Finite Group Databasebeta

← C2×#11756464 #14483240

Subgroups — C2×#11756464 #14483240

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×C3×C5×#126C211yesmaximal, characteristic, complemented
2#11756464C2116yesmaximal, direct product factor
3C2×#91786C211yesmaximal, characteristic, complemented
4C2×#91785C211yesmaximal, characteristic, complemented
5C2×#91783C211yesmaximal, characteristic, complemented
6C2×#91783C211yesmaximal, characteristic, complemented
7C2×#91782C211yesmaximal, characteristic, complemented
8C2×#91781C211yesmaximal, characteristic, complemented
9C2×#91774C211yesmaximal, characteristic, complemented
10C2×#91772C211yesmaximal, characteristic, complemented
11C2×#91771C211yesmaximal, characteristic
12C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
14C2×#91768C211yesmaximal, characteristic, complemented
15C2×C4×D60C211yesmaximal, characteristic, complemented
16C2×#91761C211yesmaximal, characteristic, complemented
17C2×#66039—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic
26C22×C4×D15C2211yescharacteristic, complemented
27C22×Dic30C2211yescharacteristic, complemented
28C3×C5×#126C2218yescomplemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
30C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
31C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×C3×C42×C5C2211yescharacteristic, complemented
36C2×#6719C2211yescharacteristic
37C2×#6719C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C2×#6714C2211yescharacteristic, complemented
45C2×#6714C2211yescharacteristic, complemented
46C2×#6714C2211yescharacteristic, complemented
47C2×C4⋊Dic15C2211yescharacteristic, complemented
48C2×C4⋊Dic15C2211yescharacteristic, complemented
49C2×#6712C2211yescharacteristic, complemented
50C2×#6712C2211yescharacteristic, complemented
51C2×#6712C2211yescharacteristic, complemented
52C2×C4×Dic15C2211yescharacteristic, complemented
53C2×C4×Dic15C2211yescharacteristic, complemented
54#91786C2218yescomplemented
55#91785C2218yescomplemented
56#91783C2218yescomplemented
57#91783C2218yescomplemented
58#91782C2218yescomplemented
59#91781C2218yescomplemented
60#91774C2218yescomplemented
61#91772C2218yescomplemented
62#91771C2218yes—
63C22⋊C4×D15C2218yescomplemented
64C22⋊C4×D15C2218yescomplemented
65#91768C2218yescomplemented
66C4×D60C2218yescomplemented
67#91761C2218yescomplemented
68C2×#5705—51nomaximal, Hall
69C2×C5×#126D311yescharacteristic, complemented
70#66039—316no—
71C2×#4043—31no—
72C2×#4042—31no—
73C2×#4040—31no—
74C2×#4040—31no—
75C2×#4039—31no—
76C2×#4038—31no—
77C2×#4031—31no—
78C2×#4029—31no—
79C2×#4028—31no—
80C2×D5×C22⋊C4—31no—
81C2×D5×C22⋊C4—31no—
82C2×#4025—31no—
83C2×C4×D20—31no—
84C2×#4018—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15—24no—
87C23×D15—24no—
88C23×D15—42no—
89C23×D15C2311yescharacteristic
90C23×D15C2314yes—
91C23×D15C2311yescharacteristic
92C23×D15C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C2×#1220—42no—
100C2×#1220C2314yes—
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C2×D60—24no—
107C2×D60—24no—
108C2×D60C2314yes—
109C2×D60C2314yes—
110C2×C4×D15—24no—
111C2×C4×D15—24no—
112C2×C4×D15—42no—
113C2×C4×D15—42no—
