Finite Group Databasebeta

← C2×#11754749 #14481393

Subgroups — C2×#11754749 #14481393

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×#91825C211yesmaximal, characteristic, complemented
2C2×C5×#938C211yesmaximal, characteristic
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C2×#91574C212yesmaximal, complemented
5C2×#91539C212yesmaximal, complemented
6C2×#91530C212yesmaximal, complemented
7C2×#91525C212yesmaximal, complemented
8#11754749C2116yesmaximal, direct product factor
9C2×#91470C211yesmaximal, characteristic, complemented
10C2×#91371C211yesmaximal, characteristic, complemented
11C2×#91365C211yesmaximal, characteristic, complemented
12C2×#91333C211yesmaximal, characteristic, complemented
13C2×#65937—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C22×C5×#67C2212yes—
17C22×C4×C5×D3C2211yescharacteristic
18C23×C3×Dic5C2212yes—
19C22×#1204C2212yes—
20C2×#6719C2212yes—
21C2×#6719C2212yes—
22#91825C2218yescomplemented
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×#217C2212yes—
25C5×#938C2218yes—
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C3×C22⋊Dic5C2212yes—
28C3×D4×Dic5C2218yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31#91574C22116yescomplemented
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6669C2212yes—
35C2×#6669C2212yes—
36C2×#6668C2212yes—
37#91539C22116yescomplemented
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41#91530C22116yescomplemented
42C2×Dic3×Dic5C2212yes—
43#91525C22116yescomplemented
44#91470C2218yescomplemented
45#91371C2218yescomplemented
46#91365C2218yescomplemented
47#91333C2218yescomplemented
48C2×#5561—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4082—31no—
51C2×#4082—32no—
52C2×#4081—32no—
53C2×D4×Dic5D311yescharacteristic, complemented
54C2×#4072—31no—
55C2×#4070—31no—
56#65937—316no—
57C2×#4034—31no—
58C2×#4033—31no—
59C2×#4025—32no—
60C2×#4024—32no—
61C24×C3×C5C2312yes—
62C23×C5×D3C2311yescharacteristic
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4C2314yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C2×Dic30—24no—
70C2×Dic30C2314yes—
71C2×C5×#67—44no—
72C2×C5×#67C2318yes—
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2311yescharacteristic
75C2×C4×C5×D3—24no—
76C2×C4×C5×D3C2314yes—
77C22×C3×Dic5—44no—
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2318yes—
82C2×#1204—44no—
83C2×#1204C2318yes—
84#6719C2318yes—
85#6719C2318yes—
86C4×Dic15C2314yes—
87C5×#217C2318yes—
88C5×C4⋊Dic3C2314yes—
89C3×C22⋊Dic5C2318yes—
90C3×C4⋊Dic5C2314yes—
91C3×C4×Dic5C2314yes—
92Dic3⋊Dic5C2314yes—
93Dic3⋊Dic5C2314yes—
94#6669C2318yes—
95#6669C2318yes—
96#6668C2318yes—
97(C2×D3)⋊Dic5C2314yes—
98(C2×D3)⋊Dic5C2318yes—
99(C2×D3)⋊Dic5C2314yes—
100Dic3×Dic5C2318yes—
101C2×C3×C4×D4—51no—
102C2×#938D511yescharacteristic
103C2×#936—51no—
104C2×#929—52no—
105C2×#924—52no—
106#5561—516no—
107C2×#897—51no—
108C2×#888—51no—
109C2×#885—52no—
110C2×#879—52no—
111C2×#872—51no—
112C2×C4×Dic6—51no—
113C22×C5×D4—32no—
114C22×C5×D4C2×D311yescharacteristic
115C23×C4×C5—31no—
116C23×Dic5C2×D312yes—
117C22×Dic10—31no—
118C22×Dic10—32no—
119C5×#121—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C22⋊C4—32no—
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5—32no—
125C2×C22⋊Dic5—31no—
126C2×C22⋊Dic5—31no—
127C2×C22⋊Dic5C2×D312yes—
128#4082—38no—
129#4082—316no—
130#4081—316no—
131D4×Dic5C2×D318yescomplemented
