Finite Group Databasebeta

← C2×C4×#14273641 #28586336

Subgroups — C2×C4×#14273641 #28586336

Order 15104.

2242 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D59C211yesmaximal, characteristic
2C22×#14273641C212yesmaximal
3C2×C4×C22⋊Dic59C211yesmaximal, characteristic, complemented
4C4×#14273641C218yesmaximal, direct product factor
5C2×#16837168C212yesmaximal, complemented
6C2×C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
7C23×C22⋊D59C2211yescharacteristic
8C23×C4×D59C411yescharacteristic, complemented
9C2×C4×C22⋊D59—21no—
10C2×C4×C22⋊D59—21no—
11C2×C4×C22⋊D59—22no—
12C2×C4×C22⋊D59—21no—
13C2×C4×C22⋊D59—21no—
14C2×C4×C22⋊D59—22no—
15C2×C4×C22⋊D59C414yescomplemented
16C2×C4×C22⋊D59C2214yes—
17C22×Dic59⋊C4C411yescharacteristic, complemented
18C22×C22⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59C2212yes—
20C22×(C2×D59)⋊C4C411yescharacteristic, complemented
21C22×C4×Dic59—21no—
22C22×C4×Dic59C411yescharacteristic, complemented
23C2×#14273641C4116yesdirect product factor
24C2×#14273641C2218yes—
25C4×C22⋊Dic59—22no—
26C4×C22⋊Dic59C2214yescomplemented
27C2×C59⋊#95—21no—
28#16837168C2218yescomplemented
29C24×C4×C59C2211yescharacteristic
30C22×C22⋊C4×C59C2212yes—
31C22×C42×C59—21no—
32C4×C22⋊C4×C59—22no—
33C4×C22⋊C4×C59C2214yescomplemented
34C2×#95×C59—21no—
35C24×D59C2×C411yescharacteristic
36C22×C22⋊D59—21no—
37C22×C22⋊D59—21no—
38C22×C22⋊D59—21no—
39C22×C22⋊D59—21no—
40C22×C22⋊D59—24no—
41C22×C22⋊D59C2×C418yes—
42C22×C22⋊D59C2×C412yes—
43C22×C22⋊D59C2312yes—
44C23×Dic59—22no—
45C23×Dic59C2×C411yescharacteristic
46C23×Dic59C2×C411yescharacteristic
47C23×Dic59C2×C411yescharacteristic
48C22×C4×D59—21no—
49C22×C4×D59—22no—
50C22×C4×D59—21no—
51C22×C4×D59—44no—
52C22×C4×D59C2×C414yescomplemented
53C4×C22⋊D59—24no—
54C4×C22⋊D59—24no—
55C4×C22⋊D59—24no—
56C4×C22⋊D59—24no—
57C4×C22⋊D59—24no—
58C4×C22⋊D59—24no—
59C4×C22⋊D59—24no—
60C4×C22⋊D59—24no—
61C2×Dic59⋊C4—21no—
62C2×Dic59⋊C4—21no—
63C2×Dic59⋊C4—22no—
64C2×Dic59⋊C4C2×C414yescomplemented
65C2×C22⋊Dic59—22no—
66C2×C22⋊Dic59—21no—
67C2×C22⋊Dic59—21no—
68C2×C22⋊Dic59—21no—
69C2×C22⋊Dic59—21no—
70C2×C22⋊Dic59—24no—
71C2×C22⋊Dic59C2×C412yes—
72C2×C22⋊Dic59C2×C418yescomplemented
73C2×C22⋊Dic59C2312yes—
74C2×C22⋊Dic59C2314yes—
75C2×(C2×D59)⋊C4—21no—
76C2×(C2×D59)⋊C4—21no—
77C2×(C2×D59)⋊C4—22no—
78C2×(C2×D59)⋊C4C2×C414yescomplemented
79C2×C4×Dic59—21no—
80C2×C4×Dic59—22no—
81C2×C4×Dic59—21no—
82C2×C4×Dic59—24no—
83C2×C4×Dic59—44no—
84C2×C4×Dic59C2×C414yescomplemented
85#14273641C2×C4132yesdirect product factor
86C59⋊#95—24no—
87C25×C59C2311yescharacteristic
88C23×C4×C59—22no—
89C23×C4×C59—44no—
90C23×C4×C59C2×C411yescharacteristic
91C23×C4×C59C2×C411yescharacteristic
92C23×C4×C59C2×C412yes—
93C23×C4×C59D411yescharacteristic
94C23×C4×C59D411yescharacteristic
95C23×C4×C59D412yes—
