Finite Group Databasebeta

← C2×#11752767 #14483293

Subgroups — C2×#11752767 #14483293

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D60C211yesmaximal, characteristic, complemented
2C2×C5×#872C211yesmaximal, characteristic, complemented
3C2×C3×#4022C211yesmaximal, characteristic, complemented
4C2×#91476C211yesmaximal, characteristic
5C2×#91473C211yesmaximal, characteristic, complemented
6C2×D3×#685C211yesmaximal, characteristic, complemented
7C2×#91433C211yesmaximal, characteristic, complemented
8C2×#91417C211yesmaximal, characteristic, complemented
9C2×#91406C211yesmaximal, characteristic, complemented
10C2×#91403C211yesmaximal, characteristic, complemented
11C2×#91377C211yesmaximal, characteristic, complemented
12C2×#91362C211yesmaximal, characteristic, complemented
13C2×#91354C211yesmaximal, characteristic, complemented
14C2×#91353C211yesmaximal, characteristic, complemented
15C2×#91351C211yesmaximal, characteristic, complemented
16#11752767C2116yesmaximal, direct product factor
17C2×#65861—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C4×C5×D3C2211yescharacteristic
23C22×#1204C2211yescharacteristic, complemented
24C22×#1203C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic, complemented
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic, complemented
31C2×C4⋊Dic15C2211yescharacteristic, complemented
32C4×D60C2218yescomplemented
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C4×C5×Dic3C2211yescharacteristic, complemented
38C5×#872C2218yescomplemented
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic, complemented
43C2×C3×#683C2211yescharacteristic, complemented
44C2×C3×#683C2211yescharacteristic, complemented
45C3×#4022C2218yescomplemented
46C2×#6669C2211yescharacteristic, complemented
47C2×#6668C2211yescharacteristic, complemented
48C2×#6667C2211yescharacteristic
49C2×#6667C2211yescharacteristic
50C2×#6667C2211yescharacteristic, complemented
51C2×#6667C2211yescharacteristic, complemented
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic, complemented
56#91476C2218yes—
57#91473C2218yescomplemented
58D3×#685C2218yescomplemented
59#91433C2218yescomplemented
60#91417C2218yescomplemented
61#91406C2218yescomplemented
62#91403C2218yescomplemented
63#91377C2218yescomplemented
64#91362C2218yescomplemented
65#91354C2218yescomplemented
66#91353C2218yescomplemented
67#91351C2218yescomplemented
68C2×#5705—51nomaximal, Hall
69C2×C5×#117—31no—
70C2×#4075—31no—
71C22×#685—31no—
72#65861—316no—
73C2×#4044—31no—
74C2×#4042—31no—
75C2×#4040—31no—
76C2×#4040—31no—
77C2×#4028—31no—
78C2×#4027—31no—
79C2×D5×C22⋊C4—31no—
80C2×#4024—31no—
81C2×#4022D311yescharacteristic, complemented
82C2×#4021—31no—
83C2×C4×D20—31no—
84C2×#4018—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×D3×D5—24no—
90C22×D3×D5—24no—
91C22×D3×D5—42no—
92C22×D3×D5C2314yes—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×D60—24no—
99C2×D60C2314yes—
100C2×C4×D15—42no—
101C2×C4×D15—42no—
102C2×C4×D15C2314yes—
103C2×C4×D15C2314yescomplemented
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C2×C4×C5×D3—24no—
108C2×C4×C5×D3C2314yes—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×#1204—42no—
113C2×#1204C2314yescomplemented
114C2×#1203—24no—
115C2×#1203C2314yes—
116C2×#1202—42no—
117C2×#1202C2314yes—
