Finite Group Databasebeta

← C2×#11754439 #14483957

Subgroups — C2×#11754439 #14483957

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91819C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C2×C3×#4072C211yesmaximal, characteristic, complemented
4C2×#91557C212yesmaximal, complemented
5C2×#91526C212yesmaximal, complemented
6C2×#91469C211yesmaximal, characteristic, complemented
7C2×#91460C211yesmaximal, characteristic, complemented
8#11754439C2116yesmaximal, direct product factor
9C2×#91428C211yesmaximal, characteristic, complemented
10C2×#91402C212yesmaximal, complemented
11C2×#91350C212yesmaximal, complemented
12C2×#91338C211yesmaximal, characteristic, complemented
13C2×#65897—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2212yes—
16C22×D60C2211yescharacteristic
17C22×C5×#67C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×#1204C2212yes—
20C22×#1203C2212yes—
21C22×#1200C2212yes—
22#91819C2218yescomplemented
23C2×#6714C2212yes—
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C4×C5×#67C2218yescomplemented
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×C22⋊Dic5C2212yes—
31C3×#4072C2218yescomplemented
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2212yes—
35#91557C22116yescomplemented
36C2×Dic3⋊Dic5C2212yes—
37C2×#6667C2212yes—
38C2×#6667C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40C2×Dic3×Dic5C2212yes—
41#91526C22116yescomplemented
42#91469C2218yescomplemented
43#91460C2218yescomplemented
44#91428C2218yescomplemented
45#91402C22116yescomplemented
46#91350C22116yescomplemented
47#91338C2218yescomplemented
48C2×#5532—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4084—32no—
51C2×#4076—31no—
52C2×#4076—31no—
53C2×#4072—31no—
54C2×#4072D311yescharacteristic, complemented
55#65897—316no—
56C2×#4038—32no—
57C2×#4031—32no—
58C2×#4031—32no—
59C2×C4×D20—31no—
60C2×#4015—31no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2312yes—
63C23×C5×D3C2311yescharacteristic
64C22×C3×C4×C5—24no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2314yes—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—44no—
69C2×#1220C2318yes—
70C22×Dic15C2312yes—
71C2×D60—24no—
72C2×D60C2314yes—
73C2×C5×#67—24no—
74C2×C5×#67C2314yes—
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C2×C4×C5×D3—24no—
79C2×C4×C5×D3C2314yes—
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2312yes—
82C2×#1204—44no—
83C2×#1204C2318yes—
84C2×#1203—44no—
85C2×#1203C2318yes—
86C2×#1200—28no—
87C2×#1200C2318yes—
88#6714C2318yes—
89C4⋊Dic15C2314yes—
90C5×#217C2314yes—
91C5×(C2×D3)⋊C4C2314yes—
92C5×Dic3⋊C4C2314yes—
93C4×C5×Dic3C2314yes—
94C3×C22⋊Dic5C2318yes—
95C3×C4⋊Dic5C2314yes—
96C3×C4⋊Dic5C2314yes—
97C3×C4×Dic5C2318yes—
98Dic3⋊Dic5C2318yes—
99#6667C2318yes—
100#6667C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×#117—51no—
104C2×#930—51no—
105C2×C4×#67D511yescharacteristic, complemented
106#5532—516no—