96C23×C4×C59D411yescharacteristic
97C23×C4×C59D411yescharacteristic
98C23×C4×C59D412yes—
99C23×C4×C59C2312yes—
100C2×C22⋊C4×C59—22no—
101C2×C22⋊C4×C59—24no—
102C2×C22⋊C4×C59C2×C418yescomplemented
103C2×C22⋊C4×C59C2314yes—
104C2×C42×C59—24no—
105C2×C42×C59—44no—
106#95×C59—24no—
107C24×C59—42no—
108C24×C59—42no—
109C24×C59C22×C411yescharacteristic
110C24×C59C22×C411yescharacteristic
111C24×C59C22×C414yes—
112C24×C59C2×D411yescharacteristic
113C24×C59C2×D411yescharacteristic
114C24×C59C2×D411yescharacteristic
115C24×C59C2×D411yescharacteristic
116C24×C59#4114yes—
117C24×C59C2411yescharacteristic
118C23×D59—21no—
119C23×D59—21no—
120C23×D59—22no—
121C23×D59—42no—
122C23×D59—42no—
123C23×D59C4214yescomplemented
124C23×D59C22×C412yes—
125C22×C4×C59—24no—
126C22×C4×C59—24no—
127C22×C4×C59—24no—
128C22×C4×C59—28no—
129C22×C4×C59—24no—
130C22×C4×C59—44no—
131C22×C4×C59—44no—
132C22×C4×C59—44no—
133C22×C4×C59—44no—
134C22×C4×C59—42no—
135C22×C4×C59—42no—
136C22×C4×C59—42no—
137C22×C4×C59—44no—
138C22×C4×C59—44no—
139C22×C4×C59C22⋊C411yescharacteristic
140C22×C4×C59C22⋊C412yes—
141C22×C4×C59C22⋊C411yescharacteristic
142C22×C4×C59C22⋊C411yescharacteristic
143C22×C4×C59C22⋊C412yes—
144C22×C4×C59C22⋊C412yes—
145C22×C4×C59C22⋊C412yes—
146C22×C4×C59C22⋊C412yes—
147C22×C4×C59C22⋊C412yes—
148C22×C4×C59C22⋊C411yescharacteristic
149C22×C4×C59C22×C412yes—
150C22×C4×C59C22×C412yes—
151C22×C4×C59C2×D412yes—
152C22×C4×C59C2×D412yes—
153C22×C4×C59C2×D412yes—
154C22×C4×C59C2×D412yes—
155C2×C22⋊D59—22no—
156C2×C22⋊D59—22no—
157C2×C22⋊D59—24no—
158C2×C22⋊D59—28no—
159C2×C22⋊D59—28no—
160C2×C22⋊D59—28no—
161C2×C22⋊D59—28no—
162C2×C22⋊D59—22no—
163C2×C22⋊D59—22no—
164C2×C22⋊D59—24no—
165C2×C22⋊D59C4218yescomplemented
166C2×C22⋊D59C22×C418yes—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—22no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—28no—
175C22×Dic59—24no—
176C22×Dic59—44no—
177C22×Dic59—44no—
178C22×Dic59—42no—
179C22×Dic59—42no—
180C22×Dic59C4214yescomplemented
181C22×Dic59C22×C412yes—
182C22×Dic59C22×C412yes—
183C22×Dic59C22×C412yes—
184C2×C4×D59—24no—
185C2×C4×D59—24no—
186C2×C4×D59—44no—
187C2×C4×D59—48no—
188C2×C4×D59—44no—
189C2×C4×D59—48no—
190C22⋊C4×C59—28no—
191C22⋊C4×C59—24no—
192C22⋊C4×C59C22×C418yescomplemented
193C42×C59—48no—
194C22⋊Dic59—22no—
195C22⋊Dic59—22no—
196C22⋊Dic59—28no—
197C22⋊Dic59—22no—
198C22⋊Dic59—22no—
199C22⋊Dic59—24no—
200C22⋊Dic59C22×C418yescomplemented
201(C2×D59)⋊C4—24no—
202(C2×D59)⋊C4—24no—
203Dic59⋊C4—24no—
204Dic59⋊C4—24no—
205C4×Dic59—24no—
206C4×Dic59—24no—
207C4×Dic59—48no—
208C23×C59—22no—
209C23×C59—22no—
210C23×C59—22no—
211C23×C59—22no—
212C23×C59—22no—
213C23×C59—22no—
214C23×C59—41no—
215C23×C59—41no—
216C23×C59—41no—
217C23×C59—41no—
218C23×C59—41no—
219C23×C59—48no—
220C23×C59—41no—
221C23×C59—41no—
