Finite Group Databasebeta

← #12272432

Subgroups — #12272432

Order 1280.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2329C211yesmaximal, characteristic, complemented
2#10614495C211yesmaximal, characteristic
3#10614494C211yesmaximal, characteristic, complemented
4#10608395C211yesmaximal, characteristic, complemented
5#10608293C211yesmaximal, characteristic, complemented
6#10608269C211yesmaximal, characteristic, complemented
7#10608241C211yesmaximal, characteristic, complemented
8#10607987C211yesmaximal, characteristic, complemented
9#10607921C211yesmaximal, characteristic, complemented
10#10607799C211yesmaximal, characteristic, complemented
11#10607767C211yesmaximal, characteristic, complemented
12#10607179C211yesmaximal, characteristic, complemented
13#10607022C211yesmaximal, characteristic, complemented
14#10606879C211yesmaximal, characteristic, complemented
15#10606878C211yesmaximal, characteristic, complemented
16#10606825C211yesmaximal, characteristic, complemented
17#10606823C211yesmaximal, characteristic, complemented
18#10606755C211yesmaximal, characteristic, complemented
19#10606713C211yesmaximal, characteristic, complemented
20#10606191C211yesmaximal, characteristic, complemented
21#10606188C211yesmaximal, characteristic
22#10606172C211yesmaximal, characteristic, complemented
23#10606153C211yesmaximal, characteristic
24#10605639C211yesmaximal, characteristic, complemented
25#10605620C211yesmaximal, characteristic
26#10605299C211yesmaximal, characteristic
27#10605178C211yesmaximal, characteristic, complemented
28C4×#4024C211yesmaximal, characteristic, complemented
29C4×#4027C211yesmaximal, characteristic
30#10605098C211yesmaximal, characteristic
31C2×#64936C211yesmaximal, characteristic, complemented
32C2×C5×C22⋊Q8C2211yescharacteristic
33C2×#4092C2211yescharacteristic
34C2×#4090C2211yescharacteristic
35C2×C4×C22⋊D5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C2×#4043C2211yescharacteristic
42C2×#4042C2211yescharacteristic
43C2×#4035C2211yescharacteristic
44C2×#4035C2211yescharacteristic
45C2×#4027C2211yescharacteristic
46C2×#4027C2211yescharacteristic
47C2×#4024C2211yescharacteristic
48C2×#4024C2211yescharacteristic
49C2×C42×D5C2211yescharacteristic
50C2×C4×Dic10C2211yescharacteristic
51C5×#391C2211yescharacteristic
52C5×#391C2211yescharacteristic
53C5×#389C2211yescharacteristic
54C5×#389C2211yescharacteristic
55C5×#387C2211yescharacteristic
56C5×#387C2211yescharacteristic
57C5×#387C2211yescharacteristic
58C5×#387C2211yescharacteristic
59C5×#385C2211yescharacteristic
60C5×#385C2211yescharacteristic
61C5×#380C2211yescharacteristic
62C4×C5×C22⋊C4C2211yescharacteristic
63C4×C5×C22⋊C4C2211yescharacteristic
64C2×C5×#95C2211yescharacteristic
65#65518C2211yescharacteristic
66#65518C2211yescharacteristic
67#65502C2211yescharacteristic
68#65502C2211yescharacteristic
69#65499C2211yescharacteristic
70#65499C2211yescharacteristic
71C4×C22⋊Dic5C2211yescharacteristic
72C2×#3963C2211yescharacteristic
73#65283C2211yescharacteristic
74#65283C2211yescharacteristic
75#65283C2211yescharacteristic
76#65281C2211yescharacteristic
77#65281C2211yescharacteristic
78#65281C2211yescharacteristic
79#65278C2211yescharacteristic
80#65274C2211yescharacteristic
81#65273C2211yescharacteristic
82#65273C2211yescharacteristic
83#65273C2211yescharacteristic
84#65273C2211yescharacteristic
85#65272C2211yescharacteristic
86#65272C2211yescharacteristic
87#65272C2211yescharacteristic
88#65272C2211yescharacteristic
89#65270C2211yescharacteristic
90#65269C2211yescharacteristic
91#65269C2211yescharacteristic
92#65269C2211yescharacteristic
93#65268C2211yescharacteristic
94#65267C2211yescharacteristic
