Finite Group Databasebeta

← C2×#11755204 #14479946

Subgroups — C2×#11755204 #14479946

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91835C211yesmaximal, characteristic, complemented
2C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4093C211yesmaximal, characteristic, complemented
4#11755204C2116yesmaximal, direct product factor
5C2×#91465C211yesmaximal, characteristic
6C2×Dic3×D20C211yesmaximal, characteristic, complemented
7C2×C4×#1200C211yesmaximal, characteristic, complemented
8C2×#91395C212yesmaximal, complemented
9C2×#91393C212yesmaximal, complemented
10C2×#91388C211yesmaximal, characteristic, complemented
11C2×#91361C212yesmaximal, complemented
12C2×#91356C212yesmaximal, complemented
13C2×#65914—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C22×#1202C2212yes—
18C22×#1200C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C22×D5×Dic3C2212yes—
21#91835C2218yescomplemented
22C2×#6714C2212yes—
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6712C2212yes—
25C5×Q8×Dic3C2218yescomplemented
26C2×C5×C4⋊Dic3C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2212yes—
29C2×C4×C5×Dic3C2211yescharacteristic
30C3×#4093C2218yescomplemented
31C2×C3×#685C2212yes—
32C2×C3×#685C2212yes—
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×Dic3⋊Dic5C2212yes—
35C2×#6669C2212yes—
36C2×#6665C2212yes—
37C2×#6665C2212yes—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91465C2218yes—
41Dic3×D20C2218yescomplemented
42C4×#1200C2218yescomplemented
43#91395C22116yescomplemented
44#91393C22116yescomplemented
45#91388C2218yescomplemented
46#91361C22116yescomplemented
47#91356C22116yescomplemented
48C2×#5680—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4093D311yescharacteristic, complemented
51C2×#4092—31no—
52#65914—316no—
53C2×#4044—32no—
54C2×#4041—31no—
55C2×#4040—32no—
56C2×#4036—31no—
57C2×C4×D20—32no—
58C2×C4×D20—31no—
59C2×#4018—32no—
60C2×C42×D5—31no—
61C23×D15C2311yescharacteristic
62C23×C3×D5C2312yes—
63C2×C3×C5×Q8—24no—
64C2×C3×C5×Q8C2314yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×Dic15C2311yescharacteristic
69C2×C4×D15—24no—
70C2×C4×D15C2314yes—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2311yescharacteristic
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×D20—24no—
77C2×C3×D20C2314yes—
78C2×#1202—28no—
79C2×#1202C2318yes—
80C2×#1200—24no—
81C2×#1200—24no—
82C2×#1200C2314yes—
83C2×#1200C2314yes—
84C2×D5×Dic3—28no—
85C2×D5×Dic3C2318yes—
86#6714C2318yes—
87C4⋊Dic15C2314yes—
88#6712C2318yes—
89C5×C4⋊Dic3C2314yes—
90C5×C4⋊Dic3C2318yes—
91C4×C5×Dic3C2318yes—
92C4×C5×Dic3C2314yes—
93C3×#685C2318yes—
94C3×#685C2318yes—
95C3×C4×Dic5C2314yes—
96Dic3⋊Dic5C2318yes—
97#6669C2318yes—
98#6665C2318yes—
99#6665C2318yes—
100Dic3×Dic5C2314yes—
101Dic3×Dic5C2314yes—
102C2×C3×#124—51no—
103C2×#946—51no—
104C2×Q8×Dic3D511yescharacteristic, complemented
105C2×#938—51no—
106C2×D4×Dic3—51no—
107#5680—516no—
108C2×#883—52no—
109C2×#67⋊C4—52no—
110C2×#879—52no—
111C2×#877—52no—
112C2×C42×D3—51no—
113C2×#870—51no—
114C22×C5×Q8C2×D311yescharacteristic
115C22×D20—32no—
116C22×D20C2×D311yescharacteristic
117C22×C4×D5—32no—
118C22×C4×D5—31no—
119C22×C4×D5—31no—
120C22×C4×D5—31no—
121C4×C5×Q8—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C4⋊C4—32no—
124C2×C42×C5—31no—
125C2×C42×C5—32no—
126#4093C2×D318yescomplemented
