Finite Group Databasebeta

← C59×#35363 #28447472

Subgroups — C59×#35363 #28447472

Order 15104.

2418 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#539C211yesmaximal, characteristic, complemented
2C2×C59×#520C211yesmaximal, characteristic, complemented
3C59×#2611C211yesmaximal, characteristic, complemented
4C59×#2604C211yesmaximal, characteristic, complemented
5C59×#2602C211yesmaximal, characteristic, complemented
6C59×#2601C211yesmaximal, characteristic, complemented
7C59×#2584C211yesmaximal, characteristic, complemented
8C59×#2583C211yesmaximal, characteristic, complemented
9C59×#2478C211yesmaximal, characteristic, complemented
10C59×#2473C211yesmaximal, characteristic, complemented
11C59×#2470C211yesmaximal, characteristic, complemented
12C59×#2466C211yesmaximal, characteristic, complemented
13C59×#2465C211yesmaximal, characteristic, complemented
14C59×#2462C211yesmaximal, characteristic, complemented
15C59×#2455C211yesmaximal, characteristic, complemented
16C59×#2449C211yesmaximal, characteristic, complemented
17C59×#2449C211yesmaximal, characteristic, complemented
18C59×#2443C211yesmaximal, characteristic, complemented
19C59×#2438C211yesmaximal, characteristic, complemented
20C59×#2430C211yesmaximal, characteristic
21C59×#2425C211yesmaximal, characteristic, complemented
22C59×#2419C211yesmaximal, characteristic, complemented
23C59×#2415C211yesmaximal, characteristic, complemented
24C59×#2413C211yesmaximal, characteristic, complemented
25C59×#2413C211yesmaximal, characteristic, complemented
26C59×#2406C211yesmaximal, characteristic, complemented
27C59×#2322C211yesmaximal, characteristic, complemented
28C59×#2322C211yesmaximal, characteristic, complemented
29C4×#121×C59C211yesmaximal, characteristic, complemented
30C2×C59×#389C211yesmaximal, characteristic, complemented
31C59×#2290C211yesmaximal, characteristic, complemented
32C22×#41×C59C2211yescharacteristic
33C59×#539—28no—
34C2×#126×C59C2211yescharacteristic
35C2×#126×C59C2211yescharacteristic
36C2×#125×C59C2211yescharacteristic
37C2×#125×C59C2211yescharacteristic
38C2×#123×C59C2211yescharacteristic
39C2×#123×C59C2211yescharacteristic
40C2×#123×C59C2211yescharacteristic
41C2×#123×C59C2211yescharacteristic
42C2×#123×C59C2211yescharacteristic
43C2×#123×C59C2211yescharacteristic
44C2×#123×C59C2211yescharacteristic
45C2×C22⋊Q8×C59C2211yescharacteristic
46C2×C22⋊Q8×C59C2211yescharacteristic
47C2×C22⋊Q8×C59C2211yescharacteristic
48C2×C22⋊Q8×C59C2211yescharacteristic
49C2×#121×C59C2211yescharacteristic
50C2×#121×C59C2211yescharacteristic
51C59×#520—28no—
52C2×C4×Q8×C59C2211yescharacteristic
53C2×C4×Q8×C59C2211yescharacteristic
54C2×C4×D4×C59C2211yescharacteristic
55C2×C4×D4×C59C2211yescharacteristic
56C2×C4×D4×C59C2211yescharacteristic
57C2×C4×D4×C59C2211yescharacteristic
58C2×C4×D4×C59C2211yescharacteristic
59C2×C4×D4×C59C2211yescharacteristic
60C2×C4×D4×C59C2211yescharacteristic
61C2×C4×D4×C59C2211yescharacteristic
62C2×#117×C59C2211yescharacteristic
63C2×#117×C59C2211yescharacteristic
64C2×#117×C59C2211yescharacteristic
65C2×#117×C59C2211yescharacteristic
66C22×C4⋊C4×C59C2211yescharacteristic
67C22×C4⋊C4×C59C2211yescharacteristic
68C22×C4⋊C4×C59C2211yescharacteristic
69C22×C4⋊C4×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C22×C42×C59C2211yescharacteristic
73C59×#400C2211yescharacteristic
74C59×#400C2211yescharacteristic
75C59×#399C2211yescharacteristic
76C59×#399C2211yescharacteristic
77C59×#398C2211yescharacteristic
78C59×#398C2211yescharacteristic
79C59×#398C2211yescharacteristic
80C59×#398C2211yescharacteristic
81C59×#398C2211yescharacteristic
82C59×#398C2211yescharacteristic
83C59×#398C2211yescharacteristic
84C59×#398C2211yescharacteristic
85C59×#397C2211yescharacteristic
86C59×#397C2211yescharacteristic
87C59×#397C2211yescharacteristic
88C59×#397C2211yescharacteristic
89C59×#396C2211yescharacteristic
90C59×#396C2211yescharacteristic
91C59×#396C2211yescharacteristic
92C59×#396C2211yescharacteristic
93C59×#395C2211yescharacteristic
94C59×#395C2211yescharacteristic
95C59×#395C2211yescharacteristic
96C59×#395C2211yescharacteristic
97C59×#395C2211yescharacteristic
98C59×#394C2211yescharacteristic
99C59×#394C2211yescharacteristic
100C59×#394C2211yescharacteristic
101C59×#394C2211yescharacteristic
102C59×#394C2211yescharacteristic
103C59×#393C2211yescharacteristic
104C59×#392C2211yescharacteristic
105C59×#391C2211yescharacteristic
106C59×#390C2211yescharacteristic
107C59×#389C2211yescharacteristic
108C59×#389C2211yescharacteristic
109C59×#389C2211yescharacteristic
110C59×#389C2211yescharacteristic
111C59×#389C2211yescharacteristic
112C59×#389C2211yescharacteristic
113C59×#389C2211yescharacteristic
114C59×#389C2211yescharacteristic
115C59×#389C2211yescharacteristic
116C59×#389C2211yescharacteristic
117C59×#389C2211yescharacteristic
118C59×#389C2211yescharacteristic
119C59×#389C2211yescharacteristic
120C59×#389C2211yescharacteristic
121C59×#389C2211yescharacteristic
122C59×#389C2211yescharacteristic
123C59×#389C2211yescharacteristic
124C59×#389C2211yescharacteristic
125C59×#388C2211yescharacteristic
126C59×#388C2211yescharacteristic
127C59×#388C2211yescharacteristic
128C59×#388C2211yescharacteristic
129C59×#388C2211yescharacteristic
130C59×#388C2211yescharacteristic
131C59×#388C2211yescharacteristic
132C59×#388C2211yescharacteristic
133C59×#388C2211yescharacteristic