95#65267C2211yescharacteristic
96#65265C2211yescharacteristic
97#65265C2211yescharacteristic
98#65265C2211yescharacteristic
99#65262C2211yescharacteristic
100#65261C2211yescharacteristic
101#65261C2211yescharacteristic
102#65261C2211yescharacteristic
103#65261C2211yescharacteristic
104#65261C2211yescharacteristic
105#65247C2211yescharacteristic
106#65247C2211yescharacteristic
107#65239C2211yescharacteristic
108#65239C2211yescharacteristic
109#65235C2211yescharacteristic
110#65235C2211yescharacteristic
111#65235C2211yescharacteristic
112#65235C2211yescharacteristic
113#65231C2211yescharacteristic
114#65231C2211yescharacteristic
115C22⋊C4×Dic5C2211yescharacteristic
116C22⋊C4×Dic5C2211yescharacteristic
117#65229C2211yescharacteristic
118#65229C2211yescharacteristic
119C4×#685C2211yescharacteristic
120C4×C4⋊Dic5C2211yescharacteristic
121#65222C2211yescharacteristic
122#65222C2211yescharacteristic
123#65222C2211yescharacteristic
124#65222C2211yescharacteristic
125C4×#683C2211yescharacteristic
126C4×#683C2211yescharacteristic
127C4×#683C2211yescharacteristic
128C42×Dic5C2211yescharacteristic
129#65218C2211yescharacteristic
130#65217C2211yescharacteristic
131#64966C2211yescharacteristic
132#64965C2211yescharacteristic
133#64958C2211yescharacteristic
134#64958C2211yescharacteristic
135#64957C2211yescharacteristic
136#64956C2211yescharacteristic
137#64956C2211yescharacteristic
138#64956C2211yescharacteristic
139#64956C2211yescharacteristic
140#64956C2211yescharacteristic
141#64955C2211yescharacteristic
142#64955C2211yescharacteristic
143#64953C2211yescharacteristic
144#64953C2211yescharacteristic
145#64948C2211yescharacteristic
146#64947C2211yescharacteristic
147#64947C2211yescharacteristic
148#64947C2211yescharacteristic
149#64946C2211yescharacteristic
150#64946C2211yescharacteristic
151#64946C2211yescharacteristic
152#64946C2211yescharacteristic
153#64946C2211yescharacteristic
154#64945C2211yescharacteristic
155#64944C2211yescharacteristic
156#64944C2211yescharacteristic
157#64943C2211yescharacteristic
158#64943C2211yescharacteristic
159#64942C2211yescharacteristic
160#64942C2211yescharacteristic
161#64941C2211yescharacteristic
162#64941C2211yescharacteristic
163#64941C2211yescharacteristic
164#64940C2211yescharacteristic
165#64940C2211yescharacteristic
166#64939C2211yescharacteristic
167#64939C2211yescharacteristic
168#64938C2211yescharacteristic
169#64938C2211yescharacteristic
170#64936C2211yescharacteristic
171#64936C2211yescharacteristic
172#64936C2211yescharacteristic
173#64936C2211yescharacteristic
174#64936C2211yescharacteristic
175#64936C2211yescharacteristic
176#64936C2211yescharacteristic
177#64936C2211yescharacteristic
178#64936C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#35017—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C22×C22⋊D5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C23×Dic5C2311yescharacteristic
196C23×Dic5C2311yescharacteristic
197C22×C4×D5C2311yescharacteristic
198C22×C4×D5C2311yescharacteristic
199C22×C4×D5C2311yescharacteristic
200C22×Dic10C2311yescharacteristic
201C22×Dic10C2311yescharacteristic
202C5×C22⋊Q8—24no—
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C4⋊C4C2311yescharacteristic
211C2×C5×C4⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219C2×C42×C5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223#4092—42no—
224#4090—42no—
225C4×C22⋊D5Q818yescomplemented
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×C4⋊Dic5—42no—
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×#683—24no—
249C2×#683—42no—
250C2×#683—42no—
251C2×#683C2311yescharacteristic
252C2×#683C2311yescharacteristic
253C2×#683C2311yescharacteristic
