Finite Group Databasebeta

← C2×#11756315 #14483252

Subgroups — C2×#11756315 #14483252

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×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×#91826C211yesmaximal, characteristic
3C2×#91824C211yesmaximal, characteristic, complemented
4C2×#91818C211yesmaximal, characteristic, complemented
5C2×C4×#1220C211yesmaximal, characteristic, complemented
6C22×#6714C211yesmaximal, characteristic, complemented
7C2×#91813C211yesmaximal, characteristic, complemented
8#11756315C2116yesmaximal, direct product factor
9C2×#91787C211yesmaximal, characteristic, complemented
10C2×#91785C211yesmaximal, characteristic, complemented
11C2×#91774C211yesmaximal, characteristic, complemented
12C2×#91772C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
14C2×#91766C211yesmaximal, characteristic, complemented
15C2×#91765C211yesmaximal, characteristic, complemented
16C2×#91761C211yesmaximal, characteristic, complemented
17C2×#65890—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic
21C23×C3×C4×C5C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic
24C23×Dic15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic
26C22×C4×D15C2211yescharacteristic
27C22×Dic30C2211yescharacteristic, complemented
28C3×C4×C5×D4C2218yescomplemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
32C2×C3×C42×C5C2211yescharacteristic, complemented
33C2×#6719C2211yescharacteristic
34C2×#6719C2211yescharacteristic
35C2×#6719C2211yescharacteristic, complemented
36C2×#6719C2211yescharacteristic, complemented
37#91826C2218yes—
38#91824C2218yescomplemented
39#91818C2218yescomplemented
40C4×#1220C2218yescomplemented
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic
46C2×#6714C2211yescharacteristic
47C2×#6714C2211yescharacteristic
48C2×#6714C2211yescharacteristic
49C2×#6714C2218yescomplemented
50C2×C4⋊Dic15C2211yescharacteristic, complemented
51#91813C2218yescomplemented
52C2×#6712C2211yescharacteristic, complemented
53C2×#6712C2211yescharacteristic, complemented
54C2×#6712C2211yescharacteristic, complemented
55C2×#6712C2211yescharacteristic, complemented
56C2×#6712C2211yescharacteristic, complemented
57C2×#6712C2211yescharacteristic, complemented
58C2×C4×Dic15C2211yescharacteristic, complemented
59C2×C4×Dic15C2211yescharacteristic, complemented
60#91787C2218yescomplemented
61#91785C2218yescomplemented
62#91774C2218yescomplemented
63#91772C2218yescomplemented
64C22⋊C4×D15C2218yescomplemented
65#91766C2218yescomplemented
66#91765C2218yescomplemented
67#91761C2218yescomplemented
68C2×#5556—51nomaximal, Hall
69C2×C4×C5×D4D311yescharacteristic, complemented
70C2×#4083—31no—
71C2×#4081—31no—
72C2×#4075—31no—
73C2×C4×C22⋊D5—31no—
74C22×#685—31no—
75C2×#4070—31no—
76#65890—316no—
77C2×#4044—31no—
78C2×#4042—31no—
79C2×#4031—31no—
80C2×#4029—31no—
81C2×D5×C22⋊C4—31no—
82C2×#4023—31no—
83C2×#4022—31no—
84C2×#4018—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15—24no—
88C23×D15—24no—
89C23×D15—42no—
90C23×D15C2311yescharacteristic
91C23×D15C2314yes—
92C23×D15C2311yescharacteristic
93C2×C3×C5×D4—24no—
94C2×C3×C5×D4C2314yes—
95C22×C3×C4×C5—42no—
96C22×C3×C4×C5—42no—
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2314yes—
