Finite Group Databasebeta

← C4×#16837317 #28510482

Subgroups — C4×#16837317 #28510482

Order 15104.

2550 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D59C211yesmaximal, characteristic
2C2×#16837317C211yesmaximal, characteristic
3C2×C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic59C211yesmaximal, characteristic, complemented
7#21422354C211yesmaximal, characteristic, complemented
8#21422347C211yesmaximal, characteristic, complemented
9#21422345C211yesmaximal, characteristic, complemented
10#21422344C211yesmaximal, characteristic, complemented
11#21422340C211yesmaximal, characteristic, complemented
12#21422339C211yesmaximal, characteristic, complemented
13#21422335C211yesmaximal, characteristic
14C4×C59⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C2×C4×C22⋊D59—24no—
19C2×C4×C22⋊D59—24no—
20C2×C4×C22⋊D59—24no—
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35#16837317C418yesdirect product factor
36C4×Dic59⋊C4—24no—
37C4×(C2×D59)⋊C4—24no—
38C4×(C2×D59)⋊C4—24no—
39C4×C22⋊Dic59—24no—
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C24×C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C22×C42×C59C2211yescharacteristic
56C22×C42×C59C2211yescharacteristic
57C4×C22⋊C4×C59—24no—
58C2×#95×C59C2211yescharacteristic
59C2×#95×C59C2211yescharacteristic
60C24×D59C2311yescharacteristic
61C22×C22⋊D59—22no—
62C22×C22⋊D59—22no—
63C22×C22⋊D59—22no—
64C22×C22⋊D59—22no—
65C22×C22⋊D59—22no—
66C22×C22⋊D59—22no—
67C22×C22⋊D59C2×C414yes—
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C22×C4×D59—22no—
76C22×C4×D59—22no—
77C22×C4×D59—22no—
78C22×C4×D59—22no—
79C22×C4×D59—22no—
80C22×C4×D59—22no—
81C22×C4×D59D414yes—
82C4×C22⋊D59—232no—
83C2×Dic59⋊C4—22no—
84C2×Dic59⋊C4—22no—
85C2×Dic59⋊C4—22no—
86C2×Dic59⋊C4—22no—
87C2×Dic59⋊C4—22no—
88C2×Dic59⋊C4—22no—
89C2×Dic59⋊C4—22no—
90C2×Dic59⋊C4—22no—
91C2×Dic59⋊C4C2×C414yescomplemented
92C2×C22⋊Dic59—22no—
93C2×C22⋊Dic59—22no—
94C2×C22⋊Dic59—22no—
95C2×C22⋊Dic59—22no—
96C2×C22⋊Dic59—22no—
97C2×C22⋊Dic59—22no—
98C2×C22⋊Dic59—22no—
99C2×C22⋊Dic59—22no—
100C2×C22⋊Dic59C2×C414yescomplemented
101C2×(C2×D59)⋊C4—22no—
102C2×(C2×D59)⋊C4—22no—
103C2×(C2×D59)⋊C4—22no—
104C2×(C2×D59)⋊C4—22no—
105C2×(C2×D59)⋊C4—22no—
106C2×(C2×D59)⋊C4—22no—
107C2×(C2×D59)⋊C4—22no—
108C2×(C2×D59)⋊C4—22no—
109C2×(C2×D59)⋊C4—22no—
110C2×(C2×D59)⋊C4—22no—
111C2×(C2×D59)⋊C4—22no—
112C2×(C2×D59)⋊C4—22no—
113C2×(C2×D59)⋊C4—22no—
114C2×(C2×D59)⋊C4C2×C414yescomplemented
115C2×(C2×D59)⋊C4C2×C414yescomplemented
116C2×C4×Dic59—22no—
117C2×C4×Dic59—22no—
118C2×C4×Dic59—22no—
119C2×C4×Dic59—22no—
120C2×C4×Dic59—22no—
121C2×C4×Dic59—22no—
122C2×C4×Dic59—22no—
123C2×C4×Dic59D414yes—
124C2×C4×Dic59D414yescomplemented
125C59⋊#95—22no—
126C59⋊#95—22no—
