Finite Group Databasebeta

← C2×#11753764 #14483567

Subgroups — C2×#11753764 #14483567

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91779C211yesmaximal, characteristic, complemented
2C2×C5×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#4043C211yesmaximal, characteristic, complemented
4C2×#91452C212yesmaximal
5C2×C4×#1201C211yesmaximal, characteristic
6C2×#91369C211yesmaximal, characteristic, complemented
7C2×#91362C212yesmaximal, complemented
8C2×#91358C211yesmaximal, characteristic, complemented
9C2×#91339C212yesmaximal, complemented
10C2×#91338C212yesmaximal, complemented
11C2×#91331C211yesmaximal, characteristic, complemented
12#11753764C2116yesmaximal, direct product factor
13C2×#65847—31nomaximal, Hall
14C22×C4×C5×D3C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×#1201C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C4⋊Dic15C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×#6712C2212yes—
23C2×C4×Dic15C2211yescharacteristic
24#91779C2218yescomplemented
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×Dic3⋊C4C2212yes—
27C5×D3×C4⋊C4C2218yescomplemented
28C2×C3×#685C2212yes—
29C2×C3×C4⋊Dic5C2212yes—
30C3×#4043C2218yescomplemented
31C2×#6669C2212yes—
32C2×#6669C2211yescharacteristic
33C2×#6668C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2212yes—
38C2×Dic3×Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40#91452C22116yes—
41C4×#1201C2218yes—
42#91369C2218yescomplemented
43#91362C22116yescomplemented
44#91358C2218yescomplemented
45#91339C22116yescomplemented
46#91338C22116yescomplemented
47#91331C2218yescomplemented
48C2×#5639—51nomaximal, Hall
49C22×C5×C4⋊C4—31no—
50C2×#4075—32no—
51C2×C4×C22⋊D5—31no—
52C2×#4072—32no—
53C2×#4070—31no—
54#65847—316no—
55C2×#4044—32no—
56C2×#4043D311yescharacteristic, complemented
57C2×#4038—31no—
58C2×#4036—31no—
59C2×#4035—32no—
60C2×#4033—31no—
61C23×C5×D3C2311yescharacteristic
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C22×C5×Dic3C2311yescharacteristic
69C22×C5×Dic3C2312yes—
70C2×C4×C5×D3—28no—
71C2×C4×C5×D3—24no—
72C2×C4×C5×D3C2314yes—
73C2×C4×C5×D3C2318yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2312yes—
76C2×C3×C4×D5—24no—
77C2×C3×C4×D5C2314yes—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×#1201—24no—
81C2×#1201C2314yes—
82C3×C5×C4⋊C4C2314yes—
83C4⋊Dic15C2318yes—
84C4⋊Dic15C2314yes—
85#6712C2318yes—
86C4×Dic15C2314yes—
87C5×C4⋊Dic3C2314yes—
88C5×Dic3⋊C4C2318yes—
89C3×#685C2318yes—
90C3×C4⋊Dic5C2318yes—
91#6669C2314yes—
92#6669C2318yes—
93#6668C2318yes—
94(C2×D3)⋊Dic5C2314yes—
95(C2×D3)⋊Dic5C2318yes—
96#6665C2314yes—
97#6665C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C22⋊Q8—51no—
101C2×#946—51no—
102C2×Q8×Dic3—51no—
103C2×C4×#67—51no—
104C2×#926—51no—
105#5639—516no—
106C2×#892—52no—
107C2×D3×C4⋊C4D511yescharacteristic, complemented
108C2×#890—51no—
109C2×#889—52no—
110C2×#883—52no—
111C2×#879—52no—
112C23×C4×C5—31no—
113C23×C4×C5—32no—
114C22×C22⋊D5—31no—
115C22×C4×D5C2×D311yescharacteristic
116C22×Dic10C2×D311yescharacteristic
117C2×C5×C4⋊C4—31no—
118C2×C5×C4⋊C4—32no—
119C2×C5×C4⋊C4—38no—
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C22⋊Dic5—32no—
122C2×C22⋊Dic5—31no—
123#4075—316no—
124C4×C22⋊D5—38no—
125C2×#685—32no—
126C2×#685—31no—
127C2×#685C2×D312yes—
128#4072—316no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D312yes—
