Finite Group Databasebeta

← #12307006

Subgroups — #12307006

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×#2319C211yesmaximal, characteristic
2#10614055C211yesmaximal, characteristic
3#10614049C211yesmaximal, characteristic
4#10608136C211yesmaximal, characteristic
5#10608132C211yesmaximal, characteristic
6#10608113C211yesmaximal, characteristic
7#10608113C211yesmaximal, characteristic
8#10607914C211yesmaximal, characteristic, complemented
9#10607900C211yesmaximal, characteristic, complemented
10#10607898C211yesmaximal, characteristic, complemented
11#10607846C211yesmaximal, characteristic, complemented
12#10607542C211yesmaximal, characteristic, complemented
13#10607516C211yesmaximal, characteristic, complemented
14#10607453C211yesmaximal, characteristic, complemented
15#10607437C211yesmaximal, characteristic, complemented
16#10607428C211yesmaximal, characteristic, complemented
17#10607428C211yesmaximal, characteristic, complemented
18#10607416C211yesmaximal, characteristic, complemented
19#10607398C211yesmaximal, characteristic, complemented
20#10605848C211yesmaximal, characteristic, complemented
21#10605824C211yesmaximal, characteristic, complemented
22#10605819C211yesmaximal, characteristic, complemented
23#10605798C211yesmaximal, characteristic, complemented
24#10605732C211yesmaximal, characteristic, complemented
25#10605689C211yesmaximal, characteristic, complemented
26#10605669C211yesmaximal, characteristic, complemented
27#10605631C211yesmaximal, characteristic, complemented
28#10605475C211yesmaximal, characteristic, complemented
29#10605444C211yesmaximal, characteristic, complemented
30#10605137C211yesmaximal, characteristic, complemented
31#10605135C211yesmaximal, characteristic, complemented
32C2×C4×C5×D4C2211yescharacteristic
33C2×#4072C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C2×#4036C2211yescharacteristic
36C2×#4034C2211yescharacteristic
37C2×#4024C2211yescharacteristic
38C2×#4024C2211yescharacteristic
39C2×#4024C2211yescharacteristic
40C2×#4024C2211yescharacteristic
41C2×#4024C2211yescharacteristic
42C2×#4024C2211yescharacteristic
43C2×#4016C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C5×#390C2211yescharacteristic
46C5×#390C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#388C2211yescharacteristic
50C5×#388C2211yescharacteristic
51C5×#388C2211yescharacteristic
52C5×#388C2211yescharacteristic
53C5×#381C2211yescharacteristic
54C5×#381C2211yescharacteristic
55C5×#380C2211yescharacteristic
56C5×#380C2211yescharacteristic
57C4×C5×C4⋊C4C2211yescharacteristic
58C5×#376C2211yescharacteristic
59#65509C2211yescharacteristic
60#65509C2211yescharacteristic
61#65509C2211yescharacteristic
62#65509C2211yescharacteristic
63#65501C2211yescharacteristic
64#65500C2211yescharacteristic
65C4×C22⋊Dic5C2211yescharacteristic
66C4×C22⋊Dic5C2211yescharacteristic
67C4×C22⋊Dic5C2211yescharacteristic
68C2×#3963C2211yescharacteristic
69#65275C2211yescharacteristic
70#65275C2211yescharacteristic
71#65274C2211yescharacteristic
72#65274C2211yescharacteristic
73#65273C2211yescharacteristic
74#65273C2211yescharacteristic
75#65273C2211yescharacteristic
76#65273C2211yescharacteristic
77#65273C2211yescharacteristic
78#65273C2211yescharacteristic
79#65273C2211yescharacteristic
80#65273C2211yescharacteristic
81#65270C2211yescharacteristic
82#65270C2211yescharacteristic
83#65270C2211yescharacteristic
84#65270C2211yescharacteristic
85#65268C2211yescharacteristic
86#65268C2211yescharacteristic
87#65268C2211yescharacteristic
88#65268C2211yescharacteristic
89#65268C2211yescharacteristic
90#65268C2211yescharacteristic
91#65265C2211yescharacteristic
92#65265C2211yescharacteristic
93#65262C2211yescharacteristic
94#65262C2211yescharacteristic
95#65240C2211yescharacteristic
96#65240C2211yescharacteristic
97#65240C2211yescharacteristic
98#65240C2211yescharacteristic
99#65239C2211yescharacteristic
100#65239C2211yescharacteristic
101#65239C2211yescharacteristic
102#65239C2211yescharacteristic
103#65239C2211yescharacteristic
104#65239C2211yescharacteristic
105#65238C2211yescharacteristic
106#65238C2211yescharacteristic
107#65238C2211yescharacteristic
108#65238C2211yescharacteristic
109#65238C2211yescharacteristic
110#65238C2211yescharacteristic
111#65237C2211yescharacteristic
112#65237C2211yescharacteristic
113#65237C2211yescharacteristic
114#65237C2211yescharacteristic
115#65237C2211yescharacteristic