254C2×#683C2311yescharacteristic
255C2×#683C2311yescharacteristic
256C2×#683C2311yescharacteristic
257C2×#683C2311yescharacteristic
258C2×#683C2311yescharacteristic
259C2×#683C2311yescharacteristic
260C2×#683C2311yescharacteristic
261C2×#683C2311yescharacteristic
262C2×#683C2311yescharacteristic
263C2×#683C2311yescharacteristic
264C2×#683C2311yescharacteristic
265C2×#683C2311yescharacteristic
266C2×#683C2311yescharacteristic
267C2×#683C2311yescharacteristic
268C2×#683C2311yescharacteristic
269C2×#683C2311yescharacteristic
270C2×#683C2311yescharacteristic
271C2×#683C2311yescharacteristic
272C2×#683C2311yescharacteristic
273C2×#683C2311yescharacteristic
274C2×#683C2311yescharacteristic
275C2×#683C2311yescharacteristic
276C2×#683C2311yescharacteristic
277C2×#683C2311yescharacteristic
278C2×#683C2311yescharacteristic
279C2×#683C2311yescharacteristic
280C2×#683C2311yescharacteristic
281C2×#683C2311yescharacteristic
282C2×#683C2311yescharacteristic
283C2×#683C2311yescharacteristic
284C2×#683C2311yescharacteristic
285C2×#683C2311yescharacteristic
286C2×C4×Dic5—42no—
287C2×C4×Dic5C2311yescharacteristic
288C2×C4×Dic5C2311yescharacteristic
289C2×C4×Dic5C2311yescharacteristic
290C2×C4×Dic5C2311yescharacteristic
291C2×C4×Dic5C2311yescharacteristic
292C2×C4×Dic5C2311yescharacteristic
293C2×C4×Dic5C2311yescharacteristic
294C2×C4×Dic5C2311yescharacteristic
295C2×C4×Dic5C2311yescharacteristic
296C2×C4×Dic5C2311yescharacteristic
297C2×C4×Dic5C2311yescharacteristic
298C2×C4×Dic5C2311yescharacteristic
299C2×C4×Dic5C2311yescharacteristic
300#4043—42no—
301#4042—42no—
302#4035—42no—
303#4035—42no—
304#4027—24no—
305#4027—24no—
306#4024—24no—
307#4024—24no—
308C42×D5—42no—
309C4×Dic10—42no—
310C5×#95C2311yescharacteristic
311C5×#95C2311yescharacteristic
312C5×#95C2311yescharacteristic
313C5×#95C2311yescharacteristic
314C5×#95C2311yescharacteristic
315C5×#95C2311yescharacteristic
316C5×#95C2311yescharacteristic
317C5×#95C2311yescharacteristic
318C5×#95C2311yescharacteristic
319C5×#95C2311yescharacteristic
320C5×#95C2311yescharacteristic
321C5×#95C2311yescharacteristic
322C5×#95C2311yescharacteristic
323C5×#95C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#3963C2311yescharacteristic
353#3963C2311yescharacteristic
354#3963C2311yescharacteristic
355#3963C2311yescharacteristic
356#3963C2311yescharacteristic
357#3963C2311yescharacteristic
358#3963C2311yescharacteristic
359#3963C2311yescharacteristic
360#3963C2311yescharacteristic
361#3963C2311yescharacteristic
362#2863—51no—
363#2859—51no—
364#2857—51no—
365#2855—51no—
366#2667—51no—
367#2667—51no—
368#2666—51no—
369#2666—51no—
370#2585—51no—
371#2585—51no—
372#2556—51no—
373#2556—51no—
374#2507—51no—
375#2502—51no—
376#2497—51no—
377#2487—51no—
378#2473—51no—
379#2473—51no—
380#2451—51no—
381#2449—51no—
382#2449—51no—
383#2440—51no—
384#2423—51no—
385#2417—51no—
386#2329—51no—
387#2329D511yescharacteristic, complemented
388#2318—51no—
389#2318—51no—
390C4×C22⋊Q8—51no—
391C2×#389—51no—
392C42×D4—51no—
393C24×C5C2411yescharacteristic
394C23×D5C2411yescharacteristic
395C2×C5×Q8—22no—
396C2×C5×Q8—41no—
397C2×C5×Q8—41no—
398C22×C4×C5—22no—
399C22×C4×C5—22no—
400C22×C4×C5—41no—
401C22×C4×C5—41no—
402C22×C4×C5—41no—
403C22×C4×C5—41no—
404C22×C4×C5—41no—
405C22×C4×C5—41no—
406C22×C4×C5C2×Q814yes—
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C22×C4×C5C2411yescharacteristic
412C22×C4×C5C2411yescharacteristic
413C22×C4×C5C2411yescharacteristic
414C22×C4×C5C2411yescharacteristic
415C22×C4×C5C2411yescharacteristic
416C22×C4×C5C2411yescharacteristic
417C22×C4×C5C2411yescharacteristic
418C22×C4×C5C2411yescharacteristic
419C22×C4×C5C2411yescharacteristic
