Finite Group Databasebeta

← C2×#11747492 #14423397

Subgroups — C2×#11747492 #14423397

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
2C2×C3×#4043C211yesmaximal, characteristic
3C22×#6662C211yesmaximal, characteristic, complemented
4C22×#6661C211yesmaximal, characteristic, complemented
5C2×#91094C211yesmaximal, characteristic, complemented
6C2×C5×#810C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic
8#11747492C218yesmaximal, direct product factor
9C2×#65097—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×#1204—21no—
15C22×D5×Dic3—21no—
16C2×D5×Dic6—24no—
17C2×D5×Dic6—24no—
18C2×D5×Dic6—22no—
19C2×D5×Dic6C2214yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×#685—21no—
24C2×C3×C4⋊Dic5—21no—
25C3×#4043—22no—
26C3×#4043C2214yes—
27C2×#6662—24no—
28C2×#6662C2214yescomplemented
29C2×#6661—24no—
30C2×#6661C2214yescomplemented
31#91094C2214yescomplemented
32C5×#810C2214yescomplemented
33#90955C2214yes—
34C2×#5050—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×#689—31no—
37C22×Dic20—31no—
38C2×#4043D311yescharacteristic
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65097—38no—
43C23×C3×D5D411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C2×Dic30—21no—
48C2×Dic30—22no—
49C2×Dic30D414yes—
50C2×Dic30C2312yes—
51C22×C5×Dic3—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6—22no—
54C2×C5×Dic6D414yes—
55C2×C5×Dic6C2312yes—
56C22×C3×Dic5—21no—
57C22×C3×Dic5D411yescharacteristic
58C2×C3×C4×D5—22no—
59C2×C3×C4×D5—22no—
60C2×C3×C4×D5D412yes—
61C2×C3×C4×D5C2312yes—
62C2×C3×Dic10—22no—
63C2×C3×Dic10—22no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10C2312yes—
66C2×#1204—28no—
67C2×#1204—24no—
68C2×D5×Dic3—28no—
69C2×D5×Dic3—24no—
70D5×Dic6—216no—
71D5×Dic6—28no—
72D5×Dic6—28no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75C2×C3⋊#168—22no—
76C2×C3⋊#168C2312yes—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2312yes—
79C3×#685—24no—
80C3×C4⋊Dic5—24no—
81#6662—28no—
82#6661—28no—
83C23×Dic6—51no—
84C2×C3×C22⋊Q8—51no—
85C22×#216—51no—
86C22×#216—51no—
87C2×#830—51no—
88#5050—58no—
89C2×#810—51no—
90C2×#810D511yescharacteristic, complemented
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—61no—
100C22×Dic10C2×D311yescharacteristic
101C22×C5×C8—31no—
102C2×C5×C4⋊C4C2×D311yescharacteristic
103C2×#689—34no—
104C2×#689—64no—
105C2×#685—21no—
106C2×C4⋊Dic5—21no—
107C22×#168—31no—
108C2×Dic20—34no—
109C2×Dic20—64no—
110#4043—22no—
111#4043C2×D314yes—
112C5×#103—34no—
113#3952—34no—
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×C5—22no—
122C2×C3×C4×C5—42no—
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D412yes—
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2411yescharacteristic
127C2×Dic15—24no—
128C2×Dic15—22no—
129Dic30—24no—
130Dic30—22no—
131Dic30C2×D414yes—
132C2×C5×Dic3—24no—
133C2×C5×Dic3—22no—
134C5×Dic6—24no—
135C5×Dic6—22no—
136C5×Dic6C2×D414yes—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—42no—
140C2×C3×Dic5C2×D412yes—
141C3×C4×D5—24no—
142C3×C4×D5—22no—
143C3×C4×D5—22no—
144C3×Dic10—22no—
145C3×Dic10—22no—
146C3×Dic10—42no—
147#1204—216no—
148D5×Dic3—216no—
149C3⋊#168—22no—
150C5×C3⋊C8—22no—
151C22×C3×Q8—51no—
152C23×C3×C4—51no—
153C23×Dic3—101no—
154C22×Dic6—51no—
155C22×Dic6—54no—
156C22×Dic6—104no—
157C22×Dic6—102no—
158C22×Dic6—101no—
159C22×Dic6—104no—
160C22×Dic6C2×D511yescharacteristic
161C3×C22⋊Q8—54no—
162C3×C22⋊Q8—102no—
163C2×C3×C4⋊C4—101no—
164C2×C3×C4⋊C4C2×D511yescharacteristic
165C2×C3×C22⋊C4—101no—
166C2×#216—54no—
167C2×#216—54no—
168C2×#216—104no—
169C2×#216—104no—
170C22×C3⋊C8—51no—
171C22×C3⋊C8C2×D511yescharacteristic
172#830—54no—
173#810—54no—
174#810C2×D514yescomplemented
175C23×D5#6711yescharacteristic
176C2×C5×Q8—34no—
177C2×C5×Q8—32no—
178C2×C5×Q8—62no—
179C2×C5×Q8—61no—
180C22×C4×C5—21no—
181C22×C4×C5—61no—
