Finite Group Databasebeta

← C2×#11754739 #14484103

Subgroups — C2×#11754739 #14484103

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×D4×Dic15C211yesmaximal, characteristic
2C2×C5×#936C211yesmaximal, characteristic
3C2×C3×#4082C211yesmaximal, characteristic
4C2×#91576C212yesmaximal, complemented
5C2×#91532C212yesmaximal, complemented
6C2×#91531C212yesmaximal, complemented
7C2×#91530C212yesmaximal, complemented
8#11754739C2116yesmaximal, direct product factor
9C2×C4×#1204C211yesmaximal, characteristic, complemented
10C2×#91385C211yesmaximal, characteristic, complemented
11C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
13C2×#66005—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C23×Dic15C2212yes—
16C22×C5×Dic6C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×#1204C2211yescharacteristic
19C2×#6719C2212yes—
20D4×Dic15C2218yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×#217C2212yes—
24C2×C5×#217C2212yes—
25C5×#936C2218yes—
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×C22⋊Dic5C2212yes—
29C3×#4082C2218yes—
30C2×C3×C4×Dic5C2211yescharacteristic
31#91576C22116yescomplemented
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2212yes—
34C2×#6669C2212yes—
35C2×#6669C2212yes—
36C2×#6669C2211yescharacteristic
37C2×#6668C2212yes—
38C2×#6668C2211yescharacteristic
39#91532C22116yescomplemented
40#91531C22116yescomplemented
41#91530C22116yescomplemented
42C2×Dic3×Dic5C2212yes—
43C2×Dic3×Dic5C2212yes—
44C4×#1204C2218yescomplemented
45#91385C2218yescomplemented
46Dic5×Dic6C2218yescomplemented
47Dic3×Dic10C2218yescomplemented
48C2×#5671—51nomaximal, Hall
49C2×C5×#124—31no—
50C2×Q8×Dic5—31no—
51C2×#4090—31no—
52C2×#4082D311yescharacteristic
53C2×D4×Dic5—31no—
54#66005—316no—
55C2×#4025—32no—
56C2×#4025—32no—
57C2×#4024—32no—
58C2×#4023—32no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2312yes—
62C2×C3×C5×D4—24no—
63C2×C3×C5×D4C2314yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15—28no—
66C22×Dic15C2312yes—
67C22×Dic15C2318yes—
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×#1204—24no—
81C2×#1204C2314yes—
82#6719C2318yes—
83C4⋊Dic15C2314yes—
84C4×Dic15C2314yes—
85C5×#217C2318yes—
86C5×#217C2318yes—
87C4×C5×Dic3C2314yes—
88C3×C22⋊Dic5C2318yes—
89C3×C22⋊Dic5C2318yes—
90C3×C4×Dic5C2314yes—
91Dic3⋊Dic5C2314yes—
92Dic3⋊Dic5C2318yes—
93#6669C2314yes—
94#6669C2318yes—
95#6669C2318yes—
96#6668C2314yes—
97#6668C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×#124—51no—
101C2×Q8×Dic3—51no—
102C2×#944—51no—
103C2×#936D511yescharacteristic
104C2×D4×Dic3—51no—
105#5671—516no—
106C2×#879—52no—
107C2×#879—52no—
108C2×#878—52no—
109C2×#877—52no—
110C2×C4×Dic6—51no—
111C2×C4×Dic6—51no—
112C22×C5×Q8—31no—
113C22×C5×D4C2×D311yescharacteristic
114C23×Dic5—32no—
115C22×Dic10—31no—
116C22×Dic10C2×D311yescharacteristic
117C5×#124—38no—
118C2×C5×C22⋊C4—32no—
119C2×C5×C22⋊C4—32no—
120C2×C42×C5—31no—
121C2×C22⋊Dic5—32no—
122C2×C22⋊Dic5C2×D312yes—
123C2×C22⋊Dic5C2×D312yes—
124Q8×Dic5—38no—
125#4090—38no—
126#4082C2×D318yes—
