Finite Group Databasebeta

← C22×#72220669 #72269148

Subgroups — C22×#72220669 #72269148

Order 12800.

31014 conjugacy classes of subgroups.

The subgroup lattice has 965 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13104814C211yesmaximal, characteristic
2C22×#11716895C414yescomplemented
3C22×C42×#1043C211yesmaximal, characteristic
4C23×#11716763C212yesmaximal
5C22×#13100501C211yesmaximal, characteristic
6C22×#11716596C412yescomplemented
7C22×C5×#3935C412yescomplemented
8C22×C42×C5⋊D5C2211yescharacteristic
9C23×#11716761C212yesmaximal
10C23×#87862C2212yes—
11C23×#87767C2212yes—
12C22×AGL(1,𝔽5)×#97—52nomaximal
13C2×#72220669C2124yesmaximal, direct product factor
14C2×#13104814C4112yescomplemented
15C2×#13104814C22112yes—
16C22×#11716763C4132yescomplemented
17C22×#11716763C22124yes—
18C2×#13100501C4112yescomplemented
19C2×#13100501C22112yes—
20C22×#11716761C4132yescomplemented
21C22×#11716761C22124yes—
22C23×C4×#1043C414yes—
23C23×C4×#1043C2211yescharacteristic
24C23×C4×#1043C2211yescharacteristic
25C2×C42×#1043C4112yes—
26C2×C42×#1043C22112yes—
27#72220669C22164yesdirect product factor
28C24×#1043C2×C412yes—
29C24×#1043C2×C412yes—
30C23×C4×C5⋊D5C2×C412yes—
31C23×C4×C5⋊D5C2311yescharacteristic
32C23×#6034C2×C414yes—
33C22×#87862C2×C4112yes—
34C22×#87862C2×C4116yes—
35C22×#87862C2×C4116yes—
36C22×#87862C23112yes—
37C22×C4×#1043—232no—
38C22×C4×#1043C2×C4148yes—
39C22×C4×#1043C2×C416yes—
40C22×C4×#1043C2×C416yes—
41C22×C4×#1043C2×C4116yes—
42C22×C4×#1043C2×C4116yes—
43C22×C4×#1043C2316yes—
44C22×C4×#1043C2316yes—
45C22×C42×C52C2×C411yescharacteristic
46C22×C4×#1039C2×C411yescharacteristic
47C22×C4×#1039C2×C412yes—
48C2×C42×C5⋊D5C2×C416yes—
49C2×C42×C5⋊D5C2×C416yes—
50C2×C42×C5⋊D5C2×C416yes—
51C2×C42×C5⋊D5C2316yes—
52C23×C5×#168C2×C414yes—
53C22×#87767C2×C4116yes—
54C22×#87767C2×C4116yes—
55C22×#87767C2×C4112yes—
56C22×#87767C23112yes—
57C2×#11716895C2×C4148yescomplemented
58#13104814C2×C4148yescomplemented
59#13104814C23116yes—
60C42×#1043C2×C4148yes—
61C42×#1043C23116yes—
62C2×#11716763C2×C41192yescomplemented
63C2×#11716763C23132yes—
64C2×#11716761C2×C41192yescomplemented
65C2×#11716761C23132yes—
66C2×C5×#3935C2×C4124yescomplemented
67C2×#11716596C2×C4124yescomplemented
68#13100501C2×C4148yescomplemented
69#13100501C23116yes—
70C22×#65676—52no—
71C23×#3992—54no—
72C23×C8×AGL(1,𝔽5)—54no—
73C22×C42×AGL(1,𝔽5)—52no—
74C22×C42×AGL(1,𝔽5)—102no—
75C2×AGL(1,𝔽5)×#97—548no—
76C22×D5×#97—52no—
77C24×C5⋊D5C22×C411yescharacteristic
78C23×#1043—216no—
79C23×#1043C42116yes—
80C23×#1043C42116yes—
81C23×#1043M16132yes—
82C23×#1043C22×C4112yes—
83C23×#1043C22×C4112yes—
84C23×C4×C52C4212yes—
85C23×C4×C52C22×C411yescharacteristic
86C23×#1039C4212yes—
87C23×#1039C22×C411yescharacteristic
88C22×C4×C5⋊D5—216no—
89C22×C4×C5⋊D5C42112yes—
90C22×C4×C5⋊D5C22×C4112yes—
91C22×C4×C5⋊D5C22×C413yes—
92C22×C4×C5⋊D5C22×C413yes—
93C22×C4×C5⋊D5C22×C413yes—
94C22×C4×C5⋊D5C22×C418yes—
95C22×C4×C5⋊D5C22×C418yes—
96C22×C4×C5⋊D5C2413yes—