127#4092—38no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685C2×D312yes—
132C2×#685C2×D312yes—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—32no—
135C2×#683—32no—
136C2×#683—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5C2×D311yescharacteristic
140#4044—316no—
141#4041—38no—
142#4040—316no—
143#4036—38no—
144C4×D20—38no—
145C4×D20—316no—
146#4018—316no—
147C42×D5—38no—
148C2×#529—151noSylow
149C23×C3×C5C2411yescharacteristic
150C22×D15—22no—
151C22×D15—22no—
152C22×D15#4114yes—
153C22×D15C2412yes—
154C22×C3×D5—24no—
155C22×C3×D5—24no—
156C22×C3×D5—24no—
157C22×C3×D5C2414yes—
158C3×C5×Q8—28no—
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×Dic15C2412yes—
166C2×Dic15C2414yes—
167C4×D15—28no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3#4114yes—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2412yes—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C2412yes—
177C2×C3×Dic5C2412yes—
178C3×D20—28no—
179#1202—216no—
180#1200—28no—
181#1200—28no—
182D5×Dic3—216no—
183C22×C3×Q8C2×D511yescharacteristic
184C22×C3×D4—51no—
185C22×#67—52no—
186C23×Dic3—52no—
187C22×C4×D3—51no—
188C22×C4×D3—51no—
189C22×C4×D3—51no—
190C3×#124—58no—
191C2×C3×C22⋊C4—52no—
192C2×C3×C22⋊C4—52no—
193C2×C3×C42—51no—
194C2×#217—52no—
195C2×#217—52no—
196#946—58no—
197Q8×Dic3C2×D518yescomplemented
198#938—58no—
199D4×Dic3—58no—
200C2×(C2×D3)⋊C4—52no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3C2×D511yescharacteristic
203C2×C4⋊Dic3C2×D512yes—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3C2×D511yescharacteristic
210C2×C4×Dic3C2×D512yes—
211#883—516no—
212#67⋊C4—516no—
213#879—516no—
214#877—516no—
215C42×D3—58no—
216#870—58no—
217C23×D5—31no—
218C23×D5C22×D312yes—
219C2×C5×Q8—24no—
220C2×C5×Q8C22×D314yes—
221C22×C4×C5—31no—
222C22×C4×C5—31no—
223C22×C4×C5—32no—
224C22×C4×C5C22×D312yes—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—31no—
227C22×Dic5—32no—
228C22×Dic5C22×D311yescharacteristic
229C22×Dic5C22×D311yescharacteristic
230C2×D20—24no—
231C2×D20—38no—
232C2×D20—68no—
233C2×D20C22×D314yes—
234C2×C4×D5—38no—
235C2×C4×D5—34no—
236C2×C4×D5—34no—
237C2×C4×D5—34no—
238C2×C4×D5—64no—
239C2×C4×D5—64no—
240C2×C4×D5—68no—
241C2×C4×D5—64no—
242C5×C4⋊C4—34no—
243C5×C4⋊C4—38no—
244C42×C5—34no—
245C42×C5—38no—
246#685—38no—
247#685—38no—
248#685—38no—
249#685C22×D318yes—
250#685C22×D318yes—
251C4⋊Dic5—34no—
252C4⋊Dic5—38no—
253#683—38no—
254#683—38no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5C22×D314yes—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—51no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—151no—
265C2×C4×Q8—31no—
266C2×C4×D4—152no—
267C2×C4×D4—151no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2×#4112yes—
273C22×C3×C5C2511yescharacteristic
274C2×D15—28no—
275C2×D15—22no—
276C2×D15—22no—
277C2×D15C2×#4114yes—
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—24no—
281C2×C3×D5—48no—
282C3×C4×C5—24no—
283C3×C4×C5C2×#4114yes—
284Dic15—24no—
285Dic15—22no—
286C3×Dic5—22no—
287C3×Dic5—22no—
288C5×Dic3—22no—
289C5×Dic3—24no—
290C5×Dic3C2×#4114yes—
291C24×C3—52no—
292C23×D3—51no—
293C2×C3×Q8—24no—
294C2×C3×Q8C22×D514yes—
295C2×C3×D4—54no—
296C2×C3×D4—104no—
297C22×C3×C4—51no—
298C22×C3×C4—51no—
299C22×C3×C4C22×D512yes—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—58no—
302C2×#67—108no—
303C22×Dic3—51no—
