Finite Group Databasebeta

← C2×#11754196 #14483526

Subgroups — C2×#11754196 #14483526

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×#1220C211yesmaximal, characteristic
2C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4070C211yesmaximal, characteristic, complemented
4C2×#91542C212yesmaximal
5C2×#91529C212yesmaximal, complemented
6C2×#91390C211yesmaximal, characteristic, complemented
7C2×#91384C211yesmaximal, characteristic, complemented
8C2×#91347C211yesmaximal, characteristic, complemented
9#11754196C2116yesmaximal, direct product factor
10C2×#91337C212yesmaximal, complemented
11C2×#91335C212yesmaximal, complemented
12C2×#91331C211yesmaximal, characteristic, complemented
13C2×#65847—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C23×C5×Dic3C2212yes—
18C22×C3×Dic10C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C4×#1220C2218yes—
21C2×#6714C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×C4⋊Dic3C2212yes—
27C2×C5×C4⋊Dic3C2218yescomplemented
28C2×C3×C22⋊Dic5C2212yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C3×#4070C2218yescomplemented
31C2×C3×#683C2212yes—
32C2×Dic3⋊Dic5C2212yes—
33C2×Dic3⋊Dic5C2212yes—
34#91542C22116yes—
35C2×#6668C2212yes—
36C2×#6668C2212yes—
37C2×#6667C2212yes—
38C2×#6667C2212yes—
39#91529C22116yescomplemented
40C2×Dic3×Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91390C2218yescomplemented
43#91384C2218yescomplemented
44#91347C2218yescomplemented
45#91337C22116yescomplemented
46#91335C22116yescomplemented
47#91331C2218yescomplemented
48C2×#5642—51nomaximal, Hall
49C22×C5×C4⋊C4—31no—
50C2×#4075—32no—
51C2×C4×C22⋊D5—31no—
52C2×#4072—32no—
53C2×#4070D311yescharacteristic, complemented
54#65847—316no—
55C2×#4044—32no—
56C2×#4043—31no—
57C2×#4038—31no—
58C2×#4036—31no—
59C2×#4035—32no—
60C2×#4033—31no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2311yescharacteristic
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C2×#1220—24no—
68C2×#1220C2314yes—
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2311yescharacteristic
72C2×C4×D15—24no—
73C2×C4×D15C2314yes—
74C22×C5×Dic3—28no—
75C22×C5×Dic3C2312yes—
76C22×C5×Dic3C2312yes—
77C22×C5×Dic3C2318yes—
78C22×C3×Dic5C2312yes—
79C22×C3×Dic5C2312yes—
80C2×C3×Dic10—24no—
81C2×C3×Dic10C2314yes—
82#6719C2314yes—
83#6714C2314yes—
84#6712C2314yes—
85C4×Dic15C2314yes—
86C5×C4⋊Dic3C2314yes—
87C5×C4⋊Dic3C2318yes—
88C5×C4⋊Dic3C2314yes—
89C3×C22⋊Dic5C2318yes—
90C3×C4⋊Dic5C2314yes—
91C3×#683C2318yes—
92Dic3⋊Dic5C2318yes—
93Dic3⋊Dic5C2318yes—
94#6668C2318yes—
95#6668C2318yes—
96#6667C2318yes—
97#6667C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C22⋊Q8—51no—
101C2×#946—51no—
102C2×Q8×Dic3—51no—
103C2×C4×#67—51no—
104C22×C4⋊Dic3D511yescharacteristic, complemented
105#5642—516no—
106C2×#898—52no—
107C2×#892—51no—
108C2×#890—51no—
109C2×#890—52no—
110C2×#886—52no—
111C2×#877—52no—
112C23×C4×C5—32no—
113C23×C4×C5C2×D311yescharacteristic
114C22×C22⋊D5—31no—
115C22×C4×D5—31no—
116C22×Dic10C2×D311yescharacteristic
117C2×C5×C4⋊C4—31no—
118C2×C5×C4⋊C4—32no—
119C2×C5×C4⋊C4—31no—
120C2×C5×C4⋊C4—38no—
121C2×C22⋊Dic5—31no—
122C2×C22⋊Dic5C2×D312yes—
123#4075—316no—
124C4×C22⋊D5—38no—
125C2×#685—31no—
126C2×#685—32no—
127C2×#685—32no—