116#65237C2211yescharacteristic
117#65236C2211yescharacteristic
118#65236C2211yescharacteristic
119#65236C2211yescharacteristic
120#65236C2211yescharacteristic
121#65235C2211yescharacteristic
122#65235C2211yescharacteristic
123#65235C2211yescharacteristic
124#65235C2211yescharacteristic
125#65231C2211yescharacteristic
126#65231C2211yescharacteristic
127#65231C2211yescharacteristic
128#65231C2211yescharacteristic
129#65226C2211yescharacteristic
130#65225C2211yescharacteristic
131C4×C4⋊Dic5C2211yescharacteristic
132#65222C2211yescharacteristic
133#65222C2211yescharacteristic
134#65222C2211yescharacteristic
135#65222C2211yescharacteristic
136#65222C2211yescharacteristic
137#65222C2211yescharacteristic
138#65221C2211yescharacteristic
139#65218C2211yescharacteristic
140#65218C2211yescharacteristic
141#65218C2211yescharacteristic
142#65217C2211yescharacteristic
143#65217C2211yescharacteristic
144#65217C2211yescharacteristic
145#65217C2211yescharacteristic
146#65217C2211yescharacteristic
147#64950C2211yescharacteristic
148#64950C2211yescharacteristic
149#64950C2211yescharacteristic
150#64950C2211yescharacteristic
151#64949C2211yescharacteristic
152#64949C2211yescharacteristic
153#64949C2211yescharacteristic
154#64949C2211yescharacteristic
155#64946C2211yescharacteristic
156#64946C2211yescharacteristic
157#64946C2211yescharacteristic
158#64946C2211yescharacteristic
159#64945C2211yescharacteristic
160#64945C2211yescharacteristic
161#64945C2211yescharacteristic
162#64945C2211yescharacteristic
163#64944C2211yescharacteristic
164#64944C2211yescharacteristic
165#64944C2211yescharacteristic
166#64944C2211yescharacteristic
167#64944C2211yescharacteristic
168#64944C2211yescharacteristic
169#64944C2211yescharacteristic
170#64944C2211yescharacteristic
171#64943C2211yescharacteristic
172#64943C2211yescharacteristic
173#64936C2211yescharacteristic
174#64936C2211yescharacteristic
175#64936C2211yescharacteristic
176#64936C2211yescharacteristic
177#64936C2211yescharacteristic
178#64936C2211yescharacteristic
179#64935C2211yescharacteristic
180#64935C2211yescharacteristic
181#64935C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36753—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C23×Dic5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C22×Dic10C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C22×Dic10C2311yescharacteristic
200C4×C5×D4Q818yescomplemented
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×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C5×C22⋊C4C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219C2×C42×C5C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C42×C5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231C2×C22⋊Dic5C2311yescharacteristic
232C2×C22⋊Dic5C2311yescharacteristic
233C2×C22⋊Dic5C2311yescharacteristic
234C2×C22⋊Dic5C2311yescharacteristic
235#4072—42no—
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
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
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×C4×Dic5—42no—
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287C2×C4×Dic5C2311yescharacteristic
288C2×C4×Dic5C2311yescharacteristic
289C2×C4×Dic5C2311yescharacteristic
290#4036—42no—
291#4034—42no—
292#4024—42no—
293#4024—42no—
294#4024—42no—
295#4024—42no—
296#4024—42no—
297#4024—42no—
298#4016—42no—
299#4015—42no—
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308C5×#95C2311yescharacteristic
309C5×#95C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
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#2807—51no—
359#2806—51no—
360#2792—51no—
361#2791—51no—
362#2788—51no—
363#2748—51no—
364#2742—51no—
365#2732—51no—
366#2729—51no—
367#2720—51no—
368#2720—51no—
369#2713—51no—
370#2704—51no—
371#2692—51no—
372#2692—51no—
373#2677—51no—
374#2667—51no—
375#2665—51no—
376#2612—51no—
377#2607—51no—
378#2606—51no—
379#2605—51no—
380#2550—51no—
381#2549—51no—
382#2441—51no—
383#2438—51no—
384#2319D511yescharacteristic
385#2318—51no—
386#2290—51no—
387C24×C5C2411yescharacteristic
388C24×C5C2411yescharacteristic
389C2×C5×D4—41no—
390C2×C5×D4—41no—
391C2×C5×D4C2×Q814yes—
392C22×C4×C5—41no—
393C22×C4×C5—41no—
394C22×C4×C5—41no—
395C22×C4×C5—41no—
396C22×C4×C5C2×Q814yes—
397C22×C4×C5C2×Q814yes—
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C22×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C22×Dic5—22no—
412C22×Dic5—22no—
413C22×Dic5—22no—