107C2×#895—51no—
108C2×#893—51no—
109C2×#892—51no—
110C2×#888—51no—
111C2×#885—52no—
112C2×#884—52no—
113C2×#875—52no—
114C2×#872—52no—
115C22×C5×D4—31no—
116C23×C4×C5—31no—
117C23×C4×C5C2×D311yescharacteristic
118C22×C22⋊D5—32no—
119C22×C22⋊D5—32no—
120C22×D20—31no—
121C22×C4×D5—32no—
122C22×Dic10—32no—
123C4×C5×D4—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C22⋊C4—31no—
126C2×C5×C22⋊C4—31no—
127C2×C42×C5—31no—
128C2×C22⋊Dic5—32no—
129C2×C22⋊Dic5C2×D312yes—
130#4084—316no—
131#4076—38no—
132#4076—38no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—32no—
136#4072—38no—
137#4072C2×D318yescomplemented
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5—32no—
140C2×C4⋊Dic5C2×D311yescharacteristic
141C2×C4⋊Dic5C2×D311yescharacteristic
142C2×C4×Dic5—32no—
143C2×C4×Dic5C2×D312yes—
144#4038—316no—
145#4031—316no—
146#4031—316no—
147C4×D20—38no—
148#4015—38no—
149C2×#555—151noSylow
150C23×C3×C5—22no—
151C23×C3×C5—22no—
152C23×C3×C5—22no—
153C23×C3×C5C2412yes—
154C23×C3×C5C2411yescharacteristic
155C22×D15—24no—
156C22×D15—24no—
157C22×D15—24no—
158C22×D15C2414yes—
159C22×C5×D3—22no—
160C22×C5×D3—22no—
161C22×C5×D3—22no—
162C22×C5×D3C2412yes—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—28no—
165C2×C3×C4×C5#4114yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168#1220—48no—
169C2×Dic15—24no—
170C2×Dic15C2414yes—
171D60—28no—
172C5×#67—28no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3—22no—
175C2×C5×Dic3#4114yes—
176C2×C5×Dic3C2412yes—
177C2×C5×Dic3C2412yes—
178C2×C5×Dic3C2412yes—
179C4×C5×D3—28no—
180C2×C3×Dic5—24no—
181C2×C3×Dic5—24no—
182C2×C3×Dic5C2414yes—
183C2×C3×Dic5C2414yes—
184#1204—48no—
185#1203—48no—
186#1200—216no—
187C23×C3×C4C2×D511yescharacteristic
188C22×#67—52no—
189C22×#67C2×D511yescharacteristic
190C22×D12—51no—
191C22×D12—52no—
192C22×C4×D3—52no—
193C22×C4×D3C2×D511yescharacteristic
194C22×Dic6—52no—
195C3×#117—58no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C4⋊C4—51no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C42—52no—
200C2×#217C2×D511yescharacteristic
201#930—58no—
202C4×#67C2×D518yescomplemented
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4—52no—
206C2×(C2×D3)⋊C4—52no—
207C2×(C2×D3)⋊C4C2×D511yescharacteristic
208C2×C4⋊Dic3—51no—
209C2×Dic3⋊C4—52no—
210C2×Dic3⋊C4C2×D511yescharacteristic
211C2×C4×Dic3—52no—
212C2×C4×Dic3C2×D511yescharacteristic
213#895—58no—
214#893—58no—
215#892—58no—
216#888—58no—
217#885—516no—
218#884—516no—
219#875—516no—
220#872—516no—
221C24×C5—31no—
222C24×C5C22×D311yescharacteristic
223C23×D5—32no—
224C2×C5×D4—34no—
225C2×C5×D4—64no—
226C22×C4×C5—24no—
227C22×C4×C5—31no—
228C22×C4×C5—31no—
229C22×C4×C5—31no—
230C22×C4×C5—34no—
231C22×C4×C5—64no—
232C22×C4×C5C22×D311yescharacteristic
233C22×C4×C5C22×D314yes—
234C22×C4×C5C22×D311yescharacteristic
235C2×C22⋊D5—38no—
236C2×C22⋊D5—38no—
237C2×C22⋊D5—124no—
238C2×C22⋊D5—124no—