114C2×C4×D15—42no—
115C2×C4×D15C2314yes—
116C2×C4×D15C2314yes—
117C2×C4×D15C2314yes—
118C2×C4×D15C2314yes—
119C2×C4×D15C2314yescomplemented
120C2×Dic30—42no—
121C2×Dic30C2314yescomplemented
122C3×C5×C4⋊C4C2314yescomplemented
123C3×C5×C4⋊C4C2314yescomplemented
124C3×C5×C4⋊C4C2314yescomplemented
125C3×C5×C22⋊C4C2314yes—
126C3×C5×C22⋊C4C2314yes—
127C3×C5×C22⋊C4C2314yes—
128C3×C42×C5C2314yescomplemented
129#6719C2314yes—
130#6719C2314yes—
131#6714C2314yes—
132#6714C2314yes—
133#6714C2314yes—
134#6714C2314yes—
135#6714C2314yes—
136#6714C2314yes—
137#6714C2314yescomplemented
138#6714C2314yescomplemented
139#6714C2314yescomplemented
140C4⋊Dic15C2314yescomplemented
141C4⋊Dic15C2314yescomplemented
142#6712C2314yescomplemented
143#6712C2314yescomplemented
144#6712C2314yescomplemented
145C4×Dic15C2314yescomplemented
146C4×Dic15C2314yescomplemented
147C2×C3×#126D511yescharacteristic, complemented
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×#872—51no—
163C24×D5—31no—
164C22×C22⋊D5—31no—
165C22×D20—31no—
166C22×D20—31no—
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C22×C4×D5—31no—
170C22×C4×D5—31no—
171C22×C4×D5—31no—
172C22×Dic10—31no—
173C5×#126C2×D318yescomplemented
174C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
175C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
176C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
177C2×C5×C22⋊C4C2×D311yescharacteristic
178C2×C5×C22⋊C4C2×D311yescharacteristic
179C2×C5×C22⋊C4C2×D311yescharacteristic
180C2×C42×C5C2×D311yescharacteristic, complemented
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×C4⋊Dic5—31no—
193C2×C4⋊Dic5—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×C4×Dic5—31no—
198C2×C4×Dic5—31no—
199#4043—38no—
200#4042—38no—
201#4040—38no—
202#4040—38no—
203#4039—38no—
204#4038—38no—
205#4031—38no—
206#4029—38no—
207#4028—38no—
208D5×C22⋊C4—38no—
209D5×C22⋊C4—38no—
210#4025—38no—
211C4×D20—38no—
212#4018—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—22no—
226C22×D15—28no—
227C22×D15—28no—
228C22×D15—44no—
229C22×D15—416no—
230C22×D15#4114yes—
231C22×D15#4114yes—
232C22×D15C2412yes—
233C22×D15C2412yes—
234C22×D15C2412yes—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5—22no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5—22no—
241C2×C3×C4×C5C2412yes—
242C2×C3×C4×C5C2412yes—
243C2×C3×C4×C5C2412yes—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247#1220—44no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—22no—
251C2×Dic15—22no—
252C2×Dic15—22no—
253C2×Dic15C2412yes—
254C2×Dic15C2412yes—
255C2×Dic15C2412yes—
256C2×Dic15C2412yes—
257C2×Dic15C2412yes—
258D60—28no—
259D60—28no—
260C4×D15—28no—
261C4×D15—28no—
262C4×D15—44no—
263C4×D15—44no—
264C4×D15—44no—
265Dic30—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×D3—51no—
275C22×Dic6—51no—
276C3×#126C2×D518yescomplemented
277C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
278C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
279C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
280C2×C3×C22⋊C4C2×D511yescharacteristic
281C2×C3×C22⋊C4C2×D511yescharacteristic
282C2×C3×C22⋊C4C2×D511yescharacteristic