134C59×#388C2211yescharacteristic
135C59×#388C2211yescharacteristic
136C59×#388C2211yescharacteristic
137C59×#387C2211yescharacteristic
138C59×#387C2211yescharacteristic
139C59×#387C2211yescharacteristic
140C59×#387C2211yescharacteristic
141C59×#387C2211yescharacteristic
142C59×#387C2211yescharacteristic
143C59×#387C2211yescharacteristic
144C59×#387C2211yescharacteristic
145C59×#387C2211yescharacteristic
146C59×#387C2211yescharacteristic
147C59×#387C2211yescharacteristic
148C59×#387C2211yescharacteristic
149C59×#386C2211yescharacteristic
150C59×#386C2211yescharacteristic
151C59×#386C2211yescharacteristic
152C59×#386C2211yescharacteristic
153C59×#386C2211yescharacteristic
154C59×#386C2211yescharacteristic
155C59×#386C2211yescharacteristic
156C59×#386C2211yescharacteristic
157C59×#386C2211yescharacteristic
158C59×#385C2211yescharacteristic
159C59×#385C2211yescharacteristic
160C59×#385C2211yescharacteristic
161C59×#385C2211yescharacteristic
162C59×#385C2211yescharacteristic
163C59×#385C2211yescharacteristic
164C59×#385C2211yescharacteristic
165C59×#385C2211yescharacteristic
166C59×#385C2211yescharacteristic
167C59×#385C2211yescharacteristic
168C59×#385C2211yescharacteristic
169C59×#385C2211yescharacteristic
170C59×#385C2211yescharacteristic
171C59×#385C2211yescharacteristic
172C59×#385C2211yescharacteristic
173C59×#385C2211yescharacteristic
174C59×#385C2211yescharacteristic
175C59×#381C2211yescharacteristic
176C59×#381C2211yescharacteristic
177C59×#381C2211yescharacteristic
178C59×#380C2211yescharacteristic
179C59×#380C2211yescharacteristic
180C4×C4⋊C4×C59C2211yescharacteristic
181C4×C4⋊C4×C59C2211yescharacteristic
182C4×C22⋊C4×C59C2211yescharacteristic
183C4×C22⋊C4×C59C2211yescharacteristic
184C4×C22⋊C4×C59C2211yescharacteristic
185C4×C22⋊C4×C59C2211yescharacteristic
186C59×#376C2211yescharacteristic
187C2×#95×C59C2211yescharacteristic
188C2×#95×C59C2211yescharacteristic
189C2×#41×C59—24no—
190C2×#41×C59—24no—
191C2×#41×C59—24no—
192C22×Q8×C59C2311yescharacteristic
193C22×Q8×C59C2311yescharacteristic
194C22×D4×C59C2311yescharacteristic
195C22×D4×C59C2311yescharacteristic
196C22×D4×C59C2311yescharacteristic
197C22×D4×C59C2311yescharacteristic
198C22×D4×C59C2311yescharacteristic
199C22×D4×C59C2311yescharacteristic
200C23×C4×C59C2311yescharacteristic
201C23×C4×C59C2311yescharacteristic
202C23×C4×C59C2311yescharacteristic
203C23×C4×C59C2311yescharacteristic
204C23×C4×C59C2311yescharacteristic
205C23×C4×C59C2311yescharacteristic
206C23×C4×C59C2311yescharacteristic
207C23×C4×C59C2311yescharacteristic
208C23×C4×C59C2311yescharacteristic
209C23×C4×C59C2311yescharacteristic
210C23×C4×C59C2311yescharacteristic
211C23×C4×C59C2311yescharacteristic
212C23×C4×C59C2311yescharacteristic
213C23×C4×C59C2311yescharacteristic
214#126×C59—24no—
215#126×C59—24no—
216#125×C59—24no—
217#125×C59—24no—
218#123×C59—24no—
219#123×C59—24no—
220#123×C59—24no—
221#123×C59—24no—
222#123×C59—24no—
223#123×C59—24no—
224#123×C59—42no—
225C22⋊Q8×C59—24no—
226C22⋊Q8×C59—24no—
227C22⋊Q8×C59—24no—
228C22⋊Q8×C59—42no—
229#121×C59—24no—
230#121×C59—24no—
231C4×Q8×C59—24no—
232C4×Q8×C59—24no—
233C4×D4×C59—24no—
234C4×D4×C59—24no—
235C4×D4×C59—24no—
236C4×D4×C59—24no—
237C4×D4×C59—24no—
238C4×D4×C59—24no—
239C4×D4×C59—42no—
240C4×D4×C59D418yescomplemented
241#117×C59—24no—
242#117×C59—24no—
243#117×C59—24no—
244#117×C59—42no—
245C2×C4⋊C4×C59—24no—
246C2×C4⋊C4×C59—24no—
247C2×C4⋊C4×C59—24no—
248C2×C4⋊C4×C59—24no—
249C2×C4⋊C4×C59—24no—
250C2×C4⋊C4×C59—42no—
251C2×C4⋊C4×C59C2311yescharacteristic
252C2×C4⋊C4×C59C2311yescharacteristic
253C2×C4⋊C4×C59C2311yescharacteristic
254C2×C4⋊C4×C59C2311yescharacteristic
255C2×C4⋊C4×C59C2311yescharacteristic
256C2×C4⋊C4×C59C2311yescharacteristic
257C2×C4⋊C4×C59C2311yescharacteristic
258C2×C4⋊C4×C59C2311yescharacteristic
259C2×C4⋊C4×C59C2311yescharacteristic
260C2×C4⋊C4×C59C2311yescharacteristic
261C2×C4⋊C4×C59C2311yescharacteristic
262C2×C4⋊C4×C59C2311yescharacteristic
263C2×C4⋊C4×C59C2311yescharacteristic
264C2×C4⋊C4×C59C2311yescharacteristic
265C2×C4⋊C4×C59C2311yescharacteristic
266C2×C4⋊C4×C59C2311yescharacteristic
267C2×C4⋊C4×C59C2311yescharacteristic
268C2×C4⋊C4×C59C2311yescharacteristic
269C2×C4⋊C4×C59C2311yescharacteristic
270C2×C4⋊C4×C59C2311yescharacteristic
271C2×C4⋊C4×C59C2311yescharacteristic
272C2×C4⋊C4×C59C2311yescharacteristic
273C2×C4⋊C4×C59C2311yescharacteristic
274C2×C4⋊C4×C59C2311yescharacteristic
275C2×C4⋊C4×C59C2311yescharacteristic
276C2×C4⋊C4×C59C2311yescharacteristic
277C2×C4⋊C4×C59C2311yescharacteristic
278C2×C4⋊C4×C59C2311yescharacteristic
279C2×C4⋊C4×C59C2311yescharacteristic
280C2×C4⋊C4×C59C2311yescharacteristic
281C2×C4⋊C4×C59C2311yescharacteristic
282C2×C4⋊C4×C59C2311yescharacteristic
283C2×C4⋊C4×C59C2311yescharacteristic
284C2×C4⋊C4×C59C2311yescharacteristic
285C2×C4⋊C4×C59C2311yescharacteristic
286C2×C4⋊C4×C59C2311yescharacteristic
287C2×C4⋊C4×C59C2311yescharacteristic
288C2×C4⋊C4×C59C2311yescharacteristic
289C2×C4⋊C4×C59C2311yescharacteristic
290C2×C4⋊C4×C59C2311yescharacteristic
291C2×C4⋊C4×C59C2311yescharacteristic
292C2×C4⋊C4×C59C2311yescharacteristic
293C2×C4⋊C4×C59C2311yescharacteristic
294C2×C4⋊C4×C59C2311yescharacteristic
295C2×C4⋊C4×C59C2311yescharacteristic
296C2×C4⋊C4×C59C2311yescharacteristic
297C2×C22⋊C4×C59C2311yescharacteristic
298C2×C22⋊C4×C59C2311yescharacteristic
299C2×C22⋊C4×C59C2311yescharacteristic
300C2×C22⋊C4×C59C2311yescharacteristic