118C2×#1200—24no—
119C2×#1200C2314yes—
120C2×D3×Dic5—42no—
121C2×D3×Dic5C2314yes—
122C3×C42×C5C2314yescomplemented
123#6714C2314yes—
124#6714C2314yescomplemented
125C4⋊Dic15C2314yescomplemented
126C5×(C2×D3)⋊C4C2314yes—
127C5×(C2×D3)⋊C4C2314yes—
128C5×Dic3⋊C4C2314yescomplemented
129C5×Dic3⋊C4C2314yescomplemented
130C4×C5×Dic3C2314yescomplemented
131C3×#685C2314yes—
132C3×#685C2314yes—
133C3×#685C2314yes—
134C3×#683C2314yescomplemented
135C3×#683C2314yescomplemented
136C3×#683C2314yescomplemented
137#6669C2314yescomplemented
138#6668C2314yescomplemented
139#6667C2314yes—
140#6667C2314yes—
141#6667C2314yescomplemented
142#6667C2314yescomplemented
143(C2×D3)⋊Dic5C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146Dic3×Dic5C2314yescomplemented
147C2×C3×#126—51no—
148#5705—516no—
149C2×#897—51no—
150C2×#896—51no—
151C2×#894—51no—
152C2×#894—51no—
153C2×#893—51no—
154C2×#892—51no—
155C2×#885—51no—
156C2×#883—51no—
157C2×#882—51no—
158C2×D3×C22⋊C4—51no—
159C2×D3×C22⋊C4—51no—
160C2×#879—51no—
161C2×C4×D12—51no—
162C2×#872D511yescharacteristic, complemented
163C24×D5—31no—
164C23×C4×C5—31no—
165C22×C22⋊D5—31no—
166C23×Dic5—31no—
167C22×D20—31no—
168C22×D20—31no—
169C22×C4×D5—31no—
170C22×C4×D5—31no—
171C22×C4×D5—31no—
172C22×Dic10—31no—
173C5×#117—38no—
174C2×C5×C4⋊C4—31no—
175C2×C5×C4⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C42×C5—31no—
179C2×C42×C5C2×D311yescharacteristic, complemented
180C2×C22⋊Dic5—31no—
181#4075—38no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—38no—
191C2×#685C2×D311yescharacteristic
192C2×#685C2×D311yescharacteristic
193C2×#685C2×D311yescharacteristic
194C2×C4⋊Dic5—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683C2×D311yescharacteristic, complemented
198C2×#683C2×D311yescharacteristic, complemented
199C2×#683C2×D311yescharacteristic, complemented
200C2×C4×Dic5—31no—
201#4044—38no—
202#4042—38no—
203#4040—38no—
204#4040—38no—
205#4028—38no—
206#4027—38no—
207D5×C22⋊C4—38no—
208#4024—38no—
209#4022C2×D318yescomplemented
210#4021—38no—
211C4×D20—38no—
212#4018—38no—
213C2×#551—151noSylow
214C23×C3×C5C2411yescharacteristic
215C22×D15—22no—
216C22×D15—22no—
217C22×D15—22no—
218C22×D15—22no—
219C22×D15—22no—
220C22×D15#4114yes—
221C22×D15C2412yes—
222C22×D15C2412yes—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3#4114yes—
226C22×C5×D3C2412yes—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—22no—
230C22×C3×D5C2412yes—
231C2×D3×D5—28no—
232C2×D3×D5—28no—
233C2×D3×D5—44no—
234C2×D3×D5—416no—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5C2412yes—
239C2×C3×C4×C5C2412yes—
240C2×C3×C4×C5C2412yes—
241C2×Dic15—22no—
242C2×Dic15—22no—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245D60—28no—
246C4×D15—44no—
247C4×D15—44no—
248C2×C5×Dic3—22no—
249C2×C5×Dic3—22no—
250C2×C5×Dic3—22no—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C2×C5×Dic3C2412yes—
254C4×C5×D3—28no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5—22no—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261#1204—44no—
262#1203—28no—
263#1202—44no—
264#1200—28no—
265D3×Dic5—44no—
266C24×D3—51no—
267C22×#67—51no—
268C22×D12—51no—
269C22×D12—51no—
270C22×C4×D3—51no—
271C22×C4×D3—51no—
272C22×C4×D3—51no—
273C22×C4×D3—51no—
274C22×C4×D3C2×D511yescharacteristic
275C22×Dic6—51no—
