Finite Group Databasebeta

← C2×#11753357 #14484062

Subgroups — C2×#11753357 #14484062

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91776C211yesmaximal, characteristic, complemented
2C2×C5×#893C211yesmaximal, characteristic
3C2×C3×#4033C211yesmaximal, characteristic, complemented
4C2×C4×#1204C211yesmaximal, characteristic, complemented
5C2×#91389C211yesmaximal, characteristic, complemented
6C2×#91373C211yesmaximal, characteristic
7C2×#91372C212yesmaximal, complemented
8C2×#91371C212yesmaximal, complemented
9C2×#91370C211yesmaximal, characteristic
10C2×#91367C212yesmaximal, complemented
11C2×#91352C212yesmaximal, complemented
12#11753357C2116yesmaximal, direct product factor
13C2×#65876—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C4×C5×D3C2212yes—
17C22×C3×Dic10C2211yescharacteristic
18C22×#1204C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×#6712C2212yes—
21C2×C4×Dic15C2212yes—
22C2×C4×Dic15C2211yescharacteristic
23#91776C2218yescomplemented
24C2×C5×(C2×D3)⋊C4C2212yes—
25C2×C4×C5×Dic3C2211yescharacteristic
26C5×#893C2218yes—
27C2×C3×#683C2212yes—
28C2×C3×C4×Dic5C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C3×#4033C2218yescomplemented
31C2×Dic3⋊Dic5C2212yes—
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2212yes—
34C2×#6669C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40C4×#1204C2218yescomplemented
41#91389C2218yescomplemented
42#91373C2218yes—
43#91372C22116yescomplemented
44#91371C22116yescomplemented
45#91370C2218yes—
46#91367C22116yescomplemented
47#91352C22116yescomplemented
48C2×#5568—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4082—31no—
51C2×#4082—31no—
52C2×#4072—32no—
53C2×#4070—32no—
54#65876—316no—
55C2×#4033—31no—
56C2×#4033D311yescharacteristic, complemented
57C2×#4025—32no—
58C2×#4025—32no—
59C2×#4015—31no—
60C2×C4×Dic10—31no—
61C23×C5×D3C2312yes—
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2312yes—
67C2×Dic30—24no—
68C2×Dic30C2314yes—
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2311yescharacteristic
71C2×C5×D12—24no—
72C2×C5×D12C2314yes—
73C2×C4×C5×D3—28no—
74C2×C4×C5×D3C2318yes—
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2312yes—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×#1204—24no—
81C2×#1204C2314yes—
82C3×C5×C4⋊C4C2314yes—
83#6712C2318yes—
84C4×Dic15C2314yes—
85C4×Dic15C2318yes—
86C5×(C2×D3)⋊C4C2318yes—
87C4×C5×Dic3C2314yes—
88C3×#683C2318yes—
89C3×C4×Dic5C2314yes—
90C3×C4×Dic5C2318yes—
91Dic3⋊Dic5C2314yes—
92Dic3⋊Dic5C2318yes—
93Dic3⋊Dic5C2318yes—
94#6669C2314yes—
95#6668C2314yes—
96(C2×D3)⋊Dic5C2318yes—
97(C2×D3)⋊Dic5C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100C2×C3×C4×Q8—51no—
101C2×#947—51no—
102C2×#944—51no—
103#5568—516no—
104C2×#898—52no—
105C2×#896—52no—
106C2×#893D511yescharacteristic
107C2×#887—51no—
108C2×#876—52no—
109C2×#875—51no—
110C2×#872—52no—
111C2×C4×Dic6—51no—
112C22×C5×D4—31no—
113C23×C4×C5—32no—
114C22×Dic10—31no—
115C22×Dic10—31no—
116C22×Dic10C2×D311yescharacteristic
117C4×C5×D4—38no—
118C2×C5×C4⋊C4C2×D311yescharacteristic
119C2×C5×C22⋊C4—32no—
120C2×C42×C5—31no—
121C2×C22⋊Dic5—32no—
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5—32no—
125#4082—38no—
126#4082—38no—