420C22×C4×C5C2411yescharacteristic
421C2×C22⋊D5—22no—
422C2×C22⋊D5—22no—
423C2×C22⋊D5C2×Q814yes—
424C22×Dic5—22no—
425C22×Dic5—22no—
426C22×Dic5—22no—
427C22×Dic5—22no—
428C22×Dic5—22no—
429C22×Dic5—22no—
430C22×Dic5—41no—
431C22×Dic5—41no—
432C22×Dic5—41no—
433C22×Dic5—41no—
434C22×Dic5—41no—
435C22×Dic5#4114yes—
436C22×Dic5C2411yescharacteristic
437C22×Dic5C2411yescharacteristic
438C22×Dic5C2411yescharacteristic
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C22×Dic5C2411yescharacteristic
442C22×Dic5C2411yescharacteristic
443C22×Dic5C2411yescharacteristic
444C22×Dic5C2411yescharacteristic
445C22×Dic5C2411yescharacteristic
446C22×Dic5C2411yescharacteristic
447C22×Dic5C2411yescharacteristic
448C22×Dic5C2411yescharacteristic
449C22×Dic5C2411yescharacteristic
450C22×Dic5C2411yescharacteristic
451C2×C4×D5—22no—
452C2×C4×D5—22no—
453C2×C4×D5—22no—
454C2×C4×D5—22no—
455C2×C4×D5—22no—
456C2×C4×D5—41no—
457C2×C4×D5—41no—
458C2×C4×D5—41no—
459C2×C4×D5C2×Q814yes—
460C2×Dic10—22no—
461C2×Dic10—22no—
462C2×Dic10—22no—
463C2×Dic10—22no—
464C2×Dic10—41no—
465C2×Dic10—41no—
466C5×C4⋊C4—22no—
467C5×C4⋊C4—22no—
468C5×C4⋊C4—22no—
469C5×C4⋊C4—41no—
470C5×C4⋊C4—41no—
471C5×C4⋊C4—41no—
472C5×C4⋊C4—41no—
473C5×C4⋊C4—41no—
474C5×C4⋊C4—41no—
475C5×C22⋊C4—22no—
476C5×C22⋊C4—22no—
477C5×C22⋊C4—22no—
478C5×C22⋊C4#4114yes—
479C42×C5—41no—
480C42×C5—41no—
481C42×C5—41no—
482C42×C5—41no—
483C22⋊Dic5—22no—
484C22⋊Dic5—22no—
485C22⋊Dic5C2×Q814yes—
486#685—22no—
487#685—22no—
488#685—41no—
489#685—41no—
490#685—41no—
491#685—41no—
492#685—41no—
493#685—41no—
494#685—41no—
495#685—41no—
496#685C2×Q814yes—
497C4⋊Dic5—22no—
498C4⋊Dic5—22no—
499C4⋊Dic5—22no—
500C4⋊Dic5—22no—
501C4⋊Dic5—22no—
502C4⋊Dic5—41no—
503C4⋊Dic5—41no—
504C4⋊Dic5—41no—
505C4⋊Dic5—41no—
506C4⋊Dic5—41no—
507#683—22no—
508#683—22no—
509#683—22no—
510#683—22no—
511#683—22no—
512#683—22no—
513#683—22no—
514#683—22no—
515#683—22no—
516#683—22no—
517#683—22no—
518#683—22no—
519#683—22no—
520#683—22no—
521#683—22no—
522#683—22no—
523#683—22no—
524#683—41no—
525#683—41no—
526#683—41no—
527#683—41no—
528#683—41no—
529#683—41no—
530#683—41no—
531#683—41no—
532#683—41no—
533#683—41no—
534#683—41no—
535#683—41no—
536#683—41no—
537#683—41no—
538#683—41no—
539#683—41no—
540#683—41no—
541#683C2×Q814yes—
542C4×Dic5—22no—
543C4×Dic5—22no—
544C4×Dic5—22no—
545C4×Dic5—22no—
546C4×Dic5—22no—
547C4×Dic5—22no—
548C4×Dic5—22no—
549C4×Dic5—41no—
550C4×Dic5—41no—
551C4×Dic5—41no—
552C4×Dic5—41no—
553C4×Dic5—41no—
554C4×Dic5C2×Q814yes—
555C2×C4⋊Q8—51no—
556C2×#125—51no—
557C2×#125—51no—
558C2×C22⋊Q8—51no—
559C2×C22⋊Q8—51no—
560C2×C22⋊Q8—51no—
561C2×C22⋊Q8—51no—
562C2×C22⋊Q8—51no—
563C2×C22⋊Q8C2×D511yescharacteristic
564C2×C4×Q8—51no—
565C2×C4×D4—51no—
566C2×C4×D4—51no—
567C2×C4×D4—51no—
568C22×C4⋊C4—51no—
569C22×C4⋊C4—51no—
570C22×C4⋊C4—51no—
571C22×C4⋊C4—51no—
572C22×C42—51no—
573C22×C42—51no—
574#400—51no—
575#400—51no—
576#400—51no—
577#400—51no—
578#399—51no—
579#399—51no—
580#399—51no—
581#399—51no—
582#398—51no—
583#398—51no—
584#398—51no—
585#398—51no—
586#398—51no—
587#398—51no—
588#398—51no—
589#398—51no—
590#398—51no—
591#398—51no—
592#398—51no—
593#398—51no—
594#398—51no—
595#398—51no—
596#398—51no—
597#398—51no—
598#396—51no—
599#396—51no—
600#396—51no—
601#396—51no—
602#395—51no—
603#395—51no—
604#395—51no—
605#395—51no—
606#391—51no—
607#391—51no—
608#391—51no—
609#391—51no—
610#391—51no—
611#391—51no—
612#391C2×D511yescharacteristic
613#391C2×D511yescharacteristic
614#389—51no—
615#389—51no—
616#389—51no—
617#389—51no—
618#389—51no—
619#389—51no—
620#389—51no—
621#389—51no—
622#389—51no—
623#389—51no—
624#389—51no—
625#389—51no—