103C22×C3×C4×C5C2314yescomplemented
104C2×#1220—24no—
105C2×#1220—42no—
106C2×#1220C2314yes—
107C2×#1220C2314yes—
108C22×Dic15—24no—
109C22×Dic15C2314yes—
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2311yescharacteristic
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C2×C4×D15—24no—
117C2×C4×D15—42no—
118C2×C4×D15C2314yes—
119C2×C4×D15C2314yes—
120C2×Dic30—42no—
121C2×Dic30C2314yescomplemented
122C3×C5×C4⋊C4C2314yescomplemented
123C3×C5×C22⋊C4C2314yes—
124C3×C5×C22⋊C4C2314yescomplemented
125C3×C42×C5C2314yescomplemented
126#6719C2314yes—
127#6719C2314yes—
128#6719C2314yescomplemented
129#6719C2314yescomplemented
130#6714C2314yes—
131#6714C2314yes—
132#6714C2314yes—
133#6714C2314yes—
134#6714C2314yes—
135#6714C2314yes—
136#6714C2314yes—
137#6714C2314yes—
138C4⋊Dic15C2314yescomplemented
139#6712C2314yescomplemented
140#6712C2314yescomplemented
141#6712C2314yescomplemented
142#6712C2314yescomplemented
143#6712C2314yescomplemented
144#6712C2314yescomplemented
145C4×Dic15C2314yescomplemented
146C4×Dic15C2314yescomplemented
147C2×C3×C4×D4D511yescharacteristic, complemented
148C2×#937—51no—
149C2×#935—51no—
150C2×#929—51no—
151C2×C4×#67—51no—
152C22×(C2×D3)⋊C4—51no—
153C2×#924—51no—
154#5556—516no—
155C2×#898—51no—
156C2×#896—51no—
157C2×#885—51no—
158C2×#883—51no—
159C2×D3×C22⋊C4—51no—
160C2×#877—51no—
161C2×#876—51no—
162C2×#872—51no—
163C24×D5—31no—
164C22×C5×D4C2×D311yescharacteristic
165C23×C4×C5C2×D311yescharacteristic
166C23×C4×C5C2×D311yescharacteristic, complemented
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C23×Dic5—31no—
170C22×C4×D5—31no—
171C22×C4×D5—31no—
172C22×Dic10—31no—
173C4×C5×D4C2×D318yescomplemented
174C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
175C2×C5×C22⋊C4C2×D311yescharacteristic
176C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
177C2×C42×C5C2×D311yescharacteristic, complemented
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5—31no—
182#4083—38no—
183#4081—38no—
184#4075—38no—
185C4×C22⋊D5—38no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—38no—
195C2×C4⋊Dic5—31no—
196#4070—38no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×C4×Dic5—31no—
204C2×C4×Dic5—31no—
205#4044—38no—
206#4042—38no—
207#4031—38no—
208#4029—38no—
209D5×C22⋊C4—38no—
210#4023—38no—
211#4022—38no—
212#4018—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5#4114yes—
220C23×C3×C5C2412yes—
221C23×C3×C5C2412yes—
222C23×C3×C5C2411yescharacteristic
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—28no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—28no—
230C22×D15—44no—
231C22×D15—416no—
232C22×D15#4114yes—
233C22×D15C2412yes—
234C22×D15C2412yes—
235C3×C5×D4—28no—
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×C5—44no—
242C2×C3×C4×C5—44no—
243C2×C3×C4×C5C2412yes—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247C2×C3×C4×C5C2412yes—
248#1220—28no—
249#1220—44no—
250C2×Dic15—22no—
251C2×Dic15—28no—
252C2×Dic15—22no—
253C2×Dic15—22no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C2×Dic15C2412yes—
261C2×Dic15C2412yes—
262C2×Dic15C2412yes—
263C4×D15—28no—
264C4×D15—44no—
265Dic30—44no—
266C24×D3—51no—
267C22×C3×D4C2×D511yescharacteristic
268C23×C3×C4C2×D511yescharacteristic