127#4072—316no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—32no—
131#4070—316no—
132C2×#683—32no—
133C2×#683—31no—
134C2×#683—31no—
135C2×#683C2×D312yes—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—32no—
138C2×C4×Dic5C2×D311yescharacteristic
139C2×C4×Dic5C2×D312yes—
140#4033—38no—
141#4033C2×D318yescomplemented
142#4025—316no—
143#4025—316no—
144#4015—38no—
145C4×Dic10—38no—
146C2×#556—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C5×D3—24no—
149C22×C5×D3—24no—
150C22×C5×D3—24no—
151C22×C5×D3C2414yes—
152C2×C3×C4×C5—24no—
153C2×C3×C4×C5#4114yes—
154C2×C3×C4×C5C2414yes—
155C2×C3×C4×C5C2412yes—
156C2×Dic15—22no—
157C2×Dic15—24no—
158C2×Dic15—22no—
159C2×Dic15C2412yes—
160C2×Dic15C2412yes—
161C2×Dic15C2414yes—
162Dic30—28no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3#4114yes—
165C2×C5×Dic3C2412yes—
166C2×C5×Dic3C2412yes—
167C5×D12—28no—
168C4×C5×D3—216no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—24no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5C2412yes—
173C2×C3×Dic5C2412yes—
174C2×C3×Dic5C2414yes—
175C3×Dic10—28no—
176#1204—28no—
177C22×C3×Q8—51no—
178C22×D12C2×D511yescharacteristic
179C22×C4×D3C2×D512yes—
180C22×Dic6—51no—
181C22×Dic6—51no—
182C3×C4×Q8—58no—
183C2×C3×C4⋊C4—52no—
184C2×C3×C4⋊C4C2×D511yescharacteristic
185C2×C3×C42—51no—
186C2×C3×C42—52no—
187#947—58no—
188#944—58no—
189C2×(C2×D3)⋊C4—52no—
190C2×(C2×D3)⋊C4—52no—
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D512yes—
194C2×C4⋊Dic3—51no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—51no—
197C2×Dic3⋊C4—51no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×C4×Dic3—51no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3C2×D511yescharacteristic
203#898—516no—
204#896—516no—
205#893C2×D518yes—
206#887—58no—
207#876—516no—
208#875—58no—
209#872—516no—
210C4×Dic6—58no—
211C24×C5—32no—
212C2×C5×D4—34no—
213C2×C5×D4—64no—
214C22×C4×C5—31no—
215C22×C4×C5—31no—
216C22×C4×C5—38no—
217C22×C4×C5—68no—
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—31no—
221C22×Dic5—32no—
222C22×Dic5—31no—
223C22×Dic5C22×D311yescharacteristic
224C22×Dic5C22×D312yes—
225C22×Dic5C22×D311yescharacteristic
226C2×Dic10—24no—
227C2×Dic10—34no—
228C2×Dic10—34no—
229C2×Dic10—64no—
230C2×Dic10—64no—
231C2×Dic10C22×D314yes—
232C5×C4⋊C4C22×D314yes—
233C5×C22⋊C4—38no—
234C42×C5—34no—
235C22⋊Dic5—38no—
236C22⋊Dic5—38no—
237C22⋊Dic5—38no—
238C22⋊Dic5—38no—
239C4⋊Dic5—34no—
240C4⋊Dic5—38no—
241C4⋊Dic5—38no—
242#683—38no—
243#683—34no—
244#683—34no—
245#683C22×D318yes—
246C4×Dic5—34no—
247C4×Dic5—38no—
248C4×Dic5C22×D314yes—
249C4×Dic5C22×D318yes—
250#556—1516no—
251C2×C4⋊Q8—151no—
252C2×#126—152no—
253C2×#126—152no—
254C2×#124—151no—
255C2×#124—151no—
256C2×C22⋊Q8—152no—
257C2×C4×Q8—51no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—31no—
261C2×#117—152no—
262C22×C3×C5C2×#4112yes—
263C22×C3×C5C2×#4112yes—
264C22×C3×C52−1+412yes—
265C22×C3×C5C2511yescharacteristic
266C2×C5×D3—24no—
267C2×C5×D3—24no—
268C2×C5×D3—24no—
269C2×C5×D3—48no—
270C3×C4×C5—24no—
271C3×C4×C5C2×#4114yes—
272Dic15—22no—
273Dic15—24no—
274Dic15—22no—
275C3×Dic5—22no—
276C3×Dic5—24no—
277C3×Dic5—22no—
278C5×Dic3—22no—
279C5×Dic3C2×#4114yes—
280C23×D3C22×D512yes—
281C2×C3×Q8—54no—
