Finite Group Databasebeta

← C2×#11753805 #14484751

Subgroups — C2×#11753805 #14484751

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×#91776C211yesmaximal, characteristic, complemented
2C2×C5×#893C211yesmaximal, characteristic, complemented
3C2×C3×#4039C211yesmaximal, characteristic, complemented
4C2×C4×#1204C211yesmaximal, characteristic, complemented
5C2×#91464C212yesmaximal, complemented
6C2×#91463C211yesmaximal, characteristic
7C2×#91452C212yesmaximal, complemented
8C2×#91447C212yesmaximal, complemented
9C2×C4×#1201C212yesmaximal, complemented
10C2×#91373C211yesmaximal, characteristic, complemented
11C2×#91364C211yesmaximal, characteristic, complemented
12#11753805C2116yesmaximal, direct product factor
13C2×#65893—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C4×C5×D3C2212yes—
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2212yes—
19C22×#1204C2211yescharacteristic
20C22×#1201C2212yes—
21C22×#1201C2212yes—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×#6712C2212yes—
24C2×C4×Dic15C2212yes—
25C2×C4×Dic15C2211yescharacteristic
26#91776C2218yescomplemented
27C2×C5×(C2×D3)⋊C4C2212yes—
28C2×C4×C5×Dic3C2211yescharacteristic
29C5×#893C2218yescomplemented
30C2×C3×#685C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4039C2218yescomplemented
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40C4×#1204C2218yescomplemented
41#91464C22116yescomplemented
42#91463C2218yes—
43#91452C22116yescomplemented
44#91447C22116yescomplemented
45C4×#1201C22116yescomplemented
46#91373C2218yescomplemented
47#91364C2218yescomplemented
48C2×#5559—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4086—31no—
51C2×#4082—31no—
52C2×#4075—32no—
53C2×C4×C22⋊D5—32no—
54#65893—316no—
55C2×#4039D311yescharacteristic, complemented
56C2×#4033—31no—
57C2×#4031—32no—
58C2×#4029—32no—
59C2×#4021—31no—
60C2×C4×Dic10—31no—
61C23×C5×D3C2312yes—
62C23×C3×D5C2312yes—
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C2×C5×D12—24no—
73C2×C5×D12C2314yes—
74C2×C4×C5×D3—44no—
75C2×C4×C5×D3C2318yes—
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×D20—24no—
79C2×C3×D20C2314yes—
80C2×C3×C4×D5—44no—
81C2×C3×C4×D5C2318yes—
82C2×#1204—24no—
83C2×#1204C2314yes—
84C2×#1201—28no—
85C2×#1201—44no—
86C2×#1201C2318yes—
87C2×#1201C2318yes—
88C3×C5×C4⋊C4C2314yes—
89#6712C2318yes—
90C4×Dic15C2318yes—
91C4×Dic15C2314yes—
92C5×(C2×D3)⋊C4C2318yes—
93C4×C5×Dic3C2314yes—
94C3×#685C2318yes—
95C3×C4×Dic5C2314yes—
96Dic3⋊Dic5C2314yes—
97#6669C2314yes—
98#6668C2314yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101#6665C2318yes—
102#6665C2318yes—
103C2×C3×C4×D4—51no—
104C2×#940—51no—
105C2×#936—51no—
106C2×#929—52no—
107C2×C4×#67—52no—
108#5559—516no—
109C2×#893D511yescharacteristic, complemented
110C2×#887—51no—
111C2×#885—52no—
112C2×#883—52no—
113C2×#875—51no—
114C2×C4×Dic6—51no—
115C22×C5×D4—31no—
116C23×C4×C5—32no—
117C22×C22⋊D5—32no—
118C22×C22⋊D5—32no—
119C22×D20C2×D311yescharacteristic
120C22×C4×D5C2×D312yes—
121C22×Dic10—31no—
122C22×Dic10—31no—
123C4×C5×D4—38no—
124C2×C5×C4⋊C4C2×D311yescharacteristic
125C2×C5×C22⋊C4—32no—
126C2×C42×C5—31no—
127C2×C22⋊Dic5—32no—
128C2×C22⋊Dic5—32no—
129#4086—38no—
130#4082—38no—
131#4075—316no—
132C4×C22⋊D5—316no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685C2×D312yes—
136C2×C4⋊Dic5—31no—
137C2×#683—32no—
