Finite Group Databasebeta

← #13044138

Subgroups — #13044138

Order 1280.

3200 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66266C211yesmaximal, characteristic, complemented
2C2×#41×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3D5×#550C211yesmaximal, characteristic
4#10617558C211yesmaximal, characteristic, complemented
5#10617558C211yesmaximal, characteristic, complemented
6#10617369C213yesmaximal, complemented
7#10617368C213yesmaximal, complemented
8#10617254C213yesmaximal, complemented
9#10617253C213yesmaximal, complemented
10#10617250C213yesmaximal, complemented
11AGL(1,𝔽5)×#121C213yesmaximal, complemented
12#10617212C211yesmaximal, characteristic, complemented
13#10617208C211yesmaximal, characteristic, complemented
14#10617179C213yesmaximal, complemented
15#10617173C213yesmaximal, complemented
16C2×D5×#41C2211yescharacteristic
17C2×D5×#41C2211yescharacteristic
18#66266—28no—
19#41×AGL(1,𝔽5)—28no—
20C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
21C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
22C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
23C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
24C2×D4×AGL(1,𝔽5)C2213yes—
25C2×D4×AGL(1,𝔽5)C2213yes—
26C2×D4×AGL(1,𝔽5)C2213yes—
27C2×D4×AGL(1,𝔽5)C2213yes—
28C2×D4×AGL(1,𝔽5)C2216yes—
29C2×#4130C2213yes—
30C2×#4130C2213yes—
31C22×C4⋊AGL(1,𝔽5)C2213yes—
32C22×C4×AGL(1,𝔽5)C2213yes—
33C5×#550C411yescharacteristic, complemented
34#66168C411yescharacteristic, complemented
35#66168C411yescharacteristic, complemented
36#66052C413yescomplemented
37D5×#127C2213yes—
38D5×#121C2213yes—
39D5×#121C2213yes—
40#65933C413yescomplemented
41#65933C413yescomplemented
42#65911C411yescharacteristic, complemented
43C4×Q8×D5C2211yescharacteristic
44#65887C413yescomplemented
45C4×D4×D5C2213yes—
46#65780C2213yes—
47#65780C2213yes—
48#65780C2213yes—
49#65780C2216yes—
50#65780C2213yes—
51#65779C2213yes—
52#65779C2216yes—
53#65779C2216yes—
54#65779C2216yes—
55#65779C2213yes—
56#65765C2213yes—
57#65765C2213yes—
58C4×C22⋊AGL(1,𝔽5)C2213yes—
59C4×C22⋊AGL(1,𝔽5)C2213yes—
60#65712C2213yes—
61#65712C2213yes—
62#65711C2211yescharacteristic
63#65711C2213yes—
64C4⋊C4×AGL(1,𝔽5)C2213yes—
65C4⋊C4×AGL(1,𝔽5)C2213yes—
66#65700C2213yes—
67#65700C2213yes—
68#65700C2216yes—
69#65699C2213yes—
70#65699C2213yes—
71C22⋊C4×AGL(1,𝔽5)C2216yes—
72#65689C2213yes—
73C4×C4⋊AGL(1,𝔽5)C2213yes—
74C4×C4⋊AGL(1,𝔽5)C2213yes—
75#65686C2213yes—
76#34295—51nomaximal, Sylow
77C23×AGL(1,𝔽5)C2313yes—
78C23×AGL(1,𝔽5)C2316yes—
79C23×AGL(1,𝔽5)C2313yes—
80C2×C5×#41C2×C411yescharacteristic, complemented
81C2×C5×#41C2×C411yescharacteristic, complemented
82D5×#41—24no—
