Finite Group Databasebeta

← C2×#11753498 #14479933

Subgroups — C2×#11753498 #14479933

Order 1920.

2464 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×#91779C211yesmaximal, characteristic, complemented
2C2×C5×#887C211yesmaximal, characteristic, complemented
3C2×C3×#4041C211yesmaximal, characteristic
4C2×Dic3×D20C211yesmaximal, characteristic, complemented
5C2×Dic3×D20C212yesmaximal, complemented
6C2×#91407C212yesmaximal, complemented
7C2×#91393C212yesmaximal, complemented
8C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
9C2×#91368C211yesmaximal, characteristic, complemented
10C2×#91362C212yesmaximal, complemented
11C2×#91359C211yesmaximal, characteristic, complemented
12#11753498C2116yesmaximal, direct product factor
13C2×#65914—31nomaximal, Hall
14C22×C5×Dic6C2211yescharacteristic
15C22×C3×D20C2211yescharacteristic
16C22×C3×D20C2212yes—
17C22×C3×C4×D5C2211yescharacteristic
18C22×D5×Dic3C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C22×D5×Dic3C2212yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C4⋊Dic15C2212yes—
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6712C2212yes—
25C2×C4×Dic15C2211yescharacteristic
26#91779C2218yescomplemented
27C2×C5×Dic3⋊C4C2212yes—
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C4×C5×Dic3C2212yes—
30C5×#887C2218yescomplemented
31C2×C3×#685C2212yes—
32C3×#4041C2218yes—
33C2×#6669C2212yes—
34C2×#6665C2212yes—
35C2×#6665C2212yes—
36C2×#6665C2212yes—
37C2×#6665C2212yes—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40Dic3×D20C22116yescomplemented
41Dic3×D20C2218yescomplemented
42#91407C22116yescomplemented
43#91393C22116yescomplemented
44C4×D5×Dic3C2218yescomplemented
45#91368C2218yescomplemented
46#91362C22116yescomplemented
47#91359C2218yescomplemented
48C2×#5600—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4093—31no—
51C2×#4092—31no—
52#65914—316no—
53C2×#4044—32no—
54C2×#4041D311yescharacteristic
55C2×#4040—32no—
56C2×#4036—31no—
57C2×C4×D20—31no—
58C2×C4×D20—32no—
59C2×#4018—32no—
60C2×C42×D5—31no—
61C23×C3×D5C2312yes—
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×C5×Dic3C2311yescharacteristic
69C22×C5×Dic3C2312yes—
70C22×C5×Dic3C2311yescharacteristic
71C2×C5×Dic6—24no—
72C2×C5×Dic6C2314yes—
73C22×C3×Dic5C2311yescharacteristic
74C2×C3×D20—28no—
75C2×C3×D20—24no—
76C2×C3×D20C2318yes—
77C2×C3×D20C2314yes—
78C2×C3×C4×D5—24no—
79C2×C3×C4×D5C2314yes—
80C2×D5×Dic3—24no—
81C2×D5×Dic3—24no—
82C2×D5×Dic3—28no—
83C2×D5×Dic3C2318yes—
84C2×D5×Dic3C2314yes—
85C2×D5×Dic3C2314yes—
86C3×C5×C4⋊C4C2314yes—
87C4⋊Dic15C2314yes—
88C4⋊Dic15C2318yes—
89#6712C2318yes—
90C4×Dic15C2314yes—
91C5×Dic3⋊C4C2318yes—
92C4×C5×Dic3C2318yes—
93C4×C5×Dic3C2314yes—
94C3×#685C2318yes—
95#6669C2318yes—
96#6665C2318yes—
97#6665C2318yes—
98#6665C2318yes—
99#6665C2318yes—
100Dic3×Dic5C2314yes—
101Dic3×Dic5C2314yes—
102C2×C3×#121—51no—
103C2×#936—51no—
104C2×#935—52no—
105C2×D4×Dic3—52no—
106C2×D4×Dic3—51no—
107C2×#924—51no—
108C22×C4×Dic3—51no—
109#5600—516no—
110C2×#890—51no—
111C2×#887D511yescharacteristic, complemented
112C2×#879—52no—
113C2×#877—52no—
114C22×C5×Q8—31no—
115C22×D20C2×D312yes—
116C22×D20C2×D311yescharacteristic
117C22×C4×D5—31no—
118C22×C4×D5—31no—
119C22×C4×D5—32no—
120C22×C4×D5C2×D311yescharacteristic
121C4×C5×Q8—38no—
122C2×C5×C4⋊C4—32no—
