Finite Group Databasebeta

← C2×#11756293 #14481324

Subgroups — C2×#11756293 #14481324

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×#91819C211yesmaximal, characteristic
3C2×#91813C211yesmaximal, characteristic, complemented
4#11756293C2116yesmaximal, direct product factor
5C2×#91787C212yesmaximal, complemented
6C2×#91785C212yesmaximal, complemented
7C2×#91774C212yesmaximal, complemented
8C2×#91772C212yesmaximal, complemented
9C2×#91764C211yesmaximal, characteristic, complemented
10C2×C4×D60C211yesmaximal, characteristic, complemented
11C2×#91758C211yesmaximal, characteristic, complemented
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#65868—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2212yes—
16C22×D60C2211yescharacteristic
17C22×C4×D15C2212yes—
18C22×Dic30C2211yescharacteristic
19C22×Dic30C2212yes—
20C3×C5×#117C2218yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C42×C5C2211yescharacteristic
26C2×C3×C42×C5C2211yescharacteristic
27C2×#6719C2212yes—
28#91819C2218yes—
29C2×#6714C2212yes—
30C2×#6714C2212yes—
31C2×#6714C2212yes—
32C2×#6714C2212yes—
33C2×C4⋊Dic15C2211yescharacteristic
34C2×C4⋊Dic15C2211yescharacteristic
35C2×C4⋊Dic15C2212yes—
36#91813C2218yescomplemented
37C2×#6712C2212yes—
38C2×#6712C2212yes—
39C2×C4×Dic15C2212yes—
40#91787C22116yescomplemented
41#91785C22116yescomplemented
42#91774C22116yescomplemented
43#91772C22116yescomplemented
44#91764C2218yescomplemented
45C4×D60C2218yescomplemented
46#91758C2218yescomplemented
47C4×Dic30C2218yescomplemented
48C2×#5534—51nomaximal, Hall
49C2×C5×#117D311yescharacteristic, complemented
50C2×#4076—31no—
51C2×#4070—31no—
52#65868—316no—
53C2×#4044—32no—
54C2×#4042—32no—
55C2×#4031—32no—
56C2×#4029—32no—
57C2×#4021—31no—
58C2×C4×D20—31no—
59C2×#4015—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2312yes—
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2314yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C2×#1220—44no—
72C2×#1220C2318yes—
73C22×Dic15C2312yes—
74C22×Dic15C2312yes—
75C22×Dic15C2312yes—
76C2×D60—24no—
77C2×D60C2314yes—
78C2×C4×D15—44no—
79C2×C4×D15C2318yes—
80C2×Dic30—24no—
81C2×Dic30—44no—
82C2×Dic30C2314yes—
83C2×Dic30C2318yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C4⋊C4C2314yes—
86C3×C5×C22⋊C4C2314yes—
87C3×C5×C22⋊C4C2314yes—
88C3×C42×C5C2314yes—
89C3×C42×C5C2314yes—
90#6719C2318yes—
91#6714C2318yes—
92#6714C2318yes—
93#6714C2318yes—
94#6714C2318yes—
95C4⋊Dic15C2314yes—
96C4⋊Dic15C2314yes—
97C4⋊Dic15C2318yes—
98#6712C2318yes—
99#6712C2318yes—
100C4×Dic15C2318yes—
101C2×C3×#117D511yescharacteristic, complemented
102C2×#930—51no—
103C2×#924—51no—
104#5534—516no—
105C2×#898—52no—
106C2×#896—52no—
107C2×#885—52no—
108C2×#883—52no—
109C2×#875—51no—
110C2×C4×D12—51no—
111C2×#869—51no—
112C2×C4×Dic6—51no—
113C23×C4×C5C2×D311yescharacteristic
114C22×C22⋊D5—32no—
115C22×D20—31no—
116C22×C4×D5—32no—
117C22×Dic10—31no—
118C22×Dic10—32no—
119C5×#117C2×D318yescomplemented
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C4⋊C4C2×D311yescharacteristic
122C2×C5×C22⋊C4C2×D311yescharacteristic
123C2×C5×C22⋊C4C2×D311yescharacteristic
124C2×C42×C5C2×D311yescharacteristic
125C2×C42×C5C2×D311yescharacteristic
126C2×C22⋊Dic5—32no—
127#4076—38no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685—32no—
132C2×C4⋊Dic5—31no—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—32no—
