—
665#711—548no—
666#711—548no—
667#711—596no—
668#711—548no—
669#711—524no—
670#711—58no—
671#711—524no—
672#711—524no—
673#711—1024no—
674#711—1024no—
675#711C22×AGL(1,𝔽5)148yescomplemented
676D4×D5—596no—
677D4×D5—524no—
678D4×D5—524no—
679D4×D5—548no—
680D4×D5—516no—
681D4×D5—548no—
682D4×D5—548no—
683D4×D5—524no—
684D4×D5—58no—
685D4×D5—524no—
686D4×D5—524no—
687D4×D5—548no—
688D4×D5—1024no—
689D4×D5—1024no—
690D4×D5C22×AGL(1,𝔽5)148yescomplemented
691#709—524no—
692#709—524no—
693#709—596no—
694#709—548no—
695#709—548no—
696#709—516no—
697#709—548no—
698#709—548no—
699#709—548no—
700#709—1024no—
701#709—1024no—
702#709C22×AGL(1,𝔽5)124yescomplemented
703#709C22×AGL(1,𝔽5)18yescomplemented
704#709C22×AGL(1,𝔽5)124yescomplemented
705#709C22×AGL(1,𝔽5)124yescomplemented
706C2×D20—524no—
707C2×D20—56no—
708C2×D20—548no—
709C2×D20—106no—
710C2×D20C22×AGL(1,𝔽5)112yescomplemented
711C2×C4×D5—524no—
712C2×C4×D5—52no—
713C2×C4×D5—512no—
714C2×C4×D5—56no—
715C2×C4×D5—512no—
716C2×C4×D5—56no—
717C2×C4×D5—512no—
718C2×C4×D5—56no—
719C2×C4×D5—512no—
720C2×C4×D5—524no—
721C2×C4×D5—516no—
722C2×C4×D5—548no—
723C2×C4×D5—548no—
724C2×C4×D5—548no—
725C2×C4×D5—102no—
726C2×C4×D5—106no—
727C2×C4×D5—1012no—
728C2×C4×D5—1012no—
729C2×C4×D5—106no—
730C2×C4×D5—106no—
731C2×C4×D5—1012no—
732C2×C4×D5—1012no—
733C2×C4×D5C22×AGL(1,𝔽5)124yescomplemented
734C2×Dic10—56no—
735C2×Dic10—524no—
736C2×Dic10—548no—
737C2×Dic10—106no—
738C2×Dic10C22×AGL(1,𝔽5)112yescomplemented
739C22⋊AGL(1,𝔽5)—596no—
740C22⋊AGL(1,𝔽5)—532no—
741C22⋊AGL(1,𝔽5)—548no—
742C22⋊AGL(1,𝔽5)—516no—
743C22⋊AGL(1,𝔽5)—548no—
744C22⋊AGL(1,𝔽5)—1048no—
745C4⋊AGL(1,𝔽5)—596no—
746C4⋊AGL(1,𝔽5)—532no—
747C4⋊AGL(1,𝔽5)—548no—
748C4⋊AGL(1,𝔽5)—516no—
749C4⋊AGL(1,𝔽5)—548no—
750C4⋊AGL(1,𝔽5)—1048no—
751C4×AGL(1,𝔽5)—532no—
752C4×AGL(1,𝔽5)—596no—
753C4×AGL(1,𝔽5)—52no—
754C4×AGL(1,𝔽5)—52no—
755C4×AGL(1,𝔽5)—512no—
756C4×AGL(1,𝔽5)—516no—
757C4×AGL(1,𝔽5)—54no—
758C4×AGL(1,𝔽5)—524no—
759C4×AGL(1,𝔽5)—512no—
760C4×AGL(1,𝔽5)—524no—
761C4×AGL(1,𝔽5)—548no—
762C4×AGL(1,𝔽5)—102no—
763C4×AGL(1,𝔽5)—102no—
764C4×AGL(1,𝔽5)—104no—
765C4×AGL(1,𝔽5)—1012no—
766C4×AGL(1,𝔽5)—1012no—
767C4×AGL(1,𝔽5)—1024no—
768C4×AGL(1,𝔽5)—1024no—
769#585—52no—
770#585—258no—
771#585—256no—
772#585—256no—
773#585—258no—
774#585—252no—
775C2×2−1+4—254no—
776C2×2−1+4—252no—
