Finite Group Databasebeta

← D59×#2395 #28754927

Subgroups — D59×#2395 #28754927

Order 15104.

3182 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D59C211yesmaximal, characteristic
2C2×#117×D59C211yesmaximal, characteristic, complemented
3#21427362C211yesmaximal, characteristic, complemented
4#21427361C211yesmaximal, characteristic, complemented
5#21427360C211yesmaximal, characteristic, complemented
6#21427359C212yesmaximal, complemented
7#21427358C211yesmaximal, characteristic, complemented
8#21427357C212yesmaximal, complemented
9#21427356C211yesmaximal, characteristic, complemented
10#21427355C211yesmaximal, characteristic, complemented
11#21427354C212yesmaximal, complemented
12#21427353C211yesmaximal, characteristic, complemented
13#21427352C212yesmaximal, complemented
14#400×D59C211yesmaximal, characteristic, complemented
15#399×D59C211yesmaximal, characteristic, complemented
16#398×D59C211yesmaximal, characteristic, complemented
17#397×D59C212yesmaximal, complemented
18#397×D59C211yesmaximal, characteristic, complemented
19#394×D59C212yesmaximal
20C4×C4⋊C4×D59C212yesmaximal, complemented
21C4×C22⋊C4×D59C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D59C212yesmaximal, complemented
23C59×#2395C211yesmaximal, characteristic, complemented
24C22×D4×D59C2211yescharacteristic
25C23×C4×D59C2211yescharacteristic
26C23×C4×D59C2211yescharacteristic
27C2×C4×D236C2211yescharacteristic
28C2×D4×Dic59C2211yescharacteristic
29C2×#14273689C2211yescharacteristic
30C2×C4×C22⋊D59C2211yescharacteristic
31C2×C4×C22⋊D59C2211yescharacteristic
32C2×(C22⋊D59)⋊C4C2211yescharacteristic
33C2×(C22⋊D59)⋊C4C2211yescharacteristic
34C4×D4×D59—28no—
35C2×#14273686C2211yescharacteristic, complemented
36C2×#14273685C2211yescharacteristic, complemented
37C2×#14273685C2211yescharacteristic, complemented
38C2×#14273684C2212yescomplemented
39C2×#14273683C2212yescomplemented
40#117×D59—28no—
41C2×C4⋊C4×D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic
44C2×C4⋊C4×D59C2212yes—
45C2×C4⋊C4×D59C2212yes—
46C2×C22⋊C4×D59C2212yes—
47C2×C22⋊C4×D59C2211yescharacteristic
48C2×C22⋊C4×D59C2211yescharacteristic
49C2×C22⋊C4×D59C2212yes—
50C2×C22⋊C4×D59C2212yes—
51C2×C22⋊C4×D59C2212yes—
52C2×C42×D59C2212yes—
53C2×C42×D59C2211yescharacteristic
54C2×C42×D59C2212yes—
55#16837344C2212yescomplemented
56#16837343C2212yescomplemented
57#16837342C2211yescharacteristic, complemented
58#16837341C2211yescharacteristic, complemented
59#16837340C2211yescharacteristic, complemented
60#16837339C2211yescharacteristic, complemented
61#16837338C2212yescomplemented
62#16837338C2211yescharacteristic, complemented
63#16837337C2211yescharacteristic, complemented
64#16837337C2212yescomplemented
65#16837336C2212yescomplemented
66#16837335C2212yescomplemented
67#16837334C2211yescharacteristic, complemented
68#16837333C2211yescharacteristic, complemented
69#16837332C2211yescharacteristic, complemented
70#16837331C2212yescomplemented
71#16837331C2212yescomplemented
72#16837331C2212yescomplemented
73#16837330C2212yescomplemented
74#16837330C2212yescomplemented
75#16837330C2212yescomplemented
76#16837329C2211yescharacteristic, complemented
77#16837329C2212yescomplemented
78#16837328C2211yescharacteristic, complemented
79#16837328C2212yescomplemented
80#16837327C2212yescomplemented
81#16837327C2211yescharacteristic, complemented
82#16837320C2212yes—
83#16837319C2212yes—
84#16837318C2212yes—
85#16837318C2212yes—
86#16837317C2212yes—
87#16837317C2212yes—
