Finite Group Databasebeta

← #12307056

Subgroups — #12307056

Order 1280.

1588 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2790C211yesmaximal, characteristic, complemented
2#10610009C211yesmaximal, characteristic, complemented
3#10609965C211yesmaximal, characteristic, complemented
4#10609735C211yesmaximal, characteristic, complemented
5#10609650C211yesmaximal, characteristic, complemented
6#10609583C211yesmaximal, characteristic, complemented
7#10609576C211yesmaximal, characteristic, complemented
8#10609548C211yesmaximal, characteristic, complemented
9#10609544C211yesmaximal, characteristic, complemented
10#10609176C211yesmaximal, characteristic
11#10609164C211yesmaximal, characteristic
12#10609060C211yesmaximal, characteristic, complemented
13#10609019C211yesmaximal, characteristic, complemented
14#10607875C211yesmaximal, characteristic, complemented
15#10607792C211yesmaximal, characteristic, complemented
16#10607437C211yesmaximal, characteristic, complemented
17#10607437C211yesmaximal, characteristic, complemented
18#10607189C211yesmaximal, characteristic
19#10607180C211yesmaximal, characteristic
20#10607179C211yesmaximal, characteristic, complemented
21#10607121C211yesmaximal, characteristic, complemented
22#10606910C211yesmaximal, characteristic, complemented
23#10606859C211yesmaximal, characteristic, complemented
24#10606300C211yesmaximal, characteristic
25#10606254C211yesmaximal, characteristic, complemented
26#10606247C211yesmaximal, characteristic
27#10606203C211yesmaximal, characteristic, complemented
28#10606146C211yesmaximal, characteristic, complemented
29#10606114C211yesmaximal, characteristic
30#10606107C211yesmaximal, characteristic, complemented
31#10606081C211yesmaximal, characteristic, complemented
32C2×#4070C2211yescharacteristic
33C2×#4043C2211yescharacteristic
34C2×#4043C2211yescharacteristic
35C2×#4042C2211yescharacteristic
36C2×#4036C2211yescharacteristic
37C2×#4034C2211yescharacteristic
38C2×#4027C2211yescharacteristic
39C2×#4024C2211yescharacteristic
40C2×#4024C2211yescharacteristic
41C2×#4023C2211yescharacteristic
42C2×C42×D5C2211yescharacteristic
43C2×#4015C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C5×#400C2211yescharacteristic
46C5×#398C2211yescharacteristic
47C5×#398C2211yescharacteristic
48C5×#398C2211yescharacteristic
49C5×#396C2211yescharacteristic
50C5×#396C2211yescharacteristic
51C5×#389C2211yescharacteristic
52C5×#388C2211yescharacteristic
53C5×#388C2211yescharacteristic
54C5×#387C2211yescharacteristic
55C5×#387C2211yescharacteristic
56C5×#385C2211yescharacteristic
57C5×#385C2211yescharacteristic
58C5×#385C2211yescharacteristic
59C5×#384C2211yescharacteristic
60#65502C2211yescharacteristic
61#65501C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63#65283C2211yescharacteristic
64#65283C2211yescharacteristic
65#65283C2211yescharacteristic
66#65281C2211yescharacteristic
67#65279C2211yescharacteristic
68#65278C2211yescharacteristic
69#65278C2211yescharacteristic
70#65276C2211yescharacteristic