414C22×Dic5—41no—
415C22×Dic5—41no—
416C22×Dic5—41no—
417C22×Dic5—41no—
418C22×Dic5—41no—
419C22×Dic5—41no—
420C22×Dic5—41no—
421C22×Dic5—41no—
422C22×Dic5—41no—
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C22×Dic5C2411yescharacteristic
436C22×Dic5C2411yescharacteristic
437C22×Dic5C2411yescharacteristic
438C22×Dic5C2411yescharacteristic
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—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C4⋊C4C2×Q814yes—
461C5×C22⋊C4—41no—
462C5×C22⋊C4—41no—
463C5×C22⋊C4—41no—
464C5×C22⋊C4—41no—
465C5×C22⋊C4—41no—
466C5×C22⋊C4—41no—
467C5×C22⋊C4—41no—
468C5×C22⋊C4—41no—
469C5×C22⋊C4C2×Q814yes—
470C5×C22⋊C4C2×Q814yes—
471C42×C5—41no—
472C42×C5—41no—
473C42×C5—41no—
474C42×C5—41no—
475C42×C5C2×Q814yes—
476C22⋊Dic5—22no—
477C22⋊Dic5—22no—
478C22⋊Dic5—22no—
479C22⋊Dic5—41no—
480C22⋊Dic5—41no—
481C22⋊Dic5—41no—
482C22⋊Dic5—41no—
483C22⋊Dic5—41no—
484C22⋊Dic5—41no—
485C22⋊Dic5—41no—
486C22⋊Dic5—41no—
487C22⋊Dic5—41no—
488C4⋊Dic5—22no—
489C4⋊Dic5—22no—
490C4⋊Dic5—22no—
491C4⋊Dic5—22no—
492C4⋊Dic5—22no—
493C4⋊Dic5—41no—
494C4⋊Dic5—41no—
495C4⋊Dic5—41no—
496C4⋊Dic5—41no—
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—
507#683—22no—
508#683—22no—
509#683—22no—
510#683—22no—
511#683—22no—
512#683—22no—
513#683—22no—
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#683—41no—
530#683—41no—
531#683—41no—
532#683—41no—
533C4×Dic5—22no—
534C4×Dic5—22no—
535C4×Dic5—41no—
536C4×Dic5—41no—
537C4×Dic5—41no—
538C4×Dic5—41no—
539C4×Dic5—41no—
540C4×Dic5—41no—
541C2×C4⋊Q8—51no—
542C2×C4⋊Q8—51no—
543C2×#125—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×D4C2×D511yescharacteristic
552C2×#117—51no—
553C22×C42—51no—
554#400—51no—
555#400—51no—
556#400—51no—
557#400—51no—
558#400—51no—
559#400—51no—
560#399—51no—
561#399—51no—
562#399—51no—
563#399—51no—
564#399—51no—
565#399—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#398—51no—
576#398—51no—
577#398—51no—
578#398—51no—
579#398—51no—
580#398—51no—
581#398—51no—
582#396—51no—
583#396—51no—
584#396—51no—
585#396—51no—
586#396—51no—
587#396—51no—
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#391—51no—
612#391—51no—
613#390C2×D511yescharacteristic
614#390C2×D511yescharacteristic
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#389C2×D511yescharacteristic
631#389C2×D511yescharacteristic
632#388—51no—
633#388—51no—
634#388—51no—
635#388—51no—
636#388C2×D511yescharacteristic
637#388C2×D511yescharacteristic
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#387—51no—
659#387—51no—
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#384—51no—
675#384—51no—
676#383—51no—
677#382—51no—
678#381—51no—
679#381C2×D511yescharacteristic
680#381C2×D511yescharacteristic
681#380—51no—
682#380—51no—
683#380—51no—
684#380—51no—
685#380—51no—
686#380C2×D511yescharacteristic
687#380C2×D511yescharacteristic
688C4×C4⋊C4—51no—
689C4×C4⋊C4C2×D511yescharacteristic
690C4×C22⋊C4—51no—
691C4×C22⋊C4—51no—
692C4×C22⋊C4—51no—
693#376—51no—
694#376C2×D511yescharacteristic
695C2×#95—51no—
696C23×C5—21no—
697C23×C5—21no—
698C23×C5—21no—
699C23×C5—21no—
700C23×C5—21no—
701C23×C5—21no—
702C23×C5—21no—
703C23×C5—21no—
704C23×C5—21no—
705C23×C5—21no—
706C23×C5—21no—
707C23×C5—21no—
708C23×C5C22×Q812yes—
709C23×C5C22×Q812yes—
710C23×C5C2511yescharacteristic
711C5×D4—44no—
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—44no—
747C2×C4×C5—44no—
748C2×C4×C5C22×Q812yes—
749C2×C4×C5C22×Q812yes—
750C2×C4×C5C22×Q812yes—
751C2×C4×C5C22×Q812yes—
752C2×C4×C5C22×Q812yes—
753C2×Dic5—21no—
754C2×Dic5—21no—
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—21no—
797C2×Dic5—21no—
798C2×Dic5—44no—
799C2×Dic5—44no—
800C2×Dic5—82no—
801C2×Dic5—82no—
802C2×Dic5H(5,𝔽2)12yes—
803C2×Dic5H(5,𝔽2)12yes—
804C2×Dic52−1+412yes—
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×D4C22×D511yescharacteristic
816C23×C4—51no—
817C23×C4—51no—
818C23×C4—51no—
819C23×C4—51no—
820C23×C4C22×D511yescharacteristic
821C23×C4C22×D511yescharacteristic
822C4⋊Q8—202no—
823C4⋊Q8—202no—
824#125—202no—
825#125—202no—
826C22⋊Q8—202no—
827C22⋊Q8—202no—
828C22⋊Q8—202no—
829C22⋊Q8—202no—
830C22⋊Q8—202no—
831C22⋊Q8—202no—
832C4×D4Dic1018yescomplemented
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⋊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⋊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⋊C4C22×D511yescharacteristic
899C2×C22⋊C4C22×D511yescharacteristic