239C22×Dic5—32no—
240C22×Dic5C22×D312yes—
241C22×Dic5C22×D312yes—
242C2×D20—34no—
243C2×D20—64no—
244C2×C4×D5—38no—
245C2×C4×D5—68no—
246C2×Dic10—38no—
247C2×Dic10—124no—
248C5×C4⋊C4—34no—
249C5×C22⋊C4—34no—
250C5×C22⋊C4—34no—
251C42×C5—34no—
252C22⋊Dic5—38no—
253C22⋊Dic5C22×D318yes—
254#685—38no—
255#685—38no—
256#685—38no—
257C4⋊Dic5—34no—
258C4⋊Dic5—38no—
259C4⋊Dic5C22×D314yes—
260C4⋊Dic5C22×D314yes—
261C4×Dic5—38no—
262C4×Dic5C22×D318yes—
263#555—1516no—
264C2×C4⋊Q8—151no—
265C2×#124—152no—
266C2×#124—152no—
267C2×#121—152no—
268C2×#121—151no—
269C2×#121—151no—
270C2×C4×D4—31no—
271C2×C4×D4—151no—
272C2×#117—51no—
273C2×#117—152no—
274C2×#117—151no—
275C22×C3×C5—22no—
276C22×C3×C5—22no—
277C22×C3×C5—22no—
278C22×C3×C5—44no—
279C22×C3×C5C2×#4112yes—
280C22×C3×C5C2×#4112yes—
281C22×C3×C5H(5,𝔽2)12yes—
282C22×C3×C5C2511yescharacteristic
283C2×D15—24no—
284C2×D15—24no—
285C2×D15—24no—
286C2×D15—48no—
287C2×C5×D3—22no—
288C2×C5×D3—22no—
289C2×C5×D3—22no—
290C2×C5×D3—44no—
291C3×C4×C5—22no—
292C3×C4×C5C2×#4114yes—
293Dic15—24no—
294C3×Dic5—24no—
295C3×Dic5—24no—
296C5×Dic3—22no—
297C5×Dic3—22no—
298C5×Dic3C2×#4114yes—
299C24×C3C22×D511yescharacteristic
300C23×D3—52no—
301C23×D3C22×D511yescharacteristic
302C22×C3×C4—24no—
303C22×C3×C4—52no—
304C22×C3×C4—52no—
305C22×C3×C4C22×D511yescharacteristic
306C22×C3×C4C22×D514yes—
307C22×C3×C4C22×D511yescharacteristic
308C2×#67—24no—
309C2×#67—58no—
310C2×#67—204no—
311C2×#67C22×D514yes—
312C22×Dic3—52no—
313C22×Dic3C22×D511yescharacteristic
314C22×Dic3C22×D511yescharacteristic
315C22×Dic3C22×D511yescharacteristic
316C2×D12—54no—
317C2×D12—58no—
318C2×D12—104no—
319C2×D12—204no—
320C2×C4×D3—24no—
321C2×C4×D3—58no—
322C2×C4×D3—108no—
323C2×C4×D3C22×D514yes—
324C2×Dic6—58no—
325C2×Dic6—204no—
326C3×C4⋊C4—54no—
327C3×C4⋊C4—54no—
328C3×C22⋊C4—58no—
329C3×C42—58no—
330#217C22×D514yes—
331(C2×D3)⋊C4—58no—
332(C2×D3)⋊C4—58no—
333(C2×D3)⋊C4—58no—
334(C2×D3)⋊C4—58no—
335(C2×D3)⋊C4C22×D514yes—
336C4⋊Dic3—54no—
337Dic3⋊C4—58no—
338Dic3⋊C4C22×D514yes—
339C4×Dic3—58no—
340C4×Dic3C22×D514yes—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—32no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5C23×D312yes—
349C23×C5C23×D311yescharacteristic
350C22×D5—34no—
351C22×D5—64no—
352C22×D5—64no—
353C22×D5—64no—
354C5×D4—68no—
355C2×C4×C5—22no—
356C2×C4×C5—28no—
357C2×C4×C5—34no—
358C2×C4×C5—32no—
359C2×C4×C5—32no—
360C2×C4×C5—32no—
361C2×C4×C5—62no—
362C2×C4×C5—62no—
363C2×C4×C5—68no—
364C2×C4×C5#23514yes—
365C2×C4×C5C23×D312yes—
366C2×C4×C5C23×D312yes—
367C22⋊D5—128no—
368C22⋊D5—128no—
369C2×Dic5—24no—
370C2×Dic5—24no—
371C2×Dic5—34no—
372C2×Dic5—64no—
373C2×Dic5C23×D314yes—
374C2×Dic5C23×D314yes—
375D20—68no—
376C4×D5—616no—
377Dic10—128no—
378C22×Q8—152no—
379C22×D4—31no—
380C22×D4—152no—
381C22×D4—152no—
382C22×D4—151no—
383C23×C4—31no—
384C23×C4—152no—
385C23×C4D3×D511yescharacteristic
