Finite Group Databasebeta

← #72223253

Subgroups — #72223253

Order 6400.

12824 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C4⋊#1043C214yesmaximal, complemented
2D4×C4⋊#1043C2112yesmaximal, complemented
3C4×#41×C5⋊D5C211yesmaximal, characteristic
4#72221041C216yesmaximal, complemented
5C2×#13107754C212yesmaximal
6#72220986C213yesmaximal, complemented
7C2×#13104700C213yesmaximal, complemented
8C2×#41×C5⋊D5C2211yescharacteristic
9#13107754—216no—
10C2×Q8×#1043C2214yes—
11C2×D4×#1043C22112yes—
12C2×#11717438C2216yes—
13C22×C4⋊#1043C2216yes—
14C22×C4⋊#1043C22112yes—
15C4×C52×#41C411yescharacteristic, complemented
16#41×#1039C411yescharacteristic, complemented
17C4×#87904C412yescomplemented
18C4×Q8×C5⋊D5C2212yes—
19C4×#87902C416yescomplemented
20C4×D4×C5⋊D5C2216yes—
21#13107053C413yescomplemented
22#117×C5⋊D5C2213yes—
23C4×#87900C413yescomplemented
24C2×C42×C5⋊D5C2213yes—
25#13104777C22112yes—
26#13104724C22124yes—
27#13104711C22124yes—
28#13104701C2216yes—
29#13104700C2213yes—
30#13104700C22112yes—
31#13104700C2216yes—
32#13104700C2211yescharacteristic
33C4×C4⋊#1043C22112yes—
34#13044026—56nomaximal
35C23×#1043C23112yes—
36C2×C52×#41C2×C411yescharacteristic
37#41×C5⋊D5D418yes—
38#41×C5⋊D5Q818yes—
39C2×#87904C2×C411yescharacteristic
40C2×Q8×C5⋊D5C2311yescharacteristic
41C2×#87902C2×C413yes—
42C2×D4×C5⋊D5C2313yes—
43C2×#87900C2×C413yes—
44C22×C4×C5⋊D5C2316yes—
45C22×C4×C5⋊D5C2313yes—
46C2×C22⋊#1043C23112yes—
47Q8×#1043—216no—
48D4×#1043—248no—
49#11717438—224no—
50C2×C4⋊#1043—224no—
51C2×C4⋊#1043—424no—
52C2×C4⋊#1043C2316yes—
53C2×C4⋊#1043C23112yes—
54C2×C4⋊#1043C23112yes—
55C2×C4⋊#1043C2312yes—
56C2×C4⋊#1043C2314yes—
57C2×C4⋊#1043C23124yes—
58C2×C4×#1043C23112yes—
59C4×C52×Q8C2×C412yescomplemented
60C4×C52×D4C2×C416yescomplemented
61C52×#117C2×C413yescomplemented
62C2×C42×C52C2×C413yescomplemented
63Q8×#1039C2×C412yescomplemented
64D4×#1039C2×C416yescomplemented
65C4×C22⋊(C5⋊D5)C2×C4112yescomplemented
66#11717246C2×C413yescomplemented
67C2×C4×#1039C2×C413yescomplemented
68C2×C4×#1039C2×C416yescomplemented
69#11717213C2×C416yescomplemented
70#11717212C2×C416yescomplemented
71C4⋊C4×C5⋊D5C2316yes—
72#11717207C2×C416yescomplemented
73#11717201C2×C4112yescomplemented
74C22⋊C4×C5⋊D5C2316yes—
75#11717197C2×C416yescomplemented
76C4×C4⋊(C5⋊D5)C2×C416yescomplemented
77#11717192C2×C416yescomplemented
78C42×C5⋊D5C2×C413yescomplemented
79C42×C5⋊D5C2×C413yescomplemented