97C22×#6034C42132yescomplemented
98C22×#6034C22×C4124yes—
99C2×#87862C42196yescomplemented
100C2×#87862C22×C4124yes—
101C2×#87862C22×C4148yes—
102C2×#87862C22×C4148yes—
103C2×#87862C2418yes—
104C2×C4×#1043—2192no—
105C2×C4×#1043C42148yes—
106C2×C4×#1043C42148yes—
107C2×C4×#1043C22×C4164yes—
108C2×C4×#1043C22×C4112yes—
109C2×C4×#1043C22×C4112yes—
110C2×C4×#1043C22×C4148yes—
111C2×C4×#1043C22×C4148yes—
112C2×C4×#1043C2414yes—
113C2×C4×#1043C2414yes—
114C2×C42×C52C4216yes—
115C2×C42×C52C22×C416yes—
116C2×C4×#1039C4216yes—
117C2×C4×#1039C42112yes—
118C2×C4×#1039C22×C416yes—
119C2×C4×#1039C22×C4112yes—
120C42×C5⋊D5C42124yes—
121C42×C5⋊D5C22×C4112yes—
122C42×C5⋊D5C22×C4112yes—
123C42×C5⋊D5C22×C4112yes—
124C42×C5⋊D5C2414yes—
125C22×C5×#168C42132yescomplemented
126C22×C5×#168C22×C4124yes—
127C2×#87767C42196yescomplemented
128C2×#87767C22×C4124yes—
129C2×#87767C22×C4148yes—
130C2×#87767C22×C4148yes—
131C2×#87767C2418yes—
132#11716895C22×C4164yescomplemented
133#11716763C22×C41128yescomplemented
134#11716761C22×C41128yescomplemented
135C5×#3935C22×C4132yescomplemented
136#11716596C22×C4132yescomplemented
137C23×C4×AGL(1,𝔽5)—52no—
138C23×C4×AGL(1,𝔽5)—52no—
139C23×C4×AGL(1,𝔽5)—58no—
140C23×C4×AGL(1,𝔽5)—108no—
141C23×C4×AGL(1,𝔽5)—102no—
142C23×C4×AGL(1,𝔽5)—102no—
143C23×D5⋊C8—54no—
144C23×C8×D5—54no—
145C22×C42×D5—52no—
146C22×C42×D5—102no—
147C22×#4002—58no—
148C22×#3992—548no—
149C22×#3992—564no—
150C22×C8×AGL(1,𝔽5)—564no—
151C22×C8×AGL(1,𝔽5)—548no—
152C2×C42×AGL(1,𝔽5)—524no—
153C2×C42×AGL(1,𝔽5)—524no—
154C2×C42×AGL(1,𝔽5)—1024no—
155C2×C42×AGL(1,𝔽5)—1024no—
156C2×#65676—524no—
157C2×#65676—524no—
158C22×C5×#97—52no—
159C22×#3947—54no—
160C22×#3935AGL(1,𝔽5)12yescomplemented
161C2×D5×#97—524no—
162C2×D5×#97—524no—
163AGL(1,𝔽5)×#97—5128no—
164C22×C4×#97—251noSylow
165C24×C52C2×C4211yescharacteristic
166C23×C5⋊D5C2×C4213yes—
167C23×C5⋊D5C2×C4214yes—
168C23×C5⋊D5C2×C4214yes—
169C23×C5⋊D5C2×M16116yes—
170C23×C5⋊D5C23×C413yes—
171C22×#1043—248no—
172C22×#1043—264no—
173C22×#1043#971128yescomplemented
174C22×#1043C2×C42148yes—
175C22×#1043C2×C42148yes—
176C22×#1043C2×M16196yes—
177C22×#1043C23×C418yes—
178C22×#1043C23×C418yes—
179C22×C4×C52—28no—
180C22×C4×C52C2×C42112yes—
181C22×C4×C52C2×C4213yes—
182C22×C4×C52C2×C4218yes—
183C22×C4×C52C23×C413yes—
184C22×#1039—28no—
185C22×#1039C2×C42112yes—
186C22×#1039C2×C4213yes—
187C22×#1039C2×C4218yes—
188C22×#1039C23×C413yes—
189C2×C4×C5⋊D5—248no—
190C2×C4×C5⋊D5—248no—
191C2×C4×C5⋊D5C2×C42124yes—
192C2×C4×C5⋊D5C2×C4216yes—
193C2×C4×C5⋊D5C2×C42112yes—
194C2×C4×C5⋊D5C2×C42112yes—
195C2×C4×C5⋊D5C2×C42124yes—
196C2×C4×C5⋊D5C2×C42124yes—
197C2×C4×C5⋊D5C23×C418yes—
198C2×C4×C5⋊D5C23×C4112yes—
199C2×C4×C5⋊D5C23×C4112yes—
200C2×C4×C5⋊D5C23×C413yes—
201C2×C4×C5⋊D5C23×C413yes—
202C2×C4×C5⋊D5C23×C413yes—
203C2×C4×C5⋊D5C2511yescharacteristic
204C2×#6034C2×C42196yescomplemented
205C2×#6034C23×C4116yes—
206#87862C2×C42196yescomplemented
207#87862C23×C4116yes—
208#87862C23×C4116yes—
209C4×#1043—2128no—