269C23×C3×C4C2×D511yescharacteristic, complemented
270C22×#67—51no—
271C22×#67—51no—
272C23×Dic3—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×Dic6—51no—
276C3×C4×D4C2×D518yescomplemented
277C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
278C2×C3×C22⋊C4C2×D511yescharacteristic
279C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
280C2×C3×C42C2×D511yescharacteristic, complemented
281C2×#217—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285#937—58no—
286#935—58no—
287#929—58no—
288C4×#67—58no—
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×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—58no—
298C2×C4⋊Dic3—51no—
299#924—58no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308#898—58no—
309#896—58no—
310#885—58no—
311#883—58no—
312D3×C22⋊C4—58no—
313#877—58no—
314#876—58no—
315#872—58no—
316C24×C5C22×D311yescharacteristic
317C24×C5C22×D311yescharacteristic
318C23×D5—31no—
319C23×D5—31no—
320C23×D5—34no—
321C23×D5—64no—
322C23×D5—64no—
323C23×D5—122no—
324C2×C5×D4—24no—
325C2×C5×D4C22×D314yes—
326C22×C4×C5—42no—
327C22×C4×C5—42no—
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C22×C4×C5C22×D314yes—
334C22×C4×C5C22×D314yescomplemented
335C2×C22⋊D5—34no—
336C2×C22⋊D5—34no—
337C2×C22⋊D5—64no—
338C2×C22⋊D5—122no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—31no—
342C22×Dic5—31no—
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—34no—
346C22×Dic5—64no—
347C2×C4×D5—34no—
348C2×C4×D5—34no—
349C2×C4×D5—64no—
350C2×C4×D5—122no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C4⋊C4C22×D314yescomplemented
354C5×C22⋊C4C22×D314yes—
355C5×C22⋊C4C22×D314yescomplemented
356C42×C5C22×D314yescomplemented
357C22⋊Dic5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369C4⋊Dic5—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375#683—34no—
376C4×Dic5—34no—
377C4×Dic5—34no—
378#551—1516no—
379C2×#126—151no—
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×D4D1511yescharacteristic, complemented
390C2×#117—151no—
391C2×#117—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—44no—
401C22×C3×C5C2×#4114yes—
402C22×C3×C5C2×#4112yes—
403C22×C3×C5C2×#4112yes—
404C22×C3×C5H(5,𝔽2)12yes—
405C22×C3×C5C2511yescharacteristic
406C2×D15—28no—
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—416no—
413C2×D15—44no—
414C2×D15C2×#4114yes—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419C3×C4×C5—22no—
420Dic15—22no—
421Dic15—22no—
422Dic15—22no—
423Dic15—22no—
424Dic15—22no—
425Dic15—22no—
426C24×C3C22×D511yescharacteristic
427C24×C3C22×D511yescharacteristic
428C23×D3—51no—
429C23×D3—51no—
430C23×D3—54no—
431C23×D3—104no—
432C23×D3—104no—
433C23×D3—202no—
434C2×C3×D4—24no—
435C2×C3×D4C22×D514yes—
436C22×C3×C4—42no—
437C22×C3×C4—42no—
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C22×C3×C4C22×D511yescharacteristic
443C22×C3×C4C22×D514yes—
444C22×C3×C4C22×D514yescomplemented
445C2×#67—54no—
446C2×#67—54no—
447C2×#67—104no—
448C2×#67—202no—
449C22×Dic3—54no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3—51no—
455C22×Dic3—51no—
456C22×Dic3—104no—
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—202no—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C4⋊C4C22×D514yescomplemented
464C3×C22⋊C4C22×D514yes—
