Finite Group Databasebeta

← C2×#11754484 #14481719

Subgroups — C2×#11754484 #14481719

Order 1920.

2592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6714C211yesmaximal, characteristic
2C2×C5×#924C211yesmaximal, characteristic, complemented
3C2×C3×#4070C211yesmaximal, characteristic, complemented
4C2×#91576C212yesmaximal, complemented
5C2×#91561C212yesmaximal
6#11754484C2116yesmaximal, direct product factor
7C2×#91429C212yesmaximal, complemented
8C2×#91424C212yesmaximal, complemented
9C2×#91419C212yesmaximal, complemented
10C2×#91411C212yesmaximal, complemented
11C2×#65968—31nomaximal, Hall
12C24×D15C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic, complemented
16C22×C3×Dic10C2211yescharacteristic, complemented
17C22×#1204C2212yescomplemented
18C22×#1200C2212yes—
19C22×#1200C2212yes—
20C2×#6714C2212yes—
21C2×#6714C2212yes—
22C2×#6714C2218yes—
23C2×C5×#217C2212yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
25C5×#924C2218yescomplemented
26C2×C5×Dic3⋊C4C2212yescomplemented
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
29C3×#4070C2218yescomplemented
30C2×C3×#683C2212yescomplemented
31#91576C22116yescomplemented
32#91561C22116yes—
33C2×Dic3⋊Dic5C2212yescomplemented
34C2×#6669C2212yescomplemented
35C2×#6668C2212yescomplemented
36C2×#6667C2212yes—
37C2×#6667C2212yes—
38#91429C22116yescomplemented
39#91424C22116yescomplemented
40#91419C22116yescomplemented
41#91411C22116yescomplemented
42C2×#5634—51nomaximal, Hall
43C2×C5×C22⋊Q8—31no—
44C2×#4092—32no—
45C22×#685—31no—
46C2×#4070D311yescharacteristic, complemented
47#65968—316no—
48C2×#4043—32no—
49C2×#4042—32no—
50C2×#4042—32no—
51C2×D5×C22⋊C4—32no—
52C2×#4024—32no—
53C24×C3×C5C2311yescharacteristic
54C23×D15—42no—
55C23×D15—42no—
56C23×D15Q818yescomplemented
57C23×D15C2312yes—
58C23×D15C2314yes—
59C22×C3×C4×C5—42no—
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2314yes—
63C22×Dic15—42no—
64C22×Dic15C2312yes—
65C22×Dic15C2314yes—
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2312yes—
68C2×C5×Dic6—42no—
69C2×C5×Dic6C2314yescomplemented
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2312yes—
72C2×C3×Dic10—42no—
73C2×C3×Dic10C2314yescomplemented
74C2×#1204—44no—
75C2×#1204C2318yescomplemented
76C2×#1200—44no—
77C2×#1200—44no—
78C2×#1200C2318yes—
79C2×#1200C2318yes—
80#6714C2318yes—
81#6714C2318yes—
82C5×#217C2318yes—
83C5×C4⋊Dic3C2314yescomplemented
84C5×Dic3⋊C4C2318yescomplemented
85C3×C22⋊Dic5C2318yes—
86C3×C4⋊Dic5C2314yescomplemented
87C3×#683C2318yescomplemented
88Dic3⋊Dic5C2318yescomplemented
89#6669C2318yescomplemented
90#6668C2318yescomplemented
91#6667C2318yes—
92#6667C2318yes—
93C2×C3×C22⋊Q8—51no—
94C2×#946—52no—
95C22×(C2×D3)⋊C4—51no—
96C2×#924D511yescharacteristic, complemented
97#5634—516no—
98C2×#897—52no—
99C2×#896—52no—
100C2×#896—52no—
101C2×D3×C22⋊C4—52no—
102C2×#878—52no—
103C24×D5—31no—
