Finite Group Databasebeta

← C2×#11753800 #14483569

Subgroups — C2×#11753800 #14483569

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
1C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
2C2×C5×#890C211yesmaximal, characteristic, complemented
3C2×C3×#4043C211yesmaximal, characteristic, complemented
4C2×C4×#1202C211yesmaximal, characteristic
5C2×#91390C211yesmaximal, characteristic, complemented
6C2×#91361C212yesmaximal, complemented
7C2×#91358C211yesmaximal, characteristic, complemented
8C2×#91354C212yesmaximal
9C2×#91347C212yesmaximal, complemented
10C2×#91346C212yesmaximal, complemented
11C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
12#11753800C2116yesmaximal, direct product factor
13C2×#66028—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×#1202C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2212yes—
22C4⋊C4×D15C2218yescomplemented
23C2×C5×C4⋊Dic3C2212yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×Dic3⋊C4C2212yes—
26C2×C4×C5×Dic3C2211yescharacteristic
27C5×#890C2218yescomplemented
28C2×C3×#685C2212yes—
29C2×C3×C4⋊Dic5C2212yes—
30C3×#4043C2218yescomplemented
31C2×Dic3⋊Dic5C2212yes—
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6668C2212yes—
34C2×#6667C2211yescharacteristic
35C2×#6667C2212yes—
36C2×#6665C2211yescharacteristic
37C2×#6665C2212yes—
38C2×Dic3×Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40C4×#1202C2218yes—
41#91390C2218yescomplemented
42#91361C22116yescomplemented
43#91358C2218yescomplemented
44#91354C22116yes—
45#91347C22116yescomplemented
46#91346C22116yescomplemented
47Dic3×Dic10C2218yescomplemented
48C2×#5639—51nomaximal, Hall
49C2×C5×#125—31no—
50#66028—316no—
51C2×#4044—32no—
52C2×#4043—31no—
53C2×#4043D311yescharacteristic, complemented
54C2×#4040—32no—
55C2×#4038—32no—
56C2×#4038—31no—
57C2×D5×C4⋊C4—31no—
58C2×#4036—32no—
59C2×C4×D20—31no—
60C2×C4×Dic10—31no—
61C23×D15C2311yescharacteristic
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2311yescharacteristic
67C2×C4×D15—28no—
68C2×C4×D15—24no—
69C2×C4×D15C2314yes—
70C2×C4×D15C2318yes—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2312yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2312yes—
76C2×C3×C4×D5—24no—
77C2×C3×C4×D5C2314yes—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×#1202—24no—
81C2×#1202C2314yes—
82C3×C5×C4⋊C4C2314yes—
83C4⋊Dic15C2314yes—
84#6712C2318yes—
85C5×C4⋊Dic3C2318yes—
86C5×C4⋊Dic3C2314yes—
87C5×Dic3⋊C4C2318yes—
88C4×C5×Dic3C2314yes—
89C3×#685C2318yes—
90C3×C4⋊Dic5C2318yes—
91Dic3⋊Dic5C2314yes—
92Dic3⋊Dic5C2318yes—
93#6668C2318yes—
94#6667C2314yes—
95#6667C2318yes—
96#6665C2314yes—
97#6665C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C22⋊Q8—51no—
101C2×#946—51no—
102C2×Q8×Dic3—51no—
103C2×C4×#67—51no—
104C2×#926—51no—
105#5639—516no—
106C2×#892—52no—
107C2×D3×C4⋊C4—51no—
108C2×#890D511yescharacteristic, complemented
109C2×#889—52no—
110C2×#883—52no—
111C2×#879—52no—
112C22×D20—31no—
113C22×C4×D5—31no—
114C22×C4×D5—32no—
115C22×C4×D5C2×D311yescharacteristic
116C22×Dic10C2×D311yescharacteristic
117C5×#125—38no—
118C2×C5×C4⋊C4—32no—
119C2×C5×C4⋊C4—31no—
120C2×C5×C4⋊C4—32no—
121C2×C5×C4⋊C4C2×D311yescharacteristic
122C2×C42×C5—31no—
123C2×#685—31no—
124C2×#685—32no—
125C2×#685—31no—
126C2×#685—32no—
