Finite Group Databasebeta

← C2×#11756362 #14481312

Subgroups — C2×#11756362 #14481312

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×#91825C211yesmaximal, characteristic, complemented
3C2×#91825C212yesmaximal, complemented
4C2×#91824C212yesmaximal, complemented
5C2×D4×Dic15C211yesmaximal, characteristic, complemented
6C2×#91815C211yesmaximal, characteristic, complemented
7C2×#91813C211yesmaximal, characteristic, complemented
8#11756362C2116yesmaximal, direct product factor
9C2×#91777C211yesmaximal, characteristic, complemented
10C2×#91776C211yesmaximal, characteristic, complemented
11C2×#91768C212yesmaximal, complemented
12C2×#91767C212yesmaximal, complemented
13C2×#65937—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C5×D4C2212yes—
16C23×C3×C4×C5C2211yescharacteristic
17C23×Dic15C2212yes—
18C22×Dic30C2211yescharacteristic
19C22×Dic30C2212yes—
20C3×C5×#121C2218yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2212yes—
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2212yes—
26C2×#6719C2212yes—
27C2×#6719C2212yes—
28C2×#6719C2212yes—
29#91825C22116yescomplemented
30#91825C2218yescomplemented
31#91824C22116yescomplemented
32D4×Dic15C2218yescomplemented
33#91815C2218yescomplemented
34C2×C4⋊Dic15C2211yescharacteristic
35C2×C4⋊Dic15C2211yescharacteristic
36C2×C4⋊Dic15C2211yescharacteristic
37#91813C2218yescomplemented
38C2×#6712C2212yes—
39C2×#6712C2212yes—
40C2×#6712C2212yes—
41C2×C4×Dic15C2211yescharacteristic
42C2×C4×Dic15C2211yescharacteristic
43C2×C4×Dic15C2212yes—
44#91777C2218yescomplemented
45#91776C2218yescomplemented
46#91768C22116yescomplemented
47#91767C22116yescomplemented
48C2×#5603—51nomaximal, Hall
49C2×C5×#121D311yescharacteristic
50C2×#4082—31no—
51C2×#4082—32no—
52C2×#4081—32no—
53C2×D4×Dic5—31no—
54C2×#4072—31no—
55C2×#4070—31no—
56#65937—316no—
57C2×#4034—31no—
58C2×#4033—31no—
59C2×#4025—32no—
60C2×#4024—32no—
61C24×C3×C5C2311yescharacteristic
62C24×C3×C5C2312yes—
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4—44no—
65C2×C3×C5×D4C2314yes—
66C2×C3×C5×D4C2318yes—
67C22×C3×C4×C5—24no—
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2314yes—
71C22×C3×C4×C5C2311yescharacteristic
72C22×Dic15—44no—
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2312yes—
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2312yes—
79C22×Dic15C2318yes—
80C2×Dic30—24no—
81C2×Dic30—44no—
82C2×Dic30C2314yes—
83C2×Dic30C2318yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C22⋊C4C2318yes—
86#6719C2318yes—
87#6719C2318yes—
88#6719C2318yes—
89#6719C2318yes—
90#6719C2314yes—
91#6719C2314yes—
92C4⋊Dic15C2314yes—
93C4⋊Dic15C2314yes—
94C4⋊Dic15C2314yes—
95#6712C2318yes—
96#6712C2318yes—
97#6712C2318yes—
98C4×Dic15C2318yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C2×C3×#121D511yescharacteristic
102C2×#936—52no—
103C2×#936—51no—
104C2×#935—52no—
105C2×D4×Dic3—51no—
106C2×#926—51no—
107C2×#924—51no—
108#5603—516no—
109C2×#888—51no—
110C2×#887—51no—
111C2×#879—52no—
112C2×#878—52no—
113C22×C5×D4C2×D311yescharacteristic
114C22×C5×D4C2×D312yes—
115C23×C4×C5C2×D311yescharacteristic
116C23×Dic5—32no—
117C22×Dic10—31no—
118C22×Dic10—32no—
119C5×#121C2×D318yes—
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C22⋊C4C2×D312yes—
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5—32no—
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5—31no—
127C2×C22⋊Dic5—31no—