135#4070—38no—
136C2×#683—32no—
137C2×#683—32no—
138C2×C4×Dic5—32no—
139#4044—316no—
140#4042—316no—
141#4031—316no—
142#4029—316no—
143#4021—38no—
144C4×D20—38no—
145#4015—38no—
146C4×Dic10—38no—
147C2×#542—151noSylow
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5C2412yes—
152C23×C3×C5C2411yescharacteristic
153C22×D15—24no—
154C22×D15—24no—
155C22×D15—24no—
156C22×D15C2414yes—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—28no—
163C2×C3×C4×C5#4114yes—
164C2×C3×C4×C5C2412yes—
165C2×C3×C4×C5C2412yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168C2×C3×C4×C5C2412yes—
169C2×C3×C4×C5C2412yes—
170#1220—48no—
171C2×Dic15—24no—
172C2×Dic15—24no—
173C2×Dic15—24no—
174C2×Dic15C2414yes—
175C2×Dic15C2414yes—
176C2×Dic15C2414yes—
177D60—28no—
178C4×D15—48no—
179Dic30—28no—
180Dic30—48no—
181C23×C3×C4C2×D511yescharacteristic
182C22×#67—52no—
183C22×D12—51no—
184C22×C4×D3—52no—
185C22×Dic6—51no—
186C22×Dic6—52no—
187C3×#117C2×D518yescomplemented
188C2×C3×C4⋊C4C2×D511yescharacteristic
189C2×C3×C4⋊C4C2×D511yescharacteristic
190C2×C3×C22⋊C4C2×D511yescharacteristic
191C2×C3×C22⋊C4C2×D511yescharacteristic
192C2×C3×C42C2×D511yescharacteristic
193C2×C3×C42C2×D511yescharacteristic
194C2×#217—52no—
195#930—58no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—52no—
203#924—58no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×C4×Dic3—52no—
207#898—516no—
208#896—516no—
209#885—516no—
210#883—516no—
211#875—58no—
212C4×D12—58no—
213#869—58no—
214C4×Dic6—58no—
215C24×C5C22×D311yescharacteristic
216C23×D5—32no—
217C22×C4×C5—24no—
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D314yes—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—38no—
226C2×C22⋊D5—124no—
227C22×Dic5—32no—
228C22×Dic5—32no—
229C22×Dic5—32no—
230C2×D20—34no—
231C2×D20—64no—
232C2×C4×D5—38no—
233C2×C4×D5—124no—
234C2×Dic10—34no—
235C2×Dic10—38no—
236C2×Dic10—64no—
237C2×Dic10—124no—
238C5×C4⋊C4C22×D314yes—
239C5×C4⋊C4C22×D314yes—
240C5×C22⋊C4C22×D314yes—
241C5×C22⋊C4C22×D314yes—
242C42×C5C22×D314yes—
243C42×C5C22×D314yes—
244C22⋊Dic5—38no—
245#685—38no—
246#685—38no—
247#685—38no—
248#685—38no—
249C4⋊Dic5—34no—
250C4⋊Dic5—34no—
251C4⋊Dic5—38no—
252#683—38no—
253#683—38no—
254C4×Dic5—38no—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—152no—
259C2×#124—151no—
260C2×#123—152no—
261C2×C22⋊Q8—151no—
262C2×C22⋊Q8—152no—
263C2×#121—151no—
264C2×C4×Q8—151no—
265C2×C4×D4—151no—
266C2×#117D1511yescharacteristic, complemented
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5—22no—
270C22×C3×C5—44no—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C22×C3×C52−1+412yes—
274C22×C3×C5C2511yescharacteristic
275C2×D15—24no—
276C2×D15—24no—
277C2×D15—24no—
278C2×D15—48no—
279C3×C4×C5—22no—
280C3×C4×C5—22no—
281C3×C4×C5—22no—
282C3×C4×C5—22no—
283C3×C4×C5—22no—
284C3×C4×C5C2×#4114yes—
285Dic15—24no—
286Dic15—24no—
287Dic15—24no—
288C24×C3C22×D511yescharacteristic
289C23×D3—52no—
290C22×C3×C4—24no—
291C22×C3×C4C22×D511yescharacteristic
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D511yescharacteristic
294C22×C3×C4C22×D514yes—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—58no—
299C2×#67—204no—
300C22×Dic3—52no—
301C22×Dic3—52no—
302C22×Dic3—52no—
303C2×D12—54no—
304C2×D12—104no—
305C2×C4×D3—58no—
306C2×C4×D3—204no—
307C2×Dic6—54no—