127C2×#685C2×D312yes—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D312yes—
132C2×#683—32no—
133C2×#683—32no—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—32no—
136#4044—316no—
137#4043—38no—
138#4043C2×D318yescomplemented
139#4040—316no—
140#4038—38no—
141#4038—316no—
142D5×C4⋊C4—38no—
143#4036—316no—
144C4×D20—38no—
145C4×Dic10—38no—
146C2×#552—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×D15—22no—
149C22×D15—22no—
150C22×D15#4114yes—
151C22×D15C2412yes—
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5—22no—
155C22×C3×D5C2412yes—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5#4114yes—
158C2×C3×C4×C5C2414yes—
159C2×C3×C4×C5C2412yes—
160C2×Dic15—22no—
161C2×Dic15—24no—
162C2×Dic15C2414yes—
163C2×Dic15C2412yes—
164C4×D15—216no—
165C4×D15—28no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3C2412yes—
170C2×C5×Dic3C2414yes—
171C2×C5×Dic3C2412yes—
172C2×C3×Dic5—24no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5C2412yes—
175C2×C3×Dic5C2414yes—
176C3×C4×D5—28no—
177C3×Dic10—28no—
178#1202—28no—
179C22×C3×Q8—51no—
180C23×C3×C4—51no—
181C22×#67—51no—
182C22×C4×D3—52no—
183C22×C4×D3—51no—
184C3×C22⋊Q8—58no—
185C2×C3×C4⋊C4—52no—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4—52no—
188C2×#217—51no—
189C2×#217—52no—
190#946—58no—
191Q8×Dic3—58no—
192C4×#67—58no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—51no—
195#926—58no—
196C2×C4⋊Dic3—51no—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3C2×D512yes—
199C2×C4⋊Dic3C2×D511yescharacteristic
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—51no—
203C2×Dic3⋊C4C2×D512yes—
204C2×C4×Dic3—52no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3C2×D511yescharacteristic
207#892—516no—
208D3×C4⋊C4—58no—
209#890C2×D518yescomplemented
210#889—516no—
211#883—516no—
212#879—516no—
213C23×D5—31no—
214C23×D5C22×D311yescharacteristic
215C22×C4×C5—31no—
216C22×C4×C5—31no—
217C22×C4×C5—32no—
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—32no—
221C22×Dic5—31no—
222C22×Dic5C22×D312yes—
223C22×Dic5C22×D311yescharacteristic
224C2×D20—34no—
225C2×D20—64no—
226C2×C4×D5—24no—
227C2×C4×D5—34no—
228C2×C4×D5—38no—
229C2×C4×D5—68no—
230C2×C4×D5—64no—
231C2×C4×D5C22×D314yes—
232C2×Dic10—24no—
233C2×Dic10C22×D314yes—
234C5×C4⋊C4—38no—
235C5×C4⋊C4—34no—
236C5×C4⋊C4—38no—
237C5×C4⋊C4C22×D314yes—
238C42×C5—34no—
239#685—34no—
240#685—38no—
241#685—34no—
242#685—38no—
243#685C22×D318yes—
244C4⋊Dic5—34no—
245C4⋊Dic5—34no—
246C4⋊Dic5—38no—
247C4⋊Dic5C22×D318yes—
248#683—38no—
249#683—38no—
250C4×Dic5—38no—
251C4×Dic5—38no—
252#552—1516no—
253C2×#126—152no—
254C2×#125—31no—
255C2×#125—152no—
256C2×#123—152no—
257C2×C22⋊Q8—51no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C2×#117—151no—
263C22×C4⋊C4—151no—
264C22×C3×C5C2×#4112yes—
265C22×C3×C5C2×#4112yes—
266C22×C3×C52−1+412yes—
267C22×C3×C5C2511yescharacteristic
268C2×D15—28no—
269C2×D15—22no—
270C2×D15—22no—
271C2×D15C2×#4114yes—
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—44no—
276C3×C4×C5—24no—
277C3×C4×C5C2×#4114yes—
278Dic15—22no—
279Dic15—24no—
280C3×Dic5—24no—
281C3×Dic5—22no—
282C5×Dic3—22no—
283C5×Dic3—22no—
284C5×Dic3—24no—
285C24×C3—51no—
286C23×D3—51no—
287C2×C3×Q8—54no—
288C2×C3×Q8—104no—
289C22×C3×C4—51no—
290C22×C3×C4—52no—
291C22×C3×C4—54no—
292C22×C3×C4—104no—
293C22×C3×C4C22×D512yes—