210C4×#1043C2×C42148yes—
211C4×#1043C2×C42148yes—
212C4×#1043C23×C4116yes—
213C4×#1043C23×C4116yes—
214C42×C52C2×C42112yes—
215C42×C52C23×C414yes—
216C4×#1039C2×C42112yes—
217C4×#1039C2×C42124yes—
218C4×#1039C23×C418yes—
219C4×#1039C23×C414yes—
220C2×C5×#168C2×C42196yescomplemented
221C2×C5×#168C23×C4116yes—
222#87767C2×C42196yescomplemented
223#87767C23×C4116yes—
224#87767C23×C4116yes—
225C24×AGL(1,𝔽5)—54no—
226C24×AGL(1,𝔽5)—54no—
227C24×AGL(1,𝔽5)—104no—
228C24×AGL(1,𝔽5)—104no—
229C23×C4×D5—52no—
230C23×C4×D5—54no—
231C23×C4×D5—104no—
232C23×C4×D5—102no—
233C23×#170—58no—
234C22×C4×AGL(1,𝔽5)—532no—
235C22×C4×AGL(1,𝔽5)—532no—
236C22×C4×AGL(1,𝔽5)—512no—
237C22×C4×AGL(1,𝔽5)—512no—
238C22×C4×AGL(1,𝔽5)—512no—
239C22×C4×AGL(1,𝔽5)—512no—
240C22×C4×AGL(1,𝔽5)—596no—
241C22×C4×AGL(1,𝔽5)—1064no—
242C22×C4×AGL(1,𝔽5)—1032no—
243C22×C4×AGL(1,𝔽5)—1032no—
244C22×C4×AGL(1,𝔽5)—1012no—
245C22×C4×AGL(1,𝔽5)—1012no—
246C22×C4×AGL(1,𝔽5)—1096no—
247C22×C4×AGL(1,𝔽5)—1012no—
248C22×C4×AGL(1,𝔽5)—1012no—
249C22×C4×AGL(1,𝔽5)—10128no—
250C22×D5⋊C8—532no—
251C22×D5⋊C8—532no—
252C22×D5⋊C8—524no—
253C22×D5⋊C8—524no—
254C23×C5×C8—54no—
255C22×C42×C5—22no—
256C22×C42×C5C2×AGL(1,𝔽5)12yes—
257C22×C4×Dic5—54no—
258C22×C4×Dic5—52no—
259C22×C4×Dic5—102no—
260C22×C4×Dic5—104no—
261C23×#168C2×AGL(1,𝔽5)14yes—
262C22×C8×D5—532no—
263C22×C8×D5—532no—
264C22×C8×D5—524no—
265C22×C8×D5—524no—
266C2×C42×D5—512no—
267C2×C42×D5—512no—
268C2×C42×D5—512no—
269C2×C42×D5—512no—
270C2×C42×D5—1012no—
271C2×C42×D5—1012no—
272C2×C42×D5—1012no—
273C2×C42×D5—1012no—
274C2×#4002—596no—
275C2×#3992—5384no—
276C2×#3992—564no—
277C2×C8×AGL(1,𝔽5)—5384no—
278C2×C8×AGL(1,𝔽5)—564no—
279C42×AGL(1,𝔽5)—596no—
280C42×AGL(1,𝔽5)—532no—
281C42×AGL(1,𝔽5)—1096no—
282C42×AGL(1,𝔽5)—1032no—
283#65676—532no—
284#65676—596no—
285C2×C5×#97—524no—
286C2×#3947—548no—
287C2×#3935C2×AGL(1,𝔽5)124yescomplemented
288D5×#97—532no—
289D5×#97—596no—
290C23×#97—251no—
291C23×#97—252no—
292C23×#97—251no—
293C23×C4×C8—252no—
294C22×C43—251no—
295C2×C4×#97—2524no—
296C23×C52C4314yes—
297C23×C52C4×M1618yes—
298C23×C52C22×C4213yes—
299C22×C5⋊D5C43112yes—
300C22×C5⋊D5C2×#97132yes—
301C22×C5⋊D5C4×M16132yes—
302C22×C5⋊D5C4×M16124yes—
303C22×C5⋊D5C22×C4216yes—
304C22×C5⋊D5C22×C4216yes—
305C22×C5⋊D5C22×C4213yes—
306C22×C5⋊D5C22×M16124yes—
307C22×C5⋊D5C24×C411yescharacteristic
308C2×#1043—296no—
309C2×#1043—216no—
310C2×#1043C2×#971192yescomplemented
311C2×#1043C22×C42116yes—
312C2×#1043C22×C42116yes—
313C2×#1043C22×M16132yes—
314C2×C4×C52—224no—
315C2×C4×C52C43112yes—
316C2×C4×C52C22×C4218yes—
317C2×C4×C52C22×C42112yes—
318C2×C4×C52C22×C4213yes—
319C2×C4×C52C24×C411yescharacteristic
320C2×#1039—224no—
321C2×#1039C43112yes—
322C2×#1039C22×C4218yes—
323C2×#1039C22×C42112yes—
324C2×#1039C22×C4213yes—
325C2×#1039C24×C411yescharacteristic
326C4×C5⋊D5—248no—
327C4×C5⋊D5—216no—
328C4×C5⋊D5C43124yes—
329C4×C5⋊D5C22×C42112yes—
330C4×C5⋊D5C22×C42112yes—
331C4×C5⋊D5C22×C4216yes—
332C4×C5⋊D5C22×C4216yes—
333C4×C5⋊D5C24×C412yes—