128#4082—316no—
129#4082—38no—
130#4081—316no—
131D4×Dic5—38no—
132#4072—38no—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—31no—
135C2×C4⋊Dic5—31no—
136#4070—38no—
137C2×#683—32no—
138C2×#683—32no—
139C2×#683—32no—
140C2×C4×Dic5—32no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143#4034—38no—
144#4033—38no—
145#4025—316no—
146#4024—316no—
147C2×#542—151noSylow
148C23×C3×C5—22no—
149C23×C3×C5—24no—
150C23×C3×C5—24no—
151C23×C3×C5—22no—
152C23×C3×C5—22no—
153C23×C3×C5—24no—
154C23×C3×C5C2412yes—
155C23×C3×C5C2414yes—
156C23×C3×C5C2411yescharacteristic
157C3×C5×D4—28no—
158C3×C5×D4—48no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—24no—
161C2×C3×C4×C5—28no—
162C2×C3×C4×C5#4114yes—
163C2×C3×C4×C5C2414yes—
164C2×C3×C4×C5C2412yes—
165C2×C3×C4×C5C2412yes—
166C2×Dic15—24no—
167C2×Dic15—22no—
168C2×Dic15—24no—
169C2×Dic15—22no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15—48no—
173C2×Dic15C2412yes—
174C2×Dic15C2412yes—
175C2×Dic15C2412yes—
176C2×Dic15C2414yes—
177C2×Dic15C2412yes—
178C2×Dic15C2414yes—
179Dic30—28no—
180Dic30—48no—
181C22×C3×D4C2×D511yescharacteristic
182C22×C3×D4C2×D512yes—
183C23×C3×C4C2×D511yescharacteristic
184C23×Dic3—52no—
185C22×Dic6—51no—
186C22×Dic6—52no—
187C3×#121C2×D518yes—
188C2×C3×C4⋊C4C2×D511yescharacteristic
189C2×C3×C22⋊C4C2×D512yes—
190C2×#217—52no—
191C2×#217—52no—
192C2×#217—52no—
193C2×#217—52no—
194C2×#217—51no—
195C2×#217—51no—
196#936—516no—
197#936—58no—
198#935—516no—
199D4×Dic3—58no—
200#926—58no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—51no—
203C2×C4⋊Dic3—51no—
204#924—58no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×Dic3⋊C4—52no—
208C2×C4×Dic3—52no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—51no—
211#888—58no—
212#887—58no—
213#879—516no—
214#878—516no—
215C24×C5C22×D311yescharacteristic
216C24×C5C22×D312yes—
217C2×C5×D4—24no—
218C2×C5×D4—44no—
219C2×C5×D4C22×D314yes—
220C2×C5×D4C22×D318yes—
221C22×C4×C5—24no—
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D312yes—
224C22×C4×C5C22×D314yes—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—31no—
227C22×Dic5—32no—
228C22×Dic5—31no—
229C22×Dic5—31no—
230C22×Dic5—32no—
231C22×Dic5—31no—
232C22×Dic5—38no—
233C22×Dic5—124no—
234C2×Dic10—34no—
235C2×Dic10—38no—
236C2×Dic10—64no—
237C2×Dic10—124no—
238C5×C4⋊C4C22×D314yes—
239C5×C22⋊C4C22×D318yes—
240C22⋊Dic5—38no—
241C22⋊Dic5—38no—
242C22⋊Dic5—38no—
243C22⋊Dic5—38no—
244C22⋊Dic5—34no—
245C22⋊Dic5—34no—
246C4⋊Dic5—34no—
247C4⋊Dic5—34no—
248C4⋊Dic5—34no—
249#683—38no—
250#683—38no—
251#683—38no—
252C4×Dic5—38no—
253C4×Dic5—34no—
254C4×Dic5—34no—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—151no—
259C2×#124—152no—
260C2×#123—152no—
261C2×C22⋊Q8—151no—
262C2×C22⋊Q8—152no—
263C2×#121D1511yescharacteristic
264C2×C4×Q8—151no—
265C2×C4×D4—151no—
266C2×#117—151no—
267C22×C3×C5—22no—
268C22×C3×C5—24no—
269C22×C3×C5—24no—
270C22×C3×C5—22no—
271C22×C3×C5—22no—
272C22×C3×C5—24no—
273C22×C3×C5—44no—
274C22×C3×C5—48no—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5H(5,𝔽2)12yes—
277C22×C3×C52−1+412yes—
278C22×C3×C5C2511yescharacteristic
279C3×C4×C5—22no—
280C3×C4×C5—24no—
281C3×C4×C5C2×#4114yes—
282Dic15—24no—
283Dic15—22no—
284Dic15—24no—
285Dic15—22no—
286Dic15—22no—
287Dic15—22no—
288C24×C3C22×D511yescharacteristic
289C24×C3C22×D512yes—
290C2×C3×D4—24no—
291C2×C3×D4—44no—
292C2×C3×D4C22×D514yes—
293C2×C3×D4C22×D518yes—
