Finite Group Databasebeta

← C2×#11754903 #14484748

Subgroups — C2×#11754903 #14484748

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91829C211yesmaximal, characteristic
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4082C211yesmaximal, characteristic, complemented
4C2×#91562C212yesmaximal, complemented
5C2×#91556C212yesmaximal, complemented
6C2×#91542C212yesmaximal, complemented
7C2×#91526C212yesmaximal, complemented
8#11754903C2116yesmaximal, direct product factor
9C2×C4×#1204C211yesmaximal, characteristic, complemented
10C2×#91418C211yesmaximal, characteristic, complemented
11C2×#91374C211yesmaximal, characteristic, complemented
12C2×#91331C211yesmaximal, characteristic, complemented
13C2×#65893—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×#1220C2212yes—
16C22×#1220C2212yes—
17C22×D60C2211yescharacteristic
18C23×C5×Dic3C2212yes—
19C22×C3×Dic10C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×#1200C2212yes—
22#91829C2218yes—
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×#217C2212yes—
25C5×D4×Dic3C2218yescomplemented
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C2×C3×C22⋊Dic5C2212yes—
30C3×#4082C2218yescomplemented
31C2×C3×C4×Dic5C2211yescharacteristic
32#91562C22116yescomplemented
33#91556C22116yescomplemented
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36#91542C22116yescomplemented
37C2×#6668C2211yescharacteristic
38C2×#6668C2212yes—
39C2×#6667C2212yes—
40C2×#6667C2212yes—
41C2×#6667C2212yes—
42C2×Dic3×Dic5C2212yes—
43#91526C22116yescomplemented
44C4×#1204C2218yescomplemented
45#91418C2218yescomplemented
46#91374C2218yescomplemented
47#91331C2218yescomplemented
48C2×#5681—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4086—31no—
51C2×#4082D311yescharacteristic, complemented
52C2×#4075—32no—
53C2×C4×C22⋊D5—32no—
54#65893—316no—
55C2×#4039—31no—
56C2×#4033—31no—
57C2×#4031—32no—
58C2×#4029—32no—
59C2×#4021—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2312yes—
62C23×D15C2312yes—
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4C2314yes—
65C22×C3×C4×C5C2311yescharacteristic
66C2×#1220—28no—
67C2×#1220—44no—
68C2×#1220C2318yes—
69C2×#1220C2318yes—
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2311yescharacteristic
72C2×D60—24no—
73C2×D60C2314yes—
74C22×C5×Dic3—44no—
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2311yescharacteristic
77C22×C5×Dic3C2312yes—
78C22×C5×Dic3C2318yes—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C2×C3×Dic10—24no—
83C2×C3×Dic10C2314yes—
84C2×#1204—24no—
85C2×#1204C2314yes—
86C2×#1200—44no—
87C2×#1200C2318yes—
88C4×Dic15C2314yes—
89C5×#217C2318yes—
90C5×C4⋊Dic3C2314yes—
91C4×C5×Dic3C2314yes—
92C3×C22⋊Dic5C2318yes—
93C3×C22⋊Dic5C2318yes—
94C3×C4×Dic5C2314yes—
95Dic3⋊Dic5C2314yes—
96#6669C2314yes—
97#6668C2314yes—