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)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×C4⋊Dic3—51no—
296C2×C4⋊Dic3—51no—
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
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#872—58no—
316C24×C5C22×D311yescharacteristic
317C23×D5—31no—
318C23×D5—31no—
319C23×D5—31no—
320C23×D5—34no—
321C23×D5—64no—
322C23×D5—64no—
323C23×D5—122no—
324C22×C4×C5C22×D311yescharacteristic
325C22×C4×C5C22×D311yescharacteristic
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D311yescharacteristic
330C2×C22⋊D5—34no—
331C2×C22⋊D5—122no—
332C22×Dic5—31no—
333C22×Dic5—31no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C2×D20—34no—
338C2×D20—34no—
339C2×D20—64no—
340C2×D20—64no—
341C2×C4×D5—34no—
342C2×C4×D5—34no—
343C2×C4×D5—34no—
344C2×C4×D5—34no—
345C2×C4×D5—34no—
346C2×C4×D5—64no—
347C2×C4×D5—64no—
348C2×C4×D5—122no—
349C2×C4×D5—122no—
350C2×C4×D5—122no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C4⋊C4C22×D314yescomplemented
354C5×C4⋊C4C22×D314yescomplemented
355C5×C4⋊C4C22×D314yescomplemented
356C5×C22⋊C4C22×D314yes—
357C5×C22⋊C4C22×D314yes—
358C5×C22⋊C4C22×D314yes—
359C42×C5C22×D314yescomplemented
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369#685—34no—
370#685—34no—
371C4⋊Dic5—34no—
372C4⋊Dic5—34no—
373#683—34no—
374#683—34no—
375#683—34no—
376C4×Dic5—34no—
377C4×Dic5—34no—
378#551—1516no—
379C2×#126—151no—
380C2×#126D1511yescharacteristic, complemented
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—151no—
391C2×#117—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—44no—
398C22×C3×C5C2×#4112yes—
399C22×C3×C5C2×#4112yes—
400C22×C3×C5H(5,𝔽2)12yes—
401C22×C3×C5C2511yescharacteristic
402C2×D15—28no—
403C2×D15—28no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15—22no—
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—416no—
412C2×D15—44no—
413C2×D15C2×#4114yes—
414C2×D15C2×#4114yes—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419C3×C4×C5—22no—
420C3×C4×C5—22no—
421Dic15—22no—
422Dic15—22no—
423Dic15—22no—
424Dic15—22no—
425Dic15—22no—
426C24×C3C22×D511yescharacteristic
427C23×D3—51no—
428C23×D3—51no—
429C23×D3—51no—
430C23×D3—54no—
431C23×D3—104no—
432C23×D3—104no—
433C23×D3—202no—
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
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×Dic3—51no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C2×D12—54no—
448C2×D12—54no—
449C2×D12—104no—
450C2×D12—104no—
451C2×C4×D3—54no—
452C2×C4×D3—54no—
453C2×C4×D3—54no—
454C2×C4×D3—54no—
455C2×C4×D3—54no—
456C2×C4×D3—104no—
457C2×C4×D3—104no—
458C2×C4×D3—202no—
459C2×C4×D3—202no—
460C2×C4×D3—202no—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C4⋊C4C22×D514yescomplemented
464C3×C4⋊C4C22×D514yescomplemented
465C3×C4⋊C4C22×D514yescomplemented
466C3×C22⋊C4C22×D514yes—
467C3×C22⋊C4C22×D514yes—
468C3×C22⋊C4C22×D514yes—
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)⋊C4—54no—
480(C2×D3)⋊C4—54no—
481C4⋊Dic3—54no—
482C4⋊Dic3—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485Dic3⋊C4—54no—
486C4×Dic3—54no—
487C4×Dic3—54no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5C23×D312yes—