132#4072—38no—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—31no—
135C2×C4⋊Dic5C2×D311yescharacteristic
136#4070—38no—
137C2×#683—32no—
138C2×#683—32no—
139C2×#683—32no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—32no—
142C2×C4×Dic5C2×D311yescharacteristic
143#4034—38no—
144#4033—38no—
145#4025—316no—
146#4024—316no—
147C2×#542—151noSylow
148C23×C3×C5—24no—
149C23×C3×C5—24no—
150C23×C3×C5—24no—
151C23×C3×C5C2414yes—
152C23×C3×C5C2411yescharacteristic
153C22×C5×D3—22no—
154C22×C5×D3—22no—
155C22×C5×D3—22no—
156C22×C5×D3C2412yes—
157C3×C5×D4—28no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×Dic15—24no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15C2414yes—
164C2×Dic15C2412yes—
165C2×Dic15C2412yes—
166Dic30—28no—
167C5×#67—48no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3C2414yes—
171C2×C5×Dic3C2412yes—
172C4×C5×D3—28no—
173C2×C3×Dic5—24no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—48no—
177C2×C3×Dic5C2412yes—
178C2×C3×Dic5C2414yes—
179C2×C3×Dic5C2412yes—
180#1204—48no—
181C22×C3×D4C2×D511yescharacteristic
182C23×C3×C4—52no—
183C22×#67C2×D512yes—
184C22×C4×D3C2×D511yescharacteristic
185C22×Dic6—51no—
186C22×Dic6—52no—
187C3×C4×D4—58no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C22⋊C4—52no—
190C2×C3×C42—51no—
191C2×#217—52no—
192C2×#217—52no—
193C2×#217C2×D512yes—
194#938C2×D518yes—
195#936—58no—
196#929—516no—
197C2×(C2×D3)⋊C4—51no—
198C2×(C2×D3)⋊C4—51no—
199C2×(C2×D3)⋊C4—52no—
200C2×C4⋊Dic3—52no—
201C2×C4⋊Dic3C2×D511yescharacteristic
202#924—516no—
203C2×Dic3⋊C4—52no—
204C2×Dic3⋊C4—51no—
205C2×Dic3⋊C4—51no—
206C2×Dic3⋊C4—52no—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—52no—
209#897—58no—
210#888—58no—
211#885—516no—
212#879—516no—
213#872—58no—
214C4×Dic6—58no—
215C24×C5—31no—
216C24×C5C22×D312yes—
217C2×C5×D4—24no—
218C2×C5×D4—38no—
219C2×C5×D4—124no—
220C2×C5×D4C22×D314yes—
221C22×C4×C5—31no—
222C22×C4×C5—32no—
223C22×C4×C5—34no—
224C22×C4×C5—64no—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—31no—
227C22×Dic5—32no—
228C22×Dic5—31no—
229C22×Dic5—44no—
230C22×Dic5C22×D311yescharacteristic
231C22×Dic5C22×D312yes—
232C22×Dic5C22×D311yescharacteristic
233C22×Dic5C22×D318yes—
234C2×Dic10—34no—
235C2×Dic10—38no—
236C2×Dic10—64no—
237C2×Dic10—124no—
238C5×C4⋊C4—34no—
239C5×C22⋊C4—38no—
240C22⋊Dic5—38no—
241C22⋊Dic5—38no—
242C22⋊Dic5—38no—
243C22⋊Dic5—34no—
244C22⋊Dic5—34no—
245C22⋊Dic5C22×D318yes—
246C4⋊Dic5—34no—
247C4⋊Dic5—34no—
248C4⋊Dic5C22×D314yes—
249#683—38no—
250#683—38no—
251#683—38no—
252C4×Dic5—34no—
253C4×Dic5—38no—
254C4×Dic5C22×D314yes—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—152no—
259C2×#124—151no—
260C2×#123—152no—
261C2×C22⋊Q8—152no—
262C2×C22⋊Q8—151no—
263C2×#121—31no—
264C2×C4×Q8—151no—
265C2×C4×D4—51no—
266C2×#117—151no—
267C22×C3×C5—24no—
268C22×C3×C5—24no—
269C22×C3×C5—24no—
270C22×C3×C5—48no—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C22×C3×C52−1+412yes—
274C22×C3×C5C2511yescharacteristic
275C2×C5×D3—22no—
276C2×C5×D3—22no—
277C2×C5×D3—22no—
278C2×C5×D3—44no—
279C3×C4×C5C2×#4114yes—
280Dic15—24no—
281Dic15—22no—
282Dic15—22no—
283C3×Dic5—24no—
284C3×Dic5—22no—
285C3×Dic5—22no—
286C5×Dic3—22no—
287C5×Dic3—24no—
288C24×C3C22×D512yes—
289C23×D3C22×D511yescharacteristic
290C2×C3×D4—24no—
291C2×C3×D4C22×D514yes—
292C22×C3×C4—51no—
293C22×C3×C4—51no—
294C22×C3×C4—52no—
295C22×C3×C4—58no—