626#389—51no—
627#389—51no—
628#389—51no—
629#389—51no—
630#389—51no—
631#389—51no—
632#389—51no—
633#389—51no—
634#389C2×D511yescharacteristic
635#389C2×D511yescharacteristic
636#388—51no—
637#388—51no—
638#388—51no—
639#388—51no—
640#387—51no—
641#387—51no—
642#387—51no—
643#387—51no—
644#387—51no—
645#387—51no—
646#387—51no—
647#387—51no—
648#387—51no—
649#387—51no—
650#387—51no—
651#387—51no—
652#387—51no—
653#387—51no—
654#387—51no—
655#387—51no—
656#387C2×D511yescharacteristic
657#387C2×D511yescharacteristic
658#387C2×D511yescharacteristic
659#387C2×D511yescharacteristic
660#386—51no—
661#386—51no—
662#386—51no—
663#386—51no—
664#385—51no—
665#385—51no—
666#385—51no—
667#385—51no—
668#385—51no—
669#385—51no—
670#385—51no—
671#385—51no—
672#385—51no—
673#385—51no—
674#385C2×D511yescharacteristic
675#385C2×D511yescharacteristic
676#384—51no—
677#384—51no—
678#384—51no—
679#383—51no—
680#383—51no—
681#382—51no—
682#382—51no—
683#381—51no—
684#381—51no—
685#380—51no—
686#380—51no—
687#380—51no—
688#380—51no—
689#380—51no—
690#380—51no—
691#380—51no—
692#380C2×D511yescharacteristic
693C4×C4⋊C4—51no—
694C4×C4⋊C4—51no—
695C4×C4⋊C4—51no—
696C4×C4⋊C4—51no—
697C4×C4⋊C4—51no—
698C4×C4⋊C4—51no—
699C4×C22⋊C4—51no—
700C4×C22⋊C4—51no—
701C4×C22⋊C4—51no—
702C4×C22⋊C4—51no—
703C4×C22⋊C4—51no—
704C4×C22⋊C4—51no—
705C4×C22⋊C4C2×D511yescharacteristic
706C4×C22⋊C4C2×D511yescharacteristic
707C2×#95—51no—
708C2×#95C2×D511yescharacteristic
709C43—51no—
710C23×C5—21no—
711C23×C5—21no—
712C23×C5—21no—
713C23×C5—21no—
714C23×C5C22×Q812yes—
715C23×C5C2×#4112yes—
716C23×C5C2×#4112yes—
717C23×C5C2511yescharacteristic
718C22×D5—21no—
719C22×D5—21no—
720C22×D5—21no—
721C22×D5—21no—
722C22×D5—21no—
723C22×D5—21no—
724C22×D5C22×Q812yes—
725C5×Q8—82no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—21no—
737C2×C4×C5—21no—
738C2×C4×C5—21no—
739C2×C4×C5—21no—
740C2×C4×C5—21no—
741C2×C4×C5—21no—
742C2×C4×C5—21no—
743C2×C4×C5—21no—
744C2×C4×C5—21no—
745C2×C4×C5—21no—
746C2×C4×C5—21no—
747C2×C4×C5—21no—
748C2×C4×C5—21no—
749C2×C4×C5—21no—
750C2×C4×C5—21no—
751C2×C4×C5—21no—
752C2×C4×C5—21no—
753C2×C4×C5—21no—
754C2×C4×C5—21no—
755C2×C4×C5—21no—
756C2×C4×C5—21no—
757C2×C4×C5—21no—
758C2×C4×C5—21no—
759C2×C4×C5—21no—
760C2×C4×C5—21no—
761C2×C4×C5—21no—
762C2×C4×C5—21no—
763C2×C4×C5—21no—
764C2×C4×C5—44no—
765C2×C4×C5—44no—
766C2×C4×C5—82no—
767C2×C4×C5C22×Q812yes—
768C2×C4×C5C22×Q812yes—
769C2×C4×C5C2×#4112yes—
770C2×C4×C5C2×#4112yes—
771C22⋊D5—28no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—28no—
783C2×Dic5—21no—
784C2×Dic5—21no—
785C2×Dic5—21no—
786C2×Dic5—21no—
787C2×Dic5—21no—
788C2×Dic5—21no—
789C2×Dic5—21no—
790C2×Dic5—21no—
791C2×Dic5—21no—
792C2×Dic5—21no—
793C2×Dic5—21no—
794C2×Dic5—21no—
795C2×Dic5—21no—
796C2×Dic5—21no—
797C2×Dic5—21no—
798C2×Dic5—21no—
799C2×Dic5—21no—
800C2×Dic5—21no—
801C2×Dic5—21no—
802C2×Dic5—21no—
803C2×Dic5—21no—
804C2×Dic5—21no—
805C2×Dic5—21no—
806C2×Dic5—21no—
807C2×Dic5—21no—
808C2×Dic5—21no—
809C2×Dic5—21no—
810C2×Dic5—44no—
811C2×Dic5—44no—
812C2×Dic5—82no—
813C2×Dic5C22×Q812yes—
814C2×Dic5C22×Q812yes—
815C2×Dic5C22×Q812yes—
816C2×Dic5C2×#4112yes—
817C2×Dic5C2×#4112yes—
818C2×Dic5H(5,𝔽2)12yes—
819C2×Dic5H(5,𝔽2)12yes—
820C2×Dic52−1+412yes—
821C4×D5—44no—
822C4×D5—44no—
823C4×D5—44no—
824Dic10—44no—
825Dic10—82no—
826C22×Q8—51no—
827C22×Q8—51no—
828C22×Q8C22×D511yescharacteristic
829C22×D4—51no—
830C23×C4—51no—
831C23×C4—51no—
832C23×C4—51no—
833C23×C4—51no—
834C23×C4—51no—
835C23×C4—51no—
836C23×C4—51no—
837C23×C4C22×D511yescharacteristic
838C23×C4C22×D511yescharacteristic
839C23×C4C22×D511yescharacteristic
840C4⋊Q8—202no—
841#125—202no—
842#125—202no—
843C22⋊Q8—24no—