334C4×C5⋊D5C24×C412yes—
335#6034C22×C42132yescomplemented
336C5×#168C22×C42132yescomplemented
337C24×D5—52no—
338C24×D5—102no—
339C23×AGL(1,𝔽5)—532no—
340C23×AGL(1,𝔽5)—564no—
341C23×AGL(1,𝔽5)—524no—
342C23×AGL(1,𝔽5)—532no—
343C23×AGL(1,𝔽5)—524no—
344C23×AGL(1,𝔽5)—1032no—
345C23×AGL(1,𝔽5)—1032no—
346C23×AGL(1,𝔽5)—1064no—
347C23×AGL(1,𝔽5)—1024no—
348C23×AGL(1,𝔽5)—1024no—
349C23×AGL(1,𝔽5)—1032no—
350C23×AGL(1,𝔽5)—1064no—
351C23×C4×C5—24no—
352C23×C4×C5—22no—
353C23×C4×C5C4×AGL(1,𝔽5)14yes—
354C23×C4×C5C22×AGL(1,𝔽5)12yes—
355C23×Dic5—52no—
356C23×Dic5—54no—
357C23×Dic5—104no—
358C23×Dic5—102no—
359C22×C4×D5—56no—
360C22×C4×D5—56no—
361C22×C4×D5—516no—
362C22×C4×D5—516no—
363C22×C4×D5—56no—
364C22×C4×D5—56no—
365C22×C4×D5—524no—
366C22×C4×D5—524no—
367C22×C4×D5—1024no—
368C22×C4×D5—106no—
369C22×C4×D5—1024no—
370C22×C4×D5—106no—
371C22×C4×D5—106no—
372C22×C4×D5—106no—
373C22×C4×D5—1016no—
374C22×C4×D5—1016no—
375C22×C4×D5—1032no—
376C22×C4×D5—1064no—
377C22×#170—564no—
378C22×#170—548no—
379C2×C4×AGL(1,𝔽5)—596no—
380C2×C4×AGL(1,𝔽5)—596no—
381C2×C4×AGL(1,𝔽5)—524no—
382C2×C4×AGL(1,𝔽5)—524no—
383C2×C4×AGL(1,𝔽5)—596no—
384C2×C4×AGL(1,𝔽5)—596no—
385C2×C4×AGL(1,𝔽5)—58no—
386C2×C4×AGL(1,𝔽5)—58no—
387C2×C4×AGL(1,𝔽5)—5128no—
388C2×C4×AGL(1,𝔽5)—1096no—
389C2×C4×AGL(1,𝔽5)—1096no—
390C2×C4×AGL(1,𝔽5)—1024no—
391C2×C4×AGL(1,𝔽5)—1024no—
392C2×C4×AGL(1,𝔽5)—10128no—
393C2×C4×AGL(1,𝔽5)—1096no—
394C2×C4×AGL(1,𝔽5)—1096no—
395C2×C4×AGL(1,𝔽5)—108no—
396C2×C4×AGL(1,𝔽5)—108no—
397C2×C4×AGL(1,𝔽5)—10384no—
398C2×C4×AGL(1,𝔽5)—10768no—
399C2×D5⋊C8—5192no—
400C2×D5⋊C8—548no—
401C2×D5⋊C8—596no—
402C2×D5⋊C8—596no—
403C2×D5⋊C8—516no—
404C22×C5×C8—532no—
405C22×C5×C8—524no—
406C2×C42×C5—212no—
407C2×C42×C5—212no—
408C2×C42×C5C4×AGL(1,𝔽5)112yes—
409C2×C42×C5C22×AGL(1,𝔽5)112yes—
410C2×C4×Dic5—524no—
411C2×C4×Dic5—512no—
412C2×C4×Dic5—524no—
413C2×C4×Dic5—512no—
414C2×C4×Dic5—1024no—
415C2×C4×Dic5—1012no—
416C2×C4×Dic5—1012no—
417C2×C4×Dic5—1024no—
418C22×#168C4×AGL(1,𝔽5)132yescomplemented
419C22×#168C22×AGL(1,𝔽5)124yes—
420C2×C8×D5—5192no—
421C2×C8×D5—596no—
422C2×C8×D5—596no—
423C2×C8×D5—548no—
424C2×C8×D5—516no—
425C42×D5—548no—
426C42×D5—524no—
427C42×D5—524no—
428C42×D5—524no—
429C42×D5—58no—
430C42×D5—1048no—
431C42×D5—1024no—
432C42×D5—1024no—
433C42×D5—1024no—
434C42×D5—108no—
435#4002—5128no—
436#3992—5256no—
437C8×AGL(1,𝔽5)—5256no—
438C5×#97—532no—
439#3947—564no—
440#3935C22×AGL(1,𝔽5)132yescomplemented
441C24×C8—252no—
442C24×C8—252no—
443C23×C42—251no—
444C23×C42—251no—
445C23×C42—251no—
446C23×C42—254no—
447C22×#97—52no—
448C22×#97—252no—
449C22×#97—2512no—
450C22×#97—2512no—
451C22×#97—2524no—
452C22×#97—2532no—
453C22×#97—2512no—
454C22×#97—254no—
455C22×#97—2512no—
456C22×C4×C8—2524no—
457C22×C4×C8—2532no—
458C2×C43—2512no—
459C2×C43—2512no—
460C4×#97—2564no—
461C22×C52C4×#97116yescomplemented
462C22×C52C2×C4316yes—
463C22×C52C2×C4×M16112yes—
464C22×C52C23×C4211yescharacteristic
465C2×C5⋊D5C4×#97148yescomplemented
466C2×C5⋊D5C2×C4316yes—
