Finite Group Databasebeta

← C2×#11748130 #14423396

Subgroups — C2×#11748130 #14423396

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Dic6C211yesmaximal, characteristic
2C22×Dic60C211yesmaximal, characteristic, complemented
3C2×#91360C211yesmaximal, characteristic
4C22×#6663C211yesmaximal, characteristic, complemented
5C2×C5×#816C211yesmaximal, characteristic, complemented
6C2×C3×#3952C211yesmaximal, characteristic
7C2×#90975C211yesmaximal, characteristic, complemented
8#11748130C218yesmaximal, direct product factor
9C2×#65097—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1204—21no—
15C22×D5×Dic3—21no—
16C2×D5×Dic6—24no—
17C2×D5×Dic6—24no—
18C2×D5×Dic6—22no—
19C2×D5×Dic6C2214yes—
20C22×C3×C5×C8C2211yescharacteristic
21C2×Dic60—24no—
22C2×Dic60C2214yescomplemented
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25C2×Dic3⋊Dic5—21no—
26C2×#6665—21no—
27#91360—22no—
28#91360C2214yes—
29C2×#6663—24no—
30C2×#6663C2214yescomplemented
31C5×#816C2214yescomplemented
32C3×#3952C2214yes—
33#90975C2214yescomplemented
34C2×#4739—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×#689—31no—
37C22×Dic20—31no—
38C2×#4043—31no—
39C2×C5×#103—31no—
40C2×#3952D311yescharacteristic
41C2×#3942—31no—
42#65097—38no—
43C23×C3×D5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15—21no—
46C22×Dic15—21no—
47C2×Dic30—21no—
48C2×Dic30—22no—
49C2×Dic30—22no—
50C2×Dic30—22no—
51C2×Dic30—21no—
52C2×Dic30D414yes—
53C2×Dic30C2312yes—
54C2×Dic30C2312yes—
55C22×C5×Dic3—21no—
56C22×C5×Dic3—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—22no—
59C2×C5×Dic6D414yes—
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5D411yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5D412yes—
65C2×C3×C4×D5C2312yes—
66C2×#1204—28no—
67C2×#1204—24no—
68C2×D5×Dic3—28no—
69C2×D5×Dic3—24no—
70D5×Dic6—216no—
71D5×Dic6—28no—
72D5×Dic6—28no—
73C2×C3×C5×C8—22no—
74C2×C3×C5×C8C2312yes—
75Dic60—28no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C3×#168—22no—
79C2×C3×#168C2312yes—
80Dic3⋊Dic5—24no—
81#6665—24no—
82#6663—28no—
83C23×Dic6—51no—
84C2×#924—51no—
85C22×Dic12—51no—
86C22×Dic12—51no—
87C2×C3×C22⋊C8—51no—
88C2×#816—51no—
89C2×#816D511yescharacteristic, complemented
90#4739—58no—
91C22×C5×Q8—31no—
92C2×Q8×D5—34no—
93C2×Q8×D5—64no—
94C2×Q8×D5—64no—
95C2×Q8×D5—62no—
96C22×C4×D5—61no—
97C22×C4×D5C2×D311yescharacteristic
98C22×Dic10—31no—
99C22×Dic10—31no—
100C22×Dic10—61no—
101C22×C5×C8C2×D311yescharacteristic
102C2×C5×C4⋊C4—31no—
103C2×#689—34no—
104C2×#689—64no—
105C2×#685—61no—
106C2×C4⋊Dic5—61no—
107C22×#168C2×D311yescharacteristic
108C2×Dic20—34no—
109C2×Dic20—64no—
110#4043—34no—
111#4043—62no—
112C5×#103—34no—
113#3952C2×D314yes—
114#3942—34no—
115C2×#451—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×C3×D5—22no—
118C22×C3×D5—22no—
119C22×C3×D5Q1614yescomplemented
120C22×C3×D5C2×D412yes—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D412yes—