127C59⋊#95—22no—
128C59⋊#95—22no—
129C59⋊#95—22no—
130C59⋊#95—22no—
131C59⋊#95—22no—
132C59⋊#95—22no—
133C59⋊#95—22no—
134C59⋊#95—22no—
135C59⋊#95—22no—
136C59⋊#95C2×C414yescomplemented
137C25×C59C2311yescharacteristic
138C23×C4×C59—22no—
139C23×C4×C59—22no—
140C23×C4×C59—22no—
141C23×C4×C59—22no—
142C23×C4×C59—22no—
143C23×C4×C59—22no—
144C23×C4×C59D414yes—
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2311yescharacteristic
149C23×C4×C59C2311yescharacteristic
150C23×C4×C59C2311yescharacteristic
151C2×C22⋊C4×C59—22no—
152C2×C22⋊C4×C59—22no—
153C2×C22⋊C4×C59—22no—
154C2×C22⋊C4×C59—22no—
155C2×C22⋊C4×C59—22no—
156C2×C22⋊C4×C59C2×C414yescomplemented
157C2×C42×C59—22no—
158C2×C42×C59—22no—
159C2×C42×C59—22no—
160C2×C42×C59—22no—
161C2×C42×C59—22no—
162C2×C42×C59—22no—
163#95×C59—22no—
164#95×C59—22no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—21no—
173C24×C59—21no—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59—21no—
177C24×C59C22×C412yes—
178C24×C59C2×D412yes—
179C24×C59#4112yes—
180C24×C59C2411yescharacteristic
181C23×D59—21no—
182C23×D59—21no—
183C23×D59—21no—
184C23×D59—21no—
185C23×D59—21no—
186C23×D59—21no—
187C23×D59—21no—
188C23×D59—21no—
189C23×D59—21no—
190C23×D59—21no—
191C23×D59—21no—
192C23×D59—21no—
193C23×D59C22×C412yes—
194C23×D59C2×D412yes—
195C23×D59#4112yes—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—28no—
227C22×C4×C59—28no—
228C22×C4×C59—28no—
229C22×C4×C59—44no—
230C22×C4×C59—44no—
231C22×C4×C59—44no—
232C22×C4×C59—44no—
233C22×C4×C59C22×C412yes—
234C22×C4×C59C22×C412yes—
235C22×C4×C59C2×D412yes—
236C22×C4×C59C2×D412yes—
237C22×C4×C59C2×D412yes—
238C22×C4×C59C2×D412yes—
239C22×C4×C59C2×D412yes—
240C22×C4×C59#4112yes—
241C22×C4×C59#4112yes—
242C22×C4×C59#4112yes—
243C22×C4×C59#4112yes—
244C22×C4×C59#4112yes—
245C2×C22⋊D59—28no—
246C2×C22⋊D59—28no—
247C2×C22⋊D59—28no—
248C2×C22⋊D59—28no—
249C2×C22⋊D59—28no—
250C2×C22⋊D59—28no—
251C2×C22⋊D59—28no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278C22×Dic59—21no—
279C22×Dic59—21no—
280C22×Dic59—21no—
281C22×Dic59—21no—
282C22×Dic59—21no—
283C22×Dic59—21no—
284C22×Dic59—21no—
285C22×Dic59—21no—
286C22×Dic59—21no—
287C22×Dic59—21no—
288C22×Dic59—21no—
289C22×Dic59—21no—
290C22×Dic59C22×C412yes—
291C22×Dic59C22×C412yes—
292C22×Dic59C22×C412yes—
293C22×Dic59C2×D412yes—
294C22×Dic59C2×D412yes—
295C22×Dic59C2×D412yes—
296C22×Dic59C2×D412yes—
297C22×Dic59C2×D412yes—
298C22×Dic59#4112yes—
299C22×Dic59#4112yes—
300C22×Dic59#4112yes—
301C2×C4×D59—28no—
302C2×C4×D59—28no—
303C2×C4×D59—28no—
304C2×C4×D59—44no—
305C2×C4×D59—44no—
306C2×C4×D59—44no—
307C2×C4×D59—44no—
308C22⋊C4×C59—28no—
309C22⋊C4×C59—28no—
310C42×C59—44no—
311C42×C59—44no—
312C22⋊Dic59—28no—
313C22⋊Dic59—28no—
314C22⋊Dic59—28no—