83D5×#41—24no—
84D5×#41—24no—
85D5×#41—24no—
86C2×#713C2×C411yescharacteristic, complemented
87C2×#713C2×C411yescharacteristic, complemented
88C2×Q8×D5C2311yescharacteristic
89C2×#711C2×C413yescomplemented
90C2×#711C2×C413yescomplemented
91C2×D4×D5C2313yes—
92C2×D4×D5C2313yes—
93C2×D4×D5C2313yes—
94C2×D4×D5C2316yes—
95C2×#709C2×C413yescomplemented
96C2×#709C2×C413yescomplemented
97C22×C4×D5C2313yes—
98C22×C4×D5C2313yes—
99C2×C22⋊AGL(1,𝔽5)C2313yes—
100C2×C22⋊AGL(1,𝔽5)C2316yes—
101C2×C22⋊AGL(1,𝔽5)C2313yes—
102C2×C22⋊AGL(1,𝔽5)C2313yes—
103C2×C22⋊AGL(1,𝔽5)C2316yes—
104C2×C22⋊AGL(1,𝔽5)C2313yes—
105C2×C22⋊AGL(1,𝔽5)C2313yes—
106C2×C22⋊AGL(1,𝔽5)C2316yes—
107C2×C22⋊AGL(1,𝔽5)C2313yes—
108Q8×AGL(1,𝔽5)—24no—
109Q8×AGL(1,𝔽5)—24no—
110Q8×AGL(1,𝔽5)—24no—
111Q8×AGL(1,𝔽5)D418yescomplemented
112D4×AGL(1,𝔽5)—212no—
113D4×AGL(1,𝔽5)—212no—
114D4×AGL(1,𝔽5)—212no—
115D4×AGL(1,𝔽5)—212no—
116D4×AGL(1,𝔽5)—412no—
117#4130—212no—
118#4130—212no—
119C2×C4⋊AGL(1,𝔽5)—212no—
120C2×C4⋊AGL(1,𝔽5)C2313yes—
121C2×C4⋊AGL(1,𝔽5)C2313yes—
122C2×C4⋊AGL(1,𝔽5)C2313yes—
123C2×C4⋊AGL(1,𝔽5)C2313yes—
124C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
125C2×C4⋊AGL(1,𝔽5)C2313yes—
126C2×C4⋊AGL(1,𝔽5)C2313yes—
127C2×C4⋊AGL(1,𝔽5)C2313yes—
128C2×C4×AGL(1,𝔽5)—212no—
129C2×C4×AGL(1,𝔽5)C2313yes—
130C2×C4×AGL(1,𝔽5)C2313yes—
131C2×C4×AGL(1,𝔽5)C2313yes—
132C2×C4×AGL(1,𝔽5)C2313yes—
133C2×C4×AGL(1,𝔽5)C2311yescharacteristic
134C2×C4×AGL(1,𝔽5)C2316yes—
135C2×C4×AGL(1,𝔽5)C2313yes—
136C5×#127C2×C413yescomplemented
137C5×#121C2×C413yescomplemented
138C5×#121C2×C413yescomplemented
139C4×C5×Q8C2×C411yescharacteristic, complemented
140C4×C5×D4C2×C413yescomplemented
141Q8×Dic5C2×C411yescharacteristic, complemented
142#4086C2×C416yescomplemented
143#4086C2×C413yescomplemented
144#4086C2×C413yescomplemented
145#4086C2×C416yescomplemented
146#4085C2×C416yescomplemented
147#4085C2×C416yescomplemented
148#4084C2×C413yescomplemented
149#4084C2×C413yescomplemented
150D4×Dic5C2×C413yescomplemented
151#4076C2×C413yescomplemented
152#4076C2×C413yescomplemented
153C4×C22⋊D5C2×C413yescomplemented
154C4×C22⋊D5C2×C413yescomplemented
155#4041C2×C413yescomplemented
156#4041C2×C413yescomplemented
157#4039C2×C413yescomplemented
158D5×C4⋊C4C2311yescharacteristic
159D5×C4⋊C4C2313yes—
160#4033C2×C413yescomplemented
161#4030C2×C416yescomplemented
162#4030C2×C416yescomplemented
163#4027C2×C413yescomplemented
164#4027C2×C413yescomplemented
165D5×C22⋊C4C2313yes—
166D5×C22⋊C4C2313yes—
167#4020C2×C413yescomplemented
168C4×D20C2×C413yescomplemented
169C42×D5C2313yes—
170C4×Dic10C2×C413yescomplemented
171(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
172(C2×AGL(1,𝔽5))⋊C4C2313yes—
