Finite Group Databasebeta

← C2×#11756292 #14483990

Subgroups — C2×#11756292 #14483990

Order 1920.

2224 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×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×C4×#1220C211yesmaximal, characteristic
3C2×#91813C211yesmaximal, characteristic, complemented
4#11756292C2116yesmaximal, direct product factor
5C2×#91786C211yesmaximal, characteristic, complemented
6C2×#91781C211yesmaximal, characteristic, complemented
7C2×#91777C211yesmaximal, characteristic, complemented
8C2×#91776C211yesmaximal, characteristic, complemented
9C2×#91774C212yesmaximal
10C2×#91768C212yesmaximal, complemented
11C2×#91765C212yesmaximal, complemented
12C2×C4×Dic30C212yesmaximal, complemented
13C2×#65867—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C22×Dic30C2212yes—
18C22×Dic30C2211yescharacteristic
19C3×C5×#117C2218yescomplemented
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2212yes—
23C2×C3×C42×C5C2212yes—
24C2×#6719C2211yescharacteristic
25C2×#6719C2212yes—
26C4×#1220C2218yes—
27C2×#6714C2211yescharacteristic
28C2×#6714C2212yes—
29C2×#6714C2212yes—
30C2×C4⋊Dic15C2212yes—
31C2×C4⋊Dic15C2211yescharacteristic
32#91813C2218yescomplemented
33C2×#6712C2211yescharacteristic
34C2×#6712C2212yes—
35C2×#6712C2212yes—
36C2×#6712C2212yes—
37C2×C4×Dic15C2211yescharacteristic
38C2×C4×Dic15C2212yes—
39C2×C4×Dic15C2212yes—
40#91786C2218yescomplemented
41#91781C2218yescomplemented
42#91777C2218yescomplemented
43#91776C2218yescomplemented
44#91774C22116yes—
45#91768C22116yescomplemented
46#91765C22116yescomplemented
47C4×Dic30C22116yescomplemented
48C2×#5533—51nomaximal, Hall
49C2×C5×#117D311yescharacteristic, complemented
50C2×C4×C22⋊D5—31no—
51C2×#4070—31no—
52#65867—316no—
53C2×#4043—31no—
54C2×#4038—31no—
55C2×#4034—31no—
56C2×#4033—31no—
57C2×#4031—32no—
58C2×#4025—32no—
59C2×#4022—32no—
60C2×C4×Dic10—32no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2311yescharacteristic
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2314yes—
68C22×C3×C4×C5C2311yescharacteristic
69C2×#1220—24no—
70C2×#1220C2314yes—
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2312yes—
74C22×Dic15C2312yes—
75C22×Dic15C2311yescharacteristic
76C2×C4×D15—24no—
77C2×C4×D15C2314yes—
78C2×Dic30—24no—
79C2×Dic30—28no—
80C2×Dic30C2318yes—
81C2×Dic30C2314yes—
82C3×C5×C4⋊C4C2314yes—
83C3×C5×C4⋊C4C2314yes—
84C3×C5×C22⋊C4C2318yes—
85C3×C42×C5C2318yes—
86#6719C2314yes—
87#6719C2318yes—
88#6714C2314yes—
89#6714C2318yes—
90#6714C2318yes—
91C4⋊Dic15C2318yes—
92C4⋊Dic15C2314yes—
93#6712C2314yes—
94#6712C2318yes—
95#6712C2318yes—
96#6712C2318yes—
97C4×Dic15C2318yes—
98C4×Dic15C2318yes—
99C4×Dic15C2314yes—
100C2×C3×#117D511yescharacteristic, complemented
101C2×C4×#67—51no—
102C2×#924—51no—
103#5533—516no—
104C2×#897—51no—
105C2×#892—51no—
106C2×#888—51no—
107C2×#887—51no—
108C2×#885—52no—
109C2×#879—52no—
110C2×#876—52no—
111C2×C4×Dic6—52no—
112C23×C4×C5C2×D311yescharacteristic
113C22×C22⋊D5—31no—
114C22×C4×D5—31no—
115C22×Dic10—32no—
116C22×Dic10—31no—
117C5×#117C2×D318yescomplemented
118C2×C5×C4⋊C4C2×D311yescharacteristic
119C2×C5×C4⋊C4C2×D311yescharacteristic
120C2×C5×C22⋊C4C2×D312yes—
121C2×C42×C5C2×D312yes—
122C2×C22⋊Dic5—31no—
123C2×C22⋊Dic5—32no—
124C4×C22⋊D5—38no—
125C2×#685—31no—
126C2×#685—32no—
127C2×#685—32no—
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5—31no—