123C2×C5×C4⋊C4C2×D311yescharacteristic
124C2×C42×C5—31no—
125C2×C42×C5—32no—
126#4093—38no—
127#4092—38no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685—32no—
132C2×#685C2×D312yes—
133C2×C4⋊Dic5—32no—
134C2×C4⋊Dic5—31no—
135C2×#683—32no—
136C2×#683—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140#4044—316no—
141#4041C2×D318yes—
142#4040—316no—
143#4036—38no—
144C4×D20—316no—
145C4×D20—38no—
146#4018—316no—
147C42×D5—38no—
148C2×#529—151noSylow
149C23×C3×C5C2411yescharacteristic
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—24no—
153C22×C3×D5—24no—
154C22×C3×D5—24no—
155C22×C3×D5#4114yes—
156C22×C3×D5C2414yes—
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×Dic15—22no—
165C2×Dic15C2412yes—
166C2×Dic15C2412yes—
167C2×Dic15C2414yes—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3#4114yes—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2412yes—
174C5×Dic6—28no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C2412yes—
177C3×D20—216no—
178C3×D20—28no—
179C3×C4×D5—28no—
180D5×Dic3—28no—
181D5×Dic3—28no—
182D5×Dic3—216no—
183C22×C3×D4—52no—
184C22×C3×D4—51no—
185C23×C3×C4—51no—
186C23×Dic3—52no—
187C23×Dic3—51no—
188C23×Dic3—51no—
189C22×Dic6C2×D511yescharacteristic
190C3×#121—58no—
191C2×C3×C4⋊C4C2×D511yescharacteristic
192C2×C3×C22⋊C4—52no—
193C2×#217—52no—
194C2×#217—52no—
195C2×#217—52no—
196C2×#217—52no—
197#936—58no—
198#935—516no—
199D4×Dic3—516no—
200D4×Dic3—58no—
201C2×C4⋊Dic3—52no—
202C2×C4⋊Dic3—51no—
203#924—58no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4C2×D512yes—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—58no—
211C2×C4×Dic3C2×D512yes—
212C2×C4×Dic3C2×D511yescharacteristic
213#890—58no—
214#887C2×D518yescomplemented
215#879—516no—
216#877—516no—
217C23×D5C22×D312yes—
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—31no—
227C22×Dic5—31no—
228C22×Dic5—32no—
229C22×Dic5C22×D311yescharacteristic
230C2×D20—28no—
231C2×D20—24no—
232C2×D20C22×D318yes—
233C2×D20C22×D314yes—
234C2×C4×D5—24no—
235C2×C4×D5—34no—
236C2×C4×D5—34no—
237C2×C4×D5—38no—
238C2×C4×D5—64no—
239C2×C4×D5—68no—
240C2×C4×D5—64no—
241C2×C4×D5C22×D314yes—
242C5×C4⋊C4—38no—
243C5×C4⋊C4C22×D314yes—
244C42×C5—34no—
245C42×C5—38no—
246#685—38no—
247#685—38no—
248#685—38no—
249#685—38no—
250#685C22×D318yes—
251C4⋊Dic5—38no—
252C4⋊Dic5—34no—
253#683—38no—
254#683—38no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5—34no—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—51no—
265C2×C4×Q8—31no—
266C2×C4×D4—152no—
267C2×C4×D4—151no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2×#4112yes—
273C22×C3×C5C2511yescharacteristic
274C2×C3×D5—28no—
275C2×C3×D5—22no—
276C2×C3×D5—22no—
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—48no—
281C2×C3×D5C2×#4114yes—
282C3×C4×C5—24no—
283C3×C4×C5C2×#4114yes—
284Dic15—22no—
285Dic15—24no—
286Dic15—22no—
287C3×Dic5—22no—
288C5×Dic3—22no—
289C5×Dic3—24no—
290C5×Dic3C2×#4114yes—
291C24×C3—51no—
292C24×C3—52no—
293C2×C3×D4—58no—
294C2×C3×D4—54no—
295C2×C3×D4—108no—
296C2×C3×D4—104no—
297C22×C3×C4—51no—
298C22×C3×C4—54no—
299C22×C3×C4—104no—
300C22×C3×C4C22×D512yes—
301C22×C3×C4C22×D511yescharacteristic
302C22×Dic3—51no—
303C22×Dic3—51no—
304C22×Dic3—52no—
305C22×Dic3—58no—
306C22×Dic3—54no—
307C22×Dic3—54no—
308C22×Dic3—104no—