492C23×C5C23×D311yescharacteristic
493C22×D5—34no—
494C22×D5—34no—
495C22×D5—32no—
496C22×D5—32no—
497C22×D5—32no—
498C22×D5—68no—
499C22×D5—68no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5—62no—
503C22×D5—62no—
504C22×D5—62no—
505C22×D5—62no—
506C22×D5—62no—
507C22×D5—124no—
508C22×D5—1216no—
509C2×C4×C5—22no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
512C2×C4×C5—22no—
513C2×C4×C5—22no—
514C2×C4×C5—22no—
515C2×C4×C5C23×D312yes—
516C2×C4×C5C23×D312yes—
517C2×C4×C5C23×D312yes—
518C2×C4×C5C23×D312yes—
519C2×C4×C5C23×D312yes—
520C2×C4×C5C23×D312yes—
521C22⋊D5—124no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—62no—
528C2×Dic5—62no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5—62no—
532D20—68no—
533D20—68no—
534C4×D5—68no—
535C4×D5—68no—
536C4×D5—124no—
537C4×D5—124no—
538C4×D5—124no—
539Dic10—124no—
540C25—151no—
541C22×Q8—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549C23×C4—151no—
550#126—158no—
551#126C2×D1518yescomplemented
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—158no—
562#117—158no—
563C2×C4⋊C4—151no—
564C2×C4⋊C4—151no—
565C2×C4⋊C4—151no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4C2×D1511yescharacteristic, complemented
569C2×C4⋊C4C2×D1511yescharacteristic, complemented
570C2×C4⋊C4C2×D1511yescharacteristic, complemented
571C2×C22⋊C4—151no—
572C2×C22⋊C4—151no—
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—158no—
583C2×C22⋊C4—158no—
584C2×C22⋊C4C2×D1511yescharacteristic
585C2×C22⋊C4C2×D1511yescharacteristic
586C2×C22⋊C4C2×D1511yescharacteristic
587C2×C42—151no—
588C2×C42—151no—
589C2×C42C2×D1511yescharacteristic, complemented
590C2×C3×C5—42no—
591C2×C3×C5#55114yescomplemented
592C2×C3×C5C22×#4111yescharacteristic
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
595D15—24no—
596D15—24no—
597D15—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3C23×D512yes—
602C23×C3C23×D511yescharacteristic
603C22×D3—54no—
604C22×D3—54no—
605C22×D3—52no—
606C22×D3—52no—
607C22×D3—52no—
608C22×D3—108no—
609C22×D3—108no—
610C22×D3—102no—
611C22×D3—102no—
612C22×D3—102no—
613C22×D3—102no—
614C22×D3—102no—
615C22×D3—102no—
616C22×D3—102no—
617C22×D3—204no—
618C22×D3—2016no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4C23×D512yes—
626C2×C3×C4C23×D512yes—
627C2×C3×C4C23×D512yes—
628C2×C3×C4C23×D512yes—
629C2×C3×C4C23×D512yes—
630C2×C3×C4C23×D512yes—
631#67—204no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—52no—
636C2×Dic3—52no—
637C2×Dic3—102no—
638C2×Dic3—102no—
639C2×Dic3—102no—
640C2×Dic3—102no—
641C2×Dic3—102no—
642D12—108no—
643D12—108no—
644C4×D3—108no—
645C4×D3—108no—
646C4×D3—204no—
647C4×D3—204no—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—22no—
653C22×C5—44no—
654C22×C5D3×#4112yes—
655C22×C5D3×#4112yes—
656C22×C5#100912yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—34no—
659C2×D5—34no—
660C2×D5—68no—
661C2×D5—68no—
662C2×D5—62no—
663C2×D5—62no—
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—22no—
675C4×C5—22no—
676C4×C5—22no—
677Dic5—62no—
678Dic5—62no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682C24—151no—
683C24—151no—
684C24—151no—
685C24—154no—