777C2×H(5,𝔽2)—254no—
778C2×H(5,𝔽2)—256no—
779C22×#41—258no—
780C22×#41—256no—
781C22×#41—251no—
782#520—258no—
783#520—2516no—
784#520—2548no—
785#520—2524no—
786#520—2524no—
787#519—252no—
788#519—2516no—
789#519—2512no—
790#518—256no—
791#518—2548no—
792#518—2512no—
793#518—2524no—
794C4×#41—254no—
795C4×#41—2512no—
796C4×#41—254no—
797C4×#41—2512no—
798C4×#41—2512no—
799C4×#41—258no—
800C4×#41—2524no—
801C4×#41—254no—
802C4×#41—2524no—
803C4×#41—2524no—
804C4×#41—2516no—
805C4×#41—2548no—
806C4×#41—258no—
807C2×C4×Q8—2512no—
808C2×C4×Q8—2516no—
809C2×C4×Q8—252no—
810C2×C4×D4—2512no—
811C2×C4×D4—2524no—
812C2×C4×D4—2548no—
813C2×C4×D4—256no—
814C2×#117—2512no—
815C2×#117—256no—
816C2×#117—2524no—
817C2×#117—253no—
818C22×C42—2512no—
819C22×C42—253no—
820C2×C52—21no—
821C2×C52—26no—
822C2×C52C25×C411yescharacteristic
823C5⋊D5—21no—
824C5⋊D5—26no—
825C5⋊D5C2×#58512yes—
826C5×D5—216no—
827C23×C5—26no—
828C23×C5—524no—
829C23×C5C23×AGL(1,𝔽5)16yes—
830C22×D5—52no—
831C22×D5—512no—
832C22×D5—56no—
833C22×D5—512no—
834C22×D5—516no—
835C22×D5—548no—
836C22×D5—102no—
837C22×D5—106no—
838C22×D5—1012no—
839C22×D5—1012no—
840C22×D5—2048no—
841C22×D5—2012no—
842C22×D5—2024no—
843C22×D5C23×AGL(1,𝔽5)124yes—
844C2×AGL(1,𝔽5)—54no—
845C2×AGL(1,𝔽5)—524no—
846C2×AGL(1,𝔽5)—54no—
847C2×AGL(1,𝔽5)—532no—
848C2×AGL(1,𝔽5)—104no—
849C2×AGL(1,𝔽5)—104no—
850C2×AGL(1,𝔽5)—1024no—
851C2×AGL(1,𝔽5)—1064no—
852C2×AGL(1,𝔽5)—108no—
853C2×AGL(1,𝔽5)—1048no—
854C2×AGL(1,𝔽5)—1016no—
855C2×AGL(1,𝔽5)—2048no—
856C2×AGL(1,𝔽5)—2096no—
857C2×AGL(1,𝔽5)—2024no—
858C2×AGL(1,𝔽5)—2012no—
859C2×AGL(1,𝔽5)—2048no—
860C2×AGL(1,𝔽5)—2048no—
861C2×AGL(1,𝔽5)—2024no—
862C5×Q8—28no—
863C5×Q8—524no—
864C5×Q8—58no—
865C5×Q8C23×AGL(1,𝔽5)18yes—
866C5×D4—224no—
867C5×D4—516no—
868C5×D4—548no—
869C5×D4—524no—
870C5×D4—58no—
871C5×D4C23×AGL(1,𝔽5)124yes—
872C2×C4×C5—26no—
873C2×C4×C5—22no—
874C2×C4×C5—212no—
875C2×C4×C5—212no—
876C2×C4×C5—524no—
877C2×C4×C5—548no—
878C2×C4×C5—516no—
879C2×C4×C5C23×AGL(1,𝔽5)16yes—
880C2×C4×C5C23×AGL(1,𝔽5)112yes—
881C2×C4×C5C23×AGL(1,𝔽5)12yes—
882C2×C4×C5C23×AGL(1,𝔽5)112yes—
883C22⋊D5—548no—
884C22⋊D5—548no—
885C22⋊D5—516no—
886C22⋊D5—516no—
887C22⋊D5—548no—
888C22⋊D5—1048no—
889C22⋊D5C23×AGL(1,𝔽5)148yes—
890C22⋊D5C23×AGL(1,𝔽5)116yes—
891C2×Dic5—56no—
892C2×Dic5—512no—
893C2×Dic5—52no—
