Finite Group Databasebeta

← C2×#11753336 #14479100

Subgroups — C2×#11753336 #14479100

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6773C211yesmaximal, characteristic
2C2×#91782C211yesmaximal, characteristic, complemented
3C2×C5×#887C211yesmaximal, characteristic, complemented
4C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#91444C212yesmaximal, complemented
6C2×C4×#1202C212yesmaximal, complemented
7C2×#91428C211yesmaximal, characteristic, complemented
8C2×#91404C212yesmaximal, complemented
9C2×#91403C212yesmaximal, complemented
10C2×#91357C211yesmaximal, characteristic, complemented
11C2×#91344C211yesmaximal, characteristic, complemented
12#11753336C2116yesmaximal, direct product factor
13C2×#65908—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C5×Dic6C2211yescharacteristic
17C22×C3×C4×D5C2212yes—
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1202C2212yes—
20C22×#1200C2212yes—
21C22×#1200C2212yes—
22C2×#6773C4116yescomplemented
23C2×#6773C2218yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×#6714C2212yes—
26C2×C4×Dic15C2211yescharacteristic
27#91782C2218yescomplemented
28C2×C5×Dic3⋊C4C2212yes—
29C2×C4×C5×Dic3C2212yes—
30C2×C4×C5×Dic3C2211yescharacteristic
31C5×#887C2218yescomplemented
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×#683C2212yes—
34C3×D5×C4⋊C4C2218yescomplemented
35C2×Dic3⋊Dic5C2212yes—
36C2×#6668C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6667C2212yes—
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×Dic3×Dic5C2212yes—
42#91444C22116yescomplemented
43C4×#1202C22116yescomplemented
44#91428C2218yescomplemented
45#91404C22116yescomplemented
46#91403C22116yescomplemented
47#91357C2218yescomplemented
48#91344C2218yescomplemented
49C2×#5504—51nomaximal, Hall
50C22×#713—31no—
51C2×C4×C5×Q8—31no—
52C2×Q8×Dic5—31no—
53#65908—316no—
54C2×#4039—32no—
55C2×#4039—31no—
56C2×D5×C4⋊C4—32no—
57C2×D5×C4⋊C4D311yescharacteristic, complemented
58C2×C4×D20—31no—
59C2×C4×D20—32no—
60C2×#4018—32no—
61C2×#4018—31no—
62C23×D15C2312yes—
63C23×C3×D5C2311yescharacteristic
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C2×D60C2×C418yescomplemented
69C2×D60C2314yes—
70C2×C4×D15—44no—
71C2×C4×D15C2318yes—
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2312yes—
75C2×C5×Dic6C2×C418yescomplemented
76C2×C5×Dic6C2314yes—
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2311yescharacteristic
79C2×C3×C4×D5—44no—
80C2×C3×C4×D5C2×C418yescomplemented
81C2×C3×C4×D5C2318yes—
82C2×C3×C4×D5C2314yes—
83C2×#1202C2×C4116yescomplemented
84C2×#1202C2318yes—
85C2×#1200—44no—
86C2×#1200C2×C4116yescomplemented
87C2×#1200C2318yes—
88C2×#1200C2318yes—
89#6773C2×C4164yescomplemented
90C3×C5×C4⋊C4C2314yes—
91#6714C2318yes—
92C4×Dic15C2314yes—
93C5×Dic3⋊C4C2318yes—
94C4×C5×Dic3C2318yes—
95C4×C5×Dic3C2314yes—
96C3×C4⋊Dic5C2314yes—
97C3×#683C2318yes—
98Dic3⋊Dic5C2318yes—
99#6668C2314yes—
100#6668C2314yes—
101#6667C2318yes—
102#6665C2314yes—
103#6665C2314yes—
104Dic3×Dic5C2318yes—