296C22×C3×C4—204no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—44no—
299C2×#67C22×D518yes—
300C22×Dic3—51no—
301C22×Dic3—52no—
302C22×Dic3—51no—
303C22×Dic3C22×D512yes—
304C22×Dic3C22×D511yescharacteristic
305C2×C4×D3—24no—
306C2×C4×D3C22×D514yes—
307C2×Dic6—54no—
308C2×Dic6—58no—
309C2×Dic6—104no—
310C2×Dic6—204no—
311C3×C4⋊C4—54no—
312C3×C22⋊C4—58no—
313C3×C42—54no—
314#217—58no—
315#217—58no—
316#217C22×D518yes—
317(C2×D3)⋊C4—54no—
318(C2×D3)⋊C4—54no—
319(C2×D3)⋊C4—58no—
320C4⋊Dic3—58no—
321C4⋊Dic3C22×D514yes—
322Dic3⋊C4—58no—
323Dic3⋊C4—58no—
324Dic3⋊C4—54no—
325Dic3⋊C4—54no—
326C4×Dic3—54no—
327C4×Dic3—58no—
328C23×C5—24no—
329C23×C5—24no—
330C23×C5—24no—
331C23×C5—32no—
332C23×C5—62no—
333C23×C5—62no—
334C23×C5—62no—
335C23×C5C23×D314yes—
336C23×C5C23×D311yescharacteristic
337C5×D4—28no—
338C5×D4—128no—
339C2×C4×C5—34no—
340C2×C4×C5—32no—
341C2×C4×C5—62no—
342C2×C4×C5—64no—
343C2×C4×C5—68no—
344C2×C4×C5#23514yes—
345C2×C4×C5C23×D312yes—
346C2×Dic5—24no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—32no—
350C2×Dic5—34no—
351C2×Dic5—32no—
352C2×Dic5—48no—
353C2×Dic5—64no—
354C2×Dic5—62no—
355C2×Dic5—62no—
356C2×Dic5C23×D312yes—
357C2×Dic5C23×D312yes—
358C2×Dic5C23×D314yes—
359Dic10—68no—
360Dic10—128no—
361C22×Q8—152no—
362C22×Q8—151no—
363C22×D4—32no—
364C22×D4D3×D511yescharacteristic
365C23×C4—31no—
366C23×C4—52no—
367C4⋊Q8—158no—
368#126—1516no—
369#124—1516no—
370#124—158no—
371#123—1516no—
372C22⋊Q8—1516no—
373C22⋊Q8—158no—
374#121—38no—
375C4×Q8—158no—
376C4×D4—58no—
377#117—158no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—51no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—151no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—152no—
384C2×C4⋊C4—152no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—52no—
387C2×C22⋊C4—151no—
388C2×C22⋊C4—151no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C42—51no—
393C2×C42—152no—
394C2×C42—151no—
395C2×C3×C5—44no—
396C2×C3×C5#54214yescomplemented
397C2×C3×C5C22×#4111yescharacteristic
398C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
399C2×C3×C5C2×2−1+411yescharacteristic
400C5×D3—42no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3C23×D514yes—
405C23×C3C23×D511yescharacteristic
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3C23×D512yes—
410C3×D4—28no—
411C2×C3×C4—52no—
412C2×C3×C4—52no—
413C2×C3×C4—54no—
414C2×C3×C4—104no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4—208no—
418C2×C3×C4#71114yes—
419C2×C3×C4C23×D512yes—
420#67—48no—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—52no—
424C2×Dic3—54no—
425C2×Dic3—52no—
426C2×Dic3—104no—
427C2×Dic3—102no—
428C2×Dic3—102no—
429C2×Dic3C23×D514yes—
430C2×Dic3C23×D512yes—
431C4×D3—28no—
432Dic6—108no—
433Dic6—208no—
434C22×C5—24no—
435C22×C5—24no—
436C22×C5—24no—
437C22×C5—48no—
438C22×C5—62no—
439C22×C5—62no—
440C22×C5—62no—
441C22×C5—124no—
442C22×C5C2×#23512yes—
443C22×C5#100412yes—
444C22×C5#101012yes—
445C22×C5C24×D311yescharacteristic
446C4×C5—62no—
447C4×C5—64no—
448C4×C5C2×#23514yes—
449Dic5—24no—
450Dic5—22no—
451Dic5—22no—
452Dic5—64no—
453Dic5—62no—
454Dic5—62no—
455C24—31no—
456C24C2×D3×D512yes—
457C2×Q8—158no—
458C2×Q8—154no—
459C2×Q8—304no—
460C2×Q8—604no—
461C2×D4—24no—
462C2×D4—38no—
463C2×D4—124no—
464C2×D4C2×D3×D514yes—
465C22×C4—32no—
466C22×C4—31no—
467C22×C4—34no—
468C22×C4—51no—
469C22×C4—51no—
470C22×C4—52no—
471C22×C4—58no—