132#4070—38no—
133C2×#683—32no—
134C2×#683—32no—
135C2×#683—31no—
136C2×#683—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—32no—
140#4044—316no—
141#4043C2×D318yescomplemented
142#4038—38no—
143#4036—38no—
144#4035—316no—
145#4033—38no—
146C2×#552—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C5×D3—22no—
149C22×C5×D3—22no—
150C22×C5×D3#4114yes—
151C22×C5×D3C2412yes—
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5—22no—
155C22×C3×D5C2412yes—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5#4114yes—
158C2×C3×C4×C5C2414yes—
159C2×C3×C4×C5C2412yes—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15—24no—
163C2×Dic15C2412yes—
164C2×Dic15C2414yes—
165C2×Dic15C2412yes—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—24no—
168C2×C5×Dic3C2414yes—
169C2×C5×Dic3C2412yes—
170C4×C5×D3—216no—
171C4×C5×D3—28no—
172C2×C3×Dic5—24no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5C2412yes—
175C2×C3×Dic5C2414yes—
176C3×C4×D5—28no—
177C3×Dic10—28no—
178#1201—28no—
179C22×C3×Q8—51no—
180C23×C3×C4—51no—
181C22×#67—51no—
182C22×C4×D3C2×D512yes—
183C22×C4×D3C2×D511yescharacteristic
184C3×C22⋊Q8—58no—
185C2×C3×C4⋊C4—52no—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4—52no—
188C2×#217—51no—
189C2×#217—52no—
190#946—58no—
191Q8×Dic3—58no—
192C4×#67—58no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—51no—
195#926—58no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—51no—
198C2×C4⋊Dic3—52no—
199C2×C4⋊Dic3C2×D511yescharacteristic
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—51no—
203C2×Dic3⋊C4C2×D512yes—
204C2×C4×Dic3—51no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3—52no—
207#892—516no—
208D3×C4⋊C4C2×D518yescomplemented
209#890—58no—
210#889—516no—
211#883—516no—
212#879—516no—
213C24×C5—31no—
214C23×D5C22×D311yescharacteristic
215C22×C4×C5—32no—
216C22×C4×C5—31no—
217C22×C4×C5—34no—
218C22×C4×C5—38no—
219C22×C4×C5—68no—
220C22×C4×C5—64no—
221C22×C4×C5C22×D312yes—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—34no—
224C2×C22⋊D5—64no—
225C22×Dic5—31no—
226C22×Dic5—32no—
227C22×Dic5—31no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D311yescharacteristic
230C2×C4×D5—24no—
231C2×C4×D5C22×D314yes—
232C2×Dic10—24no—
233C2×Dic10C22×D314yes—
234C5×C4⋊C4—38no—
235C5×C4⋊C4—34no—
236C5×C4⋊C4C22×D314yes—
237C22⋊Dic5—38no—
238C22⋊Dic5—34no—
239#685—38no—
240#685—34no—
241#685C22×D318yes—
242C4⋊Dic5—34no—
243C4⋊Dic5—38no—
244C4⋊Dic5C22×D318yes—
245#683—38no—
246#683—38no—
247#683—34no—
248#683—38no—
249C4×Dic5—34no—
250C4×Dic5—38no—
251C4×Dic5—38no—
252#552—1516no—
253C2×#126—152no—
254C2×#125—152no—
255C2×#125—151no—
256C2×#123—152no—
257C2×C22⋊Q8—51no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—151no—
262C2×#117—152no—
263C22×C4⋊C4—31no—
264C22×C3×C5C2×#4112yes—
265C22×C3×C5C2×#4112yes—
266C22×C3×C52−1+412yes—
267C22×C3×C5C2511yescharacteristic
268C2×C5×D3—28no—
269C2×C5×D3—22no—
270C2×C5×D3—22no—
271C2×C5×D3C2×#4114yes—
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—44no—
276C3×C4×C5—24no—
277C3×C4×C5C2×#4114yes—
278Dic15—22no—
279Dic15—22no—
280Dic15—24no—
281C3×Dic5—24no—
282C3×Dic5—22no—
283C5×Dic3—22no—
284C5×Dic3—24no—
285C24×C3—51no—
286C23×D3C22×D511yescharacteristic
287C2×C3×Q8—54no—
288C2×C3×Q8—104no—
289C22×C3×C4—51no—
290C22×C3×C4—52no—