304C22×Dic3—52no—
305C22×Dic3—58no—
306C22×Dic3—108no—
307C22×Dic3C22×D511yescharacteristic
308C22×Dic3C22×D512yes—
309C22×Dic3C22×D511yescharacteristic
310C2×C4×D3—54no—
311C2×C4×D3—54no—
312C2×C4×D3—54no—
313C2×C4×D3—104no—
314C2×C4×D3—104no—
315C2×C4×D3—104no—
316C3×C22⋊C4—58no—
317C3×C22⋊C4—58no—
318C3×C42—54no—
319#217—58no—
320#217—58no—
321(C2×D3)⋊C4—58no—
322C4⋊Dic3—54no—
323C4⋊Dic3C22×D514yes—
324C4⋊Dic3C22×D518yes—
325Dic3⋊C4—58no—
326Dic3⋊C4—58no—
327Dic3⋊C4—58no—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3C22×D514yes—
331C4×Dic3C22×D518yes—
332C23×C5C23×D311yescharacteristic
333C22×D5—24no—
334C22×D5—24no—
335C22×D5—24no—
336C22×D5—34no—
337C22×D5—32no—
338C22×D5—62no—
339C22×D5—62no—
340C22×D5C23×D314yes—
341C5×Q8—28no—
342C2×C4×C5—24no—
343C2×C4×C5—34no—
344C2×C4×C5—32no—
345C2×C4×C5—32no—
346C2×C4×C5—34no—
347C2×C4×C5—62no—
348C2×C4×C5—64no—
349C2×C4×C5#23714yes—
350C2×C4×C5C23×D314yes—
351C2×C4×C5C23×D312yes—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—32no—
355C2×Dic5—34no—
356C2×Dic5—62no—
357C2×Dic5—64no—
358C2×Dic5C23×D312yes—
359C2×Dic5C23×D312yes—
360D20—28no—
361D20—616no—
362C4×D5—68no—
363C4×D5—68no—
364C4×D5—616no—
365C4×D5—68no—
366C22×Q8D3×D511yescharacteristic
367C22×D4—51no—
368C22×D4—152no—
369C23×C4—151no—
370C23×C4—151no—
371C23×C4—152no—
372C23×C4—151no—
373#126—1516no—
374#125—158no—
375#124—58no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—158no—
379C4×Q8—38no—
380C4×D4—1516no—
381C4×D4—158no—
382#117—1516no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—151no—
389C2×C22⋊C4—52no—
390C2×C22⋊C4—52no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—32no—
395C2×C42—31no—
396C2×C42—51no—
397C2×C42—158no—
398C2×C42—151no—
399C2×C42—151no—
400C2×C3×C5#52914yescomplemented
401C2×C3×C5C22×#4111yescharacteristic
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404D15—24no—
405C3×D5—44no—
406C23×C3—54no—
407C23×C3—104no—
408C23×C3—104no—
409C23×C3—104no—
410C23×C3C23×D511yescharacteristic
411C22×D3—54no—
412C22×D3—52no—
413C22×D3—102no—
414C22×D3—102no—
415C3×Q8—28no—
416C3×D4—108no—
417C2×C3×C4—24no—
418C2×C3×C4—52no—
419C2×C3×C4—52no—
420C2×C3×C4—102no—
421C2×C3×C4—102no—
422C2×C3×C4#70914yes—
423C2×C3×C4C23×D514yes—
424C2×C3×C4C23×D512yes—
425#67—1016no—
426C2×Dic3—22no—
427C2×Dic3—24no—
428C2×Dic3—52no—
429C2×Dic3—54no—
430C2×Dic3—102no—
431C2×Dic3—104no—
432C2×Dic3—1016no—
433C2×Dic3#71314yes—
434C2×Dic3C23×D512yes—
435C2×Dic3C23×D514yes—
436C2×Dic3C23×D512yes—
437C4×D3—108no—
438C4×D3—108no—
439C4×D3—108no—
440C22×C5C2×#23712yes—
441C22×C5D3×#4112yes—
442C22×C5D3×#4112yes—
443C22×C5C24×D311yescharacteristic
444C2×D5—24no—
445C2×D5—24no—
446C2×D5—24no—
447C2×D5—34no—
448C2×D5—48no—
449C2×D5—68no—
450C2×D5—62no—
451C2×D5—62no—
452C4×C5—24no—
453C4×C5—34no—
454C4×C5—62no—
455C4×C5—64no—
456C4×C5C2×#23714yes—
457Dic5—22no—
458Dic5—22no—
459Dic5—62no—
460Dic5—64no—
461C24—52no—
462C24—151no—
463C2×Q8—24no—
464C2×Q8C2×D3×D514yes—
465C2×D4—54no—
466C2×D4—104no—
467C2×D4—158no—
468C2×D4—308no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—51no—
473C22×C4—51no—
474C22×C4—154no—
475C22×C4—154no—
476C22×C4—158no—
477C22×C4—151no—
478C22×C4—152no—
479C22×C4—154no—
480C22×C4—304no—
481C22×C4—308no—
482C22×C4—304no—
483C22×C4—304no—
484C22×C4C2×D3×D512yes—
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—34no—