472C22×C4—64no—
473C22×C4—151no—
474C22×C4—152no—
475C22×C4—151no—
476C22×C4—204no—
477C22×C4C2×D3×D511yescharacteristic
478C4⋊C4—34no—
479C4⋊C4—54no—
480C4⋊C4—154no—
481C4⋊C4—154no—
482C4⋊C4—158no—
483C4⋊C4—158no—
484C4⋊C4—158no—
485C22⋊C4—38no—
486C22⋊C4—58no—
487C22⋊C4—154no—
488C22⋊C4—154no—
489C22⋊C4—158no—
490C22⋊C4—158no—
491C22⋊C4—158no—
492C42—54no—
493C42—158no—
494C42—154no—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—24no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—48no—
500C22×C3C2×#71112yes—
501C22×C3#414412yes—
502C22×C3#415012yes—
503C22×C3C24×D511yescharacteristic
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—22no—
507C2×D3—44no—
508C3×C4—104no—
509C3×C4—102no—
510C3×C4—102no—
511C3×C4C2×#71114yes—
512Dic3—22no—
513Dic3—24no—
514Dic3—104no—
515Dic3—102no—
516Dic3—102no—
517C2×C5—44no—
518C2×C5—122no—
519C2×C5#556114yescomplemented
520C2×C5C22×#23511yescharacteristic
521C2×C5C2×#100411yescharacteristic
522C2×C5C2×#101011yescharacteristic
523C23—24no—
524C23—24no—
525C23—24no—
526C23—32no—
527C23—62no—
528C23—62no—
529C23—62no—
530C23C22×D3×D514yes—
531C23C22×D3×D511yescharacteristic
532Q8—308no—
533Q8—608no—
534D4—28no—
535D4—128no—
536C2×C4—34no—
537C2×C4—32no—
538C2×C4—52no—
539C2×C4—52no—
540C2×C4—54no—
541C2×C4—64no—
542C2×C4—62no—
543C2×C4—68no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—104no—
547C2×C4—152no—
548C2×C4—154no—
549C2×C4—152no—
550C2×C4—208no—
551C2×C4—302no—
552C2×C4—302no—
553C2×C4—304no—
554C2×C4#678214yes—
555C2×C4C22×D3×D512yes—
556C2×C3—44no—
557C2×C3#6593714yescomplemented
558C2×C3C22×#71111yescharacteristic
559C2×C3C2×#414411yescharacteristic
560C2×C3C2×#415011yescharacteristic
561D3—42no—
562C5C2×#556111yescharacteristic, complemented, Sylow
563C22—24no—
564C22—24no—
565C22—24no—
566C22—48no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22—124no—
571C22#9202012yes—
572C22#9202512yes—
573C22C2×#678212yes—
574C22C23×D3×D511yescharacteristic
575C4—62no—
576C4—64no—
577C4—102no—
578C4—102no—
579C4—104no—
580C4—304no—
581C4—302no—
582C4—302no—
583C4C2×#678214yes—
584C3C2×#6593711yescharacteristic, complemented, Sylow
585C2—44no—
586C2—122no—
587C2#1175474914yesdirect product factor
588C2C2×#9202011yescharacteristic
589C2C2×#9202511yescharacteristic
590C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×C5×#938C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91825C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C2×#91574C2semidirect
5. C2×#91539C2semidirect
6. C2×#91530C2semidirect
7. C2×#91525C2semidirect
8. #11754749C2direct (N × H)
9. C2×#91470C2semidirect
10. C2×#91371C2semidirect
11. C2×#91365C2semidirect
12. C2×#91333C2semidirect
22. #91825C22semidirect
28. C3×D4×Dic5C22semidirect
31. #91574C22semidirect
37. #91539C22semidirect
41. #91530C22semidirect
43. #91525C22semidirect
44. #91470C22semidirect
45. #91371C22semidirect
46. #91365C22semidirect
47. #91333C22semidirect
53. C2×D4×Dic5D3semidirect
131. D4×Dic5C2×D3semidirect
396. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
519. C2×C5#5561semidirect
557. C2×C3#65937semidirect
562. C5C2×#5561semidirect
584. C3C2×#65937semidirect
587. C2#11754749direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918252
C2×C5×#9382
C2×C3×D4×Dic52
C2×#915742
C2×#915392
C2×#915302
C2×#915252
#117547492
C2×#914702
C2×#913712
C2×#913652
C2×#913332
C2×#659373
C2×#55615