Finite Group Databasebeta

← C2×#11753712 #14483873

Subgroups — C2×#11753712 #14483873

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
2C2×C5×#887C211yesmaximal, characteristic, complemented
3C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#91469C211yesmaximal, characteristic, complemented
5C2×C4×#1202C212yesmaximal
6C2×C4×#1202C211yesmaximal, characteristic
7C2×#91383C211yesmaximal, characteristic, complemented
8C2×#91379C212yesmaximal, complemented
9C2×#91377C212yesmaximal, complemented
10C2×#91359C211yesmaximal, characteristic, complemented
11C2×#91349C212yesmaximal, complemented
12#11753712C2116yesmaximal, direct product factor
13C2×#65913—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C5×Dic6C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2212yes—
19C22×#1204C2212yes—
20C22×#1202C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2212yes—
24C4⋊C4×D15C2218yescomplemented
25C2×C5×Dic3⋊C4C2212yes—
26C2×C4×C5×Dic3C2212yes—
27C2×C4×C5×Dic3C2211yescharacteristic
28C5×#887C2218yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C3×D5×C4⋊C4C2218yescomplemented
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2212yes—
34C2×#6669C2212yes—
35C2×#6668C2212yes—
36C2×#6667C2211yescharacteristic
37C2×#6667C2212yes—
38C2×#6665C2211yescharacteristic
39C2×#6665C2212yes—
40#91469C2218yescomplemented
41C4×#1202C2218yes—
42C4×#1202C22116yes—
43#91383C2218yescomplemented
44#91379C22116yescomplemented
45#91377C22116yescomplemented
46#91359C2218yescomplemented
47#91349C22116yescomplemented
48C2×#5511—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4092—31no—
51C2×#4092—31no—
52#65913—316no—
53C2×#4042—32no—
54C2×#4042—32no—
55C2×D5×C4⋊C4—31no—
56C2×D5×C4⋊C4D311yescharacteristic, complemented
57C2×C4×D20—31no—
58C2×C4×D20—32no—
59C2×#4016—32no—
60C2×#4015—31no—
61C23×D15C2311yescharacteristic
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2311yescharacteristic
67C2×C4×D15—24no—
68C2×C4×D15—44no—
69C2×C4×D15C2314yes—
70C2×C4×D15C2318yes—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2311yescharacteristic
74C2×C5×Dic6—24no—
75C2×C5×Dic6C2314yes—
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×C4×D5—24no—
79C2×C3×C4×D5—44no—
80C2×C3×C4×D5C2314yes—
81C2×C3×C4×D5C2318yes—
82C2×#1204—44no—
83C2×#1204C2318yes—
84C2×#1202Q818yescomplemented
85C2×#1202C2314yes—
86C3×C5×C4⋊C4C2314yes—
87C4⋊Dic15C2314yes—
88#6712C2318yes—
89C5×Dic3⋊C4C2318yes—
90C4×C5×Dic3C2314yes—
91C4×C5×Dic3C2318yes—
92C3×C4⋊Dic5C2314yes—
93C3×#683C2318yes—
94Dic3⋊Dic5C2318yes—
95Dic3⋊Dic5C2314yes—
96#6669C2318yes—
97#6668C2318yes—
98#6667C2314yes—
99#6667C2318yes—
100#6665C2314yes—
101#6665C2318yes—
102C22×C3×C4⋊C4—51no—
103C2×C4×#67—51no—