301C2×C22⋊C4×C59C2311yescharacteristic
302C2×C22⋊C4×C59C2311yescharacteristic
303C2×C22⋊C4×C59C2311yescharacteristic
304C2×C22⋊C4×C59C2311yescharacteristic
305C2×C22⋊C4×C59C2311yescharacteristic
306C2×C22⋊C4×C59C2311yescharacteristic
307C2×C22⋊C4×C59C2311yescharacteristic
308C2×C22⋊C4×C59C2311yescharacteristic
309C2×C22⋊C4×C59C2311yescharacteristic
310C2×C22⋊C4×C59C2311yescharacteristic
311C2×C22⋊C4×C59C2311yescharacteristic
312C2×C22⋊C4×C59C2311yescharacteristic
313C2×C22⋊C4×C59C2311yescharacteristic
314C2×C22⋊C4×C59C2311yescharacteristic
315C2×C22⋊C4×C59C2311yescharacteristic
316C2×C22⋊C4×C59C2311yescharacteristic
317C2×C22⋊C4×C59C2311yescharacteristic
318C2×C22⋊C4×C59C2311yescharacteristic
319C2×C22⋊C4×C59C2311yescharacteristic
320C2×C22⋊C4×C59C2311yescharacteristic
321C2×C22⋊C4×C59C2311yescharacteristic
322C2×C22⋊C4×C59C2311yescharacteristic
323C2×C22⋊C4×C59C2311yescharacteristic
324C2×C22⋊C4×C59C2311yescharacteristic
325C2×C22⋊C4×C59C2311yescharacteristic
326C2×C22⋊C4×C59C2311yescharacteristic
327C2×C22⋊C4×C59C2311yescharacteristic
328C2×C22⋊C4×C59C2311yescharacteristic
329C2×C22⋊C4×C59C2311yescharacteristic
330C2×C22⋊C4×C59C2311yescharacteristic
331C2×C42×C59—42no—
332C2×C42×C59C2311yescharacteristic
333C2×C42×C59C2311yescharacteristic
334C2×C42×C59C2311yescharacteristic
335C2×C42×C59C2311yescharacteristic
336C2×C42×C59C2311yescharacteristic
337C2×C42×C59C2311yescharacteristic
338C2×C42×C59C2311yescharacteristic
339C2×C42×C59C2311yescharacteristic
340C2×C42×C59C2311yescharacteristic
341C2×C42×C59C2311yescharacteristic
342C2×C42×C59C2311yescharacteristic
343C2×C42×C59C2311yescharacteristic
344C2×C42×C59C2311yescharacteristic
345#95×C59C2311yescharacteristic
346#95×C59C2311yescharacteristic
347#95×C59C2311yescharacteristic
348#95×C59C2311yescharacteristic
349#95×C59C2311yescharacteristic
350#95×C59C2311yescharacteristic
351#95×C59C2311yescharacteristic
352#95×C59C2311yescharacteristic
353#95×C59C2311yescharacteristic
354#95×C59C2311yescharacteristic
355#95×C59C2311yescharacteristic
356#95×C59C2311yescharacteristic
357#95×C59C2311yescharacteristic
358#95×C59C2311yescharacteristic
359#95×C59C2311yescharacteristic
360#95×C59C2311yescharacteristic
361#95×C59C2311yescharacteristic
362#95×C59C2311yescharacteristic
363#95×C59C2311yescharacteristic
364#95×C59C2311yescharacteristic
365#95×C59C2311yescharacteristic
366#95×C59C2311yescharacteristic
367#95×C59C2311yescharacteristic
368#95×C59C2311yescharacteristic
369#95×C59C2311yescharacteristic
370#95×C59C2311yescharacteristic
371#95×C59C2311yescharacteristic
372#95×C59C2311yescharacteristic
373#95×C59C2311yescharacteristic
374#95×C59C2311yescharacteristic
375#95×C59C2311yescharacteristic
376#95×C59C2311yescharacteristic
377#95×C59C2311yescharacteristic
378#95×C59C2311yescharacteristic
379#95×C59C2311yescharacteristic
380#95×C59C2311yescharacteristic
381#95×C59C2311yescharacteristic
382#95×C59C2311yescharacteristic
383#95×C59C2311yescharacteristic
384#95×C59C2311yescharacteristic
385C24×C59C2411yescharacteristic
386C24×C59C2411yescharacteristic
387C24×C59C2411yescharacteristic
388C24×C59C2411yescharacteristic
389#41×C59—232no—
390C2×Q8×C59—22no—
391C2×Q8×C59—22no—
392C2×Q8×C59—22no—
393C2×Q8×C59—22no—
394C2×Q8×C59—41no—
395C2×Q8×C59—41no—
396C2×D4×C59—22no—
397C2×D4×C59—22no—
398C2×D4×C59—22no—
399C2×D4×C59—22no—
400C2×D4×C59—22no—
401C2×D4×C59—22no—
402C2×D4×C59—22no—
403C2×D4×C59—22no—
404C2×D4×C59—22no—
405C2×D4×C59—22no—
406C2×D4×C59—22no—
407C2×D4×C59—22no—
408C2×D4×C59—22no—
409C2×D4×C59—41no—
410C2×D4×C59—41no—
411C2×D4×C59—41no—
412C2×D4×C59C2×D414yes—
413C2×D4×C59#4114yes—
414C22×C4×C59—22no—
415C22×C4×C59—22no—
416C22×C4×C59—22no—
417C22×C4×C59—22no—
418C22×C4×C59—22no—
419C22×C4×C59—22no—
420C22×C4×C59—22no—
421C22×C4×C59—22no—
422C22×C4×C59—22no—
423C22×C4×C59—22no—
424C22×C4×C59—22no—
425C22×C4×C59—22no—
426C22×C4×C59—22no—
427C22×C4×C59—22no—
428C22×C4×C59—22no—
429C22×C4×C59—22no—
430C22×C4×C59—22no—
431C22×C4×C59—22no—
432C22×C4×C59—22no—
433C22×C4×C59—22no—
434C22×C4×C59—22no—
435C22×C4×C59—22no—
436C22×C4×C59—41no—
437C22×C4×C59—41no—
438C22×C4×C59—41no—
439C22×C4×C59—41no—
440C22×C4×C59—41no—
441C22×C4×C59—41no—
442C22×C4×C59—41no—
443C22×C4×C59—41no—
444C22×C4×C59—41no—
445C22×C4×C59—41no—
446C22×C4×C59—41no—
447C22×C4×C59—41no—
448C22×C4×C59—41no—
449C22×C4×C59—41no—
450C22×C4×C59—41no—
451C22×C4×C59—41no—
452C22×C4×C59—41no—
453C22×C4×C59C2×D414yes—
454C22×C4×C59C2×D414yes—
455C22×C4×C59#4114yes—
456C22×C4×C59C2411yescharacteristic
457C22×C4×C59C2411yescharacteristic
458C22×C4×C59C2411yescharacteristic
459C22×C4×C59C2411yescharacteristic
460C22×C4×C59C2411yescharacteristic
461C22×C4×C59C2411yescharacteristic
462C22×C4×C59C2411yescharacteristic
463C22×C4×C59C2411yescharacteristic
464C22×C4×C59C2411yescharacteristic
465C22×C4×C59C2411yescharacteristic
466C22×C4×C59C2411yescharacteristic
467C22×C4×C59C2411yescharacteristic
468C22×C4×C59C2411yescharacteristic
469C22×C4×C59C2411yescharacteristic
470C22×C4×C59C2411yescharacteristic
471C22×C4×C59C2411yescharacteristic
472C22×C4×C59C2411yescharacteristic
473C22×C4×C59C2411yescharacteristic
474C22×C4×C59C2411yescharacteristic
475C22×C4×C59C2411yescharacteristic
476C22×C4×C59C2411yescharacteristic
477C22×C4×C59C2411yescharacteristic
478C22×C4×C59C2411yescharacteristic
479C22×C4×C59C2411yescharacteristic
480C22×C4×C59C2411yescharacteristic