173(C2×AGL(1,𝔽5))⋊C4C2313yes—
174(C2×AGL(1,𝔽5))⋊C4C2313yes—
175(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
176(C2×AGL(1,𝔽5))⋊C4C2313yes—
177(C2×AGL(1,𝔽5))⋊C4C2316yes—
178(C2×AGL(1,𝔽5))⋊C4C2313yes—
179(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
180(C2×AGL(1,𝔽5))⋊C4C2313yes—
181(C2×AGL(1,𝔽5))⋊C4C2311yescharacteristic
182C2×#550—51no—
183C2×#520—51no—
184C2×C4×#41—51no—
185#2366—53no—
186#2363—53no—
187#2361—53no—
188#2352—53no—
189#2351—51no—
190#2341—51no—
191#2341—51no—
192#2328—53no—
193#2324—53no—
194C4×#121—53no—
195#2290—53no—
196#2276—51no—
197C23×D5C2413yes—
198C23×D5C2413yes—
199C22×AGL(1,𝔽5)—26no—
200C22×AGL(1,𝔽5)—26no—
201C22×AGL(1,𝔽5)—26no—
202C22×AGL(1,𝔽5)—212no—
203C22×AGL(1,𝔽5)—43no—
204C22×AGL(1,𝔽5)—43no—
205C22×AGL(1,𝔽5)—43no—
206C22×AGL(1,𝔽5)—46no—
207C22×AGL(1,𝔽5)—46no—
208C22×AGL(1,𝔽5)C2411yescharacteristic
209C22×AGL(1,𝔽5)C2413yes—
210C22×AGL(1,𝔽5)C2411yescharacteristic
211C22×AGL(1,𝔽5)C2413yes—
212C22×AGL(1,𝔽5)C2413yes—
213C22×AGL(1,𝔽5)C2413yes—
214C22×AGL(1,𝔽5)C2411yescharacteristic
215C22×AGL(1,𝔽5)C2411yescharacteristic
216C5×#41—24no—
217C5×#41—24no—
218C2×C5×Q8C22×C411yescharacteristic
219C2×C5×D4C22×C413yes—
220C2×C5×D4C22×C413yes—
221C2×C5×D4C22×C413yes—
222C2×C5×D4C22×C416yes—
223C22×C4×C5C22×C413yes—
224C22×C4×C5C22×C413yes—
225C2×C22⋊D5C22×C416yes—
226C2×C22⋊D5C22×C416yes—
227C2×C22⋊D5C22×C413yes—
228C2×C22⋊D5C22×C413yes—
229C2×C22⋊D5C22×C416yes—
230C2×C22⋊D5C22×C416yes—
231C22×Dic5C22×C413yes—
232C22×Dic5C22×C413yes—
233#713—24no—
234#713—24no—
235Q8×D5C2×D414yes—
236Q8×D5#4114yes—
237#711—212no—
238#711—212no—
239D4×D5—26no—
240D4×D5—26no—
241D4×D5—26no—
242D4×D5—26no—
243D4×D5—46no—
244D4×D5—46no—
245D4×D5—43no—
246D4×D5—43no—
247#709—212no—
248#709—212no—
249C2×D20C22×C413yes—
250C2×D20C22×C413yes—
251C2×D20C22×C413yes—
252C2×D20C22×C416yes—
253C2×C4×D5—26no—
254C2×C4×D5—26no—
255C2×C4×D5—26no—
256C2×C4×D5—26no—
257C2×C4×D5C22×C413yes—
258C2×C4×D5C22×C413yes—
259C2×C4×D5C22×C413yes—
260C2×C4×D5C22×C413yes—
261C2×C4×D5C2411yescharacteristic
262C2×C4×D5C2413yes—
263C2×C4×D5C2411yescharacteristic
264C2×C4×D5C2411yescharacteristic
265C2×C4×D5C2413yes—
266C2×Dic10C22×C413yes—
267C22⋊AGL(1,𝔽5)—26no—
268C22⋊AGL(1,𝔽5)—212no—
269C22⋊AGL(1,𝔽5)—26no—
270C22⋊AGL(1,𝔽5)—26no—
271C22⋊AGL(1,𝔽5)—46no—
272C22⋊AGL(1,𝔽5)—43no—
273C22⋊AGL(1,𝔽5)—43no—
274C22⋊AGL(1,𝔽5)—46no—
275C22⋊AGL(1,𝔽5)—43no—
276C4⋊AGL(1,𝔽5)—26no—
277C4⋊AGL(1,𝔽5)—22no—
278C4⋊AGL(1,𝔽5)—26no—
279C4⋊AGL(1,𝔽5)—26no—
280C4⋊AGL(1,𝔽5)—26no—
281C4⋊AGL(1,𝔽5)—26no—
282C4⋊AGL(1,𝔽5)—43no—
283C4⋊AGL(1,𝔽5)C2×D4112yes—
284C4×AGL(1,𝔽5)—22no—
285C4×AGL(1,𝔽5)—26no—
286C4×AGL(1,𝔽5)—26no—