467C2×C5⋊D5C22×#97124yes—
468C2×C5⋊D5C2×C4×M16112yes—
469C2×C5⋊D5C2×C4×M16124yes—
470C2×C5⋊D5C23×C4211yescharacteristic
471C2×C5⋊D5C23×C4211yescharacteristic
472C2×C5⋊D5C23×M1614yes—
473#1043—216no—
474#1043C22×#97132yescomplemented
475C4×C52—28no—
476C4×C52C2×C4316yes—
477C4×C52C23×C4212yes—
478#1039—28no—
479#1039C2×C4316yes—
480#1039C23×C4212yes—
481C24×C5—22no—
482C24×C5C2×C4×AGL(1,𝔽5)12yes—
483C23×D5—58no—
484C23×D5—58no—
485C23×D5—532no—
486C23×D5—56no—
487C23×D5—56no—
488C23×D5—106no—
489C23×D5—106no—
490C23×D5—108no—
491C23×D5—108no—
492C23×D5—1032no—
493C22×AGL(1,𝔽5)—516no—
494C22×AGL(1,𝔽5)—596no—
495C22×AGL(1,𝔽5)—5192no—
496C22×AGL(1,𝔽5)—5256no—
497C22×AGL(1,𝔽5)—516no—
498C22×AGL(1,𝔽5)—596no—
499C22×AGL(1,𝔽5)—1016no—
500C22×AGL(1,𝔽5)—1016no—
501C22×AGL(1,𝔽5)—1096no—
502C22×AGL(1,𝔽5)—1096no—
503C22×AGL(1,𝔽5)—10192no—
504C22×AGL(1,𝔽5)—10256no—
505C22×AGL(1,𝔽5)—1096no—
506C22×AGL(1,𝔽5)—10128no—
507C22×AGL(1,𝔽5)—10192no—
508C22×AGL(1,𝔽5)—10256no—
509C22×C4×C5—232no—
510C22×C4×C5—216no—
511C22×C4×C5—26no—
512C22×C4×C5—216no—
513C22×C4×C5—224no—
514C22×C4×C5—26no—
515C22×C4×C5C2×C4×AGL(1,𝔽5)116yes—
516C22×C4×C5C2×C4×AGL(1,𝔽5)124yes—
517C22×C4×C5C2×C4×AGL(1,𝔽5)16yes—
518C22×C4×C5C23×AGL(1,𝔽5)16yes—
519C22×Dic5—516no—
520C22×Dic5—56no—
521C22×Dic5—56no—
522C22×Dic5—524no—
523C22×Dic5—1016no—
524C22×Dic5—106no—
525C22×Dic5—1024no—
526C22×Dic5—106no—
527C22×Dic5—1032no—
528C22×Dic5—1016no—
529C2×C4×D5—548no—
530C2×C4×D5—524no—
531C2×C4×D5—524no—
532C2×C4×D5—56no—
533C2×C4×D5—524no—
534C2×C4×D5—524no—
535C2×C4×D5—56no—
536C2×C4×D5—512no—
537C2×C4×D5—548no—
538C2×C4×D5—52no—
539C2×C4×D5—56no—
540C2×C4×D5—516no—
541C2×C4×D5—548no—
542C2×C4×D5—106no—
543C2×C4×D5—1016no—
544C2×C4×D5—102no—
545C2×C4×D5—1024no—
546C2×C4×D5—1024no—
547C2×C4×D5—1024no—
548C2×C4×D5—1024no—
549C2×C4×D5—1048no—
550C2×C4×D5—1048no—
551C2×C4×D5—1012no—
552C2×C4×D5—1048no—
553C2×C4×D5—106no—
554C2×C4×D5—106no—
555C2×C4×D5—1096no—
556C2×C4×D5—1096no—
557C2×C4×D5—10192no—
558C2×C4×D5—10192no—
559C2×#170—5192no—
560C2×#170—532no—
561C4×AGL(1,𝔽5)—596no—
562C4×AGL(1,𝔽5)—596no—
563C4×AGL(1,𝔽5)—532no—
564C4×AGL(1,𝔽5)—532no—
565C4×AGL(1,𝔽5)—1096no—
566C4×AGL(1,𝔽5)—1096no—
567C4×AGL(1,𝔽5)—1032no—
568C4×AGL(1,𝔽5)—1032no—
569C4×AGL(1,𝔽5)—10256no—
570C4×AGL(1,𝔽5)—10512no—
571D5⋊C8—5192no—
572D5⋊C8—532no—
573D5⋊C8—532no—
574C2×C5×C8—596no—
575C2×C5×C8—516no—
576C42×C5—28no—
577C42×C5—224no—
578C42×C5C2×C4×AGL(1,𝔽5)124yes—
579C42×C5C23×AGL(1,𝔽5)18yes—
580C4×Dic5—516no—
581C4×Dic5—548no—
582C4×Dic5—524no—
583C4×Dic5—58no—
584C4×Dic5—1048no—
585C4×Dic5—1024no—
586C4×Dic5—1016no—
587C4×Dic5—108no—
588C2×#168C2×C4×AGL(1,𝔽5)196yescomplemented
589C2×#168C23×AGL(1,𝔽5)116yes—
590C8×D5—532no—
591C8×D5—532no—
592C8×D5—5192no—
593C24×C4—252no—
594C24×C4—251no—
595C24×C4—252no—
596C24×C4—252no—
597C23×C8—54no—
598C23×C8—2512no—
599C23×C8—2516no—
600C23×C8—2512no—
601C23×C8—2516no—
602C23×C8—2512no—
603C23×C8—2516no—
604C23×C8—2512no—
605C23×C8—2516no—
606C23×C8—254no—
