Finite Group Databasebeta

← #13044117

Subgroups — #13044117

Order 1280.

3154 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66266C212yesmaximal, complemented
2D5×#537C211yesmaximal, characteristic
3#10617555C212yesmaximal, complemented
4#10617286C214yesmaximal, complemented
5#10617285C214yesmaximal, complemented
6#10617254C214yesmaximal, complemented
7#10617253C214yesmaximal, complemented
8#10617251C214yesmaximal, complemented
9AGL(1,𝔽5)×#121C214yesmaximal, complemented
10#10617102C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
12C2×D5×#41C2212yes—
13#66266—216no—
14C2×Q8×AGL(1,𝔽5)C2214yes—
15C2×D4×AGL(1,𝔽5)C2218yes—
16C2×D4×AGL(1,𝔽5)C2214yes—
17C2×D4×AGL(1,𝔽5)C2214yes—
18C2×#4130C2212yes—
19C2×#4130C2214yes—
20C22×C4⋊AGL(1,𝔽5)C2214yes—
21C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C22×C4×AGL(1,𝔽5)C2211yescharacteristic
23C22×C4×AGL(1,𝔽5)C2212yes—
24C5×#537C411yescharacteristic, complemented
25#66167C412yescomplemented
26#65963C414yescomplemented
27D5×C22⋊Q8C2214yes—
28#65942C414yescomplemented
29D5×#121C2214yes—
30D5×#121C2214yes—
31#65931C414yescomplemented
32#65844C411yescharacteristic, complemented
33C2×D5×C4⋊C4C2211yescharacteristic
34(C2×AGL(1,𝔽5))⋊Q8C2212yes—
35(C2×AGL(1,𝔽5))⋊Q8C2212yes—
36#65780C2214yes—
37#65780C2212yes—
38#65780C2212yes—
39#65779C2214yes—
40#65779C2214yes—
41#65779C2218yes—
42#65765C2214yes—
43C4×C22⋊AGL(1,𝔽5)C2214yes—
44C4×C22⋊AGL(1,𝔽5)C2214yes—
45C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
46#65712C2214yes—
47#65712C2214yes—
48#65712C2214yes—
49#65711C2218yes—
50C4⋊C4×AGL(1,𝔽5)C2214yes—
51C4⋊C4×AGL(1,𝔽5)C2214yes—
52C4⋊C4×AGL(1,𝔽5)C2214yes—
53#65700C2218yes—
54#65700C2218yes—
55#65699C2218yes—
56C22⋊C4×AGL(1,𝔽5)C2218yes—
57#34274—51nomaximal, Sylow
58C23×AGL(1,𝔽5)C2311yescharacteristic
59C23×AGL(1,𝔽5)C2318yes—
60C23×AGL(1,𝔽5)C2311yescharacteristic
61C23×AGL(1,𝔽5)C2312yes—
62C2×C5×#41C2×C412yescomplemented
63D5×#41—28no—
64D5×#41—28no—
65C2×#713C2×C412yescomplemented
66C2×Q8×D5C2312yes—
67C2×#711C2×C414yescomplemented
68C2×#711C2×C412yescomplemented
69C2×D4×D5C2314yes—
70C2×D4×D5C2312yes—
71C2×D4×D5C2314yes—
72C2×#709C2×C412yescomplemented
73C2×#709C2×C414yescomplemented
74C22×C4×D5C2314yes—
75C22×C4×D5C2312yes—
76C22×C4×D5C2311yescharacteristic
77C2×C22⋊AGL(1,𝔽5)C2314yes—
78C2×C22⋊AGL(1,𝔽5)C2318yes—
79C2×C22⋊AGL(1,𝔽5)C2314yes—
80C2×C22⋊AGL(1,𝔽5)C2314yes—