130#4070—38no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683—32no—
134C2×#683—32no—
135C2×C4×Dic5—32no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—31no—
138#4043—38no—
139#4038—38no—
140#4034—38no—
141#4033—38no—
142#4031—316no—
143#4025—316no—
144#4022—316no—
145C4×Dic10—316no—
146C2×#556—151noSylow
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5C2412yes—
151C23×C3×C5C2411yescharacteristic
152C22×D15—22no—
153C22×D15—22no—
154C22×D15—22no—
155C22×D15C2412yes—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—24no—
159C2×C3×C4×C5—28no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2414yes—
162C2×C3×C4×C5C2412yes—
163C2×C3×C4×C5C2414yes—
164C2×C3×C4×C5C2412yes—
165#1220—28no—
166C2×Dic15—24no—
167C2×Dic15—24no—
168C2×Dic15—22no—
169C2×Dic15—22no—
170C2×Dic15#4114yes—
171C2×Dic15C2412yes—
172C2×Dic15C2412yes—
173C2×Dic15C2414yes—
174C2×Dic15C2414yes—
175C2×Dic15C2412yes—
176C4×D15—28no—
177Dic30—28no—
178Dic30—216no—
179C23×C3×C4C2×D511yescharacteristic
180C22×#67—51no—
181C22×C4×D3—51no—
182C22×Dic6—52no—
183C22×Dic6—51no—
184C3×#117C2×D518yescomplemented
185C2×C3×C4⋊C4C2×D511yescharacteristic
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4C2×D512yes—
188C2×C3×C42C2×D512yes—
189C2×#217—51no—
190C2×#217—52no—
191C4×#67—58no—
192C2×(C2×D3)⋊C4—51no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3—51no—
197#924—58no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—52no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3—51no—
205#897—58no—
206#892—58no—
207#888—58no—
208#887—58no—
209#885—516no—
210#879—516no—
211#876—516no—
212C4×Dic6—516no—
213C24×C5C22×D311yescharacteristic
214C23×D5—31no—
215C22×C4×C5—24no—
216C22×C4×C5C22×D311yescharacteristic
217C22×C4×C5C22×D312yes—
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D314yes—
220C22×C4×C5C22×D311yescharacteristic
221C2×C22⋊D5—34no—
222C2×C22⋊D5—64no—
223C22×Dic5—31no—
224C22×Dic5—32no—
225C22×Dic5—32no—
226C22×Dic5—31no—
227C22×Dic5—31no—
228C2×C4×D5—34no—
229C2×C4×D5—64no—
230C2×Dic10—38no—
231C2×Dic10—34no—
232C2×Dic10—68no—
233C2×Dic10—64no—
234C5×C4⋊C4C22×D314yes—
235C5×C4⋊C4C22×D314yes—
236C5×C22⋊C4C22×D318yes—
237C42×C5C22×D318yes—
238C22⋊Dic5—34no—
239C22⋊Dic5—38no—
240#685—34no—
241#685—38no—
242#685—38no—
243C4⋊Dic5—38no—
244C4⋊Dic5—34no—
245#683—34no—
246#683—38no—
247#683—38no—
248#683—38no—
249C4×Dic5—38no—
250C4×Dic5—38no—
251C4×Dic5—34no—
252#556—1516no—
253C2×C4⋊Q8—151no—
254C2×#126—152no—
255C2×#126—152no—
256C2×#124—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×Q8—152no—
261C2×C4×D4—151no—
262C2×#117—151no—
263C2×#117D1511yescharacteristic, complemented
264C22×C3×C5—22no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5—44no—
268C22×C3×C5C2×#4112yes—
269C22×C3×C5C2×#4112yes—
270C22×C3×C52−1+412yes—
271C22×C3×C5C2511yescharacteristic
272C2×D15—22no—
273C2×D15—22no—
274C2×D15—22no—
275C2×D15—44no—
276C3×C4×C5—24no—
277C3×C4×C5—22no—
278C3×C4×C5—24no—
279C3×C4×C5C2×#4114yes—
280Dic15—24no—
281Dic15—24no—
282Dic15—22no—
283Dic15—22no—
284Dic15C2×#4114yes—
285C24×C3C22×D511yescharacteristic
286C23×D3—51no—
287C22×C3×C4—24no—
288C22×C3×C4C22×D512yes—
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D512yes—
291C22×C3×C4C22×D514yes—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—54no—