88#16837316C2212yes—
89C4⋊C4×Dic59C2212yescomplemented
90C4⋊C4×Dic59C2212yescomplemented
91C4×Dic59⋊C4C2212yescomplemented
92C4×Dic59⋊C4C2212yescomplemented
93C4×C4⋊Dic59C2212yescomplemented
94#16837253C2212yescomplemented
95#16837253C2212yescomplemented
96C22⋊C4×Dic59C2212yescomplemented
97C22⋊C4×Dic59C2212yescomplemented
98C22⋊C4×Dic59C2212yescomplemented
99C4×(C2×D59)⋊C4C2212yescomplemented
100C4×(C2×D59)⋊C4C2212yescomplemented
101C4×(C2×D59)⋊C4C2212yescomplemented
102C4×C22⋊Dic59C2211yescharacteristic, complemented
103C4×C22⋊Dic59C2212yescomplemented
104#16837249C2212yescomplemented
105#16837249C2212yescomplemented
106#16837249C2211yescharacteristic, complemented
107#16837249C2211yescharacteristic, complemented
108#95×D59C2212yes—
109#95×D59C2212yes—
110#95×D59C2212yes—
111#95×D59C2211yescharacteristic
112#95×D59C2212yes—
113#95×D59C2211yescharacteristic
114C2×C4×D4×C59C2211yescharacteristic
115C2×#117×C59C2211yescharacteristic, complemented
116C59×#400C2211yescharacteristic, complemented
117C59×#399C2211yescharacteristic, complemented
118C59×#398C2211yescharacteristic, complemented
119C59×#397C2212yescomplemented
120C59×#397C2211yescharacteristic, complemented
121C59×#394C2212yes—
122C4×C4⋊C4×C59C2212yescomplemented
123C4×C22⋊C4×C59C2211yescharacteristic, complemented
124C4×C22⋊C4×C59C2212yescomplemented
125C24×D59C2311yescharacteristic
126C24×D59C2311yescharacteristic
127C22×D236C2311yescharacteristic
128C22×C22⋊D59C2311yescharacteristic
129C22×C22⋊D59C2311yescharacteristic
130C2×D4×D59—24no—
131C2×D4×D59—24no—
132C2×D4×D59—24no—
133C23×Dic59C2311yescharacteristic
134C23×Dic59C2311yescharacteristic
135C22×C4×D59—28no—
136C22×C4×D59—24no—
137C22×C4×D59—28no—
138C22×C4×D59D418yes—
139C22×C4×D59C2311yescharacteristic
140C22×C4×D59C2311yescharacteristic
141C22×C4×D59C2311yescharacteristic
142C22×C4×D59C2312yes—
143C22×C4×D59C2311yescharacteristic
144C22×C4×D59C2312yes—
145C22×C4×D59C2312yes—
146C22×C4×D59C2311yescharacteristic
147C22×C4×D59C2311yescharacteristic
148C22×C4×D59C2311yescharacteristic
149C22×C4×D59C2311yescharacteristic
150C22×C4×D59C2312yes—
151C22×C4×D59C2311yescharacteristic
152C4×D236—24no—
153D4×Dic59—24no—
154#14273689—24no—
155C4×C22⋊D59—24no—
156C4×C22⋊D59—24no—
157(C22⋊D59)⋊C4—24no—
158(C22⋊D59)⋊C4—24no—
159#14273686—24no—
160#14273685—24no—
161#14273685—24no—
162#14273684—28no—
163#14273683—28no—
164C2×C4⋊Dic59C2312yes—
165C2×C4⋊Dic59C2312yes—
166C2×C4⋊Dic59C2311yescharacteristic
167C2×C4⋊Dic59C2311yescharacteristic
168C2×C4⋊Dic59C2311yescharacteristic
169C2×Dic59⋊C4C2312yes—
170C2×Dic59⋊C4C2312yes—
171C2×Dic59⋊C4C2312yes—
172C2×Dic59⋊C4C2312yes—
173C2×Dic59⋊C4C2312yes—
174C2×Dic59⋊C4C2311yescharacteristic
175C2×Dic59⋊C4C2311yescharacteristic
176C2×Dic59⋊C4C2312yes—
177C4⋊C4×D59—24no—
178C4⋊C4×D59—24no—
179C4⋊C4×D59—24no—
180C4⋊C4×D59—28no—
181C4⋊C4×D59—28no—
182C2×C22⋊Dic59C2312yes—
183C2×C22⋊Dic59C2312yes—
184C2×C22⋊Dic59C2312yes—
185C2×C22⋊Dic59C2312yes—
186C2×C22⋊Dic59C2311yescharacteristic
187C2×C22⋊Dic59C2311yescharacteristic
188C2×(C2×D59)⋊C4C2312yes—
189C2×(C2×D59)⋊C4C2312yes—
190C2×(C2×D59)⋊C4C2312yes—
191C2×(C2×D59)⋊C4C2312yes—
192C2×(C2×D59)⋊C4C2312yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2311yescharacteristic
197C2×(C2×D59)⋊C4C2311yescharacteristic
198C2×(C2×D59)⋊C4C2311yescharacteristic
199C2×(C2×D59)⋊C4C2311yescharacteristic
200C22⋊C4×D59—28no—
201C22⋊C4×D59—24no—
202C22⋊C4×D59—28no—
203C22⋊C4×D59—24no—
204C22⋊C4×D59—28no—
205C22⋊C4×D59—28no—