276C3×#126—58no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C42C2×D511yescharacteristic, complemented
284C2×#217—51no—
285C2×#217—51no—
286C2×(C2×D3)⋊C4—51no—
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4C2×D511yescharacteristic
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×C4⋊Dic3—51no—
296C2×C4⋊Dic3—51no—
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4C2×D511yescharacteristic, complemented
299C2×Dic3⋊C4C2×D511yescharacteristic, complemented
300C2×C4×Dic3—51no—
301C2×C4×Dic3C2×D511yescharacteristic, complemented
302#897—58no—
303#896—58no—
304#894—58no—
305#894—58no—
306#893—58no—
307#892—58no—
308#885—58no—
309#883—58no—
310#882—58no—
311D3×C22⋊C4—58no—
312D3×C22⋊C4—58no—
313#879—58no—
314C4×D12—58no—
315#872C2×D518yescomplemented
316C24×C5—31no—
317C23×D5—31no—
318C23×D5—31no—
319C23×D5—34no—
320C23×D5—64no—
321C23×D5—64no—
322C23×D5—122no—
323C23×D5C22×D311yescharacteristic
324C22×C4×C5—31no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—34no—
328C22×C4×C5—64no—
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C2×C22⋊D5—34no—
333C2×C22⋊D5—64no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—34no—
337C22×Dic5—122no—
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341C2×D20—34no—
342C2×D20—34no—
343C2×D20—64no—
344C2×D20—122no—
345C2×C4×D5—34no—
346C2×C4×D5—34no—
347C2×C4×D5—34no—
348C2×C4×D5—64no—
349C2×C4×D5—122no—
350C2×C4×D5—122no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C4⋊C4—34no—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4—34no—
357C42×C5—34no—
358C42×C5C22×D314yescomplemented
359C22⋊Dic5—34no—
360#685—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685C22×D314yes—
369#685C22×D314yes—
370#685C22×D314yes—
371C4⋊Dic5—34no—
372#683—34no—
373#683—34no—
374#683C22×D314yescomplemented
375#683C22×D314yescomplemented
376#683C22×D314yescomplemented
377C4×Dic5—34no—
378#551—1516no—
379C2×#126—51no—
380C2×#126—151no—
381C2×#124—151no—
382C2×#123—151no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×#120—151no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×#117—31no—
391C2×#117—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C3×C5C2×#4112yes—
395C22×C3×C5C2×#4112yes—
396C22×C3×C5H(5,𝔽2)12yes—
397C22×C3×C5C2511yescharacteristic
398C2×D15—28no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—44no—
405C2×D15C2×#4114yes—
406C2×C5×D3—28no—
407C2×C5×D3—22no—
408C2×C5×D3—22no—
409C2×C5×D3C2×#4114yes—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—22no—
413C2×C3×D5—44no—
414D3×D5—416no—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×C4×C5—22no—
418Dic15—22no—
419Dic15—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C3×Dic5—22no—
423C5×Dic3—22no—
424C5×Dic3—22no—
425C5×Dic3—22no—
426C24×C3—51no—
427C23×D3—51no—
428C23×D3—51no—
429C23×D3—54no—
430C23×D3—104no—
431C23×D3—104no—
432C23×D3—202no—
433C23×D3C22×D511yescharacteristic
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—51no—
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C2×#67—54no—
441C2×#67—202no—
442C22×Dic3—51no—
443C22×Dic3—51no—
444C22×Dic3C22×D511yescharacteristic
445C22×Dic3C22×D511yescharacteristic
446C22×Dic3C22×D511yescharacteristic
447C2×D12—54no—
448C2×D12—54no—
449C2×D12—104no—
450C2×D12—104no—
451C2×C4×D3—24no—