481C22×C4×C59C2411yescharacteristic
482C22×C4×C59C2411yescharacteristic
483C4⋊C4×C59—22no—
484C4⋊C4×C59—22no—
485C4⋊C4×C59—22no—
486C4⋊C4×C59—22no—
487C4⋊C4×C59—22no—
488C4⋊C4×C59—22no—
489C4⋊C4×C59—22no—
490C4⋊C4×C59—22no—
491C4⋊C4×C59—22no—
492C4⋊C4×C59—22no—
493C4⋊C4×C59—22no—
494C4⋊C4×C59—22no—
495C4⋊C4×C59—22no—
496C4⋊C4×C59—22no—
497C4⋊C4×C59—22no—
498C4⋊C4×C59—22no—
499C4⋊C4×C59—22no—
500C4⋊C4×C59—22no—
501C4⋊C4×C59—22no—
502C4⋊C4×C59—22no—
503C4⋊C4×C59—22no—
504C4⋊C4×C59—22no—
505C4⋊C4×C59—22no—
506C4⋊C4×C59—22no—
507C4⋊C4×C59—22no—
508C4⋊C4×C59—22no—
509C4⋊C4×C59—22no—
510C4⋊C4×C59—22no—
511C4⋊C4×C59—22no—
512C4⋊C4×C59—22no—
513C4⋊C4×C59—22no—
514C4⋊C4×C59—22no—
515C4⋊C4×C59—22no—
516C4⋊C4×C59—22no—
517C4⋊C4×C59—22no—
518C4⋊C4×C59—22no—
519C4⋊C4×C59—22no—
520C4⋊C4×C59—41no—
521C4⋊C4×C59—41no—
522C4⋊C4×C59—41no—
523C4⋊C4×C59—41no—
524C4⋊C4×C59—41no—
525C4⋊C4×C59—41no—
526C4⋊C4×C59—41no—
527C4⋊C4×C59—41no—
528C4⋊C4×C59C2×D414yes—
529C22⋊C4×C59—22no—
530C22⋊C4×C59—22no—
531C22⋊C4×C59—22no—
532C22⋊C4×C59—22no—
533C22⋊C4×C59—22no—
534C22⋊C4×C59—22no—
535C22⋊C4×C59—22no—
536C22⋊C4×C59—22no—
537C22⋊C4×C59—22no—
538C22⋊C4×C59—22no—
539C22⋊C4×C59—22no—
540C22⋊C4×C59—22no—
541C22⋊C4×C59—22no—
542C22⋊C4×C59—22no—
543C22⋊C4×C59—22no—
544C22⋊C4×C59—22no—
545C22⋊C4×C59—22no—
546C22⋊C4×C59—22no—
547C22⋊C4×C59—22no—
548C22⋊C4×C59—22no—
549C22⋊C4×C59—22no—
550C22⋊C4×C59—22no—
551C22⋊C4×C59—22no—
552C22⋊C4×C59—22no—
553C22⋊C4×C59—22no—
554C22⋊C4×C59—22no—
555C22⋊C4×C59—22no—
556C22⋊C4×C59—41no—
557C22⋊C4×C59—41no—
558C22⋊C4×C59—41no—
559C22⋊C4×C59—41no—
560C22⋊C4×C59—41no—
561C22⋊C4×C59C2×D414yes—
562C22⋊C4×C59C2×D414yes—
563C42×C59—22no—
564C42×C59—22no—
565C42×C59—22no—
566C42×C59—22no—
567C42×C59—22no—
568C42×C59—22no—
569C42×C59—22no—
570C42×C59—22no—
571C42×C59—41no—
572C42×C59—41no—
573C42×C59—41no—
574C42×C59—41no—
575C42×C59C2×D414yes—
576C23×C59—21no—
577C23×C59—21no—
578C23×C59—21no—
579C23×C59—21no—
580C23×C59—21no—
581C23×C59—21no—
582C23×C59—21no—
583C23×C59—21no—
584C23×C59—21no—
585C23×C59—21no—
586C23×C59—21no—
587C23×C59—21no—
588C23×C59—21no—
589C23×C59—21no—
590C23×C59—21no—
591C23×C59—21no—
592C23×C59—21no—
593C23×C59—21no—
594C23×C59—21no—
595C23×C59—21no—
596C23×C59—21no—
597C23×C59—21no—
598C23×C59—21no—
599C23×C59C22×D412yes—
600C23×C59C22×D412yes—
601C23×C59C2×#4112yes—
602C23×C59C2×#4112yes—
603C23×C59C2×#4112yes—
604C23×C59C2511yescharacteristic
605Q8×C59—28no—
606Q8×C59—82no—
607D4×C59—28no—
608D4×C59—28no—
609D4×C59—28no—
610D4×C59—44no—
611D4×C59—44no—
612D4×C59—82no—
613C2×C4×C59—28no—
614C2×C4×C59—28no—
615C2×C4×C59—28no—
616C2×C4×C59—28no—
617C2×C4×C59—21no—
618C2×C4×C59—21no—
619C2×C4×C59—21no—
620C2×C4×C59—21no—
621C2×C4×C59—21no—
622C2×C4×C59—21no—
623C2×C4×C59—21no—
624C2×C4×C59—21no—
625C2×C4×C59—21no—
626C2×C4×C59—21no—
627C2×C4×C59—21no—
628C2×C4×C59—21no—
629C2×C4×C59—21no—
630C2×C4×C59—21no—
631C2×C4×C59—21no—
632C2×C4×C59—21no—
633C2×C4×C59—21no—
634C2×C4×C59—21no—
635C2×C4×C59—21no—
636C2×C4×C59—21no—
637C2×C4×C59—21no—
638C2×C4×C59—21no—
639C2×C4×C59—21no—
640C2×C4×C59—21no—
641C2×C4×C59—21no—
642C2×C4×C59—21no—
643C2×C4×C59—21no—
644C2×C4×C59—21no—
645C2×C4×C59—21no—
646C2×C4×C59—21no—
647C2×C4×C59—21no—
648C2×C4×C59—21no—
649C2×C4×C59—21no—
650C2×C4×C59—21no—
651C2×C4×C59—21no—
652C2×C4×C59—21no—
653C2×C4×C59—21no—
654C2×C4×C59—21no—
655C2×C4×C59—21no—
656C2×C4×C59—21no—
657C2×C4×C59—21no—
658C2×C4×C59—21no—
659C2×C4×C59—21no—
660C2×C4×C59—21no—
661C2×C4×C59—21no—
662C2×C4×C59—21no—
663C2×C4×C59—21no—
664C2×C4×C59—21no—
665C2×C4×C59—21no—
666C2×C4×C59—21no—
667C2×C4×C59—21no—
668C2×C4×C59—21no—
669C2×C4×C59—21no—
670C2×C4×C59—21no—
671C2×C4×C59—21no—
672C2×C4×C59—21no—
673C2×C4×C59—21no—
674C2×C4×C59—21no—
675C2×C4×C59—21no—
676C2×C4×C59—21no—
677C2×C4×C59—21no—
678C2×C4×C59—21no—
679C2×C4×C59—21no—
680C2×C4×C59—21no—
681C2×C4×C59—21no—
682C2×C4×C59—21no—
683C2×C4×C59—21no—
684C2×C4×C59—21no—
685C2×C4×C59—21no—
686C2×C4×C59—21no—
687C2×C4×C59—44no—
688C2×C4×C59—44no—
689C2×C4×C59—44no—
690C2×C4×C59—44no—
691C2×C4×C59—82no—
692C2×C4×C59—82no—
693C2×C4×C59—82no—
694C2×C4×C59—82no—
695C2×C4×C59—82no—
696C2×C4×C59—82no—
697C2×C4×C59C22×D412yes—
698C2×C4×C59C22×D412yes—
699C2×C4×C59C22×D412yes—
700C2×C4×C59C22×D412yes—
701C2×C4×C59C22×D412yes—
702C2×C4×C59C2×#4112yes—
703C2×C4×C59C2×#4112yes—
704C2×C4×C59C2×#4112yes—
705C2×C4×C59H(5,𝔽2)12yes—
706C2×C4×C592−1+412yes—
707C2×C4×C592−1+412yes—
708#35363C5911yesmaximal, characteristic, direct product factor, Sylow
709C22×C59—22no—
710C22×C59—22no—
711C22×C59—22no—
712C22×C59—22no—
713C22×C59—22no—
714C22×C59—22no—
715C22×C59—22no—
716C22×C59—22no—
717C22×C59—22no—
718C22×C59—22no—
719C22×C59—22no—
720C22×C59—22no—
721C22×C59—41no—
722C22×C59—41no—
723C22×C59—41no—
724C22×C59—41no—
725C22×C59—41no—
726C22×C59—41no—
727C22×C59—41no—
728C22×C59—41no—
729C22×C59—41no—
730C22×C59—41no—
731C22×C59—41no—
732C22×C59—41no—
733C22×C59—41no—
734C22×C59—41no—
735C22×C59—41no—
736C22×C59#52514yes—
737C22×C59C23×D411yescharacteristic
738C22×C59C22×#4111yescharacteristic
739C22×C59C22×#4111yescharacteristic
740C22×C59C2×H(5,𝔽2)11yescharacteristic
741C22×C59C2×2−1+411yescharacteristic
742C22×C59C2×2−1+411yescharacteristic
743C22×C59#58511yescharacteristic
744C4×C59—22no—
745C4×C59—22no—
746C4×C59—22no—
747C4×C59—22no—
748C4×C59—22no—
749C4×C59—22no—
750C4×C59—22no—
751C4×C59—22no—