71#65276C2211yescharacteristic
72#65276C2211yescharacteristic
73#65276C2211yescharacteristic
74#65274C2211yescharacteristic
75#65274C2211yescharacteristic
76#65274C2211yescharacteristic
77#65274C2211yescharacteristic
78#65274C2211yescharacteristic
79#65274C2211yescharacteristic
80#65274C2211yescharacteristic
81#65273C2211yescharacteristic
82#65273C2211yescharacteristic
83#65273C2211yescharacteristic
84#65273C2211yescharacteristic
85#65273C2211yescharacteristic
86#65273C2211yescharacteristic
87#65272C2211yescharacteristic
88#65272C2211yescharacteristic
89#65270C2211yescharacteristic
90#65270C2211yescharacteristic
91#65270C2211yescharacteristic
92#65270C2211yescharacteristic
93#65268C2211yescharacteristic
94#65268C2211yescharacteristic
95#65268C2211yescharacteristic
96#65268C2211yescharacteristic
97#65267C2211yescharacteristic
98#65267C2211yescharacteristic
99#65267C2211yescharacteristic
100#65267C2211yescharacteristic
101#65266C2211yescharacteristic
102C4⋊C4×Dic5C2211yescharacteristic
103#65263C2211yescharacteristic
104#65263C2211yescharacteristic
105#65262C2211yescharacteristic
106#65262C2211yescharacteristic
107#65262C2211yescharacteristic
108#65261C2211yescharacteristic
109#65261C2211yescharacteristic
110#65261C2211yescharacteristic
111#65261C2211yescharacteristic
112#65261C2211yescharacteristic
113#65261C2211yescharacteristic
114#65247C2211yescharacteristic
115#65246C2211yescharacteristic
116#65246C2211yescharacteristic
117#65245C2211yescharacteristic
118#65245C2211yescharacteristic
119#65240C2211yescharacteristic
120#65240C2211yescharacteristic
121#65239C2211yescharacteristic
122#65239C2211yescharacteristic
123#65239C2211yescharacteristic
124#65237C2211yescharacteristic
125#65237C2211yescharacteristic
126#65237C2211yescharacteristic
127#65237C2211yescharacteristic
128#65236C2211yescharacteristic
129#65236C2211yescharacteristic
130#65232C2211yescharacteristic
131#65231C2211yescharacteristic
132C22⋊C4×Dic5C2211yescharacteristic
133C22⋊C4×Dic5C2211yescharacteristic
134#65229C2211yescharacteristic
135#65222C2211yescharacteristic
136#65222C2211yescharacteristic
137#65222C2211yescharacteristic
138C4×#683C2211yescharacteristic
139#64966C2211yescharacteristic
140#64965C2211yescharacteristic
141#64962C2211yescharacteristic
142#64962C2211yescharacteristic
143#64959C2211yescharacteristic
144#64958C2211yescharacteristic
145#64957C2211yescharacteristic
146#64957C2211yescharacteristic
147#64956C2211yescharacteristic
148#64955C2211yescharacteristic
149#64953C2211yescharacteristic
150#64953C2211yescharacteristic
151#64950C2211yescharacteristic
152#64950C2211yescharacteristic
153#64950C2211yescharacteristic
154#64950C2211yescharacteristic
155#64949C2211yescharacteristic
156#64949C2211yescharacteristic
157#64948C2211yescharacteristic
158#64947C2211yescharacteristic
159#64947C2211yescharacteristic
160#64946C2211yescharacteristic
161#64945C2211yescharacteristic
162#64945C2211yescharacteristic
163#64945C2211yescharacteristic
164#64945C2211yescharacteristic
165#64945C2211yescharacteristic