138C2×#683—31no—
139C2×#683—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—32no—
142C2×C4×Dic5C2×D311yescharacteristic
143#4039C2×D318yescomplemented
144#4033—38no—
145#4031—316no—
146#4029—316no—
147#4021—38no—
148C4×Dic10—38no—
149C2×#559—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×C5×D3—24no—
152C22×C5×D3—24no—
153C22×C5×D3—24no—
154C22×C5×D3C2414yes—
155C22×C3×D5—24no—
156C22×C3×D5—24no—
157C22×C3×D5—24no—
158C22×C3×D5C2414yes—
159C2×C3×C4×C5—24no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2414yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—24no—
164C2×Dic15—22no—
165C2×Dic15#4114yes—
166C2×Dic15C2414yes—
167C2×Dic15C2412yes—
168C2×Dic15C2412yes—
169Dic30—28no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3C2412yes—
173C2×C5×Dic3C2412yes—
174C5×D12—28no—
175C4×C5×D3—48no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2412yes—
180C3×D20—28no—
181C3×C4×D5—48no—
182#1204—28no—
183#1201—216no—
184#1201—48no—
185C22×C3×D4—51no—
186C23×C3×C4—52no—
187C22×#67—52no—
188C22×#67—52no—
189C22×D12C2×D511yescharacteristic
190C22×C4×D3C2×D512yes—
191C22×Dic6—51no—
192C22×Dic6—51no—
193C3×C4×D4—58no—
194C2×C3×C4⋊C4C2×D511yescharacteristic
195C2×C3×C22⋊C4—52no—
196C2×C3×C42—51no—
197C2×#217—52no—
198C2×#217—52no—
199#940—58no—
200#936—58no—
201#929—516no—
202C4×#67—516no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4C2×D512yes—
206C2×C4⋊Dic3—51no—
207C2×Dic3⋊C4—52no—
208C2×Dic3⋊C4—51no—
209C2×Dic3⋊C4—51no—
210C2×C4×Dic3—51no—
211C2×C4×Dic3—52no—
212C2×C4×Dic3C2×D511yescharacteristic
213#893C2×D518yescomplemented
214#887—58no—
215#885—516no—
216#883—516no—
217#875—58no—
218C4×Dic6—58no—
219C24×C5—32no—
220C23×D5C22×D312yes—
221C2×C5×D4—34no—
222C2×C5×D4—64no—
223C22×C4×C5—31no—
224C22×C4×C5—31no—
225C22×C4×C5—38no—
226C22×C4×C5—124no—
227C22×C4×C5C22×D312yes—
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—32no—
235C22×Dic5—31no—
236C22×Dic5C22×D311yescharacteristic
237C22×Dic5C22×D311yescharacteristic
238C2×D20—24no—
239C2×D20C22×D314yes—
240C2×C4×D5—44no—
241C2×C4×D5C22×D318yes—
242C2×Dic10—34no—
243C2×Dic10—34no—
244C2×Dic10—64no—
245C2×Dic10—64no—
246C5×C4⋊C4C22×D314yes—
247C5×C22⋊C4—38no—
248C42×C5—34no—
249C22⋊Dic5—38no—
250C22⋊Dic5—38no—
251#685—38no—
252#685—38no—
253#685C22×D318yes—
254C4⋊Dic5—34no—
255#683—38no—
256#683—34no—
257#683—34no—
258C4×Dic5—34no—
259C4×Dic5—38no—
260C4×Dic5C22×D314yes—
261#559—1516no—
262C2×#127—151no—
263C2×#124—151no—
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—51no—
272C2×C4×D4—152no—
273C22×C3×C5C2×#4112yes—
274C22×C3×C5C2×#4112yes—
275C22×C3×C5H(5,𝔽2)12yes—
276C22×C3×C5C2511yescharacteristic
277C2×C5×D3—24no—
278C2×C5×D3—24no—
279C2×C5×D3—24no—
280C2×C5×D3—48no—
281C2×C3×D5—24no—
282C2×C3×D5—24no—
283C2×C3×D5—24no—
284C2×C3×D5—48no—
285C3×C4×C5—24no—
286C3×C4×C5C2×#4114yes—
287Dic15—24no—
288Dic15—22no—
289Dic15C2×#4114yes—
290C3×Dic5—22no—
291C3×Dic5—22no—
292C5×Dic3—22no—
293C5×Dic3—22no—
294C24×C3—52no—
295C23×D3C22×D512yes—
296C2×C3×D4—54no—
297C2×C3×D4—104no—
298C22×C3×C4—51no—
299C22×C3×C4—51no—
300C22×C3×C4—58no—
301C22×C3×C4—204no—
302C22×C3×C4C22×D512yes—
303C22×C3×C4C22×D511yescharacteristic
304C2×#67—58no—
305C2×#67—58no—
306C2×#67—108no—
307C2×#67—204no—
308C22×Dic3—51no—
309C22×Dic3—51no—
310C22×Dic3—52no—
311C22×Dic3C22×D511yescharacteristic