487C4⋊C4—38no—
488C4⋊C4—158no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4—154no—
492C22⋊C4—58no—
493C22⋊C4—58no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—34no—
498C42—38no—
499C42—54no—
500C42—154no—
501C42—154no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—104no—
504C22×C3—104no—
505C22×C3—104no—
506C22×C3—208no—
507C22×C3C2×#70912yes—
508C22×C3C2×#71312yes—
509C22×C3D5×#4112yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—54no—
512C2×D3—108no—
513C2×D3—102no—
514C2×D3—102no—
515C3×C4—24no—
516C3×C4—102no—
517C3×C4—102no—
518C3×C4C2×#70914yes—
519Dic3—22no—
520Dic3—24no—
521Dic3—102no—
522Dic3—104no—
523Dic3C2×#71314yes—
524C2×C5#568014yescomplemented
525C2×C5C22×#23711yescharacteristic
526C2×C5C2×D3×#4111yescharacteristic
527C2×C5C2×D3×#4111yescharacteristic
528D5—44no—
529D5—64no—
530C23—54no—
531C23—104no—
532C23—104no—
533C23—104no—
534C23—154no—
535C23—152no—
536C23—302no—
537C23—302no—
538C23C22×D3×D511yescharacteristic
539Q8—28no—
540D4—108no—
541D4—3016no—
542C2×C4—24no—
543C2×C4—34no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—34no—
547C2×C4—52no—
548C2×C4—52no—
549C2×C4—62no—
550C2×C4—64no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—152no—
554C2×C4—154no—
555C2×C4—308no—
556C2×C4—3016no—
557C2×C4—308no—
558C2×C4—304no—
559C2×C4—302no—
560C2×C4—308no—
561C2×C4#677914yes—
562C2×C4C22×D3×D514yes—
563C2×C4C22×D3×D512yes—
564C2×C3—204no—
565C2×C3#6591414yescomplemented
566C2×C3C22×#70911yescharacteristic
567C2×C3C22×#71311yescharacteristic
568C2×C3C2×D5×#4111yescharacteristic
569D3—104no—
570C5C2×#568011yescharacteristic, complemented, Sylow
571C22—104no—
572C22—104no—
573C22—104no—
574C22—154no—
575C22—208no—
576C22—302no—
577C22—308no—
578C22—302no—
579C22D3×#71312yes—
580C22#9203412yes—
581C22C2×#677912yes—
582C22C23×D3×D511yescharacteristic
583C4—24no—
584C4—34no—
585C4—62no—
586C4—64no—
587C4—102no—
588C4—102no—
589C4—302no—
590C4—304no—
591C4C2×#677914yes—
592C3C2×#6591411yescharacteristic, complemented, Sylow
593C2—204no—
594C2—304no—
595C2#1175520414yesdirect product factor
596C2C2×D3×#71311yescharacteristic
597C2C2×#9203411yescharacteristic
598C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC2×#91465C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#91835C2semidirect
2. C2×C5×Q8×Dic3C2semidirect
3. C2×C3×#4093C2semidirect
4. #11755204C2direct (N × H)
6. C2×Dic3×D20C2semidirect
7. C2×C4×#1200C2semidirect
8. C2×#91395C2semidirect
9. C2×#91393C2semidirect
10. C2×#91388C2semidirect
11. C2×#91361C2semidirect
12. C2×#91356C2semidirect
21. #91835C22semidirect
25. C5×Q8×Dic3C22semidirect
30. C3×#4093C22semidirect
41. Dic3×D20C22semidirect
42. C4×#1200C22semidirect
43. #91395C22semidirect
44. #91393C22semidirect
45. #91388C22semidirect
46. #91361C22semidirect
47. #91356C22semidirect
50. C2×#4093D3semidirect
104. C2×Q8×Dic3D5semidirect
126. #4093C2×D3semidirect
197. Q8×Dic3C2×D5semidirect
400. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
524. C2×C5#5680semidirect
565. C2×C3#65914semidirect
570. C5C2×#5680semidirect
592. C3C2×#65914semidirect
595. C2#11755204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918352
C2×C5×Q8×Dic32
C2×C3×#40932
#117552042
C2×#914652
C2×Dic3×D202
C2×C4×#12002
C2×#913952
C2×#913932
C2×#913882
C2×#913612
C2×#913562
C2×#659143
C2×#56805