166#64945C2211yescharacteristic
167#64944C2211yescharacteristic
168#64942C2211yescharacteristic
169#64942C2211yescharacteristic
170#64942C2211yescharacteristic
171#64942C2211yescharacteristic
172#64941C2211yescharacteristic
173#64941C2211yescharacteristic
174#64940C2211yescharacteristic
175#64939C2211yescharacteristic
176#64937C2211yescharacteristic
177#64937C2211yescharacteristic
178#64936C2211yescharacteristic
179#64936C2211yescharacteristic
180#64935C2211yescharacteristic
181#64935C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36754—51nomaximal, Sylow
188C23×C4×C5C2311yescharacteristic
189C22×C22⋊D5C2311yescharacteristic
190C23×Dic5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C22×Dic10C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C22×Dic10C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
213C2×C5×C4⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C5×C22⋊C4C2311yescharacteristic
218C2×C5×C22⋊C4C2311yescharacteristic
219C2×C5×C22⋊C4C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
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×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
250C2×C4⋊Dic5C2311yescharacteristic
251C2×C4⋊Dic5C2311yescharacteristic
252C2×C4⋊Dic5C2311yescharacteristic
253C2×C4⋊Dic5C2311yescharacteristic
254C2×C4⋊Dic5C2311yescharacteristic
255#4070—42no—
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×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287C2×C4×Dic5C2311yescharacteristic
288#4043—42no—
289#4043—42no—
290#4042—42no—
291#4036—42no—
292#4034—42no—
293#4027Q818yescomplemented
294#4024—42no—
295#4024—42no—
296#4023—42no—
297C42×D5—42no—
298#4015—42no—
299#4015—42no—
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308C5×#95C2311yescharacteristic
309C5×#95C2311yescharacteristic
310C5×#95C2311yescharacteristic
311C5×#95C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
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#2857—51no—
357#2855—51no—
358#2802—51no—
359#2792—51no—
360#2790D511yescharacteristic, complemented
361#2788—51no—
362#2784—51no—
363#2780—51no—
364#2774—51no—
365#2768—51no—
366#2734—51no—
367#2729—51no—
368#2729—51no—
369#2704—51no—
370#2704—51no—
371#2692—51no—
372#2683—51no—
373#2677—51no—
374#2667—51no—
375#2665—51no—
376#2612—51no—
377#2608—51no—
378#2606—51no—
379#2605—51no—
380#2550—51no—
381#2549—51no—
382#2439—51no—
383#2438—51no—
384#2319—51no—
385#2318—51no—
386#2290—51no—
387C24×C5C2411yescharacteristic
388C23×D5C2411yescharacteristic
389C22×C4×C5—41no—
390C22×C4×C5—41no—
391C22×C4×C5—41no—
392C22×C4×C5C2411yescharacteristic
393C22×C4×C5C2411yescharacteristic
394C22×C4×C5C2411yescharacteristic
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C2×C22⋊D5—41no—
407C2×C22⋊D5—41no—
408C2×C22⋊D5C2×Q814yes—
409C22×Dic5—41no—
410C22×Dic5—41no—
411C22×Dic5—41no—
412C22×Dic5—41no—
413C22×Dic5—41no—
414C22×Dic5C2×Q814yes—
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C2×C4×D5—22no—
431C2×C4×D5—22no—
432C2×C4×D5—22no—
433C2×C4×D5—41no—
