Finite Group Databasebeta

← C2×#11752619 #14484046

Subgroups — C2×#11752619 #14484046

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×C4×Dic30C211yesmaximal, characteristic, complemented
2C2×C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×#4021C211yesmaximal, characteristic
4C2×#91434C211yesmaximal, characteristic
5C2×#91431C212yesmaximal, complemented
6C2×#91393C212yesmaximal, complemented
7C2×#91385C211yesmaximal, characteristic, complemented
8C2×#91368C211yesmaximal, characteristic
9C2×#91363C212yesmaximal, complemented
10C2×#91362C212yesmaximal, complemented
11C2×#91331C211yesmaximal, characteristic, complemented
12#11752619C2116yesmaximal, direct product factor
13C2×#65902—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×D5×Dic3C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C4×Dic30C2218yescomplemented
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C5×Dic3⋊C4C2212yes—
28C2×C4×C5×Dic3C2212yes—
29C4×C5×Dic6C2218yescomplemented
30C2×C3×#685C2212yes—
31C2×C3×#685C2212yes—
32C3×#4021C2218yes—
33C2×#6669C2212yes—
34C2×#6669C2212yes—
35C2×#6668C2212yes—
36C2×#6665C2212yes—
37C2×#6665C2212yes—
38C2×#6665C2212yes—
39C2×Dic3×Dic5C2212yes—
40#91434C2218yes—
41#91431C22116yescomplemented
42#91393C22116yescomplemented
43#91385C2218yescomplemented
44#91368C2218yes—
45#91363C22116yescomplemented
46#91362C22116yescomplemented
47#91331C2218yescomplemented
48C2×#5671—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4093—31no—
51C2×#4090—31no—
52#65902—316no—
53C2×#4044—32no—
54C2×#4042—32no—
55C2×#4039—31no—
56C2×#4033—31no—
57C2×#4022—32no—
58C2×#4021D311yescharacteristic
59C2×#4018—32no—
60C2×C4×Dic10—31no—
61C23×C3×D5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C2×Dic30—24no—
70C2×Dic30C2314yes—
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C22×C3×Dic5C2312yes—
76C2×C3×D20—24no—
77C2×C3×D20C2314yes—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×D5×Dic3—28no—
81C2×D5×Dic3C2318yes—
82C3×C42×C5C2314yes—
83C4⋊Dic15C2314yes—
84#6712C2314yes—
85#6712C2314yes—
86C4×Dic15C2314yes—
87C4×Dic15C2314yes—
88C5×C4⋊Dic3C2314yes—
89C5×Dic3⋊C4C2318yes—
90C4×C5×Dic3C2318yes—
91C3×#685C2318yes—
92C3×#685C2318yes—
93#6669C2318yes—
94#6669C2318yes—
95#6668C2318yes—
96#6665C2318yes—
97#6665C2318yes—
98#6665C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×#124—51no—
101C2×Q8×Dic3—51no—
102C2×#944—51no—
103C2×#936—51no—
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×Dic6D511yescharacteristic, complemented
112C22×C5×Q8—31no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—32no—
115C22×Dic10—31no—
116C22×Dic10C2×D311yescharacteristic
117C4×C5×Q8—38no—
118C2×C5×C4⋊C4—31no—
119C2×C5×C4⋊C4—32no—
120C2×C42×C5—32no—
121C2×C42×C5C2×D311yescharacteristic
122#4093—38no—
123#4090—38no—
124C2×#685—32no—
125C2×#685—32no—
126C2×#685—32no—
127C2×#685C2×D312yes—
128C2×#685C2×D312yes—
129C2×C4⋊Dic5—31no—
130C2×#683—31no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683—32no—
134C2×#683—32no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—32no—
138#4044—316no—