105C22×#235—51no—
106C22×C3×C4⋊C4—51no—
107C2×C4×#67—52no—
108C2×C4×#67—52no—
109C2×#926—51no—
110#5504—516no—
111C2×#893—51no—
112C2×#893—51no—
113C2×#892—52no—
114C2×D3×C4⋊C4—52no—
115C2×#887—51no—
116C2×#887D511yescharacteristic, complemented
117C22×C5×Q8—31no—
118C2×#713—316no—
119C2×#713—38no—
120C22×D20—32no—
121C22×D20—31no—
122C22×C4×D5—32no—
123C22×C4×D5—32no—
124C22×C4×D5—32no—
125C22×C4×D5C2×D312yes—
126C22×C4×D5C2×D311yescharacteristic
127C4×C5×Q8—38no—
128C2×C5×C4⋊C4—32no—
129C2×C5×C4⋊C4C2×D311yescharacteristic
130C2×C42×C5—32no—
131C2×C42×C5—31no—
132Q8×Dic5—38no—
133C2×#685—31no—
134C2×#685—31no—
135C2×#685—32no—
136C2×#685—32no—
137C2×C4⋊Dic5—32no—
138C2×C4⋊Dic5C2×D311yescharacteristic
139C2×#683—31no—
140C2×#683—31no—
141C2×#683C2×D312yes—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—32no—
144#4039—316no—
145#4039—38no—
146D5×C4⋊C4—316no—
147D5×C4⋊C4C2×D318yescomplemented
148C4×D20—316no—
149C4×D20—38no—
150#4018—38no—
151#4018—316no—
152C2×#520—151noSylow
153C23×C3×C5C2411yescharacteristic
154C22×D15—24no—
155C22×D15—24no—
156C22×D15C22×C418yes—
157C22×D15C2414yes—
158C22×C3×D5—22no—
159C22×C3×D5—22no—
160C22×C3×D5C22×C414yes—
161C22×C3×D5C2412yes—
162C2×C3×C4×C5—24no—
163C2×C3×C4×C5C22×C414yes—
164C2×C3×C4×C5C2414yes—
165C2×C3×C4×C5C2412yes—
166C2×Dic15—22no—
167C2×Dic15—22no—
168C2×Dic15C2412yes—
169C2×Dic15C2412yes—
170D60C22×C4116yescomplemented
171C4×D15—48no—
172C2×C5×Dic3—22no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3C22×C418yes—
175C2×C5×Dic3C2412yes—
176C2×C5×Dic3C2412yes—
177C2×C5×Dic3C2414yes—
178C5×Dic6C22×C4116yescomplemented
179C2×C3×Dic5—24no—
180C2×C3×Dic5C22×C414yes—
181C2×C3×Dic5C2414yes—
182C2×C3×Dic5C2412yes—
183C3×C4×D5—48no—
184C3×C4×D5C22×C4116yescomplemented
185#1202C22×C4132yescomplemented
186#1200—48no—
187#1200C22×C4132yescomplemented
188C23×C3×C4—51no—
189C23×C3×C4—52no—
190C22×#67—52no—
191C2×#235—516no—
192C2×#235—58no—
193C22×D12—51no—
194C22×C4×D3—52no—
195C22×C4×D3—52no—
196C22×C4×D3—52no—
197C22×Dic6C2×D511yescharacteristic
198C2×C3×C4⋊C4—51no—
199C2×C3×C4⋊C4—52no—
200C2×C3×C4⋊C4—58no—
201C2×C3×C4⋊C4C2×D511yescharacteristic
202C2×#217—51no—
203C2×#217—51no—
204C4×#67—516no—
205C4×#67—516no—
206C2×(C2×D3)⋊C4—52no—
207C2×(C2×D3)⋊C4—52no—
208#926—58no—
209C2×C4⋊Dic3—51no—
210C2×C4⋊Dic3—51no—
211C2×Dic3⋊C4—52no—
212C2×Dic3⋊C4C2×D512yes—
213C2×C4×Dic3—51no—
214C2×C4×Dic3—52no—
215C2×C4×Dic3C2×D512yes—
216C2×C4×Dic3C2×D511yescharacteristic
217#893—58no—
218#893—58no—
219#892—516no—
220D3×C4⋊C4—516no—
221#887—58no—
222#887C2×D518yescomplemented
223C23×D5—32no—
224C23×D5C22×D311yescharacteristic
225C2×C5×Q8—38no—
226C2×C5×Q8—34no—
227C22×C4×C5—32no—
228C22×C4×C5—31no—
229C22×C4×C5—31no—
230C22×C4×C5C22×D312yes—
231C22×C4×C5C22×D311yescharacteristic
232C22×Dic5—31no—
233C22×Dic5—31no—
234C22×Dic5C22×D312yes—
235C22×Dic5C22×D311yescharacteristic
236#713—364no—
237C2×D20—316no—
238C2×D20—38no—
239C2×D20—38no—
240C2×D20—34no—
241C2×C4×D5—316no—