80C42×C5⋊D5C2×C416yescomplemented
81C42×C5⋊D5C2311yescharacteristic
82C42×C5⋊D5C2316yes—
83C42×C5⋊D5C2313yes—
84C4×#6045C2×C416yescomplemented
85#11716874C23124yes—
86C2×#66266—512no—
87C4×D5×#41—56no—
88Q8×C4⋊AGL(1,𝔽5)—524no—
89D4×C4⋊AGL(1,𝔽5)—572no—
90#10617131—536no—
91#10617048—518no—
92C2×#65688—518no—
93C23×C5⋊D5C2413yes—
94C22×#1043—224no—
95C22×#1043—424no—
96C22×#1043C2414yes—
97C22×#1043C24112yes—
98C52×#41C4⋊C418yescomplemented
99C2×C52×Q8C22×C411yescharacteristic
100C2×C52×D4C22×C413yes—
101C22×C4×C52C22×C416yes—
102C22×C4×C52C22×C413yes—
103C2×C22⋊(C5⋊D5)C22×C416yes—
104C22×#1039C22×C416yes—
105C22×#1039C22×C413yes—
106#87904C4⋊C418yescomplemented
107Q8×C5⋊D5C2×D414yes—
108Q8×C5⋊D5C2×Q814yes—
109#87902C4⋊C4124yescomplemented
110D4×C5⋊D5C2×D4112yes—
111D4×C5⋊D5C2×Q8112yes—
112#87900C4⋊C4124yescomplemented
113C2×C4⋊(C5⋊D5)C22×C413yes—
114C2×C4×C5⋊D5—212no—
115C2×C4×C5⋊D5—212no—
116C2×C4×C5⋊D5C22×C416yes—
117C2×C4×C5⋊D5C22×C416yes—
118C2×C4×C5⋊D5C22×C413yes—
119C2×C4×C5⋊D5C22×C413yes—
120C2×C4×C5⋊D5C2×D4112yes—
121C2×C4×C5⋊D5C2×Q8112yes—
122C2×C4×C5⋊D5C2416yes—
123C2×C4×C5⋊D5C2413yes—
124C2×C4×C5⋊D5C2411yescharacteristic
125C2×C4×C5⋊D5C2412yes—
126C2×#6045C22×C413yes—
127C22⋊#1043—224no—
128C4⋊#1043—212no—
129C4⋊#1043—224no—
130C4⋊#1043—24no—
131C4⋊#1043—224no—
132C4⋊#1043—28no—
133C4⋊#1043—424no—
134C4×#1043—224no—
135C52×C4⋊C4C22×C416yes—
136C52×C22⋊C4C22×C416yes—
137C42×C52C22×C416yes—
138C42×C52C22×C411yescharacteristic
139C42×C52C22×C413yes—
140C22⋊#1039C22×C416yes—
141#87808C22×C4112yes—
142C4⋊#1039C22×C416yes—
143#87806C22×C4112yes—
144C4×#1039C22×C416yes—
145C4×#1039C22×C412yes—
146C4×#1039C22×C411yescharacteristic
147C4×#1039C22×C413yes—
148C4×#1039C22×C416yes—
149C4×#1039C22×C416yes—
150C4×#1039C22×C416yes—
151C2×D5×#41—56no—
152#66266—1096no—
153C2×Q8×AGL(1,𝔽5)—524no—
154C2×D4×AGL(1,𝔽5)—572no—
155C2×#4130—536no—
156C22×C4⋊AGL(1,𝔽5)—536no—
157C22×C4⋊AGL(1,𝔽5)—572no—
158C4×C5×#41AGL(1,𝔽5)16yescomplemented
159#41×Dic5—56no—
160C4×#713—512no—
161C4×Q8×D5—512no—
162C4×D4×D5—536no—
163C4×#711—536no—
164#65856—518no—
165D5×#117—518no—
166C4×#709—518no—
167C2×C42×D5—518no—
168#65765—572no—
169#65712—5144no—
170#65699—5144no—
171#65689—536no—
172#65688—536no—
173#65688—572no—
174#65688—518no—
175#65688—56no—
176C4×C4⋊AGL(1,𝔽5)—572no—
177#34183—251noSylow
178C23×C52C23×C413yes—
179C22×C5⋊D5—26no—
180C22×C5⋊D5—26no—
181C22×C5⋊D5C23×C413yes—