294C2×#67—104no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3—51no—
298C22×Dic3—52no—
299C22×Dic3—52no—
300C2×C4×D3—54no—
301C2×C4×D3—104no—
302C2×Dic6—58no—
303C2×Dic6—54no—
304C2×Dic6—108no—
305C2×Dic6—104no—
306C3×C4⋊C4C22×D514yes—
307C3×C4⋊C4C22×D514yes—
308C3×C22⋊C4C22×D518yes—
309C3×C42C22×D518yes—
310#217—54no—
311#217—58no—
312(C2×D3)⋊C4—54no—
313(C2×D3)⋊C4—58no—
314(C2×D3)⋊C4—58no—
315C4⋊Dic3—58no—
316C4⋊Dic3—54no—
317Dic3⋊C4—54no—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321C4×Dic3—58no—
322C4×Dic3—58no—
323C4×Dic3—54no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5C23×D312yes—
328C23×C5C23×D311yescharacteristic
329C22×D5—32no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5—62no—
333C2×C4×C5—22no—
334C2×C4×C5—24no—
335C2×C4×C5—24no—
336C2×C4×C5—28no—
337C2×C4×C5#23514yes—
338C2×C4×C5C23×D314yes—
339C2×C4×C5C23×D312yes—
340C2×C4×C5C23×D314yes—
341C2×C4×C5C23×D312yes—
342C22⋊D5—68no—
343C2×Dic5—34no—
344C2×Dic5—32no—
345C2×Dic5—32no—
346C2×Dic5—32no—
347C2×Dic5—34no—
348C2×Dic5—34no—
349C2×Dic5—64no—
350C2×Dic5—62no—
351C2×Dic5—64no—
352C2×Dic5—62no—
353C4×D5—68no—
354Dic10—616no—
355Dic10—68no—
356C22×Q8—151no—
357C22×Q8—152no—
358C22×D4—151no—
359C23×C4—151no—
360C23×C4C2×D1511yescharacteristic
361C4⋊Q8—158no—
362#126—1516no—
363#126—1516no—
364#124—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×Q8—1516no—
369C4×D4—158no—
370#117—158no—
371#117C2×D1518yescomplemented
372C2×C4⋊C4—151no—
373C2×C4⋊C4—151no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4C2×D1511yescharacteristic
379C2×C4⋊C4C2×D1511yescharacteristic
380C2×C22⋊C4—151no—
381C2×C22⋊C4—152no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—151no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4C2×D1512yes—
386C2×C42—152no—
387C2×C42—151no—
388C2×C42—152no—
389C2×C42C2×D1512yes—
390C2×C3×C5—42no—
391C2×C3×C5#55614yescomplemented
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C22×#4111yescharacteristic
394C2×C3×C5C2×2−1+411yescharacteristic
395D15—42no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3C23×D512yes—
400C23×C3C23×D511yescharacteristic
401C22×D3—52no—
402C22×D3—102no—
403C22×D3—102no—
404C22×D3—102no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—28no—
409C2×C3×C4#70914yes—
410C2×C3×C4C23×D514yes—
411C2×C3×C4C23×D512yes—
412C2×C3×C4C23×D514yes—
413C2×C3×C4C23×D512yes—
414#67—108no—
415C2×Dic3—54no—
416C2×Dic3—52no—
417C2×Dic3—52no—
418C2×Dic3—52no—
419C2×Dic3—54no—
420C2×Dic3—54no—
421C2×Dic3—104no—
422C2×Dic3—102no—
423C2×Dic3—104no—
424C2×Dic3—102no—
425C4×D3—108no—
426Dic6—1016no—
427Dic6—108no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—44no—
432C22×C5C2×#23512yes—
433C22×C5D3×#4112yes—
434C22×C5#101012yes—
435C22×C5C24×D311yescharacteristic
436C2×D5—62no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—124no—
440C4×C5—22no—
441C4×C5—24no—
442C4×C5—24no—
443C4×C5C2×#23514yes—
444Dic5—34no—
445Dic5—64no—
446Dic5—62no—
447Dic5—64no—
448Dic5—62no—
449C24—151no—
450C24C22×D1511yescharacteristic
451C2×Q8—154no—
452C2×Q8—158no—
453C2×Q8—308no—
454C2×Q8—304no—
455C2×D4—154no—
456C2×D4—304no—
457C22×C4—24no—
458C22×C4—151no—
459C22×C4—151no—
460C22×C4—151no—
461C22×C4—152no—
462C22×C4—152no—
463C22×C4—154no—
464C22×C4—304no—
465C22×C4C22×D1514yes—
466C22×C4C22×D1512yes—
467C22×C4C22×D1511yescharacteristic
468C22×C4C22×D1512yes—