465C3×C22⋊C4C22×D514yescomplemented
466C3×C42C22×D514yescomplemented
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471(C2×D3)⋊C4—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—
479C4⋊Dic3—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—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×C5—22no—
492C23×C5—22no—
493C23×C5#23514yes—
494C23×C5C23×D312yes—
495C23×C5C23×D312yes—
496C23×C5C23×D311yescharacteristic
497C22×D5—34no—
498C22×D5—32no—
499C22×D5—32no—
500C22×D5—68no—
501C22×D5—62no—
502C22×D5—62no—
503C22×D5—68no—
504C22×D5—62no—
505C22×D5—62no—
506C22×D5—62no—
507C22×D5—124no—
508C22×D5—1216no—
509C5×D4—28no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
512C2×C4×C5—22no—
513C2×C4×C5—22no—
514C2×C4×C5—22no—
515C2×C4×C5—44no—
516C2×C4×C5—44no—
517C2×C4×C5C23×D312yes—
518C2×C4×C5C23×D312yes—
519C2×C4×C5C23×D312yes—
520C2×C4×C5C23×D312yes—
521C2×C4×C5C23×D312yes—
522C22⋊D5—68no—
523C22⋊D5—124no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—32no—
528C2×Dic5—32no—
529C2×Dic5—32no—
530C2×Dic5—68no—
531C2×Dic5—62no—
532C2×Dic5—62no—
533C2×Dic5—62no—
534C2×Dic5—62no—
535C2×Dic5—62no—
536C2×Dic5—62no—
537C4×D5—68no—
538C4×D5—124no—
539Dic10—124no—
540C25—151no—
541C22×Q8—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4C2×D1511yescharacteristic
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4C2×D1511yescharacteristic
549C23×C4C2×D1511yescharacteristic, complemented
550#126—158no—
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×D4C2×D1518yescomplemented
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⋊C4—151no—
569C2×C4⋊C4—151no—
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—158no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—158no—
585C2×C22⋊C4C2×D1511yescharacteristic
586C2×C22⋊C4C2×D1511yescharacteristic, complemented
587C2×C42—151no—
588C2×C42—151no—
589C2×C42C2×D1511yescharacteristic, complemented
590C2×C3×C5—24no—
591C2×C3×C5—42no—
592C2×C3×C5#55114yescomplemented
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C22×#4111yescharacteristic
595C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
596D15—24no—
597D15—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3#70914yes—
604C23×C3C23×D512yes—
605C23×C3C23×D512yes—
606C23×C3C23×D511yescharacteristic
607C22×D3—54no—
608C22×D3—52no—
609C22×D3—52no—
610C22×D3—108no—
611C22×D3—102no—
612C22×D3—102no—
613C22×D3—108no—
614C22×D3—102no—
615C22×D3—102no—
616C22×D3—102no—
617C22×D3—204no—
618C22×D3—2016no—
619C3×D4—28no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—44no—
626C2×C3×C4—44no—
627C2×C3×C4C23×D512yes—
628C2×C3×C4C23×D512yes—
629C2×C3×C4C23×D512yes—
630C2×C3×C4C23×D512yes—
631C2×C3×C4C23×D512yes—
632#67—108no—
633#67—204no—
634C2×Dic3—52no—
635C2×Dic3—52no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—52no—
640C2×Dic3—108no—
641C2×Dic3—102no—
642C2×Dic3—102no—
643C2×Dic3—102no—
644C2×Dic3—102no—
645C2×Dic3—102no—
646C2×Dic3—102no—
647C4×D3—108no—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—28no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—44no—
657C22×C5C2×#23514yes—
658C22×C5C2×#23512yes—
659C22×C5#100412yes—