222C23×C59—48no—
223C23×C59—41no—
224C23×C59C2×C4212yes—
225C23×C59C2×C4212yes—
226C23×C59C2×C22⋊C411yescharacteristic
227C23×C59C2×C22⋊C411yescharacteristic
228C23×C59C2×C22⋊C411yescharacteristic
229C23×C59C2×C22⋊C411yescharacteristic
230C23×C59#11712yes—
231C23×C59#11712yes—
232C23×C59C4×D414yes—
233C23×C59C4×D414yes—
234C23×C59C4×D414yes—
235C23×C59C4×D414yes—
236C23×C59C23×C411yescharacteristic
237C23×C59C23×C412yes—
238C23×C59C22×D411yescharacteristic
239C23×C59C22×D411yescharacteristic
240C23×C59C2×#4112yes—
241C22×D59—22no—
242C22×D59—22no—
243C22×D59—24no—
244C22×D59—24no—
245C22×D59—42no—
246C22×D59—42no—
247C22×D59—48no—
248C22×D59—42no—
249C22×D59—42no—
250C22×D59—42no—
251C22×D59—48no—
252C22×D59—42no—
253C22×D59C2×C4214yescomplemented
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—24no—
258C2×C4×C59—24no—
259C2×C4×C59—24no—
260C2×C4×C59—24no—
261C2×C4×C59—24no—
262C2×C4×C59—24no—
263C2×C4×C59—28no—
264C2×C4×C59—42no—
265C2×C4×C59—42no—
266C2×C4×C59—42no—
267C2×C4×C59—42no—
268C2×C4×C59—42no—
269C2×C4×C59—42no—
270C2×C4×C59—44no—
271C2×C4×C59—44no—
272C2×C4×C59—416no—
273C2×C4×C59#9914yescomplemented
274C2×C4×C59C2×C22⋊C412yes—
275C2×C4×C59C2×C22⋊C412yes—
276C2×C4×C59C2×C22⋊C412yes—
277C2×C4×C59C2×C22⋊C412yes—
278C22⋊D59—28no—
279C22⋊D59—28no—
280C22⋊D59—28no—
281C22⋊D59—28no—
282C2×Dic59—22no—
283C2×Dic59—22no—
284C2×Dic59—24no—
285C2×Dic59—24no—
286C2×Dic59—22no—
287C2×Dic59—22no—
288C2×Dic59—28no—
289C2×Dic59—44no—
290C2×Dic59—42no—
291C2×Dic59—44no—
292C2×Dic59—416no—
293C2×Dic59—42no—
294C2×Dic59—42no—
295C2×Dic59—42no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59C2×C4214yescomplemented
299C4×D59—48no—
300C4×D59—48no—
301C2×C4×#99—591nomaximal, Sylow
302C22×C59—21no—
303C22×C59—21no—
304C22×C59—21no—
305C22×C59—21no—
306C22×C59—21no—
307C22×C59—21no—
308C22×C59—21no—
309C22×C59—21no—
310C22×C59—21no—
311C22×C59—21no—
312C22×C59—21no—
313C22×C59—21no—
314C22×C59—28no—
315C22×C59—28no—
316C22×C59—24no—
317C22×C59—24no—
318C22×C59—42no—
319C22×C59—42no—
320C22×C59—44no—
321C22×C59—44no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59C4×C22⋊C412yes—
325C22×C59C4×C22⋊C412yes—
326C22×C59C4×C22⋊C412yes—
327C22×C59C4×C22⋊C412yes—
328C22×C59C2×#9912yes—
329C22×C59#41012yes—
330C22×C59C22×C4211yescharacteristic
331C22×C59C22×C22⋊C411yescharacteristic
332C22×C59C2×#11711yescharacteristic
333C22×C59C2×C4×D412yes—
334C22×C59C2×C4×D412yes—
335C2×D59—24no—
336C2×D59—44no—
337C2×D59—48no—
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—48no—
341C2×D59—44no—
342C4×C59—22no—
343C4×C59—22no—
344C4×C59—22no—
345C4×C59—48no—
346C4×C59C2×#9914yescomplemented
347Dic59—24no—
348Dic59—48no—
349Dic59—42no—
350Dic59—42no—
351C22×C4×D4—591no—
352C22×#99—592no—
353C2×C4×C22⋊C4—591no—
354C2×C4×C22⋊C4D5911yescharacteristic, complemented