452C2×C4×D3—54no—
453C2×C4×D3—54no—
454C2×C4×D3—54no—
455C2×C4×D3—54no—
456C2×C4×D3—104no—
457C2×C4×D3—202no—
458C2×C4×D3—202no—
459C2×C4×D3—202no—
460C2×C4×D3C22×D514yes—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—54no—
468C3×C22⋊C4—54no—
469C3×C42C22×D514yescomplemented
470#217—54no—
471#217—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477(C2×D3)⋊C4—54no—
478(C2×D3)⋊C4—54no—
479(C2×D3)⋊C4C22×D514yes—
480(C2×D3)⋊C4C22×D514yes—
481C4⋊Dic3—54no—
482C4⋊Dic3—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4C22×D514yescomplemented
485Dic3⋊C4C22×D514yescomplemented
486C4×Dic3—54no—
487C4×Dic3C22×D514yescomplemented
488C23×C5—34no—
489C23×C5—32no—
490C23×C5—62no—
491C23×C5—62no—
492C23×C5C23×D311yescharacteristic
493C22×D5—22no—
494C22×D5—22no—
495C22×D5—22no—
496C22×D5—34no—
497C22×D5—32no—
498C22×D5—32no—
499C22×D5—68no—
500C22×D5—68no—
501C22×D5—62no—
502C22×D5—62no—
503C22×D5—62no—
504C22×D5—62no—
505C22×D5—62no—
506C22×D5—124no—
507C22×D5—1216no—
508C22×D5C23×D312yes—
509C2×C4×C5—22no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
512C2×C4×C5—32no—
513C2×C4×C5—32no—
514C2×C4×C5—32no—
515C2×C4×C5—68no—
516C2×C4×C5—62no—
517C2×C4×C5—62no—
518C2×C4×C5—62no—
519C2×C4×C5C23×D312yes—
520C2×C4×C5C23×D312yes—
521C2×C4×C5C23×D312yes—
522C22⋊D5—68no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—22no—
526C2×Dic5—32no—
527C2×Dic5—32no—
528C2×Dic5—62no—
529C2×Dic5—62no—
530C2×Dic5—124no—
531C2×Dic5C23×D312yes—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534D20—68no—
535D20—124no—
536C4×D5—68no—
537C4×D5—124no—
538C4×D5—124no—
539Dic10—124no—
540C25—151no—
541C22×Q8—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—31no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549C23×C4—151no—
550#126—58no—
551#126—158no—
552#124—158no—
553#123—158no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558#120—158no—
559C4×D4—158no—
560C4×D4—158no—
561#117—38no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—158no—
577C2×C22⋊C4—158no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C42—31no—
588C2×C42—151no—
589C2×C42D3×D511yescharacteristic, complemented
590C2×C3×C5#55114yescomplemented
591C2×C3×C5C22×#4111yescharacteristic
592C2×C3×C5C22×#4111yescharacteristic
593C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
594D15—24no—
595D15—42no—
596C3×D5—42no—
597C5×D3—24no—
598C23×C3—52no—
599C23×C3—102no—
600C23×C3—102no—
601C23×C3—102no—
602C23×C3C23×D511yescharacteristic
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—54no—
606C22×D3—52no—
607C22×D3—52no—
608C22×D3—108no—
609C22×D3—102no—
610C22×D3—102no—
611C22×D3—102no—
612C22×D3—102no—
613C22×D3—102no—
614C22×D3—108no—
615C22×D3—204no—
616C22×D3—2016no—
617C22×D3#70914yes—
618C22×D3C23×D512yes—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—52no—
623C2×C3×C4—52no—
624C2×C3×C4—52no—
625C2×C3×C4—102no—
626C2×C3×C4—102no—
627C2×C3×C4—102no—
628C2×C3×C4C23×D512yes—
629C2×C3×C4C23×D512yes—
630C2×C3×C4C23×D512yes—
631#67—204no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—52no—
636C2×Dic3—52no—
637C2×Dic3—102no—
638C2×Dic3—102no—
639C2×Dic3C23×D512yes—
640C2×Dic3C23×D512yes—
641C2×Dic3C23×D512yes—
642D12—108no—
643D12—108no—
644C4×D3—28no—
645C4×D3—108no—
646C4×D3—204no—