434C2×C4×D5—41no—
435C2×C4×D5—41no—
436C2×C4×D5—41no—
437C2×C4×D5—41no—
438C2×C4×D5C2×Q814yes—
439C2×Dic10—22no—
440C2×Dic10—22no—
441C2×Dic10—22no—
442C2×Dic10—41no—
443C2×Dic10—41no—
444C2×Dic10—41no—
445C2×Dic10—41no—
446C2×Dic10—41no—
447C2×Dic10—41no—
448C2×Dic10—41no—
449C2×Dic10—41no—
450C2×Dic10—41no—
451C2×Dic10—41no—
452C2×Dic10—41no—
453C2×Dic10—41no—
454C5×C4⋊C4—22no—
455C5×C4⋊C4—22no—
456C5×C4⋊C4—22no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C4⋊C4—41no—
461C5×C4⋊C4—41no—
462C5×C4⋊C4—41no—
463C5×C4⋊C4—41no—
464C5×C4⋊C4—41no—
465C5×C4⋊C4—41no—
466C5×C4⋊C4—41no—
467C5×C4⋊C4—41no—
468C5×C22⋊C4—22no—
469C5×C22⋊C4—22no—
470C5×C22⋊C4—41no—
471C5×C22⋊C4—41no—
472C5×C22⋊C4—41no—
473C5×C22⋊C4C2×Q814yes—
474C42×C5—22no—
475C42×C5—41no—
476C22⋊Dic5—22no—
477C22⋊Dic5—41no—
478C22⋊Dic5—41no—
479C22⋊Dic5—41no—
480C22⋊Dic5—41no—
481#685—41no—
482#685—41no—
483#685—41no—
484#685—41no—
485#685—41no—
486#685—41no—
487#685—41no—
488#685—41no—
489#685—41no—
490#685—41no—
491#685C2×Q814yes—
492C4⋊Dic5—22no—
493C4⋊Dic5—22no—
494C4⋊Dic5—22no—
495C4⋊Dic5—22no—
496C4⋊Dic5—22no—
497C4⋊Dic5—41no—
498C4⋊Dic5—41no—
499C4⋊Dic5—41no—
500C4⋊Dic5—41no—
501C4⋊Dic5—41no—
502C4⋊Dic5—41no—
503C4⋊Dic5—41no—
504C4⋊Dic5—41no—
505C4⋊Dic5—41no—
506C4⋊Dic5—41no—
507C4⋊Dic5—41no—
508C4⋊Dic5—41no—
509#683—22no—
510#683—22no—
511#683—22no—
512#683—22no—
513#683—41no—
514#683—41no—
515#683—41no—
516#683—41no—
517#683—41no—
518#683—41no—
519#683—41no—
520#683—41no—
521#683—41no—
522#683—41no—
523#683—41no—
524#683—41no—
525#683—41no—
526#683—41no—
527#683—41no—
528#683—41no—
529#683C2×Q814yes—
530C4×Dic5—22no—
531C4×Dic5—41no—
532C4×Dic5—41no—
533C4×Dic5—41no—
534C4×Dic5—41no—
535C4×Dic5—41no—
536C4×Dic5—41no—
537C4×Dic5—41no—
538C4×Dic5—41no—
539C4×Dic5—41no—
540C4×Dic5C2×Q814yes—
541C2×C4⋊Q8—51no—
542C2×C4⋊Q8—51no—
543C2×C4⋊Q8—51no—
544C2×#125—51no—
545C2×C22⋊Q8—51no—
546C2×C22⋊Q8—51no—
547C2×C22⋊Q8—51no—
548C2×C22⋊Q8—51no—
549C2×C22⋊Q8—51no—
550C2×C22⋊Q8—51no—
551C2×C4×D4—51no—
552C2×#117—51no—
553C22×C42—51no—
554#400—51no—
555#400—51no—
556#400—51no—
557#400—51no—
558#400—51no—
559#400C2×D511yescharacteristic
560#399—51no—
561#399—51no—
562#398—51no—
563#398—51no—
564#398—51no—
565#398—51no—
566#398—51no—
567#398—51no—
568#398—51no—
569#398—51no—
570#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398C2×D511yescharacteristic
576#398C2×D511yescharacteristic
577#398C2×D511yescharacteristic
578#396—51no—
579#396—51no—
580#396—51no—
581#396—51no—
582#396—51no—
583#396—51no—
584#396—51no—
585#396—51no—
586#396C2×D511yescharacteristic
587#396C2×D511yescharacteristic
588#395—51no—
589#395—51no—
590#395—51no—
591#395—51no—
592#395—51no—
593#395—51no—
594#395—51no—
595#395—51no—
596#395—51no—
597#395—51no—
598#393—51no—
599#393—51no—
600#393—51no—
601#393—51no—
602#391—51no—
603#391—51no—
604#391—51no—
605#391—51no—
606#391—51no—
607#391—51no—
608#391—51no—
609#391—51no—
610#391—51no—
611#390—51no—
612#390—51no—
613#389—51no—
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#389C2×D511yescharacteristic