844C22⋊Q8—104no—
845C22⋊Q8—104no—
846C22⋊Q8—202no—
847C22⋊Q8—202no—
848C22⋊Q8—202no—
849C4×Q8—202no—
850C4×D4—58no—
851C4×D4—104no—
852C4×D4—104no—
853C2×C4⋊C4—51no—
854C2×C4⋊C4—51no—
855C2×C4⋊C4—51no—
856C2×C4⋊C4—51no—
857C2×C4⋊C4—51no—
858C2×C4⋊C4—51no—
859C2×C4⋊C4—51no—
860C2×C4⋊C4—51no—
861C2×C4⋊C4—51no—
862C2×C4⋊C4—51no—
863C2×C4⋊C4—51no—
864C2×C4⋊C4—51no—
865C2×C4⋊C4—51no—
866C2×C4⋊C4—51no—
867C2×C4⋊C4—51no—
868C2×C4⋊C4—51no—
869C2×C4⋊C4—51no—
870C2×C4⋊C4—51no—
871C2×C4⋊C4—51no—
872C2×C4⋊C4—51no—
873C2×C4⋊C4—51no—
874C2×C4⋊C4—51no—
875C2×C4⋊C4—51no—
876C2×C4⋊C4—51no—
877C2×C4⋊C4—51no—
878C2×C4⋊C4—51no—
879C2×C4⋊C4—51no—
880C2×C4⋊C4—51no—
881C2×C4⋊C4—51no—
882C2×C4⋊C4—51no—
883C2×C4⋊C4—51no—
884C2×C4⋊C4—51no—
885C2×C4⋊C4—51no—
886C2×C4⋊C4—51no—
887C2×C4⋊C4—51no—
888C2×C4⋊C4—51no—
889C2×C4⋊C4—51no—
890C2×C4⋊C4—51no—
891C2×C4⋊C4—51no—
892C2×C4⋊C4—51no—
893C2×C4⋊C4—51no—
894C2×C4⋊C4—51no—
895C2×C4⋊C4—51no—
896C2×C4⋊C4—51no—
897C2×C4⋊C4—51no—
898C2×C4⋊C4—104no—
899C2×C4⋊C4—202no—
900C2×C4⋊C4—202no—
901C2×C4⋊C4—202no—
902C2×C4⋊C4C22×D511yescharacteristic
903C2×C4⋊C4C22×D511yescharacteristic
904C2×C4⋊C4C22×D511yescharacteristic
905C2×C4⋊C4C22×D511yescharacteristic
906C2×C4⋊C4C22×D511yescharacteristic
907C2×C4⋊C4C22×D511yescharacteristic
908C2×C4⋊C4C22×D511yescharacteristic
909C2×C4⋊C4C22×D511yescharacteristic
910C2×C4⋊C4C22×D511yescharacteristic
911C2×C22⋊C4—51no—
912C2×C22⋊C4—51no—
913C2×C22⋊C4—51no—
914C2×C22⋊C4—51no—
915C2×C22⋊C4—51no—
916C2×C22⋊C4—51no—
917C2×C22⋊C4—51no—
918C2×C22⋊C4—51no—
919C2×C22⋊C4—51no—
920C2×C22⋊C4—51no—
921C2×C22⋊C4—51no—
922C2×C22⋊C4—51no—
923C2×C22⋊C4—51no—
924C2×C22⋊C4—51no—
925C2×C22⋊C4C22×D511yescharacteristic
926C2×C22⋊C4C22×D511yescharacteristic
927C2×C22⋊C4C22×D511yescharacteristic
928C2×C22⋊C4C22×D511yescharacteristic
929C2×C42—51no—
930C2×C42—51no—
931C2×C42—51no—
932C2×C42—51no—
933C2×C42—51no—
934C2×C42—51no—
935C2×C42—51no—
936C2×C42—51no—
937C2×C42—51no—
938C2×C42—51no—
939C2×C42—51no—
940C2×C42—51no—
941C2×C42—51no—
942C2×C42—202no—
943C2×C42—202no—
944C2×C42C22×D511yescharacteristic
945C2×C42C22×D511yescharacteristic
946C2×C42C22×D511yescharacteristic
947C2×C42C22×D511yescharacteristic
948#95—51no—
949#95—51no—
950#95—51no—
951#95—51no—
952#95—51no—
953#95—51no—
954#95—51no—
955#95—51no—
956#95—51no—
957#95—51no—
958#95—51no—
959#95—51no—
960#95—51no—
961#95—51no—
962#95—51no—
963#95—51no—
964#95—51no—
965#95—51no—
966#95—51no—
967#95—51no—
968#95—51no—
969#95—51no—
970#95—51no—
971#95—51no—
972#95—51no—
973#95—51no—
974#95—51no—
975#95—51no—
976#95—51no—
977#95—51no—
978#95—51no—
979#95—51no—
980#95—51no—
981#95—51no—
982#95—51no—
983#95—51no—
984#95—51no—
985#95—51no—
986#95C22×D511yescharacteristic
987#95C22×D511yescharacteristic
988#95C22×D511yescharacteristic
989#95C22×D511yescharacteristic
990#95C22×D511yescharacteristic
991#95C22×D511yescharacteristic
992#95C22×D511yescharacteristic
993#95C22×D511yescharacteristic
994#95C22×D511yescharacteristic
995#95C22×D511yescharacteristic
996#95C22×D511yescharacteristic
997#95C22×D511yescharacteristic
998#95C22×D511yescharacteristic
999#95C22×D511yescharacteristic
1000C22×C5—22no—
1001C22×C5—22no—
1002C22×C5—22no—
1003C22×C5—22no—
1004C22×C5—22no—
1005C22×C5—22no—
1006C22×C5#53314yes—
1007C22×C5C23×Q811yescharacteristic
1008C22×C5C22×#4111yescharacteristic
1009C22×C5C22×#4111yescharacteristic
1010C22×C5C2×H(5,𝔽2)11yescharacteristic
1011C22×C5C2×H(5,𝔽2)11yescharacteristic
1012C22×C5C2×2−1+411yescharacteristic
1013C22×C5#58511yescharacteristic
1014C2×D5—22no—
1015C2×D5—22no—
1016C2×D5—22no—
1017C2×D5—41no—
1018C2×D5—41no—
1019C2×D5—41no—
1020C2×D5—41no—
1021C4×C5—22no—
1022C4×C5—22no—