128#4072—316no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132#4070C2×D318yescomplemented
133C2×#683—31no—
134C2×#683—32no—
135C2×#683—32no—
136C2×#683C2×D312yes—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—32no—
140#4044—316no—
141#4043—38no—
142#4038—38no—
143#4036—38no—
144#4035—316no—
145#4033—38no—
146C2×#552—151noSylow
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5#4114yes—
150C23×C3×C5C2412yes—
151C23×C3×C5C2411yescharacteristic
152C22×D15—22no—
153C22×D15—22no—
154C22×D15—22no—
155C22×D15C2412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161#1220—28no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15C2412yes—
166C2×Dic15C2412yes—
167C2×Dic15C2412yes—
168C4×D15—28no—
169C2×C5×Dic3—216no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3—24no—
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2414yes—
174C2×C3×Dic5—24no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5C2414yes—
177C2×C3×Dic5C2414yes—
178C3×Dic10—28no—
179C22×C3×Q8—51no—
180C23×C3×C4C2×D511yescharacteristic
181C22×#67—51no—
182C23×Dic3C2×D512yes—
183C22×C4×D3—51no—
184C3×C22⋊Q8—58no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—52no—
187C2×C3×C22⋊C4—52no—
188C2×#217—51no—
189#946—58no—
190Q8×Dic3—58no—
191C4×#67—58no—
192C2×(C2×D3)⋊C4—51no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3C2×D512yes—
198C2×C4⋊Dic3C2×D511yescharacteristic
199C2×C4⋊Dic3C2×D511yescharacteristic
200C2×C4⋊Dic3C2×D518yescomplemented
201C2×Dic3⋊C4—51no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204C2×C4×Dic3—51no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3—52no—
207#898—516no—
208#892—58no—
209#890—516no—
210#890—58no—
211#886—516no—
212#877—516no—
213C24×C5C22×D311yescharacteristic
214C23×D5—31no—
215C22×C4×C5—24no—
216C22×C4×C5—32no—
217C22×C4×C5—32no—
218C22×C4×C5—38no—
219C22×C4×C5—68no—
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D314yes—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—34no—
224C2×C22⋊D5—64no—
225C22×Dic5—31no—
226C22×Dic5—31no—
227C22×Dic5—31no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D312yes—
230C2×C4×D5—34no—
231C2×C4×D5—64no—
232C2×Dic10—24no—
233C2×Dic10C22×D314yes—
234C5×C4⋊C4—34no—
235C5×C4⋊C4—38no—
236C5×C4⋊C4—34no—
237C22⋊Dic5—34no—
238C22⋊Dic5C22×D318yes—
239#685—34no—
240#685—38no—
241#685—38no—
242C4⋊Dic5—38no—
243C4⋊Dic5—38no—
244C4⋊Dic5C22×D314yes—
245#683—34no—
246#683—38no—
247#683—38no—
248#683C22×D318yes—
249C4×Dic5—34no—
250C4×Dic5—38no—
251C4×Dic5—38no—
252#552—1516no—
253C2×#126—152no—
254C2×#125—152no—
255C2×#125—151no—
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—31no—
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×D15—22no—
273C2×D15—22no—
274C2×D15—22no—
275C2×D15—44no—
276C3×C4×C5—22no—
277C3×C4×C5C2×#4114yes—
278Dic15—22no—
279Dic15—22no—
280Dic15—22no—
281C3×Dic5—24no—
282C3×Dic5—24no—
283C5×Dic3—24no—
284C5×Dic3—24no—
285C24×C3C22×D511yescharacteristic
286C23×D3—51no—
287C2×C3×Q8—54no—
288C2×C3×Q8—104no—
289C22×C3×C4—24no—
290C22×C3×C4—52no—
291C22×C3×C4—52no—
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D514yes—
294C22×C3×C4C22×D511yescharacteristic
295C2×#67—54no—
296C2×#67—104no—
297C22×Dic3—28no—
298C22×Dic3—51no—
299C22×Dic3—51no—
