Finite Group Databasebeta

← C2×#11754248 #14483527

Subgroups — C2×#11754248 #14483527

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#924C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
4C2×#91537C212yesmaximal
5C2×#91532C212yesmaximal, complemented
6C2×#91388C211yesmaximal, characteristic, complemented
7#11754248C2116yesmaximal, direct product factor
8C2×#91362C212yesmaximal, complemented
9C2×#91359C211yesmaximal, characteristic, complemented
10C2×#91358C211yesmaximal, characteristic, complemented
11C2×#91343C212yesmaximal, complemented
12C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
13C2×#65976—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C23×Dic15C2212yes—
16C22×C5×Dic6C2211yescharacteristic
17C22×C3×C22⋊D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C2×C4⋊Dic15C2212yes—
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4⋊Dic15C2218yescomplemented
23C2×C5×#217C2212yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C5×#924C2218yescomplemented
26C2×C5×Dic3⋊C4C2212yes—
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C3×C4×C22⋊D5C2218yes—
29C2×C3×#685C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2212yes—
33C2×Dic3⋊Dic5C2212yes—
34C2×#6669C2212yes—
35C2×#6669C2212yes—
36#91537C22116yes—
37C2×#6665C2212yes—
38C2×#6665C2212yes—
39#91532C22116yescomplemented
40C2×Dic3×Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91388C2218yescomplemented
43#91362C22116yescomplemented
44#91359C2218yescomplemented
45#91358C2218yescomplemented
46#91343C22116yescomplemented
47Dic5×Dic6C2218yescomplemented
48C2×#5541—51nomaximal, Hall
49C2×C5×C22⋊Q8—31no—
50C2×#4092—31no—
51C2×Q8×Dic5—31no—
52C2×C4×C22⋊D5D311yescharacteristic
53C22×C4⋊Dic5—31no—
54#65976—316no—
55C2×#4044—32no—
56C2×#4038—31no—
57C2×#4036—32no—
58C2×#4036—31no—
59C2×#4032—32no—
60C2×#4023—32no—
61C24×C3×C5C2311yescharacteristic
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15—28no—
68C22×Dic15C2312yes—
69C22×Dic15C2318yes—
70C22×Dic15C2312yes—
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C2×C3×C22⋊D5—24no—
76C2×C3×C22⋊D5C2314yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5C2314yes—
82C4⋊Dic15C2314yes—
83C4⋊Dic15C2318yes—
84C4⋊Dic15C2314yes—
85C5×#217C2318yes—
86C5×C4⋊Dic3C2314yes—
87C5×Dic3⋊C4C2318yes—
88C3×C22⋊Dic5C2314yes—
89C3×#685C2314yes—
90C3×#683C2314yes—
91C3×C4×Dic5C2314yes—
92Dic3⋊Dic5C2318yes—
93Dic3⋊Dic5C2318yes—
94#6669C2318yes—
95#6669C2318yes—
96#6665C2318yes—
97#6665C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C4×D4—51no—
101C2×#935—52no—
102C2×#926—51no—
103C22×C4⋊Dic3—51no—
104C2×#924—51no—
105C2×#924D511yescharacteristic, complemented
106#5541—516no—
107C2×#889—52no—
108C2×#879—52no—
109C2×#877—52no—
110C2×#870—51no—
111C2×C4×Dic6—51no—
112C22×C5×Q8—31no—
113C23×C4×C5C2×D311yescharacteristic
114C22×C22⋊D5C2×D311yescharacteristic
115C23×Dic5—32no—
116C22×C4×D5C2×D311yescharacteristic
117C5×C22⋊Q8—38no—
118C2×C5×C4⋊C4—31no—
119C2×C5×C4⋊C4—32no—
120C2×C5×C22⋊C4—32no—
121C2×C22⋊Dic5C2×D311yescharacteristic
122#4092—38no—
123Q8×Dic5—38no—
124C4×C22⋊D5C2×D318yes—
125C2×#685—32no—
126C2×#685—32no—
127C2×#685C2×D311yescharacteristic
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—31no—
131C2×C4⋊Dic5—38no—