242C2×C4×D5—38no—
243C2×C4×D5—38no—
244C2×C4×D5—38no—
245C2×C4×D5—44no—
246C2×C4×D5—124no—
247C2×C4×D5—124no—
248C2×C4×D5C4×D318yescomplemented
249C2×C4×D5C22×D318yes—
250C2×C4×D5C22×D314yes—
251C5×C4⋊C4—38no—
252C5×C4⋊C4C22×D314yes—
253C42×C5—38no—
254C42×C5—34no—
255#685—34no—
256#685—34no—
257#685—38no—
258#685—38no—
259C4⋊Dic5—38no—
260C4⋊Dic5C22×D314yes—
261#683—34no—
262#683—34no—
263#683C22×D318yes—
264C4×Dic5—34no—
265C4×Dic5—38no—
266C22×#41—151no—
267#520—1516no—
268C2×C4×Q8—31no—
269C2×C4×Q8—151no—
270C2×C4×D4—151no—
271C2×C4×D4—152no—
272C2×C4×D4—152no—
273C2×C4×D4—151no—
274C2×#117—152no—
275C2×#117—151no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—152no—
278C22×C3×C5C23×C412yes—
279C22×C3×C5H(5,𝔽2)12yes—
280C22×C3×C52−1+412yes—
281C22×C3×C5C2511yescharacteristic
282C2×D15—216no—
283C2×D15—24no—
284C2×D15—24no—
285C2×D15C23×C418yes—
286C2×C3×D5—28no—
287C2×C3×D5—22no—
288C2×C3×D5—22no—
289C2×C3×D5C23×C414yes—
290C3×C4×C5—24no—
291C3×C4×C5C23×C414yes—
292Dic15—22no—
293Dic15—22no—
294C3×Dic5—24no—
295C3×Dic5C23×C414yes—
296C5×Dic3—22no—
297C5×Dic3—22no—
298C5×Dic3C23×C418yes—
299C24×C3—51no—
300C23×D3—52no—
301C22×C3×C4—51no—
302C22×C3×C4—58no—
303C22×C3×C4—54no—
304C22×C3×C4—52no—
305C22×C3×C4—58no—
306C22×C3×C4—204no—
307C22×C3×C4C22×D512yes—
308C22×C3×C4C22×D511yescharacteristic
309C2×#67—516no—
310C2×#67—58no—
311C22×Dic3—51no—
312C22×Dic3—51no—
313C22×Dic3C22×D511yescharacteristic
314C22×Dic3C22×D511yescharacteristic
315C22×Dic3C22×D512yes—
316#235—564no—
317C2×D12—58no—
318C2×D12—54no—
319C2×C4×D3—516no—
320C2×C4×D3—58no—
321C2×C4×D3—58no—
322C2×C4×D3—58no—
323C2×C4×D3—204no—
324C2×C4×D3—204no—
325C2×Dic6C4×D518yescomplemented
326C2×Dic6C22×D514yes—
327C3×C4⋊C4—58no—
328C3×C4⋊C4—54no—
329C3×C4⋊C4C22×D514yes—
330#217—54no—
331#217—54no—
332(C2×D3)⋊C4—58no—
333(C2×D3)⋊C4—58no—
334C4⋊Dic3—54no—
335C4⋊Dic3—54no—
336Dic3⋊C4—58no—
337Dic3⋊C4C22×D518yes—
338C4×Dic3—54no—
339C4×Dic3—58no—
340C4×Dic3C22×D518yes—
341C4×Dic3C22×D514yes—
342C23×C5C23×D311yescharacteristic
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—38no—
346C22×D5—34no—
347C22×D5—64no—
348C22×D5—64no—
349C22×D5C2×C4×D314yes—
350C22×D5C23×D312yes—
351C5×Q8—316no—
352C2×C4×C5—24no—
353C2×C4×C5—38no—
354C2×C4×C5—34no—
355C2×C4×C5—32no—
356C2×C4×C5—32no—
357C2×C4×C5—62no—
358C2×C4×C5—62no—
359C2×C4×C5C2×C4×D314yes—
360C2×C4×C5C23×D314yes—
361C2×C4×C5C23×D312yes—
362C2×Dic5—24no—
363C2×Dic5—32no—
364C2×Dic5—32no—
365C2×Dic5—62no—
366C2×Dic5—62no—
367C2×Dic5C2×C4×D314yes—
368C2×Dic5C23×D314yes—
369C2×Dic5C23×D312yes—
370D20—332no—
371D20—316no—
372C4×D5—332no—
373C4×D5—48no—
374C4×D5—128no—
375C4×D5—128no—
376C4×D5C2×C4×D3116yescomplemented
377C2×#41—158no—
378C2×#41—1516no—
379C22×Q8—31no—
380C22×D4—152no—
381C22×D4—151no—
382C23×C4—51no—
383C23×C4—52no—
384C23×C4—152no—
385C23×C4—152no—
386C23×C4—152no—
387C4×Q8—38no—
388C4×Q8—158no—
389C4×D4—158no—
390C4×D4—1516no—
391C4×D4—1516no—
392C4×D4—158no—
393#117—1516no—