104C2×C4×#67—52no—
105C2×#924—51no—
106C2×#924—52no—
107#5511—516no—
108C2×#897—51no—
109C2×#896—52no—
110C2×D3×C4⋊C4—51no—
111C2×#889—52no—
112C2×#888—51no—
113C2×#887D511yescharacteristic, complemented
114C22×C5×Q8—31no—
115C22×D20—31no—
116C22×C4×D5—31no—
117C22×C4×D5—32no—
118C22×C4×D5C2×D311yescharacteristic
119C22×C4×D5C2×D312yes—
120C22×Dic10—32no—
121C4×C5×Q8—38no—
122C2×C5×C4⋊C4—32no—
123C2×C5×C4⋊C4C2×D311yescharacteristic
124C2×C42×C5—31no—
125C2×C42×C5—32no—
126#4092—38no—
127#4092—38no—
128C2×#685—31no—
129C2×#685—32no—
130C2×#685—31no—
131C2×#685—32no—
132C2×C4⋊Dic5—31no—
133C2×C4⋊Dic5—32no—
134C2×C4⋊Dic5—31no—
135C2×C4⋊Dic5C2×D311yescharacteristic
136C2×#683—32no—
137C2×#683—32no—
138C2×#683—32no—
139C2×#683C2×D312yes—
140#4042—316no—
141#4042—316no—
142D5×C4⋊C4—38no—
143D5×C4⋊C4C2×D318yescomplemented
144C4×D20—316no—
145C4×D20—38no—
146#4016—316no—
147#4015—38no—
148C2×#554—151noSylow
149C23×C3×C5C2411yescharacteristic
150C22×D15—22no—
151C22×D15—22no—
152C22×D15C2×Q814yes—
153C22×D15C2412yes—
154C22×C3×D5—22no—
155C22×C3×D5—22no—
156C22×C3×D5C2×Q814yes—
157C22×C3×D5C2412yes—
158C2×C3×C4×C5—24no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15—24no—
164C2×Dic15C2412yes—
165C2×Dic15C2414yes—
166C4×D15—28no—
167C4×D15—48no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C2×Q814yes—
171C2×C5×Dic3C2414yes—
172C2×C5×Dic3C2412yes—
173C2×C5×Dic3C2412yes—
174C5×Dic6—28no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—24no—
177C2×C3×Dic5C2414yes—
178C2×C3×Dic5C2412yes—
179C3×C4×D5—28no—
180C3×C4×D5—48no—
181#1204—48no—
182#1202C2×Q8116yescomplemented
183C23×C3×C4—51no—
184C23×C3×C4—52no—
185C22×#67—51no—
186C22×C4×D3—51no—
187C22×C4×D3—52no—
188C22×Dic6—52no—
189C22×Dic6C2×D511yescharacteristic
190C2×C3×C4⋊C4—51no—
191C2×C3×C4⋊C4—52no—
192C2×C3×C4⋊C4—58no—
193C2×C3×C4⋊C4C2×D511yescharacteristic
194C2×#217—51no—
195C2×#217—52no—
196C4×#67—58no—
197C4×#67—516no—
198C2×(C2×D3)⋊C4—51no—
199C2×(C2×D3)⋊C4—52no—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—52no—
202#924—58no—
203#924—516no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—51no—
207C2×Dic3⋊C4—52no—
208C2×Dic3⋊C4C2×D512yes—
209C2×C4×Dic3C2×D511yescharacteristic
210C2×C4×Dic3C2×D512yes—
211#897—58no—
212#896—516no—
213D3×C4⋊C4—58no—
214#889—516no—
215#888—58no—
216#887C2×D518yescomplemented
217C23×D5—31no—
218C23×D5C22×D311yescharacteristic
219C2×C5×Q8—34no—
220C2×C5×Q8—64no—
221C22×C4×C5—31no—
222C22×C4×C5—31no—
223C22×C4×C5—32no—
224C22×C4×C5C22×D312yes—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—32no—
227C22×Dic5—31no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D311yescharacteristic
230C2×D20—38no—
231C2×D20—34no—
232C2×C4×D5—24no—