315(C2×D59)⋊C4—28no—
316(C2×D59)⋊C4—28no—
317(C2×D59)⋊C4—28no—
318(C2×D59)⋊C4—28no—
319(C2×D59)⋊C4—28no—
320Dic59⋊C4—28no—
321Dic59⋊C4—28no—
322Dic59⋊C4—28no—
323C4×Dic59—28no—
324C4×Dic59—28no—
325C4×Dic59—44no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59C4×D414yes—
361C23×C59C23×C411yescharacteristic
362C23×C59C22×D411yescharacteristic
363C23×C59C22×D411yescharacteristic
364C23×C59C22×D411yescharacteristic
365C23×C59C22×D411yescharacteristic
366C23×C59C2×#4111yescharacteristic
367C23×C59C2×#4111yescharacteristic
368C23×C59C2×#4111yescharacteristic
369C23×C59C2×#4111yescharacteristic
370C23×C59C2×#4111yescharacteristic
371C23×C59C2×#4111yescharacteristic
372C23×C59C2×#4111yescharacteristic
373C23×C59C2×#4111yescharacteristic
374C23×C59C2×#4111yescharacteristic
375C23×C59C2×#4111yescharacteristic
376C22×D59—22no—
377C22×D59—22no—
378C22×D59—22no—
379C22×D59—22no—
380C22×D59—22no—
381C22×D59—22no—
382C22×D59—22no—
383C22×D59—22no—
384C22×D59—22no—
385C22×D59—22no—
386C22×D59—22no—
387C22×D59—22no—
388C22×D59—22no—
389C22×D59—22no—
390C22×D59—22no—
391C22×D59—22no—
392C22×D59—22no—
393C22×D59—22no—
394C22×D59—41no—
395C22×D59—41no—
396C22×D59—41no—
397C22×D59—41no—
398C22×D59—41no—
399C22×D59—41no—
400C22×D59—41no—
401C22×D59—41no—
402C22×D59—41no—
403C22×D59—41no—
404C22×D59—41no—
405C22×D59—41no—
406C22×D59—41no—
407C22×D59—41no—
408C22×D59—41no—
409C22×D59—41no—
410C22×D59C4×D414yes—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×C4×C59—41no—
441C2×C4×C59—41no—
442C2×C4×C59—41no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—416no—
447C2×C4×C59#12014yes—
448C2×C4×C59#12114yes—
449C2×C4×C59#12114yes—
450C2×C4×C59#12114yes—
451C2×C4×C59#12314yes—
452C2×C4×C59#12314yes—
453C2×C4×C59#12414yes—
454C22⋊D59—232no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—22no—
460C2×Dic59—22no—
461C2×Dic59—22no—
462C2×Dic59—22no—
463C2×Dic59—22no—
464C2×Dic59—22no—
465C2×Dic59—22no—
466C2×Dic59—22no—
467C2×Dic59—22no—
468C2×Dic59—22no—
469C2×Dic59—22no—
470C2×Dic59—22no—
471C2×Dic59—22no—
472C2×Dic59—22no—
473C2×Dic59—22no—
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—41no—
483C2×Dic59—41no—
484C2×Dic59—41no—
485C2×Dic59—41no—
486C2×Dic59—41no—
487C2×Dic59—41no—
488C2×Dic59—41no—
489C2×Dic59—41no—
490C2×Dic59—41no—
491C2×Dic59—41no—
492C2×Dic59—41no—
493C2×Dic59—41no—
494C2×Dic59—41no—
495C2×Dic59—41no—
496C2×Dic59—41no—
497C2×Dic59—41no—
498C2×Dic59—41no—
499C2×Dic59—41no—
500C2×Dic59—41no—
501C2×Dic59—41no—
502C2×Dic59C4×D414yes—
503C2×Dic59C4×D414yescomplemented
504C4×D59—416no—
505C4×#394—591nomaximal, Sylow
506C22×C59—24no—
507C22×C59—24no—
508C22×C59—24no—
509C22×C59—42no—
510C22×C59—42no—
511C22×C59—42no—
512C22×C59—42no—
513C22×C59—42no—
