Finite Group Databasebeta

← C2×#11754422 #14479852

Subgroups — C2×#11754422 #14479852

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×#91813C211yesmaximal, characteristic, complemented
2C22×C4×C5×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4076C211yesmaximal, characteristic
4C2×Dic3×C22⋊D5C212yesmaximal, complemented
5C2×#91536C212yesmaximal, complemented
6#11754422C2116yesmaximal, direct product factor
7C2×Dic3×D20C211yesmaximal, characteristic, complemented
8C2×#91393C212yesmaximal, complemented
9C2×#91381C211yesmaximal, characteristic, complemented
10C2×#91364C211yesmaximal, characteristic, complemented
11C2×#91363C212yesmaximal, complemented
12C2×#91340C211yesmaximal, characteristic, complemented
13C2×#65813—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C23×C5×Dic3C2211yescharacteristic
17C23×C5×Dic3C2211yescharacteristic
18C22×C3×C22⋊D5C2212yes—
19C22×C3×D20C2211yescharacteristic
20C22×D5×Dic3C2212yes—
21C2×#6719C2212yes—
22C2×C4⋊Dic15C2211yescharacteristic
23#91813C2218yescomplemented
24C2×#6712C2212yes—
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C4×C5×Dic3C2218yescomplemented
30C3×#4076C2218yes—
31C2×C3×#685C2212yes—
32C2×C3×C4⋊Dic5C2211yescharacteristic
33Dic3×C22⋊D5C22116yescomplemented
34C2×#6669C2212yes—
35C2×#6669C2212yes—
36C2×#6668C2212yes—
37#91536C22116yescomplemented
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40C2×#6665C2212yes—
41C2×Dic3×Dic5C2212yes—
42Dic3×D20C2218yescomplemented
43#91393C22116yescomplemented
44#91381C2218yescomplemented
45#91364C2218yescomplemented
46#91363C22116yescomplemented
47#91340C2218yescomplemented
48C2×#5600—51nomaximal, Hall
49C22×C42×C5—31no—
50C2×#4076D311yescharacteristic
51C2×#4075—32no—
52C2×C4×C22⋊D5—32no—
53C2×#4070—31no—
54#65813—316no—
55C2×#4022—32no—
56C2×#4021—31no—
57C2×C4×D20—31no—
58C2×#4018—32no—
59C2×#4016—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2311yescharacteristic
62C23×C3×D5C2312yes—
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×Dic15C2312yes—
69C2×Dic30—24no—
70C2×Dic30C2314yes—
71C22×C5×Dic3—24no—
72C22×C5×Dic3—24no—
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2311yescharacteristic
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2314yes—
77C22×C5×Dic3C2314yes—
78C22×C5×Dic3C2311yescharacteristic
79C2×C3×C22⋊D5—28no—
80C2×C3×C22⋊D5C2318yes—
81C22×C3×Dic5C2312yes—
82C2×C3×D20—24no—
83C2×C3×D20C2314yes—
84C2×D5×Dic3—28no—
85C2×D5×Dic3C2318yes—
86#6719C2318yes—
87C4⋊Dic15C2314yes—
88#6712C2318yes—
89C4×C5×Dic3C2314yes—
90C4×C5×Dic3C2314yes—
91C4×C5×Dic3C2314yes—
92C4×C5×Dic3C2314yes—
93C3×#685C2318yes—
94C3×C4⋊Dic5C2314yes—
95#6669C2318yes—
96#6669C2318yes—
97#6668C2318yes—
98#6665C2318yes—
99#6665C2318yes—
100#6665C2318yes—
101Dic3×Dic5C2318yes—
102C2×C3×#121—51no—
103C2×#936—51no—
104C2×#935—52no—
105C2×D4×Dic3—52no—
106C2×D4×Dic3—51no—
107C2×#924—51no—
108C22×C4×Dic3D511yescharacteristic, complemented
109#5600—516no—
110C2×#890—51no—
111C2×#887—51no—
112C2×#879—52no—
113C2×#877—52no—
114C23×C4×C5—31no—
115C23×C4×C5—31no—
116C23×C4×C5C2×D311yescharacteristic
117C22×C22⋊D5C2×D312yes—
118C22×D20C2×D311yescharacteristic
119C22×C4×D5—32no—
120C22×Dic10—31no—
121C2×C42×C5—31no—
122C2×C42×C5—31no—
123C2×C42×C5—31no—
124C2×C42×C5—31no—
125C2×C42×C5—38no—
126C2×C22⋊Dic5—32no—
127#4076C2×D318yes—
128#4075—316no—
129C4×C22⋊D5—316no—
130C2×#685—32no—
131C2×#685—32no—
132C2×#685—32no—
133C2×#685C2×D312yes—