139#4042—316no—
140#4039—38no—
141#4033—38no—
142#4022—316no—
143#4021C2×D318yes—
144#4018—316no—
145C4×Dic10—38no—
146C2×#556—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C3×D5—24no—
149C22×C3×D5—24no—
150C22×C3×D5—24no—
151C22×C3×D5C2414yes—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5#4114yes—
155C2×C3×C4×C5C2412yes—
156C2×C3×C4×C5C2412yes—
157C2×C3×C4×C5C2412yes—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15#4114yes—
162C2×Dic15C2412yes—
163C2×Dic15C2412yes—
164C2×Dic15C2412yes—
165C2×Dic15C2412yes—
166Dic30—28no—
167C2×C5×Dic3—24no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3C2414yes—
170C2×C5×Dic3C2414yes—
171C5×Dic6—28no—
172C2×C3×Dic5—24no—
173C2×C3×Dic5C2414yes—
174C3×D20—28no—
175C3×Dic10—28no—
176D5×Dic3—216no—
177C22×C3×Q8—51no—
178C22×C3×D4—51no—
179C23×Dic3—52no—
180C22×Dic6—51no—
181C22×Dic6C2×D511yescharacteristic
182C3×#124—58no—
183C2×C3×C22⋊C4—52no—
184C2×C3×C22⋊C4—52no—
185C2×C3×C42C2×D511yescharacteristic
186C2×#217—52no—
187C2×#217—52no—
188C2×#217—52no—
189Q8×Dic3—58no—
190#944—58no—
191#936—58no—
192D4×Dic3—58no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—52no—
195C2×C4⋊Dic3C2×D511yescharacteristic
196C2×Dic3⋊C4—51no—
197C2×Dic3⋊C4—51no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4C2×D512yes—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—51no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3C2×D512yes—
205#879—516no—
206#879—516no—
207#878—516no—
208#877—516no—
209C4×Dic6—58no—
210C4×Dic6C2×D518yescomplemented
211C23×D5C22×D312yes—
212C2×C5×Q8—34no—
213C2×C5×Q8—64no—
214C22×C4×C5—32no—
215C22×C4×C5—32no—
216C22×C4×C5C22×D311yescharacteristic
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D311yescharacteristic
219C22×Dic5—31no—
220C22×Dic5—31no—
221C22×Dic5—31no—
222C22×Dic5—31no—
223C22×Dic5C22×D312yes—
224C2×D20—24no—
225C2×D20C22×D314yes—
226C2×C4×D5—38no—
227C2×C4×D5—68no—
228C2×Dic10—24no—
229C2×Dic10—34no—
230C2×Dic10—64no—
231C2×Dic10C22×D314yes—
232C5×C4⋊C4—38no—
233C5×C4⋊C4—34no—
234C42×C5—38no—
235C42×C5C22×D314yes—
236#685—38no—
237#685—38no—
238#685—38no—
239#685C22×D318yes—
240#685C22×D318yes—
241C4⋊Dic5—34no—
242#683—34no—
243#683—34no—
244#683—38no—
245#683—38no—
246#683—38no—
247C4×Dic5—34no—
248C4×Dic5—34no—
249C4×Dic5—38no—
250#556—1516no—
251C2×C4⋊Q8—151no—
252C2×#126—152no—
253C2×#126—152no—
254C2×#124—51no—
255C2×#124—151no—
256C2×C22⋊Q8—152no—
257C2×C4×Q8—31no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C22×C3×C5C2×#4112yes—
263C22×C3×C5C2×#4112yes—
264C22×C3×C52−1+412yes—
265C22×C3×C5C2511yescharacteristic
266C2×C3×D5—24no—
267C2×C3×D5—24no—
268C2×C3×D5—24no—
269C2×C3×D5—48no—
270C3×C4×C5—22no—
271C3×C4×C5—22no—
272C3×C4×C5C2×#4114yes—
273Dic15—22no—
274Dic15—22no—
275Dic15—22no—
276Dic15C2×#4114yes—
277C3×Dic5—24no—
278C5×Dic3—24no—
279C5×Dic3—24no—
280C24×C3—52no—
281C2×C3×Q8—54no—
282C2×C3×Q8—104no—
283C2×C3×D4—54no—
284C2×C3×D4—104no—
285C22×C3×C4—52no—
286C22×C3×C4C22×D511yescharacteristic
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—51no—
290C22×Dic3—51no—