894C2×Dic5—512no—
895C2×Dic5—548no—
896C2×Dic5—516no—
897C2×Dic5—106no—
898C2×Dic5—102no—
899C2×Dic5—1012no—
900C2×Dic5—1012no—
901C2×Dic5C23×AGL(1,𝔽5)124yes—
902D20—516no—
903D20—548no—
904D20—524no—
905D20—1024no—
906D20C23×AGL(1,𝔽5)124yes—
907D20C23×AGL(1,𝔽5)18yes—
908C4×D5—516no—
909C4×D5—548no—
910C4×D5—52no—
911C4×D5—512no—
912C4×D5—512no—
913C4×D5—52no—
914C4×D5—512no—
915C4×D5—512no—
916C4×D5—512no—
917C4×D5—52no—
918C4×D5—512no—
919C4×D5—52no—
920C4×D5—548no—
921C4×D5—516no—
922C4×D5—102no—
923C4×D5—102no—
924C4×D5—1012no—
925C4×D5—1012no—
926C4×D5—1012no—
927C4×D5—1012no—
928C4×D5—1012no—
929C4×D5—102no—
930C4×D5—102no—
931C4×D5—1012no—
932C4×D5C23×AGL(1,𝔽5)116yes—
933C4×D5C23×AGL(1,𝔽5)148yes—
934Dic10—524no—
935Dic10—548no—
936Dic10—516no—
937Dic10—1024no—
938Dic10C23×AGL(1,𝔽5)124yes—
939Dic10C23×AGL(1,𝔽5)18yes—
9402−1+4—58no—
9412−1+4—54no—
9422−1+4—258no—
9432−1+4—2516no—
9442−1+4—2524no—
9452−1+4—2524no—
9462−1+4—2512no—
947H(5,𝔽2)—58no—
948H(5,𝔽2)—512no—
949H(5,𝔽2)—2524no—
950H(5,𝔽2)—2524no—
951H(5,𝔽2)—2548no—
952H(5,𝔽2)—2524no—
953H(5,𝔽2)—258no—
954H(5,𝔽2)—2512no—
955C2×#41—516no—
956C2×#41—512no—
957C2×#41—2512no—
958C2×#41—2548no—
959C2×#41—2512no—
960C2×#41—2512no—
961C2×#41—2548no—
962C2×#41—2516no—
963C2×#41—2512no—
964C2×#41—254no—
965C2×#41—258no—
966C2×#41—2524no—
967C2×#41—2512no—
968C2×#41—2512no—
969C2×#41—2512no—
970C2×#41—2512no—
971C2×#41—2512no—
972C2×#41—2512no—
973C2×#41—254no—
974C2×#41—254no—
975C2×#41—254no—
976C2×#41—254no—
977C2×#41—251no—
978C2×#41—253no—
979C2×#41—253no—
980C2×#41D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
981C22×Q8—258no—
982C22×Q8—256no—
983C22×Q8—251no—
984C22×D4—2512no—
985C22×D4—2524no—
986C22×D4—256no—
987C22×D4—253no—
988C23×C4—2512no—
989C23×C4—253no—
990C23×C4—256no—
991C23×C4—2524no—
992C4×Q8—258no—
993C4×Q8—2524no—
994C4×Q8—258no—
995C4×Q8—2516no—
996C4×Q8—2548no—
997C4×Q8—2524no—
998C4×Q8—2524no—
999C4×Q8—258no—
1000C4×D4—2516no—
1001C4×D4—2548no—
1002C4×D4—258no—
1003C4×D4—2524no—
1004C4×D4—2524no—
1005C4×D4—2548no—
1006C4×D4—2548no—
1007C4×D4—2548no—
1008C4×D4—2548no—
1009C4×D4—2596no—
1010C4×D4—2524no—
1011C4×D4—2524no—
1012C4×D4—2524no—
1013#117—2512no—
1014#117—254no—
1015#117—258no—
1016#117—2524no—
1017#117—2512no—
1018#117—2512no—
1019#117—2512no—
1020#117—2548no—