287C4×AGL(1,𝔽5)—26no—
288C4×AGL(1,𝔽5)—26no—
289C4×AGL(1,𝔽5)—46no—
290C4×AGL(1,𝔽5)C2×D4112yes—
291C5×C4⋊C4C22×C411yescharacteristic
292C5×C4⋊C4C22×C413yes—
293C5×C22⋊C4C22×C413yes—
294C5×C22⋊C4C22×C413yes—
295C42×C5C22×C413yes—
296C22⋊Dic5C22×C413yes—
297C22⋊Dic5C22×C413yes—
298#685C22×C413yes—
299#685C22×C413yes—
300#685C22×C413yes—
301#685C22×C413yes—
302C4⋊Dic5C22×C413yes—
303C4⋊Dic5C22×C411yescharacteristic
304#683C22×C416yes—
305#683C22×C411yescharacteristic
306#683C22×C411yescharacteristic
307C4×Dic5C22×C413yes—
308C4×Dic5C22×C413yes—
309C4×Dic5C22×C413yes—
310C22×#41—51no—
311C22×#41—51no—
312#550—51no—
313#550—51no—
314#550—53no—
315#550—53no—
316#550—53no—
317#550—51no—
318#550—53no—
319#550AGL(1,𝔽5)11yescharacteristic, complemented
320C2×#127—53no—
321C2×#121—53no—
322C2×#121—53no—
323#520—108no—
324C4×#41—108no—
325C2×C4×Q8—51no—
326C2×C4×Q8—51no—
327C2×C4×Q8—51no—
328C2×C4×Q8—51no—
329C2×C4×Q8—51no—
330C2×C4×D4—53no—
331C2×C4×D4—53no—
332C2×C4×D4—53no—
333C2×C4×D4—53no—
334C2×C4×D4—53no—
335C2×C4×D4—56no—
336C2×#117—53no—
337C2×#117—53no—
338C22×C4⋊C4—53no—
339C22×C42—53no—
340#390—53no—
341#390—56no—
342#390—53no—
343#390—53no—
344#390—53no—
345#389—53no—
346#389—53no—
347#388—56no—
348#388—53no—
349#388—53no—
350#387—53no—
351#387—51no—
352#386—56no—
353#386—53no—
354#386—56no—
355#386—56no—
356#386—53no—
357#385—53no—
358#385—53no—
359#382—53no—
360#380—53no—
361#380—53no—
362C4×C4⋊C4—53no—
363C4×C4⋊C4—53no—
364C4×C4⋊C4—53no—
365C4×C4⋊C4—53no—
366C4×C22⋊C4—53no—
367C4×C22⋊C4—53no—
368C4×C22⋊C4—56no—
369#376—53no—
370C23×C5C23×C413yes—
371C23×C5C23×C413yes—
372C22×D5—23no—
373C22×D5—23no—
374C22×D5—23no—
375C22×D5—23no—
376C22×D5—23no—
377C22×D5—23no—
378C22×D5—23no—
379C22×D5—23no—
380C22×D5—23no—
381C22×D5—23no—
382C22×D5—23no—
383C22×D5—23no—
384C22×D5C23×C413yes—
385C22×D5C23×C413yes—
386C22×D5C2511yescharacteristic
387C2×AGL(1,𝔽5)—21no—
388C2×AGL(1,𝔽5)—23no—
389C2×AGL(1,𝔽5)—21no—
390C2×AGL(1,𝔽5)—21no—
391C2×AGL(1,𝔽5)—21no—
392C2×AGL(1,𝔽5)—23no—
393C2×AGL(1,𝔽5)—21no—
394C2×AGL(1,𝔽5)—23no—
395C2×AGL(1,𝔽5)—23no—
396C2×AGL(1,𝔽5)—21no—
397C2×AGL(1,𝔽5)—23no—
398C2×AGL(1,𝔽5)—23no—
399C2×AGL(1,𝔽5)—23no—
400C2×AGL(1,𝔽5)—21no—
401C2×AGL(1,𝔽5)—23no—
402C2×AGL(1,𝔽5)—21no—
403C2×AGL(1,𝔽5)—23no—
404C2×AGL(1,𝔽5)—21no—
405C2×AGL(1,𝔽5)—21no—
406C2×AGL(1,𝔽5)—23no—
407C2×AGL(1,𝔽5)—23no—
408C2×AGL(1,𝔽5)—412no—
409C2×AGL(1,𝔽5)—412no—
410C2×AGL(1,𝔽5)—812no—
411C2×AGL(1,𝔽5)C22×D412yes—
412C2×AGL(1,𝔽5)C22×D416yes—
413C2×AGL(1,𝔽5)H(5,𝔽2)12yes—
414C5×Q8C4×D414yescomplemented
415C5×D4—26no—
416C5×D4—26no—
417C5×D4—43no—
418C5×D4—46no—
419C2×C4×C5—26no—
420C2×C4×C5—26no—
421C2×C4×C5C23×C411yescharacteristic