294C22×C3×C4—24no—
295C22×C3×C4C22×D512yes—
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D514yes—
298C22×C3×C4C22×D511yescharacteristic
299C22×Dic3—51no—
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—52no—
303C22×Dic3—51no—
304C22×Dic3—52no—
305C22×Dic3—58no—
306C22×Dic3—204no—
307C2×Dic6—54no—
308C2×Dic6—58no—
309C2×Dic6—104no—
310C2×Dic6—204no—
311C3×C4⋊C4C22×D514yes—
312C3×C22⋊C4C22×D518yes—
313#217—58no—
314#217—58no—
315#217—58no—
316#217—58no—
317#217—54no—
318#217—54no—
319C4⋊Dic3—54no—
320C4⋊Dic3—54no—
321C4⋊Dic3—54no—
322Dic3⋊C4—58no—
323Dic3⋊C4—58no—
324Dic3⋊C4—58no—
325C4×Dic3—58no—
326C4×Dic3—54no—
327C4×Dic3—54no—
328C23×C5—22no—
329C23×C5—24no—
330C23×C5—24no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—24no—
334C23×C5C23×D312yes—
335C23×C5C23×D314yes—
336C23×C5C23×D311yescharacteristic
337C5×D4—28no—
338C5×D4—48no—
339C2×C4×C5—22no—
340C2×C4×C5—24no—
341C2×C4×C5—28no—
342C2×C4×C5#23714yes—
343C2×C4×C5C23×D314yes—
344C2×C4×C5C23×D312yes—
345C2×C4×C5C23×D312yes—
346C2×Dic5—32no—
347C2×Dic5—32no—
348C2×Dic5—32no—
349C2×Dic5—34no—
350C2×Dic5—32no—
351C2×Dic5—34no—
352C2×Dic5—64no—
353C2×Dic5—62no—
354C2×Dic5—64no—
355C2×Dic5—62no—
356C2×Dic5—62no—
357C2×Dic5—62no—
358C2×Dic5—128no—
359Dic10—68no—
360Dic10—128no—
361C22×Q8—151no—
362C22×Q8—152no—
363C22×D4C2×D1511yescharacteristic
364C22×D4C2×D1512yes—
365C23×C4—152no—
366C23×C4C2×D1511yescharacteristic
367C4⋊Q8—158no—
368#126—1516no—
369#124—158no—
370#124—1516no—
371#123—1516no—
372C22⋊Q8—158no—
373C22⋊Q8—1516no—
374#121C2×D1518yes—
375C4×Q8—158no—
376C4×D4—158no—
377#117—158no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—152no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—152no—
384C2×C4⋊C4C2×D1511yescharacteristic
385C2×C22⋊C4—151no—
386C2×C22⋊C4—151no—
387C2×C22⋊C4—152no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4C2×D1512yes—
392C2×C42—151no—
393C2×C42—151no—
394C2×C42—152no—
395C2×C3×C5—42no—
396C2×C3×C5—44no—
397C2×C3×C5#54214yescomplemented
398C2×C3×C5C22×#4111yescharacteristic
399C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
400C2×C3×C5C2×2−1+411yescharacteristic
401C23×C3—22no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—24no—
407C23×C3C23×D512yes—
408C23×C3C23×D514yes—
409C23×C3C23×D511yescharacteristic
410C3×D4—28no—
411C3×D4—48no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—28no—
415C2×C3×C4#71114yes—
416C2×C3×C4C23×D514yes—
417C2×C3×C4C23×D512yes—
418C2×C3×C4C23×D512yes—
419C2×Dic3—52no—
420C2×Dic3—52no—
421C2×Dic3—52no—
422C2×Dic3—54no—
423C2×Dic3—52no—
424C2×Dic3—54no—
425C2×Dic3—104no—
426C2×Dic3—102no—
427C2×Dic3—104no—
428C2×Dic3—102no—
429C2×Dic3—102no—
430C2×Dic3—102no—
431C2×Dic3—208no—
432Dic6—108no—
433Dic6—208no—
434C22×C5—22no—
435C22×C5—24no—
436C22×C5—24no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—24no—
440C22×C5—44no—
441C22×C5—48no—
442C22×C5C2×#23712yes—
443C22×C5#100412yes—
444C22×C5#101012yes—
445C22×C5C24×D311yescharacteristic
446C4×C5—22no—
447C4×C5—24no—
448C4×C5C2×#23714yes—
449Dic5—64no—
450Dic5—62no—
451Dic5—64no—
452Dic5—62no—
453Dic5—62no—
454Dic5—62no—
455C24C22×D1511yescharacteristic
456C24C22×D1512yes—
457C2×Q8—154no—
458C2×Q8—158no—
459C2×Q8—304no—
460C2×Q8—604no—
461C2×D4—24no—
462C2×D4—44no—
463C2×D4C22×D1514yes—
464C2×D4C22×D1518yes—
465C22×C4—24no—
466C22×C4—151no—
467C22×C4—151no—
468C22×C4—152no—