132C2×C4⋊Dic5—32no—
133C2×C4⋊Dic5—32no—
134C2×#683—32no—
135C2×#683—32no—
136C2×#683C2×D311yescharacteristic
137C2×C4×Dic5—32no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5C2×D311yescharacteristic
140#4044—316no—
141#4038—38no—
142#4036—316no—
143#4036—38no—
144#4032—316no—
145#4023—316no—
146C2×#552—151noSylow
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5#4114yes—
150C23×C3×C5C2412yes—
151C23×C3×C5C2411yescharacteristic
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5—22no—
155C22×C3×D5C2412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161C2×Dic15—216no—
162C2×Dic15—24no—
163C2×Dic15—24no—
164C2×Dic15C2414yes—
165C2×Dic15C2414yes—
166C2×C5×Dic3—24no—
167C2×C5×Dic3—24no—
168C2×C5×Dic3C2414yes—
169C2×C5×Dic3C2414yes—
170C5×Dic6—28no—
171C3×C22⋊D5—28no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5C2412yes—
176C2×C3×Dic5C2412yes—
177C2×C3×Dic5C2412yes—
178C3×C4×D5—28no—
179C22×C3×D4—51no—
180C23×C3×C4—51no—
181C23×C3×C4C2×D511yescharacteristic
182C23×Dic3—52no—
183C22×Dic6C2×D511yescharacteristic
184C3×C4×D4—58no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C22⋊C4—51no—
187C2×C3×C22⋊C4—51no—
188C2×C3×C42—51no—
189C2×#217—52no—
190C2×#217—52no—
191C2×#217C2×D512yes—
192#935—516no—
193#926—58no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—58no—
198C2×C4⋊Dic3C2×D511yescharacteristic
199#924—58no—
200#924C2×D518yescomplemented
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4C2×D512yes—
206C2×C4×Dic3—52no—
207C2×C4×Dic3—52no—
208#889—516no—
209#879—516no—
210#877—516no—
211#870—58no—
212C4×Dic6—58no—
213C24×C5C22×D311yescharacteristic
214C23×D5C22×D311yescharacteristic
215C2×C5×Q8—34no—
216C2×C5×Q8—64no—
217C22×C4×C5—24no—
218C22×C4×C5—32no—
219C22×C4×C5—32no—
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D314yes—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—24no—
224C2×C22⋊D5C22×D314yes—
225C22×Dic5—38no—
226C22×Dic5—32no—
227C22×Dic5—32no—
228C22×Dic5—68no—
229C22×Dic5C22×D311yescharacteristic
230C22×Dic5C22×D311yescharacteristic
231C22×Dic5C22×D311yescharacteristic
232C2×C4×D5—24no—
233C2×C4×D5C22×D314yes—
234C5×C4⋊C4—38no—
235C5×C4⋊C4—34no—
236C5×C22⋊C4—38no—
237C22⋊Dic5C22×D314yes—
238#685—38no—
239#685—38no—
240#685C22×D314yes—
241C4⋊Dic5—38no—
242C4⋊Dic5—34no—
243C4⋊Dic5—34no—
244C4⋊Dic5—38no—
245C4⋊Dic5—38no—
246#683—38no—
247#683—38no—
248#683C22×D314yes—
249C4×Dic5—38no—
250C4×Dic5—38no—
251C4×Dic5C22×D314yes—
252#552—1516no—
253C2×#126—152no—
254C2×#125—151no—
255C2×#125—152no—
256C2×#123—152no—
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—51no—
261C2×#117—152no—
262C2×#117—151no—
263C22×C4⋊C4—151no—
264C22×C3×C5—28no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5C2×#4114yes—
269C22×C3×C5C2×#4112yes—
270C22×C3×C52−1+412yes—
271C22×C3×C5C2511yescharacteristic
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—44no—
276C3×C4×C5—22no—
277C3×C4×C5C2×#4114yes—
278Dic15—24no—
279Dic15—24no—
280C3×Dic5—22no—
281C3×Dic5—22no—
282C3×Dic5—22no—
283C5×Dic3—24no—
284C5×Dic3—24no—
285C24×C3—51no—
286C24×C3C22×D511yescharacteristic
287C2×C3×D4—54no—
288C2×C3×D4—104no—
289C22×C3×C4—24no—
290C22×C3×C4—51no—
291C22×C3×C4—51no—
292C22×C3×C4—51no—
293C22×C3×C4—54no—