422C2×C4×C5C23×C413yes—
423C2×C4×C5C23×C411yescharacteristic
424C2×C4×C5C23×C411yescharacteristic
425C2×C4×C5C23×C413yes—
426C22⋊D5—212no—
427C22⋊D5—212no—
428C22⋊D5—43no—
429C22⋊D5—43no—
430C22⋊D5—46no—
431C22⋊D5—46no—
432C2×Dic5—26no—
433C2×Dic5—26no—
434C2×Dic5C23×C411yescharacteristic
435C2×Dic5C23×C413yes—
436C2×Dic5C23×C411yescharacteristic
437C2×Dic5C23×C411yescharacteristic
438C2×Dic5C23×C413yes—
439D20—26no—
440D20—26no—
441D20—43no—
442D20—46no—
443C4×D5—21no—
444C4×D5—21no—
445C4×D5—21no—
446C4×D5—21no—
447C4×D5—23no—
448C4×D5—23no—
449C4×D5—21no—
450C4×D5—21no—
451C4×D5—26no—
452C4×D5—26no—
453C4×D5—26no—
454C4×D5—26no—
455C4×D5C22×D416yes—
456C4×D5C2×#4116yes—
457Dic10C4×D4112yescomplemented
458C2×#41—51no—
459C2×#41—51no—
460C2×#41—53no—
461C2×#41—53no—
462C2×#41—53no—
463C2×#41—53no—
464C2×#41—104no—
465C2×#41—104no—
466C2×#41—104no—
467C2×#41—104no—
468C2×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
469C2×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
470C22×Q8—51no—
471C22×D4—53no—
472C22×D4—53no—
473C22×D4—56no—
474C22×D4—53no—
475C23×C4—53no—
476C23×C4—53no—
477C23×C4—53no—
478C23×C4—56no—
479C23×C4—53no—
480#127—56no—
481#127—56no—
482#127—53no—
483#127—53no—
484#127—53no—
485#127C2×AGL(1,𝔽5)13yescomplemented
486#121—53no—
487#121—53no—
488#121—56no—
489#121—56no—
490#121—53no—
491#121—53no—
492#121—53no—
493#121—53no—
494#121—56no—
495#121—56no—
496#121C2×AGL(1,𝔽5)13yescomplemented
497#121C2×AGL(1,𝔽5)13yescomplemented
498C4×Q8—58no—
499C4×Q8—51no—
500C4×Q8—53no—
501C4×Q8—53no—
502C4×Q8—104no—
503C4×Q8—104no—
504C4×Q8—104no—
505C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
506C4×D4—53no—
507C4×D4—53no—
508C4×D4—53no—
509C4×D4—53no—
510C4×D4—53no—
511C4×D4—53no—
512C4×D4—53no—
513C4×D4—1012no—
514C4×D4—1012no—
515C4×D4—1012no—
516C4×D4—1012no—
517C4×D4—2012no—
518C4×D4C2×AGL(1,𝔽5)13yescomplemented
519#117—1012no—
520#117—1012no—
521C2×C4⋊C4—53no—
522C2×C4⋊C4—51no—
523C2×C4⋊C4—53no—
524C2×C4⋊C4—53no—
525C2×C4⋊C4—53no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—53no—
528C2×C4⋊C4—53no—
529C2×C4⋊C4—53no—
530C2×C4⋊C4—53no—
531C2×C4⋊C4—1012no—
532C2×C22⋊C4—53no—
533C2×C22⋊C4—53no—
534C2×C22⋊C4—53no—
535C2×C22⋊C4—56no—
536C2×C22⋊C4—53no—
537C2×C22⋊C4—53no—
538C2×C22⋊C4—56no—
539C2×C22⋊C4—56no—
540C2×C22⋊C4—53no—
541C2×C22⋊C4—53no—
542C2×C22⋊C4—53no—
543C2×C42—53no—
544C2×C42—53no—
545C2×C42—53no—
546C2×C42—53no—
547C2×C42—53no—
548C2×C42—53no—
549C2×C42—51no—
550C2×C42—56no—
551C2×C42—1012no—
552#95—51no—
553#95—53no—
554#95—53no—
555#95—53no—
556#95—53no—
557#95—51no—
558#95—51no—
559#95—53no—
560#95—56no—
561#95—51no—