233C2×C4×D5—34no—
234C2×C4×D5—38no—
235C2×C4×D5—44no—
236C2×C4×D5—64no—
237C2×C4×D5—124no—
238C2×C4×D5C22×D314yes—
239C2×C4×D5C22×D318yes—
240C2×Dic10—38no—
241C2×Dic10—124no—
242C5×C4⋊C4—38no—
243C5×C4⋊C4C22×D314yes—
244C42×C5—34no—
245C42×C5—38no—
246#685—34no—
247#685—38no—
248#685—34no—
249#685—38no—
250C4⋊Dic5—34no—
251C4⋊Dic5—38no—
252C4⋊Dic5—34no—
253C4⋊Dic5C22×D314yes—
254#683—38no—
255#683—38no—
256#683—38no—
257#683C22×D318yes—
258#554—1516no—
259C2×C4⋊Q8—151no—
260C2×#125—152no—
261C2×C22⋊Q8—152no—
262C2×C22⋊Q8—152no—
263C2×C22⋊Q8—151no—
264C2×C22⋊Q8—151no—
265C2×C4×Q8—31no—
266C2×C4×D4—152no—
267C2×C4×D4—151no—
268C22×C4⋊C4—51no—
269C22×C4⋊C4—151no—
270C22×C3×C5C22×Q812yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C22×C3×C5C2511yescharacteristic
274C2×D15—28no—
275C2×D15—22no—
276C2×D15—22no—
277C2×D15C22×Q814yes—
278C2×C3×D5—28no—
279C2×C3×D5—22no—
280C2×C3×D5—22no—
281C2×C3×D5C22×Q814yes—
282C3×C4×C5—24no—
283C3×C4×C5C2×#4114yes—
284Dic15—22no—
285Dic15—24no—
286C3×Dic5—22no—
287C3×Dic5—24no—
288C5×Dic3—24no—
289C5×Dic3—22no—
290C5×Dic3C22×Q814yes—
291C24×C3—51no—
292C23×D3—51no—
293C22×C3×C4—51no—
294C22×C3×C4—52no—
295C22×C3×C4—54no—
296C22×C3×C4—58no—
297C22×C3×C4—104no—
298C22×C3×C4—204no—
299C22×C3×C4C22×D512yes—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—58no—
302C2×#67—54no—
303C22×Dic3—51no—
304C22×Dic3—52no—
305C22×Dic3C22×D512yes—
306C22×Dic3C22×D511yescharacteristic
307C22×Dic3C22×D511yescharacteristic
308C2×C4×D3—54no—
309C2×C4×D3—58no—
310C2×C4×D3—104no—
311C2×C4×D3—204no—
312C2×Dic6—24no—
313C2×Dic6—58no—
314C2×Dic6—204no—
315C2×Dic6C22×D514yes—
316C3×C4⋊C4—58no—
317C3×C4⋊C4—54no—
318C3×C4⋊C4C22×D514yes—
319#217—54no—
320#217—58no—
321(C2×D3)⋊C4—54no—
322(C2×D3)⋊C4—58no—
323C4⋊Dic3—54no—
324C4⋊Dic3—58no—
325Dic3⋊C4—58no—
326Dic3⋊C4—58no—
327Dic3⋊C4—58no—
328Dic3⋊C4—54no—
329Dic3⋊C4C22×D518yes—
330C4×Dic3C22×D514yes—
331C4×Dic3C22×D518yes—
332C23×C5C23×D311yescharacteristic
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—34no—
336C22×D5—32no—
337C22×D5—62no—
338C22×D5—62no—
339C22×D5D3×Q814yes—
340C22×D5C23×D312yes—
341C5×Q8—68no—
342C2×C4×C5—24no—
343C2×C4×C5—34no—
344C2×C4×C5—32no—
345C2×C4×C5—34no—
346C2×C4×C5—32no—
347C2×C4×C5—64no—
348C2×C4×C5—62no—
349C2×C4×C5#23514yes—
350C2×C4×C5C23×D314yes—
351C2×C4×C5C23×D312yes—
352C2×Dic5—22no—
353C2×Dic5—24no—
354C2×Dic5—32no—
355C2×Dic5—34no—
356C2×Dic5—62no—
357C2×Dic5—64no—
358C2×Dic5C23×D312yes—
359C2×Dic5C23×D314yes—
360D20—316no—
361C4×D5—28no—
362C4×D5—48no—
363C4×D5—68no—
364C4×D5—128no—
365Dic10—128no—
366C22×Q8—31no—
367C22×Q8—152no—
368C22×D4—151no—
369C23×C4—51no—
370C23×C4—52no—
371C23×C4—151no—
372C23×C4—152no—
373C4⋊Q8—158no—
374#125—1516no—