127D4×Dic5—38no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683—31no—
134C2×#683—32no—
135C2×#683—32no—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—32no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5C2×D311yescharacteristic
140#4025—316no—
141#4025—316no—
142#4024—316no—
143#4023—316no—
144C4×Dic10—38no—
145C4×Dic10—38no—
146C2×#556—151noSylow
147C23×C3×C5—24no—
148C23×C3×C5—24no—
149C23×C3×C5—24no—
150C23×C3×C5C2414yes—
151C23×C3×C5C2411yescharacteristic
152C3×C5×D4—28no—
153C2×C3×C4×C5#4114yes—
154C2×C3×C4×C5C2412yes—
155C2×Dic15—24no—
156C2×Dic15—22no—
157C2×Dic15—216no—
158C2×Dic15#4114yes—
159C2×Dic15C2414yes—
160C2×Dic15C2412yes—
161C2×Dic15C2412yes—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—24no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3C2412yes—
166C2×C5×Dic3C2414yes—
167C2×C5×Dic3C2412yes—
168C5×Dic6—28no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—24no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5C2412yes—
173C2×C3×Dic5C2414yes—
174C2×C3×Dic5C2412yes—
175C3×Dic10—28no—
176#1204—28no—
177C22×C3×Q8—51no—
178C22×C3×D4C2×D511yescharacteristic
179C23×Dic3—52no—
180C22×Dic6—51no—
181C22×Dic6C2×D511yescharacteristic
182C3×#124—58no—
183C2×C3×C22⋊C4—52no—
184C2×C3×C22⋊C4—52no—
185C2×C3×C42—51no—
186C2×#217—52no—
187C2×#217C2×D512yes—
188C2×#217C2×D512yes—
189Q8×Dic3—58no—
190#944—58no—
191#936C2×D518yes—
192D4×Dic3—58no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×Dic3⋊C4—51no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3C2×D511yescharacteristic
205#879—516no—
206#879—516no—
207#878—516no—
208#877—516no—
209C4×Dic6—58no—
210C4×Dic6—58no—
211C24×C5C22×D312yes—
212C2×C5×Q8—34no—
213C2×C5×Q8—64no—
214C2×C5×D4—24no—
215C2×C5×D4C22×D314yes—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—32no—
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—31no—
221C22×Dic5—31no—
222C22×Dic5—32no—
223C22×Dic5—38no—
224C22×Dic5—68no—
225C22×Dic5C22×D311yescharacteristic
226C22×Dic5C22×D312yes—
227C22×Dic5C22×D311yescharacteristic
228C2×Dic10—24no—
229C2×Dic10—34no—
230C2×Dic10—64no—
231C2×Dic10C22×D314yes—
232C5×C22⋊C4—38no—
233C5×C22⋊C4—38no—
234C42×C5—34no—
235C22⋊Dic5—38no—
236C22⋊Dic5C22×D318yes—
237C22⋊Dic5C22×D318yes—
238C4⋊Dic5—34no—
239C4⋊Dic5—34no—
240C4⋊Dic5—38no—
241#683—38no—
242#683—34no—
243#683—34no—
244#683—38no—
245#683—38no—
246C4×Dic5—34no—
247C4×Dic5—38no—
248C4×Dic5—38no—
249C4×Dic5C22×D314yes—
250#556—1516no—
251C2×C4⋊Q8—151no—
252C2×#126—152no—
253C2×#126—152no—
254C2×#124—31no—
255C2×#124—51no—
256C2×C22⋊Q8—152no—
257C2×C4×Q8—151no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C22×C3×C5—24no—
263C22×C3×C5—24no—
264C22×C3×C5—24no—
265C22×C3×C5—48no—
266C22×C3×C5C2×#4112yes—
267C22×C3×C5C2×#4112yes—
268C22×C3×C52−1+412yes—
269C22×C3×C5C2511yescharacteristic
270C3×C4×C5C2×#4114yes—
271Dic15—24no—
272Dic15—22no—
273Dic15C2×#4114yes—
274C3×Dic5—22no—
275C3×Dic5—24no—
276C3×Dic5—22no—
277C5×Dic3—22no—
278C5×Dic3—24no—
279C5×Dic3—22no—
280C24×C3C22×D512yes—
281C2×C3×Q8—54no—
282C2×C3×Q8—104no—