562#95—53no—
563C22×C5—23no—
564C22×C5—23no—
565C22×C5—23no—
566C22×C5—23no—
567C22×C5—23no—
568C22×C5—23no—
569C22×C5C24×C411yescharacteristic
570C2×D5—23no—
571C2×D5—23no—
572C2×D5—23no—
573C2×D5—23no—
574C2×D5—23no—
575C2×D5—23no—
576C2×D5—43no—
577C2×D5—43no—
578C2×D5—43no—
579C2×D5—43no—
580C2×D5—43no—
581C2×D5—43no—
582C2×D5—43no—
583C2×D5—43no—
584C2×D5C23×D411yescharacteristic
585C2×D5C22×#4111yescharacteristic
586C2×D5C2×H(5,𝔽2)11yescharacteristic
587C2×D5#58511yescharacteristic
588C2×D5#58511yescharacteristic
589C2×D5#58511yescharacteristic
590AGL(1,𝔽5)—22no—
591AGL(1,𝔽5)—22no—
592AGL(1,𝔽5)—26no—
593AGL(1,𝔽5)—41no—
594AGL(1,𝔽5)—43no—
595AGL(1,𝔽5)—43no—
596AGL(1,𝔽5)—43no—
597AGL(1,𝔽5)—41no—
598C4×C5—21no—
599C4×C5—21no—
600C4×C5—21no—
601C4×C5—23no—
602C4×C5C2×C4×D416yes—
603Dic5—21no—
604Dic5—21no—
605Dic5—21no—
606Dic5—23no—
607Dic5C2×C4×D416yes—
608C24—53no—
609C24—53no—
610#41—24no—
611#41—24no—
612#41—1012no—
613#41—1012no—
614#41—1012no—
615#41—1012no—
616#41—104no—
617#41—104no—
618C2×Q8—54no—
619C2×Q8—54no—
620C2×Q8—53no—
621C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
622C2×D4—56no—
623C2×D4—56no—
624C2×D4—53no—
625C2×D4—53no—
626C2×D4—56no—
627C2×D4—56no—
628C2×D4—53no—
629C2×D4—53no—
630C2×D4—53no—
631C2×D4—56no—
632C2×D4—106no—
633C2×D4—106no—
634C2×D4—106no—
635C2×D4—106no—
636C2×D4—206no—
637C2×D4—206no—
638C2×D4—203no—
639C2×D4—203no—
640C2×D4C22×AGL(1,𝔽5)13yes—
641C2×D4C22×AGL(1,𝔽5)13yes—
642C2×D4C22×AGL(1,𝔽5)13yes—
643C2×D4C22×AGL(1,𝔽5)16yes—
644C22×C4—53no—
645C22×C4—51no—
646C22×C4—53no—
647C22×C4—51no—
648C22×C4—53no—
649C22×C4—53no—
650C22×C4—51no—
651C22×C4—51no—
652C22×C4—53no—
653C22×C4—51no—
654C22×C4—53no—
655C22×C4—53no—
656C22×C4—53no—
657C22×C4—53no—
658C22×C4—51no—
659C22×C4—53no—
660C22×C4—53no—
661C22×C4—53no—
662C22×C4—51no—
663C22×C4—106no—
664C22×C4—106no—
665C22×C4—106no—
666C22×C4—106no—
667C22×C4—106no—
668C22×C4—106no—
669C22×C4—106no—
670C22×C4—1012no—
671C22×C4—203no—
672C22×C4—203no—
673C22×C4—203no—
674C22×C4—206no—
675C22×C4—206no—
676C22×C4C22×AGL(1,𝔽5)13yes—
677C22×C4C22×AGL(1,𝔽5)13yes—
678C4⋊C4—512no—
679C4⋊C4—51no—
680C4⋊C4—51no—
681C4⋊C4—51no—
682C4⋊C4—56no—
683C4⋊C4—53no—
684C4⋊C4—106no—
685C4⋊C4—106no—
686C4⋊C4—102no—
687C4⋊C4—106no—
688C4⋊C4—106no—
689C4⋊C4—106no—
690C4⋊C4—203no—
691C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
692C4⋊C4C22×AGL(1,𝔽5)13yes—
693C22⋊C4—53no—
694C22⋊C4—53no—
695C22⋊C4—53no—
696C22⋊C4—53no—
697C22⋊C4—53no—
698C22⋊C4—53no—
699C22⋊C4—106no—
700C22⋊C4—106no—
701C22⋊C4—1012no—
702C22⋊C4—106no—
703C22⋊C4—206no—
704C22⋊C4—203no—
705C22⋊C4—206no—
706C22⋊C4—203no—
707C22⋊C4—203no—