686C24—304no—
687C24—304no—
688C24—602no—
689C24C22×D1511yescharacteristic
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—151no—
699C22×C4—151no—
700C22×C4—151no—
701C22×C4—151no—
702C22×C4—151no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—304no—
709C22×C4—304no—
710C22×C4—602no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4C22×D1511yescharacteristic
714C22×C4C22×D1511yescharacteristic
715C22×C4C22×D1511yescharacteristic
716C22×C4C22×D1511yescharacteristic
717C22×C4C22×D1511yescharacteristic
718C22×C4C22×D1511yescharacteristic
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4C22×D1514yescomplemented
725C4⋊C4C22×D1514yescomplemented
726C4⋊C4C22×D1514yescomplemented
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4C22×D1514yes—
739C22⋊C4C22×D1514yes—
740C22⋊C4C22×D1514yes—
741C42—154no—
742C42—154no—
743C42C22×D1514yescomplemented
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—44no—
749C22×C3D5×#4112yes—
750C22×C3D5×#4112yes—
751C22×C3#414912yes—
752C22×C3C24×D511yescharacteristic
753C2×D3—54no—
754C2×D3—54no—
755C2×D3—102no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—108no—
760C2×D3—108no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—2016no—
765C2×D3—204no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—22no—
772Dic3—102no—
773Dic3—102no—
774Dic3—102no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—42no—
778C2×C5#570514yescomplemented
779C2×C5C2×D3×#4111yescharacteristic
780C2×C5C2×D3×#4111yescharacteristic
781C2×C5C2×#100911yescharacteristic
782D5—64no—
783D5—64no—
784D5—122no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—154no—
789C23—154no—
790C23—152no—
791C23—152no—
792C23—152no—
793C23—308no—
794C23—308no—
795C23—302no—
796C23—302no—
797C23—302no—
798C23—302no—
799C23—302no—
800C23—302no—
801C23—302no—
802C23—604no—
803C23—6016no—
804C23C23×D1512yes—
805C23C23×D1511yescharacteristic
806Q8—604no—
807D4—308no—
808D4—308no—
809D4—604no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—152no—
821C2×C4—308no—
822C2×C4—308no—
823C2×C4—302no—
824C2×C4—302no—
825C2×C4—302no—
826C2×C4—302no—
827C2×C4—302no—
828C2×C4—604no—
829C2×C4—604no—
830C2×C4—604no—
831C2×C4C23×D1512yes—
832C2×C4C23×D1512yes—
833C2×C4C23×D1512yes—
834C2×C4C23×D1512yes—
835C2×C4C23×D1512yes—
836C2×C4C23×D1512yes—
837C2×C3—42no—
838C2×C3#6603914yescomplemented
839C2×C3C2×D5×#4111yescharacteristic
840C2×C3C2×D5×#4111yescharacteristic
841C2×C3C2×#414911yescharacteristic
842D3—104no—
843D3—104no—
844D3—202no—
845C5C2×#570511yescharacteristic, complemented, Sylow
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—154no—
851C22—154no—
852C22—302no—
853C22—302no—
854C22—302no—
855C22—302no—
856C22—308no—
857C22—308no—
858C22—302no—
859C22—302no—
860C22—302no—
861C22—6016no—
862C22—604no—
863C22#41×D1512yes—
864C22#41×D1512yes—
865C22#9210012yes—
866C22C24×D1511yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—302no—
874C4—302no—
875C4—302no—
876C4—302no—
877C4—302no—
878C3C2×#6603911yescharacteristic, complemented, Sylow
879C2—42no—
880C2—304no—
881C2—304no—
882C2—602no—
883C2#1175646414yesdirect product factor
884C2C2×#41×D1511yescharacteristic