752C4×C59—22no—
753C4×C59—22no—
754C4×C59—22no—
755C4×C59—41no—
756C4×C59—41no—
757C4×C59—41no—
758C4×C59—41no—
759C4×C59—41no—
760C4×C59—41no—
761C4×C59—41no—
762C4×C59—41no—
763C4×C59—41no—
764C4×C59—41no—
765C4×C59—41no—
766C4×C59—41no—
767C4×C59—41no—
768C4×C59—41no—
769C4×C59—41no—
770C4×C59—41no—
771C2×#539C2×C5911yescharacteristic, complemented
772C2×#520C2×C5911yescharacteristic, complemented
773#2611C2×C5911yescharacteristic, complemented
774#2604C2×C5911yescharacteristic, complemented
775#2602C2×C5911yescharacteristic, complemented
776#2601C2×C5911yescharacteristic, complemented
777#2584C2×C5911yescharacteristic, complemented
778#2583C2×C5911yescharacteristic, complemented
779#2478C2×C5911yescharacteristic, complemented
780#2473C2×C5911yescharacteristic, complemented
781#2470C2×C5911yescharacteristic, complemented
782#2466C2×C5911yescharacteristic, complemented
783#2465C2×C5911yescharacteristic, complemented
784#2462C2×C5911yescharacteristic, complemented
785#2455C2×C5911yescharacteristic, complemented
786#2449C2×C5911yescharacteristic, complemented
787#2449C2×C5911yescharacteristic, complemented
788#2443C2×C5911yescharacteristic, complemented
789#2438C2×C5911yescharacteristic, complemented
790#2430C2×C5911yescharacteristic
791#2425C2×C5911yescharacteristic, complemented
792#2419C2×C5911yescharacteristic, complemented
793#2415C2×C5911yescharacteristic, complemented
794#2413C2×C5911yescharacteristic, complemented
795#2413C2×C5911yescharacteristic, complemented
796#2406C2×C5911yescharacteristic, complemented
797#2322C2×C5911yescharacteristic, complemented
798#2322C2×C5911yescharacteristic, complemented
799C4×#121C2×C5911yescharacteristic, complemented
800C2×#389C2×C5911yescharacteristic, complemented
801#2290C2×C5911yescharacteristic, complemented
802C2×C59—24no—
803C2×C59—42no—
804C2×C59—42no—
805C2×C59—81no—
806C2×C59C2×#52511yescharacteristic
807C2×C59#349211yescharacteristic
808C2×C59#349611yescharacteristic
809C2×C59#349911yescharacteristic
810C2×C59#350711yescharacteristic
811C2×C59#351511yescharacteristic
812C2×C59#352011yescharacteristic
813C22×#41C22×C5911yescharacteristic
814#539—28no—
815C2×#126C22×C5911yescharacteristic
816C2×#126C22×C5911yescharacteristic
817C2×#125C22×C5911yescharacteristic
818C2×#125C22×C5911yescharacteristic
819C2×#123C22×C5911yescharacteristic
820C2×#123C22×C5911yescharacteristic
821C2×#123C22×C5911yescharacteristic
822C2×#123C22×C5911yescharacteristic
823C2×#123C22×C5911yescharacteristic
824C2×#123C22×C5911yescharacteristic
825C2×#123C22×C5911yescharacteristic
826C2×C22⋊Q8C22×C5911yescharacteristic
827C2×C22⋊Q8C22×C5911yescharacteristic
828C2×C22⋊Q8C22×C5911yescharacteristic
829C2×C22⋊Q8C22×C5911yescharacteristic
830C2×#121C22×C5911yescharacteristic
831C2×#121C22×C5911yescharacteristic
832#520—28no—
833C2×C4×Q8C22×C5911yescharacteristic
834C2×C4×Q8C22×C5911yescharacteristic
835C2×C4×D4C22×C5911yescharacteristic
836C2×C4×D4C22×C5911yescharacteristic
837C2×C4×D4C22×C5911yescharacteristic
838C2×C4×D4C22×C5911yescharacteristic
839C2×C4×D4C22×C5911yescharacteristic
840C2×C4×D4C22×C5911yescharacteristic
841C2×C4×D4C22×C5911yescharacteristic
842C2×C4×D4C22×C5911yescharacteristic
843C2×#117C22×C5911yescharacteristic
844C2×#117C22×C5911yescharacteristic
845C2×#117C22×C5911yescharacteristic
846C2×#117C22×C5911yescharacteristic
847C22×C4⋊C4C22×C5911yescharacteristic
848C22×C4⋊C4C22×C5911yescharacteristic
849C22×C4⋊C4C22×C5911yescharacteristic
850C22×C4⋊C4C22×C5911yescharacteristic
851C22×C4⋊C4C22×C5911yescharacteristic
852C22×C4⋊C4C22×C5911yescharacteristic
853C22×C42C22×C5911yescharacteristic
854#400C22×C5911yescharacteristic
855#400C22×C5911yescharacteristic
856#399C22×C5911yescharacteristic
857#399C22×C5911yescharacteristic
858#398C22×C5911yescharacteristic
859#398C22×C5911yescharacteristic
860#398C22×C5911yescharacteristic
861#398C22×C5911yescharacteristic
862#398C22×C5911yescharacteristic
863#398C22×C5911yescharacteristic
864#398C22×C5911yescharacteristic
865#398C22×C5911yescharacteristic
866#397C22×C5911yescharacteristic
867#397C22×C5911yescharacteristic
868#397C22×C5911yescharacteristic
869#397C22×C5911yescharacteristic
870#396C22×C5911yescharacteristic
871#396C22×C5911yescharacteristic
872#396C22×C5911yescharacteristic
873#396C22×C5911yescharacteristic
874#395C22×C5911yescharacteristic
875#395C22×C5911yescharacteristic
876#395C22×C5911yescharacteristic
877#395C22×C5911yescharacteristic
878#395C22×C5911yescharacteristic
879#394C22×C5911yescharacteristic
880#394C22×C5911yescharacteristic
881#394C22×C5911yescharacteristic
882#394C22×C5911yescharacteristic
883#394C22×C5911yescharacteristic
884#393C22×C5911yescharacteristic
885#392C22×C5911yescharacteristic
886#391C22×C5911yescharacteristic
887#390C22×C5911yescharacteristic
888#389C22×C5911yescharacteristic
889#389C22×C5911yescharacteristic
890#389C22×C5911yescharacteristic
891#389C22×C5911yescharacteristic
892#389C22×C5911yescharacteristic
893#389C22×C5911yescharacteristic
894#389C22×C5911yescharacteristic
895#389C22×C5911yescharacteristic
896#389C22×C5911yescharacteristic
897#389C22×C5911yescharacteristic
898#389C22×C5911yescharacteristic
899#389C22×C5911yescharacteristic
900#389C22×C5911yescharacteristic
901#389C22×C5911yescharacteristic
902#389C22×C5911yescharacteristic
903#389C22×C5911yescharacteristic
904#389C22×C5911yescharacteristic
905#389C22×C5911yescharacteristic