206C2×C4×Dic59C2312yes—
207C2×C4×Dic59C2312yes—
208C2×C4×Dic59C2312yes—
209C2×C4×Dic59C2312yes—
210C2×C4×Dic59C2312yes—
211C2×C4×Dic59C2312yes—
212C2×C4×Dic59C2311yescharacteristic
213C2×C4×Dic59C2311yescharacteristic
214C2×C4×Dic59C2311yescharacteristic
215C42×D59—28no—
216C42×D59—24no—
217C42×D59—28no—
218C59⋊#95C2311yescharacteristic
219C59⋊#95C2312yes—
220C59⋊#95C2312yes—
221C59⋊#95C2311yescharacteristic
222C59⋊#95C2312yes—
223C59⋊#95C2312yes—
224C59⋊#95C2312yes—
225C59⋊#95C2312yes—
226C59⋊#95C2312yes—
227C59⋊#95C2312yes—
228C59⋊#95C2312yes—
229C59⋊#95C2312yes—
230C59⋊#95C2312yes—
231C59⋊#95C2312yes—
232C59⋊#95C2312yes—
233C59⋊#95C2312yes—
234C22×D4×C59C2311yescharacteristic
235C23×C4×C59C2311yescharacteristic
236C23×C4×C59C2311yescharacteristic
237C4×D4×C59—24no—
238#117×C59—24no—
239C2×C4⋊C4×C59C2312yes—
240C2×C4⋊C4×C59C2312yes—
241C2×C4⋊C4×C59C2311yescharacteristic
242C2×C4⋊C4×C59C2311yescharacteristic
243C2×C4⋊C4×C59C2311yescharacteristic
244C2×C22⋊C4×C59C2312yes—
245C2×C22⋊C4×C59C2312yes—
246C2×C22⋊C4×C59C2312yes—
247C2×C22⋊C4×C59C2312yes—
248C2×C22⋊C4×C59C2311yescharacteristic
249C2×C22⋊C4×C59C2311yescharacteristic
250C2×C42×C59C2312yes—
251C2×C42×C59C2312yes—
252C2×C42×C59C2311yescharacteristic
253#95×C59C2312yes—
254#95×C59C2311yescharacteristic
255#95×C59C2312yes—
256#95×C59C2311yescharacteristic
257#95×C59C2312yes—
258#95×C59C2312yes—
259C24×C59C2411yescharacteristic
260C24×C59C2411yescharacteristic
261C23×D59—22no—
262C23×D59—24no—
263C23×D59—24no—
264C23×D59—24no—
265C23×D59—24no—
266C23×D59—22no—
267C23×D59—22no—
268C23×D59—22no—
269C23×D59C2×D414yes—
270C23×D59#4114yes—
271C23×D59C2411yescharacteristic
272C23×D59C2411yescharacteristic
273C23×D59C2411yescharacteristic
274C2×D4×C59—22no—
275C2×D4×C59—22no—
276C2×D4×C59—22no—
277C22×C4×C59—24no—
278C22×C4×C59—22no—
279C22×C4×C59—24no—
280C22×C4×C59C2×D414yes—
281C22×C4×C59C2412yes—
282C22×C4×C59C2411yescharacteristic
283C22×C4×C59C2412yes—
284C22×C4×C59C2412yes—
285C22×C4×C59C2411yescharacteristic
286C22×C4×C59C2411yescharacteristic
287C22×C4×C59C2412yes—
288C22×C4×C59C2411yescharacteristic
289C22×C4×C59C2411yescharacteristic
290C2×C22⋊D59—22no—
291C2×C22⋊D59—22no—
292C2×C22⋊D59—22no—
293C2×C22⋊D59—22no—
294C2×C22⋊D59—22no—
295C2×C22⋊D59—22no—
296C22×Dic59—24no—
297C22×Dic59—22no—
298C22×Dic59—24no—
299C22×Dic59C2×D414yes—
300C22×Dic59C2412yes—
301C22×Dic59C2411yescharacteristic
302C22×Dic59C2412yes—
303C22×Dic59C2412yes—
304C22×Dic59C2411yescharacteristic
305C22×Dic59C2411yescharacteristic
306C22×Dic59C2412yes—
307C22×Dic59C2411yescharacteristic
308C22×Dic59C2411yescharacteristic
309D4×D59—232no—
310C2×D236—22no—
311C2×D236—22no—
312C2×D236—22no—
313C2×C4×D59—22no—
314C2×C4×D59—24no—
315C2×C4×D59—24no—
316C2×C4×D59—24no—
317C2×C4×D59—22no—
318C2×C4×D59—24no—
319C2×C4×D59—24no—
320C2×C4×D59—232no—
321C2×C4×D59—22no—
322C2×C4×D59—24no—
323C2×C4×D59—24no—
324C2×C4×D59—22no—
325C2×C4×D59—24no—
326C2×C4×D59—24no—
327C2×C4×D59—24no—
328C2×C4×D59—24no—
329C2×C4×D59—24no—
330C2×C4×D59—24no—
331C2×C4×D59—24no—
332C2×C4×D59—24no—
333C2×C4×D59—24no—
334C2×C4×D59—22no—
335C2×C4×D59—24no—
336C2×C4×D59—22no—
337C2×C4×D59—24no—
338C2×C4×D59—416no—
339C2×C4×D59C2×D414yes—
340C2×C4×D59C2×D414yes—
341C2×C4×D59C2×D414yes—
342C2×C4×D59C2×D414yes—
343C2×C4×D59#4118yes—
344C2×C4×D59#4114yes—
345C2×C4×D59#4118yes—
346C4⋊C4×C59—22no—
347C4⋊C4×C59—22no—
348C4⋊C4×C59—22no—
349C4⋊C4×C59—24no—
350C4⋊C4×C59—24no—
351C22⋊C4×C59—24no—
352C22⋊C4×C59—22no—
353C22⋊C4×C59—24no—