294C22×C3×C4—104no—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D514yes—
297C22×C3×C4C22×D511yescharacteristic
298C22×Dic3—58no—
299C22×Dic3—52no—
300C22×Dic3—52no—
301C22×Dic3—108no—
302C22×Dic3C22×D512yes—
303C22×Dic3C22×D512yes—
304C2×Dic6—24no—
305C2×Dic6C22×D514yes—
306C3×C4⋊C4—54no—
307C3×C22⋊C4—54no—
308C3×C22⋊C4—54no—
309C3×C42—54no—
310#217—58no—
311#217—58no—
312#217C22×D518yes—
313C4⋊Dic3—54no—
314C4⋊Dic3—54no—
315C4⋊Dic3—58no—
316C4⋊Dic3C22×D514yes—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321Dic3⋊C4C22×D518yes—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5#23514yes—
327C23×C5C23×D312yes—
328C23×C5C23×D311yescharacteristic
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5C23×D312yes—
333C5×Q8—68no—
334C2×C4×C5—22no—
335C2×C4×C5—28no—
336C2×C4×C5—34no—
337C2×C4×C5—34no—
338C2×C4×C5—64no—
339C2×C4×C5—64no—
340C2×C4×C5#23714yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C22⋊D5—28no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—34no—
348C2×Dic5—34no—
349C2×Dic5—616no—
350C2×Dic5—64no—
351C2×Dic5—64no—
352C2×Dic5C23×D312yes—
353C2×Dic5C23×D312yes—
354C2×Dic5C23×D312yes—
355C4×D5—28no—
356C22×Q8—31no—
357C22×D4—51no—
358C23×C4—51no—
359C23×C4—152no—
360C23×C4D3×D511yescharacteristic
361#126—1516no—
362#125—158no—
363#125—1516no—
364#123—1516no—
365C22⋊Q8—38no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4—58no—
369#117—1516no—
370#117—158no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—158no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—51no—
384C2×C22⋊C4—51no—
385C2×C22⋊C4—152no—
386C2×C22⋊C4—152no—
387C2×C42—51no—
388C2×C42—152no—
389C2×C42—152no—
390C2×C3×C5—24no—
391C2×C3×C5#55214yescomplemented
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C22×#4111yescharacteristic
394C2×C3×C5C2×2−1+411yescharacteristic
395C3×D5—42no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—52no—
399C23×C3—102no—
400C23×C3—102no—
401C23×C3—102no—
402C23×C3#71314yes—
403C23×C3C23×D512yes—
404C23×C3C23×D511yescharacteristic
405C3×D4—108no—
406C2×C3×C4—22no—
407C2×C3×C4—28no—
408C2×C3×C4—52no—
409C2×C3×C4—52no—
410C2×C3×C4—52no—
411C2×C3×C4—102no—
412C2×C3×C4—102no—
413C2×C3×C4—102no—
414C2×C3×C4—108no—
415C2×C3×C4#71114yes—
416C2×C3×C4C23×D512yes—
417C2×C3×C4C23×D512yes—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—54no—
421C2×Dic3—54no—
422C2×Dic3—1016no—
423C2×Dic3—104no—
424C2×Dic3—104no—
425C2×Dic3C23×D514yes—
426C2×Dic3C23×D514yes—
427Dic6—28no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—28no—
431C22×C5C2×#23514yes—
432C22×C5C2×#23512yes—
433C22×C5C2×#23712yes—
434C22×C5#101012yes—
435C22×C5C24×D311yescharacteristic
436C2×D5—22no—
437C2×D5—22no—
438C2×D5—22no—
439C2×D5—44no—
440C4×C5—22no—
441C4×C5—64no—
442C4×C5—64no—
443C4×C5C2×#23714yes—
444Dic5—22no—
445Dic5—22no—
446Dic5—22no—
447Dic5—64no—
448Dic5—64no—
449C24—51no—
450C24C2×D3×D511yescharacteristic
451C2×Q8—34no—
452C2×Q8—64no—
453C2×D4—54no—
454C2×D4—104no—
455C22×C4—24no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—51no—
459C22×C4—51no—
460C22×C4—51no—
461C22×C4—54no—
462C22×C4—104no—
463C22×C4—158no—
464C22×C4—152no—
465C22×C4—152no—
466C22×C4—308no—
467C22×C4C2×D3×D514yes—