900C2×C22⋊C4C22×D511yescharacteristic
901C2×C22⋊C4C22×D511yescharacteristic
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—202no—
917C2×C42C22×D511yescharacteristic
918C2×C42C22×D511yescharacteristic
919C2×C42C22×D511yescharacteristic
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#95—51no—
967#95—51no—
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—22no—
982C22×C5—22no—
983C22×C5—22no—
984C22×C5—41no—
985C22×C5—41no—
986C22×C5—41no—
987C22×C5—41no—
988C22×C5—41no—
989C22×C5—41no—
990C22×C5—41no—
991C22×C5—41no—
992C22×C5C23×Q811yescharacteristic
993C22×C5C2×H(5,𝔽2)11yescharacteristic
994C22×C5C2×H(5,𝔽2)11yescharacteristic
995C22×C5C2×2−1+411yescharacteristic
996C22×C5#58511yescharacteristic
997C22×C5#58511yescharacteristic
998C22×C5#58511yescharacteristic
999C4×C5—22no—
1000C4×C5—22no—
1001C4×C5—22no—
1002C4×C5—22no—
1003C4×C5—22no—
1004C4×C5—41no—
1005C4×C5—41no—
1006C4×C5—41no—
1007C4×C5—41no—
1008C4×C5—41no—
1009C4×C5—41no—
1010C4×C5—41no—
1011C4×C5—41no—
1012Dic5—22no—
1013Dic5—22no—
1014Dic5—22no—
1015Dic5—41no—
1016Dic5—41no—
1017Dic5—41no—
1018Dic5—41no—
1019Dic5—41no—
1020Dic5—41no—
1021Dic5—41no—
1022Dic5—41no—
1023Dic5—41no—
1024Dic5—41no—
1025Dic5—41no—
1026Dic5—41no—
1027Dic5—41no—
1028C24C23×D511yescharacteristic
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—41no—
1046C2×D4—41no—
1047C2×D4C2×Dic1014yes—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—51no—
1053C22×C4—51no—
1054C22×C4—51no—
1055C22×C4—51no—
1056C22×C4—51no—
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×C4C2×Dic1014yes—
1081C22×C4C2×Dic1014yes—
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—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—41no—
1101C4⋊C4—102no—
1102C4⋊C4—102no—
1103C4⋊C4—102no—
1104C4⋊C4—102no—
1105C4⋊C4—102no—
1106C4⋊C4—102no—
1107C4⋊C4—102no—
1108C4⋊C4—102no—
1109C4⋊C4—102no—
1110C4⋊C4—102no—
1111C4⋊C4—102no—
1112C4⋊C4—102no—
1113C4⋊C4—201no—
1114C4⋊C4—201no—
1115C4⋊C4—201no—
1116C4⋊C4—201no—
1117C4⋊C4—201no—
1118C4⋊C4—201no—
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⋊C4C2×Dic1014yes—
1147C22⋊C4—41no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—41no—
1151C22⋊C4—41no—
1152C22⋊C4—41no—
1153C22⋊C4—41no—
1154C22⋊C4—41no—
1155C22⋊C4—102no—
1156C22⋊C4—102no—
1157C22⋊C4—102no—
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⋊C4C2×Dic1014yes—
1168C22⋊C4C2×Dic1014yes—
1169C42—41no—
1170C42—41no—
1171C42—41no—
1172C42—41no—
1173C42—102no—
1174C42—102no—
1175C42—201no—
1176C42—201no—
1177C42—201no—
1178C42—201no—
1179C42—201no—
1180C42—201no—
1181C42C2×Dic1014yes—
1182C2×C5—42no—
1183C2×C5—42no—
1184C2×C5#345811yescharacteristic
1185C2×C5#350111yescharacteristic
1186C2×C5#350311yescharacteristic
1187C2×C5#353511yescharacteristic
1188C2×C5#354211yescharacteristic
1189C2×C5#355711yescharacteristic
1190C2×C5#356211yescharacteristic
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—21no—
1202C23—21no—
1203C23C22×Dic1012yes—
1204C23C22×Dic1012yes—
1205C23C24×D511yescharacteristic
1206Q8—402no—
1207Q8—402no—
1208Q8—402no—
1209Q8—402no—
1210Q8—402no—
1211D4—44no—
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—44no—
1247C2×C4—44no—
1248C2×C4—52no—
1249C2×C4—52no—
1250C2×C4—52no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
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—402no—
1299C2×C4—402no—
1300C2×C4C22×Dic1012yes—
1301C2×C4C22×Dic1012yes—
1302C2×C4C22×Dic1012yes—
1303C2×C4C22×Dic1012yes—
1304C2×C4C22×Dic1012yes—
1305C5#3675311yescharacteristic, complemented, Sylow
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22C23×Dic1011yescharacteristic
1321C22#6628311yescharacteristic
1322C22#6628311yescharacteristic
1323C22D5×H(5,𝔽2)11yescharacteristic
1324C22D5×H(5,𝔽2)11yescharacteristic
1325C22#6628511yescharacteristic
1326C22D5×2−1+411yescharacteristic
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—102no—
1341C4—102no—
1342C4—102no—
1343C4—201no—
1344C4—201no—
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—42no—
1358C2#1061762611yescharacteristic
1359C2#1061776111yescharacteristic
1360C2#1061779011yescharacteristic
1361C2#1061837511yescharacteristic
1362C2#1061838211yescharacteristic
1363C2#1061844011yescharacteristic
1364C2#1061846111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2319C2
prime radicalC22×C5×D4C23
hypercenter#2319D5
hypocenterC5#36753
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2319