98#6668C2318yes—
99#6667C2318yes—
100#6667C2318yes—
101#6667C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×#124—51no—
104C2×#947—51no—
105C2×Q8×Dic3—51no—
106C2×#940—51no—
107C2×D4×Dic3D511yescharacteristic, complemented
108#5681—516no—
109C2×#886—52no—
110C2×#885—52no—
111C2×#883—52no—
112C2×#67⋊C4—52no—
113C2×C4×D12—51no—
114C2×C4×Dic6—51no—
115C22×C5×D4C2×D311yescharacteristic
116C23×C4×C5—32no—
117C22×C22⋊D5—32no—
118C22×C22⋊D5—32no—
119C22×D20—31no—
120C22×C4×D5—32no—
121C22×Dic10—31no—
122C22×Dic10C2×D311yescharacteristic
123C4×C5×D4—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C22⋊C4—32no—
126C2×C42×C5—31no—
127C2×C22⋊Dic5C2×D312yes—
128C2×C22⋊Dic5C2×D312yes—
129#4086—38no—
130#4082C2×D318yescomplemented
131#4075—316no—
132C4×C22⋊D5—316no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—32no—
136C2×C4⋊Dic5—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×#683—32no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—32no—
142C2×C4×Dic5C2×D311yescharacteristic
143#4039—38no—
144#4033—38no—
145#4031—316no—
146#4029—316no—
147#4021—38no—
148C4×Dic10—38no—
149C2×#559—151noSylow
150C23×C3×C5—24no—
151C23×C3×C5—24no—
152C23×C3×C5—24no—
153C23×C3×C5C2414yes—
154C23×C3×C5C2411yescharacteristic
155C22×D15—24no—
156C22×D15—24no—
157C22×D15—24no—
158C22×D15C2414yes—
159C3×C5×D4—28no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162#1220—216no—
163#1220—48no—
164C2×Dic15—22no—
165C2×Dic15#4114yes—
166C2×Dic15C2412yes—
167C2×Dic15C2412yes—
168D60—28no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—48no—
173C2×C5×Dic3C2414yes—
174C2×C5×Dic3C2412yes—
175C2×C5×Dic3C2412yes—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—24no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5C2414yes—
180C2×C3×Dic5C2412yes—
181C2×C3×Dic5C2412yes—
182C3×Dic10—28no—
183#1204—28no—
184#1200—48no—
185C22×C3×Q8—51no—
186C22×C3×D4C2×D511yescharacteristic
187C22×#67—52no—
188C22×#67—52no—
189C23×Dic3C2×D512yes—
190C22×D12—51no—
191C22×C4×D3—52no—
192C22×Dic6—51no—
193C3×#124—58no—
194C2×C3×C22⋊C4—52no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C42—51no—
197C2×#217C2×D512yes—
198#947—58no—
199Q8×Dic3—58no—
200#940—58no—
201D4×Dic3C2×D518yescomplemented
202C2×(C2×D3)⋊C4—52no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×C4⋊Dic3—51no—
206C2×C4⋊Dic3—52no—
207C2×C4⋊Dic3C2×D511yescharacteristic
208C2×Dic3⋊C4—51no—
209C2×Dic3⋊C4—51no—
210C2×C4×Dic3—51no—
211C2×C4×Dic3—52no—
212C2×C4×Dic3C2×D511yescharacteristic
213#886—516no—
214#885—516no—
215#883—516no—
216#67⋊C4—516no—
217C4×D12—58no—
218C4×Dic6—58no—
219C24×C5C22×D312yes—
220C23×D5—32no—
221C2×C5×D4—24no—
222C2×C5×D4C22×D314yes—
223C22×C4×C5—31no—
224C22×C4×C5—31no—
225C22×C4×C5—32no—
226C22×C4×C5—38no—
227C22×C4×C5—124no—
228C22×C4×C5C22×D311yescharacteristic