291C22×Dic3—51no—
292C22×Dic3—51no—
293C22×Dic3—58no—
294C22×Dic3—108no—
295C22×Dic3C22×D512yes—
296C22×Dic3C22×D512yes—
297C2×Dic6—24no—
298C2×Dic6—54no—
299C2×Dic6—104no—
300C2×Dic6C22×D514yes—
301C3×C22⋊C4—58no—
302C3×C22⋊C4—58no—
303C3×C42C22×D514yes—
304#217—58no—
305#217—58no—
306#217—58no—
307C4⋊Dic3—54no—
308C4⋊Dic3—58no—
309C4⋊Dic3C22×D514yes—
310Dic3⋊C4—54no—
311Dic3⋊C4—54no—
312Dic3⋊C4—58no—
313Dic3⋊C4—58no—
314Dic3⋊C4C22×D518yes—
315C4×Dic3—54no—
316C4×Dic3—54no—
317C4×Dic3—58no—
318C4×Dic3C22×D518yes—
319C23×C5C23×D311yescharacteristic
320C22×D5—24no—
321C22×D5—24no—
322C22×D5—24no—
323C22×D5C23×D314yes—
324C5×Q8—68no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—34no—
328C2×C4×C5—34no—
329C2×C4×C5—64no—
330C2×C4×C5—64no—
331C2×C4×C5#23714yes—
332C2×C4×C5C23×D312yes—
333C2×C4×C5C23×D312yes—
334C2×C4×C5C23×D312yes—
335C2×Dic5—24no—
336C2×Dic5—34no—
337C2×Dic5—32no—
338C2×Dic5—32no—
339C2×Dic5—32no—
340C2×Dic5—32no—
341C2×Dic5—62no—
342C2×Dic5—62no—
343C2×Dic5—62no—
344C2×Dic5C23×D314yes—
345D20—28no—
346C4×D5—616no—
347Dic10—28no—
348Dic10—68no—
349C22×Q8—31no—
350C22×Q8—51no—
351C22×Q8—151no—
352C22×D4—51no—
353C23×C4—152no—
354C4⋊Q8—158no—
355#126—1516no—
356#126—1516no—
357#124—58no—
358#124—158no—
359C22⋊Q8—1516no—
360C4×Q8—38no—
361C4×Q8—158no—
362C4×Q8—158no—
363C4×D4—158no—
364#117—1516no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—152no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—152no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—151no—
373C2×C22⋊C4—52no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—152no—
377C2×C22⋊C4—152no—
378C2×C42—32no—
379C2×C42—152no—
380C2×C42—151no—
381C2×C42—151no—
382C2×C42D3×D511yescharacteristic
383C2×C3×C5#55614yescomplemented
384C2×C3×C5C22×#4111yescharacteristic
385C2×C3×C5C22×#4111yescharacteristic
386C2×C3×C5C2×2−1+411yescharacteristic
387C3×D5—44no—
388C23×C3—54no—
389C23×C3—104no—
390C23×C3—104no—
391C23×C3—104no—
392C23×C3C23×D511yescharacteristic
393C3×Q8—108no—
394C3×D4—108no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—54no—
398C2×C3×C4—104no—
399C2×C3×C4#70914yes—
400C2×C3×C4C23×D512yes—
401C2×C3×C4C23×D512yes—
402C2×C3×C4C23×D512yes—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—54no—
406C2×Dic3—52no—
407C2×Dic3—52no—
408C2×Dic3—52no—
409C2×Dic3—52no—
410C2×Dic3—1016no—
411C2×Dic3—102no—
412C2×Dic3—102no—
413C2×Dic3—102no—
414C2×Dic3C23×D514yes—
415C2×Dic3C23×D514yes—
416Dic6—28no—
417Dic6—108no—
418C22×C5C2×#23712yes—
419C22×C5D3×#4112yes—
420C22×C5#101012yes—
421C22×C5C24×D311yescharacteristic
422C2×D5—24no—
423C2×D5—24no—
424C2×D5—24no—
425C2×D5—48no—
426C4×C5—22no—
427C4×C5—22no—
428C4×C5—64no—
429C4×C5—64no—
430C4×C5C2×#23714yes—
431Dic5—24no—
432Dic5—34no—
433Dic5—62no—
434Dic5—62no—
435Dic5—62no—
436C24—52no—
437C2×Q8—34no—
438C2×Q8—54no—
439C2×Q8—64no—
440C2×Q8—104no—
441C2×Q8—154no—
442C2×Q8—304no—
443C2×D4—54no—
444C2×D4—104no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—52no—
448C22×C4—158no—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—308no—