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—38no—
472C4⋊C4—54no—
473C4⋊C4—158no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—154no—
478C4⋊C4—154no—
479C4⋊C4—158no—
480C22⋊C4—38no—
481C22⋊C4—54no—
482C22⋊C4—54no—
483C22⋊C4—158no—
484C22⋊C4—158no—
485C42—54no—
486C42—158no—
487C42—158no—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—28no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—102no—
493C22×C3—102no—
494C22×C3—102no—
495C22×C3—204no—
496C22×C3C2×#71112yes—
497C22×C3C2×#71314yes—
498C22×C3C2×#71312yes—
499C22×C3#415012yes—
500C22×C3C24×D511yescharacteristic
501C3×C4—22no—
502C3×C4—102no—
503C3×C4—102no—
504C3×C4—102no—
505C3×C4C2×#71114yes—
506Dic3—24no—
507Dic3—24no—
508Dic3—104no—
509Dic3—104no—
510C2×C5—24no—
511C2×C5#554114yescomplemented
512C2×C5C22×#23511yescharacteristic
513C2×C5C22×#23711yescharacteristic
514C2×C5C2×#101011yescharacteristic
515D5—42no—
516C23—22no—
517C23—22no—
518C23—52no—
519C23—102no—
520C23—102no—
521C23—102no—
522C23#677314yes—
523C23C22×D3×D512yes—
524C23C22×D3×D511yescharacteristic
525Q8—68no—
526D4—108no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—52no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—64no—
535C2×C4—64no—
536C2×C4—102no—
537C2×C4—102no—
538C2×C4—102no—
539C2×C4—108no—
540C2×C4—154no—
541C2×C4—154no—
542C2×C4—3016no—
543C2×C4—304no—
544C2×C4—304no—
545C2×C4#678014yes—
546C2×C4C22×D3×D512yes—
547C2×C4C22×D3×D512yes—
548C2×C3—24no—
549C2×C3—202no—
550C2×C3#6597614yescomplemented
551C2×C3C22×#71111yescharacteristic
552C2×C3C22×#71311yescharacteristic
553C2×C3C2×#415011yescharacteristic
554C5C2×#554111yescharacteristic, complemented, Sylow
555C22—28no—
556C22—22no—
557C22—22no—
558C22—102no—
559C22—102no—
560C22—102no—
561C22—204no—
562C22#9200112yes—
563C22C2×#677314yes—
564C22C2×#677312yes—
565C22C2×#678012yes—
566C22C23×D3×D511yescharacteristic
567C4—22no—
568C4—64no—
569C4—64no—
570C4—102no—
571C4—102no—
572C4—102no—
573C4—304no—
574C4—304no—
575C4C2×#678014yes—
576C3C2×#6597611yescharacteristic, complemented, Sylow
577C2—24no—
578C2—202no—
579C2#1175424814yesdirect product factor
580C2C2×#9200111yescharacteristic
581C2C22×#677311yescharacteristic
582C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#552
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. C22×C4⋊Dic15C2semidirect
2. C2×C5×#924C2semidirect
5. C2×#91532C2semidirect
6. C2×#91388C2semidirect
7. #11754248C2direct (N × H)
8. C2×#91362C2semidirect
9. C2×#91359C2semidirect
10. C2×#91358C2semidirect
11. C2×#91343C2semidirect
12. C2×Dic5×Dic6C2semidirect
22. C2×C4⋊Dic15C22semidirect
25. C5×#924C22semidirect
39. #91532C22semidirect
42. #91388C22semidirect
43. #91362C22semidirect
44. #91359C22semidirect
45. #91358C22semidirect
46. #91343C22semidirect
47. Dic5×Dic6C22semidirect
105. C2×#924D5semidirect
200. #924C2×D5semidirect
391. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
511. C2×C5#5541semidirect
550. C2×C3#65976semidirect
554. C5C2×#5541semidirect
576. C3C2×#65976semidirect
579. C2#11754248direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic152
C2×C5×#9242
C2×C3×C4×C22⋊D52
C2×#915372
C2×#915322
C2×#913882
#117542482
C2×#913622
C2×#913592
C2×#913582
C2×#913432
C2×Dic5×Dic62
C2×#659763
C2×#55415