104C22×C5×Q8—31no—
105C23×C4×C5C2×D311yescharacteristic
106C23×Dic5—31no—
107C22×C4×D5—32no—
108C22×C4×D5—32no—
109C22×Dic10—32no—
110C22×Dic10C2×D311yescharacteristic, complemented
111C5×C22⋊Q8—38no—
112C2×C5×C4⋊C4—31no—
113C2×C5×C4⋊C4—32no—
114C2×C5×C22⋊C4—32no—
115C2×C22⋊Dic5C2×D312yes—
116#4092—316no—
117C2×#685—32no—
118C2×#685—32no—
119C2×#685—38no—
120C2×#685—32no—
121C2×#685—32no—
122C2×C4⋊Dic5—32no—
123C2×C4⋊Dic5C2×D311yescharacteristic, complemented
124#4070C2×D318yescomplemented
125C2×#683—32no—
126C2×#683—32no—
127C2×#683C2×D312yescomplemented
128#4043—316no—
129#4042—316no—
130#4042—316no—
131D5×C22⋊C4—316no—
132#4024—316no—
133C2×#543—151noSylow
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5C2×Q814yes—
137C23×C3×C5C2412yes—
138C23×C3×C5C2411yescharacteristic
139C22×D15—24no—
140C22×D15—24no—
141C22×D15—416no—
142C22×D15—44no—
143C22×D15—44no—
144C22×D15C2×Q818yes—
145C22×D15C2×Q8116yescomplemented
146C22×D15C2414yes—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—44no—
150C2×C3×C4×C5C2412yes—
151C2×C3×C4×C5C2412yes—
152C2×Dic15—24no—
153C2×Dic15—44no—
154C2×Dic15C2414yes—
155C2×C5×Dic3—24no—
156C2×C5×Dic3—24no—
157C2×C5×Dic3C2414yes—
158C2×C5×Dic3C2414yes—
159C5×Dic6—44no—
160C2×C3×Dic5—24no—
161C2×C3×Dic5—24no—
162C2×C3×Dic5C2414yes—
163C2×C3×Dic5C2414yes—
164C3×Dic10—44no—
165#1204—48no—
166#1200—48no—
167#1200—48no—
168C24×D3—51no—
169C22×C3×Q8—51no—
170C23×C3×C4C2×D511yescharacteristic
171C23×Dic3—51no—
172C22×C4×D3—52no—
173C22×C4×D3—52no—
174C22×Dic6—52no—
175C22×Dic6C2×D511yescharacteristic, complemented
176C3×C22⋊Q8—58no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C4⋊C4—52no—
179C2×C3×C22⋊C4—52no—
180C2×#217C2×D512yes—
181#946—516no—
182C2×(C2×D3)⋊C4—58no—
183C2×(C2×D3)⋊C4—52no—
184C2×(C2×D3)⋊C4—52no—
185C2×(C2×D3)⋊C4—52no—
186C2×(C2×D3)⋊C4—52no—
187C2×C4⋊Dic3—52no—
188C2×C4⋊Dic3C2×D511yescharacteristic, complemented
189#924C2×D518yescomplemented
190C2×Dic3⋊C4—52no—
191C2×Dic3⋊C4—52no—
192C2×Dic3⋊C4C2×D512yescomplemented
193#897—516no—
194#896—516no—
195#896—516no—
196D3×C22⋊C4—516no—
197#878—516no—
198C24×C5C22×D311yescharacteristic
199C23×D5—32no—
200C23×D5—38no—
201C23×D5—34no—
202C23×D5—122no—
203C23×D5—122no—
204C2×C5×Q8—34no—
205C2×C5×Q8—122no—
206C22×C4×C5—32no—
207C22×C4×C5—32no—
208C22×C4×C5—42no—
209C22×C4×C5C22×D311yescharacteristic
210C22×C4×C5C22×D311yescharacteristic
211C22×C4×C5C22×D314yes—
212C22×Dic5—32no—
213C22×Dic5—34no—
214C22×Dic5—122no—
215C22×Dic5C22×D312yes—
216C22×Dic5C22×D312yes—
217C2×C4×D5—38no—
218C2×C4×D5—38no—
219C2×C4×D5—124no—
220C2×C4×D5—124no—
221C2×Dic10—38no—
222C2×Dic10—42no—
223C2×Dic10—124no—
224C2×Dic10C22×D314yescomplemented
225C5×C4⋊C4—38no—
226C5×C4⋊C4—34no—
227C5×C22⋊C4—38no—
228C22⋊Dic5C22×D318yes—
229#685—38no—
230#685—38no—
231#685—38no—
232#685—38no—
233C4⋊Dic5—38no—
234C4⋊Dic5C22×D314yescomplemented
235#683—38no—