469C22×C4C22×D1511yescharacteristic
470C4⋊C4—154no—
471C4⋊C4—154no—
472C4⋊C4—158no—
473C4⋊C4—158no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4C22×D1514yes—
477C4⋊C4C22×D1514yes—
478C22⋊C4—154no—
479C22⋊C4—158no—
480C22⋊C4—158no—
481C22⋊C4—154no—
482C22⋊C4—158no—
483C22⋊C4C22×D1518yes—
484C42—158no—
485C42—154no—
486C42—158no—
487C42C22×D1518yes—
488C3×C5C2×#55611yescharacteristic, complemented, Hall
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—44no—
493C22×C3C2×#70912yes—
494C22×C3D5×#4112yes—
495C22×C3#415012yes—
496C22×C3C24×D511yescharacteristic
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—204no—
501C3×C4—22no—
502C3×C4—24no—
503C3×C4—24no—
504C3×C4C2×#70914yes—
505Dic3—54no—
506Dic3—104no—
507Dic3—102no—
508Dic3—104no—
509Dic3—102no—
510C2×C5—42no—
511C2×C5#553314yescomplemented
512C2×C5C22×#23511yescharacteristic
513C2×C5C2×D3×#4111yescharacteristic
514C2×C5C2×#101011yescharacteristic
515D5—122no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—152no—
520C23—302no—
521C23—302no—
522C23—302no—
523C23C23×D1512yes—
524C23C23×D1511yescharacteristic
525Q8—3016no—
526Q8—308no—
527D4—308no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—28no—
532C2×C4—154no—
533C2×C4—152no—
534C2×C4—152no—
535C2×C4—152no—
536C2×C4—154no—
537C2×C4—154no—
538C2×C4—302no—
539C2×C4—304no—
540C2×C4—304no—
541C2×C4—302no—
542C2×C4—308no—
543C2×C4#681714yes—
544C2×C4C23×D1514yes—
545C2×C4C23×D1512yes—
546C2×C4C23×D1514yes—
547C2×C4C23×D1512yes—
548C2×C3—42no—
549C2×C3#6586714yescomplemented
550C2×C3C22×#70911yescharacteristic
551C2×C3C2×D5×#4111yescharacteristic
552C2×C3C2×#415011yescharacteristic
553D3—202no—
554C5C2×#553311yescharacteristic, complemented, Sylow
555C22—22no—
556C22—22no—
557C22—22no—
558C22—44no—
559C22—302no—
560C22—302no—
561C22—302no—
562C22—604no—
563C22C2×#681712yes—
564C22#41×D1512yes—
565C22#9210112yes—
566C22C24×D1511yescharacteristic
567C4—22no—
568C4—24no—
569C4—24no—
570C4—154no—
571C4—302no—
572C4—304no—
573C4—304no—
574C4—302no—
575C4C2×#681714yes—
576C3C2×#6586711yescharacteristic, complemented, Sylow
577C2—42no—
578C2—602no—
579C2#1175629214yesdirect product factor
580C2C22×#681711yescharacteristic
581C2C2×#41×D1511yescharacteristic
582C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×#117D15
hypocenterC3×C5C2×#556
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. #11756292C2direct (N × H)
5. C2×#91786C2semidirect
6. C2×#91781C2semidirect
7. C2×#91777C2semidirect
8. C2×#91776C2semidirect
10. C2×#91768C2semidirect
11. C2×#91765C2semidirect
12. C2×C4×Dic30C2semidirect
19. C3×C5×#117C22semidirect
32. #91813C22semidirect
40. #91786C22semidirect
41. #91781C22semidirect
42. #91777C22semidirect
43. #91776C22semidirect
45. #91768C22semidirect
46. #91765C22semidirect
47. C4×Dic30C22semidirect
49. C2×C5×#117D3semidirect
100. C2×C3×#117D5semidirect
117. C5×#117C2×D3semidirect
184. C3×#117C2×D5semidirect
263. C2×#117D15semidirect
371. #117C2×D15semidirect
391. C2×C3×C5#556semidirect
488. C3×C5C2×#556semidirect
511. C2×C5#5533semidirect
549. C2×C3#65867semidirect
554. C5C2×#5533semidirect
576. C3C2×#65867semidirect
579. C2#11756292direct (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×C4×#12202
C2×#918132
#117562922
C2×#917862
C2×#917812
C2×#917772
C2×#917762
C2×#917742
C2×#917682
C2×#917652
C2×C4×Dic302
C2×#658673
C2×#55335