81C2×C22⋊AGL(1,𝔽5)C2314yes—
82C2×C22⋊AGL(1,𝔽5)C2314yes—
83Q8×AGL(1,𝔽5)—216no—
84D4×AGL(1,𝔽5)—232no—
85D4×AGL(1,𝔽5)—216no—
86D4×AGL(1,𝔽5)—48no—
87#4130—28no—
88#4130—216no—
89C2×C4⋊AGL(1,𝔽5)—216no—
90C2×C4⋊AGL(1,𝔽5)D418yescomplemented
91C2×C4⋊AGL(1,𝔽5)C2318yes—
92C2×C4⋊AGL(1,𝔽5)C2312yes—
93C2×C4⋊AGL(1,𝔽5)C2312yes—
94C2×C4⋊AGL(1,𝔽5)C2314yes—
95C2×C4⋊AGL(1,𝔽5)C2314yes—
96C2×C4⋊AGL(1,𝔽5)C2314yes—
97C2×C4×AGL(1,𝔽5)—24no—
98C2×C4×AGL(1,𝔽5)—44no—
99C2×C4×AGL(1,𝔽5)C2318yes—
100C2×C4×AGL(1,𝔽5)C2314yes—
101C2×C4×AGL(1,𝔽5)C2312yes—
102C2×C4×AGL(1,𝔽5)C2312yes—
103C2×C4×AGL(1,𝔽5)C2314yes—
104C2×C4×AGL(1,𝔽5)C2314yes—
105C5×C22⋊Q8C2×C414yescomplemented
106C5×#121C2×C414yescomplemented
107C5×#121C2×C414yescomplemented
108C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
109#4092C2×C414yescomplemented
110#4085C2×C418yescomplemented
111#4085C2×C418yescomplemented
112#4084C2×C414yescomplemented
113#4084C2×C414yescomplemented
114#4076C2×C414yescomplemented
115#4076C2×C414yescomplemented
116C2×C4⋊Dic5C2×C411yescharacteristic, complemented
117#4070C2×C414yescomplemented
118C2×#683C2×C412yescomplemented
119#4043C2×C414yescomplemented
120#4042C2×C418yescomplemented
121#4041C2×C414yescomplemented
122#4041C2×C414yescomplemented
123D5×C4⋊C4C2×C414yescomplemented
124D5×C4⋊C4C2314yes—
125D5×C4⋊C4C2314yes—
126#4030C2×C418yescomplemented
127#4030C2×C418yescomplemented
128D5×C22⋊C4C2318yes—
129#4024C2×C418yescomplemented
130(C2×AGL(1,𝔽5))⋊C4C2314yes—
131(C2×AGL(1,𝔽5))⋊C4C2318yes—
132(C2×AGL(1,𝔽5))⋊C4C2314yes—
133(C2×AGL(1,𝔽5))⋊C4C2318yes—
134(C2×AGL(1,𝔽5))⋊C4C2314yes—
135(C2×AGL(1,𝔽5))⋊C4C2314yes—
136C2×#537—51no—
137C2×#520—52no—
138#2363—54no—
139#2362—54no—
140#2361—54no—
141#2360—54no—
142#2325—54no—
143#2316—51no—
144C4×#121—54no—
145#2297—52no—
146C2×C4×C4⋊C4—51no—
147C23×D5C2414yes—
148C23×D5C2411yescharacteristic
149C22×AGL(1,𝔽5)—22no—
150C22×AGL(1,𝔽5)—22no—
151C22×AGL(1,𝔽5)—22no—
152C22×AGL(1,𝔽5)—22no—
153C22×AGL(1,𝔽5)—216no—
154C22×AGL(1,𝔽5)—42no—
155C22×AGL(1,𝔽5)—42no—
156C22×AGL(1,𝔽5)—41no—
157C22×AGL(1,𝔽5)—41no—
158C22×AGL(1,𝔽5)—48no—
159C22×AGL(1,𝔽5)—48no—
160C22×AGL(1,𝔽5)C2×D418yes—
161C22×AGL(1,𝔽5)C2414yes—
162C22×AGL(1,𝔽5)C2412yes—
163C22×AGL(1,𝔽5)C2414yes—
164C22×AGL(1,𝔽5)C2414yes—
165C22×AGL(1,𝔽5)C2411yescharacteristic
166C22×AGL(1,𝔽5)C2411yescharacteristic
167C5×#41—28no—
168C2×C5×Q8C22×C412yes—
169C2×C5×D4C22×C412yes—
170C2×C5×D4C22×C414yes—