394#117—158no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—52no—
397C2×C4⋊C4—51no—
398C2×C4⋊C4—58no—
399C2×C4⋊C4—1516no—
400C2×C4⋊C4—151no—
401C2×C4⋊C4—152no—
402C2×C4⋊C4—151no—
403C2×C4⋊C4D3×D511yescharacteristic
404C2×C22⋊C4—152no—
405C2×C22⋊C4—151no—
406C2×C22⋊C4—151no—
407C2×C22⋊C4—152no—
408C2×C42—32no—
409C2×C42—31no—
410C2×C42—152no—
411C2×C42—151no—
412C2×C3×C5#52014yescomplemented
413C2×C3×C5C24×C411yescharacteristic
414C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
415C2×C3×C5C2×2−1+411yescharacteristic
416D15—28no—
417C3×D5—24no—
418C23×C3—54no—
419C23×C3—52no—
420C23×C3—102no—
421C23×C3—102no—
422C23×C3C23×D511yescharacteristic
423C22×D3—58no—
424C22×D3—54no—
425C22×D3—104no—
426C22×D3—104no—
427C2×C3×C4—24no—
428C2×C3×C4—54no—
429C2×C3×C4—52no—
430C2×C3×C4—516no—
431C2×C3×C4—54no—
432C2×C3×C4—104no—
433C2×C3×C4—208no—
434C2×C3×C4C2×C4×D514yes—
435C2×C3×C4C23×D514yes—
436C2×C3×C4C23×D512yes—
437#67—532no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—52no—
441C2×Dic3—52no—
442C2×Dic3—102no—
443C2×Dic3—102no—
444C2×Dic3C2×C4×D518yes—
445C2×Dic3C23×D512yes—
446C2×Dic3C23×D512yes—
447C2×Dic3C23×D514yes—
448D12—516no—
449C4×D3—532no—
450C4×D3—208no—
451C4×D3—208no—
452Dic6C2×C4×D5116yescomplemented
453C22×C5C22×C4×D312yes—
454C22×C5#100412yes—
455C22×C5#100712yes—
456C22×C5C24×D311yescharacteristic
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—28no—
460C2×D5—38no—
461C2×D5—64no—
462C2×D5—64no—
463C2×D5—616no—
464C2×D5C22×C4×D314yes—
465C4×C5—24no—
466C4×C5—38no—
467C4×C5—62no—
468C4×C5—62no—
469C4×C5C22×C4×D314yes—
470Dic5—24no—
471Dic5—62no—
472Dic5—62no—
473Dic5C22×C4×D314yes—
474C24—51no—
475C24—152no—
476#41—1564no—
477C2×Q8—38no—
478C2×Q8—34no—
479C2×D4—158no—
480C2×D4—1516no—
481C2×D4—158no—
482C2×D4—154no—
483C22×C4—32no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—51no—
487C22×C4—58no—
488C22×C4—54no—
489C22×C4—52no—
490C22×C4—58no—
491C22×C4—158no—
492C22×C4—1516no—
493C22×C4—158no—
494C22×C4—151no—
495C22×C4—151no—
496C22×C4—158no—
497C22×C4—204no—
498C22×C4—604no—
499C22×C4—604no—
500C22×C4C2×D3×D512yes—
501C22×C4C2×D3×D511yescharacteristic
502C4⋊C4—38no—
503C4⋊C4—58no—
504C4⋊C4—54no—
505C4⋊C4—154no—
506C4⋊C4—158no—
507C4⋊C4—154no—
508C4⋊C4C2×D3×D514yes—
509C22⋊C4—158no—
510C22⋊C4—154no—
511C22⋊C4—154no—
512C22⋊C4—158no—
513C42—38no—
514C42—34no—
515C42—158no—
516C42—154no—
517C3×C5C2×#52011yescharacteristic, complemented, Hall
518C22×C3—54no—
519C22×C3—108no—
520C22×C3—102no—
521C22×C3—102no—
522C22×C3C22×C4×D512yes—
523C22×C3#414712yes—
524C22×C3#414912yes—
525C22×C3C24×D511yescharacteristic
526C2×D3—58no—
527C2×D3—1016no—
528C2×D3—104no—
529C2×D3—104no—
530C3×C4—24no—
531C3×C4—54no—
532C3×C4—104no—
533C3×C4C22×C4×D514yes—
534Dic3—22no—
535Dic3—22no—
536Dic3—102no—
537Dic3—102no—
538Dic3C22×C4×D518yes—
539C2×C5#550414yescomplemented
540C2×C5C23×C4×D311yescharacteristic
541C2×C5C2×#100411yescharacteristic
542C2×C5C2×#100711yescharacteristic
543D5—24no—