386C4⋊Q8—158no—
387#124—1516no—
388#124—1516no—
389#121—1516no—
390#121—158no—
391#121—158no—
392C4×D4—38no—
393C4×D4—158no—
394#117—58no—
395#117—1516no—
396#117—158no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—51no—
399C2×C4⋊C4—51no—
400C2×C4⋊C4—152no—
401C2×C4⋊C4—151no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—52no—
405C2×C22⋊C4—152no—
406C2×C22⋊C4—152no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—152no—
409C2×C42—31no—
410C2×C42—52no—
411C2×C42—152no—
412C2×C3×C5—42no—
413C2×C3×C5#55514yescomplemented
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C22×#4111yescharacteristic
416C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
417D15—44no—
418C5×D3—42no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3C23×D512yes—
423C23×C3C23×D511yescharacteristic
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—54no—
428C22×D3—104no—
429C22×D3—104no—
430C22×D3—104no—
431C22×D3C23×D512yes—
432C2×C3×C4—22no—
433C2×C3×C4—28no—
434C2×C3×C4—54no—
435C2×C3×C4—54no—
436C2×C3×C4—104no—
437C2×C3×C4—104no—
438C2×C3×C4#71114yes—
439C2×C3×C4C23×D512yes—
440C2×C3×C4C23×D512yes—
441#67—28no—
442#67—208no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—54no—
446C2×Dic3—104no—
447C2×Dic3#70914yes—
448C2×Dic3C23×D512yes—
449C2×Dic3C23×D512yes—
450C2×Dic3C23×D512yes—
451D12—108no—
452D12—208no—
453C4×D3—28no—
454C4×D3—1016no—
455Dic6—208no—
456C22×C5—22no—
457C22×C5—22no—
458C22×C5—22no—
459C22×C5—44no—
460C22×C5—62no—
461C22×C5—62no—
462C22×C5—62no—
463C22×C5—124no—
464C22×C5C2×#23512yes—
465C22×C5D3×#4112yes—
466C22×C5#100912yes—
467C22×C5C24×D311yescharacteristic
468C2×D5—64no—
469C2×D5—64no—
470C2×D5—64no—
471C2×D5—128no—
472C4×C5—22no—
473C4×C5—34no—
474C4×C5—62no—
475C4×C5—62no—
476C4×C5C2×#23514yes—
477Dic5—24no—
478Dic5—24no—
479Dic5—64no—
480C24—31no—
481C24—152no—
482C24C2×D3×D511yescharacteristic
483C2×Q8—158no—
484C2×Q8—604no—
485C2×D4—34no—
486C2×D4—64no—
487C2×D4—158no—
488C2×D4—158no—
489C2×D4—154no—
490C2×D4—304no—
491C2×D4—604no—
492C2×D4—604no—
493C22×C4—24no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—34no—
498C22×C4—52no—
499C22×C4—52no—
500C22×C4—64no—
501C22×C4—158no—
502C22×C4—152no—
503C22×C4—308no—
504C22×C4C2×D3×D514yes—
505C22×C4C2×D3×D511yescharacteristic
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—54no—
509C4⋊C4—54no—
510C4⋊C4—158no—
511C4⋊C4—154no—
512C22⋊C4—34no—
513C22⋊C4—34no—
514C22⋊C4—58no—
515C22⋊C4—158no—
516C22⋊C4—158no—
517C22⋊C4—158no—
518C22⋊C4—158no—
519C42—34no—
520C42—58no—
521C42—158no—
522C3×C5C2×#55511yescharacteristic, complemented, Hall
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—44no—
527C22×C3C2×#70912yes—
528C22×C3C2×#71112yes—
529C22×C3#414912yes—
530C22×C3C24×D511yescharacteristic
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—44no—
535C2×D3—104no—
536C2×D3—104no—
537C2×D3—104no—
538C2×D3—208no—
539C3×C4—22no—