354C22⋊C4×C59—22no—
355C22⋊C4×C59—24no—
356C22⋊C4×C59—24no—
357C42×C59—24no—
358C42×C59—22no—
359C42×C59—24no—
360C22⋊Dic59—24no—
361C22⋊Dic59—22no—
362C22⋊Dic59—24no—
363C22⋊Dic59—22no—
364C22⋊Dic59—24no—
365C22⋊Dic59—24no—
366(C2×D59)⋊C4—24no—
367(C2×D59)⋊C4—24no—
368(C2×D59)⋊C4—22no—
369(C2×D59)⋊C4—22no—
370(C2×D59)⋊C4—24no—
371(C2×D59)⋊C4—24no—
372(C2×D59)⋊C4—22no—
373(C2×D59)⋊C4—24no—
374(C2×D59)⋊C4—24no—
375(C2×D59)⋊C4—22no—
376(C2×D59)⋊C4—24no—
377(C2×D59)⋊C4—24no—
378C4⋊Dic59—22no—
379C4⋊Dic59—22no—
380C4⋊Dic59—24no—
381C4⋊Dic59—22no—
382C4⋊Dic59—24no—
383Dic59⋊C4—22no—
384Dic59⋊C4—24no—
385Dic59⋊C4—24no—
386Dic59⋊C4—24no—
387Dic59⋊C4—22no—
388Dic59⋊C4—24no—
389Dic59⋊C4—24no—
390Dic59⋊C4—24no—
391C4×Dic59—24no—
392C4×Dic59—22no—
393C4×Dic59—24no—
394C4×Dic59—24no—
395C4×Dic59—24no—
396C4×Dic59—22no—
397C4×Dic59—22no—
398C4×Dic59—24no—
399C4×Dic59—24no—
400C23×C59—21no—
401C23×C59—22no—
402C23×C59—22no—
403C23×C59—22no—
404C23×C59—22no—
405C23×C59—21no—
406C23×C59—21no—
407C23×C59—21no—
408C23×C59C22×D412yes—
409C23×C59C2×#4112yes—
410C23×C59C2511yescharacteristic
411C22×D59—21no—
412C22×D59—22no—
413C22×D59—22no—
414C22×D59—22no—
415C22×D59—22no—
416C22×D59—21no—
417C22×D59—21no—
418C22×D59—21no—
419C22×D59—28no—
420C22×D59—28no—
421C22×D59—28no—
422C22×D59—216no—
423C22×D59—28no—
424C22×D59—44no—
425C22×D59—48no—
426C22×D59—48no—
427C22×D59—48no—
428C22×D59—44no—
429C22×D59C22×D412yes—
430C22×D59C22×D412yes—
431C22×D59C2×#4112yes—
432C22×D59C2×#4114yes—
433C22×D59C2×#4112yes—
434C22×D59C2×#4112yes—
435C22×D59C2×#4114yes—
436D4×C59—28no—
437C2×C4×C59—21no—
438C2×C4×C59—22no—
439C2×C4×C59—22no—
440C2×C4×C59—22no—
441C2×C4×C59—21no—
442C2×C4×C59—28no—
443C2×C4×C59—22no—
444C2×C4×C59—22no—
445C2×C4×C59—21no—
446C2×C4×C59—21no—
447C2×C4×C59—22no—
448C2×C4×C59—22no—
449C2×C4×C59—22no—
450C2×C4×C59—22no—
451C2×C4×C59—22no—
452C2×C4×C59—22no—
453C2×C4×C59—22no—
454C2×C4×C59—22no—
455C2×C4×C59—22no—
456C2×C4×C59—44no—
457C2×C4×C59C22×D412yes—
458C2×C4×C59C22×D412yes—
459C2×C4×C59C2×#4112yes—
460C2×C4×C59C2×#4114yes—
461C2×C4×C59C2×#4114yes—
462C22⋊D59—28no—
463C22⋊D59—28no—
464C2×Dic59—21no—
465C2×Dic59—22no—
466C2×Dic59—22no—
467C2×Dic59—22no—
468C2×Dic59—21no—
469C2×Dic59—28no—
470C2×Dic59—22no—
471C2×Dic59—22no—
472C2×Dic59—21no—
473C2×Dic59—21no—
474C2×Dic59—22no—
475C2×Dic59—22no—
476C2×Dic59—22no—
477C2×Dic59—22no—
478C2×Dic59—22no—
479C2×Dic59—22no—
480C2×Dic59—22no—
481C2×Dic59—22no—
482C2×Dic59—22no—
483C2×Dic59—44no—
484C2×Dic59C22×D412yes—
485C2×Dic59C22×D412yes—
486C2×Dic59C2×#4112yes—
487C2×Dic59C2×#4114yes—
488C2×Dic59C2×#4114yes—
489D236—28no—
490C4×D59—28no—
491C4×D59—28no—
492C4×D59—216no—
493C4×D59—28no—
494C4×D59—28no—
495C4×D59—44no—
496C4×D59—48no—
497C4×D59—48no—
498C4×D59—44no—
499C4×D59—48no—
500C4×D59—44no—
501C4×D59—44no—
502C4×D59#123116yes—
503C2×#2395—591nomaximal, Sylow
504C22×C59—22no—
505C22×C59—22no—
506C22×C59—22no—
507C22×C59—24no—
508C22×C59—22no—
509C22×C59—41no—
510C22×C59—42no—
511C22×C59—42no—
512C22×C59—42no—
513C22×C59—41no—
514C22×C59C23×D411yescharacteristic
515C22×C59C22×#4112yes—
516C22×C59C22×#4111yescharacteristic
517C22×C59C22×#4111yescharacteristic
518C22×C59C22×#4112yes—
519C2×D59—22no—
520C2×D59—22no—
521C2×D59—22no—
522C2×D59—24no—
523C2×D59—22no—
524C2×D59—41no—
525C2×D59—42no—
526C2×D59—42no—
527C2×D59—42no—
528C2×D59—41no—
529C2×D59—416no—
530C2×D59—416no—
531C2×D59C2×#12314yes—
532C2×D59#52514yes—
533C2×D59#52918yes—
534C2×D59#52918yes—