355C4×#99—598no—
356C2×#342—592no—
357C2×C59—22no—
358C2×C59—22no—
359C2×C59—21no—
360C2×C59—22no—
361C2×C59—21no—
362C2×C59—22no—
363C2×C59—22no—
364C2×C59C4×#9914yescomplemented
365C2×C59C2×C4×C22⋊C411yescharacteristic
366C2×C59C22×#9911yescharacteristic
367C2×C59C2×#41011yescharacteristic
368D59—44no—
369C23×D4—591no—
370C24×C4—591no—
371C24×C4C2×D5911yescharacteristic
372C2×C4×D4—594no—
373C2×C4×D4—594no—
374C2×C4×D4—1181no—
375C2×C4×D4—1182no—
376C2×C4×D4—1181no—
377C2×C4×D4—1181no—
378C2×C4×D4—1182no—
379C2×C4×D4—1181no—
380C22×C4⋊C4—591no—
381C22×C22⋊C4—592no—
382C22×C22⋊C4—591no—
383C22×C22⋊C4—591no—
384C22×C22⋊C4C2×D5912yes—
385C22×C42—21no—
386C22×C42—591no—
387C22×C42—1181no—
388C2×#99—5916no—
389C2×#99—598no—
390C4×C22⋊C4—22no—
391C4×C22⋊C4—594no—
392C4×C22⋊C4—1182no—
393C4×C22⋊C4C2×D5914yescomplemented
394C2×#95—21no—
395C2×#95—1181no—
396#342—598no—
397C59C2×C4×#9911yescharacteristic, complemented, Sylow
398C25—591no—
399C25C22×D5911yescharacteristic
400C22×D4—592no—
401C22×D4—598no—
402C22×D4—592no—
403C22×D4—1181no—
404C22×D4—1181no—
405C22×D4—1184no—
406C22×D4—1181no—
407C22×D4—1181no—
408C23×C4—22no—
409C23×C4—44no—
410C23×C4—591no—
411C23×C4—591no—
412C23×C4—591no—
413C23×C4—594no—
414C23×C4—1182no—
415C23×C4—1182no—
416C23×C4—1181no—
417C23×C4—1181no—
418C23×C4—2364no—
419C23×C4C4×D5911yescharacteristic
420C23×C4C4×D5911yescharacteristic
421C23×C4C4×D5912yes—
422C23×C4D23611yescharacteristic
423C23×C4D23611yescharacteristic
424C23×C4D23612yes—
425C23×C4C22⋊D5911yescharacteristic
426C23×C4C22⋊D5911yescharacteristic
427C23×C4C22⋊D5912yes—
428C23×C4C22×D5912yes—
429C4×D4—1184no—
430C4×D4—1184no—
431C4×D4—1184no—
432C4×D4—1184no—
433C4×D4—1184no—
434C4×D4—1184no—
435C4×D4—1184no—
436C4×D4—1184no—
437C2×C4⋊C4—594no—
438C2×C4⋊C4—1181no—
439C2×C4⋊C4—1181no—
440C2×C4⋊C4—1182no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—598no—
444C2×C22⋊C4—594no—
445C2×C22⋊C4—592no—
446C2×C22⋊C4—592no—
447C2×C22⋊C4—594no—
448C2×C22⋊C4—1181no—
449C2×C22⋊C4—1181no—
450C2×C22⋊C4—1182no—
451C2×C22⋊C4—1184no—
452C2×C22⋊C4—1181no—
453C2×C22⋊C4—1181no—
454C2×C22⋊C4—1181no—
455C2×C22⋊C4—1181no—
456C2×C22⋊C4—1182no—
457C2×C22⋊C4C4×D5918yescomplemented
458C2×C22⋊C4C22×D5914yes—
459C2×C42—24no—
460C2×C42—44no—
461C2×C42—594no—
462C2×C42—1181no—
463C2×C42—1182no—
464C2×C42—1181no—
465C2×C42—1184no—
466C2×C42—2364no—
467#99—5932no—
468#95—24no—
469#95—1184no—
470C24—42no—
471C24—42no—
472C24—594no—
473C24—592no—
474C24—1181no—
475C24—1181no—
476C24—1182no—
477C24—2362no—
478C24—2362no—
479C24C2×C4×D5911yescharacteristic
480C24C2×C4×D5911yescharacteristic
481C24C2×C4×D5914yes—
482C24C2×D23611yescharacteristic
483C24C2×D23611yescharacteristic
484C24#1174568514yes—
485C24C2×C22⋊D5911yescharacteristic
486C24C2×C22⋊D5911yescharacteristic