514C22×C59—42no—
515C22×C59—42no—
516C22×C59—42no—
517C22×C59—42no—
518C22×C59—42no—
519C22×C59—42no—
520C22×C59—42no—
521C22×C59C2×C4×D411yescharacteristic
522C22×C59C2×C4×D411yescharacteristic
523C22×C59C2×C4×D411yescharacteristic
524C22×C59C2×C4×D411yescharacteristic
525C22×C59C4×#4111yescharacteristic
526C22×C59C4×#4111yescharacteristic
527C22×C59C4×#4111yescharacteristic
528C22×C59C2×#12011yescharacteristic
529C22×C59C2×#12111yescharacteristic
530C22×C59C2×#12111yescharacteristic
531C22×C59C2×#12111yescharacteristic
532C22×C59C2×#12311yescharacteristic
533C22×C59C2×#12311yescharacteristic
534C22×C59#52511yescharacteristic
535C22×C59#52511yescharacteristic
536C22×C59#52511yescharacteristic
537C22×C59#52511yescharacteristic
538C22×C59#52511yescharacteristic
539C22×C59#52511yescharacteristic
540C22×C59#52511yescharacteristic
541C22×C59#52511yescharacteristic
542C22×C59C2×#12411yescharacteristic
543C22×C59#52911yescharacteristic
544C22×C59#52911yescharacteristic
545C22×C59#52911yescharacteristic
546C22×C59#52911yescharacteristic
547C22×C59#52911yescharacteristic
548C22×C59#52911yescharacteristic
549C22×C59#52911yescharacteristic
550C22×C59#52911yescharacteristic
551C22×C59#52911yescharacteristic
552C22×C59#53211yescharacteristic
553C22×C59#53211yescharacteristic
554C22×C59#53211yescharacteristic
555C22×C59#53211yescharacteristic
556C2×D59—24no—
557C2×D59—24no—
558C2×D59—24no—
559C2×D59—42no—
560C2×D59—42no—
561C2×D59—42no—
562C2×D59—42no—
563C2×D59—42no—
564C2×D59—42no—
565C2×D59—42no—
566C2×D59—42no—
567C2×D59—42no—
568C2×D59—42no—
569C2×D59—42no—
570C2×D59—42no—
571C4×C59—42no—
572C4×C59—42no—
573C4×C59—42no—
574C4×C59—42no—
575C4×C59—42no—
576C4×C59#39418yescomplemented
577Dic59—24no—
578Dic59—24no—
579Dic59—42no—
580Dic59—42no—
581Dic59—42no—
582Dic59—42no—
583Dic59—42no—
584C22×C4×D4—591no—
585C2×#394—591no—
586C2×C4×C4⋊C4—591no—
587C2×C4×C22⋊C4—591no—
588C2×C4×C22⋊C4—591no—
589C2×C4×C22⋊C4—591no—
590C2×C4×C22⋊C4D5911yescharacteristic, complemented
591#1442—591no—
592#1441—591no—
593#1440—591no—
594#1440—591no—
595#1439—591no—
596#1439—591no—
597#1438—591no—
598C4×#95—591no—
599C2×C59—44no—
600C2×C59C4×#12011yescharacteristic
601C2×C59C4×#12111yescharacteristic
602C2×C59C4×#12111yescharacteristic
603C2×C59C4×#12111yescharacteristic
604C2×C59C4×#12311yescharacteristic
605C2×C59C4×#12311yescharacteristic
606C2×C59C4×#12411yescharacteristic
607C2×C59C2×#39411yescharacteristic
608C2×C59#238811yescharacteristic
609C2×C59#239211yescharacteristic
610C2×C59#239211yescharacteristic
611C2×C59#239211yescharacteristic
612C2×C59#239511yescharacteristic
613C2×C59#239511yescharacteristic
614C2×C59#239811yescharacteristic
615D59—44no—
616C23×D4—591no—
617C24×C4—591no—
618C24×C4C2×D5911yescharacteristic