906#388C22×C5911yescharacteristic
907#388C22×C5911yescharacteristic
908#388C22×C5911yescharacteristic
909#388C22×C5911yescharacteristic
910#388C22×C5911yescharacteristic
911#388C22×C5911yescharacteristic
912#388C22×C5911yescharacteristic
913#388C22×C5911yescharacteristic
914#388C22×C5911yescharacteristic
915#388C22×C5911yescharacteristic
916#388C22×C5911yescharacteristic
917#388C22×C5911yescharacteristic
918#387C22×C5911yescharacteristic
919#387C22×C5911yescharacteristic
920#387C22×C5911yescharacteristic
921#387C22×C5911yescharacteristic
922#387C22×C5911yescharacteristic
923#387C22×C5911yescharacteristic
924#387C22×C5911yescharacteristic
925#387C22×C5911yescharacteristic
926#387C22×C5911yescharacteristic
927#387C22×C5911yescharacteristic
928#387C22×C5911yescharacteristic
929#387C22×C5911yescharacteristic
930#386C22×C5911yescharacteristic
931#386C22×C5911yescharacteristic
932#386C22×C5911yescharacteristic
933#386C22×C5911yescharacteristic
934#386C22×C5911yescharacteristic
935#386C22×C5911yescharacteristic
936#386C22×C5911yescharacteristic
937#386C22×C5911yescharacteristic
938#386C22×C5911yescharacteristic
939#385C22×C5911yescharacteristic
940#385C22×C5911yescharacteristic
941#385C22×C5911yescharacteristic
942#385C22×C5911yescharacteristic
943#385C22×C5911yescharacteristic
944#385C22×C5911yescharacteristic
945#385C22×C5911yescharacteristic
946#385C22×C5911yescharacteristic
947#385C22×C5911yescharacteristic
948#385C22×C5911yescharacteristic
949#385C22×C5911yescharacteristic
950#385C22×C5911yescharacteristic
951#385C22×C5911yescharacteristic
952#385C22×C5911yescharacteristic
953#385C22×C5911yescharacteristic
954#385C22×C5911yescharacteristic
955#385C22×C5911yescharacteristic
956#381C22×C5911yescharacteristic
957#381C22×C5911yescharacteristic
958#381C22×C5911yescharacteristic
959#380C22×C5911yescharacteristic
960#380C22×C5911yescharacteristic
961C4×C4⋊C4C22×C5911yescharacteristic
962C4×C4⋊C4C22×C5911yescharacteristic
963C4×C22⋊C4C22×C5911yescharacteristic
964C4×C22⋊C4C22×C5911yescharacteristic
965C4×C22⋊C4C22×C5911yescharacteristic
966C4×C22⋊C4C22×C5911yescharacteristic
967#376C22×C5911yescharacteristic
968C2×#95C22×C5911yescharacteristic
969C2×#95C22×C5911yescharacteristic
970C59#3536311yescharacteristic, direct product factor, Sylow
971C2×#41—24no—
972C2×#41—24no—
973C2×#41—24no—
974C22×Q8C23×C5911yescharacteristic
975C22×Q8C23×C5911yescharacteristic
976C22×D4C23×C5911yescharacteristic
977C22×D4C23×C5911yescharacteristic
978C22×D4C23×C5911yescharacteristic
979C22×D4C23×C5911yescharacteristic
980C22×D4C23×C5911yescharacteristic
981C22×D4C23×C5911yescharacteristic
982C23×C4C23×C5911yescharacteristic
983C23×C4C23×C5911yescharacteristic
984C23×C4C23×C5911yescharacteristic
985C23×C4C23×C5911yescharacteristic
986C23×C4C23×C5911yescharacteristic
987C23×C4C23×C5911yescharacteristic
988C23×C4C23×C5911yescharacteristic
989C23×C4C23×C5911yescharacteristic
990C23×C4C23×C5911yescharacteristic
991C23×C4C23×C5911yescharacteristic
992C23×C4C23×C5911yescharacteristic
993C23×C4C23×C5911yescharacteristic
994C23×C4C23×C5911yescharacteristic
995C23×C4C23×C5911yescharacteristic
996#126—24no—
997#126—24no—
998#125—24no—
999#125—24no—
1000#123—24no—
1001#123—24no—
1002#123—24no—
1003#123—24no—
1004#123—24no—
1005#123—24no—
1006#123—42no—
1007C22⋊Q8—24no—
1008C22⋊Q8—24no—
1009C22⋊Q8—24no—
1010C22⋊Q8—42no—
1011#121—24no—
1012#121—24no—
1013C4×Q8—24no—
1014C4×Q8—24no—
1015C4×D4—24no—
1016C4×D4—24no—
1017C4×D4—24no—
1018C4×D4—24no—
1019C4×D4—24no—
1020C4×D4—24no—
1021C4×D4—42no—
1022C4×D4D4×C5918yescomplemented
1023#117—24no—
1024#117—24no—
1025#117—24no—
1026#117—42no—
1027C2×C4⋊C4—24no—
1028C2×C4⋊C4—24no—
1029C2×C4⋊C4—24no—
1030C2×C4⋊C4—24no—
1031C2×C4⋊C4—24no—
1032C2×C4⋊C4—42no—
1033C2×C4⋊C4C23×C5911yescharacteristic
1034C2×C4⋊C4C23×C5911yescharacteristic
1035C2×C4⋊C4C23×C5911yescharacteristic
1036C2×C4⋊C4C23×C5911yescharacteristic
1037C2×C4⋊C4C23×C5911yescharacteristic
1038C2×C4⋊C4C23×C5911yescharacteristic
1039C2×C4⋊C4C23×C5911yescharacteristic
1040C2×C4⋊C4C23×C5911yescharacteristic
1041C2×C4⋊C4C23×C5911yescharacteristic
1042C2×C4⋊C4C23×C5911yescharacteristic
1043C2×C4⋊C4C23×C5911yescharacteristic
1044C2×C4⋊C4C23×C5911yescharacteristic
1045C2×C4⋊C4C23×C5911yescharacteristic
1046C2×C4⋊C4C23×C5911yescharacteristic
1047C2×C4⋊C4C23×C5911yescharacteristic
1048C2×C4⋊C4C23×C5911yescharacteristic
1049C2×C4⋊C4C23×C5911yescharacteristic
1050C2×C4⋊C4C23×C5911yescharacteristic
1051C2×C4⋊C4C23×C5911yescharacteristic
1052C2×C4⋊C4C23×C5911yescharacteristic
1053C2×C4⋊C4C23×C5911yescharacteristic
1054C2×C4⋊C4C23×C5911yescharacteristic
1055C2×C4⋊C4C23×C5911yescharacteristic
1056C2×C4⋊C4C23×C5911yescharacteristic
1057C2×C4⋊C4C23×C5911yescharacteristic
1058C2×C4⋊C4C23×C5911yescharacteristic
1059C2×C4⋊C4C23×C5911yescharacteristic
1060C2×C4⋊C4C23×C5911yescharacteristic
1061C2×C4⋊C4C23×C5911yescharacteristic
1062C2×C4⋊C4C23×C5911yescharacteristic
1063C2×C4⋊C4C23×C5911yescharacteristic
1064C2×C4⋊C4C23×C5911yescharacteristic
1065C2×C4⋊C4C23×C5911yescharacteristic
1066C2×C4⋊C4C23×C5911yescharacteristic
1067C2×C4⋊C4C23×C5911yescharacteristic
1068C2×C4⋊C4C23×C5911yescharacteristic
1069C2×C4⋊C4C23×C5911yescharacteristic
1070C2×C4⋊C4C23×C5911yescharacteristic
1071C2×C4⋊C4C23×C5911yescharacteristic
1072C2×C4⋊C4C23×C5911yescharacteristic
1073C2×C4⋊C4C23×C5911yescharacteristic
1074C2×C4⋊C4C23×C5911yescharacteristic