607C22×C42—256no—
608C22×C42—2516no—
609C22×C42—256no—
610C22×C42—2516no—
611C22×C42—256no—
612C22×C42—256no—
613C22×C42—252no—
614C22×C42—251no—
615C22×C42—256no—
616C22×C42—256no—
617C22×C42—256no—
618C22×C42—256no—
619C22×C42—2548no—
620C22×C42—5032no—
621C22×C42D5⋊AGL(1,𝔽5)11yescharacteristic
622C2×#97—524no—
623C2×#97—2516no—
624C2×#97—2548no—
625C2×#97—2524no—
626C2×#97—2548no—
627C2×#97—2516no—
628C2×#97—25192no—
629C2×#97—2532no—
630C2×#97—2548no—
631C2×C4×C8—25192no—
632C2×C4×C8—2532no—
633C43—2516no—
634C43—2548no—
635C2×C52C2×C4×#97112yescomplemented
636C2×C52C22×C4311yescharacteristic
637C2×C52C22×C4×M1612yes—
638C5⋊D5C2×C4×#97112yescomplemented
639C5⋊D5C23×#9712yes—
640C5⋊D5C22×C4×M1612yes—
641C23×C5—216no—
642C23×C5—28no—
643C23×C5—26no—
644C23×C5C42×AGL(1,𝔽5)18yes—
645C23×C5M16×AGL(1,𝔽5)116yes—
646C23×C5C22×C4×AGL(1,𝔽5)16yes—
647C22×D5—52no—
648C22×D5—56no—
649C22×D5—548no—
650C22×D5—548no—
651C22×D5—564no—
652C22×D5—564no—
653C22×D5—524no—
654C22×D5—512no—
655C22×D5—512no—
656C22×D5—1048no—
657C22×D5—102no—
658C22×D5—1024no—
659C22×D5—1064no—
660C22×D5—1048no—
661C22×D5—1064no—
662C22×D5—106no—
663C22×D5—1012no—
664C22×D5—1012no—
665C2×AGL(1,𝔽5)—564no—
666C2×AGL(1,𝔽5)—5384no—
667C2×AGL(1,𝔽5)—532no—
668C2×AGL(1,𝔽5)—532no—
669C2×AGL(1,𝔽5)—1064no—
670C2×AGL(1,𝔽5)—10384no—
671C2×AGL(1,𝔽5)—1032no—
672C2×AGL(1,𝔽5)—1032no—
673C2×AGL(1,𝔽5)—1032no—
674C2×AGL(1,𝔽5)—10192no—
675C2×AGL(1,𝔽5)—1064no—
676C2×AGL(1,𝔽5)—10384no—
677C2×C4×C5—296no—
678C2×C4×C5—248no—
679C2×C4×C5—224no—
680C2×C4×C5—224no—
681C2×C4×C5—216no—
682C2×C4×C5—26no—
683C2×C4×C5—22no—
684C2×C4×C5C42×AGL(1,𝔽5)124yes—
685C2×C4×C5C22×C4×AGL(1,𝔽5)124yes—
686C2×C4×C5C22×C4×AGL(1,𝔽5)116yes—
687C2×C4×C5C22×C4×AGL(1,𝔽5)16yes—
688C2×C4×C5C24×AGL(1,𝔽5)12yes—
689C2×Dic5—52no—
690C2×Dic5—56no—
691C2×Dic5—524no—
692C2×Dic5—524no—
693C2×Dic5—516no—
694C2×Dic5—102no—
695C2×Dic5—1024no—
696C2×Dic5—106no—
697C2×Dic5—1016no—
698C2×Dic5—1024no—
699C2×Dic5—1096no—
700C2×Dic5—1048no—
701C4×D5—54no—
702C4×D5—54no—
703C4×D5—524no—
704C4×D5—548no—
705C4×D5—524no—
706C4×D5—512no—
707C4×D5—512no—
708C4×D5—104no—
709C4×D5—104no—
710C4×D5—1048no—
711C4×D5—1012no—
712C4×D5—1012no—
713C4×D5—1024no—
714C4×D5—1024no—
715C4×D5—1032no—
716C4×D5—1096no—
717C4×D5—1064no—
718C4×D5—10192no—
719#170—564no—
720C5×C8—532no—
721#168C22×C4×AGL(1,𝔽5)132yescomplemented
722C25—251no—
723C23×C4—2516no—
724C23×C4—2512no—
725C23×C4—2532no—
726C23×C4—251no—
727C23×C4—253no—
728C23×C4—253no—
729C23×C4—258no—
730C23×C4—258no—
731C23×C4—253no—
732C23×C4—253no—
733C23×C4—2516no—
734C23×C4—2512no—
735C23×C4—252no—
736C23×C4—2512no—
737C23×C4—2512no—
738C23×C4—5016no—
739C23×C4—5016no—
740C23×C4#8783012yes—
741C23×C4C2×D5⋊AGL(1,𝔽5)11yescharacteristic
742C22×C8—524no—
743C22×C8—532no—
744C22×C8—258no—
745C22×C8—2548no—
746C22×C8—2548no—
747C22×C8—2524no—
748C22×C8—2596no—
749C22×C8—2596no—
750C22×C8—2548no—
751C22×C8—258no—
752C22×C8—2548no—
753C22×C8—2524no—
754C22×C8—2532no—
755C22×C8—2524no—