1023C4×C5—22no—
1024C4×C5—22no—
1025C4×C5—41no—
1026C4×C5—41no—
1027C4×C5—41no—
1028C4×C5—41no—
1029C4×C5—41no—
1030C4×C5—41no—
1031C4×C5—41no—
1032C4×C5—41no—
1033C4×C5—41no—
1034C4×C5—41no—
1035Dic5—22no—
1036Dic5—22no—
1037Dic5—22no—
1038Dic5—22no—
1039Dic5—22no—
1040Dic5—41no—
1041Dic5—41no—
1042Dic5—41no—
1043Dic5—41no—
1044Dic5—41no—
1045Dic5—41no—
1046Dic5—41no—
1047Dic5—41no—
1048Dic5—41no—
1049Dic5#53914yes—
1050C24—51no—
1051C24C23×D511yescharacteristic
1052C2×Q8—22no—
1053C2×Q8—41no—
1054C2×Q8—41no—
1055C2×Q8—102no—
1056C2×Q8—102no—
1057C2×Q8—102no—
1058C2×Q8—102no—
1059C2×Q8—201no—
1060C2×Q8—201no—
1061C2×D4—54no—
1062C2×D4—102no—
1063C2×D4—102no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—51no—
1073C22×C4—54no—
1074C22×C4—51no—
1075C22×C4—51no—
1076C22×C4—51no—
1077C22×C4—51no—
1078C22×C4—51no—
1079C22×C4—54no—
1080C22×C4—51no—
1081C22×C4—51no—
1082C22×C4—51no—
1083C22×C4—51no—
1084C22×C4—51no—
1085C22×C4—51no—
1086C22×C4—51no—
1087C22×C4—51no—
1088C22×C4—51no—
1089C22×C4—102no—
1090C22×C4—102no—
1091C22×C4—102no—
1092C22×C4—102no—
1093C22×C4—102no—
1094C22×C4—102no—
1095C22×C4—102no—
1096C22×C4—102no—
1097C22×C4—102no—
1098C22×C4—102no—
1099C22×C4—102no—
1100C22×C4—201no—
1101C22×C4—201no—
1102C22×C4—201no—
1103C22×C4—201no—
1104C22×C4—201no—
1105C22×C4—201no—
1106C22×C4—201no—
1107C22×C4—201no—
1108C22×C4Q8×D514yes—
1109C22×C4C23×D511yescharacteristic
1110C22×C4C23×D511yescharacteristic
1111C22×C4C23×D511yescharacteristic
1112C22×C4C23×D511yescharacteristic
1113C22×C4C23×D511yescharacteristic
1114C22×C4C23×D511yescharacteristic
1115C22×C4C23×D511yescharacteristic
1116C22×C4C23×D511yescharacteristic
1117C22×C4C23×D511yescharacteristic
1118C22×C4C23×D511yescharacteristic
1119C22×C4C23×D511yescharacteristic
1120C22×C4C23×D511yescharacteristic
1121C22×C4C23×D511yescharacteristic
1122C22×C4C23×D511yescharacteristic
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—41no—
1132C4⋊C4—54no—
1133C4⋊C4—102no—
1134C4⋊C4—102no—
1135C4⋊C4—102no—
1136C4⋊C4—102no—
1137C4⋊C4—102no—
1138C4⋊C4—102no—
1139C4⋊C4—102no—
1140C4⋊C4—102no—
1141C4⋊C4—102no—
1142C4⋊C4—102no—
1143C4⋊C4—102no—
1144C4⋊C4—102no—
1145C4⋊C4—102no—
1146C4⋊C4—102no—
1147C4⋊C4—102no—
1148C4⋊C4—102no—
1149C4⋊C4—102no—
1150C4⋊C4—102no—
1151C4⋊C4—102no—
1152C4⋊C4—102no—
1153C4⋊C4—102no—
1154C4⋊C4—102no—
1155C4⋊C4—201no—
1156C4⋊C4—201no—
1157C4⋊C4—201no—
1158C4⋊C4—201no—
1159C4⋊C4—201no—
1160C4⋊C4—201no—
1161C4⋊C4—201no—
1162C4⋊C4—201no—
1163C4⋊C4—201no—
1164C4⋊C4—201no—
1165C4⋊C4—201no—
1166C4⋊C4—201no—
1167C4⋊C4—201no—
1168C4⋊C4—201no—
1169C4⋊C4—201no—
1170C4⋊C4—201no—
1171C4⋊C4—201no—
1172C4⋊C4—201no—
1173C4⋊C4—201no—
1174C4⋊C4—201no—
1175C4⋊C4—201no—
1176C4⋊C4—201no—
1177C22⋊C4—22no—
1178C22⋊C4—22no—
1179C22⋊C4—22no—
1180C22⋊C4—54no—
1181C22⋊C4—54no—
1182C22⋊C4—102no—
1183C22⋊C4—102no—
1184C22⋊C4—102no—
1185C22⋊C4—102no—
1186C22⋊C4—201no—
1187C22⋊C4—201no—
1188C22⋊C4—201no—
1189C22⋊C4—201no—
1190C22⋊C4—201no—
1191C22⋊C4—201no—
1192C22⋊C4—201no—
1193C22⋊C4—201no—
1194C22⋊C4#70914yes—
1195C42—41no—
1196C42—41no—
1197C42—41no—
1198C42—41no—
1199C42—54no—
1200C42—102no—
1201C42—102no—
1202C42—102no—
1203C42—102no—
1204C42—102no—
1205C42—102no—
1206C42—102no—
1207C42—201no—
1208C42—201no—
1209C42—201no—
1210C42—201no—
1211C42—201no—
1212C2×C5—24no—
1213C2×C5C2×#53311yescharacteristic
1214C2×C5C2×#53911yescharacteristic
1215C2×C5#346011yescharacteristic
1216C2×C5#350111yescharacteristic
1217C2×C5#350311yescharacteristic
1218C2×C5#351511yescharacteristic
1219C2×C5#351911yescharacteristic
1220D5—42no—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—21no—
1225C23—52no—
1226C23—101no—
1227C23—101no—
1228C23—101no—