236#683—38no—
237#683C22×D318yescomplemented
238#543—1516no—
239C2×C22⋊Q8—31no—
240C2×C22⋊Q8—51no—
241C2×C22⋊Q8—152no—
242C2×C22⋊Q8—152no—
243C2×C22⋊Q8—152no—
244C2×C22⋊Q8—152no—
245C2×C22⋊Q8—152no—
246C22×C22⋊C4—152no—
247C22×C22⋊C4—151no—
248C22×C3×C5—28no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5C22×Q814yes—
252C22×C3×C5C22×Q812yes—
253C22×C3×C5H(5,𝔽2)12yes—
254C22×C3×C5H(5,𝔽2)12yes—
255C22×C3×C5C2511yescharacteristic
256C2×D15—216no—
257C2×D15—24no—
258C2×D15—24no—
259C2×D15—416no—
260C2×D15C22×Q818yes—
261C3×C4×C5—22no—
262C3×C4×C5—22no—
263Dic15—24no—
264C3×Dic5—24no—
265C3×Dic5—24no—
266C5×Dic3—24no—
267C5×Dic3—24no—
268C24×C3C22×D511yescharacteristic
269C23×D3—52no—
270C23×D3—58no—
271C23×D3—54no—
272C23×D3—202no—
273C23×D3—202no—
274C2×C3×Q8—54no—
275C2×C3×Q8—202no—
276C22×C3×C4—42no—
277C22×C3×C4—52no—
278C22×C3×C4—52no—
279C22×C3×C4C22×D511yescharacteristic
280C22×C3×C4C22×D511yescharacteristic
281C22×C3×C4C22×D514yes—
282C22×Dic3—52no—
283C22×Dic3—54no—
284C22×Dic3—202no—
285C22×Dic3C22×D512yes—
286C22×Dic3C22×D512yes—
287C2×C4×D3—58no—
288C2×C4×D3—58no—
289C2×C4×D3—204no—
290C2×C4×D3—204no—
291C2×Dic6—42no—
292C2×Dic6—58no—
293C2×Dic6—204no—
294C2×Dic6C22×D514yescomplemented
295C3×C4⋊C4—58no—
296C3×C4⋊C4—54no—
297C3×C22⋊C4—58no—
298#217C22×D518yes—
299(C2×D3)⋊C4—58no—
300(C2×D3)⋊C4—58no—
301(C2×D3)⋊C4—58no—
302(C2×D3)⋊C4—58no—
303C4⋊Dic3—58no—
304C4⋊Dic3C22×D514yescomplemented
305Dic3⋊C4—58no—
306Dic3⋊C4—58no—
307Dic3⋊C4C22×D518yescomplemented
308C23×C5—22no—
309C23×C5—22no—
310C23×C5D3×Q814yes—
311C23×C5C23×D312yes—
312C23×C5C23×D311yescharacteristic
313C22×D5—38no—
314C22×D5—34no—
315C22×D5—316no—
316C22×D5—64no—
317C22×D5—64no—
318C22×D5—1216no—
319C22×D5—124no—
320C22×D5—124no—
321C5×Q8—124no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—34no—
325C2×C4×C5—34no—
326C2×C4×C5—44no—
327C2×C4×C5—64no—
328C2×C4×C5—64no—
329C2×C4×C5C23×D312yes—
330C2×C4×C5C23×D312yes—
331C2×Dic5—24no—
332C2×Dic5—24no—
333C2×Dic5—34no—
334C2×Dic5—64no—
335C2×Dic5—124no—
336C2×Dic5C23×D314yes—
337C2×Dic5C23×D314yes—
338C4×D5—128no—
339C4×D5—128no—
340Dic10—44no—
341Dic10—128no—
342C25—151no—
343C22×Q8—31no—
344C22×Q8—51no—
345C22×Q8—152no—
346C23×C4—152no—
347C23×C4—152no—
348C23×C4—151no—
349C23×C4D3×D511yescharacteristic
350C22⋊Q8—38no—
351C22⋊Q8—58no—
352C22⋊Q8—1516no—
353C22⋊Q8—1516no—
354C22⋊Q8—1516no—
355C22⋊Q8—1516no—
356C22⋊Q8—1516no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—52no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—152no—
362C2×C4⋊C4—152no—
363C2×C4⋊C4—152no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—52no—
366C2×C22⋊C4—1516no—
367C2×C22⋊C4—152no—
368C2×C22⋊C4—152no—
369C2×C22⋊C4—152no—
370C2×C22⋊C4—152no—
371C2×C22⋊C4—158no—
372C2×C3×C5—24no—
373C2×C3×C5#54314yescomplemented
374C2×C3×C5C23×Q811yescharacteristic