134C2×C4⋊Dic5—31no—
135C2×C4⋊Dic5C2×D311yescharacteristic
136#4070—38no—
137C2×#683—32no—
138C2×#683—32no—
139C2×#683—32no—
140C2×#683—32no—
141C2×C4×Dic5—32no—
142#4022—316no—
143#4021—38no—
144C4×D20—38no—
145#4018—316no—
146#4016—38no—
147C4×Dic10—38no—
148C2×#529—151noSylow
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5#4114yes—
152C23×C3×C5C2412yes—
153C23×C3×C5C2411yescharacteristic
154C22×C3×D5—24no—
155C22×C3×D5—24no—
156C22×C3×D5—24no—
157C22×C3×D5C2414yes—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—28no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—24no—
164C2×Dic15—24no—
165C2×Dic15C2414yes—
166C2×Dic15C2414yes—
167Dic30—28no—
168C2×C5×Dic3—28no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—28no—
173C2×C5×Dic3#4114yes—
174C2×C5×Dic3C2412yes—
175C2×C5×Dic3C2412yes—
176C2×C5×Dic3C2412yes—
177C2×C5×Dic3C2412yes—
178C3×C22⋊D5—216no—
179C2×C3×Dic5—24no—
180C2×C3×Dic5C2414yes—
181C3×D20—28no—
182D5×Dic3—216no—
183C22×C3×D4—52no—
184C22×C3×D4—51no—
185C23×C3×C4C2×D511yescharacteristic
186C23×Dic3—52no—
187C23×Dic3C2×D511yescharacteristic
188C23×Dic3C2×D511yescharacteristic
189C22×Dic6—51no—
190C3×#121—58no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C22⋊C4—52no—
193C2×#217—52no—
194C2×#217—52no—
195C2×#217—52no—
196C2×#217—52no—
197#936—58no—
198#935—516no—
199D4×Dic3—516no—
200D4×Dic3—58no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—52no—
203#924—58no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×C4×Dic3—52no—
208C2×C4×Dic3C2×D511yescharacteristic
209C2×C4×Dic3C2×D511yescharacteristic
210C2×C4×Dic3C2×D511yescharacteristic
211C2×C4×Dic3C2×D511yescharacteristic
212C2×C4×Dic3C2×D518yescomplemented
213#890—58no—
214#887—58no—
215#879—516no—
216#877—516no—
217C24×C5C22×D311yescharacteristic
218C23×D5C22×D312yes—
219C22×C4×C5—24no—
220C22×C4×C5—31no—
221C22×C4×C5—31no—
222C22×C4×C5—31no—
223C22×C4×C5—31no—
224C22×C4×C5—34no—
225C22×C4×C5—34no—
226C22×C4×C5—64no—
227C22×C4×C5—64no—
228C22×C4×C5C22×D311yescharacteristic
229C22×C4×C5C22×D314yes—
230C22×C4×C5C22×D311yescharacteristic
231C2×C22⋊D5—28no—
232C2×C22⋊D5C22×D318yes—
233C22×Dic5—32no—
234C22×Dic5—32no—
235C22×Dic5C22×D312yes—
236C2×D20—24no—
237C2×D20C22×D314yes—
238C2×C4×D5—38no—
239C2×C4×D5—68no—
240C2×Dic10—34no—
241C2×Dic10—64no—
242C42×C5—34no—
243C42×C5—34no—
244C42×C5—34no—
245C42×C5—34no—
246C22⋊Dic5—38no—
247#685—38no—
248#685—38no—
249#685—38no—
250#685C22×D318yes—
251C4⋊Dic5—34no—
252C4⋊Dic5C22×D314yes—
253#683—38no—
254#683—38no—
255#683—38no—
256#683—38no—
257C4×Dic5—38no—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—51no—
265C2×C4×Q8—151no—
266C2×C4×D4—151no—
267C2×C4×D4—152no—
268C2×#117—152no—
269C22×C42—31no—
270C22×C3×C5—28no—
271C22×C3×C5—22no—
272C22×C3×C5—22no—
273C22×C3×C5C2×#4114yes—
274C22×C3×C5C2×#4112yes—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5C2511yescharacteristic
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—24no—
281C2×C3×D5—48no—
282C3×C4×C5—22no—
283C3×C4×C5C2×#4114yes—
284Dic15—24no—
285Dic15—24no—
286C3×Dic5—24no—
287C5×Dic3—22no—
288C5×Dic3—22no—
289C5×Dic3—22no—
290C5×Dic3C2×#4114yes—
291C24×C3—52no—
292C24×C3C22×D511yescharacteristic
293C2×C3×D4—58no—
294C2×C3×D4—54no—
295C2×C3×D4—108no—
296C2×C3×D4—104no—
297C22×C3×C4—24no—
298C22×C3×C4—52no—
299C22×C3×C4C22×D511yescharacteristic
300C22×C3×C4C22×D514yes—
301C22×C3×C4C22×D511yescharacteristic