312C22×Dic3C22×D511yescharacteristic
313C2×D12—24no—
314C2×D12C22×D514yes—
315C2×C4×D3—44no—
316C2×C4×D3C22×D518yes—
317C2×Dic6—54no—
318C2×Dic6—54no—
319C2×Dic6—104no—
320C2×Dic6—104no—
321C3×C4⋊C4C22×D514yes—
322C3×C22⋊C4—58no—
323C3×C42—54no—
324#217—58no—
325#217—58no—
326(C2×D3)⋊C4—58no—
327(C2×D3)⋊C4—58no—
328(C2×D3)⋊C4C22×D518yes—
329C4⋊Dic3—54no—
330Dic3⋊C4—58no—
331Dic3⋊C4—54no—
332Dic3⋊C4—54no—
333C4×Dic3—54no—
334C4×Dic3—58no—
335C4×Dic3C22×D514yes—
336C23×C5—34no—
337C23×C5—64no—
338C23×C5—64no—
339C23×C5—64no—
340C23×C5C23×D311yescharacteristic
341C22×D5—24no—
342C22×D5—24no—
343C22×D5—24no—
344C22×D5C23×D314yes—
345C5×D4—68no—
346C2×C4×C5—24no—
347C2×C4×C5—32no—
348C2×C4×C5—32no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—128no—
352C2×C4×C5#23514yes—
353C2×C4×C5C23×D314yes—
354C2×C4×C5C23×D312yes—
355C22⋊D5—616no—
356C22⋊D5—128no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—34no—
360C2×Dic5—32no—
361C2×Dic5—32no—
362C2×Dic5—34no—
363C2×Dic5—64no—
364C2×Dic5—62no—
365C2×Dic5C23×D312yes—
366C2×Dic5C23×D312yes—
367D20—28no—
368C4×D5—48no—
369Dic10—68no—
370Dic10—68no—
371C22×Q8—151no—
372C22×Q8—151no—
373C22×D4—31no—
374C22×D4—51no—
375C22×D4—152no—
376C22×D4—152no—
377C23×C4—32no—
378C23×C4—52no—
379#127—158no—
380#124—158no—
381#124—158no—
382#124—1516no—
383#123—1516no—
384#123—1516no—
385C4×Q8—158no—
386C4×Q8—158no—
387C4×D4—38no—
388C4×D4—58no—
389C4×D4—1516no—
390C2×C4⋊C4—151no—
391C2×C4⋊C4—151no—
392C2×C4⋊C4—151no—
393C2×C4⋊C4—152no—
394C2×C4⋊C4D3×D511yescharacteristic
395C2×C22⋊C4—32no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—152no—
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#55914yescomplemented
406C2×C3×C5C22×#4111yescharacteristic
407C2×C3×C5C22×#4111yescharacteristic
408C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
409C3×D5—44no—
410C5×D3—44no—
411C23×C3—54no—
412C23×C3—104no—
413C23×C3—104no—
414C23×C3—104no—
415C23×C3C23×D511yescharacteristic
416C22×D3—24no—
417C22×D3—24no—
418C22×D3—24no—
419C22×D3C23×D514yes—
420C3×D4—108no—
421C2×C3×C4—24no—
422C2×C3×C4—52no—
423C2×C3×C4—52no—
424C2×C3×C4—102no—
425C2×C3×C4—102no—
426C2×C3×C4—208no—
427C2×C3×C4#70914yes—
428C2×C3×C4C23×D514yes—
429C2×C3×C4C23×D512yes—
430#67—1016no—
431#67—208no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—54no—
435C2×Dic3—52no—
436C2×Dic3—52no—
437C2×Dic3—54no—
438C2×Dic3—104no—
439C2×Dic3—102no—
440C2×Dic3C23×D512yes—
441C2×Dic3C23×D512yes—
442D12—28no—
443C4×D3—48no—
444Dic6—108no—
445Dic6—108no—
446C22×C5—64no—
447C22×C5—64no—
448C22×C5—64no—
449C22×C5—128no—
450C22×C5C2×#23512yes—
451C22×C5#100412yes—
452C22×C5D3×#4112yes—
453C22×C5C24×D311yescharacteristic
454C2×D5—24no—
455C2×D5—24no—
456C2×D5—24no—
457C2×D5—48no—
458C4×C5—24no—
459C4×C5—62no—
460C4×C5—62no—
461C4×C5C2×#23514yes—
462Dic5—22no—
463Dic5—22no—
464Dic5—34no—
465Dic5—64no—
466Dic5—62no—
467C24—32no—
468C24—52no—
469C2×Q8—154no—
470C2×Q8—154no—
471C2×Q8—304no—
472C2×Q8—304no—
473C2×D4—34no—
474C2×D4—54no—
475C2×D4—64no—
476C2×D4—104no—
477C2×D4—158no—
478C2×D4—158no—
479C2×D4—308no—
480C2×D4—604no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—38no—
484C22×C4—51no—
485C22×C4—51no—
486C22×C4—58no—
487C22×C4—124no—
488C22×C4—151no—
489C22×C4—152no—
490C22×C4—151no—
491C22×C4—204no—
492C22×C4C2×D3×D512yes—