1021#117—2548no—
1022#117—2548no—
1023#117—2512no—
1024C2×C4⋊C4—2524no—
1025C2×C4⋊C4—2512no—
1026C2×C4⋊C4—2548no—
1027C2×C4⋊C4—256no—
1028C2×C22⋊C4—2512no—
1029C2×C22⋊C4—2524no—
1030C2×C22⋊C4—2548no—
1031C2×C22⋊C4—256no—
1032C2×C42—256no—
1033C2×C42—253no—
1034C2×C42—2512no—
1035C2×C42—2524no—
1036C2×C42—2512no—
1037C2×C42—256no—
1038C2×C42—2524no—
1039C2×C42—2548no—
1040C2×C42—251no—
1041C2×C42—256no—
1042C2×C42—258no—
1043C52C4×#58511yescharacteristic, complemented, Sylow
1044C22×C5—22no—
1045C22×C5—212no—
1046C22×C5—46no—
1047C22×C5—412no—
1048C22×C5—516no—
1049C22×C5—2024no—
1050C22×C5C24×AGL(1,𝔽5)12yes—
1051C22×C5C24×AGL(1,𝔽5)112yes—
1052C2×D5—424no—
1053C2×D5—52no—
1054C2×D5—512no—
1055C2×D5—52no—
1056C2×D5—102no—
1057C2×D5—102no—
1058C2×D5—1012no—
1059C2×D5—1032no—
1060C2×D5—104no—
1061C2×D5—1024no—
1062C2×D5—108no—
1063C2×D5—2024no—
1064C2×D5—2048no—
1065C2×D5—2012no—
1066C2×D5—206no—
1067C2×D5—2024no—
1068C2×D5—2012no—
1069C2×D5C24×AGL(1,𝔽5)116yes—
1070AGL(1,𝔽5)—58no—
1071AGL(1,𝔽5)—108no—
1072AGL(1,𝔽5)—104no—
1073AGL(1,𝔽5)—1024no—
1074AGL(1,𝔽5)—1032no—
1075AGL(1,𝔽5)—108no—
1076AGL(1,𝔽5)—2024no—
1077C4×C5—212no—
1078C4×C5—22no—
1079C4×C5—22no—
1080C4×C5—516no—
1081C4×C5C24×AGL(1,𝔽5)112yes—
1082C4×C5C24×AGL(1,𝔽5)12yes—
1083C4×C5C24×AGL(1,𝔽5)12yes—
1084Dic5—512no—
1085Dic5—52no—
1086Dic5—52no—
1087Dic5—1012no—
1088Dic5—102no—
1089Dic5—102no—
1090Dic5C24×AGL(1,𝔽5)116yes—
1091C24—2512no—
1092C24—253no—
1093#41—516no—
1094#41—548no—
1095#41—524no—
1096#41—58no—
1097#41—524no—
1098#41—524no—
1099#41—258no—
1100#41—2524no—
1101#41—2524no—
1102#41—2524no—
1103#41—2596no—
1104#41—2548no—
1105#41—2548no—
1106#41—258no—
1107#41—2524no—
1108#41—2524no—
1109#41—2524no—
1110#41—258no—
1111#41—2524no—
1112#41—2524no—
1113#41—2524no—
1114#41—254no—
1115#41—254no—
1116#41—2512no—
1117#41—2512no—
1118#41—2512no—
1119#41—2512no—
1120#41C2×D5⋊AGL(1,𝔽5)14yescomplemented
1121#41C2×D5⋊AGL(1,𝔽5)14yescomplemented
1122C2×Q8—516no—
1123C2×Q8—512no—
1124C2×Q8—2512no—
1125C2×Q8—2548no—
1126C2×Q8—2512no—
1127C2×Q8—254no—
1128C2×Q8—2512no—
1129C2×Q8—2512no—
1130C2×Q8—254no—
1131C2×Q8—254no—
1132C2×Q8—253no—
1133C2×Q8C2×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
1134C2×D4—524no—
1135C2×D4—548no—
1136C2×D4—512no—
1137C2×D4—2548no—
1138C2×D4—2524no—