294C22×C3×C4C22×D511yescharacteristic
295C2×#67—54no—
296C2×#67—104no—
297C22×Dic3—52no—
298C22×Dic3—51no—
299C22×Dic3C22×D511yescharacteristic
300C22×Dic3C22×D512yes—
301C22×Dic3C22×D511yescharacteristic
302C2×C4×D3—58no—
303C2×C4×D3—54no—
304C2×C4×D3—108no—
305C2×C4×D3—104no—
306C3×C4⋊C4—58no—
307C3×C4⋊C4C22×D514yes—
308C3×C22⋊C4—58no—
309#217—54no—
310#217—58no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—54no—
313C4⋊Dic3—54no—
314C4⋊Dic3—58no—
315C4⋊Dic3C22×D518yes—
316C4⋊Dic3C22×D514yes—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319Dic3⋊C4—54no—
320Dic3⋊C4C22×D518yes—
321C4×Dic3—58no—
322C4×Dic3—58no—
323C4×Dic3C22×D514yes—
324C23×C5C23×D311yescharacteristic
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—34no—
329C22×D5—32no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5C23×D312yes—
333C2×C4×C5—24no—
334C2×C4×C5—32no—
335C2×C4×C5—34no—
336C2×C4×C5—32no—
337C2×C4×C5—62no—
338C2×C4×C5—64no—
339C2×C4×C5—62no—
340C2×C4×C5#23714yes—
341C2×C4×C5C23×D314yes—
342C2×C4×C5C23×D312yes—
343C2×Dic5—24no—
344C2×Dic5—22no—
345C2×Dic5—34no—
346C2×Dic5—32no—
347C2×Dic5—62no—
348C2×Dic5—64no—
349C2×Dic5C23×D312yes—
350C2×Dic5C23×D314yes—
351D20—68no—
352C4×D5—28no—
353C4×D5—616no—
354C4×D5—68no—
355Dic10—28no—
356C22×Q8—51no—
357C22×D4—151no—
358C23×C4—51no—
359C23×C4—152no—
360C23×C4—151no—
361#126—1516no—
362#125—38no—
363#125—1516no—
364#123—1516no—
365C22⋊Q8—58no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4—158no—
369#117—1516no—
370#117—158no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—52no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—158no—
381C2×C4⋊C4D3×D511yescharacteristic
382C2×C22⋊C4—52no—
383C2×C22⋊C4—151no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—152no—
386C2×C22⋊C4—151no—
387C2×C42—31no—
388C2×C42—152no—
389C2×C42—152no—
390C2×C3×C5#55214yescomplemented
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394D15—24no—
395C3×D5—42no—
396C23×C3—52no—
397C23×C3—102no—
398C23×C3—102no—
399C23×C3—102no—
400C23×C3C23×D511yescharacteristic
401C22×D3—54no—
402C22×D3—52no—
403C22×D3—102no—
404C22×D3—102no—
405C3×Q8—108no—
406C2×C3×C4—24no—
407C2×C3×C4—52no—
408C2×C3×C4—54no—
409C2×C3×C4—102no—
410C2×C3×C4—104no—
411C2×C3×C4—108no—
412C2×C3×C4#71314yes—
413C2×C3×C4C23×D514yes—
414C2×C3×C4C23×D512yes—
415#67—108no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—24no—
419C2×Dic3—54no—
420C2×Dic3—52no—
421C2×Dic3—102no—
422C2×Dic3—104no—
423C2×Dic3C23×D512yes—
424C2×Dic3C23×D514yes—
425C2×Dic3C23×D512yes—
426C4×D3—1016no—
427C4×D3—108no—
428C22×C5C2×#23712yes—
429C22×C5#100712yes—
430C22×C5D3×#4112yes—
431C22×C5C24×D311yescharacteristic
432C2×D5—22no—
433C2×D5—22no—
434C2×D5—22no—
435C2×D5—34no—
436C2×D5—44no—
437C2×D5—68no—
438C2×D5—62no—
439C2×D5—62no—
440C4×C5—24no—
441C4×C5—62no—
442C4×C5—64no—
443C4×C5—62no—
444C4×C5C2×#23714yes—
445Dic5—24no—
446Dic5—22no—
447Dic5—62no—
448Dic5—64no—
449C24—51no—
450C24—151no—
451C2×Q8—54no—
452C2×Q8—104no—
453C2×D4—154no—
454C2×D4—304no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—32no—
458C22×C4—51no—
459C22×C4—52no—
460C22×C4—54no—
461C22×C4—104no—
462C22×C4—152no—
463C22×C4—151no—
464C22×C4—158no—
465C22×C4—154no—
466C22×C4—308no—
467C22×C4—304no—
468C22×C4C2×D3×D512yes—