493C22×C4C2×D3×D511yescharacteristic
494C4⋊C4—154no—
495C4⋊C4—154no—
496C4⋊C4—154no—
497C4⋊C4—158no—
498C4⋊C4C2×D3×D514yes—
499C22⋊C4—38no—
500C22⋊C4—58no—
501C22⋊C4—158no—
502C22⋊C4—158no—
503C22⋊C4—158no—
504C22⋊C4—158no—
505C42—34no—
506C42—54no—
507C42—158no—
508C42—154no—
509C3×C5C2×#55911yescharacteristic, complemented, Hall
510C22×C3—104no—
511C22×C3—104no—
512C22×C3—104no—
513C22×C3—208no—
514C22×C3C2×#70912yes—
515C22×C3#414412yes—
516C22×C3D5×#4112yes—
517C22×C3C24×D511yescharacteristic
518C2×D3—24no—
519C2×D3—24no—
520C2×D3—24no—
521C2×D3—48no—
522C3×C4—24no—
523C3×C4—102no—
524C3×C4—102no—
525C3×C4C2×#70914yes—
526Dic3—22no—
527Dic3—22no—
528Dic3—54no—
529Dic3—104no—
530Dic3—102no—
531C2×C5—124no—
532C2×C5#555914yescomplemented
533C2×C5C22×#23511yescharacteristic
534C2×C5C2×#100411yescharacteristic
535C2×C5C2×D3×#4111yescharacteristic
536D5—44no—
537C23—34no—
538C23—54no—
539C23—64no—
540C23—64no—
541C23—64no—
542C23—104no—
543C23—104no—
544C23—104no—
545C23C22×D3×D511yescharacteristic
546Q8—308no—
547Q8—308no—
548D4—68no—
549D4—108no—
550D4—3016no—
551D4—608no—
552C2×C4—24no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—52no—
556C2×C4—52no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—128no—
562C2×C4—154no—
563C2×C4—152no—
564C2×C4—154no—
565C2×C4—152no—
566C2×C4—208no—
567C2×C4—304no—
568C2×C4—302no—
569C2×C4#677114yes—
570C2×C4C22×D3×D514yes—
571C2×C4C22×D3×D512yes—
572C2×C3—204no—
573C2×C3#6589314yescomplemented
574C2×C3C22×#70911yescharacteristic
575C2×C3C2×#414411yescharacteristic
576C2×C3C2×D5×#4111yescharacteristic
577D3—44no—
578C5C2×#555911yescharacteristic, complemented, Sylow
579C22—64no—
580C22—64no—
581C22—64no—
582C22—104no—
583C22—104no—
584C22—104no—
585C22—128no—
586C22—208no—
587C22C2×#677112yes—
588C22#9202512yes—
589C22#9203412yes—
590C22C23×D3×D511yescharacteristic
591C4—24no—
592C4—62no—
593C4—62no—
594C4—102no—
595C4—102no—
596C4—154no—
597C4—304no—
598C4—302no—
599C4C2×#677114yes—
600C3C2×#6589311yescharacteristic, complemented, Sylow
601C2—124no—
602C2—204no—
603C2#1175380514yesdirect product factor
604C2C22×#677111yescharacteristic
605C2C2×#9202511yescharacteristic
606C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91463C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91776C2semidirect
2. C2×C5×#893C2semidirect
3. C2×C3×#4039C2semidirect
4. C2×C4×#1204C2semidirect
5. C2×#91464C2semidirect
7. C2×#91452C2semidirect
8. C2×#91447C2semidirect
9. C2×C4×#1201C2semidirect
10. C2×#91373C2semidirect
11. C2×#91364C2semidirect
12. #11753805C2direct (N × H)
26. #91776C22semidirect
29. C5×#893C22semidirect
32. C3×#4039C22semidirect
40. C4×#1204C22semidirect
41. #91464C22semidirect
43. #91452C22semidirect
44. #91447C22semidirect
45. C4×#1201C22semidirect
46. #91373C22semidirect
47. #91364C22semidirect
55. C2×#4039D3semidirect
109. C2×#893D5semidirect
143. #4039C2×D3semidirect
213. #893C2×D5semidirect
405. C2×C3×C5#559semidirect
509. C3×C5C2×#559semidirect
532. C2×C5#5559semidirect
573. C2×C3#65893semidirect
578. C5C2×#5559semidirect
600. C3C2×#65893semidirect
603. C2#11753805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917762
C2×C5×#8932
C2×C3×#40392
C2×C4×#12042
C2×#914642
C2×#914632
C2×#914522
C2×#914472
C2×C4×#12012
C2×#913732
C2×#913642
#117538052
C2×#658933
C2×#55595