1139C2×D4—2524no—
1140C2×D4—258no—
1141C2×D4—2512no—
1142C2×D4—254no—
1143C2×D4—2524no—
1144C2×D4—2524no—
1145C2×D4—2512no—
1146C2×D4—2512no—
1147C2×D4—2596no—
1148C2×D4—2512no—
1149C2×D4—256no—
1150C2×D4—2512no—
1151C2×D4—2512no—
1152C2×D4—253no—
1153C2×D4C2×D5⋊AGL(1,𝔽5)13yescomplemented
1154C22×C4—524no—
1155C22×C4—258no—
1156C22×C4—2512no—
1157C22×C4—2524no—
1158C22×C4—2524no—
1159C22×C4—2524no—
1160C22×C4—2524no—
1161C22×C4—253no—
1162C22×C4—256no—
1163C22×C4—251no—
1164C22×C4—256no—
1165C22×C4—253no—
1166C22×C4—256no—
1167C22×C4—253no—
1168C22×C4—256no—
1169C22×C4—253no—
1170C22×C4—2516no—
1171C22×C4—252no—
1172C22×C4—2512no—
1173C22×C4—2524no—
1174C22×C4—2548no—
1175C22×C4—2512no—
1176C22×C4—256no—
1177C22×C4—10048no—
1178C22×C4—10012no—
1179C22×C4C2×D5⋊AGL(1,𝔽5)13yescomplemented
1180C4⋊C4—2516no—
1181C4⋊C4—2548no—
1182C4⋊C4—2524no—
1183C4⋊C4—258no—
1184C4⋊C4—2524no—
1185C22⋊C4—258no—
1186C22⋊C4—2524no—
1187C22⋊C4—2516no—
1188C22⋊C4—2548no—
1189C22⋊C4—2524no—
1190C42—251no—
1191C42—258no—
1192C42—251no—
1193C42—256no—
1194C42—2516no—
1195C42—252no—
1196C42—2512no—
1197C42—2548no—
1198C42—2524no—
1199C42—2512no—
1200C42—256no—
1201C2×C5—24no—
1202C2×C5—212no—
1203C2×C5—22no—
1204C2×C5—22no—
1205C2×C5—412no—
1206C2×C5—1016no—
1207C2×C5C25×AGL(1,𝔽5)12yes—
1208D5—216no—
1209D5—54no—
1210D5—104no—
1211D5—104no—
1212D5—102no—
1213D5—1012no—
1214D5—2012no—
1215C23—524no—
1216C23—258no—
1217C23—2524no—
1218C23—251no—
1219C23—256no—
1220C23—256no—
1221C23—253no—
1222C23—1006no—
1223C23—10024no—
1224C23C22×D5⋊AGL(1,𝔽5)13yes—
1225Q8—524no—
1226Q8—58no—
1227Q8—258no—
1228Q8—2524no—
1229Q8—2512no—
1230Q8C22×D5⋊AGL(1,𝔽5)14yes—
1231D4—548no—
1232D4—516no—
1233D4—524no—
1234D4—58no—
1235D4—2548no—
1236D4—2516no—
1237D4—258no—
1238D4—2524no—
1239D4—2524no—
1240D4—2512no—
1241D4C22×D5⋊AGL(1,𝔽5)112yes—
1242C2×C4—524no—
1243C2×C4—548no—
1244C2×C4—516no—
1245C2×C4—258no—
1246C2×C4—2524no—
1247C2×C4—2516no—
1248C2×C4—2548no—
1249C2×C4—252no—
1250C2×C4—256no—
1251C2×C4—251no—
1252C2×C4—256no—
1253C2×C4—253no—
1254C2×C4—256no—
1255C2×C4—251no—
1256C2×C4—256no—
1257C2×C4—251no—
1258C2×C4—256no—
1259C2×C4—256no—
1260C2×C4—256no—
1261C2×C4—251no—
1262C2×C4—256no—
1263C2×C4—251no—
1264C2×C4—2516no—
1265C2×C4—252no—
1266C2×C4—2512no—
1267C2×C4—5032no—
1268C2×C4—504no—
1269C2×C4—5024no—