619C2×C4×D4—1184no—
620C2×C4×D4—1184no—
621C2×C4×D4—1184no—
622C22×C4⋊C4—591no—
623C22×C4⋊C4—591no—
624C22×C4⋊C4—591no—
625C22×C22⋊C4—591no—
626C22×C22⋊C4—591no—
627C22×C22⋊C4—591no—
628C22×C22⋊C4—591no—
629C22×C22⋊C4—591no—
630C22×C22⋊C4—591no—
631C22×C22⋊C4—591no—
632C22×C22⋊C4—591no—
633C22×C22⋊C4C2×D5911yescharacteristic
634C22×C22⋊C4C2×D5911yescharacteristic
635C22×C42—591no—
636C22×C42—591no—
637C22×C42—591no—
638C22×C42C2×D5911yescharacteristic
639C22×C42C2×D5911yescharacteristic
640#394—598no—
641C4×C4⋊C4—1184no—
642C4×C22⋊C4—24no—
643C4×C22⋊C4—1184no—
644C4×C22⋊C4—1184no—
645C4×C22⋊C4—1184no—
646C2×#95—591no—
647C2×#95—591no—
648C2×#95—591no—
649C2×#95—591no—
650C2×#95—591no—
651C2×#95—591no—
652C2×#95—591no—
653C2×#95—591no—
654C2×#95—591no—
655C2×#95—591no—
656C2×#95—591no—
657C2×#95—591no—
658C2×#95C2×D5911yescharacteristic
659C2×#95C2×D5911yescharacteristic
660C59C4×#39411yescharacteristic, complemented, Sylow
661C25—591no—
662C25C22×D5911yescharacteristic
663C22×D4—594no—
664C22×D4—1182no—
665C22×D4—1182no—
666C22×D4—1182no—
667C22×D4—1182no—
668C22×D4—1182no—
669C22×D4—1182no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—591no—
677C23×C4—591no—
678C23×C4—591no—
679C23×C4—591no—
680C23×C4—591no—
681C23×C4—591no—
682C23×C4—591no—
683C23×C4—594no—
684C23×C4—1182no—
685C23×C4—1182no—
686C23×C4—1182no—
687C23×C4—1182no—
688C23×C4—1182no—
689C23×C4—1182no—
690C23×C4C22⋊D5914yes—
691C23×C4C22×D5911yescharacteristic
692C23×C4C22×D5911yescharacteristic
693C23×C4C22×D5911yescharacteristic
694C23×C4C22×D5911yescharacteristic
695C23×C4C22×D5911yescharacteristic
696C23×C4C22×D5911yescharacteristic
697C4×D4—11832no—
698C2×C4⋊C4—594no—
699C2×C4⋊C4—1182no—
700C2×C4⋊C4—1182no—
701C2×C4⋊C4—1182no—
702C2×C4⋊C4—1182no—
703C2×C4⋊C4—1182no—
704C2×C4⋊C4—1182no—
705C2×C4⋊C4—1182no—
706C2×C4⋊C4—1182no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—594no—
713C2×C22⋊C4—594no—
714C2×C22⋊C4—594no—
715C2×C22⋊C4—1182no—
716C2×C22⋊C4—1182no—
717C2×C22⋊C4—1182no—
718C2×C22⋊C4—1182no—
719C2×C22⋊C4—1182no—
720C2×C22⋊C4—1182no—
721C2×C22⋊C4—1182no—
722C2×C22⋊C4—1182no—
723C2×C22⋊C4—1182no—
724C2×C22⋊C4—1182no—
725C2×C22⋊C4—1182no—
726C2×C22⋊C4—1182no—
727C2×C22⋊C4—1182no—
728C2×C22⋊C4—1182no—
729C2×C22⋊C4—1182no—
730C2×C22⋊C4—1182no—
731C2×C22⋊C4—1182no—
732C2×C22⋊C4—1182no—
733C2×C22⋊C4—1182no—
734C2×C22⋊C4—1182no—
735C2×C22⋊C4—1182no—
736C2×C22⋊C4C4×D5914yescomplemented
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—22no—
740C2×C42—22no—
741C2×C42—22no—
742C2×C42—22no—
743C2×C42—594no—
744C2×C42—594no—
745C2×C42—1182no—
746C2×C42—1182no—
747C2×C42—1182no—
748C2×C42—1182no—
749C2×C42—1182no—
750C2×C42—1182no—
751C2×C42—1182no—
752#95—22no—
753#95—22no—
754#95—594no—