309C22×Dic3—104no—
310C22×Dic3—108no—
311C22×Dic3C22×D511yescharacteristic
312C22×Dic3C22×D512yes—
313C22×Dic3C22×D511yescharacteristic
314C2×Dic6—24no—
315C2×Dic6C22×D514yes—
316C3×C4⋊C4C22×D514yes—
317C3×C22⋊C4—58no—
318#217—58no—
319#217—58no—
320#217—58no—
321#217—58no—
322C4⋊Dic3—58no—
323C4⋊Dic3—54no—
324Dic3⋊C4—58no—
325Dic3⋊C4—58no—
326Dic3⋊C4C22×D518yes—
327C4×Dic3—54no—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3C22×D518yes—
331C4×Dic3C22×D514yes—
332C23×C5C23×D311yescharacteristic
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—24no—
336C22×D5—24no—
337C22×D5—24no—
338C22×D5#23714yes—
339C22×D5C23×D314yes—
340C22×D5C23×D312yes—
341C5×Q8—68no—
342C2×C4×C5—24no—
343C2×C4×C5—34no—
344C2×C4×C5—32no—
345C2×C4×C5—32no—
346C2×C4×C5—34no—
347C2×C4×C5—62no—
348C2×C4×C5—64no—
349C2×C4×C5#23714yes—
350C2×C4×C5C23×D314yes—
351C2×C4×C5C23×D312yes—
352C2×Dic5—22no—
353C2×Dic5—32no—
354C2×Dic5—32no—
355C2×Dic5—34no—
356C2×Dic5—62no—
357C2×Dic5—62no—
358C2×Dic5—64no—
359C2×Dic5C23×D312yes—
360D20—216no—
361D20—28no—
362C4×D5—28no—
363C4×D5—68no—
364C4×D5—616no—
365C4×D5—68no—
366C22×Q8—31no—
367C22×D4—52no—
368C22×D4—51no—
369C23×C4—51no—
370C23×C4—152no—
371C23×C4—151no—
372C23×C4—151no—
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—58no—
379C4×Q8—38no—
380C4×D4—158no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—152no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—151no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4D3×D511yescharacteristic
389C2×C22⋊C4—52no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—32no—
395C2×C42—31no—
396C2×C42—158no—
397C2×C42—151no—
398C2×C42—151no—
399C2×C42—151no—
400C2×C3×C5#52914yescomplemented
401C2×C3×C5C22×#4111yescharacteristic
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C3×D5—24no—
405C3×D5—44no—
406C23×C3—54no—
407C23×C3—52no—
408C23×C3—54no—
409C23×C3—102no—
410C23×C3—102no—
411C23×C3—104no—
412C23×C3—104no—
413C23×C3—104no—
414C23×C3C23×D511yescharacteristic
415C3×D4—1016no—
416C3×D4—108no—
417C2×C3×C4—24no—
418C2×C3×C4—52no—
419C2×C3×C4—102no—
420C2×C3×C4—108no—
421C2×C3×C4#70914yes—
422C2×C3×C4C23×D514yes—
423C2×C3×C4C23×D512yes—
424C2×Dic3—24no—
425C2×Dic3—22no—
426C2×Dic3—52no—
427C2×Dic3—52no—
428C2×Dic3—54no—
429C2×Dic3—108no—
430C2×Dic3—102no—
431C2×Dic3—104no—
432C2×Dic3—102no—
433C2×Dic3—108no—
434C2×Dic3—1016no—
435C2×Dic3#71314yes—
436C2×Dic3C23×D512yes—
437C2×Dic3C23×D514yes—
438C2×Dic3C23×D512yes—
439Dic6—28no—
440C22×C5C2×#23712yes—
441C22×C5C2×#23712yes—
442C22×C5D3×#4112yes—
443C22×C5C24×D311yescharacteristic
444C2×D5—22no—
445C2×D5—22no—
446C2×D5—28no—
447C2×D5—24no—
448C2×D5—24no—
449C2×D5—24no—
450C2×D5—48no—
451C2×D5C2×#23714yes—
452C4×C5—24no—
453C4×C5—34no—
454C4×C5—62no—
455C4×C5—64no—
456C4×C5C2×#23714yes—
457Dic5—22no—
458Dic5—62no—
459Dic5—62no—
460Dic5—64no—
461C24—51no—
462C24—52no—
463C2×Q8—34no—
464C2×Q8—64no—
465C2×D4—58no—
466C2×D4—54no—
467C2×D4—108no—
468C2×D4—104no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—51no—
473C22×C4—54no—
474C22×C4—104no—
475C22×C4—154no—
476C22×C4—154no—
477C22×C4—158no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—152no—
481C22×C4—304no—
482C22×C4—308no—
483C22×C4—304no—
484C22×C4C2×D3×D512yes—
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—38no—