302C22×Dic3—24no—
303C22×Dic3—24no—
304C22×Dic3—52no—
305C22×Dic3—52no—
306C22×Dic3—58no—
307C22×Dic3—108no—
308C22×Dic3C22×D511yescharacteristic
309C22×Dic3C22×D511yescharacteristic
310C22×Dic3C22×D511yescharacteristic
311C22×Dic3C22×D514yes—
312C22×Dic3C22×D514yes—
313C22×Dic3C22×D511yescharacteristic
314C2×Dic6—54no—
315C2×Dic6—104no—
316C3×C4⋊C4—54no—
317C3×C22⋊C4—58no—
318#217—58no—
319#217—58no—
320#217—58no—
321#217—58no—
322C4⋊Dic3—54no—
323C4⋊Dic3—58no—
324Dic3⋊C4—58no—
325Dic3⋊C4—58no—
326Dic3⋊C4—58no—
327C4×Dic3—58no—
328C4×Dic3C22×D514yes—
329C4×Dic3C22×D514yes—
330C4×Dic3C22×D514yes—
331C4×Dic3C22×D514yes—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5#23714yes—
335C23×C5C23×D312yes—
336C23×C5C23×D311yescharacteristic
337C22×D5—24no—
338C22×D5—24no—
339C22×D5—24no—
340C22×D5C23×D314yes—
341C2×C4×C5—22no—
342C2×C4×C5—28no—
343C2×C4×C5—34no—
344C2×C4×C5—32no—
345C2×C4×C5—32no—
346C2×C4×C5—32no—
347C2×C4×C5—32no—
348C2×C4×C5—68no—
349C2×C4×C5—68no—
350C2×C4×C5—62no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5#23714yes—
354C2×C4×C5C23×D312yes—
355C2×C4×C5C23×D312yes—
356C22⋊D5—216no—
357C2×Dic5—24no—
358C2×Dic5—34no—
359C2×Dic5—34no—
360C2×Dic5—64no—
361C2×Dic5—64no—
362C2×Dic5C23×D314yes—
363D20—28no—
364C4×D5—616no—
365Dic10—68no—
366C22×Q8—151no—
367C22×D4—52no—
368C22×D4—51no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—152no—
372C23×C4D3×D511yescharacteristic
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—58no—
379C4×Q8—158no—
380C4×D4—158no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—51no—
384C2×C4⋊C4—152no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—151no—
389C2×C22⋊C4—52no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—31no—
395C2×C42—31no—
396C2×C42—31no—
397C2×C42—31no—
398C2×C42—38no—
399C2×C42—152no—
400C2×C3×C5—24no—
401C2×C3×C5#52914yescomplemented
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C2×C3×C5C22×#4111yescharacteristic
405C3×D5—44no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—54no—
409C23×C3—104no—
410C23×C3—104no—
411C23×C3—104no—
412C23×C3#70914yes—
413C23×C3C23×D512yes—
414C23×C3C23×D511yescharacteristic
415C3×D4—1016no—
416C3×D4—108no—
417C2×C3×C4—22no—
418C2×C3×C4—28no—
419C2×C3×C4—54no—
420C2×C3×C4—104no—
421C2×C3×C4#70914yes—
422C2×C3×C4C23×D512yes—
423C2×C3×C4C23×D512yes—
424C2×Dic3—28no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—28no—
429C2×Dic3—54no—
430C2×Dic3—54no—
431C2×Dic3—104no—
432C2×Dic3—104no—
433C2×Dic3—1016no—
434C2×Dic3#70914yes—
435C2×Dic3C23×D512yes—
436C2×Dic3C23×D512yes—
437C2×Dic3C23×D512yes—
438C2×Dic3C23×D512yes—
439Dic6—108no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—28no—
443C22×C5C2×#23714yes—
444C22×C5C2×#23712yes—
445C22×C5C2×#23712yes—
446C22×C5D3×#4112yes—
447C22×C5C24×D311yescharacteristic
448C2×D5—24no—
449C2×D5—24no—
450C2×D5—24no—
451C2×D5—48no—
452C4×C5—22no—
453C4×C5—34no—
454C4×C5—62no—
455C4×C5—62no—
456C4×C5—62no—
457C4×C5C2×#23714yes—
458Dic5—24no—
459Dic5—64no—
460Dic5—64no—
461C24—52no—
462C24C2×D3×D511yescharacteristic
463C2×Q8—154no—
464C2×Q8—304no—
465C2×D4—58no—
466C2×D4—54no—
467C2×D4—108no—
468C2×D4—104no—
469C22×C4—24no—
470C22×C4—31no—
471C22×C4—34no—
472C22×C4—34no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—52no—
477C22×C4—64no—
478C22×C4—64no—
479C22×C4—158no—
480C22×C4—152no—
481C22×C4—152no—
482C22×C4—308no—
483C22×C4C2×D3×D514yes—
484C22×C4C2×D3×D511yescharacteristic