1270C2×C4—10024no—
1271C2×C4—10048no—
1272C2×C4—10012no—
1273C2×C4—1006no—
1274C2×C4C22×D5⋊AGL(1,𝔽5)16yes—
1275C2×C4C22×D5⋊AGL(1,𝔽5)13yes—
1276C2×C4C22×D5⋊AGL(1,𝔽5)16yes—
1277C2×C4C22×D5⋊AGL(1,𝔽5)11yescharacteristic
1278C5—22no—
1279C5AGL(1,𝔽5)×#58512yescomplemented
1280C22—43no—
1281C22—516no—
1282C22—2024no—
1283C22—251no—
1284C22—251no—
1285C22—256no—
1286C22—502no—
1287C22—5012no—
1288C22—5016no—
1289C22—1003no—
1290C22—1006no—
1291C22—10024no—
1292C22C23×D5⋊AGL(1,𝔽5)16yes—
1293C22C23×D5⋊AGL(1,𝔽5)11yescharacteristic
1294C4—516no—
1295C4—254no—
1296C4—251no—
1297C4—256no—
1298C4—251no—
1299C4—5016no—
1300C4—502no—
1301C4—5012no—
1302C4C23×D5⋊AGL(1,𝔽5)16yes—
1303C4C23×D5⋊AGL(1,𝔽5)11yescharacteristic
1304C4C23×D5⋊AGL(1,𝔽5)11yescharacteristic
1305C2—21no—
1306C2—26no—
1307C2—1016no—
1308C2—252no—
1309C2—501no—
1310C2—506no—
1311C2C24×D5⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC4C23×D5⋊AGL(1,𝔽5)
commutator, socleC2×C52C25×C4
FrattiniC2C24×D5⋊AGL(1,𝔽5)
FittingC2×C52×#41C2×C4
prime radical#72220977C2
cosocleC2×C5⋊D5C26
hypercenterC2×#41D5⋊AGL(1,𝔽5)
hypocenterC52C4×#585
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #72221019C2semidirect
2. #72220994C2semidirect
3. #72220989C2semidirect
4. #41×D5⋊AGL(1,𝔽5)C2semidirect
5. #72220985C2semidirect
7. #72220961C2semidirect
8. #72220956C2semidirect
9. C2×#41×#1043C2semidirect
10. C2×#13107559C2semidirect
11. #72213412C2semidirect
13. C5×#66283C4semidirect
14. #13107844C4semidirect
15. #13107841C4semidirect
19. #13107835C4semidirect
21. #13107825C4semidirect
23. #13107815C4semidirect
25. #13107775C22semidirect
26. #41×#1044C22semidirect
27. #13107771C22semidirect
28. #13107767C22semidirect
29. C2×#11717451C22semidirect
30. #41×#1043C22semidirect
31. #41×#1043C22semidirect
32. #41×#1043C22semidirect
33. C2×Q8×#1043C22semidirect
34. C2×D4×#1043C22semidirect
35. C2×#11717438C22semidirect
36. C22×C4×#1043C22semidirect
37. #13107590C22semidirect
38. C2×#11717375C22semidirect
39. #13107576C22semidirect
40. #13107575C22semidirect
41. Q8×D5⋊AGL(1,𝔽5)C22semidirect
42. #13107571C22semidirect
43. #13107570C22semidirect
44. #13107569C22semidirect
45. #13107568C22semidirect
46. D4×D5⋊AGL(1,𝔽5)C22semidirect
47. #13107564C22semidirect
48. #13107563C22semidirect
49. #13107562C22semidirect
50. #13107561C22semidirect