Complements

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

NH ≅ G/Ntype
8. #10607914C2semidirect
9. #10607900C2semidirect
10. #10607898C2semidirect
11. #10607846C2semidirect
12. #10607542C2semidirect
13. #10607516C2semidirect
14. #10607453C2semidirect
15. #10607437C2semidirect
16. #10607428C2semidirect
17. #10607428C2semidirect
18. #10607416C2semidirect
19. #10607398C2semidirect
20. #10605848C2semidirect
21. #10605824C2semidirect
22. #10605819C2semidirect
23. #10605798C2semidirect
24. #10605732C2semidirect
25. #10605689C2semidirect
26. #10605669C2semidirect
27. #10605631C2semidirect
28. #10605475C2semidirect
29. #10605444C2semidirect
30. #10605137C2semidirect
31. #10605135C2semidirect
200. C4×C5×D4Q8semidirect
832. C4×D4Dic10semidirect
1305. C5#36753semidirect

Maximal subgroups

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

subgroupindex
C5×#23192
#106140552
#106140492
#106081362
#106081322
#106081132
#106079142
#106079002
#106078982
#106078462
#106075422
#106075162
#106074532
#106074372
#106074282
#106074162
#106073982
#106058482
#106058242
#106058192
#106057982
#106057322
#106056892
#106056692
#106056312
#106054752
#106054442
#106051372
#106051352
#367535