647C4×D3—204no—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—34no—
651C22×C5—68no—
652C22×C5—62no—
653C22×C5—62no—
654C22×C5D3×#4112yes—
655C22×C5D3×#4112yes—
656C22×C5#100912yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—34no—
662C2×D5—44no—
663C2×D5—68no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—1216no—
670C2×D5—124no—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—22no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—62no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—62no—
681Dic5—62no—
682C24—31no—
683C24—51no—
684C24—154no—
685C24—151no—
686C24—151no—
687C24—304no—
688C24—304no—
689C24—602no—
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—154no—
693C2×D4—154no—
694C2×D4—154no—
695C2×D4—304no—
696C2×D4—304no—
697C2×D4—602no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—34no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—64no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—154no—
711C22×C4—154no—
712C22×C4—304no—
713C22×C4—602no—
714C22×C4—602no—
715C22×C4—602no—
716C22×C4C2×D3×D511yescharacteristic
717C22×C4C2×D3×D511yescharacteristic
718C22×C4C2×D3×D511yescharacteristic
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—54no—
722C4⋊C4—54no—
723C4⋊C4—54no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4—154no—
739C22⋊C4—154no—
740C22⋊C4—154no—
741C42—34no—
742C42—154no—
743C42C2×D3×D514yescomplemented
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—102no—
746C22×C3—102no—
747C22×C3—102no—
748C22×C3—204no—
749C22×C3C2×#70912yes—
750C22×C3D5×#4112yes—
751C22×C3#414912yes—
752C22×C3C24×D511yescharacteristic
753C2×D3—28no—
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—54no—
757C2×D3—108no—
758C2×D3—102no—
759C2×D3—102no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—2016no—
764C2×D3—204no—
765C2×D3C2×#70914yes—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—102no—
770C3×C4—102no—
771C3×C4—102no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—64no—
778C2×C5#570514yescomplemented
779C2×C5C2×D3×#4111yescharacteristic
780C2×C5C2×D3×#4111yescharacteristic
781C2×C5C2×#100911yescharacteristic
782D5—42no—
783D5—64no—
784D5—122no—
785C23—34no—
786C23—32no—
787C23—52no—
788C23—62no—
789C23—62no—
790C23—102no—
791C23—102no—
792C23—102no—
793C23—154no—
794C23—152no—
795C23—152no—
796C23—308no—
797C23—308no—
798C23—302no—
799C23—302no—
800C23—302no—
801C23—302no—
802C23—302no—
803C23—604no—
804C23—6016no—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—308no—
808D4—308no—
809D4—604no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—52no—
817C2×C4—52no—
818C2×C4—52no—
819C2×C4—68no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—152no—
827C2×C4—152no—
828C2×C4—308no—
829C2×C4—302no—
830C2×C4—302no—
831C2×C4—604no—
832C2×C4—604no—
833C2×C4—604no—
834C2×C4C22×D3×D512yes—
835C2×C4C22×D3×D512yes—
836C2×C4C22×D3×D512yes—
837C2×C3—202no—
838C2×C3#6586114yescomplemented
839C2×C3C22×#70911yescharacteristic
840C2×C3C2×D5×#4111yescharacteristic
841C2×C3C2×#414911yescharacteristic
842D3—24no—
843D3—104no—
844D3—202no—
845C5C2×#570511yescharacteristic, complemented, Sylow
846C22—34no—
847C22—68no—
848C22—62no—
849C22—62no—
850C22—102no—
851C22—102no—
852C22—102no—
853C22—154no—
854C22—204no—
855C22—308no—
856C22—302no—
857C22—302no—
858C22—302no—