708C22⋊C4C22×AGL(1,𝔽5)13yes—
709C22⋊C4C22×AGL(1,𝔽5)13yes—
710C42—512no—
711C42—53no—
712C42—53no—
713C42—53no—
714C42—102no—
715C42—106no—
716C42—106no—
717C42—106no—
718C42—106no—
719C42—206no—
720C42C22×AGL(1,𝔽5)13yes—
721C2×C5—43no—
722C2×C5—43no—
723C2×C5C22×C4×D411yescharacteristic
724C2×C5#342811yescharacteristic
725C2×C5C4×H(5,𝔽2)11yescharacteristic
726D5—43no—
727D5—43no—
728D5#348711yescharacteristic
729D5#348811yescharacteristic
730D5#351711yescharacteristic
731D5#352411yescharacteristic
732C23—51no—
733C23—53no—
734C23—53no—
735C23—103no—
736C23—103no—
737C23—103no—
738C23—103no—
739C23—103no—
740C23—103no—
741C23—103no—
742C23—103no—
743C23—103no—
744C23—103no—
745C23—103no—
746C23—103no—
747C23C23×AGL(1,𝔽5)13yes—
748C23C23×AGL(1,𝔽5)13yes—
749Q8—512no—
750Q8D4×AGL(1,𝔽5)14yescomplemented
751D4—26no—
752D4—26no—
753D4—43no—
754D4—46no—
755D4—1012no—
756D4—1012no—
757D4—106no—
758D4—106no—
759D4—203no—
760D4—206no—
761D4—203no—
762D4—203no—
763D4—206no—
764D4—206no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—53no—
768C2×C4—56no—
769C2×C4—56no—
770C2×C4—52no—
771C2×C4—56no—
772C2×C4—52no—
773C2×C4—51no—
774C2×C4—53no—
775C2×C4—51no—
776C2×C4—51no—
777C2×C4—106no—
778C2×C4—106no—
779C2×C4—101no—
780C2×C4—103no—
781C2×C4—101no—
782C2×C4—103no—
783C2×C4—101no—
784C2×C4—101no—
785C2×C4—101no—
786C2×C4—101no—
787C2×C4—106no—
788C2×C4—106no—
789C2×C4—101no—
790C2×C4—103no—
791C2×C4—101no—
792C2×C4—101no—
793C2×C4—101no—
794C2×C4—103no—
795C2×C4—106no—
796C2×C4—106no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—103no—
800C2×C4—103no—
801C2×C4—103no—
802C2×C4—103no—
803C2×C4—101no—
804C2×C4—103no—
805C2×C4—101no—
806C2×C4—101no—
807C2×C4—103no—
808C2×C4—103no—
809C2×C4—103no—
810C2×C4—103no—
811C2×C4—101no—
812C2×C4—2012no—
813C2×C4—2012no—
814C2×C4—4012no—
815C2×C4C23×AGL(1,𝔽5)11yescharacteristic
816C2×C4C23×AGL(1,𝔽5)13yes—
817C2×C4C23×AGL(1,𝔽5)11yescharacteristic
818C2×C4C23×AGL(1,𝔽5)11yescharacteristic
819C2×C4C23×AGL(1,𝔽5)13yes—
820C5#3429511yescharacteristic, complemented, Sylow
821C22—23no—
822C22—23no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—51no—
828C22—51no—
829C22—51no—
830C22—51no—
831C22—51no—
832C22—51no—
833C22—103no—
834C22—103no—
835C22—103no—
836C22—103no—
837C22—103no—
838C22—103no—
839C22—203no—
840C22—203no—
841C22—203no—
842C22—203no—
843C22—203no—
844C22—203no—
845C22—203no—
846C22—203no—
847C22C24×AGL(1,𝔽5)11yescharacteristic
848C4—21no—
849C4—21no—
850C4—21no—
851C4—23no—
852C4—56no—
853C4—102no—
854C4—102no—
855C4—106no—
856C4—101no—
857C4—101no—
858C4—101no—
859C4—103no—
860C4—203no—
861C4—203no—
862C4—201no—
863C4—203no—
864C4—201no—