632#388—51no—
633#388—51no—
634#388—51no—
635#388—51no—
636#388—51no—
637#388—51no—
638#388C2×D511yescharacteristic
639#388C2×D511yescharacteristic
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#387—51no—
657#387—51no—
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#385C2×D511yescharacteristic
672#385C2×D511yescharacteristic
673#385C2×D511yescharacteristic
674#384C2×D511yescharacteristic
675#383—51no—
676#382—51no—
677#382—51no—
678#381—51no—
679#381—51no—
680#381—51no—
681#380—51no—
682#380—51no—
683#380—51no—
684#380—51no—
685#380—51no—
686#380—51no—
687#380—51no—
688C4×C4⋊C4—51no—
689C4×C4⋊C4—51no—
690C4×C22⋊C4—51no—
691C4×C22⋊C4—51no—
692C4×C22⋊C4—51no—
693#376—51no—
694#376—51no—
695C2×#95—51no—
696C23×C5—21no—
697C23×C5—21no—
698C23×C5—21no—
699C23×C5—21no—
700C23×C5—21no—
701C23×C5—21no—
702C23×C5C22×Q812yes—
703C23×C5C2511yescharacteristic
704C22×D5—21no—
705C22×D5—21no—
706C22×D5—21no—
707C22×D5—21no—
708C22×D5—21no—
709C22×D5—21no—
710C22×D5C22×Q812yes—
711C2×C4×C5—21no—
712C2×C4×C5—21no—
713C2×C4×C5—21no—
714C2×C4×C5—21no—
715C2×C4×C5—21no—
716C2×C4×C5—21no—
717C2×C4×C5—21no—
718C2×C4×C5—21no—
719C2×C4×C5—21no—
720C2×C4×C5—21no—
721C2×C4×C5—21no—
722C2×C4×C5—21no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
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—82no—
750C2×C4×C5C22×Q812yes—
751C2×C4×C5C22×Q812yes—
752C2×C4×C5H(5,𝔽2)12yes—
753C2×C4×C52−1+412yes—
754C22⋊D5—44no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
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—21no—
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—44no—
797C2×Dic5—82no—
798C2×Dic5C22×Q812yes—
799C2×Dic5C22×Q812yes—
800C2×Dic5C22×Q812yes—
801C2×Dic5H(5,𝔽2)12yes—
802C4×D5—44no—
803C4×D5—44no—
804C4×D5—44no—
805Dic10—82no—
806Dic10—82no—
807Dic10—82no—
808Dic10—82no—
809Dic10—82no—
810C22×Q8—51no—
811C22×Q8—51no—
812C22×Q8—51no—
813C22×Q8—51no—
814C22×Q8—51no—
815C22×D4—51no—
816C23×C4—51no—
817C23×C4—51no—
818C23×C4—51no—
819C23×C4—51no—
820C23×C4—51no—
821C23×C4C22×D511yescharacteristic
822C4⋊Q8—202no—
823C4⋊Q8—202no—
824C4⋊Q8—202no—
825#125—202no—
826C22⋊Q8—202no—
827C22⋊Q8—202no—
828C22⋊Q8—202no—
829C22⋊Q8—202no—
830C22⋊Q8—202no—
831C22⋊Q8—202no—
832C4×D4—58no—
833#117—202no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—51no—
836C2×C4⋊C4—51no—
837C2×C4⋊C4—51no—
838C2×C4⋊C4—51no—
839C2×C4⋊C4—51no—
840C2×C4⋊C4—51no—
841C2×C4⋊C4—51no—
842C2×C4⋊C4—51no—
843C2×C4⋊C4—51no—
844C2×C4⋊C4—51no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4—51no—
847C2×C4⋊C4—51no—
848C2×C4⋊C4—51no—
849C2×C4⋊C4—51no—
850C2×C4⋊C4—51no—
851C2×C4⋊C4—51no—
852C2×C4⋊C4—51no—
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⋊C4C22×D511yescharacteristic
873C2×C4⋊C4C22×D511yescharacteristic
874C2×C4⋊C4C22×D511yescharacteristic
875C2×C4⋊C4C22×D511yescharacteristic
876C2×C4⋊C4C22×D511yescharacteristic
877C2×C4⋊C4C22×D511yescharacteristic
878C2×C4⋊C4C22×D511yescharacteristic
879C2×C4⋊C4C22×D511yescharacteristic
880C2×C4⋊C4C22×D511yescharacteristic