182C22×C5⋊D5C22×D416yes—
183C22×C5⋊D5C22×Q816yes—
184C22×C5⋊D5C2511yescharacteristic
185C2×#1043—24no—
186C2×#1043—212no—
187C2×#1043—224no—
188C2×#1043—28no—
189C2×#1043—824no—
190C52×Q8C2×C4⋊C414yescomplemented
191C52×D4C2×C4⋊C4112yescomplemented
192C2×C4×C52—212no—
193C2×C4×C52C2×C4⋊C4112yescomplemented
194C2×C4×C52C23×C416yes—
195C2×C4×C52C23×C411yescharacteristic
196C2×C4×C52C23×C413yes—
197C2×C4×C52C23×C412yes—
198C22⋊(C5⋊D5)C2×C4⋊C4124yescomplemented
199C2×#1039—212no—
200C2×#1039C2×C4⋊C4112yescomplemented
201C2×#1039C23×C416yes—
202C2×#1039C23×C413yes—
203C2×#1039C23×C411yescharacteristic
204C2×#1039C23×C412yes—
205C4⋊(C5⋊D5)C2×C4⋊C4112yescomplemented
206C4×C5⋊D5—26no—
207C4×C5⋊D5—26no—
208C4×C5⋊D5—212no—
209C4×C5⋊D5—212no—
210C4×C5⋊D5C2×C4⋊C4112yescomplemented
211C4×C5⋊D5C2×C4⋊C4112yescomplemented
212C4×C5⋊D5C22×D416yes—
213C4×C5⋊D5C22×D412yes—
214C4×C5⋊D5C22×Q812yes—
215C4×C5⋊D5C22×Q816yes—
216C4×C5⋊D5H(5,𝔽2)14yes—
217C4×C5⋊D52−1+414yes—
218#6045C2×C4⋊C4112yescomplemented
219C23×AGL(1,𝔽5)—572no—
220C2×C5×#41C2×AGL(1,𝔽5)16yes—
221D5×#41—548no—
222D5×#41—548no—
223C2×#713—56no—
224C2×Q8×D5—56no—
225C2×#711—518no—
226C2×D4×D5—518no—
227C2×#709—518no—
228C22×C4×D5—518no—
229C22×C4×D5—536no—
230C2×C22⋊AGL(1,𝔽5)—572no—
231Q8×AGL(1,𝔽5)—1096no—
232D4×AGL(1,𝔽5)—10288no—
233#4130—10144no—
234C2×C4⋊AGL(1,𝔽5)—524no—
235C2×C4⋊AGL(1,𝔽5)—572no—
236C2×C4⋊AGL(1,𝔽5)—536no—
237C2×C4⋊AGL(1,𝔽5)—572no—
238C2×C4⋊AGL(1,𝔽5)—512no—
239C2×C4⋊AGL(1,𝔽5)—5144no—
240C2×C4⋊AGL(1,𝔽5)—10144no—
241C2×C4⋊AGL(1,𝔽5)—20144no—
242C2×C4×AGL(1,𝔽5)—572no—
243C4×C5×Q8C2×AGL(1,𝔽5)112yescomplemented
244C4×C5×D4C2×AGL(1,𝔽5)136yescomplemented
245C5×#117C2×AGL(1,𝔽5)118yescomplemented
246C2×C42×C5C2×AGL(1,𝔽5)118yescomplemented
247Q8×Dic5—512no—
248D4×Dic5—536no—
249C4×C22⋊D5—572no—
250#4072—518no—
251C2×C4×Dic5—518no—
252C2×C4×Dic5—536no—
253#4039—536no—
254#4038—536no—
255D5×C4⋊C4—536no—
256#4033—536no—
257#4027—572no—
258D5×C22⋊C4—536no—
259#4023—536no—
260C4×D20—536no—
261#4018—536no—
262C42×D5—56no—
263C42×D5—518no—
264C42×D5—518no—
265C42×D5—518no—
266C42×D5—536no—
267C42×D5—536no—
268C4×Dic10—536no—
269(C2×AGL(1,𝔽5))⋊C4—5144no—
270C2×#520—252no—
271C2×C4×#41—251no—
272Q8×C4⋊C4—254no—
273D4×C4⋊C4—2512no—
274#2317—256no—
275#2285—253no—
276C2×#384—253no—
277C22×C52—26no—
278C22×C52C22×C4⋊C416yes—
279C22×C52C24×C411yescharacteristic
280C2×C5⋊D5—26no—
281C2×C5⋊D5—26no—
282C2×C5⋊D5—26no—