375C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
376C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
377D15—28no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3Q8×D514yes—
381C23×C3C23×D512yes—
382C23×C3C23×D511yescharacteristic
383C22×D3—58no—
384C22×D3—54no—
385C22×D3—516no—
386C22×D3—104no—
387C22×D3—104no—
388C22×D3—2016no—
389C22×D3—204no—
390C22×D3—204no—
391C3×Q8—204no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—44no—
395C2×C3×C4—54no—
396C2×C3×C4—54no—
397C2×C3×C4—104no—
398C2×C3×C4—104no—
399C2×C3×C4C23×D512yes—
400C2×C3×C4C23×D512yes—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—54no—
404C2×Dic3—104no—
405C2×Dic3—204no—
406C2×Dic3C23×D514yes—
407C2×Dic3C23×D514yes—
408C4×D3—208no—
409C4×D3—208no—
410Dic6—44no—
411Dic6—208no—
412C22×C5—28no—
413C22×C5—22no—
414C22×C5—22no—
415C22×C5#100412yes—
416C22×C5C2×D3×Q814yes—
417C22×C5C2×D3×Q812yes—
418C22×C5#100912yes—
419C22×C5C24×D311yescharacteristic
420C2×D5—38no—
421C2×D5—616no—
422C2×D5—64no—
423C2×D5—64no—
424C2×D5—1216no—
425C4×C5—22no—
426C4×C5—22no—
427C4×C5—64no—
428C4×C5—64no—
429Dic5—24no—
430Dic5—24no—
431Dic5—64no—
432C24—152no—
433C24—158no—
434C24—154no—
435C24—602no—
436C24—602no—
437C24C2×D3×D511yescharacteristic
438C2×Q8—34no—
439C2×Q8—54no—
440C2×Q8—122no—
441C2×Q8—158no—
442C2×Q8—202no—
443C2×Q8—604no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—42no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—158no—
450C22×C4—158no—
451C22×C4—152no—
452C22×C4—154no—
453C22×C4—604no—
454C22×C4—604no—
455C22×C4—602no—
456C22×C4C2×D3×D511yescharacteristic
457C22×C4C2×D3×D511yescharacteristic
458C22×C4C2×D3×D514yes—
459C4⋊C4—38no—
460C4⋊C4—34no—
461C4⋊C4—58no—
462C4⋊C4—54no—
463C4⋊C4—158no—
464C4⋊C4—158no—
465C4⋊C4—158no—
466C22⋊C4—38no—
467C22⋊C4—58no—
468C22⋊C4—158no—
469C22⋊C4—158no—
470C22⋊C4—158no—
471C22⋊C4—158no—
472C3×C5C2×#54311yescharacteristic, complemented, Hall
473C22×C3—28no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3#414412yes—
477C22×C3C2×Q8×D514yes—
478C22×C3C2×Q8×D512yes—
479C22×C3#414912yes—
480C22×C3C24×D511yescharacteristic
481C2×D3—58no—
482C2×D3—1016no—
483C2×D3—104no—
484C2×D3—104no—
485C2×D3—2016no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—104no—
489C3×C4—104no—
490Dic3—24no—
491Dic3—24no—
492Dic3—104no—
493C2×C5—24no—
494C2×C5#563414yescomplemented
495C2×C5C2×#100411yescharacteristic
496C2×C5C22×D3×Q811yescharacteristic
497C2×C5C2×#100911yescharacteristic
498D5—68no—
499C23—22no—
500C23—22no—
501C23—158no—
502C23—154no—
503C23—1516no—
504C23—304no—
505C23—304no—
506C23—604no—
507C23—604no—
508C23—6016no—
509C23D15⋊Q814yes—
510C23C22×D3×D512yes—
511C23C22×D3×D511yescharacteristic
512Q8—124no—
513Q8—204no—
514Q8—608no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—34no—
518C2×C4—34no—
519C2×C4—44no—
520C2×C4—54no—
521C2×C4—54no—
522C2×C4—64no—
523C2×C4—64no—
524C2×C4—104no—