282C2×C3×Q8—104no—
283C22×C3×C4—51no—
284C22×C3×C4—52no—
285C22×C3×C4—51no—
286C22×C3×C4C22×D512yes—
287C22×C3×C4C22×D511yescharacteristic
288C22×Dic3—51no—
289C22×Dic3—52no—
290C22×Dic3—51no—
291C22×Dic3C22×D511yescharacteristic
292C22×Dic3C22×D511yescharacteristic
293C2×D12—24no—
294C2×D12C22×D514yes—
295C2×C4×D3—28no—
296C2×C4×D3C22×D518yes—
297C2×Dic6—54no—
298C2×Dic6—54no—
299C2×Dic6—104no—
300C2×Dic6—104no—
301C3×C4⋊C4—58no—
302C3×C4⋊C4C22×D514yes—
303C3×C42—54no—
304C3×C42—58no—
305(C2×D3)⋊C4—58no—
306(C2×D3)⋊C4—58no—
307(C2×D3)⋊C4—58no—
308(C2×D3)⋊C4—58no—
309(C2×D3)⋊C4C22×D518yes—
310C4⋊Dic3—54no—
311Dic3⋊C4—58no—
312Dic3⋊C4—54no—
313Dic3⋊C4—54no—
314Dic3⋊C4—58no—
315Dic3⋊C4—58no—
316C4×Dic3—54no—
317C4×Dic3—58no—
318C4×Dic3C22×D514yes—
319C23×C5—34no—
320C23×C5—64no—
321C23×C5—64no—
322C23×C5—64no—
323C23×C5C23×D311yescharacteristic
324C5×D4—68no—
325C2×C4×C5—24no—
326C2×C4×C5—34no—
327C2×C4×C5—32no—
328C2×C4×C5—32no—
329C2×C4×C5—616no—
330C2×C4×C5—62no—
331C2×C4×C5#23514yes—
332C2×C4×C5C23×D314yes—
333C2×C4×C5C23×D312yes—
334C2×Dic5—24no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—32no—
338C2×Dic5—32no—
339C2×Dic5—34no—
340C2×Dic5—64no—
341C2×Dic5—62no—
342C2×Dic5—62no—
343C2×Dic5C23×D312yes—
344C2×Dic5C23×D312yes—
345C2×Dic5C23×D314yes—
346Dic10—28no—
347Dic10—68no—
348Dic10—68no—
349C22×Q8—51no—
350C22×Q8—151no—
351C22×Q8—151no—
352C22×D4—31no—
353C23×C4—32no—
354C4⋊Q8—158no—
355#126—1516no—
356#126—1516no—
357#124—158no—
358#124—158no—
359C22⋊Q8—1516no—
360C4×Q8—58no—
361C4×Q8—158no—
362C4×Q8—158no—
363C4×D4—38no—
364#117—1516no—
365C2×C4⋊C4—52no—
366C2×C4⋊C4—151no—
367C2×C4⋊C4—152no—
368C2×C4⋊C4—151no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—152no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4D3×D511yescharacteristic
373C2×C22⋊C4—32no—
374C2×C22⋊C4—152no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—152no—
377C2×C22⋊C4—152no—
378C2×C42—31no—
379C2×C42—52no—
380C2×C42—51no—
381C2×C42—152no—
382C2×C42—151no—
383C2×C3×C5#55614yescomplemented
384C2×C3×C5C22×#4111yescharacteristic
385C2×C3×C5C22×#4111yescharacteristic
386C2×C3×C5C2×2−1+411yescharacteristic
387C5×D3—44no—
388C23×C3C23×D511yescharacteristic
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3C23×D514yes—
393C3×Q8—108no—
394C2×C3×C4—24no—
395C2×C3×C4—52no—
396C2×C3×C4—54no—
397C2×C3×C4—52no—
398C2×C3×C4—104no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4#70914yes—
402C2×C3×C4C23×D514yes—
403C2×C3×C4C23×D512yes—
404C2×Dic3—22no—
405C2×Dic3—52no—
406C2×Dic3—54no—
407C2×Dic3—52no—
408C2×Dic3—104no—
409C2×Dic3—102no—
410C2×Dic3—102no—
411C2×Dic3#71114yes—
412C2×Dic3C23×D512yes—
413C2×Dic3C23×D512yes—
414D12—28no—
415C4×D3—216no—
416Dic6—108no—
417Dic6—108no—
418C22×C5—64no—
419C22×C5—64no—
420C22×C5—64no—
421C22×C5—128no—
422C22×C5C2×#23512yes—
423C22×C5#100712yes—
424C22×C5D3×#4112yes—
425C22×C5C24×D311yescharacteristic
426C4×C5—24no—
427C4×C5—34no—
428C4×C5—62no—
429C4×C5C2×#23514yes—
430Dic5—24no—
431Dic5—22no—
432Dic5—22no—
433Dic5—64no—
434Dic5—62no—
435Dic5—62no—
436C24—32no—
437C2×Q8—54no—
438C2×Q8—104no—
439C2×Q8—154no—
440C2×Q8—154no—
441C2×Q8—304no—
442C2×Q8—304no—
443C2×D4—34no—