660C22×C5D3×#4112yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—34no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—68no—
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—
676Dic5—62no—
677Dic5—62no—
678Dic5—62no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682C24—151no—
683C24—151no—
684C24—154no—
685C24—304no—
686C24—304no—
687C24—602no—
688C24C22×D1511yescharacteristic
689C24C22×D1511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—24no—
693C2×D4—154no—
694C2×D4—154no—
695C2×D4—304no—
696C2×D4—602no—
697C2×D4C22×D1514yes—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—154no—
701C22×C4—151no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—154no—
708C22×C4—154no—
709C22×C4—304no—
710C22×C4—304no—
711C22×C4—602no—
712C22×C4C22×D1511yescharacteristic
713C22×C4C22×D1511yescharacteristic
714C22×C4C22×D1511yescharacteristic
715C22×C4C22×D1511yescharacteristic
716C22×C4C22×D1511yescharacteristic
717C22×C4C22×D1514yes—
718C22×C4C22×D1514yescomplemented
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
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⋊C4—154no—
739C22⋊C4C22×D1514yes—
740C22⋊C4C22×D1514yescomplemented
741C42—154no—
742C42—154no—
743C42C22×D1514yescomplemented
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—44no—
752C22×C3C2×#70914yes—
753C22×C3C2×#70912yes—
754C22×C3#414412yes—
755C22×C3D5×#4112yes—
756C22×C3C24×D511yescharacteristic
757C2×D3—54no—
758C2×D3—108no—
759C2×D3—102no—
760C2×D3—102no—
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—
771Dic3—102no—
772Dic3—102no—
773Dic3—102no—
774Dic3—102no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—24no—
778C2×C5—42no—
779C2×C5#555614yescomplemented
780C2×C5C22×#23511yescharacteristic
781C2×C5C2×#100411yescharacteristic
782C2×C5C2×D3×#4111yescharacteristic
783D5—64no—
784D5—122no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—154no—
791C23—152no—
792C23—152no—
793C23—308no—
794C23—302no—
795C23—302no—
796C23—308no—
797C23—302no—
798C23—302no—
799C23—302no—
800C23—604no—
801C23—6016no—
802C23#681714yes—
803C23C23×D1512yes—
804C23C23×D1512yes—
805C23C23×D1511yescharacteristic
806Q8—604no—
807D4—28no—
808D4—308no—
809D4—604no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—152no—
821C2×C4—152no—
822C2×C4—152no—
823C2×C4—308no—
824C2×C4—308no—
825C2×C4—302no—
826C2×C4—302no—
827C2×C4—302no—
828C2×C4—302no—
829C2×C4—302no—
830C2×C4—302no—
831C2×C4—604no—
832C2×C4C23×D1512yes—
833C2×C4C23×D1512yes—
834C2×C4C23×D1512yes—
835C2×C4C23×D1512yes—
836C2×C4C23×D1512yes—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3#6589014yescomplemented
840C2×C3C22×#70911yescharacteristic
841C2×C3C2×#414411yescharacteristic
842C2×C3C2×D5×#4111yescharacteristic
843D3—104no—
844D3—202no—
845C5C2×#555611yescharacteristic, complemented, Sylow
846C22—28no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—154no—
854C22—308no—
855C22—302no—
856C22—302no—
857C22—302no—
858C22—302no—
859C22—302no—
860C22—6016no—
861C22—604no—
862C22C2×#681714yes—
863C22C2×#681712yes—
864C22#9209512yes—
865C22#41×D1512yes—
866C22C24×D1511yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—302no—
873C4—302no—
874C4—302no—
875C4—302no—
876C4—302no—
877C4—302no—
878C3C2×#6589011yescharacteristic, complemented, Sylow