51. D5⋊#4130C22semidirect
52. #13107559C22semidirect
53. #13107559C22semidirect
54. #13107559C22semidirect
55. #13107559C22semidirect
56. #13107559C22semidirect
57. #13107559C22semidirect
58. C2×#11717363C22semidirect
59. C2×C4×D5⋊AGL(1,𝔽5)C22semidirect
60. C2×#11717356C22semidirect
61. #13107542C22semidirect
62. C2×#11717353C22semidirect
66. C2×C52×#41C2×C4semidirect
67. #41×C5⋊D5C2×C4semidirect
68. #41×C5⋊D5C2×C4semidirect
71. C2×#87904C2×C4semidirect
73. C2×#87902C2×C4semidirect
75. C2×#87900C2×C4semidirect
77. C5×#4150C2×C4semidirect
78. C5×#4149C2×C4semidirect
79. C5×D5×#41C2×C4semidirect
80. C5×#4147C2×C4semidirect
81. C5×#4144C2×C4semidirect
82. C2×C5×#709C2×C4semidirect
83. #11717495C2×C4semidirect
85. C2×#87880C2×C4semidirect
86. #11717485C2×C4semidirect
88. D5×#713C2×C4semidirect
90. #11717481C2×C4semidirect
91. #11717480C2×C4semidirect
92. #11717479C2×C4semidirect
93. #11717478C2×C4semidirect
95. D5×#711C2×C4semidirect
97. #11717474C2×C4semidirect
98. #11717473C2×C4semidirect
99. #11717472C2×C4semidirect
100. #11717471C2×C4semidirect
101. #11717471C2×C4semidirect
102. #11717471C2×C4semidirect
103. #11717471C2×C4semidirect
108. D5×#709C2×C4semidirect
111. C2×#87873C2×C4semidirect
113. #11717463C2×C4semidirect
114. #11717462C2×C4semidirect
115. C2×#87871C2×C4semidirect
190. C52×#41C22×C4semidirect
191. C52×#41C22×C4semidirect
192. C2×C52×Q8C22×C4semidirect
193. C2×C52×D4C22×C4semidirect
194. C22×C4×C52C22×C4semidirect
195. C2×C22⋊(C5⋊D5)C22×C4semidirect
196. C22×#1039C22×C4semidirect
197. #87904C22×C4semidirect
198. #87904C22×C4semidirect
199. Q8×C5⋊D5C22×C4semidirect
201. #87902C22×C4semidirect
202. #87902C22×C4semidirect
203. D4×C5⋊D5C22×C4semidirect
205. #87900C22×C4semidirect
206. #87900C22×C4semidirect
207. C2×C4⋊(C5⋊D5)C22×C4semidirect
208. C2×C4×C5⋊D5C22×C4semidirect
209. C2×C4×C5⋊D5C22×C4semidirect
210. C2×C4×C5⋊D5C22×C4semidirect
211. C2×C4×C5⋊D5C22×C4semidirect
216. C2×#6045C22×C4semidirect
217. C2×C5×C22⋊D5C22×C4semidirect
218. C5×#713C22×C4semidirect
219. C5×Q8×D5C22×C4semidirect
220. C5×#711C22×C4semidirect
221. C5×D4×D5C22×C4semidirect
222. C5×#709C22×C4semidirect
223. C5×#709C22×C4semidirect
224. C5×#709C22×C4semidirect
225. C5×#709C22×C4semidirect
226. C2×C5×D20C22×C4semidirect
227. C2×C4×C5×D5C22×C4semidirect