123C2×C3×C4×C5C2×D412yes—
124C2×C3×C4×C5C2411yescharacteristic
125C2×Dic15—24no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—42no—
129Dic30—24no—
130Dic30—22no—
131Dic30—22no—
132Dic30—22no—
133Dic30—42no—
134Dic30C2×D414yes—
135C2×C5×Dic3—24no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—42no—
139C5×Dic6—24no—
140C5×Dic6—22no—
141C5×Dic6C2×D414yes—
142C2×C3×Dic5—22no—
143C2×C3×Dic5C2×D412yes—
144C3×C4×D5—24no—
145C3×C4×D5—22no—
146C3×C4×D5—22no—
147#1204—216no—
148D5×Dic3—216no—
149C3×C5×C8—22no—
150C3×#168—22no—
151C23×C3×C4—51no—
152C23×Dic3—101no—
153C22×Dic6—51no—
154C22×Dic6—51no—
155C22×Dic6—54no—
156C22×Dic6—104no—
157C22×Dic6—102no—
158C22×Dic6—101no—
159C22×Dic6—104no—
160C22×Dic6C2×D511yescharacteristic
161C22×C3×C8—51no—
162C22×C3×C8C2×D511yescharacteristic
163C2×#217—101no—
164C2×C4⋊Dic3C2×D511yescharacteristic
165#924—54no—
166#924—102no—
167C2×Dic3⋊C4—101no—
168C2×Dic12—54no—
169C2×Dic12—54no—
170C2×Dic12—104no—
171C2×Dic12—104no—
172C3×C22⋊C8—54no—
173#816—54no—
174#816C2×D514yescomplemented
175C23×D5D1211yescharacteristic
176C2×C5×Q8—34no—
177C2×C5×Q8—32no—
178C2×C5×Q8—61no—
179C2×C5×Q8—62no—
180C22×C4×C5—61no—
181C22×C4×C5—61no—
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—61no—
184C22×Dic5—61no—
185C22×Dic5D1211yescharacteristic
186Q8×D5—68no—
187Q8×D5—68no—
188Q8×D5—616no—
189C2×C4×D5—22no—
190C2×C4×D5—22no—
191C2×C4×D5—68no—
192C2×C4×D5—64no—
193C2×C4×D5D1212yes—
194C2×C4×D5C22×D312yes—
195C2×Dic10—34no—
196C2×Dic10—32no—
197C2×Dic10—32no—
198C2×Dic10—68no—
199C2×Dic10—61no—
200C2×Dic10—62no—
201C2×Dic10—64no—
202C2×Dic10—62no—
203C2×Dic10—62no—
204C2×Dic10—61no—
205C2×C5×C8—22no—
206C2×C5×C8C22×D312yes—
207C5×C4⋊C4—32no—
208C5×C4⋊C4—61no—
209#689—68no—
210#685—64no—
211C4⋊Dic5—64no—
212C2×#168—22no—
213C2×#168C22×D312yes—
214Dic20—68no—
215C23×Q8—151no—
216C22×Q16—151no—
217C22×Q16—151no—
218C2×C22⋊Q8—151no—
219#451—158no—
220C2×#103—31no—
221C2×#103—151no—
222C2×C22⋊C8—51no—
223C22×C3×C5#12012yes—
224C22×C3×C5C2×Q1612yes—
225C22×C3×C5#13712yes—
226C22×C3×C5C22×D411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—22no—
229C2×C3×D5—28no—
230C2×C3×D5C2×Q1614yescomplemented
231C3×C4×C5#12012yes—
232C3×C4×C5C22×D411yescharacteristic
233C3×C4×C5C22×D411yescharacteristic
234Dic15—24no—
235Dic15—42no—
236C3×Dic5—22no—
237C5×Dic3—24no—
238C5×Dic3—42no—
239C24×C3—51no—
240C22×C3×C4—51no—
241C22×C3×C4—52no—
242C22×C3×C4—52no—
243C22×C3×C4—102no—
244C22×C3×C4—102no—
245C22×C3×C4C22×D511yescharacteristic
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—104no—
249C22×Dic3—108no—
250C22×Dic3—101no—
251C22×Dic3—101no—
252C2×Dic6—21no—
253C2×Dic6—22no—
254C2×Dic6—54no—
255C2×Dic6—52no—
256C2×Dic6—52no—
257C2×Dic6—108no—
258C2×Dic6—1016no—
259C2×Dic6—104no—
260C2×Dic6—108no—
261C2×Dic6—102no—
262C2×Dic6—101no—
263C2×Dic6—108no—
264C2×Dic6—102no—
265C2×Dic6—102no—
266C2×Dic6—101no—
267C2×Dic6D2014yes—