283C2×C5⋊D5—212no—
284C2×C5⋊D5C22×C4⋊C416yes—
285C2×C5⋊D5C23×D411yescharacteristic
286C2×C5⋊D5C23×Q811yescharacteristic
287C2×C5⋊D5C2×H(5,𝔽2)12yes—
288C2×C5⋊D5C2×2−1+412yes—
289#1043—412no—
290#1043—44no—
291C4×C52—26no—
292C4×C52C22×C4⋊C416yes—
293C4×C52C22×C4⋊C412yes—
294C4×C52#52014yescomplemented
295#1039—26no—
296#1039C22×C4⋊C416yes—
297#1039C22×C4⋊C412yes—
298#1039#52014yescomplemented
299C23×D5—518no—
300C22×AGL(1,𝔽5)—524no—
301C22×AGL(1,𝔽5)—572no—
302C22×AGL(1,𝔽5)—10144no—
303C22×AGL(1,𝔽5)—20144no—
304C5×#41C4⋊AGL(1,𝔽5)148yescomplemented
305C2×C5×Q8C22×AGL(1,𝔽5)16yes—
306C2×C5×D4C22×AGL(1,𝔽5)118yes—
307C22×C4×C5C22×AGL(1,𝔽5)136yes—
308C22×C4×C5C22×AGL(1,𝔽5)118yes—
309C2×C22⋊D5—536no—
310C22×Dic5—518no—
311C22×Dic5—536no—
312#713—548no—
313Q8×D5—524no—
314Q8×D5—524no—
315#711—5144no—
316D4×D5—572no—
317D4×D5—572no—
318#709—5144no—
319C2×D20—518no—
320C2×C4×D5—572no—
321C2×C4×D5—572no—
322C2×C4×D5—518no—
323C2×C4×D5—56no—
324C2×C4×D5—512no—
325C2×C4×D5—518no—
326C2×C4×D5—518no—
327C2×C4×D5—536no—
328C2×C4×D5—536no—
329C2×C4×D5—536no—
330C2×C4×D5—1072no—
331C2×C4×D5—1072no—
332C2×Dic10—518no—
333C22⋊AGL(1,𝔽5)—10144no—
334C4⋊AGL(1,𝔽5)—1072no—
335C4⋊AGL(1,𝔽5)—10144no—
336C4⋊AGL(1,𝔽5)—10144no—
337C4⋊AGL(1,𝔽5)—1024no—
338C4⋊AGL(1,𝔽5)—1048no—
339C4⋊AGL(1,𝔽5)—20144no—
340C4×AGL(1,𝔽5)—10144no—
341C5×C4⋊C4C22×AGL(1,𝔽5)136yes—
342C5×C22⋊C4C22×AGL(1,𝔽5)136yes—
343C42×C5C22×AGL(1,𝔽5)16yes—
344C42×C5C22×AGL(1,𝔽5)118yes—
345C42×C5C22×AGL(1,𝔽5)136yes—
346C22⋊Dic5—536no—
347#685—572no—
348C4⋊Dic5—536no—
349#683—572no—
350C4×Dic5—536no—
351C4×Dic5—56no—
352C4×Dic5—512no—
353C4×Dic5—518no—
354C4×Dic5—536no—
355C4×Dic5—536no—
356C4×Dic5—536no—
357C22×#41—251no—
358#520—5016no—
359C4×#41—251no—
360C4×#41—252no—
361C4×#41—256no—
362C4×#41—253no—
363C4×#41—253no—
364C4×#41#104311yescharacteristic, complemented
365C2×C4×Q8—252no—
366C2×C4×Q8—254no—
367C2×C4×D4—256no—
368C2×C4×D4—2512no—
369C2×#117—253no—
370C2×#117—256no—
371C22×C4⋊C4—256no—
372C22×C4⋊C4—2512no—
373C22×C42—253no—
374#389—2524no—
375#385—2524no—
376#384—256no—
377#384—2512no—
378#384—253no—
379#384—251no—
380#382—256no—
381#380—2512no—
382C4×C4⋊C4—2512no—
383C2×C52—26no—
384C2×C52C23×C4⋊C411yescharacteristic
385C2×C52C2×#52012yes—
386C5⋊D5—26no—
387C5⋊D5#349811yescharacteristic
388C5⋊D5#349911yescharacteristic
389C5⋊D5#350312yes—
390C23×C5C23×AGL(1,𝔽5)118yes—
391C22×D5—56no—
392C22×D5—536no—
393C22×D5—536no—