444C2×D4—64no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—38no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—52no—
451C22×C4—68no—
452C22×C4—151no—
453C22×C4—152no—
454C22×C4—151no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—58no—
458C4⋊C4—154no—
459C4⋊C4—158no—
460C4⋊C4—154no—
461C4⋊C4—154no—
462C4⋊C4—158no—
463C4⋊C4—158no—
464C4⋊C4C2×D3×D514yes—
465C22⋊C4—38no—
466C22⋊C4—158no—
467C22⋊C4—158no—
468C22⋊C4—158no—
469C22⋊C4—158no—
470C42—34no—
471C42—58no—
472C42—54no—
473C42—158no—
474C42—154no—
475C3×C5C2×#55611yescharacteristic, complemented, Hall
476C22×C3C2×#70912yes—
477C22×C3C2×#71112yes—
478C22×C3#415012yes—
479C22×C3C24×D511yescharacteristic
480C2×D3—24no—
481C2×D3—24no—
482C2×D3—24no—
483C2×D3—48no—
484C3×C4—24no—
485C3×C4—104no—
486C3×C4—102no—
487C3×C4—102no—
488C3×C4C2×#70914yes—
489Dic3—22no—
490Dic3—104no—
491Dic3—102no—
492Dic3—102no—
493Dic3C2×#71114yes—
494C2×C5—124no—
495C2×C5#556814yescomplemented
496C2×C5C22×#23511yescharacteristic
497C2×C5C2×#100711yescharacteristic
498C2×C5C2×D3×#4111yescharacteristic
499C23—34no—
500C23—64no—
501C23—64no—
502C23—64no—
503C23C22×D3×D511yescharacteristic
504Q8—108no—
505Q8—308no—
506Q8—308no—
507D4—68no—
508C2×C4—24no—
509C2×C4—34no—
510C2×C4—32no—
511C2×C4—32no—
512C2×C4—52no—
513C2×C4—52no—
514C2×C4—54no—
515C2×C4—616no—
516C2×C4—62no—
517C2×C4—104no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—152no—
521C2×C4—154no—
522C2×C4—152no—
523C2×C4—304no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4#677114yes—
527C2×C4C22×D3×D514yes—
528C2×C4C22×D3×D512yes—
529C2×C3#6587614yescomplemented
530C2×C3C22×#70911yescharacteristic
531C2×C3C22×#71111yescharacteristic
532C2×C3C2×#415011yescharacteristic
533D3—44no—
534C5C2×#556811yescharacteristic, complemented, Sylow
535C22—64no—
536C22—64no—
537C22—64no—
538C22—128no—
539C22C2×#677112yes—
540C22D3×#71112yes—
541C22#9203012yes—
542C22C23×D3×D511yescharacteristic
543C4—24no—
544C4—34no—
545C4—62no—
546C4—104no—
547C4—102no—
548C4—102no—
549C4—304no—
550C4—302no—
551C4—302no—
552C4C2×#677114yes—
553C3C2×#6587611yescharacteristic, complemented, Sylow
554C2—124no—
555C2#1175335714yesdirect product factor
556C2C22×#677111yescharacteristic
557C2C2×D3×#71111yescharacteristic
558C2C2×#9203011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#556
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×#91776C2semidirect
3. C2×C3×#4033C2semidirect
4. C2×C4×#1204C2semidirect
5. C2×#91389C2semidirect
7. C2×#91372C2semidirect
8. C2×#91371C2semidirect
10. C2×#91367C2semidirect
11. C2×#91352C2semidirect
12. #11753357C2direct (N × H)
23. #91776C22semidirect
30. C3×#4033C22semidirect
40. C4×#1204C22semidirect
41. #91389C22semidirect
43. #91372C22semidirect
44. #91371C22semidirect
46. #91367C22semidirect
47. #91352C22semidirect
56. C2×#4033D3semidirect
141. #4033C2×D3semidirect
383. C2×C3×C5#556semidirect
475. C3×C5C2×#556semidirect
495. C2×C5#5568semidirect
529. C2×C3#65876semidirect
534. C5C2×#5568semidirect
553. C3C2×#65876semidirect
555. C2#11753357direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917762
C2×C5×#8932
C2×C3×#40332
C2×C4×#12042
C2×#913892
C2×#913732
C2×#913722
C2×#913712
C2×#913702
C2×#913672
C2×#913522
#117533572
C2×#658763
C2×#55685