881C2×C4⋊C4C22×D511yescharacteristic
882C2×C4⋊C4C22×D511yescharacteristic
883C2×C4⋊C4C22×D511yescharacteristic
884C2×C4⋊C4C22×D511yescharacteristic
885C2×C4⋊C4C22×D511yescharacteristic
886C2×C22⋊C4—51no—
887C2×C22⋊C4—51no—
888C2×C22⋊C4—51no—
889C2×C22⋊C4—51no—
890C2×C22⋊C4—51no—
891C2×C22⋊C4—51no—
892C2×C22⋊C4—51no—
893C2×C22⋊C4—51no—
894C2×C22⋊C4—51no—
895C2×C22⋊C4—51no—
896C2×C22⋊C4—51no—
897C2×C22⋊C4—51no—
898C2×C22⋊C4—51no—
899C2×C22⋊C4—51no—
900C2×C22⋊C4—51no—
901C2×C22⋊C4—51no—
902C2×C22⋊C4C22×D511yescharacteristic
903C2×C22⋊C4C22×D511yescharacteristic
904C2×C22⋊C4C22×D511yescharacteristic
905C2×C22⋊C4C22×D511yescharacteristic
906C2×C22⋊C4C22×D511yescharacteristic
907C2×C22⋊C4C22×D511yescharacteristic
908C2×C42—51no—
909C2×C42—51no—
910C2×C42—51no—
911C2×C42—51no—
912C2×C42—51no—
913C2×C42—51no—
914C2×C42—51no—
915C2×C42—51no—
916C2×C42—51no—
917C2×C42—51no—
918C2×C42—51no—
919C2×C42—202no—
920C2×C42C22×D511yescharacteristic
921C2×C42C22×D511yescharacteristic
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95—51no—
947#95—51no—
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#95C22×D511yescharacteristic
967#95C22×D511yescharacteristic
968#95C22×D511yescharacteristic
969#95C22×D511yescharacteristic
970#95C22×D511yescharacteristic
971#95C22×D511yescharacteristic
972#95C22×D511yescharacteristic
973#95C22×D511yescharacteristic
974#95C22×D511yescharacteristic
975#95C22×D511yescharacteristic
976#95C22×D511yescharacteristic
977#95C22×D511yescharacteristic
978C22×C5—22no—
979C22×C5—22no—
980C22×C5—22no—
981C22×C5—41no—
982C22×C5—41no—
983C22×C5—41no—
984C22×C5—41no—
985C22×C5C23×Q811yescharacteristic
986C22×C5C2×H(5,𝔽2)11yescharacteristic
987C22×C5C2×H(5,𝔽2)11yescharacteristic
988C22×C5C2×2−1+411yescharacteristic
989C22×C5#58511yescharacteristic
990C22×C5#58511yescharacteristic
991C22×C5#58511yescharacteristic
992C2×D5—22no—
993C2×D5—22no—
994C2×D5—22no—
995C2×D5—41no—
996C2×D5—41no—
997C2×D5—41no—
998C2×D5—41no—
999C4×C5—22no—
1000C4×C5—22no—
1001C4×C5—22no—
1002C4×C5—22no—
1003C4×C5—41no—
1004C4×C5—41no—
1005C4×C5—41no—
1006C4×C5—41no—
1007C4×C5—41no—
1008C4×C5—41no—
1009C4×C5—41no—
1010C4×C5—41no—
1011C4×C5—41no—
1012C4×C5—41no—
1013Dic5—22no—
1014Dic5—22no—
1015Dic5—22no—
1016Dic5—22no—
1017Dic5—41no—
1018Dic5—41no—
1019Dic5—41no—
1020Dic5—41no—
1021Dic5—41no—
1022Dic5—41no—
1023Dic5—41no—
1024Dic5—41no—
1025Dic5—41no—
1026Dic5—41no—
1027Dic5—41no—
1028C24—51no—
1029C24C23×D511yescharacteristic
1030C2×Q8—102no—
1031C2×Q8—102no—
1032C2×Q8—102no—
1033C2×Q8—201no—
1034C2×Q8—201no—
1035C2×Q8—201no—
1036C2×Q8—201no—
1037C2×Q8—201no—
1038C2×Q8—201no—
1039C2×Q8—201no—
1040C2×Q8—201no—
1041C2×Q8—201no—
1042C2×Q8—201no—
1043C2×Q8—201no—
1044C2×Q8—201no—
1045C2×D4—54no—
1046C2×D4—201no—
1047C2×D4—201no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—51no—
1052C22×C4—51no—
1053C22×C4—51no—
1054C22×C4—51no—
1055C22×C4—54no—
1056C22×C4—54no—
1057C22×C4—51no—
1058C22×C4—51no—
1059C22×C4—51no—
1060C22×C4—51no—
1061C22×C4—51no—
1062C22×C4—51no—