755#95—1182no—
756#95—1182no—
757#95—1182no—
758#95—1182no—
759#95—1182no—
760#95—1182no—
761#95—1182no—
762#95—1182no—
763#95—1182no—
764#95—1182no—
765#95—1182no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—592no—
779C24—592no—
780C24—592no—
781C24—1181no—
782C24—1181no—
783C24—1181no—
784C24—1181no—
785C24—1181no—
786C24—1181no—
787C24—1181no—
788C24—1181no—
789C24—1181no—
790C24—1181no—
791C24—1181no—
792C24—1181no—
793C24C2×C4×D5912yes—
794C24#1174568512yes—
795C24C2×C22⋊D5912yes—
796C24C23×D5911yescharacteristic
797C2×D4—1188no—
798C2×D4—1188no—
799C2×D4—1188no—
800C2×D4—1188no—
801C2×D4—1188no—
802C2×D4—1188no—
803C2×D4—1188no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—28no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—592no—
842C22×C4—592no—
843C22×C4—592no—
844C22×C4—592no—
845C22×C4—592no—
846C22×C4—592no—
847C22×C4—592no—
848C22×C4—592no—
849C22×C4—592no—
850C22×C4—592no—
851C22×C4—592no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—1181no—
856C22×C4—1181no—
857C22×C4—1181no—
858C22×C4—1181no—
859C22×C4—1181no—
860C22×C4—1181no—
861C22×C4—1181no—
862C22×C4—1181no—
863C22×C4—1181no—
864C22×C4—1181no—
865C22×C4—1181no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—1181no—
871C22×C4—1181no—
872C22×C4—1181no—
873C22×C4—1181no—
874C22×C4—1181no—
875C22×C4—1181no—
876C22×C4—1181no—
877C22×C4—1181no—
878C22×C4—1181no—
879C22×C4—1181no—
880C22×C4—1181no—
881C22×C4—1181no—
882C22×C4—1181no—
883C22×C4—1181no—
884C22×C4—1181no—
885C22×C4—1181no—
886C22×C4—1181no—
887C22×C4—1181no—
888C22×C4—1181no—
889C22×C4—1181no—
890C22×C4—1188no—
891C22×C4—1188no—
892C22×C4—1188no—
893C22×C4—2364no—
894C22×C4—2364no—
895C22×C4—2364no—
896C22×C4—2364no—
897C22×C4C2×C4×D5912yes—
898C22×C4C2×C4×D5912yes—
899C22×C4#1174568512yes—
900C22×C4#1174568512yes—
901C22×C4#1174568512yes—
902C22×C4#1174568512yes—
903C22×C4D4×D5912yes—
904C22×C4D4×D5912yes—
905C22×C4D4×D5912yes—
906C22×C4#1174568712yes—
907C22×C4C2×C22⋊D5912yes—
908C22×C4C2×C22⋊D5912yes—
909C4⋊C4—1188no—
910C4⋊C4—1188no—
911C4⋊C4—1188no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—1188no—
915C22⋊C4—1188no—
916C22⋊C4—1188no—
917C22⋊C4—1188no—
918C22⋊C4—1188no—
919C22⋊C4—1188no—
920C22⋊C4—1188no—
921C22⋊C4—1188no—
922C42—44no—
923C42—44no—
924C42—1188no—
925C42—1188no—
926C42—2364no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—594no—
962C23—1182no—
963C23—1182no—
964C23—1182no—
965C23—1182no—
966C23—1182no—
967C23—1182no—
968C23—1182no—
969C23—1182no—
970C23—1182no—
971C23—1182no—
972C23—1182no—
973C23—1182no—
974C23—1182no—
975C23—1182no—
976C23—1182no—
977C23—1182no—
978C23—1182no—
979C23—1182no—
980C23—2361no—
981C23—2361no—
982C23—2361no—
983C23—2361no—
984C23—2361no—