487C24C23×D5911yescharacteristic
488C2×D4—598no—
489C2×D4—598no—
490C2×D4—1182no—
491C2×D4—1182no—
492C2×D4—1184no—
493C2×D4—1188no—
494C2×D4—1188no—
495C2×D4—1188no—
496C2×D4—1188no—
497C2×D4—1182no—
498C2×D4—1182no—
499C2×D4—1184no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—24no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—594no—
515C22×C4—592no—
516C22×C4—592no—
517C22×C4—592no—
518C22×C4—1181no—
519C22×C4—1181no—
520C22×C4—1182no—
521C22×C4—1181no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—1181no—
525C22×C4—1188no—
526C22×C4—1184no—
527C22×C4—1184no—
528C22×C4—1184no—
529C22×C4—2364no—
530C22×C4—2368no—
531C22×C4—2368no—
532C22×C4—2364no—
533C22×C4—2364no—
534C22×C4—2364no—
535C22×C4—2362no—
536C22×C4—2362no—
537C22×C4(C2×D59)⋊C411yescharacteristic
538C22×C4(C2×D59)⋊C412yes—
539C22×C4(C2×D59)⋊C411yescharacteristic
540C22×C4(C2×D59)⋊C411yescharacteristic
541C22×C4(C2×D59)⋊C412yes—
542C22×C4(C2×D59)⋊C412yes—
543C22×C4(C2×D59)⋊C412yes—
544C22×C4(C2×D59)⋊C412yes—
545C22×C4(C2×D59)⋊C412yes—
546C22×C4(C2×D59)⋊C411yescharacteristic
547C22×C4C2×C4×D5912yes—
548C22×C4C2×C4×D5912yes—
549C22×C4C2×D23612yes—
550C22×C4C2×D23612yes—
551C22×C4C2×C22⋊D5912yes—
552C22×C4C2×C22⋊D5912yes—
553C4⋊C4—1184no—
554C4⋊C4—1184no—
555C22⋊C4—28no—
556C22⋊C4—24no—
557C22⋊C4—598no—
558C22⋊C4—1182no—
559C22⋊C4—1182no—
560C22⋊C4—1188no—
561C22⋊C4—1182no—
562C22⋊C4—1182no—
563C22⋊C4—1184no—
564C22⋊C4—1184no—
565C22⋊C4—1184no—
566C22⋊C4C2×C4×D5918yescomplemented
567C42—48no—
568C42—1184no—
569C42—1184no—
570C42—2368no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—48no—
582C23—41no—
583C23—41no—
584C23—48no—
585C23—41no—
586C23—41no—
587C23—594no—
588C23—1184no—
589C23—1184no—
590C23—1182no—
591C23—1182no—
592C23—2362no—
593C23—2368no—
594C23—2362no—
595C23—2362no—
596C23—2368no—
597C23—2362no—
598C23—2362no—
599C23—2362no—
600C23C42×D5912yes—
601C23C42×D5912yes—
602C23C2×(C2×D59)⋊C411yescharacteristic
603C23C2×(C2×D59)⋊C411yescharacteristic
604C23C2×(C2×D59)⋊C411yescharacteristic
605C23C2×(C2×D59)⋊C411yescharacteristic
606C23#1427368412yes—
607C23#1427368412yes—
608C23C4×C22⋊D5914yes—
609C23C4×C22⋊D5914yes—
610C23C4×D23614yes—
611C23C4×D23614yes—
612C23C22×C4×D5911yescharacteristic
613C23C22×C4×D5912yes—
614C23C22×C22⋊D5911yescharacteristic
615C23C22×D23611yescharacteristic
616C23C2×#1174568512yes—
617D4—1188no—
618D4—1188no—
619D4—1188no—
620D4—1188no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—416no—
639C2×C4—44no—
640C2×C4—594no—
641C2×C4—1184no—
642C2×C4—1184no—
643C2×C4—1182no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1188no—
648C2×C4—2368no—
649C2×C4—2364no—
650C2×C4—23616no—
651C2×C4—2364no—
652C2×C4—2362no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4—2362no—
656C2×C4—2368no—
657C2×C4—2362no—