394C22×D5—518no—
395C22×D5—1036no—
396C22×D5—1036no—
397C2×AGL(1,𝔽5)—1024no—
398C2×AGL(1,𝔽5)—1072no—
399C2×AGL(1,𝔽5)—10144no—
400C2×AGL(1,𝔽5)—1048no—
401C2×AGL(1,𝔽5)—40144no—
402C5×Q8C2×C4⋊AGL(1,𝔽5)124yescomplemented
403C5×D4C2×C4⋊AGL(1,𝔽5)172yescomplemented
404C2×C4×C5—272no—
405C2×C4×C5C2×C4⋊AGL(1,𝔽5)172yescomplemented
406C2×C4×C5C23×AGL(1,𝔽5)136yes—
407C2×C4×C5C23×AGL(1,𝔽5)16yes—
408C2×C4×C5C23×AGL(1,𝔽5)118yes—
409C2×C4×C5C23×AGL(1,𝔽5)112yes—
410C22⋊D5—5144no—
411C2×Dic5—572no—
412C2×Dic5—56no—
413C2×Dic5—512no—
414C2×Dic5—518no—
415C2×Dic5—536no—
416C2×Dic5—1072no—
417D20—572no—
418C4×D5—572no—
419C4×D5—572no—
420C4×D5—536no—
421C4×D5—512no—
422C4×D5—512no—
423C4×D5—536no—
424C4×D5—524no—
425C4×D5—524no—
426C4×D5—1072no—
427C4×D5—1036no—
428C4×D5—1036no—
429C4×D5—1072no—
430Dic10—572no—
431C2×#41—258no—
432C2×#41—258no—
433C2×#41—251no—
434C2×#41—253no—
435C2×#41—253no—
436C2×#41C2×#104311yescharacteristic
437C22×Q8—251no—
438C22×D4—253no—
439C23×C4—253no—
440C23×C4—256no—
441C23×C4—2512no—
442C4×Q8—252no—
443C4×Q8—256no—
444C4×Q8—256no—
445C4×Q8—5016no—
446C4×Q8C2×#104312yescomplemented
447C4×D4—256no—
448C4×D4—2512no—
449C4×D4—256no—
450C4×D4—2512no—
451C4×D4—256no—
452C4×D4—5048no—
453C4×D4C2×#104316yescomplemented
454#117—253no—
455#117—256no—
456#117—256no—
457#117—256no—
458#117—5024no—
459#117C2×#104313yescomplemented
460C2×C4⋊C4—256no—
461C2×C4⋊C4—256no—
462C2×C4⋊C4—2512no—
463C2×C4⋊C4—2512no—
464C2×C4⋊C4—252no—
465C2×C4⋊C4—254no—
466C2×C4⋊C4—2524no—
467C2×C4⋊C4—5024no—
468C2×C4⋊C4—10024no—
469C2×C22⋊C4—256no—
470C2×C22⋊C4—2512no—
471C2×C42—256no—
472C2×C42—253no—
473C2×C42—253no—
474C2×C42—256no—
475C2×C42—256no—
476C2×C42—253no—
477C2×C42—253no—
478C2×C42—251no—
479C2×C42—2512no—
480C2×C42C2×#104313yescomplemented
481#95—2524no—
482C52#3418311yescharacteristic, complemented, Sylow
483C22×C5—236no—
484C22×C5C22×C4⋊AGL(1,𝔽5)136yes—
485C22×C5C24×AGL(1,𝔽5)16yes—
486C2×D5—56no—
487C2×D5—56no—
488C2×D5—512no—
489C2×D5—512no—
490C2×D5—536no—
491C2×D5—1036no—
492C2×D5—1036no—
493C2×D5—1072no—
494C2×D5—1036no—
495AGL(1,𝔽5)—2024no—
496AGL(1,𝔽5)—2072no—
497C4×C5—236no—
498C4×C5C22×C4⋊AGL(1,𝔽5)136yes—
499C4×C5C22×C4⋊AGL(1,𝔽5)112yes—
500C4×C5#66266124yescomplemented
501Dic5—536no—
502Dic5—512no—
503Dic5—524no—
504Dic5—1036no—
505C24—253no—
506#41—258no—
507#41—2524no—
508#41—2524no—
509#41C4⋊#104318yescomplemented
510C2×Q8—254no—
511C2×Q8—254no—
512C2×Q8—253no—