283C2×C3×D4—24no—
284C2×C3×D4C22×D514yes—
285C22×C3×C4—51no—
286C22×C3×C4—52no—
287C22×C3×C4—51no—
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—51no—
290C22×Dic3—58no—
291C22×Dic3—52no—
292C22×Dic3—51no—
293C22×Dic3—108no—
294C22×Dic3C22×D511yescharacteristic
295C22×Dic3C22×D512yes—
296C22×Dic3C22×D511yescharacteristic
297C2×Dic6—24no—
298C2×Dic6—54no—
299C2×Dic6—104no—
300C2×Dic6C22×D514yes—
301C3×C22⋊C4—58no—
302C3×C22⋊C4—58no—
303C3×C42—54no—
304#217—58no—
305#217C22×D518yes—
306#217C22×D518yes—
307C4⋊Dic3—54no—
308C4⋊Dic3—54no—
309C4⋊Dic3—58no—
310Dic3⋊C4—54no—
311Dic3⋊C4—58no—
312Dic3⋊C4—58no—
313Dic3⋊C4—58no—
314Dic3⋊C4—54no—
315C4×Dic3—54no—
316C4×Dic3—58no—
317C4×Dic3—58no—
318C4×Dic3C22×D514yes—
319C23×C5—24no—
320C23×C5—24no—
321C23×C5—24no—
322C23×C5C23×D314yes—
323C23×C5C23×D311yescharacteristic
324C5×Q8—68no—
325C5×D4—28no—
326C2×C4×C5—32no—
327C2×C4×C5—34no—
328C2×C4×C5—32no—
329C2×C4×C5—64no—
330C2×C4×C5—62no—
331C2×C4×C5—62no—
332C2×C4×C5#23714yes—
333C2×C4×C5C23×D312yes—
334C2×Dic5—24no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—34no—
338C2×Dic5—32no—
339C2×Dic5—34no—
340C2×Dic5—32no—
341C2×Dic5—616no—
342C2×Dic5—64no—
343C2×Dic5—62no—
344C2×Dic5C23×D312yes—
345C2×Dic5C23×D314yes—
346C2×Dic5C23×D312yes—
347Dic10—28no—
348Dic10—68no—
349C22×Q8—31no—
350C22×Q8—51no—
351C22×Q8—151no—
352C22×D4D3×D511yescharacteristic
353C23×C4—152no—
354C4⋊Q8—158no—
355#126—1516no—
356#126—1516no—
357#124—38no—
358#124—58no—
359C22⋊Q8—1516no—
360C4×Q8—158no—
361C4×Q8—158no—
362C4×Q8—158no—
363C4×D4—158no—
364#117—1516no—
365C2×C4⋊C4—151no—
366C2×C4⋊C4—152no—
367C2×C4⋊C4—152no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4—151no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—52no—
376C2×C22⋊C4—52no—
377C2×C22⋊C4—152no—
378C2×C42—31no—
379C2×C42—51no—
380C2×C42—152no—
381C2×C42—152no—
382C2×C42—151no—
383C2×C3×C5—44no—
384C2×C3×C5#55614yescomplemented
385C2×C3×C5C22×#4111yescharacteristic
386C2×C3×C5C22×#4111yescharacteristic
387C2×C3×C5C2×2−1+411yescharacteristic
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3C23×D514yes—
392C23×C3C23×D511yescharacteristic
393C3×Q8—108no—
394C3×D4—28no—
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#71114yes—
402C2×C3×C4C23×D512yes—
403C2×Dic3—24no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—54no—
407C2×Dic3—52no—
408C2×Dic3—54no—
409C2×Dic3—52no—
410C2×Dic3—1016no—
411C2×Dic3—104no—
412C2×Dic3—102no—
413C2×Dic3C23×D512yes—
414C2×Dic3C23×D514yes—
415C2×Dic3C23×D512yes—
416Dic6—28no—
417Dic6—108no—
418C22×C5—24no—
419C22×C5—24no—
420C22×C5—24no—
421C22×C5—48no—
422C22×C5C2×#23712yes—
423C22×C5D3×#4112yes—
424C22×C5#101012yes—
425C22×C5C24×D311yescharacteristic
426C4×C5—64no—
427C4×C5—62no—
428C4×C5—62no—
429C4×C5C2×#23714yes—
430Dic5—24no—
431Dic5—22no—
432Dic5—22no—
433Dic5—34no—
434Dic5—64no—
435Dic5—62no—
436C24C2×D3×D512yes—
437C2×Q8—34no—
438C2×Q8—54no—
439C2×Q8—64no—
440C2×Q8—104no—
441C2×Q8—154no—
442C2×Q8—304no—
443C2×D4—24no—
444C2×D4C2×D3×D514yes—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—52no—