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—38no—
472C4⋊C4—38no—
473C4⋊C4—58no—
474C4⋊C4—154no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—154no—
478C4⋊C4—158no—
479C4⋊C4C2×D3×D514yes—
480C22⋊C4—58no—
481C22⋊C4—154no—
482C22⋊C4—158no—
483C22⋊C4—158no—
484C22⋊C4—154no—
485C42—34no—
486C42—158no—
487C42—158no—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—102no—
490C22×C3—102no—
491C22×C3—102no—
492C22×C3—204no—
493C22×C3C2×#71312yes—
494C22×C3D5×#4112yes—
495C22×C3#415012yes—
496C22×C3C24×D511yescharacteristic
497C2×D3—54no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—108no—
501C3×C4—24no—
502C3×C4—102no—
503C3×C4—104no—
504C3×C4C2×#71314yes—
505Dic3—22no—
506Dic3—22no—
507Dic3—24no—
508Dic3—102no—
509Dic3—104no—
510C2×C5#563914yescomplemented
511C2×C5C22×#23711yescharacteristic
512C2×C5C2×#100711yescharacteristic
513C2×C5C2×D3×#4111yescharacteristic
514D5—42no—
515D5—64no—
516C23—52no—
517C23—102no—
518C23—102no—
519C23—102no—
520C23—154no—
521C23—152no—
522C23—302no—
523C23—302no—
524C23C22×D3×D511yescharacteristic
525Q8—108no—
526D4—308no—
527C2×C4—24no—
528C2×C4—32no—
529C2×C4—32no—
530C2×C4—34no—
531C2×C4—52no—
532C2×C4—54no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—64no—
536C2×C4—102no—
537C2×C4—104no—
538C2×C4—108no—
539C2×C4—154no—
540C2×C4—152no—
541C2×C4—3016no—
542C2×C4—302no—
543C2×C4—304no—
544C2×C4—308no—
545C2×C4#676614yes—
546C2×C4C22×D3×D514yes—
547C2×C4C22×D3×D512yes—
548C2×C3—202no—
549C2×C3#6602814yescomplemented
550C2×C3C22×#71311yescharacteristic
551C2×C3C2×D5×#4111yescharacteristic
552C2×C3C2×#415011yescharacteristic
553D3—104no—
554C5C2×#563911yescharacteristic, complemented, Sylow
555C22—102no—
556C22—102no—
557C22—102no—
558C22—154no—
559C22—204no—
560C22—308no—
561C22—302no—
562C22—302no—
563C22C2×#676612yes—
564C22#9202412yes—
565C22#9203012yes—
566C22C23×D3×D511yescharacteristic
567C4—24no—
568C4—62no—
569C4—62no—
570C4—64no—
571C4—102no—
572C4—104no—
573C4—302no—
574C4—304no—
575C4C2×#676614yes—
576C3C2×#6602811yescharacteristic, complemented, Sylow
577C2—202no—
578C2—304no—
579C2#1175380014yesdirect product factor
580C2C22×#676611yescharacteristic
581C2C2×#9202411yescharacteristic
582C2C2×#9203011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#552
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×C4⋊C4×D15C2semidirect
2. C2×C5×#890C2semidirect
3. C2×C3×#4043C2semidirect
5. C2×#91390C2semidirect
6. C2×#91361C2semidirect
7. C2×#91358C2semidirect
9. C2×#91347C2semidirect
10. C2×#91346C2semidirect
11. C2×Dic3×Dic10C2semidirect
12. #11753800C2direct (N × H)
22. C4⋊C4×D15C22semidirect
27. C5×#890C22semidirect
30. C3×#4043C22semidirect
41. #91390C22semidirect
42. #91361C22semidirect
43. #91358C22semidirect
45. #91347C22semidirect
46. #91346C22semidirect
47. Dic3×Dic10C22semidirect
53. C2×#4043D3semidirect
108. C2×#890D5semidirect
138. #4043C2×D3semidirect
209. #890C2×D5semidirect
390. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
510. C2×C5#5639semidirect
549. C2×C3#66028semidirect
554. C5C2×#5639semidirect
576. C3C2×#66028semidirect
579. C2#11753800direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×C5×#8902
C2×C3×#40432
C2×C4×#12022
C2×#913902
C2×#913612
C2×#913582
C2×#913542
C2×#913472
C2×#913462
C2×Dic3×Dic102
#117538002
C2×#660283
C2×#56395