985C23—2361no—
986C23—2361no—
987C23—2361no—
988C23—2361no—
989C23—2361no—
990C23—2361no—
991C23—2361no—
992C23—2361no—
993C23—2361no—
994C23—2361no—
995C23—2361no—
996C23C4×C22⋊D5914yes—
997C23C22×C4×D5911yescharacteristic
998C23C2×D4×D5911yescharacteristic
999C23C2×D4×D5911yescharacteristic
1000C23C2×D4×D5911yescharacteristic
1001C23C22×C22⋊D5911yescharacteristic
1002C23#41×D5911yescharacteristic
1003C23#41×D5911yescharacteristic
1004C23#41×D5911yescharacteristic
1005C23#41×D5911yescharacteristic
1006C23C2×#1174568711yescharacteristic
1007C23C2×#1174568511yescharacteristic
1008C23C2×#1174568511yescharacteristic
1009C23C2×#1174568511yescharacteristic
1010C23C2×#1174568511yescharacteristic
1011C23C2×#1174568511yescharacteristic
1012D4—11832no—
1013C2×C4—22no—
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—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—416no—
1049C2×C4—594no—
1050C2×C4—594no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—1182no—
1057C2×C4—1182no—
1058C2×C4—1182no—
1059C2×C4—1182no—
1060C2×C4—1182no—
1061C2×C4—1182no—
1062C2×C4—1182no—
1063C2×C4—1182no—
1064C2×C4—1182no—
1065C2×C4—1182no—
1066C2×C4—1182no—
1067C2×C4—1182no—
1068C2×C4—1182no—
1069C2×C4—1182no—
1070C2×C4—1182no—
1071C2×C4—1182no—
1072C2×C4—1182no—
1073C2×C4—1182no—
1074C2×C4—1182no—
1075C2×C4—1182no—
1076C2×C4—1182no—
1077C2×C4—1182no—
1078C2×C4—2361no—
1079C2×C4—2361no—
1080C2×C4—2361no—
1081C2×C4—2361no—
1082C2×C4—2361no—
1083C2×C4—2361no—
1084C2×C4—2361no—
1085C2×C4—2361no—
1086C2×C4—2361no—
1087C2×C4—2361no—
1088C2×C4—2361no—
1089C2×C4—2361no—
1090C2×C4—2361no—
1091C2×C4—2361no—
1092C2×C4—2361no—
1093C2×C4—2361no—
1094C2×C4—2361no—
1095C2×C4—2361no—
1096C2×C4—2361no—
1097C2×C4—2361no—
1098C2×C4—23616no—
1099C2×C4#1427369514yes—
1100C2×C4#1427369914yes—
1101C2×C4#1427370014yes—
1102C2×C4#1427370014yes—
1103C2×C4#1427370914yes—
1104C2×C4#1427371014yes—
1105C2×C4#1427371314yes—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—1184no—
1122C22—1184no—
1123C22—1184no—
1124C22—2362no—
1125C22—2362no—
1126C22—2362no—
1127C22—2362no—
1128C22—2362no—
1129C22—2362no—
1130C22—2362no—
1131C22—2362no—
1132C22—2362no—
1133C22—2362no—
1134C22—2362no—
1135C22—2362no—
1136C22C4×D4×D5911yescharacteristic
1137C22C4×D4×D5911yescharacteristic
1138C22C4×D4×D5911yescharacteristic
1139C22C2×C4×C22⋊D5911yescharacteristic
1140C22C4×#1174568711yescharacteristic
1141C22C4×#1174568511yescharacteristic
1142C22C4×#1174568511yescharacteristic
1143C22C2×#1427369511yescharacteristic
1144C22C2×#1427369911yescharacteristic
1145C22C2×#1427370011yescharacteristic
1146C22C2×#1427370011yescharacteristic
1147C22C2×#1427370911yescharacteristic
1148C22C2×#1427371011yescharacteristic
1149C22#1683790911yescharacteristic