229C2×C22⋊D5—38no—
230C2×C22⋊D5—38no—
231C2×C22⋊D5—68no—
232C2×C22⋊D5—124no—
233C22×Dic5—31no—
234C22×Dic5—31no—
235C22×Dic5C22×D311yescharacteristic
236C22×Dic5C22×D312yes—
237C22×Dic5C22×D311yescharacteristic
238C2×D20—34no—
239C2×D20—64no—
240C2×C4×D5—38no—
241C2×C4×D5—124no—
242C2×Dic10—24no—
243C2×Dic10—34no—
244C2×Dic10—64no—
245C2×Dic10C22×D314yes—
246C5×C4⋊C4—34no—
247C5×C22⋊C4—38no—
248C42×C5—34no—
249C22⋊Dic5C22×D318yes—
250C22⋊Dic5C22×D318yes—
251#685—38no—
252#685—38no—
253#685—38no—
254C4⋊Dic5—34no—
255#683—34no—
256#683—38no—
257#683—34no—
258C4×Dic5—34no—
259C4×Dic5—38no—
260C4×Dic5C22×D314yes—
261#559—1516no—
262C2×#127—151no—
263C2×#124—51no—
264C2×#124—151no—
265C2×#124—152no—
266C2×#123—152no—
267C2×#123—152no—
268C2×C4×Q8—151no—
269C2×C4×Q8—151no—
270C2×C4×D4—31no—
271C2×C4×D4—151no—
272C2×C4×D4—152no—
273C22×C3×C5—24no—
274C22×C3×C5—24no—
275C22×C3×C5—24no—
276C22×C3×C5—48no—
277C22×C3×C5C2×#4112yes—
278C22×C3×C5C2×#4112yes—
279C22×C3×C5H(5,𝔽2)12yes—
280C22×C3×C5C2511yescharacteristic
281C2×D15—24no—
282C2×D15—24no—
283C2×D15—24no—
284C2×D15—48no—
285C3×C4×C5C2×#4114yes—
286Dic15—22no—
287Dic15C2×#4114yes—
288C3×Dic5—22no—
289C3×Dic5—24no—
290C3×Dic5—22no—
291C5×Dic3—22no—
292C5×Dic3—24no—
293C5×Dic3—22no—
294C24×C3C22×D512yes—
295C23×D3—52no—
296C2×C3×Q8—54no—
297C2×C3×Q8—104no—
298C2×C3×D4—24no—
299C2×C3×D4C22×D514yes—
300C22×C3×C4—52no—
301C22×C3×C4—51no—
302C22×C3×C4—51no—
303C22×C3×C4C22×D511yescharacteristic
304C2×#67—58no—
305C2×#67—58no—
306C2×#67—108no—
307C2×#67—204no—
308C22×Dic3—44no—
309C22×Dic3—51no—
310C22×Dic3—51no—
311C22×Dic3C22×D512yes—
312C22×Dic3C22×D511yescharacteristic
313C22×Dic3C22×D511yescharacteristic
314C22×Dic3C22×D518yes—
315C2×D12—54no—
316C2×D12—104no—
317C2×C4×D3—58no—
318C2×C4×D3—204no—
319C2×Dic6—54no—
320C2×Dic6—104no—
321C3×C22⋊C4—58no—
322C3×C22⋊C4—58no—
323C3×C42—54no—
324#217C22×D518yes—
325(C2×D3)⋊C4—58no—
326(C2×D3)⋊C4—58no—
327(C2×D3)⋊C4—58no—
328C4⋊Dic3—54no—
329C4⋊Dic3—58no—
330C4⋊Dic3C22×D514yes—
331Dic3⋊C4—54no—
332Dic3⋊C4—54no—
333C4×Dic3—54no—
334C4×Dic3—58no—
335C4×Dic3C22×D514yes—
336C23×C5—24no—
337C23×C5—24no—
338C23×C5—24no—
339C23×C5C23×D314yes—
340C23×C5C23×D311yescharacteristic
341C22×D5—34no—
342C22×D5—64no—
343C22×D5—64no—
344C22×D5—64no—
345C5×D4—28no—
346C2×C4×C5—34no—
347C2×C4×C5—32no—
348C2×C4×C5—32no—
349C2×C4×C5—62no—
350C2×C4×C5—64no—
351C2×C4×C5—62no—
352C2×C4×C5—128no—
353C2×C4×C5#23714yes—
354C2×C4×C5C23×D312yes—
355C22⋊D5—616no—
356C22⋊D5—128no—
357C2×Dic5—24no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—34no—
361C2×Dic5—32no—
362C2×Dic5—32no—
363C2×Dic5—62no—
364C2×Dic5C23×D314yes—
365C2×Dic5C23×D312yes—
366C2×Dic5C23×D312yes—
367D20—68no—
368C4×D5—128no—
369Dic10—28no—
370Dic10—68no—
371C22×Q8—51no—