171C2×C5×D4C22×C414yes—
172C22×C4×C5C22×C414yes—
173C22×C4×C5C22×C412yes—
174C22×C4×C5C22×C411yescharacteristic
175C2×C22⋊D5C22×C414yes—
176C2×C22⋊D5C22×C414yes—
177C2×C22⋊D5C22×C414yes—
178C2×C22⋊D5C22×C418yes—
179C22×Dic5C22×C414yes—
180C22×Dic5C22×C412yes—
181C22×Dic5C22×C411yescharacteristic
182#713—28no—
183Q8×D5—24no—
184Q8×D5—24no—
185#711—216no—
186#711—28no—
187D4×D5—28no—
188D4×D5—28no—
189D4×D5—24no—
190D4×D5—24no—
191D4×D5—44no—
192D4×D5—44no—
193#709—28no—
194#709—216no—
195C2×D20C22×C414yes—
196C2×D20C22×C412yes—
197C2×D20C22×C414yes—
198C2×C4×D5—28no—
199C2×C4×D5—28no—
200C2×C4×D5—42no—
201C2×C4×D5—42no—
202C2×C4×D5C22×C414yes—
203C2×C4×D5C22×C414yes—
204C2×C4×D5C22×C414yes—
205C2×C4×D5C22×C412yes—
206C2×C4×D5C2×D414yes—
207C2×C4×D5#4114yes—
208C2×C4×D5C2414yes—
209C2×C4×D5C2414yes—
210C2×C4×D5C2412yes—
211C2×Dic10C22×C414yes—
212C2×Dic10C22×C412yes—
213C22⋊AGL(1,𝔽5)—28no—
214C22⋊AGL(1,𝔽5)—216no—
215C22⋊AGL(1,𝔽5)—28no—
216C22⋊AGL(1,𝔽5)—28no—
217C22⋊AGL(1,𝔽5)—44no—
218C22⋊AGL(1,𝔽5)—44no—
219C4⋊AGL(1,𝔽5)—216no—
220C4⋊AGL(1,𝔽5)—24no—
221C4⋊AGL(1,𝔽5)—24no—
222C4⋊AGL(1,𝔽5)—44no—
223C4⋊AGL(1,𝔽5)—44no—
224C4⋊AGL(1,𝔽5)C2×D4116yes—
225C4×AGL(1,𝔽5)—216no—
226C4×AGL(1,𝔽5)—28no—
227C4×AGL(1,𝔽5)—28no—
228C4×AGL(1,𝔽5)—24no—
229C4×AGL(1,𝔽5)—24no—
230C4×AGL(1,𝔽5)—44no—
231C5×C4⋊C4C22×C414yes—
232C5×C4⋊C4C22×C414yes—
233C5×C22⋊C4C22×C418yes—
234C22⋊Dic5C22×C418yes—
235#685C22×C418yes—
236#685C22×C418yes—
237C4⋊Dic5C22×C414yes—
238C4⋊Dic5C22×C414yes—
239#683C22×C418yes—
240#683C22×C418yes—
241C22×#41—52no—
242#537—52no—
243#537—54no—
244#537—54no—
245#537—54no—
246#537—51no—
247#537AGL(1,𝔽5)11yescharacteristic, complemented
248C2×C22⋊Q8—54no—
249C2×#121—54no—
250C2×#121—54no—
251#520—1016no—
252C2×C4×Q8—54no—
253C2×C4×D4—58no—
254C2×C4×D4—54no—
255C2×C4×D4—54no—
256C2×#117—52no—
257C2×#117—54no—
258C22×C4⋊C4—51no—
259C22×C4⋊C4—51no—
260C22×C4⋊C4—54no—
261C22×C42—51no—
262C22×C42—52no—
263#391—52no—
264#391—52no—
265#390—52no—
266#390—52no—
267#390—54no—
268#389—54no—
269#389—54no—
270#389—54no—
271#388—58no—
272#388—58no—
273#387—58no—
274#386—54no—
275#386—58no—
276#386—54no—
277#385—58no—
278#380—54no—
279C4×C4⋊C4—54no—
280C4×C4⋊C4—54no—
281C4×C4⋊C4—54no—
282C4×C22⋊C4—58no—
283C4×C22⋊C4—54no—
284C4×C22⋊C4—54no—
285C2×#95—52no—
286C23×C5C23×C414yes—
287C23×C5C23×C411yescharacteristic
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—21no—