1150C22#1683791111yescharacteristic
1151C22#1683791111yescharacteristic
1152C22#1683791111yescharacteristic
1153C22#1683791111yescharacteristic
1154C22#1683791111yescharacteristic
1155C22#1683791111yescharacteristic
1156C22#1683791311yescharacteristic
1157C22C2×#1427371311yescharacteristic
1158C22#1683793011yescharacteristic
1159C22#1683793011yescharacteristic
1160C22#1683793011yescharacteristic
1161C22#1683793011yescharacteristic
1162C22#1683793211yescharacteristic
1163C22#1683793211yescharacteristic
1164C22#1683793411yescharacteristic
1165C22#1683793611yescharacteristic
1166C22#1683793611yescharacteristic
1167C22#1683794811yescharacteristic
1168C22#1683794911yescharacteristic
1169C22#1683794911yescharacteristic
1170C22#1683794911yescharacteristic
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—1184no—
1177C4—1184no—
1178C4—2362no—
1179C4—2362no—
1180C4—2362no—
1181C4—2362no—
1182C4—2362no—
1183C4#1683731718yesdirect product factor
1184C2—44no—
1185C2—2364no—
1186C2C4×#1427369511yescharacteristic
1187C2C4×#1427369911yescharacteristic
1188C2C4×#1427370011yescharacteristic
1189C2C4×#1427370011yescharacteristic
1190C2C4×#1427370911yescharacteristic
1191C2C4×#1427371011yescharacteristic
1192C2C4×#1427371311yescharacteristic
1193C2C2×#1683731711yescharacteristic
1194C2#2142731111yescharacteristic
1195C2#2142733811yescharacteristic
1196C2#2142734011yescharacteristic
1197C2#2142734011yescharacteristic
1198C2#2142735311yescharacteristic
1199C2#2142735711yescharacteristic
1200C2#2142738311yescharacteristic
subgroupG/H
centerC23×C4C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC2×C4×C22⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C4×#394
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic59⋊C4C2semidirect
4. C2×C4×(C2×D59)⋊C4C2semidirect
5. C2×C4×(C2×D59)⋊C4C2semidirect
6. C2×C4×C22⋊Dic59C2semidirect
7. #21422354C2semidirect
8. #21422347C2semidirect
9. #21422345C2semidirect
10. #21422344C2semidirect
11. #21422340C2semidirect
12. #21422339C2semidirect
14. C4×C59⋊#95C2semidirect
15. C2×C4×C22⋊C4×C59C2semidirect
35. #16837317C4direct (N × H)
91. C2×Dic59⋊C4C2×C4semidirect
100. C2×C22⋊Dic59C2×C4semidirect
114. C2×(C2×D59)⋊C4C2×C4semidirect
115. C2×(C2×D59)⋊C4C2×C4semidirect
124. C2×C4×Dic59D4semidirect
136. C59⋊#95C2×C4semidirect
156. C2×C22⋊C4×C59C2×C4semidirect
503. C2×Dic59C4×D4semidirect
576. C4×C59#394semidirect
590. C2×C4×C22⋊C4D59semidirect
660. C59C4×#394semidirect
736. C2×C22⋊C4C4×D59semidirect
1183. C4#16837317direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D592
C2×#168373172
C2×C4×Dic59⋊C42
C2×C4×(C2×D59)⋊C42
C2×C4×C22⋊Dic592
#214223542
#214223472
#214223452
#214223442
#214223402
#214223392
#214223352
C4×C59⋊#952
C2×C4×C22⋊C4×C592
C4×#39459