372C22×Q8—151no—
373C22×D4—152no—
374C22×D4—152no—
375C22×D4—151no—
376C22×D4D3×D511yescharacteristic
377C23×C4—32no—
378C23×C4—152no—
379#127—158no—
380#124—58no—
381#124—158no—
382#124—1516no—
383#123—1516no—
384#123—1516no—
385C4×Q8—158no—
386C4×Q8—158no—
387C4×D4—38no—
388C4×D4—158no—
389C4×D4—1516no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—151no—
392C2×C4⋊C4—151no—
393C2×C4⋊C4—151no—
394C2×C4⋊C4—152no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—52no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C42—31no—
402C2×C42—51no—
403C2×C42—152no—
404C2×C42—151no—
405C2×C3×C5—44no—
406C2×C3×C5#55914yescomplemented
407C2×C3×C5C22×#4111yescharacteristic
408C2×C3×C5C22×#4111yescharacteristic
409C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
410D15—44no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3C23×D514yes—
415C23×C3C23×D511yescharacteristic
416C22×D3—54no—
417C22×D3—104no—
418C22×D3—104no—
419C22×D3—104no—
420C3×Q8—108no—
421C3×D4—28no—
422C2×C3×C4—54no—
423C2×C3×C4—52no—
424C2×C3×C4—52no—
425C2×C3×C4—104no—
426C2×C3×C4—102no—
427C2×C3×C4—102no—
428C2×C3×C4#70914yes—
429C2×C3×C4C23×D512yes—
430#67—1016no—
431#67—208no—
432C2×Dic3—24no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—48no—
436C2×Dic3—54no—
437C2×Dic3—52no—
438C2×Dic3—52no—
439C2×Dic3—102no—
440C2×Dic3C23×D514yes—
441C2×Dic3C23×D512yes—
442C2×Dic3C23×D512yes—
443D12—108no—
444C4×D3—208no—
445Dic6—108no—
446C22×C5—24no—
447C22×C5—24no—
448C22×C5—24no—
449C22×C5—48no—
450C22×C5C2×#23712yes—
451C22×C5D3×#4112yes—
452C22×C5#100912yes—
453C22×C5C24×D311yescharacteristic
454C2×D5—64no—
455C2×D5—64no—
456C2×D5—64no—
457C2×D5—128no—
458C4×C5—62no—
459C4×C5—64no—
460C4×C5—62no—
461C4×C5C2×#23714yes—
462Dic5—24no—
463Dic5—22no—
464Dic5—22no—
465Dic5—34no—
466Dic5—62no—
467C24—152no—
468C24C2×D3×D512yes—
469C2×Q8—54no—
470C2×Q8—104no—
471C2×Q8—154no—
472C2×Q8—304no—
473C2×D4—24no—
474C2×D4—158no—
475C2×D4—158no—
476C2×D4—154no—
477C2×D4—308no—
478C2×D4—304no—
479C2×D4—604no—
480C2×D4C2×D3×D514yes—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—32no—
484C22×C4—38no—
485C22×C4—51no—
486C22×C4—51no—
487C22×C4—52no—
488C22×C4—124no—
489C22×C4—158no—
490C22×C4—151no—
491C22×C4—151no—
492C22×C4—604no—
493C22×C4C2×D3×D511yescharacteristic
494C4⋊C4—34no—
495C4⋊C4—154no—
496C4⋊C4—154no—
497C4⋊C4—158no—
498C4⋊C4—154no—
499C22⋊C4—38no—
500C22⋊C4—58no—
501C22⋊C4—58no—
502C22⋊C4—158no—
503C22⋊C4—158no—
504C22⋊C4—158no—
505C42—34no—
506C42—54no—
507C42—158no—
508C42—154no—
509C3×C5C2×#55911yescharacteristic, complemented, Hall
510C22×C3—24no—
511C22×C3—24no—
512C22×C3—24no—
513C22×C3—48no—
514C22×C3C2×#70912yes—
515C22×C3#414412yes—
516C22×C3D5×#4112yes—
517C22×C3C24×D511yescharacteristic
518C2×D3—104no—
519C2×D3—104no—
520C2×D3—104no—