513C2×Q8C22×#104311yescharacteristic
514C2×D4—256no—
515C2×D4—2512no—
516C2×D4—2512no—
517C2×D4—253no—
518C2×D4C22×#104313yes—
519C22×C4—253no—
520C22×C4—2512no—
521C22×C4—2512no—
522C22×C4—253no—
523C22×C4—251no—
524C22×C4—252no—
525C22×C4—253no—
526C22×C4—253no—
527C22×C4—256no—
528C22×C4—256no—
529C22×C4—256no—
530C22×C4—256no—
531C22×C4—254no—
532C22×C4—2512no—
533C22×C4—5012no—
534C22×C4—5012no—
535C22×C4—5024no—
536C22×C4—10024no—
537C22×C4C22×#104316yes—
538C22×C4C22×#104313yes—
539C4⋊C4—2512no—
540C4⋊C4—256no—
541C4⋊C4—5012no—
542C4⋊C4—5024no—
543C4⋊C4—5024no—
544C4⋊C4—504no—
545C4⋊C4—508no—
546C4⋊C4—10024no—
547C4⋊C4C22×#104316yes—
548C22⋊C4—256no—
549C22⋊C4—2512no—
550C22⋊C4—5024no—
551C22⋊C4C22×#104316yes—
552C42—251no—
553C42—252no—
554C42—256no—
555C42—253no—
556C42—256no—
557C42—256no—
558C42—256no—
559C42—5024no—
560C42C22×#104311yescharacteristic
561C42C22×#104313yes—
562C42C22×#104316yes—
563C2×C5—236no—
564C2×C5C23×C4⋊AGL(1,𝔽5)16yes—
565C2×C5C2×#66266112yes—
566D5—56no—
567D5—56no—
568D5—512no—
569D5—1036no—
570C23—251no—
571C23—256no—
572C23—256no—
573C23—253no—
574C23—506no—
575C23—506no—
576C23C23×#104313yes—
577Q8—2512no—
578Q8C2×C4⋊#104314yescomplemented
579D4—2524no—
580D4—2512no—
581D4C2×C4⋊#1043112yescomplemented
582C2×C4—212no—
583C2×C4—2512no—
584C2×C4—251no—
585C2×C4—252no—
586C2×C4—253no—
587C2×C4—256no—
588C2×C4—252no—
589C2×C4—252no—
590C2×C4—256no—
591C2×C4—2512no—
592C2×C4—2512no—
593C2×C4—254no—
594C2×C4—254no—
595C2×C4—256no—
596C2×C4—5012no—
597C2×C4—506no—
598C2×C4—506no—
599C2×C4—5012no—
600C2×C4—5012no—
601C2×C4—504no—
602C2×C4—5012no—
603C2×C4—5024no—
604C2×C4—508no—
605C2×C4—20024no—
606C2×C4C2×C4⋊#1043112yescomplemented
607C2×C4C23×#104316yes—
608C2×C4C23×#104311yescharacteristic
609C2×C4C23×#104313yes—
610C2×C4C23×#104312yes—
611C5#1304402616yescomplemented
612C22—26no—
613C22—251no—
614C22—251no—
615C22—252no—
616C22—252no—
617C22—256no—
618C22—506no—
619C22—506no—
620C22—5012no—
621C22—506no—
622C22C22×C4⋊#104316yes—
623C22C24×#104311yescharacteristic
624C4—26no—
625C4—252no—
626C4—256no—
627C4—254no—
628C4—506no—
629C4—10012no—
630C4—1004no—
631C4C22×C4⋊#104312yes—
632C4C22×C4⋊#104316yes—
633C4#1310775414yescomplemented
634C2—26no—
635C2—251no—
636C2—251no—
637C2—252no—
638C2—506no—
639C2C23×C4⋊#104311yescharacteristic
640C2C2×#1310775412yes—
subgroupG/H
center, FrattiniC22C24×#1043
commutator, socleC22×C52C24×C4