1229C23—101no—
1230C23—101no—
1231C23—101no—
1232C23C2×#70912yes—
1233C23C2×Q8×D512yes—
1234C23D5×#4112yes—
1235C23C24×D511yescharacteristic
1236Q8—82no—
1237Q8—204no—
1238Q8—402no—
1239D4—108no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—44no—
1279C2×C4—44no—
1280C2×C4—52no—
1281C2×C4—52no—
1282C2×C4—52no—
1283C2×C4—52no—
1284C2×C4—52no—
1285C2×C4—52no—
1286C2×C4—52no—
1287C2×C4—52no—
1288C2×C4—82no—
1289C2×C4—108no—
1290C2×C4—101no—
1291C2×C4—101no—
1292C2×C4—101no—
1293C2×C4—101no—
1294C2×C4—101no—
1295C2×C4—101no—
1296C2×C4—101no—
1297C2×C4—101no—
1298C2×C4—101no—
1299C2×C4—101no—
1300C2×C4—101no—
1301C2×C4—101no—
1302C2×C4—101no—
1303C2×C4—101no—
1304C2×C4—101no—
1305C2×C4—101no—
1306C2×C4—101no—
1307C2×C4—101no—
1308C2×C4—101no—
1309C2×C4—101no—
1310C2×C4—101no—
1311C2×C4—101no—
1312C2×C4—101no—
1313C2×C4—101no—
1314C2×C4—101no—
1315C2×C4—101no—
1316C2×C4—101no—
1317C2×C4—101no—
1318C2×C4—101no—
1319C2×C4—101no—
1320C2×C4—101no—
1321C2×C4—101no—
1322C2×C4—101no—
1323C2×C4—101no—
1324C2×C4—101no—
1325C2×C4—101no—
1326C2×C4—101no—
1327C2×C4—204no—
1328C2×C4—204no—
1329C2×C4—204no—
1330C2×C4—204no—
1331C2×C4—204no—
1332C2×C4—402no—
1333C2×C4C2×#70912yes—
1334C2×C4C2×#70912yes—
1335C2×C4C2×Q8×D512yes—
1336C2×C4C2×Q8×D512yes—
1337C5#3501711yescharacteristic, complemented, Sylow
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—22no—
1344C22—102no—
1345C22—102no—
1346C22—102no—
1347C22—201no—
1348C22—201no—
1349C22—201no—
1350C22—201no—
1351C22#6591214yes—
1352C22C22×#70911yescharacteristic
1353C22C22×Q8×D511yescharacteristic
1354C22C2×D5×#4111yescharacteristic
1355C22D5×H(5,𝔽2)11yescharacteristic
1356C22D5×H(5,𝔽2)11yescharacteristic
1357C22#6628511yescharacteristic
1358C22D5×2−1+411yescharacteristic
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—54no—
1374C4—102no—
1375C4—102no—
1376C4—102no—
1377C4—102no—
1378C4—102no—
1379C4—201no—
1380C4—201no—
1381C4—201no—
1382C4—201no—
1383C4—201no—
1384C4—201no—
1385C4—201no—
1386C4—201no—
1387C4—201no—
1388C2—24no—
1389C2—202no—
1390C2C2×#6591211yescharacteristic
1391C2#1061777211yescharacteristic
1392C2#1061779611yescharacteristic
1393C2#1061829011yescharacteristic
1394C2D5×#53911yescharacteristic
1395C2#1061847511yescharacteristic
1396C2#1061848711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2329C2
prime radicalC22×C22⋊D5C23
hypercenter#2329D5
hypocenterC5#35017
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2329

Complements

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

NH ≅ G/Ntype
1. C5×#2329C2semidirect
3. #10614494C2semidirect
4. #10608395C2semidirect
5. #10608293C2semidirect
6. #10608269C2semidirect
7. #10608241C2semidirect
8. #10607987C2semidirect
9. #10607921C2semidirect
10. #10607799C2semidirect
11. #10607767C2semidirect
12. #10607179C2semidirect
13. #10607022C2semidirect
14. #10606879C2semidirect
15. #10606878C2semidirect
16. #10606825C2semidirect
17. #10606823C2semidirect
18. #10606755C2semidirect
19. #10606713C2semidirect
20. #10606191C2semidirect
22. #10606172C2semidirect
24. #10605639C2semidirect
27. #10605178C2semidirect
28. C4×#4024C2semidirect
31. C2×#64936C2semidirect
225. C4×C22⋊D5Q8semidirect
387. #2329D5semidirect
1337. C5#35017semidirect

Maximal subgroups

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

subgroupindex
C5×#23292
#106144952
#106144942
#106083952
#106082932
#106082692
#106082412
#106079872
#106079212
#106077992
#106077672
#106071792
#106070222
#106068792
#106068782
#106068252
#106068232
#106067552
#106067132
#106061912
#106061882
#106061722
#106061532
#106056392
#106056202
#106052992
#106051782
C4×#40242
C4×#40272
#106050982
C2×#649362
#350175