859C22—302no—
860C22—302no—
861C22—6016no—
862C22—604no—
863C22D3×#70912yes—
864C22#9201612yes—
865C22#9201912yes—
866C22C23×D3×D511yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—62no—
871C4—62no—
872C4—62no—
873C4—102no—
874C4—102no—
875C4—102no—
876C4—302no—
877C4—302no—
878C3C2×#6586111yescharacteristic, complemented, Sylow
879C2—64no—
880C2—202no—
881C2—304no—
882C2—602no—
883C2#1175276714yesdirect product factor
884C2C2×D3×#70911yescharacteristic
885C2C2×#9201611yescharacteristic
886C2C2×#9201911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC2×#91476C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×D60C2semidirect
2. C2×C5×#872C2semidirect
3. C2×C3×#4022C2semidirect
5. C2×#91473C2semidirect
6. C2×D3×#685C2semidirect
7. C2×#91433C2semidirect
8. C2×#91417C2semidirect
9. C2×#91406C2semidirect
10. C2×#91403C2semidirect
11. C2×#91377C2semidirect
12. C2×#91362C2semidirect
13. C2×#91354C2semidirect
14. C2×#91353C2semidirect
15. C2×#91351C2semidirect
16. #11752767C2direct (N × H)
21. C22×C4×D15C22semidirect
23. C22×#1204C22semidirect
28. C2×C3×C42×C5C22semidirect
30. C2×#6714C22semidirect
31. C2×C4⋊Dic15C22semidirect
32. C4×D60C22semidirect
35. C2×C5×Dic3⋊C4C22semidirect
36. C2×C5×Dic3⋊C4C22semidirect
37. C2×C4×C5×Dic3C22semidirect
38. C5×#872C22semidirect
42. C2×C3×#683C22semidirect
43. C2×C3×#683C22semidirect
44. C2×C3×#683C22semidirect
45. C3×#4022C22semidirect
46. C2×#6669C22semidirect
47. C2×#6668C22semidirect
50. C2×#6667C22semidirect
51. C2×#6667C22semidirect
55. C2×Dic3×Dic5C22semidirect
57. #91473C22semidirect
58. D3×#685C22semidirect
59. #91433C22semidirect
60. #91417C22semidirect
61. #91406C22semidirect
62. #91403C22semidirect
63. #91377C22semidirect
64. #91362C22semidirect
65. #91354C22semidirect
66. #91353C22semidirect
67. #91351C22semidirect
81. C2×#4022D3semidirect
103. C2×C4×D15C23semidirect
113. C2×#1204C23semidirect
122. C3×C42×C5C23semidirect
124. #6714C23semidirect
125. C4⋊Dic15C23semidirect
128. C5×Dic3⋊C4C23semidirect
129. C5×Dic3⋊C4C23semidirect
130. C4×C5×Dic3C23semidirect
134. C3×#683C23semidirect
135. C3×#683C23semidirect
136. C3×#683C23semidirect
137. #6669C23semidirect
138. #6668C23semidirect
141. #6667C23semidirect
142. #6667C23semidirect
146. Dic3×Dic5C23semidirect
162. C2×#872D5semidirect
179. C2×C42×C5C2×D3semidirect
197. C2×#683C2×D3semidirect
198. C2×#683C2×D3semidirect
199. C2×#683C2×D3semidirect
209. #4022C2×D3semidirect
283. C2×C3×C42C2×D5semidirect
298. C2×Dic3⋊C4C2×D5semidirect
299. C2×Dic3⋊C4C2×D5semidirect
301. C2×C4×Dic3C2×D5semidirect
315. #872C2×D5semidirect
358. C42×C5C22×D3semidirect
374. #683C22×D3semidirect
375. #683C22×D3semidirect
376. #683C22×D3semidirect
469. C3×C42C22×D5semidirect
484. Dic3⋊C4C22×D5semidirect
485. Dic3⋊C4C22×D5semidirect
487. C4×Dic3C22×D5semidirect
589. C2×C42D3×D5semidirect
590. C2×C3×C5#551semidirect
743. C42C2×D3×D5semidirect
744. C3×C5C2×#551semidirect
778. C2×C5#5705semidirect
838. C2×C3#65861semidirect
845. C5C2×#5705semidirect
878. C3C2×#65861semidirect
883. C2#11752767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D602
C2×C5×#8722
C2×C3×#40222
C2×#914762
C2×#914732
C2×D3×#6852
C2×#914332
C2×#914172
C2×#914062
C2×#914032
C2×#913772
C2×#913622
C2×#913542
C2×#913532
C2×#913512
#117527672
C2×#658613
C2×#57055