FittingC4×C52×#41C4
prime radicalC2×#41×C5⋊D5C22
cosocleC22×C5⋊D5C25
hypercenterC4×#41#1043
hypocenterC52#34183
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. Q8×C4⋊#1043C2semidirect
2. D4×C4⋊#1043C2semidirect
4. #72221041C2semidirect
6. #72220986C2semidirect
7. C2×#13104700C2semidirect
15. C4×C52×#41C4semidirect
16. #41×#1039C4semidirect
17. C4×#87904C4semidirect
19. C4×#87902C4semidirect
21. #13107053C4semidirect
23. C4×#87900C4semidirect
59. C4×C52×Q8C2×C4semidirect
60. C4×C52×D4C2×C4semidirect
61. C52×#117C2×C4semidirect
62. C2×C42×C52C2×C4semidirect
63. Q8×#1039C2×C4semidirect
64. D4×#1039C2×C4semidirect
65. C4×C22⋊(C5⋊D5)C2×C4semidirect
66. #11717246C2×C4semidirect
67. C2×C4×#1039C2×C4semidirect
68. C2×C4×#1039C2×C4semidirect
69. #11717213C2×C4semidirect
70. #11717212C2×C4semidirect
72. #11717207C2×C4semidirect
73. #11717201C2×C4semidirect
75. #11717197C2×C4semidirect
76. C4×C4⋊(C5⋊D5)C2×C4semidirect
77. #11717192C2×C4semidirect
78. C42×C5⋊D5C2×C4semidirect
79. C42×C5⋊D5C2×C4semidirect
80. C42×C5⋊D5C2×C4semidirect
84. C4×#6045C2×C4semidirect
98. C52×#41C4⋊C4semidirect
106. #87904C4⋊C4semidirect
109. #87902C4⋊C4semidirect
112. #87900C4⋊C4semidirect
158. C4×C5×#41AGL(1,𝔽5)semidirect
190. C52×Q8C2×C4⋊C4semidirect
191. C52×D4C2×C4⋊C4semidirect
193. C2×C4×C52C2×C4⋊C4semidirect
198. C22⋊(C5⋊D5)C2×C4⋊C4semidirect
200. C2×#1039C2×C4⋊C4semidirect
205. C4⋊(C5⋊D5)C2×C4⋊C4semidirect
210. C4×C5⋊D5C2×C4⋊C4semidirect
211. C4×C5⋊D5C2×C4⋊C4semidirect
218. #6045C2×C4⋊C4semidirect
243. C4×C5×Q8C2×AGL(1,𝔽5)semidirect
244. C4×C5×D4C2×AGL(1,𝔽5)semidirect
245. C5×#117C2×AGL(1,𝔽5)semidirect
246. C2×C42×C5C2×AGL(1,𝔽5)semidirect
294. C4×C52#520semidirect
298. #1039#520semidirect
304. C5×#41C4⋊AGL(1,𝔽5)semidirect
364. C4×#41#1043semidirect
402. C5×Q8C2×C4⋊AGL(1,𝔽5)semidirect
403. C5×D4C2×C4⋊AGL(1,𝔽5)semidirect
405. C2×C4×C5C2×C4⋊AGL(1,𝔽5)semidirect
446. C4×Q8C2×#1043semidirect
453. C4×D4C2×#1043semidirect
459. #117C2×#1043semidirect
480. C2×C42C2×#1043semidirect
482. C52#34183semidirect
500. C4×C5#66266semidirect
509. #41C4⋊#1043semidirect
578. Q8C2×C4⋊#1043semidirect
581. D4C2×C4⋊#1043semidirect
606. C2×C4C2×C4⋊#1043semidirect
611. C5#13044026semidirect
633. C4#13107754semidirect

Maximal subgroups

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

subgroupindex
Q8×C4⋊#10432
D4×C4⋊#10432
C4×#41×C5⋊D52
#722210412
C2×#131077542
#722209862
C2×#131047002
#130440265