308C2×Dic6—58no—
309C2×Dic6—104no—
310C2×Dic6—204no—
311C3×C4⋊C4C22×D514yes—
312C3×C4⋊C4C22×D514yes—
313C3×C22⋊C4C22×D514yes—
314C3×C22⋊C4C22×D514yes—
315C3×C42C22×D514yes—
316C3×C42C22×D514yes—
317#217—58no—
318(C2×D3)⋊C4—58no—
319(C2×D3)⋊C4—58no—
320(C2×D3)⋊C4—58no—
321(C2×D3)⋊C4—58no—
322C4⋊Dic3—54no—
323C4⋊Dic3—54no—
324C4⋊Dic3—58no—
325Dic3⋊C4—58no—
326Dic3⋊C4—58no—
327C4×Dic3—58no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5C23×D312yes—
332C23×C5C23×D311yescharacteristic
333C22×D5—34no—
334C22×D5—64no—
335C22×D5—64no—
336C22×D5—64no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—28no—
343C2×C4×C5#23514yes—
344C2×C4×C5C23×D312yes—
345C2×C4×C5C23×D312yes—
346C2×C4×C5C23×D312yes—
347C2×C4×C5C23×D312yes—
348C2×C4×C5C23×D312yes—
349C2×C4×C5C23×D312yes—
350C22⋊D5—128no—
351C2×Dic5—34no—
352C2×Dic5—34no—
353C2×Dic5—34no—
354C2×Dic5—64no—
355C2×Dic5—64no—
356C2×Dic5—64no—
357D20—68no—
358C4×D5—128no—
359Dic10—68no—
360Dic10—128no—
361C22×Q8—151no—
362C22×Q8—152no—
363C22×D4—152no—
364C22×D4—151no—
365C23×C4—152no—
366C23×C4C2×D1511yescharacteristic
367C4⋊Q8—158no—
368#126—1516no—
369#124—1516no—
370#124—158no—
371#123—1516no—
372C22⋊Q8—158no—
373C22⋊Q8—1516no—
374#121—158no—
375C4×Q8—158no—
376C4×D4—158no—
377#117C2×D1518yescomplemented
378C2×C4⋊C4—151no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—152no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4C2×D1511yescharacteristic
384C2×C4⋊C4C2×D1511yescharacteristic
385C2×C22⋊C4—152no—
386C2×C22⋊C4—152no—
387C2×C22⋊C4—152no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4C2×D1511yescharacteristic
391C2×C22⋊C4C2×D1511yescharacteristic
392C2×C42—152no—
393C2×C42C2×D1511yescharacteristic
394C2×C42C2×D1511yescharacteristic
395C2×C3×C5—42no—
396C2×C3×C5#54214yescomplemented
397C2×C3×C5C22×#4111yescharacteristic
398C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
399C2×C3×C5C2×2−1+411yescharacteristic
400D15—44no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3C23×D512yes—
405C23×C3C23×D511yescharacteristic
406C22×D3—54no—
407C22×D3—104no—
408C22×D3—104no—
409C22×D3—104no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—28no—
416C2×C3×C4#70914yes—
417C2×C3×C4C23×D512yes—
418C2×C3×C4C23×D512yes—
419C2×C3×C4C23×D512yes—
420C2×C3×C4C23×D512yes—
421C2×C3×C4C23×D512yes—
422C2×C3×C4C23×D512yes—
423#67—208no—
424C2×Dic3—54no—
425C2×Dic3—54no—
426C2×Dic3—54no—
427C2×Dic3—104no—
428C2×Dic3—104no—
429C2×Dic3—104no—
430D12—108no—
431C4×D3—208no—
432Dic6—108no—
433Dic6—208no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—44no—
438C22×C5C2×#23512yes—
439C22×C5#100912yes—
440C22×C5#101012yes—
441C22×C5C24×D311yescharacteristic
442C2×D5—64no—
443C2×D5—64no—
444C2×D5—64no—
445C2×D5—128no—
446C4×C5—22no—
447C4×C5—22no—
448C4×C5—22no—
449C4×C5—22no—
450C4×C5—22no—
451C4×C5C2×#23514yes—
452Dic5—64no—
453Dic5—64no—
454Dic5—64no—
455C24—152no—
456C24C22×D1511yescharacteristic
457C2×Q8—154no—
458C2×Q8—158no—
459C2×Q8—304no—
460C2×Q8—604no—
461C2×D4—158no—
462C2×D4—154no—
463C2×D4—304no—
464C2×D4—604no—
465C22×C4—24no—
466C22×C4—152no—
467C22×C4—152no—
468C22×C4—152no—
469C22×C4—158no—
470C22×C4—604no—
471C22×C4C22×D1514yes—
472C22×C4C22×D1511yescharacteristic
473C22×C4C22×D1511yescharacteristic
474C22×C4C22×D1511yescharacteristic
475C22×C4C22×D1511yescharacteristic
476C22×C4C22×D1511yescharacteristic