535C2×D59#53214yes—
536C4×C59—22no—
537C4×C59—22no—
538C4×C59—24no—
539C4×C59—41no—
540C4×C59—42no—
541C4×C59—42no—
542C4×C59—42no—
543C4×C59—41no—
544C4×C59C2×#12314yes—
545Dic59—22no—
546Dic59—22no—
547Dic59—24no—
548Dic59—41no—
549Dic59—42no—
550Dic59—42no—
551Dic59—42no—
552Dic59—41no—
553Dic59C2×#12314yes—
554C22×C4×D4—591no—
555C22×#117—591no—
556#2395—591no—
557#2395—591no—
558#2395—591no—
559#2395—592no—
560#2395—591no—
561#2395—592no—
562#2395—592no—
563#2395—591no—
564#2395—592no—
565#2395—591no—
566#2395—591no—
567#2395D5911yescharacteristic, direct product factor
568C2×#400—591no—
569C2×#399—591no—
570C2×#398—591no—
571C2×#397—592no—
572C2×#397—591no—
573C2×#394—592no—
574C2×C4×C4⋊C4—592no—
575C2×C4×C22⋊C4—591no—
576C2×C4×C22⋊C4—592no—
577C2×C59—42no—
578C2×C59—42no—
579C2×C59C22×#12311yescharacteristic
580C2×C59C2×#52511yescharacteristic
581C2×C59C2×#52912yes—
582C2×C59C2×#52912yes—
583C2×C59C2×#53211yescharacteristic
584D59—42no—
585D59—42no—
586D59#239518yesdirect product factor
587C23×D4—591no—
588C24×C4—591no—
589C24×C4—591no—
590C2×C4×D4—591no—
591C2×C4×D4—591no—
592C2×C4×D4—591no—
593C2×C4×D4—591no—
594C2×C4×D4—591no—
595C2×C4×D4—591no—
596C2×C4×D4—591no—
597C2×C4×D4—1188no—
598C2×C4×D4C2×D5911yescharacteristic
599C2×#117—591no—
600C2×#117—591no—
601C2×#117—591no—
602C2×#117—592no—
603C2×#117—592no—
604C2×#117—1188no—
605C2×#117C2×D5911yescharacteristic, complemented
606C22×C4⋊C4—592no—
607C22×C4⋊C4—591no—
608C22×C4⋊C4—592no—
609C22×C4⋊C4—591no—
610C22×C4⋊C4—591no—
611C22×C22⋊C4—592no—
612C22×C22⋊C4—592no—
613C22×C22⋊C4—592no—
614C22×C22⋊C4—592no—
615C22×C22⋊C4—591no—
616C22×C22⋊C4—591no—
617C22×C42—592no—
618C22×C42—591no—
619C22×C42—592no—
620#400—591no—
621#400—591no—
622#400—591no—
623#400—592no—
624#400—592no—
625#400C2×D5911yescharacteristic, complemented
626#399—592no—
627#399—591no—
628#399—592no—
629#399—591no—
630#399—591no—
631#399C2×D5911yescharacteristic, complemented
632#398—591no—
633#398—591no—
634#398—592no—
635#398—591no—
636#398—592no—
637#398C2×D5911yescharacteristic, complemented
638#397—592no—
639#397—591no—
640#397—592no—
641#397—591no—
642#397—592no—
643#397—592no—
644#397—592no—
645#397—592no—
646#397—591no—
647#397—592no—
648#397—592no—
649#397—592no—
650#397C2×D5912yescomplemented
651#397C2×D5911yescharacteristic, complemented
652#394—592no—
653#394—592no—
654#394—592no—
655#394—592no—
656#394—592no—
657#394—592no—
658#394—592no—
659#394C2×D5912yes—
660C4×C4⋊C4—592no—
661C4×C4⋊C4—592no—
662C4×C4⋊C4—592no—
663C4×C4⋊C4—592no—
664C4×C4⋊C4—592no—
665C4×C4⋊C4—592no—
666C4×C4⋊C4—592no—
667C4×C4⋊C4C2×D5912yescomplemented
668C4×C22⋊C4—592no—
669C4×C22⋊C4—591no—
670C4×C22⋊C4—592no—
671C4×C22⋊C4—592no—
672C4×C22⋊C4—592no—
673C4×C22⋊C4—592no—
674C4×C22⋊C4—592no—
675C4×C22⋊C4—592no—
676C4×C22⋊C4—592no—
677C4×C22⋊C4—592no—
678C4×C22⋊C4—591no—
679C4×C22⋊C4—591no—
680C4×C22⋊C4C2×D5912yescomplemented
681C4×C22⋊C4C2×D5911yescharacteristic, complemented
682C2×#95—592no—
683C2×#95—592no—
684C2×#95—592no—
685C2×#95—591no—
686C2×#95—592no—
687C2×#95—591no—
688C59C2×#239511yescharacteristic, complemented, Sylow
689C25—591no—
690C25—591no—
691C22×D4—591no—
692C22×D4—591no—
693C22×D4—591no—
694C22×D4—1184no—
695C22×D4—1184no—
696C22×D4—1184no—
697C22×D4C22×D5911yescharacteristic
698C23×C4—591no—
699C23×C4—591no—
700C23×C4—598no—
701C23×C4—592no—
702C23×C4—591no—
703C23×C4—591no—
704C23×C4—591no—
705C23×C4—591no—
706C23×C4—591no—
707C23×C4—591no—
708C23×C4—592no—