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—54no—
487C4⋊C4—158no—
488C4⋊C4—158no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4—154no—
492C22⋊C4—58no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—34no—
498C42—34no—
499C42—34no—
500C42—34no—
501C42—158no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—28no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—104no—
507C22×C3—104no—
508C22×C3—104no—
509C22×C3—208no—
510C22×C3C2×#70914yes—
511C22×C3C2×#70912yes—
512C22×C3C2×#70912yes—
513C22×C3C2×#70912yes—
514C22×C3C24×D511yescharacteristic
515C3×C4—22no—
516C3×C4—104no—
517C3×C4C2×#70914yes—
518Dic3—22no—
519Dic3—22no—
520Dic3—22no—
521Dic3—104no—
522Dic3—104no—
523Dic3C2×#70914yes—
524C2×C5—24no—
525C2×C5#560014yescomplemented
526C2×C5C22×#23711yescharacteristic
527C2×C5C22×#23711yescharacteristic
528C2×C5C2×D3×#4111yescharacteristic
529D5—44no—
530C23—22no—
531C23—22no—
532C23—54no—
533C23—104no—
534C23—104no—
535C23—104no—
536C23#676514yes—
537C23C22×D3×D512yes—
538C23C22×D3×D511yescharacteristic
539Q8—308no—
540D4—1016no—
541D4—108no—
542C2×C4—22no—
543C2×C4—28no—
544C2×C4—34no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—32no—
548C2×C4—32no—
549C2×C4—54no—
550C2×C4—68no—
551C2×C4—68no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—104no—
556C2×C4—154no—
557C2×C4—154no—
558C2×C4—3016no—
559C2×C4—304no—
560C2×C4—304no—
561C2×C4#677914yes—
562C2×C4C22×D3×D512yes—
563C2×C4C22×D3×D512yes—
564C2×C3—24no—
565C2×C3—204no—
566C2×C3#6581314yescomplemented
567C2×C3C22×#70911yescharacteristic
568C2×C3C22×#70911yescharacteristic
569C2×C3C22×#70911yescharacteristic
570C5C2×#560011yescharacteristic, complemented, Sylow
571C22—22no—
572C22—28no—
573C22—22no—
574C22—104no—
575C22—104no—
576C22—104no—
577C22—208no—
578C22C2×#676514yes—
579C22C2×#676512yes—
580C22D3×#70912yes—
581C22C2×#677912yes—
582C22C23×D3×D511yescharacteristic
583C4—22no—
584C4—34no—
585C4—62no—
586C4—62no—
587C4—62no—
588C4—104no—
589C4—304no—
590C4—304no—
591C4C2×#677914yes—
592C3C2×#6581311yescharacteristic, complemented, Sylow
593C2—24no—
594C2—204no—
595C2#1175442214yesdirect product factor
596C2C22×#676511yescharacteristic
597C2C2×D3×#70911yescharacteristic
598C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC2×C3×#4076C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#529
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×#91813C2semidirect
2. C22×C4×C5×Dic3C2semidirect
4. C2×Dic3×C22⋊D5C2semidirect
5. C2×#91536C2semidirect
6. #11754422C2direct (N × H)
7. C2×Dic3×D20C2semidirect
8. C2×#91393C2semidirect
9. C2×#91381C2semidirect
10. C2×#91364C2semidirect
11. C2×#91363C2semidirect
12. C2×#91340C2semidirect
23. #91813C22semidirect
29. C2×C4×C5×Dic3C22semidirect
33. Dic3×C22⋊D5C22semidirect
37. #91536C22semidirect
42. Dic3×D20C22semidirect
43. #91393C22semidirect
44. #91381C22semidirect
45. #91364C22semidirect
46. #91363C22semidirect
47. #91340C22semidirect
108. C22×C4×Dic3D5semidirect
212. C2×C4×Dic3C2×D5semidirect
401. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
525. C2×C5#5600semidirect
566. C2×C3#65813semidirect
570. C5C2×#5600semidirect
592. C3C2×#65813semidirect
595. C2#11754422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918132
C22×C4×C5×Dic32
C2×C3×#40762
C2×Dic3×C22⋊D52
C2×#915362
#117544222
C2×Dic3×D202
C2×#913932
C2×#913812
C2×#913642
C2×#913632
C2×#913402
C2×#658133
C2×#56005