268C2×Dic6C22×D512yes—
269C2×C3×C8—22no—
270C2×C3×C8—52no—
271C2×C3×C8—102no—
272C2×C3×C8C22×D512yes—
273#217—104no—
274C4⋊Dic3—21no—
275C4⋊Dic3C22×D512yes—
276Dic3⋊C4—104no—
277Dic12—108no—
278Dic12—108no—
279C23×C5C2×D1211yescharacteristic
280C22×D5—22no—
281C22×D5—22no—
282C22×D5Dic1214yescomplemented
283C22×D5C2×D1212yes—
284C5×Q8—34no—
285C5×Q8—64no—
286C5×Q8—62no—
287C2×C4×C5—64no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5—122no—
291C2×C4×C5C2×D1211yescharacteristic
292C2×C4×C5D3×D412yes—
293C2×C4×C5D3×D412yes—
294C2×C4×C5C23×D311yescharacteristic
295C2×Dic5—22no—
296C2×Dic5—64no—
297C2×Dic5—62no—
298C2×Dic5—62no—
299C2×Dic5—122no—
300C2×Dic5C2×D1212yes—
301C4×D5—24no—
302C4×D5—22no—
303C4×D5—22no—
304C4×D5—616no—
305Dic10—34no—
306Dic10—616no—
307Dic10—64no—
308Dic10—62no—
309Dic10—62no—
310Dic10—62no—
311Dic10—122no—
312C5×C8—22no—
313#168—22no—
314C22×Q8—31no—
315C22×Q8—154no—
316C22×Q8—151no—
317C22×Q8—151no—
318C22×Q8—301no—
319C22×Q8—302no—
320C22×Q8—304no—
321C22×Q8—304no—
322C23×C4—51no—
323C23×C4—301no—
324C2×Q16—154no—
325C2×Q16—154no—
326C2×Q16—304no—
327C2×Q16—304no—
328C22×C8—51no—
329C22×C8D3×D511yescharacteristic
330C22⋊Q8—154no—
331C22⋊Q8—302no—
332C2×C4⋊C4—31no—
333C2×C4⋊C4—301no—
334C2×C22⋊C4—301no—
335#103—34no—
336#103—154no—
337C22⋊C8—54no—
338C2×C3×C5#45114yescomplemented
339C2×C3×C5C2×#12011yescharacteristic
340C2×C3×C5C22×Q1611yescharacteristic
341C2×C3×C5C2×#13711yescharacteristic
342C3×D5—24no—
343C23×C3—52no—
344C23×C3—54no—
345C23×C3—102no—
346C23×C3—102no—
347C23×C3D4×D511yescharacteristic
348C2×C3×C4—52no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4—102no—
352C2×C3×C4—104no—
353C2×C3×C4C2×D2012yes—
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4D4×D512yes—
356C2×C3×C4C23×D511yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—24no—
359C2×Dic3—22no—
360C2×Dic3—42no—
361C2×Dic3—1016no—
362C2×Dic3—102no—
363C2×Dic3—104no—
364C2×Dic3—102no—
365C2×Dic3—202no—
366Dic6—22no—
367Dic6—24no—
368Dic6—54no—
369Dic6—1016no—
370Dic6—102no—
371Dic6—104no—
372Dic6—102no—
373Dic6—102no—
374Dic6—202no—
375Dic6C2×D2014yes—
376C3×C8—22no—
377C3×C8—102no—
378C22×C5#88212yes—
379C22×C5C2×Dic1212yes—
380C22×C5#90912yes—
381C22×C5C22×D1211yescharacteristic
382C2×D5—22no—
383C2×D5—22no—
384C2×D5—28no—
385C2×D5C2×Dic1214yescomplemented
386C4×C5—64no—
387C4×C5—122no—
388C4×C5#88212yes—
389C4×C5C2×D3×D411yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—22no—
392Dic5—64no—
393Dic5—122no—
394C24—51no—
395C2×Q8—34no—
396C2×Q8—32no—
397C2×Q8—61no—
398C2×Q8—62no—
399C2×Q8—154no—
400C2×Q8—152no—
401C2×Q8—152no—
402C2×Q8—304no—
403C2×Q8—308no—
404C2×Q8—308no—
405C2×Q8—308no—
406C2×Q8—3016no—
407C2×Q8—301no—
408C2×Q8—301no—
409C2×Q8—302no—
410C2×Q8—302no—
411C2×Q8—302no—
412C22×C4—51no—
413C22×C4—52no—
414C22×C4—52no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—102no—
418C22×C4—102no—
419C22×C4—304no—
420C22×C4—308no—