658C2×C4—2362no—
659C2×C4#1427364114yesdirect product factor
660C2×C4C2×(C2×D59)⋊C412yes—
661C2×C4C2×(C2×D59)⋊C412yes—
662C2×C4C2×(C2×D59)⋊C412yes—
663C2×C4C2×(C2×D59)⋊C412yes—
664C22—28no—
665C22—28no—
666C22—24no—
667C22—24no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—42no—
681C22—42no—
682C22—44no—
683C22—44no—
684C22—42no—
685C22—42no—
686C22—1184no—
687C22—2364no—
688C22—2368no—
689C22—2364no—
690C22—2368no—
691C22—2362no—
692C22—2362no—
693C22C4×(C2×D59)⋊C412yes—
694C22C4×(C2×D59)⋊C412yes—
695C22C4×(C2×D59)⋊C412yes—
696C22C4×(C2×D59)⋊C412yes—
697C22C2×#1427364112yes—
698C22#1683737512yes—
699C22C2×C42×D5911yescharacteristic
700C22C22×(C2×D59)⋊C411yescharacteristic
701C22C2×#1427368411yescharacteristic
702C22C2×C4×C22⋊D5912yes—
703C22C2×C4×D23612yes—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—48no—
708C4—1184no—
709C4—2368no—
710C4—2362no—
711C4—2362no—
712C4C2×#1427364114yesdirect product factor
713C2—22no—
714C2—22no—
715C2—22no—
716C2—21no—
717C2—21no—
718C2—22no—
719C2—22no—
720C2—2364no—
721C2C4×#1427364114yesdirect product factor
722C2C2×C4×(C2×D59)⋊C411yescharacteristic
723C2C22×#1427364111yescharacteristic
724C2C2×#1683737511yescharacteristic
subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC22×C59C22×C42
FrattiniC24C23×D59
FittingC2×C4×C22⋊C4×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC23×C22⋊D59C22
cosocleC24×C59C24
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C2×C4×#99
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic59C2semidirect
4. C4×#14273641C2direct (N × H)
5. C2×#16837168C2semidirect
6. C2×C4×C22⋊C4×C59C2semidirect
8. C23×C4×D59C4semidirect
15. C2×C4×C22⋊D59C4semidirect
17. C22×Dic59⋊C4C4semidirect
20. C22×(C2×D59)⋊C4C4semidirect
22. C22×C4×Dic59C4semidirect
23. C2×#14273641C4direct (N × H)
26. C4×C22⋊Dic59C22semidirect
28. #16837168C22semidirect
33. C4×C22⋊C4×C59C22semidirect
52. C22×C4×D59C2×C4semidirect
64. C2×Dic59⋊C4C2×C4semidirect
72. C2×C22⋊Dic59C2×C4semidirect
78. C2×(C2×D59)⋊C4C2×C4semidirect
84. C2×C4×Dic59C2×C4semidirect
85. #14273641C2×C4direct (N × H)
102. C2×C22⋊C4×C59C2×C4semidirect
123. C23×D59C42semidirect
165. C2×C22⋊D59C42semidirect
180. C22×Dic59C42semidirect
192. C22⋊C4×C59C22×C4semidirect
200. C22⋊Dic59C22×C4semidirect
253. C22×D59C2×C42semidirect
273. C2×C4×C59#99semidirect
298. C2×Dic59C2×C42semidirect
346. C4×C59C2×#99semidirect
354. C2×C4×C22⋊C4D59semidirect
364. C2×C59C4×#99semidirect
393. C4×C22⋊C4C2×D59semidirect
397. C59C2×C4×#99semidirect
457. C2×C22⋊C4C4×D59semidirect
566. C22⋊C4C2×C4×D59semidirect
659. C2×C4#14273641direct (N × H)
712. C4C2×#14273641direct (N × H)
721. C2C4×#14273641direct (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
C22×#142736412
C2×C4×C22⋊Dic592
C4×#142736412
C2×#168371682
C2×C4×C22⋊C4×C592
C2×C4×#9959