709C23×C4—592no—
710C23×C4—592no—
711C23×C4—591no—
712C23×C4—591no—
713C23×C4—591no—
714C23×C4—1188no—
715C23×C4—1184no—
716C23×C4—1188no—
717C23×C4C22×D5911yescharacteristic
718C23×C4C22×D5911yescharacteristic
719C4×D4—24no—
720C4×D4—1184no—
721C4×D4—1184no—
722C4×D4—1184no—
723C4×D4—1184no—
724C4×D4—1184no—
725C4×D4—1184no—
726C4×D4—1184no—
727#117—24no—
728#117—1188no—
729#117—1188no—
730#117—1184no—
731#117—1184no—
732#117—1184no—
733C2×C4⋊C4—592no—
734C2×C4⋊C4—591no—
735C2×C4⋊C4—592no—
736C2×C4⋊C4—591no—
737C2×C4⋊C4—591no—
738C2×C4⋊C4—591no—
739C2×C4⋊C4—591no—
740C2×C4⋊C4—592no—
741C2×C4⋊C4—592no—
742C2×C4⋊C4—592no—
743C2×C4⋊C4—592no—
744C2×C4⋊C4—592no—
745C2×C4⋊C4—592no—
746C2×C4⋊C4—1184no—
747C2×C4⋊C4—1184no—
748C2×C4⋊C4—1184no—
749C2×C4⋊C4—1188no—
750C2×C4⋊C4—1188no—
751C2×C4⋊C4C22×D5911yescharacteristic
752C2×C4⋊C4C22×D5911yescharacteristic
753C2×C4⋊C4C22×D5911yescharacteristic
754C2×C4⋊C4C22×D5912yes—
755C2×C4⋊C4C22×D5912yes—
756C2×C22⋊C4—592no—
757C2×C22⋊C4—591no—
758C2×C22⋊C4—591no—
759C2×C22⋊C4—592no—
760C2×C22⋊C4—592no—
761C2×C22⋊C4—592no—
762C2×C22⋊C4—592no—
763C2×C22⋊C4—592no—
764C2×C22⋊C4—591no—
765C2×C22⋊C4—591no—
766C2×C22⋊C4—591no—
767C2×C22⋊C4—591no—
768C2×C22⋊C4—592no—
769C2×C22⋊C4—592no—
770C2×C22⋊C4—592no—
771C2×C22⋊C4—592no—
772C2×C22⋊C4—592no—
773C2×C22⋊C4—592no—
774C2×C22⋊C4—1184no—
775C2×C22⋊C4—1188no—
776C2×C22⋊C4—1188no—
777C2×C22⋊C4—1188no—
778C2×C22⋊C4—1184no—
779C2×C22⋊C4—1188no—
780C2×C22⋊C4C22×D5912yes—
781C2×C22⋊C4C22×D5911yescharacteristic
782C2×C22⋊C4C22×D5911yescharacteristic
783C2×C22⋊C4C22×D5912yes—
784C2×C22⋊C4C22×D5912yes—
785C2×C22⋊C4C22×D5912yes—
786C2×C42—592no—
787C2×C42—592no—
788C2×C42—591no—
789C2×C42—591no—
790C2×C42—592no—
791C2×C42—592no—
792C2×C42—592no—
793C2×C42—591no—
794C2×C42—592no—
795C2×C42—1188no—
796C2×C42—1184no—
797C2×C42—1188no—
798C2×C42C22×D5912yes—
799C2×C42C22×D5911yescharacteristic
800C2×C42C22×D5912yes—
801#95—592no—
802#95—592no—
803#95—592no—
804#95—592no—
805#95—591no—
806#95—592no—
807#95—592no—
808#95—592no—
809#95—591no—
810#95—592no—
811#95—592no—
812#95—592no—
813#95—592no—
814#95—592no—
815#95—592no—
816#95—592no—
817#95C22×D5912yes—
818#95C22×D5911yescharacteristic
819#95C22×D5912yes—
820#95C22×D5911yescharacteristic
821#95C22×D5912yes—
822#95C22×D5912yes—
823C24—591no—
824C24—594no—
825C24—594no—
826C24—591no—
827C24—591no—
828C24—1182no—
829C24—1184no—
830C24—1184no—
831C24—1184no—
832C24—1184no—
833C24—1182no—
834C24—1182no—
835C24—1182no—
836C24C23×D5911yescharacteristic
837C24C23×D5911yescharacteristic
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—1182no—
842C2×D4—1182no—
843C2×D4—1182no—
844C2×D4—1182no—
845C2×D4—11832no—
846C2×D4—1182no—
847C2×D4—1182no—
848C2×D4—1182no—
849C2×D4—1182no—
850C2×D4—1182no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—591no—
855C22×C4—594no—
856C22×C4—598no—
857C22×C4—594no—
858C22×C4—592no—
859C22×C4—591no—
860C22×C4—591no—
861C22×C4—594no—
862C22×C4—594no—
863C22×C4—594no—
864C22×C4—598no—
865C22×C4—594no—
866C22×C4—592no—
867C22×C4—591no—
868C22×C4—591no—
869C22×C4—592no—
870C22×C4—592no—
871C22×C4—1184no—
872C22×C4—11832no—
873C22×C4—1182no—
874C22×C4—1184no—
875C22×C4—1182no—
876C22×C4—1184no—
877C22×C4—1184no—
878C22×C4—1184no—
879C22×C4—1182no—
880C22×C4—1182no—
881C22×C4—1184no—
882C22×C4—1184no—
883C22×C4—1184no—
884C22×C4—1182no—
885C22×C4—1184no—
886C22×C4—1184no—
887C22×C4—1184no—
888C22×C4—1184no—
889C22×C4—1184no—
890C22×C4—1184no—
891C22×C4—1184no—