469C22×C4—151no—
470C22×C4—151no—
471C22×C4—152no—
472C22×C4—158no—
473C22×C4—604no—
474C22×C4C22×D1514yes—
475C22×C4C22×D1512yes—
476C22×C4C22×D1511yescharacteristic
477C22×C4C22×D1511yescharacteristic
478C4⋊C4—154no—
479C4⋊C4—154no—
480C4⋊C4—154no—
481C4⋊C4—158no—
482C4⋊C4—158no—
483C4⋊C4—158no—
484C4⋊C4C22×D1514yes—
485C22⋊C4—154no—
486C22⋊C4—154no—
487C22⋊C4—158no—
488C22⋊C4—158no—
489C22⋊C4—158no—
490C22⋊C4—158no—
491C22⋊C4C22×D1518yes—
492C42—154no—
493C42—154no—
494C42—158no—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—24no—
502C22×C3—44no—
503C22×C3—48no—
504C22×C3C2×#71112yes—
505C22×C3#414412yes—
506C22×C3#415012yes—
507C22×C3C24×D511yescharacteristic
508C3×C4—22no—
509C3×C4—24no—
510C3×C4C2×#71114yes—
511Dic3—104no—
512Dic3—102no—
513Dic3—104no—
514Dic3—102no—
515Dic3—102no—
516Dic3—102no—
517C2×C5—42no—
518C2×C5—44no—
519C2×C5#560314yescomplemented
520C2×C5C22×#23711yescharacteristic
521C2×C5C2×#100411yescharacteristic
522C2×C5C2×#101011yescharacteristic
523C23—22no—
524C23—24no—
525C23—24no—
526C23—22no—
527C23—22no—
528C23—24no—
529C23C23×D1512yes—
530C23C23×D1514yes—
531C23C23×D1511yescharacteristic
532Q8—308no—
533Q8—608no—
534D4—28no—
535D4—48no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—28no—
539C2×C4—152no—
540C2×C4—152no—
541C2×C4—154no—
542C2×C4—152no—
543C2×C4—152no—
544C2×C4—154no—
545C2×C4—304no—
546C2×C4—302no—
547C2×C4—304no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C4—302no—
551C2×C4—608no—
552C2×C4#681914yes—
553C2×C4C23×D1514yes—
554C2×C4C23×D1512yes—
555C2×C4C23×D1512yes—
556C2×C3—42no—
557C2×C3—44no—
558C2×C3#6593714yescomplemented
559C2×C3C22×#71111yescharacteristic
560C2×C3C2×#414411yescharacteristic
561C2×C3C2×#415011yescharacteristic
562C5C2×#560311yescharacteristic, complemented, Sylow
563C22—22no—
564C22—24no—
565C22—24no—
566C22—22no—
567C22—22no—
568C22—24no—
569C22—44no—
570C22—48no—
571C22C2×#681912yes—
572C22#9209512yes—
573C22#9210112yes—
574C22C24×D1511yescharacteristic
575C4—22no—
576C4—24no—
577C4—304no—
578C4—302no—
579C4—304no—
580C4—302no—
581C4—302no—
582C4—302no—
583C4C2×#681914yes—
584C3C2×#6593711yescharacteristic, complemented, Sylow
585C2—42no—
586C2—44no—
587C2#1175636214yesdirect product factor
588C2C22×#681911yescharacteristic
589C2C2×#9209511yescharacteristic
590C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
Fitting, prime radicalC2×C3×C5×#121C2
socleC23×C3×C5C24
hypercenterC2×#121D15
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#91825C2semidirect
3. C2×#91825C2semidirect
4. C2×#91824C2semidirect
5. C2×D4×Dic15C2semidirect
6. C2×#91815C2semidirect
7. C2×#91813C2semidirect
8. #11756362C2direct (N × H)
9. C2×#91777C2semidirect
10. C2×#91776C2semidirect
11. C2×#91768C2semidirect
12. C2×#91767C2semidirect
29. #91825C22semidirect
30. #91825C22semidirect
31. #91824C22semidirect
32. D4×Dic15C22semidirect
33. #91815C22semidirect
37. #91813C22semidirect
44. #91777C22semidirect
45. #91776C22semidirect
46. #91768C22semidirect
47. #91767C22semidirect
397. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
519. C2×C5#5603semidirect
558. C2×C3#65937semidirect
562. C5C2×#5603semidirect
584. C3C2×#65937semidirect
587. C2#11756362direct (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×#1212
C2×#918252
C2×#918242
C2×D4×Dic152
C2×#918152
C2×#918132
#117563622
C2×#917772
C2×#917762
C2×#917682
C2×#917672
C2×#659373
C2×#56035