540C3×C4—104no—
541C3×C4—104no—
542C3×C4C2×#71114yes—
543Dic3—22no—
544Dic3—22no—
545Dic3—104no—
546Dic3C2×#70914yes—
547C2×C5—42no—
548C2×C5—122no—
549C2×C5#553214yescomplemented
550C2×C5C22×#23511yescharacteristic
551C2×C5C2×D3×#4111yescharacteristic
552C2×C5C2×#100911yescharacteristic
553D5—124no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—32no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23—154no—
562C23—304no—
563C23—304no—
564C23—304no—
565C23C22×D3×D512yes—
566C23C22×D3×D511yescharacteristic
567Q8—608no—
568D4—68no—
569D4—308no—
570D4—608no—
571D4—608no—
572C2×C4—22no—
573C2×C4—28no—
574C2×C4—34no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—54no—
579C2×C4—54no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—68no—
583C2×C4—104no—
584C2×C4—104no—
585C2×C4—154no—
586C2×C4—3016no—
587C2×C4—304no—
588C2×C4#678214yes—
589C2×C4C22×D3×D512yes—
590C2×C4C22×D3×D512yes—
591C2×C3—42no—
592C2×C3#6589714yescomplemented
593C2×C3C22×#70911yescharacteristic
594C2×C3C22×#71111yescharacteristic
595C2×C3C2×#414911yescharacteristic
596D3—42no—
597D3—204no—
598C5C2×#553211yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—44no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—124no—
607C22—304no—
608C22—304no—
609C22—304no—
610C22—608no—
611C22D3×#70912yes—
612C22#9201912yes—
613C22C2×#678212yes—
614C22C23×D3×D511yescharacteristic
615C4—22no—
616C4—34no—
617C4—62no—
618C4—62no—
619C4—104no—
620C4—104no—
621C4—304no—
622C4C2×#678214yes—
623C3C2×#6589711yescharacteristic, complemented, Sylow
624C2—42no—
625C2—122no—
626C2—604no—
627C2#1175443914yesdirect product factor
628C2C2×D3×#70911yescharacteristic
629C2C2×#9201911yescharacteristic
630C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#555
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91819C2semidirect
2. C2×C4×C5×#67C2semidirect
3. C2×C3×#4072C2semidirect
4. C2×#91557C2semidirect
5. C2×#91526C2semidirect
6. C2×#91469C2semidirect
7. C2×#91460C2semidirect
8. #11754439C2direct (N × H)
9. C2×#91428C2semidirect
10. C2×#91402C2semidirect
11. C2×#91350C2semidirect
12. C2×#91338C2semidirect
22. #91819C22semidirect
26. C4×C5×#67C22semidirect
31. C3×#4072C22semidirect
35. #91557C22semidirect
41. #91526C22semidirect
42. #91469C22semidirect
43. #91460C22semidirect
44. #91428C22semidirect
45. #91402C22semidirect
46. #91350C22semidirect
47. #91338C22semidirect
54. C2×#4072D3semidirect
105. C2×C4×#67D5semidirect
137. #4072C2×D3semidirect
202. C4×#67C2×D5semidirect
413. C2×C3×C5#555semidirect
522. C3×C5C2×#555semidirect
549. C2×C5#5532semidirect
592. C2×C3#65897semidirect
598. C5C2×#5532semidirect
623. C3C2×#65897semidirect
627. C2#11754439direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918192
C2×C4×C5×#672
C2×C3×#40722
C2×#915572
C2×#915262
C2×#914692
C2×#914602
#117544392
C2×#914282
C2×#914022
C2×#913502
C2×#913382
C2×#658973
C2×#55325