756C2×C42—254no—
757C2×C42—254no—
758C2×C42—2512no—
759C2×C42—2512no—
760C2×C42—2548no—
761C2×C42—2548no—
762C2×C42—2548no—
763C2×C42—2548no—
764C2×C42—256no—
765C2×C42—2512no—
766C2×C42—2512no—
767C2×C42—256no—
768C2×C42—254no—
769C2×C42—2512no—
770C2×C42—2512no—
771C2×C42—2512no—
772C2×C42—2524no—
773C2×C42—2564no—
774C2×C42—50192no—
775C2×C42#8783016yes—
776C2×C42C2×D5⋊AGL(1,𝔽5)16yes—
777#97—532no—
778#97—2532no—
779#97—25128no—
780#97—2564no—
781C4×C8—25128no—
782C52C22×C4×#9711yescharacteristic, complemented, Sylow
783C22×C5—212no—
784C22×C5—224no—
785C22×C5—22no—
786C22×C5—232no—
787C22×C5AGL(1,𝔽5)×#97132yescomplemented
788C22×C5C2×C42×AGL(1,𝔽5)112yes—
789C22×C5C2×M16×AGL(1,𝔽5)124yes—
790C22×C5C23×C4×AGL(1,𝔽5)12yes—
791C2×D5—52no—
792C2×D5—52no—
793C2×D5—512no—
794C2×D5—548no—
795C2×D5—548no—
796C2×D5—596no—
797C2×D5—524no—
798C2×D5—58no—
799C2×D5—1048no—
800C2×D5—1024no—
801C2×D5—1048no—
802C2×D5—102no—
803C2×D5—102no—
804C2×D5—1096no—
805C2×D5—1012no—
806C2×D5—108no—
807AGL(1,𝔽5)—564no—
808AGL(1,𝔽5)—1064no—
809AGL(1,𝔽5)—1032no—
810AGL(1,𝔽5)—1064no—
811C4×C5—232no—
812C4×C5—216no—
813C4×C5—212no—
814C4×C5—24no—
815C4×C5C2×C42×AGL(1,𝔽5)112yes—
816C4×C5C23×C4×AGL(1,𝔽5)14yes—
817Dic5—54no—
818Dic5—512no—
819Dic5—104no—
820Dic5—1012no—
821Dic5—1032no—
822Dic5—1016no—
823C24—2516no—
824C24—254no—
825C24—254no—
826C24—253no—
827C24—253no—
828C24C2×#8783011yescharacteristic
829C22×C4—28no—
830C22×C4—258no—
831C22×C4—2548no—
832C22×C4—2596no—
833C22×C4—25128no—
834C22×C4—258no—
835C22×C4—253no—
836C22×C4—253no—
837C22×C4—2512no—
838C22×C4—2512no—
839C22×C4—2524no—
840C22×C4—2512no—
841C22×C4—2512no—
842C22×C4—2524no—
843C22×C4—253no—
844C22×C4—253no—
845C22×C4—256no—
846C22×C4—251no—
847C22×C4—253no—
848C22×C4—258no—
849C22×C4—2548no—
850C22×C4—2512no—
851C22×C4—258no—
852C22×C4—2524no—
853C22×C4—5048no—
854C22×C4—5048no—
855C22×C4—5048no—
856C22×C4—5064no—
857C22×C4—508no—
858C22×C4C4×D5⋊AGL(1,𝔽5)18yes—
859C22×C4C2×#87830112yes—
860C22×C4C2×#8783013yes—
861C22×C4C22×D5⋊AGL(1,𝔽5)13yes—
862C2×C8—596no—
863C2×C8—516no—
864C2×C8—2516no—
865C2×C8—2516no—
866C2×C8—2596no—
867C2×C8—2516no—
868C2×C8—2516no—
869C2×C8—2516no—
870C2×C8—2596no—
871C2×C8—2596no—
872C42—2516no—
873C42—2516no—
874C42—2548no—
875C42—2548no—
876C42—258no—
877C42—2524no—
878C42—2512no—
879C42—254no—
880C42—50128no—
881C42C2×#87830112yes—
882C42C22×D5⋊AGL(1,𝔽5)14yes—
883C2×C5—22no—
884C2×C5—24no—
885C2×C5—224no—
886C2×C5C2×AGL(1,𝔽5)×#97124yescomplemented
887C2×C5C22×C42×AGL(1,𝔽5)12yes—
888C2×C5C22×M16×AGL(1,𝔽5)14yes—
889D5—524no—
890D5—54no—
891D5—54no—
892D5—1024no—
893D5—104no—
894D5—104no—
895C23—256no—
896C23—256no—
897C23—2512no—
898C23—2524no—
899C23—2524no—
900C23—251no—
901C23—253no—
902C23—2532no—
903C23—2532no—
904C23#1310390518yes—
905C23C4×#8783014yes—
906C23C22×#8783013yes—
907C2×C4—224no—
908C2×C4—2516no—
909C2×C4—2532no—
910C2×C4—25192no—
911C2×C4—2512no—
912C2×C4—2512no—
913C2×C4—251no—
914C2×C4—253no—
915C2×C4—256no—
916C2×C4—256no—