375C22⋊Q8—1516no—
376C22⋊Q8—1516no—
377C22⋊Q8—158no—
378C22⋊Q8—158no—
379C4×Q8—38no—
380C4×D4—1516no—
381C4×D4—158no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—52no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—58no—
386C2×C4⋊C4—151no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—152no—
389C2×C4⋊C4—152no—
390C2×C4⋊C4—152no—
391C2×C4⋊C4—151no—
392C2×C4⋊C4—158no—
393C2×C4⋊C4D3×D511yescharacteristic
394C2×C22⋊C4—151no—
395C2×C22⋊C4—152no—
396C2×C22⋊C4—151no—
397C2×C22⋊C4—152no—
398C2×C42—32no—
399C2×C42—31no—
400C2×C3×C5#55414yescomplemented
401C2×C3×C5C23×Q811yescharacteristic
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
404D15—24no—
405C3×D5—24no—
406C23×C3—54no—
407C23×C3—52no—
408C23×C3—102no—
409C23×C3—102no—
410C23×C3C23×D511yescharacteristic
411C22×D3—54no—
412C22×D3—52no—
413C22×D3—102no—
414C22×D3—102no—
415C2×C3×C4—24no—
416C2×C3×C4—52no—
417C2×C3×C4—54no—
418C2×C3×C4—102no—
419C2×C3×C4—104no—
420C2×C3×C4—108no—
421C2×C3×C4—208no—
422C2×C3×C4#70914yes—
423C2×C3×C4C23×D514yes—
424C2×C3×C4C23×D512yes—
425#67—516no—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—52no—
429C2×Dic3—54no—
430C2×Dic3—102no—
431C2×Dic3—104no—
432C2×Dic3Q8×D514yes—
433C2×Dic3C23×D514yes—
434C2×Dic3C23×D512yes—
435C2×Dic3C23×D512yes—
436C4×D3—108no—
437C4×D3—208no—
438Dic6—28no—
439Dic6—208no—
440C22×C5C2×#23512yes—
441C22×C5#100412yes—
442C22×C5C2×D3×Q812yes—
443C22×C5C24×D311yescharacteristic
444C2×D5—22no—
445C2×D5—22no—
446C2×D5—28no—
447C2×D5—34no—
448C2×D5—62no—
449C2×D5—62no—
450C2×D5—68no—
451C2×D5C2×D3×Q814yes—
452C4×C5—24no—
453C4×C5—34no—
454C4×C5—64no—
455C4×C5—62no—
456C4×C5C2×#23514yes—
457Dic5—22no—
458Dic5—24no—
459Dic5—62no—
460Dic5—64no—
461C24—51no—
462C24—151no—
463C2×Q8—34no—
464C2×Q8—64no—
465C2×Q8—158no—
466C2×Q8—604no—
467C2×D4—154no—
468C2×D4—158no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—51no—
473C22×C4—52no—
474C22×C4—54no—
475C22×C4—58no—
476C22×C4—104no—
477C22×C4—151no—
478C22×C4—152no—
479C22×C4—154no—
480C22×C4—158no—
481C22×C4—204no—
482C22×C4—304no—
483C22×C4—604no—
484C22×C4C2×D3×D512yes—
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—38no—
487C4⋊C4—58no—
488C4⋊C4—54no—
489C4⋊C4—154no—
490C4⋊C4—158no—
491C4⋊C4—158no—
492C4⋊C4—158no—
493C4⋊C4—158no—
494C4⋊C4—154no—
495C4⋊C4C2×D3×D514yes—
496C22⋊C4—154no—
497C22⋊C4—158no—
498C22⋊C4—154no—
499C22⋊C4—158no—
500C42—38no—
501C42—34no—
502C3×C5C2×#55411yescharacteristic, complemented, Hall
503C22×C3—54no—
504C22×C3—108no—
505C22×C3—102no—
506C22×C3—102no—
507C22×C3C2×#70912yes—
508C22×C3C2×Q8×D512yes—
509C22×C3#414912yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—54no—
512C2×D3—108no—
513C2×D3—102no—
514C2×D3—102no—