451C22×C4—151no—
452C22×C4—158no—
453C22×C4—152no—
454C22×C4—151no—
455C22×C4—308no—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—154no—
458C4⋊C4—158no—
459C4⋊C4—158no—
460C4⋊C4—158no—
461C4⋊C4—154no—
462C4⋊C4—154no—
463C4⋊C4—158no—
464C4⋊C4—154no—
465C22⋊C4—38no—
466C22⋊C4—38no—
467C22⋊C4—58no—
468C22⋊C4—58no—
469C22⋊C4—158no—
470C42—34no—
471C42—54no—
472C42—158no—
473C42—158no—
474C42—154no—
475C3×C5C2×#55611yescharacteristic, complemented, Hall
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—48no—
480C22×C3C2×#71112yes—
481C22×C3D5×#4112yes—
482C22×C3#415012yes—
483C22×C3C24×D511yescharacteristic
484C3×C4—104no—
485C3×C4—102no—
486C3×C4—102no—
487C3×C4C2×#71114yes—
488Dic3—24no—
489Dic3—22no—
490Dic3—22no—
491Dic3—54no—
492Dic3—104no—
493Dic3—102no—
494C2×C5—44no—
495C2×C5#567114yescomplemented
496C2×C5C22×#23711yescharacteristic
497C2×C5C2×D3×#4111yescharacteristic
498C2×C5C2×#101011yescharacteristic
499C23—24no—
500C23—24no—
501C23—24no—
502C23C22×D3×D514yes—
503C23C22×D3×D511yescharacteristic
504Q8—68no—
505Q8—108no—
506Q8—308no—
507D4—28no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—34no—
511C2×C4—52no—
512C2×C4—52no—
513C2×C4—54no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—64no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—104no—
520C2×C4—154no—
521C2×C4—152no—
522C2×C4—154no—
523C2×C4—152no—
524C2×C4—3016no—
525C2×C4—302no—
526C2×C4—304no—
527C2×C4#678014yes—
528C2×C4C22×D3×D512yes—
529C2×C3—44no—
530C2×C3#6600514yescomplemented
531C2×C3C22×#71111yescharacteristic
532C2×C3C2×D5×#4111yescharacteristic
533C2×C3C2×#415011yescharacteristic
534C5C2×#567111yescharacteristic, complemented, Sylow
535C22—24no—
536C22—24no—
537C22—24no—
538C22—48no—
539C22#9202012yes—
540C22#9202412yes—
541C22C2×#678012yes—
542C22C23×D3×D511yescharacteristic
543C4—64no—
544C4—62no—
545C4—62no—
546C4—104no—
547C4—102no—
548C4—102no—
549C4—154no—
550C4—302no—
551C4—304no—
552C4C2×#678014yes—
553C3C2×#6600511yescharacteristic, complemented, Sylow
554C2—44no—
555C2#1175473914yesdirect product factor
556C2C2×#9202011yescharacteristic
557C2C2×#9202411yescharacteristic
558C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#91576C2semidirect
5. C2×#91532C2semidirect
6. C2×#91531C2semidirect
7. C2×#91530C2semidirect
8. #11754739C2direct (N × H)
9. C2×C4×#1204C2semidirect
10. C2×#91385C2semidirect
11. C2×Dic5×Dic6C2semidirect
12. C2×Dic3×Dic10C2semidirect
31. #91576C22semidirect
39. #91532C22semidirect
40. #91531C22semidirect
41. #91530C22semidirect
44. C4×#1204C22semidirect
45. #91385C22semidirect
46. Dic5×Dic6C22semidirect
47. Dic3×Dic10C22semidirect
384. C2×C3×C5#556semidirect
475. C3×C5C2×#556semidirect
495. C2×C5#5671semidirect
530. C2×C3#66005semidirect
534. C5C2×#5671semidirect
553. C3C2×#66005semidirect
555. C2#11754739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C2×C5×#9362
C2×C3×#40822
C2×#915762
C2×#915322
C2×#915312
C2×#915302
#117547392
C2×C4×#12042
C2×#913852
C2×Dic5×Dic62
C2×Dic3×Dic102
C2×#660053
C2×#56715