291C22×D5—21no—
292C22×D5—24no—
293C22×D5—24no—
294C22×D5—24no—
295C22×D5—24no—
296C22×D5—24no—
297C22×D5—24no—
298C22×D5C23×C414yes—
299C22×D5C23×C411yescharacteristic
300C22×D5C22×D412yes—
301C22×D5C2×#4112yes—
302C22×D5C2511yescharacteristic
303C2×AGL(1,𝔽5)—28no—
304C2×AGL(1,𝔽5)—21no—
305C2×AGL(1,𝔽5)—21no—
306C2×AGL(1,𝔽5)—24no—
307C2×AGL(1,𝔽5)—21no—
308C2×AGL(1,𝔽5)—21no—
309C2×AGL(1,𝔽5)—24no—
310C2×AGL(1,𝔽5)—24no—
311C2×AGL(1,𝔽5)—24no—
312C2×AGL(1,𝔽5)—22no—
313C2×AGL(1,𝔽5)—24no—
314C2×AGL(1,𝔽5)—24no—
315C2×AGL(1,𝔽5)—24no—
316C2×AGL(1,𝔽5)—22no—
317C2×AGL(1,𝔽5)—22no—
318C2×AGL(1,𝔽5)—24no—
319C2×AGL(1,𝔽5)—48no—
320C2×AGL(1,𝔽5)—44no—
321C2×AGL(1,𝔽5)—816no—
322C2×AGL(1,𝔽5)C22×D418yes—
323C2×AGL(1,𝔽5)H(5,𝔽2)12yes—
324C2×AGL(1,𝔽5)2−1+412yes—
325C5×Q8—24no—
326C5×D4—28no—
327C5×D4—24no—
328C5×D4—44no—
329C2×C4×C5—28no—
330C2×C4×C5—42no—
331C2×C4×C5C4×D414yescomplemented
332C2×C4×C5C23×C414yes—
333C2×C4×C5C23×C414yes—
334C2×C4×C5C23×C412yes—
335C22⋊D5—28no—
336C22⋊D5—28no—
337C22⋊D5—28no—
338C22⋊D5—48no—
339C2×Dic5—28no—
340C2×Dic5—42no—
341C2×Dic5C4×D414yescomplemented
342C2×Dic5C23×C414yes—
343C2×Dic5C23×C414yes—
344C2×Dic5C23×C412yes—
345D20—28no—
346D20—24no—
347D20—44no—
348C4×D5—24no—
349C4×D5—24no—
350C4×D5—24no—
351C4×D5—24no—
352C4×D5—28no—
353C4×D5—28no—
354C4×D5—44no—
355C4×D5C4×D418yescomplemented
356C4×D5C22×D414yes—
357C4×D5C2×#4114yes—
358Dic10—24no—
359Dic10—28no—
360C2×#41—52no—
361C2×#41—54no—
362C2×#41—52no—
363C2×#41—54no—
364C2×#41—52no—
365C2×#41—108no—
366C2×#41—108no—
367C2×#41C2×AGL(1,𝔽5)12yescomplemented
368C22×Q8—52no—
369C22×D4—54no—
370C22×D4—52no—
371C22×D4—54no—
372C23×C4—51no—
373C23×C4—52no—
374C23×C4—54no—
375C23×C4—52no—
376C23×C4—51no—
377C23×C4—58no—
378C23×C4—51no—
379C22⋊Q8—54no—
380C22⋊Q8—54no—
381C22⋊Q8—58no—
382C22⋊Q8—54no—
383C22⋊Q8—58no—
384C22⋊Q8C2×AGL(1,𝔽5)14yescomplemented
385#121—54no—
386#121—54no—
387#121—58no—
388#121—58no—
389#121—54no—
390#121—54no—
391#121—54no—
392#121—54no—
393#121—58no—
394#121—58no—
395#121C2×AGL(1,𝔽5)14yescomplemented
396#121C2×AGL(1,𝔽5)14yescomplemented
397C4×Q8—1016no—
398C4×D4—1016no—
399C4×D4—1032no—
400C4×D4—208no—
401#117—1016no—
402#117—108no—
403C2×C4⋊C4—54no—
404C2×C4⋊C4—58no—
405C2×C4⋊C4—52no—
406C2×C4⋊C4—51no—
407C2×C4⋊C4—54no—
408C2×C4⋊C4—54no—
409C2×C4⋊C4—54no—
410C2×C4⋊C4—52no—
411C2×C4⋊C4—58no—
412C2×C4⋊C4—52no—
413C2×C4⋊C4—54no—
414C2×C4⋊C4—54no—