421C22×C4—301no—
422C22×C4—301no—
423C22×C4C2×D3×D511yescharacteristic
424Q16—308no—
425Q16—308no—
426C2×C8—22no—
427C2×C8—52no—
428C2×C8—102no—
429C2×C8C2×D3×D512yes—
430C4⋊C4—32no—
431C4⋊C4—61no—
432C4⋊C4—304no—
433C22⋊C4—304no—
434C3×C5C2×#45111yescharacteristic, complemented, Hall
435C22×C3—54no—
436C22×C3—102no—
437C22×C3—102no—
438C22×C3—108no—
439C22×C3#402812yes—
440C22×C3#406112yes—
441C22×C3D5×Q1612yes—
442C22×C3C2×D4×D511yescharacteristic
443C3×C4—102no—
444C3×C4#402812yes—
445C3×C4C22×D2011yescharacteristic
446C3×C4C2×D4×D511yescharacteristic
447Dic3—24no—
448Dic3—42no—
449Dic3—104no—
450Dic3—202no—
451C2×C5#473914yescomplemented
452C2×C5C2×#88211yescharacteristic
453C2×C5C22×Dic1211yescharacteristic
454C2×C5C2×#90911yescharacteristic
455D5—24no—
456C23—52no—
457C23—54no—
458C23—102no—
459C23—102no—
460C23D5×D1211yescharacteristic
461Q8—34no—
462Q8—64no—
463Q8—62no—
464Q8—154no—
465Q8—3016no—
466Q8—304no—
467Q8—302no—
468Q8—302no—
469Q8—302no—
470Q8—602no—
471C2×C4—52no—
472C2×C4—64no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—102no—
476C2×C4—104no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—122no—
480C2×C4—3016no—
481C2×C4—304no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—602no—
485C2×C4D5×D1211yescharacteristic
486C2×C4D3×D2012yes—
487C2×C4#679012yes—
488C2×C4C22×D3×D511yescharacteristic
489C8—22no—
490C8—102no—
491C2×C3—104no—
492C2×C3#6509714yescomplemented
493C2×C3C2×#402811yescharacteristic
494C2×C3C2×#406111yescharacteristic
495C2×C3C2×D5×Q1611yescharacteristic
496C5C2×#473911yescharacteristic, complemented, Sylow
497C22—54no—
498C22—102no—
499C22—108no—
500C22—102no—
501C22D5×Dic1212yes—
502C22#9126012yes—
503C22#9147612yes—
504C22C2×D5×D1211yescharacteristic
505C4—64no—
506C4—102no—
507C4—122no—
508C4—304no—
509C4—602no—
510C4#9147612yes—
511C4C2×D3×D2011yescharacteristic
512C4C2×#679011yescharacteristic
513C3C2×#6509711yescharacteristic, complemented, Sylow
514C2—104no—
515C2#1174813014yesdirect product factor
516C2C2×D5×Dic1211yescharacteristic
517C2C2×#9126011yescharacteristic
518C2C2×#9147611yescharacteristic
subgroupG/H
centerC23D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×Dic60C2semidirect
4. C22×#6663C2semidirect
5. C2×C5×#816C2semidirect
7. C2×#90975C2semidirect
8. #11748130C2direct (N × H)
22. C2×Dic60C22semidirect
30. C2×#6663C22semidirect
31. C5×#816C22semidirect
33. #90975C22semidirect
89. C2×#816D5semidirect
119. C22×C3×D5Q16semidirect
174. #816C2×D5semidirect
230. C2×C3×D5C2×Q16semidirect
282. C22×D5Dic12semidirect
338. C2×C3×C5#451semidirect
385. C2×D5C2×Dic12semidirect
434. C3×C5C2×#451semidirect
451. C2×C5#4739semidirect
492. C2×C3#65097semidirect
496. C5C2×#4739semidirect
513. C3C2×#65097semidirect
515. C2#11748130direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C22×Dic602
C2×#913602
C22×#66632
C2×C5×#8162
C2×C3×#39522
C2×#909752
#117481302
C2×#650973
C2×#47395