521C2×D3—208no—
522C3×C4—104no—
523C3×C4—102no—
524C3×C4—102no—
525C3×C4C2×#70914yes—
526Dic3—24no—
527Dic3—22no—
528Dic3—22no—
529Dic3—54no—
530Dic3—102no—
531C2×C5—44no—
532C2×C5#568114yescomplemented
533C2×C5C22×#23711yescharacteristic
534C2×C5C2×D3×#4111yescharacteristic
535C2×C5C2×#100911yescharacteristic
536D5—124no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—154no—
541C23—304no—
542C23—304no—
543C23—304no—
544C23C22×D3×D514yes—
545C23C22×D3×D511yescharacteristic
546Q8—108no—
547Q8—308no—
548D4—28no—
549D4—3016no—
550D4—308no—
551D4—608no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—34no—
555C2×C4—52no—
556C2×C4—52no—
557C2×C4—54no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—64no—
561C2×C4—102no—
562C2×C4—102no—
563C2×C4—104no—
564C2×C4—128no—
565C2×C4—154no—
566C2×C4—152no—
567C2×C4—152no—
568C2×C4—302no—
569C2×C4—608no—
570C2×C4#677914yes—
571C2×C4C22×D3×D512yes—
572C2×C3—44no—
573C2×C3#6589314yescomplemented
574C2×C3C22×#70911yescharacteristic
575C2×C3C2×#414411yescharacteristic
576C2×C3C2×D5×#4111yescharacteristic
577D3—204no—
578C5C2×#568111yescharacteristic, complemented, Sylow
579C22—24no—
580C22—24no—
581C22—24no—
582C22—48no—
583C22—304no—
584C22—304no—
585C22—304no—
586C22—608no—
587C22#9202412yes—
588C22#9202712yes—
589C22C2×#677912yes—
590C22C23×D3×D511yescharacteristic
591C4—62no—
592C4—62no—
593C4—64no—
594C4—104no—
595C4—102no—
596C4—102no—
597C4—154no—
598C4—302no—
599C4C2×#677914yes—
600C3C2×#6589311yescharacteristic, complemented, Sylow
601C2—44no—
602C2—604no—
603C2#1175490314yesdirect product factor
604C2C2×#9202411yescharacteristic
605C2C2×#9202711yescharacteristic
606C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×#91829C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×D4×Dic3C2semidirect
3. C2×C3×#4082C2semidirect
4. C2×#91562C2semidirect
5. C2×#91556C2semidirect
6. C2×#91542C2semidirect
7. C2×#91526C2semidirect
8. #11754903C2direct (N × H)
9. C2×C4×#1204C2semidirect
10. C2×#91418C2semidirect
11. C2×#91374C2semidirect
12. C2×#91331C2semidirect
25. C5×D4×Dic3C22semidirect
30. C3×#4082C22semidirect
32. #91562C22semidirect
33. #91556C22semidirect
36. #91542C22semidirect
43. #91526C22semidirect
44. C4×#1204C22semidirect
45. #91418C22semidirect
46. #91374C22semidirect
47. #91331C22semidirect
51. C2×#4082D3semidirect
107. C2×D4×Dic3D5semidirect
130. #4082C2×D3semidirect
201. D4×Dic3C2×D5semidirect
406. C2×C3×C5#559semidirect
509. C3×C5C2×#559semidirect
532. C2×C5#5681semidirect
573. C2×C3#65893semidirect
578. C5C2×#5681semidirect
600. C3C2×#65893semidirect
603. C2#11754903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C5×D4×Dic32
C2×C3×#40822
C2×#915622
C2×#915562
C2×#915422
C2×#915262
#117549032
C2×C4×#12042
C2×#914182
C2×#913742
C2×#913312
C2×#658933
C2×#56815