1075C2×C4⋊C4C23×C5911yescharacteristic
1076C2×C4⋊C4C23×C5911yescharacteristic
1077C2×C4⋊C4C23×C5911yescharacteristic
1078C2×C4⋊C4C23×C5911yescharacteristic
1079C2×C22⋊C4C23×C5911yescharacteristic
1080C2×C22⋊C4C23×C5911yescharacteristic
1081C2×C22⋊C4C23×C5911yescharacteristic
1082C2×C22⋊C4C23×C5911yescharacteristic
1083C2×C22⋊C4C23×C5911yescharacteristic
1084C2×C22⋊C4C23×C5911yescharacteristic
1085C2×C22⋊C4C23×C5911yescharacteristic
1086C2×C22⋊C4C23×C5911yescharacteristic
1087C2×C22⋊C4C23×C5911yescharacteristic
1088C2×C22⋊C4C23×C5911yescharacteristic
1089C2×C22⋊C4C23×C5911yescharacteristic
1090C2×C22⋊C4C23×C5911yescharacteristic
1091C2×C22⋊C4C23×C5911yescharacteristic
1092C2×C22⋊C4C23×C5911yescharacteristic
1093C2×C22⋊C4C23×C5911yescharacteristic
1094C2×C22⋊C4C23×C5911yescharacteristic
1095C2×C22⋊C4C23×C5911yescharacteristic
1096C2×C22⋊C4C23×C5911yescharacteristic
1097C2×C22⋊C4C23×C5911yescharacteristic
1098C2×C22⋊C4C23×C5911yescharacteristic
1099C2×C22⋊C4C23×C5911yescharacteristic
1100C2×C22⋊C4C23×C5911yescharacteristic
1101C2×C22⋊C4C23×C5911yescharacteristic
1102C2×C22⋊C4C23×C5911yescharacteristic
1103C2×C22⋊C4C23×C5911yescharacteristic
1104C2×C22⋊C4C23×C5911yescharacteristic
1105C2×C22⋊C4C23×C5911yescharacteristic
1106C2×C22⋊C4C23×C5911yescharacteristic
1107C2×C22⋊C4C23×C5911yescharacteristic
1108C2×C22⋊C4C23×C5911yescharacteristic
1109C2×C22⋊C4C23×C5911yescharacteristic
1110C2×C22⋊C4C23×C5911yescharacteristic
1111C2×C22⋊C4C23×C5911yescharacteristic
1112C2×C22⋊C4C23×C5911yescharacteristic
1113C2×C42—42no—
1114C2×C42C23×C5911yescharacteristic
1115C2×C42C23×C5911yescharacteristic
1116C2×C42C23×C5911yescharacteristic
1117C2×C42C23×C5911yescharacteristic
1118C2×C42C23×C5911yescharacteristic
1119C2×C42C23×C5911yescharacteristic
1120C2×C42C23×C5911yescharacteristic
1121C2×C42C23×C5911yescharacteristic
1122C2×C42C23×C5911yescharacteristic
1123C2×C42C23×C5911yescharacteristic
1124C2×C42C23×C5911yescharacteristic
1125C2×C42C23×C5911yescharacteristic
1126C2×C42C23×C5911yescharacteristic
1127#95C23×C5911yescharacteristic
1128#95C23×C5911yescharacteristic
1129#95C23×C5911yescharacteristic
1130#95C23×C5911yescharacteristic
1131#95C23×C5911yescharacteristic
1132#95C23×C5911yescharacteristic
1133#95C23×C5911yescharacteristic
1134#95C23×C5911yescharacteristic
1135#95C23×C5911yescharacteristic
1136#95C23×C5911yescharacteristic
1137#95C23×C5911yescharacteristic
1138#95C23×C5911yescharacteristic
1139#95C23×C5911yescharacteristic
1140#95C23×C5911yescharacteristic
1141#95C23×C5911yescharacteristic
1142#95C23×C5911yescharacteristic
1143#95C23×C5911yescharacteristic
1144#95C23×C5911yescharacteristic
1145#95C23×C5911yescharacteristic
1146#95C23×C5911yescharacteristic
1147#95C23×C5911yescharacteristic
1148#95C23×C5911yescharacteristic
1149#95C23×C5911yescharacteristic
1150#95C23×C5911yescharacteristic
1151#95C23×C5911yescharacteristic
1152#95C23×C5911yescharacteristic
1153#95C23×C5911yescharacteristic
1154#95C23×C5911yescharacteristic
1155#95C23×C5911yescharacteristic
1156#95C23×C5911yescharacteristic
1157#95C23×C5911yescharacteristic
1158#95C23×C5911yescharacteristic
1159#95C23×C5911yescharacteristic
1160#95C23×C5911yescharacteristic
1161#95C23×C5911yescharacteristic
1162#95C23×C5911yescharacteristic
1163#95C23×C5911yescharacteristic
1164#95C23×C5911yescharacteristic
1165#95C23×C5911yescharacteristic
1166#95C23×C5911yescharacteristic
1167C24C24×C5911yescharacteristic
1168C24C24×C5911yescharacteristic
1169C24C24×C5911yescharacteristic
1170C24C24×C5911yescharacteristic
1171#41—232no—
1172C2×Q8—22no—
1173C2×Q8—22no—
1174C2×Q8—22no—
1175C2×Q8—22no—
1176C2×Q8—41no—
1177C2×Q8—41no—
1178C2×D4—22no—
1179C2×D4—22no—
1180C2×D4—22no—
1181C2×D4—22no—
1182C2×D4—22no—
1183C2×D4—22no—
1184C2×D4—22no—
1185C2×D4—22no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—22no—
1189C2×D4—22no—
1190C2×D4—22no—
1191C2×D4—41no—
1192C2×D4—41no—
1193C2×D4—41no—
1194C2×D4C2×D4×C5914yes—
1195C2×D4#41×C5914yes—
1196C22×C4—22no—
1197C22×C4—22no—
1198C22×C4—22no—
1199C22×C4—22no—
1200C22×C4—22no—
1201C22×C4—22no—
1202C22×C4—22no—
1203C22×C4—22no—
1204C22×C4—22no—
1205C22×C4—22no—
1206C22×C4—22no—
1207C22×C4—22no—
1208C22×C4—22no—
1209C22×C4—22no—
1210C22×C4—22no—
1211C22×C4—22no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4C2×D4×C5914yes—
1236C22×C4C2×D4×C5914yes—
1237C22×C4#41×C5914yes—
1238C22×C4C24×C5911yescharacteristic
1239C22×C4C24×C5911yescharacteristic
1240C22×C4C24×C5911yescharacteristic
1241C22×C4C24×C5911yescharacteristic
1242C22×C4C24×C5911yescharacteristic
1243C22×C4C24×C5911yescharacteristic
1244C22×C4C24×C5911yescharacteristic
1245C22×C4C24×C5911yescharacteristic
1246C22×C4C24×C5911yescharacteristic
1247C22×C4C24×C5911yescharacteristic
1248C22×C4C24×C5911yescharacteristic
1249C22×C4C24×C5911yescharacteristic
1250C22×C4C24×C5911yescharacteristic
1251C22×C4C24×C5911yescharacteristic
1252C22×C4C24×C5911yescharacteristic
1253C22×C4C24×C5911yescharacteristic
1254C22×C4C24×C5911yescharacteristic
1255C22×C4C24×C5911yescharacteristic
1256C22×C4C24×C5911yescharacteristic
1257C22×C4C24×C5911yescharacteristic
1258C22×C4C24×C5911yescharacteristic
1259C22×C4C24×C5911yescharacteristic
1260C22×C4C24×C5911yescharacteristic
1261C22×C4C24×C5911yescharacteristic
1262C22×C4C24×C5911yescharacteristic
1263C22×C4C24×C5911yescharacteristic
1264C22×C4C24×C5911yescharacteristic
1265C4⋊C4—22no—