892C22×C4—1184no—
893C22×C4—1184no—
894C22×C4—1182no—
895C22×C4—1184no—
896C22×C4—1184no—
897C22×C4—1182no—
898C22×C4—1184no—
899C22×C4—23616no—
900C22×C4D4×D5914yes—
901C22×C4C23×D5912yes—
902C22×C4C23×D5911yescharacteristic
903C22×C4C23×D5911yescharacteristic
904C22×C4C23×D5912yes—
905C22×C4C23×D5912yes—
906C22×C4C23×D5911yescharacteristic
907C22×C4C23×D5912yes—
908C22×C4C23×D5911yescharacteristic
909C22×C4C23×D5911yescharacteristic
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—1184no—
916C4⋊C4—1184no—
917C4⋊C4—1182no—
918C4⋊C4—1182no—
919C4⋊C4—1184no—
920C4⋊C4—1184no—
921C4⋊C4—1184no—
922C4⋊C4—1184no—
923C4⋊C4—1182no—
924C4⋊C4—1182no—
925C4⋊C4—1182no—
926C4⋊C4—1184no—
927C4⋊C4—1184no—
928C22⋊C4—24no—
929C22⋊C4—22no—
930C22⋊C4—24no—
931C22⋊C4—22no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—1182no—
935C22⋊C4—1184no—
936C22⋊C4—1184no—
937C22⋊C4—1184no—
938C22⋊C4—1184no—
939C22⋊C4—1182no—
940C22⋊C4—1182no—
941C22⋊C4—1184no—
942C22⋊C4—1184no—
943C22⋊C4—1182no—
944C22⋊C4—1184no—
945C22⋊C4—1184no—
946C22⋊C4—1184no—
947C22⋊C4—1182no—
948C22⋊C4—1184no—
949C22⋊C4—1182no—
950C22⋊C4—1184no—
951C22⋊C4—1184no—
952C42—24no—
953C42—22no—
954C42—24no—
955C42—1184no—
956C42—1184no—
957C42—1182no—
958C42—1182no—
959C42—1184no—
960C42—1184no—
961C42—1184no—
962C42—1182no—
963C42—1184no—
964C23—21no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—592no—
973C23—594no—
974C23—592no—
975C23—594no—
976C23—592no—
977C23—592no—
978C23—592no—
979C23—1188no—
980C23—1188no—
981C23—1188no—
982C23—11816no—
983C23—1188no—
984C23—1181no—
985C23—1182no—
986C23—1182no—
987C23—1182no—
988C23—1182no—
989C23—1181no—
990C23—1181no—
991C23—1181no—
992C23—2364no—
993C23—2368no—
994C23—2368no—
995C23—2368no—
996C23—2364no—
997C23C2×D4×D5912yes—
998C23#41×D5912yes—
999C23C24×D5911yescharacteristic
1000D4—28no—
1001D4—1188no—
1002D4—1188no—
1003D4—1188no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—28no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—44no—
1024C2×C4—592no—
1025C2×C4—594no—
1026C2×C4—5916no—
1027C2×C4—592no—
1028C2×C4—594no—
1029C2×C4—592no—
1030C2×C4—1188no—
1031C2×C4—11816no—
1032C2×C4—1188no—
1033C2×C4—1188no—
1034C2×C4—1188no—
1035C2×C4—1181no—
1036C2×C4—1182no—
1037C2×C4—1182no—
1038C2×C4—1182no—
1039C2×C4—1181no—
1040C2×C4—1188no—
1041C2×C4—1181no—
1042C2×C4—1182no—
1043C2×C4—1182no—
1044C2×C4—1181no—
1045C2×C4—1182no—
1046C2×C4—1182no—
1047C2×C4—1182no—
1048C2×C4—1182no—
1049C2×C4—1182no—
1050C2×C4—1182no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—2364no—
1055C2×C4—2368no—
1056C2×C4—2368no—
1057C2×C4—2364no—
1058C2×C4—2368no—
1059C2×C4—2364no—
1060C2×C4—2364no—
1061C2×C4—2364no—
1062C2×C4C2×D4×D5912yes—
1063C2×C4C2×D4×D5912yes—
1064C2×C4#41×D5914yes—
1065C2×C4#41×D5912yes—
1066C2×C4#41×D5914yes—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—24no—
1071C22—22no—
1072C22—41no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—41no—
1077C22—594no—
1078C22—594no—
1079C22—598no—
1080C22—598no—
1081C22—594no—
1082C22—1182no—
1083C22—1182no—
1084C22—1182no—
1085C22—1184no—
1086C22—1182no—
1087C22—23616no—
1088C22—23616no—
1089C22—2361no—
1090C22—2362no—
1091C22—2362no—
1092C22—2362no—
1093C22—2361no—
1094C22C22×D4×D5911yescharacteristic
1095C22C2×#41×D5912yes—
1096C22C2×#41×D5911yescharacteristic
1097C22C2×#41×D5911yescharacteristic
1098C22C2×#41×D5912yes—
1099C4—22no—
1100C4—22no—
1101C4—24no—
1102C4—41no—
1103C4—42no—
1104C4—42no—
1105C4—41no—
1106C4—42no—
1107C4—594no—