515C3×C4—24no—
516C3×C4—102no—
517C3×C4—104no—
518C3×C4C2×#70914yes—
519Dic3—24no—
520Dic3—22no—
521Dic3—102no—
522Dic3—104no—
523Dic3C2×Q8×D514yes—
524C2×C5#551114yescomplemented
525C2×C5C22×#23511yescharacteristic
526C2×C5C2×#100411yescharacteristic
527C2×C5C22×D3×Q811yescharacteristic
528D5—24no—
529D5—64no—
530C23—54no—
531C23—52no—
532C23—102no—
533C23—102no—
534C23—154no—
535C23—152no—
536C23—302no—
537C23—302no—
538C23C22×D3×D511yescharacteristic
539Q8—68no—
540Q8—608no—
541D4—1516no—
542C2×C4—24no—
543C2×C4—34no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—34no—
547C2×C4—52no—
548C2×C4—54no—
549C2×C4—64no—
550C2×C4—62no—
551C2×C4—102no—
552C2×C4—104no—
553C2×C4—108no—
554C2×C4—152no—
555C2×C4—154no—
556C2×C4—208no—
557C2×C4—302no—
558C2×C4—304no—
559C2×C4—308no—
560C2×C4—608no—
561C2×C4#677114yes—
562C2×C4C22×D3×D514yes—
563C2×C4C22×D3×D512yes—
564C2×C3—104no—
565C2×C3#6591314yescomplemented
566C2×C3C22×#70911yescharacteristic
567C2×C3C22×Q8×D511yescharacteristic
568C2×C3C2×#414911yescharacteristic
569D3—104no—
570C5C2×#551111yescharacteristic, complemented, Sylow
571C22—54no—
572C22—102no—
573C22—102no—
574C22—108no—
575C22—154no—
576C22—302no—
577C22—302no—
578C22—308no—
579C22C2×#677112yes—
580C22#9202612yes—
581C22D3×Q8×D512yes—
582C22C23×D3×D511yescharacteristic
583C4—24no—
584C4—34no—
585C4—64no—
586C4—62no—
587C4—102no—
588C4—104no—
589C4—302no—
590C4—304no—
591C4C2×#677114yes—
592C3C2×#6591311yescharacteristic, complemented, Sylow
593C2—104no—
594C2—304no—
595C2#1175371214yesdirect product factor
596C2C22×#677111yescharacteristic
597C2C2×#9202611yescharacteristic
598C2C2×D3×Q8×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D15C2semidirect
2. C2×C5×#887C2semidirect
3. C2×C3×D5×C4⋊C4C2semidirect
4. C2×#91469C2semidirect
7. C2×#91383C2semidirect
8. C2×#91379C2semidirect
9. C2×#91377C2semidirect
10. C2×#91359C2semidirect
11. C2×#91349C2semidirect
12. #11753712C2direct (N × H)
24. C4⋊C4×D15C22semidirect
28. C5×#887C22semidirect
31. C3×D5×C4⋊C4C22semidirect
40. #91469C22semidirect
43. #91383C22semidirect
44. #91379C22semidirect
45. #91377C22semidirect
46. #91359C22semidirect
47. #91349C22semidirect
56. C2×D5×C4⋊C4D3semidirect
84. C2×#1202Q8semidirect
113. C2×#887D5semidirect
143. D5×C4⋊C4C2×D3semidirect
182. #1202C2×Q8semidirect
216. #887C2×D5semidirect
400. C2×C3×C5#554semidirect
502. C3×C5C2×#554semidirect
524. C2×C5#5511semidirect
565. C2×C3#65913semidirect
570. C5C2×#5511semidirect
592. C3C2×#65913semidirect
595. C2#11753712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×C5×#8872
C2×C3×D5×C4⋊C42
C2×#914692
C2×C4×#12022
C2×#913832
C2×#913792
C2×#913772
C2×#913592
C2×#913492
#117537122
C2×#659133
C2×#55115