879C2—24no—
880C2—42no—
881C2—304no—
882C2—602no—
883C2#1175631514yesdirect product factor
884C2C22×#681711yescharacteristic
885C2C2×#9209511yescharacteristic
886C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×#91826C2
hypercenterC2×C4×D4D15
hypocenterC3×C5C2×#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C2×#91824C2semidirect
4. C2×#91818C2semidirect
5. C2×C4×#1220C2semidirect
6. C22×#6714C2semidirect
7. C2×#91813C2semidirect
8. #11756315C2direct (N × H)
9. C2×#91787C2semidirect
10. C2×#91785C2semidirect
11. C2×#91774C2semidirect
12. C2×#91772C2semidirect
13. C2×C22⋊C4×D15C2semidirect
14. C2×#91766C2semidirect
15. C2×#91765C2semidirect
16. C2×#91761C2semidirect
21. C23×C3×C4×C5C22semidirect
27. C22×Dic30C22semidirect
28. C3×C4×C5×D4C22semidirect
29. C2×C3×C5×C4⋊C4C22semidirect
31. C2×C3×C5×C22⋊C4C22semidirect
32. C2×C3×C42×C5C22semidirect
35. C2×#6719C22semidirect
36. C2×#6719C22semidirect
38. #91824C22semidirect
39. #91818C22semidirect
40. C4×#1220C22semidirect
49. C2×#6714C22semidirect
50. C2×C4⋊Dic15C22semidirect
51. #91813C22semidirect
52. C2×#6712C22semidirect
53. C2×#6712C22semidirect
54. C2×#6712C22semidirect
55. C2×#6712C22semidirect
56. C2×#6712C22semidirect
57. C2×#6712C22semidirect
58. C2×C4×Dic15C22semidirect
59. C2×C4×Dic15C22semidirect
60. #91787C22semidirect
61. #91785C22semidirect
62. #91774C22semidirect
63. #91772C22semidirect
64. C22⋊C4×D15C22semidirect
65. #91766C22semidirect
66. #91765C22semidirect
67. #91761C22semidirect
69. C2×C4×C5×D4D3semidirect
103. C22×C3×C4×C5C23semidirect
121. C2×Dic30C23semidirect
122. C3×C5×C4⋊C4C23semidirect
124. C3×C5×C22⋊C4C23semidirect
125. C3×C42×C5C23semidirect
128. #6719C23semidirect
129. #6719C23semidirect
138. C4⋊Dic15C23semidirect
139. #6712C23semidirect
140. #6712C23semidirect
141. #6712C23semidirect
142. #6712C23semidirect
143. #6712C23semidirect
144. #6712C23semidirect
145. C4×Dic15C23semidirect
146. C4×Dic15C23semidirect
147. C2×C3×C4×D4D5semidirect
166. C23×C4×C5C2×D3semidirect
173. C4×C5×D4C2×D3semidirect
174. C2×C5×C4⋊C4C2×D3semidirect
176. C2×C5×C22⋊C4C2×D3semidirect
177. C2×C42×C5C2×D3semidirect
269. C23×C3×C4C2×D5semidirect
276. C3×C4×D4C2×D5semidirect
277. C2×C3×C4⋊C4C2×D5semidirect
279. C2×C3×C22⋊C4C2×D5semidirect
280. C2×C3×C42C2×D5semidirect
334. C22×C4×C5C22×D3semidirect
353. C5×C4⋊C4C22×D3semidirect
355. C5×C22⋊C4C22×D3semidirect
356. C42×C5C22×D3semidirect
389. C2×C4×D4D15semidirect
444. C22×C3×C4C22×D5semidirect
463. C3×C4⋊C4C22×D5semidirect
465. C3×C22⋊C4C22×D5semidirect
466. C3×C42C22×D5semidirect
549. C23×C4C2×D15semidirect
560. C4×D4C2×D15semidirect
570. C2×C4⋊C4C2×D15semidirect
586. C2×C22⋊C4C2×D15semidirect
589. C2×C42C2×D15semidirect
592. C2×C3×C5#551semidirect
718. C22×C4C22×D15semidirect
726. C4⋊C4C22×D15semidirect
740. C22⋊C4C22×D15semidirect
743. C42C22×D15semidirect
744. C3×C5C2×#551semidirect
779. C2×C5#5556semidirect
839. C2×C3#65890semidirect
845. C5C2×#5556semidirect
878. C3C2×#65890semidirect
883. C2#11756315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×#918262
C2×#918242
C2×#918182
C2×C4×#12202
C22×#67142
C2×#918132
#117563152
C2×#917872
C2×#917852
C2×#917742
C2×#917722
C2×C22⋊C4×D152
C2×#917662
C2×#917652
C2×#917612
C2×#658903
C2×#55565