454C22×C4C2×D3×D511yescharacteristic
455C22×C4C2×D3×D511yescharacteristic
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—34no—
458C4⋊C4—38no—
459C4⋊C4—158no—
460C4⋊C4—158no—
461C4⋊C4—158no—
462C4⋊C4—154no—
463C4⋊C4—154no—
464C4⋊C4—154no—
465C22⋊C4—58no—
466C22⋊C4—58no—
467C22⋊C4—158no—
468C22⋊C4—158no—
469C22⋊C4—158no—
470C42—38no—
471C42—158no—
472C42—154no—
473C42—154no—
474C42C2×D3×D514yes—
475C3×C5C2×#55611yescharacteristic, complemented, Hall
476C22×C3—104no—
477C22×C3—104no—
478C22×C3—104no—
479C22×C3—208no—
480C22×C3C2×#70912yes—
481C22×C3#414712yes—
482C22×C3D5×#4112yes—
483C22×C3C24×D511yescharacteristic
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—104no—
487C3×C4C2×#70914yes—
488Dic3—24no—
489Dic3—24no—
490Dic3—54no—
491Dic3—102no—
492Dic3—102no—
493Dic3—102no—
494C2×C5#567114yescomplemented
495C2×C5C22×#23711yescharacteristic
496C2×C5C2×D3×#4111yescharacteristic
497C2×C5C2×#101011yescharacteristic
498D5—44no—
499C23—54no—
500C23—104no—
501C23—104no—
502C23—104no—
503C23C22×D3×D511yescharacteristic
504Q8—68no—
505Q8—108no—
506Q8—308no—
507D4—108no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—34no—
511C2×C4—34no—
512C2×C4—54no—
513C2×C4—64no—
514C2×C4—64no—
515C2×C4—104no—
516C2×C4—154no—
517C2×C4—152no—
518C2×C4—152no—
519C2×C4—152no—
520C2×C4—152no—
521C2×C4—3016no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4#676514yes—
526C2×C4C22×D3×D512yes—
527C2×C4C22×D3×D512yes—
528C2×C4C22×D3×D512yes—
529C2×C3—204no—
530C2×C3#6590214yescomplemented
531C2×C3C22×#70911yescharacteristic
532C2×C3C2×#414711yescharacteristic
533C2×C3C2×D5×#4111yescharacteristic
534C5C2×#567111yescharacteristic, complemented, Sylow
535C22—104no—
536C22—104no—
537C22—104no—
538C22—208no—
539C22C2×#676512yes—
540C22#9200012yes—
541C22#9201612yes—
542C22C23×D3×D511yescharacteristic
543C4—22no—
544C4—22no—
545C4—64no—
546C4—64no—
547C4—104no—
548C4—154no—
549C4—302no—
550C4—302no—
551C4—302no—
552C4C2×#676514yes—
553C3C2×#6590211yescharacteristic, complemented, Sylow
554C2—204no—
555C2#1175261914yesdirect product factor
556C2C22×#676511yescharacteristic
557C2C2×#9200011yescharacteristic
558C2C2×#9201611yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic30C2semidirect
2. C2×C4×C5×Dic6C2semidirect
5. C2×#91431C2semidirect
6. C2×#91393C2semidirect
7. C2×#91385C2semidirect
9. C2×#91363C2semidirect
10. C2×#91362C2semidirect
11. C2×#91331C2semidirect
12. #11752619C2direct (N × H)
25. C4×Dic30C22semidirect
29. C4×C5×Dic6C22semidirect
41. #91431C22semidirect
42. #91393C22semidirect
43. #91385C22semidirect
45. #91363C22semidirect
46. #91362C22semidirect
47. #91331C22semidirect
111. C2×C4×Dic6D5semidirect
210. C4×Dic6C2×D5semidirect
383. C2×C3×C5#556semidirect
475. C3×C5C2×#556semidirect
494. C2×C5#5671semidirect
530. C2×C3#65902semidirect
534. C5C2×#5671semidirect
553. C3C2×#65902semidirect
555. C2#11752619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C2×C4×C5×Dic62
C2×C3×#40212
C2×#914342
C2×#914312
C2×#913932
C2×#913852
C2×#913682
C2×#913632
C2×#913622
C2×#913312
#117526192
C2×#659023
C2×#56715