1108C4—1182no—
1109C4—1182no—
1110C4—1184no—
1111C4—2361no—
1112C4—2362no—
1113C4—2362no—
1114C4—2361no—
1115C4—2362no—
1116C4#123×D5914yes—
1117C2—42no—
1118C2—42no—
1119C2—598no—
1120C2—2362no—
1121C2—2362no—
1122C2C2×#123×D5911yescharacteristic
1123C2#525×D5911yescharacteristic
1124C2#529×D5912yes—
1125C2#529×D5912yes—
1126C2#532×D5911yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutator, socle, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC59×#2395C2
prime radicalC22×D4×D59C22
hypercenter#2395D59
hypocenterC59C2×#2395
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. C2×#117×D59C2semidirect
3. #21427362C2semidirect
4. #21427361C2semidirect
5. #21427360C2semidirect
6. #21427359C2semidirect
7. #21427358C2semidirect
8. #21427357C2semidirect
9. #21427356C2semidirect
10. #21427355C2semidirect
11. #21427354C2semidirect
12. #21427353C2semidirect
13. #21427352C2semidirect
14. #400×D59C2semidirect
15. #399×D59C2semidirect
16. #398×D59C2semidirect
17. #397×D59C2semidirect
18. #397×D59C2semidirect
20. C4×C4⋊C4×D59C2semidirect
21. C4×C22⋊C4×D59C2semidirect
22. C4×C22⋊C4×D59C2semidirect
23. C59×#2395C2semidirect
35. C2×#14273686C22semidirect
36. C2×#14273685C22semidirect
37. C2×#14273685C22semidirect
38. C2×#14273684C22semidirect
39. C2×#14273683C22semidirect
55. #16837344C22semidirect
56. #16837343C22semidirect
57. #16837342C22semidirect
58. #16837341C22semidirect
59. #16837340C22semidirect
60. #16837339C22semidirect
61. #16837338C22semidirect
62. #16837338C22semidirect
63. #16837337C22semidirect
64. #16837337C22semidirect
65. #16837336C22semidirect
66. #16837335C22semidirect
67. #16837334C22semidirect
68. #16837333C22semidirect
69. #16837332C22semidirect
70. #16837331C22semidirect
71. #16837331C22semidirect
72. #16837331C22semidirect
73. #16837330C22semidirect
74. #16837330C22semidirect
75. #16837330C22semidirect
76. #16837329C22semidirect
77. #16837329C22semidirect
78. #16837328C22semidirect
79. #16837328C22semidirect
80. #16837327C22semidirect
81. #16837327C22semidirect
89. C4⋊C4×Dic59C22semidirect
90. C4⋊C4×Dic59C22semidirect
91. C4×Dic59⋊C4C22semidirect
92. C4×Dic59⋊C4C22semidirect
93. C4×C4⋊Dic59C22semidirect
94. #16837253C22semidirect
95. #16837253C22semidirect
96. C22⋊C4×Dic59C22semidirect
97. C22⋊C4×Dic59C22semidirect
98. C22⋊C4×Dic59C22semidirect
99. C4×(C2×D59)⋊C4C22semidirect
100. C4×(C2×D59)⋊C4C22semidirect
101. C4×(C2×D59)⋊C4C22semidirect
102. C4×C22⋊Dic59C22semidirect
103. C4×C22⋊Dic59C22semidirect
104. #16837249C22semidirect
105. #16837249C22semidirect
106. #16837249C22semidirect
107. #16837249C22semidirect
115. C2×#117×C59C22semidirect
116. C59×#400C22semidirect
117. C59×#399C22semidirect
118. C59×#398C22semidirect
119. C59×#397C22semidirect
120. C59×#397C22semidirect
122. C4×C4⋊C4×C59C22semidirect
123. C4×C22⋊C4×C59C22semidirect
124. C4×C22⋊C4×C59C22semidirect
567. #2395D59direct (N × H)
586. D59#2395direct (N × H)
605. C2×#117C2×D59semidirect
625. #400C2×D59semidirect
631. #399C2×D59semidirect
637. #398C2×D59semidirect
650. #397C2×D59semidirect
651. #397C2×D59semidirect
667. C4×C4⋊C4C2×D59semidirect
680. C4×C22⋊C4C2×D59semidirect
681. C4×C22⋊C4C2×D59semidirect
688. C59C2×#2395semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D592
C2×#117×D592
#214273622
#214273612
#214273602
#214273592
#214273582
#214273572
#214273562
#214273552
#214273542
#214273532
#214273522
#400×D592
#399×D592
#398×D592
#397×D592
#394×D592
C4×C4⋊C4×D592
C4×C22⋊C4×D592
C59×#23952
C2×#239559