1063C22×C4—51no—
1064C22×C4—51no—
1065C22×C4—51no—
1066C22×C4—51no—
1067C22×C4—51no—
1068C22×C4—102no—
1069C22×C4—102no—
1070C22×C4—102no—
1071C22×C4—201no—
1072C22×C4—201no—
1073C22×C4—201no—
1074C22×C4—201no—
1075C22×C4—201no—
1076C22×C4—201no—
1077C22×C4—201no—
1078C22×C4—201no—
1079C22×C4—201no—
1080C22×C4—201no—
1081C22×C4C23×D511yescharacteristic
1082C22×C4C23×D511yescharacteristic
1083C22×C4C23×D511yescharacteristic
1084C22×C4C23×D511yescharacteristic
1085C22×C4C23×D511yescharacteristic
1086C22×C4C23×D511yescharacteristic
1087C22×C4C23×D511yescharacteristic
1088C22×C4C23×D511yescharacteristic
1089C22×C4C23×D511yescharacteristic
1090C22×C4C23×D511yescharacteristic
1091C22×C4C23×D511yescharacteristic
1092C22×C4C23×D511yescharacteristic
1093C22×C4C23×D511yescharacteristic
1094C22×C4C23×D511yescharacteristic
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
1106C4⋊C4—41no—
1107C4⋊C4—41no—
1108C4⋊C4—41no—
1109C4⋊C4—54no—
1110C4⋊C4—102no—
1111C4⋊C4—102no—
1112C4⋊C4—102no—
1113C4⋊C4—102no—
1114C4⋊C4—102no—
1115C4⋊C4—102no—
1116C4⋊C4—102no—
1117C4⋊C4—102no—
1118C4⋊C4—102no—
1119C4⋊C4—201no—
1120C4⋊C4—201no—
1121C4⋊C4—201no—
1122C4⋊C4—201no—
1123C4⋊C4—201no—
1124C4⋊C4—201no—
1125C4⋊C4—201no—
1126C4⋊C4—201no—
1127C4⋊C4—201no—
1128C4⋊C4—201no—
1129C4⋊C4—201no—
1130C4⋊C4—201no—
1131C4⋊C4—201no—
1132C4⋊C4—201no—
1133C4⋊C4—201no—
1134C4⋊C4—201no—
1135C4⋊C4—201no—
1136C4⋊C4—201no—
1137C4⋊C4—201no—
1138C4⋊C4—201no—
1139C4⋊C4—201no—
1140C4⋊C4—201no—
1141C4⋊C4—201no—
1142C4⋊C4—201no—
1143C4⋊C4—201no—
1144C4⋊C4—201no—
1145C4⋊C4—201no—
1146C4⋊C4—201no—
1147C22⋊C4—22no—
1148C22⋊C4—22no—
1149C22⋊C4—41no—
1150C22⋊C4—41no—
1151C22⋊C4—41no—
1152C22⋊C4—54no—
1153C22⋊C4—102no—
1154C22⋊C4—201no—
1155C22⋊C4—201no—
1156C22⋊C4—201no—
1157C22⋊C4—201no—
1158C22⋊C4—201no—
1159C22⋊C4—201no—
1160C22⋊C4—201no—
1161C22⋊C4—201no—
1162C22⋊C4—201no—
1163C22⋊C4—201no—
1164C22⋊C4—201no—
1165C22⋊C4—201no—
1166C22⋊C4—201no—
1167C22⋊C4—201no—
1168C22⋊C4Q8×D514yes—
1169C42—22no—
1170C42—41no—
1171C42—54no—
1172C42—102no—
1173C42—201no—
1174C42—201no—
1175C42—201no—
1176C42—201no—
1177C42—201no—
1178C42—201no—
1179C42—201no—
1180C42—201no—
1181C42—201no—
1182C2×C5—42no—
1183C2×C5#345811yescharacteristic
1184C2×C5#350111yescharacteristic
1185C2×C5#350311yescharacteristic
1186C2×C5#353411yescharacteristic
1187C2×C5#354111yescharacteristic
1188C2×C5#355111yescharacteristic
1189C2×C5#356511yescharacteristic
1190D5—42no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—52no—
1198C23—101no—
1199C23—101no—
1200C23—101no—
1201C23—101no—
1202C23—101no—
1203C23—101no—
1204C23C2×Q8×D512yes—
1205C23C24×D511yescharacteristic
1206Q8—402no—
1207Q8—402no—
1208Q8—402no—
1209Q8—402no—
1210Q8—402no—
1211D4—204no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
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—52no—
1251C2×C4—52no—
1252C2×C4—52no—
1253C2×C4—52no—
1254C2×C4—82no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—101no—
1262C2×C4—101no—
1263C2×C4—101no—
1264C2×C4—101no—
1265C2×C4—101no—