917C2×C4—2512no—
918C2×C4—2524no—
919C2×C4—252no—
920C2×C4—252no—
921C2×C4—2512no—
922C2×C4—2516no—
923C2×C4—258no—
924C2×C4—5016no—
925C2×C4—5048no—
926C2×C4—5016no—
927C2×C4—5096no—
928C2×C4—5024no—
929C2×C4C4×#87830112yes—
930C2×C4C2×C4×D5⋊AGL(1,𝔽5)112yes—
931C2×C4C22×#8783018yes—
932C2×C4C22×#8783013yes—
933C2×C4C23×D5⋊AGL(1,𝔽5)11yescharacteristic
934C8—532no—
935C8—2532no—
936C5—22no—
937C5C22×AGL(1,𝔽5)×#9712yescomplemented
938C22—251no—
939C22—251no—
940C22—256no—
941C22—254no—
942C22—2512no—
943C22—2524no—
944C22—2524no—
945C22—2548no—
946C22#72220669116yesdirect product factor
947C22C2×#13103905112yes—
948C22C23×#8783011yescharacteristic
949C22C2×C4×#8783016yes—
950C4—28no—
951C4—2532no—
952C4—252no—
953C4—256no—
954C4—5016no—
955C4—508no—
956C4C22×C4×D5⋊AGL(1,𝔽5)12yes—
957C4C2×C4×#8783016yes—
958C2—252no—
959C2—252no—
960C2—2512no—
961C2C2×#72220669112yesdirect product factor
962C2C22×C4×#8783011yescharacteristic
963C2C22×#1310390512yes—
subgroupG/H
centerC23×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C22×C43
FrattiniC2×C4C23×D5⋊AGL(1,𝔽5)
FittingC22×C42×C52C2×C4
socleC24×C52C2×C42
prime radicalC24×C5⋊D5C22×C4
cosocleC2×C4×C5⋊D5C25
hypercenterC22×C42D5⋊AGL(1,𝔽5)
hypocenterC52C22×C4×#97
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C22×#11716895C4semidirect
6. C22×#11716596C4semidirect
7. C22×C5×#3935C4semidirect
13. C2×#72220669C2direct (N × H)
14. C2×#13104814C4semidirect
16. C22×#11716763C4semidirect
18. C2×#13100501C4semidirect
20. C22×#11716761C4semidirect
27. #72220669C22direct (N × H)
57. C2×#11716895C2×C4semidirect
58. #13104814C2×C4semidirect
62. C2×#11716763C2×C4semidirect
64. C2×#11716761C2×C4semidirect
66. C2×C5×#3935C2×C4semidirect
67. C2×#11716596C2×C4semidirect
68. #13100501C2×C4semidirect
97. C22×#6034C42semidirect
99. C2×#87862C42semidirect
125. C22×C5×#168C42semidirect
127. C2×#87767C42semidirect
132. #11716895C22×C4semidirect
133. #11716763C22×C4semidirect
134. #11716761C22×C4semidirect
135. C5×#3935C22×C4semidirect
136. #11716596C22×C4semidirect
160. C22×#3935AGL(1,𝔽5)semidirect
173. C22×#1043#97semidirect
204. C2×#6034C2×C42semidirect
206. #87862C2×C42semidirect
220. C2×C5×#168C2×C42semidirect
222. #87767C2×C42semidirect
287. C2×#3935C2×AGL(1,𝔽5)semidirect
310. C2×#1043C2×#97semidirect
335. #6034C22×C42semidirect
336. C5×#168C22×C42semidirect
418. C22×#168C4×AGL(1,𝔽5)semidirect
440. #3935C22×AGL(1,𝔽5)semidirect
461. C22×C52C4×#97semidirect
465. C2×C5⋊D5C4×#97semidirect
474. #1043C22×#97semidirect
588. C2×#168C2×C4×AGL(1,𝔽5)semidirect
635. C2×C52C2×C4×#97semidirect
638. C5⋊D5C2×C4×#97semidirect
721. #168C22×C4×AGL(1,𝔽5)semidirect
782. C52C22×C4×#97semidirect
787. C22×C5AGL(1,𝔽5)×#97semidirect
886. C2×C5C2×AGL(1,𝔽5)×#97semidirect
937. C5C22×AGL(1,𝔽5)×#97semidirect
946. C22#72220669direct (N × H)
961. C2C2×#72220669direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131048142
C22×C42×#10432
C23×#117167632
C22×#131005012
C23×#117167612
C22×AGL(1,𝔽5)×#975
C2×#722206692