525C2×C4—104no—
526C2×C4—154no—
527C2×C4—304no—
528C2×C4—608no—
529C2×C4—608no—
530C2×C4—604no—
531C2×C4C22×D3×D512yes—
532C2×C4C22×D3×D512yes—
533C2×C3—24no—
534C2×C3#6596814yescomplemented
535C2×C3C2×#414411yescharacteristic
536C2×C3C22×Q8×D511yescharacteristic
537C2×C3C2×#414911yescharacteristic
538D3—108no—
539C5C2×#563411yescharacteristic, complemented, Sylow
540C22—22no—
541C22—22no—
542C22—28no—
543C22—158no—
544C22—304no—
545C22—304no—
546C22—3016no—
547C22—6016no—
548C22C2×D15⋊Q814yes—
549C22C2×D15⋊Q812yes—
550C22#9201912yes—
551C22#9204912yes—
552C22C23×D3×D511yescharacteristic
553C4—22no—
554C4—22no—
555C4—64no—
556C4—64no—
557C4—104no—
558C4—104no—
559C4—304no—
560C3C2×#6596811yescharacteristic, complemented, Sylow
561C2—24no—
562C2—308no—
563C2#1175448414yesdirect product factor
564C2C22×D15⋊Q811yescharacteristic
565C2C2×#9201911yescharacteristic
566C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC24×D15C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#543
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. C2×C5×#924C2semidirect
3. C2×C3×#4070C2semidirect
4. C2×#91576C2semidirect
6. #11754484C2direct (N × H)
7. C2×#91429C2semidirect
8. C2×#91424C2semidirect
9. C2×#91419C2semidirect
10. C2×#91411C2semidirect
15. C22×C5×Dic6C22semidirect
16. C22×C3×Dic10C22semidirect
17. C22×#1204C22semidirect
24. C2×C5×C4⋊Dic3C22semidirect
25. C5×#924C22semidirect
26. C2×C5×Dic3⋊C4C22semidirect
28. C2×C3×C4⋊Dic5C22semidirect
29. C3×#4070C22semidirect
30. C2×C3×#683C22semidirect
31. #91576C22semidirect
33. C2×Dic3⋊Dic5C22semidirect
34. C2×#6669C22semidirect
35. C2×#6668C22semidirect
38. #91429C22semidirect
39. #91424C22semidirect
40. #91419C22semidirect
41. #91411C22semidirect
46. C2×#4070D3semidirect
56. C23×D15Q8semidirect
69. C2×C5×Dic6C23semidirect
73. C2×C3×Dic10C23semidirect
75. C2×#1204C23semidirect
83. C5×C4⋊Dic3C23semidirect
84. C5×Dic3⋊C4C23semidirect
86. C3×C4⋊Dic5C23semidirect
87. C3×#683C23semidirect
88. Dic3⋊Dic5C23semidirect
89. #6669C23semidirect
90. #6668C23semidirect
96. C2×#924D5semidirect
110. C22×Dic10C2×D3semidirect
123. C2×C4⋊Dic5C2×D3semidirect
124. #4070C2×D3semidirect
127. C2×#683C2×D3semidirect
145. C22×D15C2×Q8semidirect
175. C22×Dic6C2×D5semidirect
188. C2×C4⋊Dic3C2×D5semidirect
189. #924C2×D5semidirect
192. C2×Dic3⋊C4C2×D5semidirect
224. C2×Dic10C22×D3semidirect
234. C4⋊Dic5C22×D3semidirect
237. #683C22×D3semidirect
294. C2×Dic6C22×D5semidirect
304. C4⋊Dic3C22×D5semidirect
307. Dic3⋊C4C22×D5semidirect
373. C2×C3×C5#543semidirect
472. C3×C5C2×#543semidirect
494. C2×C5#5634semidirect
534. C2×C3#65968semidirect
539. C5C2×#5634semidirect
560. C3C2×#65968semidirect
563. C2#11754484direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67142
C2×C5×#9242
C2×C3×#40702
C2×#915762
C2×#915612
#117544842
C2×#914292
C2×#914242
C2×#914192
C2×#914112
C2×#659683
C2×#56345