1266C2×C4—101no—
1267C2×C4—101no—
1268C2×C4—101no—
1269C2×C4—101no—
1270C2×C4—101no—
1271C2×C4—101no—
1272C2×C4—101no—
1273C2×C4—101no—
1274C2×C4—101no—
1275C2×C4—101no—
1276C2×C4—101no—
1277C2×C4—101no—
1278C2×C4—101no—
1279C2×C4—101no—
1280C2×C4—101no—
1281C2×C4—101no—
1282C2×C4—101no—
1283C2×C4—101no—
1284C2×C4—101no—
1285C2×C4—101no—
1286C2×C4—101no—
1287C2×C4—101no—
1288C2×C4—101no—
1289C2×C4—101no—
1290C2×C4—101no—
1291C2×C4—101no—
1292C2×C4—101no—
1293C2×C4—101no—
1294C2×C4—101no—
1295C2×C4—101no—
1296C2×C4—204no—
1297C2×C4—204no—
1298C2×C4—204no—
1299C2×C4—204no—
1300C2×C4—402no—
1301C2×C4C2×Q8×D512yes—
1302C2×C4C2×Q8×D512yes—
1303C2×C4#414912yes—
1304C2×C4#415012yes—
1305C5#3675411yescharacteristic, complemented, Sylow
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—102no—
1314C22—102no—
1315C22—102no—
1316C22—201no—
1317C22—201no—
1318C22—201no—
1319C22—201no—
1320C22C22×Q8×D511yescharacteristic
1321C22C2×#414911yescharacteristic
1322C22C2×#415011yescharacteristic
1323C22D5×H(5,𝔽2)11yescharacteristic
1324C22#6628511yescharacteristic
1325C22#6628511yescharacteristic
1326C22#6628711yescharacteristic
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—102no—
1342C4—102no—
1343C4—102no—
1344C4—102no—
1345C4—201no—
1346C4—201no—
1347C4—201no—
1348C4—201no—
1349C4—201no—
1350C4—201no—
1351C4—201no—
1352C4—201no—
1353C4—201no—
1354C4—201no—
1355C4—201no—
1356C2—42no—
1357C2—202no—
1358C2#1061835911yescharacteristic
1359C2#1061844211yescharacteristic
1360C2#1061848211yescharacteristic
1361C2#1061879411yescharacteristic
1362C2#1061882711yescharacteristic
1363C2#1061884911yescharacteristic
1364C2#1061897711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2790C2
prime radicalC22×C22⋊D5C23
hypercenter#2790D5
hypocenterC5#36754
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2790

Complements

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

NH ≅ G/Ntype
1. C5×#2790C2semidirect
2. #10610009C2semidirect
3. #10609965C2semidirect
4. #10609735C2semidirect
5. #10609650C2semidirect
6. #10609583C2semidirect
7. #10609576C2semidirect
8. #10609548C2semidirect
9. #10609544C2semidirect
12. #10609060C2semidirect
13. #10609019C2semidirect
14. #10607875C2semidirect
15. #10607792C2semidirect
16. #10607437C2semidirect
17. #10607437C2semidirect
20. #10607179C2semidirect
21. #10607121C2semidirect
22. #10606910C2semidirect
23. #10606859C2semidirect
25. #10606254C2semidirect
27. #10606203C2semidirect
28. #10606146C2semidirect
30. #10606107C2semidirect
31. #10606081C2semidirect
293. #4027Q8semidirect
360. #2790D5semidirect
1305. C5#36754semidirect

Maximal subgroups

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

subgroupindex
C5×#27902
#106100092
#106099652
#106097352
#106096502
#106095832
#106095762
#106095482
#106095442
#106091762
#106091642
#106090602
#106090192
#106078752
#106077922
#106074372
#106071892
#106071802
#106071792
#106071212
#106069102
#106068592
#106063002
#106062542
#106062472
#106062032
#106061462
#106061142
#106061072
#106060812
#367545