477C22×C4C22×D1511yescharacteristic
478C4⋊C4—154no—
479C4⋊C4—154no—
480C4⋊C4—158no—
481C4⋊C4—158no—
482C4⋊C4—158no—
483C4⋊C4C22×D1514yes—
484C4⋊C4C22×D1514yes—
485C22⋊C4—158no—
486C22⋊C4—158no—
487C22⋊C4—158no—
488C22⋊C4—158no—
489C22⋊C4—158no—
490C22⋊C4C22×D1514yes—
491C22⋊C4C22×D1514yes—
492C42—158no—
493C42C22×D1514yes—
494C42C22×D1514yes—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—44no—
500C22×C3C2×#70912yes—
501C22×C3#414912yes—
502C22×C3#415012yes—
503C22×C3C24×D511yescharacteristic
504C2×D3—104no—
505C2×D3—104no—
506C2×D3—104no—
507C2×D3—208no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4C2×#70914yes—
514Dic3—104no—
515Dic3—104no—
516Dic3—104no—
517C2×C5—42no—
518C2×C5#553414yescomplemented
519C2×C5C22×#23511yescharacteristic
520C2×C5C2×#100911yescharacteristic
521C2×C5C2×#101011yescharacteristic
522D5—124no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—154no—
527C23—304no—
528C23—304no—
529C23—304no—
530C23C23×D1512yes—
531C23C23×D1511yescharacteristic
532Q8—308no—
533Q8—608no—
534D4—308no—
535D4—608no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—28no—
542C2×C4—154no—
543C2×C4—154no—
544C2×C4—154no—
545C2×C4—304no—
546C2×C4—304no—
547C2×C4—304no—
548C2×C4—608no—
549C2×C4#681714yes—
550C2×C4C23×D1512yes—
551C2×C4C23×D1512yes—
552C2×C4C23×D1512yes—
553C2×C4C23×D1512yes—
554C2×C4C23×D1512yes—
555C2×C4C23×D1512yes—
556C2×C3—42no—
557C2×C3#6586814yescomplemented
558C2×C3C22×#70911yescharacteristic
559C2×C3C2×#414911yescharacteristic
560C2×C3C2×#415011yescharacteristic
561D3—204no—
562C5C2×#553411yescharacteristic, complemented, Sylow
563C22—22no—
564C22—22no—
565C22—22no—
566C22—44no—
567C22—304no—
568C22—304no—
569C22—304no—
570C22—608no—
571C22C2×#681712yes—
572C22#9210012yes—
573C22#9210112yes—
574C22C24×D1511yescharacteristic
575C4—22no—
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—304no—
581C4—304no—
582C4—304no—
583C4C2×#681714yes—
584C3C2×#6586811yescharacteristic, complemented, Sylow
585C2—42no—
586C2—604no—
587C2#1175629314yesdirect product factor
588C2C22×#681711yescharacteristic
589C2C2×#9210011yescharacteristic
590C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC2×#91819C2
hypercenterC2×#117D15
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
3. C2×#91813C2semidirect
4. #11756293C2direct (N × H)
5. C2×#91787C2semidirect
6. C2×#91785C2semidirect
7. C2×#91774C2semidirect
8. C2×#91772C2semidirect
9. C2×#91764C2semidirect
10. C2×C4×D60C2semidirect
11. C2×#91758C2semidirect
12. C2×C4×Dic30C2semidirect
20. C3×C5×#117C22semidirect
36. #91813C22semidirect
40. #91787C22semidirect
41. #91785C22semidirect
42. #91774C22semidirect
43. #91772C22semidirect
44. #91764C22semidirect
45. C4×D60C22semidirect
46. #91758C22semidirect
47. C4×Dic30C22semidirect
49. C2×C5×#117D3semidirect
101. C2×C3×#117D5semidirect
119. C5×#117C2×D3semidirect
187. C3×#117C2×D5semidirect
266. C2×#117D15semidirect
377. #117C2×D15semidirect
396. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
518. C2×C5#5534semidirect
557. C2×C3#65868semidirect
562. C5C2×#5534semidirect
584. C3C2×#65868semidirect
587. C2#11756293direct (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×#1172
C2×#918192
C2×#918132
#117562932
C2×#917872
C2×#917852
C2×#917742
C2×#917722
C2×#917642
C2×C4×D602
C2×#917582
C2×C4×Dic302
C2×#658683
C2×#55345