487C4⋊C4—158no—
488C4⋊C4—158no—
489C4⋊C4—154no—
490C4⋊C4—158no—
491C4⋊C4C2×D3×D514yes—
492C22⋊C4—58no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—34no—
498C42—38no—
499C42—154no—
500C42—154no—
501C42—154no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—54no—
504C22×C3—108no—
505C22×C3—102no—
506C22×C3—102no—
507C22×C3—104no—
508C22×C3—104no—
509C22×C3—104no—
510C22×C3—208no—
511C22×C3C2×#70912yes—
512C22×C3C2×#71312yes—
513C22×C3D5×#4112yes—
514C22×C3C24×D511yescharacteristic
515C3×C4—24no—
516C3×C4—102no—
517C3×C4C2×#70914yes—
518Dic3—24no—
519Dic3—22no—
520Dic3—102no—
521Dic3—104no—
522Dic3—102no—
523Dic3C2×#71314yes—
524C2×C5#560014yescomplemented
525C2×C5C22×#23711yescharacteristic
526C2×C5C22×#23711yescharacteristic
527C2×C5C2×D3×#4111yescharacteristic
528D5—24no—
529D5—44no—
530C23—54no—
531C23—52no—
532C23—54no—
533C23—102no—
534C23—102no—
535C23—104no—
536C23—104no—
537C23—104no—
538C23C22×D3×D511yescharacteristic
539Q8—68no—
540D4—1016no—
541D4—108no—
542C2×C4—24no—
543C2×C4—34no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—34no—
547C2×C4—52no—
548C2×C4—64no—
549C2×C4—62no—
550C2×C4—102no—
551C2×C4—108no—
552C2×C4—152no—
553C2×C4—152no—
554C2×C4—154no—
555C2×C4—308no—
556C2×C4—3016no—
557C2×C4—308no—
558C2×C4—302no—
559C2×C4—302no—
560C2×C4—304no—
561C2×C4#676514yes—
562C2×C4C22×D3×D514yes—
563C2×C4C22×D3×D512yes—
564C2×C3—104no—
565C2×C3—204no—
566C2×C3#6591414yescomplemented
567C2×C3C22×#70911yescharacteristic
568C2×C3C22×#71311yescharacteristic
569C2×C3C2×D5×#4111yescharacteristic
570C5C2×#560011yescharacteristic, complemented, Sylow
571C22—54no—
572C22—108no—
573C22—102no—
574C22—102no—
575C22—104no—
576C22—104no—
577C22—104no—
578C22—208no—
579C22C2×#676512yes—
580C22D5×#23712yes—
581C22D3×#71312yes—
582C22C23×D3×D511yescharacteristic
583C4—24no—
584C4—34no—
585C4—64no—
586C4—62no—
587C4—102no—
588C4—302no—
589C4—302no—
590C4—304no—
591C4C2×#676514yes—
592C3C2×#6591411yescharacteristic, complemented, Sylow
593C2—104no—
594C2—204no—
595C2#1175349814yesdirect product factor
596C2C22×#676511yescharacteristic
597C2C2×D5×#23711yescharacteristic
598C2C2×D3×#71311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC2×C3×#4041C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#529
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×#887C2semidirect
4. C2×Dic3×D20C2semidirect
5. C2×Dic3×D20C2semidirect
6. C2×#91407C2semidirect
7. C2×#91393C2semidirect
8. C2×C4×D5×Dic3C2semidirect
9. C2×#91368C2semidirect
10. C2×#91362C2semidirect
11. C2×#91359C2semidirect
12. #11753498C2direct (N × H)
26. #91779C22semidirect
30. C5×#887C22semidirect
40. Dic3×D20C22semidirect
41. Dic3×D20C22semidirect
42. #91407C22semidirect
43. #91393C22semidirect
44. C4×D5×Dic3C22semidirect
45. #91368C22semidirect
46. #91362C22semidirect
47. #91359C22semidirect
111. C2×#887D5semidirect
214. #887C2×D5semidirect
400. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
524. C2×C5#5600semidirect
566. C2×C3#65914semidirect
570. C5C2×#5600semidirect
592. C3C2×#65914semidirect
595. C2#11753498direct (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×#8872
C2×C3×#40412
C2×Dic3×D202
C2×#914072
C2×#913932
C2×C4×D5×Dic32
C2×#913682
C2×#913622
C2×#913592
#117534982
C2×#659143
C2×#56005