228. C2×C5×Dic10C22×C4semidirect
229. #87886C22×C4semidirect
230. #87886C22×C4semidirect
233. D5×C22⋊D5C22×C4semidirect
234. C2×#6039C22×C4semidirect
235. C2×#6038C22×C4semidirect
236. C2×#6037C22×C4semidirect
238. #87880C22×C4semidirect
239. #87880C22×C4semidirect
240. #87880C22×C4semidirect
241. #87880C22×C4semidirect
242. #87879C22×C4semidirect
243. C2×D5×Dic5C22×C4semidirect
244. #87877C22×C4semidirect
245. #87877C22×C4semidirect
248. D5×D20C22×C4semidirect
249. C4×D52C22×C4semidirect
250. C4×D52C22×C4semidirect
253. #87874C22×C4semidirect
254. #87873C22×C4semidirect
255. #87873C22×C4semidirect
256. #87873C22×C4semidirect
257. #87873C22×C4semidirect
258. #87872C22×C4semidirect
259. #87872C22×C4semidirect
262. #87871C22×C4semidirect
263. #87871C22×C4semidirect
264. #87871C22×C4semidirect
265. #87871C22×C4semidirect
266. #87870C22×C4semidirect
267. D5×Dic10C22×C4semidirect
300. #66283AGL(1,𝔽5)semidirect
424. C2×C5×#41C2×AGL(1,𝔽5)semidirect
429. #4150C2×AGL(1,𝔽5)semidirect
434. #4149C2×AGL(1,𝔽5)semidirect
456. D5×#41C2×AGL(1,𝔽5)semidirect
460. #4147C2×AGL(1,𝔽5)semidirect
473. #4144C2×AGL(1,𝔽5)semidirect
488. C2×#709C2×AGL(1,𝔽5)semidirect
585. #1043#585semidirect
618. C5×#41C22×AGL(1,𝔽5)semidirect
619. C5×#41C22×AGL(1,𝔽5)semidirect
623. C2×C5×Q8C22×AGL(1,𝔽5)semidirect
628. C2×C5×D4C22×AGL(1,𝔽5)semidirect
631. C22×C4×C5C22×AGL(1,𝔽5)semidirect
637. C2×C22⋊D5C22×AGL(1,𝔽5)semidirect
650. #713C22×AGL(1,𝔽5)semidirect
660. Q8×D5C22×AGL(1,𝔽5)semidirect
675. #711C22×AGL(1,𝔽5)semidirect
690. D4×D5C22×AGL(1,𝔽5)semidirect
702. #709C22×AGL(1,𝔽5)semidirect
703. #709C22×AGL(1,𝔽5)semidirect
704. #709C22×AGL(1,𝔽5)semidirect
705. #709C22×AGL(1,𝔽5)semidirect
710. C2×D20C22×AGL(1,𝔽5)semidirect
733. C2×C4×D5C22×AGL(1,𝔽5)semidirect
738. C2×Dic10C22×AGL(1,𝔽5)semidirect
980. C2×#41D5⋊AGL(1,𝔽5)semidirect
1043. C52C4×#585semidirect
1120. #41C2×D5⋊AGL(1,𝔽5)semidirect
1121. #41C2×D5⋊AGL(1,𝔽5)semidirect
1133. C2×Q8C2×D5⋊AGL(1,𝔽5)semidirect
1153. C2×D4C2×D5⋊AGL(1,𝔽5)semidirect
1179. C22×C4C2×D5⋊AGL(1,𝔽5)semidirect
1279. C5AGL(1,𝔽5)×#585semidirect

Maximal subgroups

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

subgroupindex
#722210192
#722209942
#722209892
#41×D5⋊AGL(1,𝔽5)2
#722209852
#722209772
#722209612
#722209562
C2×#41×#10432
C2×#131075592
#722134122
AGL(1,𝔽5)×#5855