1266C4⋊C4—22no—
1267C4⋊C4—22no—
1268C4⋊C4—22no—
1269C4⋊C4—22no—
1270C4⋊C4—22no—
1271C4⋊C4—22no—
1272C4⋊C4—22no—
1273C4⋊C4—22no—
1274C4⋊C4—22no—
1275C4⋊C4—22no—
1276C4⋊C4—22no—
1277C4⋊C4—22no—
1278C4⋊C4—22no—
1279C4⋊C4—22no—
1280C4⋊C4—22no—
1281C4⋊C4—22no—
1282C4⋊C4—22no—
1283C4⋊C4—22no—
1284C4⋊C4—22no—
1285C4⋊C4—22no—
1286C4⋊C4—22no—
1287C4⋊C4—22no—
1288C4⋊C4—22no—
1289C4⋊C4—22no—
1290C4⋊C4—22no—
1291C4⋊C4—22no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—22no—
1297C4⋊C4—22no—
1298C4⋊C4—22no—
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—22no—
1302C4⋊C4—41no—
1303C4⋊C4—41no—
1304C4⋊C4—41no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4C2×D4×C5914yes—
1311C22⋊C4—22no—
1312C22⋊C4—22no—
1313C22⋊C4—22no—
1314C22⋊C4—22no—
1315C22⋊C4—22no—
1316C22⋊C4—22no—
1317C22⋊C4—22no—
1318C22⋊C4—22no—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—22no—
1323C22⋊C4—22no—
1324C22⋊C4—22no—
1325C22⋊C4—22no—
1326C22⋊C4—22no—
1327C22⋊C4—22no—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4C2×D4×C5914yes—
1344C22⋊C4C2×D4×C5914yes—
1345C42—22no—
1346C42—22no—
1347C42—22no—
1348C42—22no—
1349C42—22no—
1350C42—22no—
1351C42—22no—
1352C42—22no—
1353C42—41no—
1354C42—41no—
1355C42—41no—
1356C42—41no—
1357C42C2×D4×C5914yes—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—21no—
1377C23—21no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23C22×D4×C5912yes—
1382C23C22×D4×C5912yes—
1383C23C2×#41×C5912yes—
1384C23C2×#41×C5912yes—
1385C23C2×#41×C5912yes—
1386C23C25×C5911yescharacteristic
1387Q8—28no—
1388Q8—82no—
1389D4—28no—
1390D4—28no—
1391D4—28no—
1392D4—44no—
1393D4—44no—
1394D4—82no—
1395C2×C4—28no—
1396C2×C4—28no—
1397C2×C4—28no—
1398C2×C4—28no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—44no—
1470C2×C4—44no—
1471C2×C4—44no—
1472C2×C4—44no—
1473C2×C4—82no—
1474C2×C4—82no—
1475C2×C4—82no—
1476C2×C4—82no—
1477C2×C4—82no—
1478C2×C4—82no—
1479C2×C4C22×D4×C5912yes—
1480C2×C4C22×D4×C5912yes—
1481C2×C4C22×D4×C5912yes—
1482C2×C4C22×D4×C5912yes—
1483C2×C4C22×D4×C5912yes—
1484C2×C4C2×#41×C5912yes—
1485C2×C4C2×#41×C5912yes—
1486C2×C4C2×#41×C5912yes—
1487C2×C4H(5,𝔽2)×C5912yes—
1488C2×C42−1+4×C5912yes—
1489C2×C42−1+4×C5912yes—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—22no—
1501C22—22no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22C59×#52514yes—
1518C22C23×D4×C5911yescharacteristic
1519C22C22×#41×C5911yescharacteristic
1520C22C22×#41×C5911yescharacteristic
1521C22C2×H(5,𝔽2)×C5911yescharacteristic
1522C22C2×2−1+4×C5911yescharacteristic
1523C22C2×2−1+4×C5911yescharacteristic
1524C22C59×#58511yescharacteristic
1525C4—22no—
1526C4—22no—
1527C4—22no—
1528C4—22no—
1529C4—22no—
1530C4—22no—
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—41no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—41no—
1547C4—41no—
1548C4—41no—
1549C4—41no—
1550C4—41no—
1551C4—41no—
1552C2—24no—
1553C2—42no—
1554C2—42no—
1555C2—81no—
1556C2C2×C59×#52511yescharacteristic
1557C2C59×#349211yescharacteristic
1558C2C59×#349611yescharacteristic
1559C2C59×#349911yescharacteristic
1560C2C59×#350711yescharacteristic
1561C2C59×#351511yescharacteristic
1562C2C59×#352011yescharacteristic
subgroupG/H
center, socleC23×C59C25
commutator, Frattini, cosocleC23C25×C59
prime radicalC59×#2430C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#539C2semidirect
2. C2×C59×#520C2semidirect
3. C59×#2611C2semidirect
4. C59×#2604C2semidirect
5. C59×#2602C2semidirect
6. C59×#2601C2semidirect
7. C59×#2584C2semidirect
8. C59×#2583C2semidirect
9. C59×#2478C2semidirect
10. C59×#2473C2semidirect
11. C59×#2470C2semidirect
12. C59×#2466C2semidirect
13. C59×#2465C2semidirect
14. C59×#2462C2semidirect
15. C59×#2455C2semidirect
16. C59×#2449C2semidirect
17. C59×#2449C2semidirect
18. C59×#2443C2semidirect
19. C59×#2438C2semidirect
21. C59×#2425C2semidirect
22. C59×#2419C2semidirect
23. C59×#2415C2semidirect
24. C59×#2413C2semidirect
25. C59×#2413C2semidirect
26. C59×#2406C2semidirect
27. C59×#2322C2semidirect
28. C59×#2322C2semidirect
29. C4×#121×C59C2semidirect
30. C2×C59×#389C2semidirect
31. C59×#2290C2semidirect
240. C4×D4×C59D4semidirect
708. #35363C59direct (N × H)
771. C2×#539C2×C59semidirect
772. C2×#520C2×C59semidirect
773. #2611C2×C59semidirect
774. #2604C2×C59semidirect
775. #2602C2×C59semidirect
776. #2601C2×C59semidirect
777. #2584C2×C59semidirect
778. #2583C2×C59semidirect
779. #2478C2×C59semidirect
780. #2473C2×C59semidirect
781. #2470C2×C59semidirect
782. #2466C2×C59semidirect
783. #2465C2×C59semidirect
784. #2462C2×C59semidirect
785. #2455C2×C59semidirect
786. #2449C2×C59semidirect
787. #2449C2×C59semidirect
788. #2443C2×C59semidirect
789. #2438C2×C59semidirect
791. #2425C2×C59semidirect
792. #2419C2×C59semidirect
793. #2415C2×C59semidirect
794. #2413C2×C59semidirect
795. #2413C2×C59semidirect
796. #2406C2×C59semidirect
797. #2322C2×C59semidirect
798. #2322C2×C59semidirect
799. C4×#121C2×C59semidirect
800. C2×#389C2×C59semidirect
801. #2290C2×C59semidirect
970. C59#35363direct (N × H)
1022. C4×D4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5392
C2×C59×#5202
C59×#26112
C59×#26042
C59×#26022
C59×#26012
C59×#25842
C59×#25832
C59×#24782
C59×#24732
C59×#24702
C59×#24662
C59×#24652
C59×#24622
C59×#24552
C59×#24492
C59×#24432
C59×#24382
C59×#24302
C59×#24252
C59×#24192
C59×#24152
C59×#24132
C59×#24062
C59×#23222
C4×#121×C592
C2×C59×#3892
C59×#22902
#3536359