415C2×C4⋊C4—1016no—
416C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
417C2×C22⋊C4—58no—
418C2×C22⋊C4—54no—
419C2×C22⋊C4—58no—
420C2×C22⋊C4—54no—
421C2×C22⋊C4—54no—
422C2×C22⋊C4—54no—
423C2×C22⋊C4—54no—
424C2×C42—54no—
425C2×C42—58no—
426C2×C42—54no—
427C2×C42—52no—
428C2×C42—52no—
429C2×C42—54no—
430C2×C42—104no—
431C2×C42—204no—
432#95—58no—
433#95—54no—
434#95—54no—
435#95—58no—
436#95—54no—
437#95—54no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—24no—
441C22×C5—24no—
442C22×C5—24no—
443C22×C5C2×C4×D412yes—
444C22×C5C24×C411yescharacteristic
445C2×D5—21no—
446C2×D5—21no—
447C2×D5—22no—
448C2×D5—22no—
449C2×D5—22no—
450C2×D5—22no—
451C2×D5—24no—
452C2×D5—24no—
453C2×D5—24no—
454C2×D5—44no—
455C2×D5—44no—
456C2×D5—44no—
457C2×D5—44no—
458C2×D5C2×C4×D412yes—
459C2×D5C23×D411yescharacteristic
460C2×D5C22×#4111yescharacteristic
461C2×D5C2×H(5,𝔽2)11yescharacteristic
462C2×D5C2×2−1+411yescharacteristic
463C2×D5#58511yescharacteristic
464C2×D5#58511yescharacteristic
465AGL(1,𝔽5)—22no—
466AGL(1,𝔽5)—22no—
467AGL(1,𝔽5)—28no—
468AGL(1,𝔽5)—42no—
469AGL(1,𝔽5)—44no—
470AGL(1,𝔽5)—44no—
471C4×C5—24no—
472C4×C5—24no—
473C4×C5C2×C4×D414yes—
474Dic5—24no—
475Dic5—24no—
476Dic5C2×C4×D414yes—
477C24—51no—
478C24—54no—
479#41—28no—
480#41—1016no—
481#41—1016no—
482#41—108no—
483#41—108no—
484#41—108no—
485C2×Q8—54no—
486C2×Q8—52no—
487C2×Q8—104no—
488C2×Q8—104no—
489C2×Q8C22×AGL(1,𝔽5)12yes—
490C2×D4—54no—
491C2×D4—54no—
492C2×D4—54no—
493C2×D4—58no—
494C2×D4—54no—
495C2×D4—52no—
496C2×D4—54no—
497C2×D4—104no—
498C2×D4—104no—
499C2×D4—108no—
500C2×D4—108no—
501C2×D4—204no—
502C2×D4—204no—
503C2×D4C22×AGL(1,𝔽5)14yes—
504C2×D4C22×AGL(1,𝔽5)12yes—
505C2×D4C22×AGL(1,𝔽5)14yes—
506C22×C4—51no—
507C22×C4—54no—
508C22×C4—54no—
509C22×C4—52no—
510C22×C4—52no—
511C22×C4—51no—
512C22×C4—51no—
513C22×C4—54no—
514C22×C4—54no—
515C22×C4—58no—
516C22×C4—52no—
517C22×C4—54no—
518C22×C4—54no—
519C22×C4—54no—
520C22×C4—54no—
521C22×C4—54no—
522C22×C4—52no—
523C22×C4—54no—
524C22×C4—54no—
525C22×C4—108no—
526C22×C4—108no—
527C22×C4—102no—
528C22×C4—102no—
529C22×C4—1016no—
530C22×C4—102no—
531C22×C4—102no—
532C22×C4—202no—
533C22×C4—202no—
534C22×C4—202no—
535C22×C4—202no—
536C22×C4—201no—
537C22×C4—201no—
538C22×C4—208no—
539C22×C4—208no—
540C22×C4C22×AGL(1,𝔽5)14yes—
541C22×C4C22×AGL(1,𝔽5)12yes—
542C22×C4C22×AGL(1,𝔽5)11yescharacteristic
543C4⋊C4—516no—