865C4C2×D4×AGL(1,𝔽5)16yes—
866C2—43no—
867C2—43no—
868C2—51no—
869C2—51no—
870C2—51no—
871C2—51no—
872C2—203no—
873C2—203no—
874C2C22×D4×AGL(1,𝔽5)11yescharacteristic
875C2#1061941211yescharacteristic
876C2AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#550C4
prime radicalD5×#550C2
cosocleC22×D5C25
hypercenter#550AGL(1,𝔽5)
hypocenterC5#34295
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#66266C2semidirect
2. C2×#41×AGL(1,𝔽5)C2semidirect
4. #10617558C2semidirect
5. #10617558C2semidirect
6. #10617369C2semidirect
7. #10617368C2semidirect
8. #10617254C2semidirect
9. #10617253C2semidirect
10. #10617250C2semidirect
11. AGL(1,𝔽5)×#121C2semidirect
12. #10617212C2semidirect
13. #10617208C2semidirect
14. #10617179C2semidirect
15. #10617173C2semidirect
33. C5×#550C4semidirect
34. #66168C4semidirect
35. #66168C4semidirect
36. #66052C4semidirect
40. #65933C4semidirect
41. #65933C4semidirect
42. #65911C4semidirect
44. #65887C4semidirect
80. C2×C5×#41C2×C4semidirect
81. C2×C5×#41C2×C4semidirect
86. C2×#713C2×C4semidirect
87. C2×#713C2×C4semidirect
89. C2×#711C2×C4semidirect
90. C2×#711C2×C4semidirect
95. C2×#709C2×C4semidirect
96. C2×#709C2×C4semidirect
111. Q8×AGL(1,𝔽5)D4semidirect
136. C5×#127C2×C4semidirect
137. C5×#121C2×C4semidirect
138. C5×#121C2×C4semidirect
139. C4×C5×Q8C2×C4semidirect
140. C4×C5×D4C2×C4semidirect
141. Q8×Dic5C2×C4semidirect
142. #4086C2×C4semidirect
143. #4086C2×C4semidirect
144. #4086C2×C4semidirect
145. #4086C2×C4semidirect
146. #4085C2×C4semidirect
147. #4085C2×C4semidirect
148. #4084C2×C4semidirect
149. #4084C2×C4semidirect
150. D4×Dic5C2×C4semidirect
151. #4076C2×C4semidirect
152. #4076C2×C4semidirect
153. C4×C22⋊D5C2×C4semidirect
154. C4×C22⋊D5C2×C4semidirect
155. #4041C2×C4semidirect
156. #4041C2×C4semidirect
157. #4039C2×C4semidirect
160. #4033C2×C4semidirect
161. #4030C2×C4semidirect
162. #4030C2×C4semidirect
163. #4027C2×C4semidirect
164. #4027C2×C4semidirect
167. #4020C2×C4semidirect
168. C4×D20C2×C4semidirect
170. C4×Dic10C2×C4semidirect
319. #550AGL(1,𝔽5)semidirect
414. C5×Q8C4×D4semidirect
457. Dic10C4×D4semidirect
468. C2×#41C2×AGL(1,𝔽5)semidirect
469. C2×#41C2×AGL(1,𝔽5)semidirect
485. #127C2×AGL(1,𝔽5)semidirect
496. #121C2×AGL(1,𝔽5)semidirect
497. #121C2×AGL(1,𝔽5)semidirect
505. C4×Q8C2×AGL(1,𝔽5)semidirect
518. C4×D4C2×AGL(1,𝔽5)semidirect
750. Q8D4×AGL(1,𝔽5)semidirect
820. C5#34295semidirect

Maximal subgroups

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

subgroupindex
C2×#662662
C2×#41×AGL(1,𝔽5)2
D5×#5502
#106175582
#106173692
#106173682
#106172542
#106172532
#106172502
AGL(1,𝔽5)×#1212
#106172122
#106172082
#106171792
#106171732
#342955