544D5—68no—
545C23—54no—
546C23—52no—
547C23—102no—
548C23—102no—
549C23—158no—
550C23—154no—
551C23—304no—
552C23—304no—
553C23C22×D3×D511yescharacteristic
554Q8—316no—
555D4—1532no—
556D4—1516no—
557C2×C4—24no—
558C2×C4—38no—
559C2×C4—34no—
560C2×C4—32no—
561C2×C4—32no—
562C2×C4—54no—
563C2×C4—52no—
564C2×C4—516no—
565C2×C4—54no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—104no—
569C2×C4—1532no—
570C2×C4—152no—
571C2×C4—152no—
572C2×C4—208no—
573C2×C4—302no—
574C2×C4—302no—
575C2×C4—608no—
576C2×C4—608no—
577C2×C4C4×D3×D514yes—
578C2×C4C22×D3×D514yes—
579C2×C4C22×D3×D512yes—
580C2×C3—104no—
581C2×C3#6590814yescomplemented
582C2×C3C23×C4×D511yescharacteristic
583C2×C3C2×#414711yescharacteristic
584C2×C3C2×#414911yescharacteristic
585D3—108no—
586C5C2×#550411yescharacteristic, complemented, Sylow
587C22—54no—
588C22—108no—
589C22—102no—
590C22—102no—
591C22—158no—
592C22—3016no—
593C22—304no—
594C22—304no—
595C22C2×C4×D3×D512yes—
596C22#9202612yes—
597C22#9202912yes—
598C22C23×D3×D511yescharacteristic
599C4—24no—
600C4—38no—
601C4—54no—
602C4—62no—
603C4—62no—
604C4—104no—
605C4—302no—
606C4—302no—
607C4C2×C4×D3×D514yes—
608C3C2×#6590811yescharacteristic, complemented, Sylow
609C2—104no—
610C2—308no—
611C2#1175333614yesdirect product factor
612C2C22×C4×D3×D511yescharacteristic
613C2C2×#9202611yescharacteristic
614C2C2×#9202911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×#6773C2
cosocleC22×C3×C5C25
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91782C2semidirect
3. C2×C5×#887C2semidirect
4. C2×C3×D5×C4⋊C4C2semidirect
5. C2×#91444C2semidirect
6. C2×C4×#1202C2semidirect
7. C2×#91428C2semidirect
8. C2×#91404C2semidirect
9. C2×#91403C2semidirect
10. C2×#91357C2semidirect
11. C2×#91344C2semidirect
12. #11753336C2direct (N × H)
22. C2×#6773C4semidirect
27. #91782C22semidirect
31. C5×#887C22semidirect
34. C3×D5×C4⋊C4C22semidirect
42. #91444C22semidirect
43. C4×#1202C22semidirect
44. #91428C22semidirect
45. #91404C22semidirect
46. #91403C22semidirect
47. #91357C22semidirect
48. #91344C22semidirect
57. C2×D5×C4⋊C4D3semidirect
68. C2×D60C2×C4semidirect
75. C2×C5×Dic6C2×C4semidirect
80. C2×C3×C4×D5C2×C4semidirect
83. C2×#1202C2×C4semidirect
86. C2×#1200C2×C4semidirect
89. #6773C2×C4semidirect
116. C2×#887D5semidirect
147. D5×C4⋊C4C2×D3semidirect
170. D60C22×C4semidirect
178. C5×Dic6C22×C4semidirect
184. C3×C4×D5C22×C4semidirect
185. #1202C22×C4semidirect
187. #1200C22×C4semidirect
222. #887C2×D5semidirect
248. C2×C4×D5C4×D3semidirect
325. C2×Dic6C4×D5semidirect
376. C4×D5C2×C4×D3semidirect
412. C2×C3×C5#520semidirect
452. Dic6C2×C4×D5semidirect
517. C3×C5C2×#520semidirect
539. C2×C5#5504semidirect
581. C2×C3#65908semidirect
586. C5C2×#5504semidirect
608. C3C2×#65908semidirect
611. C2#11753336direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67732
C2×#917822
C2×C5×#8872
C2×C3×D5×C4⋊C42
C2×#914442
C2×C4×#12022
C2×#914282
C2×#914042
C2×#914032
C2×#913572
C2×#913442
#117533362
C2×#659083
C2×#55045