300C22×Dic3—51no—
301C22×Dic3C22×D518yes—
302C22×Dic3C22×D512yes—
303C22×Dic3C22×D512yes—
304C2×C4×D3—54no—
305C2×C4×D3—104no—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C22⋊C4—58no—
309#217—54no—
310(C2×D3)⋊C4—54no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—58no—
313C4⋊Dic3—58no—
314C4⋊Dic3—58no—
315C4⋊Dic3C22×D518yes—
316C4⋊Dic3C22×D514yes—
317C4⋊Dic3C22×D514yes—
318Dic3⋊C4—54no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321C4×Dic3—54no—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5#23914yes—
327C23×C5C23×D312yes—
328C23×C5C23×D311yescharacteristic
329C22×D5—32no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5—62no—
333C2×C4×C5—22no—
334C2×C4×C5—28no—
335C2×C4×C5—34no—
336C2×C4×C5—34no—
337C2×C4×C5—616no—
338C2×C4×C5—64no—
339C2×C4×C5—64no—
340C2×C4×C5#23714yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C22⋊D5—68no—
344C2×Dic5—24no—
345C2×Dic5—24no—
346C2×Dic5—32no—
347C2×Dic5—32no—
348C2×Dic5—32no—
349C2×Dic5—62no—
350C2×Dic5—62no—
351C2×Dic5—62no—
352C2×Dic5C23×D314yes—
353C2×Dic5C23×D314yes—
354C4×D5—68no—
355Dic10—28no—
356C22×Q8—51no—
357C22×D4—151no—
358C23×C4—32no—
359C23×C4—151no—
360C23×C4D3×D511yescharacteristic
361#126—1516no—
362#125—1516no—
363#125—158no—
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—31no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—38no—
375C2×C4⋊C4—51no—
376C2×C4⋊C4—52no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—151no—
382C2×C22⋊C4—52no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—151no—
387C2×C42—152no—
388C2×C42—152no—
389C2×C42—151no—
390C2×C3×C5—24no—
391C2×C3×C5#55214yescomplemented
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C22×#4111yescharacteristic
394C2×C3×C5C2×2−1+411yescharacteristic
395D15—42no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3#71114yes—
399C23×C3C23×D512yes—
400C23×C3C23×D511yescharacteristic
401C22×D3—52no—
402C22×D3—102no—
403C22×D3—102no—
404C22×D3—102no—
405C3×Q8—108no—
406C2×C3×C4—22no—
407C2×C3×C4—28no—
408C2×C3×C4—54no—
409C2×C3×C4—54no—
410C2×C3×C4—104no—
411C2×C3×C4—104no—
412C2×C3×C4#70914yes—
413C2×C3×C4C23×D512yes—
414C2×C3×C4C23×D512yes—
415#67—108no—
416C2×Dic3—216no—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—52no—
420C2×Dic3—52no—
421C2×Dic3—52no—
422C2×Dic3—102no—
423C2×Dic3—102no—
424C2×Dic3—102no—
425C2×Dic3C23×D514yes—
426C2×Dic3C23×D514yes—
427C4×D3—108no—
428C22×C5—28no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5C2×#23712yes—
432C22×C5C2×#23914yes—
433C22×C5C2×#23912yes—
434C22×C5#101012yes—
435C22×C5C24×D311yescharacteristic
436C2×D5—62no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—124no—
440C4×C5—22no—
441C4×C5—64no—
442C4×C5—64no—
443C4×C5C2×#23714yes—
444Dic5—24no—
445Dic5—24no—
446Dic5—62no—
447Dic5—62no—
448Dic5—62no—
449C24—151no—
450C24C2×D3×D511yescharacteristic
451C2×Q8—54no—
452C2×Q8—104no—
453C2×D4—154no—
454C2×D4—304no—
455C22×C4—24no—
456C22×C4—38no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—52no—
460C22×C4—52no—
461C22×C4—68no—
462C22×C4—151no—
463C22×C4—151no—
464C22×C4—151no—
465C22×C4—154no—
466C22×C4—304no—
467C22×C4C2×D3×D514yes—
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—34no—
472C4⋊C4—38no—