291C22×C3×C4—54no—
292C22×C3×C4—104no—
293C22×C3×C4C22×D512yes—
294C22×C3×C4C22×D511yescharacteristic
295C2×#67—54no—
296C2×#67—104no—
297C22×Dic3—51no—
298C22×Dic3—51no—
299C22×Dic3—52no—
300C22×Dic3C22×D512yes—
301C22×Dic3C22×D511yescharacteristic
302C2×C4×D3—28no—
303C2×C4×D3—24no—
304C2×C4×D3C22×D518yes—
305C2×C4×D3C22×D514yes—
306C3×C4⋊C4—58no—
307C3×C4⋊C4C22×D514yes—
308C3×C22⋊C4—58no—
309#217—54no—
310#217—58no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—54no—
313C4⋊Dic3—58no—
314C4⋊Dic3—54no—
315C4⋊Dic3—58no—
316C4⋊Dic3C22×D514yes—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319Dic3⋊C4—54no—
320Dic3⋊C4C22×D518yes—
321C4×Dic3—54no—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C23×C5—34no—
325C23×C5—32no—
326C23×C5—62no—
327C23×C5—62no—
328C23×C5C23×D311yescharacteristic
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5C23×D312yes—
333C2×C4×C5—24no—
334C2×C4×C5—34no—
335C2×C4×C5—32no—
336C2×C4×C5—616no—
337C2×C4×C5—62no—
338C2×C4×C5—64no—
339C2×C4×C5—68no—
340C2×C4×C5#23714yes—
341C2×C4×C5C23×D314yes—
342C2×C4×C5C23×D312yes—
343C22⋊D5—68no—
344C2×Dic5—24no—
345C2×Dic5—22no—
346C2×Dic5—32no—
347C2×Dic5—32no—
348C2×Dic5—34no—
349C2×Dic5—62no—
350C2×Dic5—64no—
351C2×Dic5—62no—
352C2×Dic5C23×D312yes—
353C2×Dic5C23×D314yes—
354C4×D5—28no—
355Dic10—28no—
356C22×Q8—51no—
357C22×D4—151no—
358C23×C4—32no—
359C23×C4—31no—
360C23×C4—51no—
361#126—1516no—
362#125—1516no—
363#125—158no—
364#123—1516no—
365C22⋊Q8—58no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4—158no—
369#117—158no—
370#117—1516no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—38no—
374C2×C4⋊C4—52no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4D3×D511yescharacteristic
382C2×C22⋊C4—52no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—151no—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—152no—
387C2×C42—152no—
388C2×C42—152no—
389C2×C42—151no—
390C2×C3×C5#55214yescomplemented
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394C3×D5—42no—
395C5×D3—24no—
396C23×C3—52no—
397C23×C3—102no—
398C23×C3—102no—
399C23×C3—102no—
400C23×C3C23×D511yescharacteristic
401C22×D3—22no—
402C22×D3—22no—
403C22×D3#71114yes—
404C22×D3C23×D512yes—
405C3×Q8—108no—
406C2×C3×C4—24no—
407C2×C3×C4—52no—
408C2×C3×C4—54no—
409C2×C3×C4—102no—
410C2×C3×C4—104no—
411C2×C3×C4—108no—
412C2×C3×C4#70914yes—
413C2×C3×C4C23×D514yes—
414C2×C3×C4C23×D512yes—
415#67—108no—
416C2×Dic3—22no—
417C2×Dic3—24no—
418C2×Dic3—52no—
419C2×Dic3—52no—
420C2×Dic3—54no—
421C2×Dic3—102no—
422C2×Dic3—102no—
423C2×Dic3—104no—
424C2×Dic3C23×D514yes—
425C2×Dic3C23×D512yes—
426C4×D3—216no—
427C4×D3—28no—
428C22×C5—34no—
429C22×C5—68no—
430C22×C5—62no—
431C22×C5—62no—
432C22×C5C2×#23712yes—
433C22×C5#100712yes—
434C22×C5D3×#4112yes—
435C22×C5C24×D311yescharacteristic
436C2×D5—22no—
437C2×D5—22no—
438C2×D5—22no—
439C2×D5—44no—
440C4×C5—24no—
441C4×C5—62no—
442C4×C5—64no—
443C4×C5C2×#23714yes—
444Dic5—24no—
445Dic5—22no—
446Dic5—62no—
447Dic5—64no—
448Dic5—62no—
449C24—31no—
450C24—51no—
451C2×Q8—54no—
452C2×Q8—104no—
453C2×D4—154no—
454C2×D4—304no—
455C22×C4—32no—
456C22×C4—31no—
457C22×C4—38no—
458C22×C4—34no—
459C22×C4—51no—
460C22×C4—52no—
461C22×C4—54no—
462C22×C4—68no—
463C22×C4—64no—
464C22×C4—104no—
465C22×C4—151no—
466C22×C4—152no—
467C22×C4—151no—
468C22×C4C2×D3×D512yes—