544C4⋊C4—58no—
545C4⋊C4—54no—
546C4⋊C4—58no—
547C4⋊C4—54no—
548C4⋊C4—104no—
549C4⋊C4—1016no—
550C4⋊C4—104no—
551C4⋊C4—204no—
552C4⋊C4—204no—
553C4⋊C4C22×AGL(1,𝔽5)14yes—
554C4⋊C4C22×AGL(1,𝔽5)14yes—
555C22⋊C4—58no—
556C22⋊C4—58no—
557C22⋊C4—58no—
558C22⋊C4—1016no—
559C22⋊C4—108no—
560C22⋊C4—108no—
561C22⋊C4—108no—
562C22⋊C4—204no—
563C22⋊C4—204no—
564C22⋊C4C22×AGL(1,𝔽5)18yes—
565C42—104no—
566C42—104no—
567C42—108no—
568C42—108no—
569C42—1016no—
570C42—204no—
571C2×C5—22no—
572C2×C5—44no—
573C2×C5C22×C4×D411yescharacteristic
574C2×C5C4×H(5,𝔽2)11yescharacteristic
575C2×C5C4×2−1+411yescharacteristic
576D5—22no—
577D5—44no—
578D5#349211yescharacteristic
579D5#349311yescharacteristic
580D5#349611yescharacteristic
581D5#349711yescharacteristic
582C23—51no—
583C23—52no—
584C23—52no—
585C23—51no—
586C23—54no—
587C23—101no—
588C23—101no—
589C23—101no—
590C23—101no—
591C23—104no—
592C23—104no—
593C23—104no—
594C23—104no—
595C23—104no—
596C23—104no—
597C23C23×AGL(1,𝔽5)14yes—
598C23C23×AGL(1,𝔽5)11yescharacteristic
599Q8—24no—
600Q8—108no—
601Q8—104no—
602D4—28no—
603D4—24no—
604D4—44no—
605D4—108no—
606D4—108no—
607D4—108no—
608D4—108no—
609D4—104no—
610D4—204no—
611D4—208no—
612C2×C4—28no—
613C2×C4—42no—
614C2×C4—54no—
615C2×C4—52no—
616C2×C4—54no—
617C2×C4—54no—
618C2×C4—58no—
619C2×C4—52no—
620C2×C4—58no—
621C2×C4—52no—
622C2×C4—54no—
623C2×C4—54no—
624C2×C4—108no—
625C2×C4—104no—
626C2×C4—104no—
627C2×C4—104no—
628C2×C4—104no—
629C2×C4—108no—
630C2×C4—101no—
631C2×C4—101no—
632C2×C4—104no—
633C2×C4—101no—
634C2×C4—101no—
635C2×C4—104no—
636C2×C4—108no—
637C2×C4—108no—
638C2×C4—104no—
639C2×C4—102no—
640C2×C4—104no—
641C2×C4—104no—
642C2×C4—104no—
643C2×C4—102no—
644C2×C4—102no—
645C2×C4—104no—
646C2×C4—104no—
647C2×C4—204no—
648C2×C4—202no—
649C2×C4—208no—
650C2×C4—204no—
651C2×C4—4016no—
652C2×C4D4×AGL(1,𝔽5)14yescomplemented
653C2×C4C23×AGL(1,𝔽5)14yes—
654C2×C4C23×AGL(1,𝔽5)14yes—
655C2×C4C23×AGL(1,𝔽5)12yes—
656C5#3427411yescharacteristic, complemented, Sylow
657C22—21no—
658C22—21no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—51no—
663C22—51no—
664C22—51no—
665C22—51no—
666C22—51no—
667C22—51no—
668C22—52no—
669C22—102no—
670C22—102no—
671C22—102no—
672C22—102no—
673C22—101no—
674C22—101no—
675C22—104no—
676C22—104no—
677C22—104no—
678C22—204no—
679C22—204no—
680C22—204no—
681C22—204no—
682C22C2×D4×AGL(1,𝔽5)12yes—