473C4⋊C4—54no—
474C4⋊C4—58no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—158no—
478C4⋊C4—158no—
479C4⋊C4—154no—
480C22⋊C4—58no—
481C22⋊C4—158no—
482C22⋊C4—158no—
483C22⋊C4—154no—
484C22⋊C4—154no—
485C42—158no—
486C42—158no—
487C42—154no—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—28no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3C2×#70912yes—
493C22×C3C2×#71114yes—
494C22×C3C2×#71112yes—
495C22×C3#414712yes—
496C22×C3C24×D511yescharacteristic
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—204no—
501C3×C4—22no—
502C3×C4—104no—
503C3×C4—104no—
504C3×C4C2×#70914yes—
505Dic3—24no—
506Dic3—24no—
507Dic3—102no—
508Dic3—102no—
509Dic3—102no—
510C2×C5—24no—
511C2×C5#564214yescomplemented
512C2×C5C22×#23711yescharacteristic
513C2×C5C22×#23911yescharacteristic
514C2×C5C2×#101011yescharacteristic
515D5—122no—
516C23—22no—
517C23—22no—
518C23—152no—
519C23—302no—
520C23—302no—
521C23—302no—
522C23#676814yes—
523C23C22×D3×D512yes—
524C23C22×D3×D511yescharacteristic
525Q8—108no—
526D4—308no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—54no—
532C2×C4—54no—
533C2×C4—616no—
534C2×C4—64no—
535C2×C4—64no—
536C2×C4—104no—
537C2×C4—104no—
538C2×C4—152no—
539C2×C4—152no—
540C2×C4—152no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—308no—
545C2×C4#677914yes—
546C2×C4C22×D3×D512yes—
547C2×C4C22×D3×D512yes—
548C2×C3—24no—
549C2×C3#6584714yescomplemented
550C2×C3C22×#70911yescharacteristic
551C2×C3C22×#71111yescharacteristic
552C2×C3C2×#414711yescharacteristic
553D3—202no—
554C5C2×#564211yescharacteristic, complemented, Sylow
555C22—22no—
556C22—22no—
557C22—28no—
558C22—302no—
559C22—302no—
560C22—302no—
561C22—604no—
562C22#9200012yes—
563C22C2×#676814yes—
564C22C2×#676812yes—
565C22C2×#677912yes—
566C22C23×D3×D511yescharacteristic
567C4—22no—
568C4—64no—
569C4—64no—
570C4—104no—
571C4—104no—
572C4—302no—
573C4—302no—
574C4—302no—
575C4C2×#677914yes—
576C3C2×#6584711yescharacteristic, complemented, Sylow
577C2—24no—
578C2—602no—
579C2#1175419614yesdirect product factor
580C2C2×#9200011yescharacteristic
581C2C22×#676811yescharacteristic
582C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×#1220C22
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
2. C22×C5×C4⋊Dic3C2semidirect
3. C2×C3×#4070C2semidirect
5. C2×#91529C2semidirect
6. C2×#91390C2semidirect
7. C2×#91384C2semidirect
8. C2×#91347C2semidirect
9. #11754196C2direct (N × H)
10. C2×#91337C2semidirect
11. C2×#91335C2semidirect
12. C2×#91331C2semidirect
27. C2×C5×C4⋊Dic3C22semidirect
30. C3×#4070C22semidirect
39. #91529C22semidirect
42. #91390C22semidirect
43. #91384C22semidirect
44. #91347C22semidirect
45. #91337C22semidirect
46. #91335C22semidirect
47. #91331C22semidirect
53. C2×#4070D3semidirect
104. C22×C4⋊Dic3D5semidirect
132. #4070C2×D3semidirect
200. C2×C4⋊Dic3C2×D5semidirect
391. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
511. C2×C5#5642semidirect
549. C2×C3#65847semidirect
554. C5C2×#5642semidirect
576. C3C2×#65847semidirect
579. C2#11754196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C22×C5×C4⋊Dic32
C2×C3×#40702
C2×#915422
C2×#915292
C2×#913902
C2×#913842
C2×#913472
#117541962
C2×#913372
C2×#913352
C2×#913312
C2×#658473
C2×#56425