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—38no—
472C4⋊C4—58no—
473C4⋊C4—154no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4—154no—
477C4⋊C4—158no—
478C4⋊C4—158no—
479C4⋊C4C2×D3×D514yes—
480C22⋊C4—58no—
481C22⋊C4—158no—
482C22⋊C4—154no—
483C22⋊C4—154no—
484C22⋊C4—158no—
485C42—158no—
486C42—158no—
487C42—154no—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—102no—
490C22×C3—102no—
491C22×C3—102no—
492C22×C3—204no—
493C22×C3C2×#70912yes—
494C22×C3C2×#71112yes—
495C22×C3#414712yes—
496C22×C3C24×D511yescharacteristic
497C2×D3—28no—
498C2×D3—22no—
499C2×D3—22no—
500C2×D3C2×#71114yes—
501C3×C4—24no—
502C3×C4—102no—
503C3×C4—104no—
504C3×C4C2×#70914yes—
505Dic3—22no—
506Dic3—24no—
507Dic3—102no—
508Dic3—102no—
509Dic3—104no—
510C2×C5—64no—
511C2×C5#563914yescomplemented
512C2×C5C22×#23711yescharacteristic
513C2×C5C2×#100711yescharacteristic
514C2×C5C2×D3×#4111yescharacteristic
515D5—42no—
516C23—34no—
517C23—32no—
518C23—52no—
519C23—62no—
520C23—62no—
521C23—102no—
522C23—102no—
523C23—102no—
524C23C22×D3×D511yescharacteristic
525Q8—108no—
526D4—308no—
527C2×C4—24no—
528C2×C4—34no—
529C2×C4—32no—
530C2×C4—52no—
531C2×C4—54no—
532C2×C4—616no—
533C2×C4—62no—
534C2×C4—64no—
535C2×C4—68no—
536C2×C4—102no—
537C2×C4—104no—
538C2×C4—108no—
539C2×C4—152no—
540C2×C4—154no—
541C2×C4—152no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—304no—
545C2×C4#676514yes—
546C2×C4C22×D3×D514yes—
547C2×C4C22×D3×D512yes—
548C2×C3—202no—
549C2×C3#6584714yescomplemented
550C2×C3C22×#70911yescharacteristic
551C2×C3C22×#71111yescharacteristic
552C2×C3C2×#414711yescharacteristic
553D3—24no—
554C5C2×#563911yescharacteristic, complemented, Sylow
555C22—34no—
556C22—68no—
557C22—62no—
558C22—62no—
559C22—102no—
560C22—102no—
561C22—102no—
562C22—204no—
563C22C2×#676512yes—
564C22D3×#71112yes—
565C22#9202912yes—
566C22C23×D3×D511yescharacteristic
567C4—24no—
568C4—62no—
569C4—64no—
570C4—102no—
571C4—104no—
572C4—302no—
573C4—302no—
574C4—304no—
575C4C2×#676514yes—
576C3C2×#6584711yescharacteristic, complemented, Sylow
577C2—64no—
578C2—202no—
579C2#1175376414yesdirect product factor
580C2C22×#676511yescharacteristic
581C2C2×D3×#71111yescharacteristic
582C2C2×#9202911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#552
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×#91779C2semidirect
2. C2×C5×D3×C4⋊C4C2semidirect
3. C2×C3×#4043C2semidirect
6. C2×#91369C2semidirect
7. C2×#91362C2semidirect
8. C2×#91358C2semidirect
9. C2×#91339C2semidirect
10. C2×#91338C2semidirect
11. C2×#91331C2semidirect
12. #11753764C2direct (N × H)
24. #91779C22semidirect
27. C5×D3×C4⋊C4C22semidirect
30. C3×#4043C22semidirect
42. #91369C22semidirect
43. #91362C22semidirect
44. #91358C22semidirect
45. #91339C22semidirect
46. #91338C22semidirect
47. #91331C22semidirect
56. C2×#4043D3semidirect
107. C2×D3×C4⋊C4D5semidirect
141. #4043C2×D3semidirect
208. D3×C4⋊C4C2×D5semidirect
390. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
511. C2×C5#5639semidirect
549. C2×C3#65847semidirect
554. C5C2×#5639semidirect
576. C3C2×#65847semidirect
579. C2#11753764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917792
C2×C5×D3×C4⋊C42
C2×C3×#40432
C2×#914522
C2×C4×#12012
C2×#913692
C2×#913622
C2×#913582
C2×#913392
C2×#913382
C2×#913312
#117537642
C2×#658473
C2×#56395