885C2C2×#41×D1511yescharacteristic
886C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#126C2
socleC23×C3×C5C24
prime radicalC2×#91771C2
hypercenterC2×#126D15
hypocenterC3×C5C2×#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#126C2semidirect
2. #11756464C2direct (N × H)
3. C2×#91786C2semidirect
4. C2×#91785C2semidirect
5. C2×#91783C2semidirect
6. C2×#91783C2semidirect
7. C2×#91782C2semidirect
8. C2×#91781C2semidirect
9. C2×#91774C2semidirect
10. C2×#91772C2semidirect
12. C2×C22⋊C4×D15C2semidirect
13. C2×C22⋊C4×D15C2semidirect
14. C2×#91768C2semidirect
15. C2×C4×D60C2semidirect
16. C2×#91761C2semidirect
26. C22×C4×D15C22semidirect
27. C22×Dic30C22semidirect
28. C3×C5×#126C22semidirect
29. C2×C3×C5×C4⋊C4C22semidirect
30. C2×C3×C5×C4⋊C4C22semidirect
31. C2×C3×C5×C4⋊C4C22semidirect
35. C2×C3×C42×C5C22semidirect
44. C2×#6714C22semidirect
45. C2×#6714C22semidirect
46. C2×#6714C22semidirect
47. C2×C4⋊Dic15C22semidirect
48. C2×C4⋊Dic15C22semidirect
49. C2×#6712C22semidirect
50. C2×#6712C22semidirect
51. C2×#6712C22semidirect
52. C2×C4×Dic15C22semidirect
53. C2×C4×Dic15C22semidirect
54. #91786C22semidirect
55. #91785C22semidirect
56. #91783C22semidirect
57. #91783C22semidirect
58. #91782C22semidirect
59. #91781C22semidirect
60. #91774C22semidirect
61. #91772C22semidirect
63. C22⋊C4×D15C22semidirect
64. C22⋊C4×D15C22semidirect
65. #91768C22semidirect
66. C4×D60C22semidirect
67. #91761C22semidirect
69. C2×C5×#126D3semidirect
119. C2×C4×D15C23semidirect
121. C2×Dic30C23semidirect
122. C3×C5×C4⋊C4C23semidirect
123. C3×C5×C4⋊C4C23semidirect
124. C3×C5×C4⋊C4C23semidirect
128. C3×C42×C5C23semidirect
137. #6714C23semidirect
138. #6714C23semidirect
139. #6714C23semidirect
140. C4⋊Dic15C23semidirect
141. C4⋊Dic15C23semidirect
142. #6712C23semidirect
143. #6712C23semidirect
144. #6712C23semidirect
145. C4×Dic15C23semidirect
146. C4×Dic15C23semidirect
147. C2×C3×#126D5semidirect
173. C5×#126C2×D3semidirect
174. C2×C5×C4⋊C4C2×D3semidirect
175. C2×C5×C4⋊C4C2×D3semidirect
176. C2×C5×C4⋊C4C2×D3semidirect
180. C2×C42×C5C2×D3semidirect
276. C3×#126C2×D5semidirect
277. C2×C3×C4⋊C4C2×D5semidirect
278. C2×C3×C4⋊C4C2×D5semidirect
279. C2×C3×C4⋊C4C2×D5semidirect
283. C2×C3×C42C2×D5semidirect
353. C5×C4⋊C4C22×D3semidirect
354. C5×C4⋊C4C22×D3semidirect
355. C5×C4⋊C4C22×D3semidirect
359. C42×C5C22×D3semidirect
380. C2×#126D15semidirect
463. C3×C4⋊C4C22×D5semidirect
464. C3×C4⋊C4C22×D5semidirect
465. C3×C4⋊C4C22×D5semidirect
469. C3×C42C22×D5semidirect
551. #126C2×D15semidirect
568. C2×C4⋊C4C2×D15semidirect
569. C2×C4⋊C4C2×D15semidirect
570. C2×C4⋊C4C2×D15semidirect
589. C2×C42C2×D15semidirect
591. C2×C3×C5#551semidirect
724. C4⋊C4C22×D15semidirect
725. C4⋊C4C22×D15semidirect
726. C4⋊C4C22×D15semidirect
743. C42C22×D15semidirect
744. C3×C5C2×#551semidirect
778. C2×C5#5705semidirect
838. C2×C3#66039semidirect
845. C5C2×#5705semidirect
878. C3C2×#66039semidirect
883. C2#11756464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1262
#117564642
C2×#917862
C2×#917852
C2×#917832
C2×#917822
C2×#917812
C2×#917742
C2×#917722
C2×#917712
C2×C22⋊C4×D152
C2×#917682
C2×C4×D602
C2×#917612
C2×#660393
C2×#57055