683C22C24×AGL(1,𝔽5)11yescharacteristic
684C4—24no—
685C4—24no—
686C4—54no—
687C4—102no—
688C4—102no—
689C4—108no—
690C4—104no—
691C4—104no—
692C4—202no—
693C4—204no—
694C4—204no—
695C4C2×D4×AGL(1,𝔽5)14yes—
696C2—22no—
697C2—44no—
698C2—51no—
699C2—51no—
700C2—51no—
701C2—51no—
702C2—102no—
703C2—204no—
704C2C22×D4×AGL(1,𝔽5)11yescharacteristic
705C2AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic
706C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#537C4
prime radicalD5×#537C2
cosocleC22×D5C25
hypercenter#537AGL(1,𝔽5)
hypocenterC5#34274
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#66266C2semidirect
3. #10617555C2semidirect
4. #10617286C2semidirect
5. #10617285C2semidirect
6. #10617254C2semidirect
7. #10617253C2semidirect
8. #10617251C2semidirect
9. AGL(1,𝔽5)×#121C2semidirect
10. #10617102C2semidirect
11. C2×C4⋊C4×AGL(1,𝔽5)C2semidirect
24. C5×#537C4semidirect
25. #66167C4semidirect
26. #65963C4semidirect
28. #65942C4semidirect
31. #65931C4semidirect
32. #65844C4semidirect
62. C2×C5×#41C2×C4semidirect
65. C2×#713C2×C4semidirect
67. C2×#711C2×C4semidirect
68. C2×#711C2×C4semidirect
72. C2×#709C2×C4semidirect
73. C2×#709C2×C4semidirect
90. C2×C4⋊AGL(1,𝔽5)D4semidirect
105. C5×C22⋊Q8C2×C4semidirect
106. C5×#121C2×C4semidirect
107. C5×#121C2×C4semidirect
108. C2×C5×C4⋊C4C2×C4semidirect
109. #4092C2×C4semidirect
110. #4085C2×C4semidirect
111. #4085C2×C4semidirect
112. #4084C2×C4semidirect
113. #4084C2×C4semidirect
114. #4076C2×C4semidirect
115. #4076C2×C4semidirect
116. C2×C4⋊Dic5C2×C4semidirect
117. #4070C2×C4semidirect
118. C2×#683C2×C4semidirect
119. #4043C2×C4semidirect
120. #4042C2×C4semidirect
121. #4041C2×C4semidirect
122. #4041C2×C4semidirect
123. D5×C4⋊C4C2×C4semidirect
126. #4030C2×C4semidirect
127. #4030C2×C4semidirect
129. #4024C2×C4semidirect
247. #537AGL(1,𝔽5)semidirect
331. C2×C4×C5C4×D4semidirect
341. C2×Dic5C4×D4semidirect
355. C4×D5C4×D4semidirect
367. C2×#41C2×AGL(1,𝔽5)semidirect
384. C22⋊Q8C2×AGL(1,𝔽5)semidirect
395. #121C2×AGL(1,𝔽5)semidirect
396. #121C2×AGL(1,𝔽5)semidirect
416. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
652. C2×C4D4×AGL(1,𝔽5)semidirect
656. C5#34274semidirect

Maximal subgroups

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

subgroupindex
C2×#662662
D5×#5372
#106175552
#106172862
#106172852
#106172542
#106172532
#106172512
AGL(1,𝔽5)×#1212
#106171022
C2×C4⋊C4×AGL(1,𝔽5)2
#342745