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—21no—
184C22×Dic5—61no—
185C22×Dic5#6711yescharacteristic
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×D5#6712yes—
194C2×C4×D5C22×D312yes—
195C2×Dic10—22no—
196C2×Dic10—22no—
197C2×Dic10—21no—
198C2×Dic10—34no—
199C2×Dic10—32no—
200C2×Dic10—68no—
201C2×Dic10—62no—
202C2×Dic10—61no—
203C2×Dic10—64no—
204C2×Dic10C22×D312yes—
205C2×C5×C8—32no—
206C2×C5×C8—62no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4C22×D312yes—
209#689—68no—
210#685—24no—
211C4⋊Dic5—24no—
212C2×#168—32no—
213C2×#168—62no—
214Dic20—68no—
215C23×Q8—151no—
216C22×Q16—151no—
217C22×Q16—151no—
218C2×C22⋊Q8—51no—
219#451—158no—
220C2×#103—31no—
221C2×#103—151no—
222C2×C22⋊C8—151no—
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—42no—
232C3×C4×C5#12012yes—
233C3×C4×C5C22×D411yescharacteristic
234C3×C4×C5C22×D411yescharacteristic
235Dic15—24no—
236C3×Dic5—22no—
237C3×Dic5—42no—
238C5×Dic3—24no—
239C24×C3—51no—
240C2×C3×Q8—52no—
241C2×C3×Q8—101no—
242C2×C3×Q8—102no—
243C2×C3×Q8—102no—
244C22×C3×C4—21no—
245C22×C3×C4—51no—
246C22×C3×C4—52no—
247C22×C3×C4—52no—
248C22×C3×C4—102no—
249C22×C3×C4—102no—
250C22×C3×C4—101no—
251C22×C3×C4C22×D511yescharacteristic
252C22×Dic3—21no—
253C22×Dic3—104no—
254C22×Dic3—108no—
255C22×Dic3—101no—
256C2×Dic6—22no—
257C2×Dic6—21no—
258C2×Dic6—54no—
259C2×Dic6—52no—
260C2×Dic6—108no—
261C2×Dic6—1016no—
262C2×Dic6—104no—
263C2×Dic6—108no—
264C2×Dic6—102no—
265C2×Dic6—101no—
266C2×Dic6—108no—
267C2×Dic6D2014yes—
268C2×Dic6C22×D512yes—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—104no—
271C3×C4⋊C4C22×D512yes—
272C3×C22⋊C4—104no—
273#216—108no—
274#216—108no—
275C2×C3⋊C8—22no—
276C2×C3⋊C8—52no—
277C2×C3⋊C8—102no—
278C2×C3⋊C8C22×D512yes—
279C23×C5C2×#6711yescharacteristic
280C22×D5—22no—
281C22×D5—22no—
282C22×D5#21614yescomplemented
283C22×D5C2×#6712yes—
284C5×Q8—34no—
285C5×Q8—64no—
286C5×Q8—62no—
287C2×C4×C5—22no—
288C2×C4×C5—42no—
289C2×C4×C5—64no—
290C2×C4×C5—62no—
291C2×C4×C5D3×D412yes—
292C2×C4×C5D3×D412yes—
293C2×C4×C5C2×#6711yescharacteristic
294C2×C4×C5C23×D311yescharacteristic
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—42no—
298C2×Dic5—64no—
299C2×Dic5—62no—
300C2×Dic5C2×#6712yes—
301C4×D5—24no—
302C4×D5—22no—
303C4×D5—22no—
304C4×D5—616no—
305Dic10—22no—
306Dic10—22no—
307Dic10—34no—
308Dic10—42no—
309Dic10—616no—
310Dic10—64no—
311Dic10—62no—
312C5×C8—62no—
313#168—62no—
314C22×Q8—31no—
315C22×Q8—51no—
316C22×Q8—154no—
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—31no—
329C22×C8—151no—
330C22⋊Q8—54no—
331C22⋊Q8—102no—
332C2×C4⋊C4—101no—
333C2×C4⋊C4D3×D511yescharacteristic
334C2×C22⋊C4—101no—
335#103—34no—
336#103—154no—
337C22⋊C8—154no—
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
348C3×Q8—102no—
349C3×Q8—102no—
350C3×Q8—202no—
351C2×C3×C4—22no—
352C2×C3×C4—42no—
353C2×C3×C4—52no—
354C2×C3×C4—102no—
355C2×C3×C4—102no—
356C2×C3×C4—102no—
357C2×C3×C4—104no—
358C2×C3×C4—102no—
359C2×C3×C4—202no—
360C2×C3×C4C2×D2012yes—
361C2×C3×C4D4×D512yes—
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4C23×D511yescharacteristic
364C2×Dic3—22no—
365C2×Dic3—24no—
366C2×Dic3—1016no—
367C2×Dic3—102no—
368C2×Dic3—104no—
369Dic6—22no—
370Dic6—24no—
371Dic6—54no—
372Dic6—1016no—
373Dic6—102no—
374Dic6—104no—
375Dic6C2×D2014yes—
376C3⋊C8—22no—
377C3⋊C8—102no—
378C22×C5#93712yes—
379C22×C5C2×#21612yes—
380C22×C5#95112yes—
381C22×C5C22×#6711yescharacteristic
382C2×D5—22no—
383C2×D5—28no—
384C2×D5—22no—
385C2×D5C2×#21614yescomplemented
386C4×C5—42no—
387C4×C5—64no—
388C4×C5#93712yes—
389C4×C5C2×D3×D411yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—22no—
392Dic5—42no—
393Dic5—64no—
394C24—51no—
395C2×Q8—34no—
396C2×Q8—32no—
397C2×Q8—52no—
398C2×Q8—62no—
399C2×Q8—61no—
400C2×Q8—101no—
401C2×Q8—102no—
402C2×Q8—102no—
403C2×Q8—154no—
404C2×Q8—152no—
405C2×Q8—304no—
406C2×Q8—308no—
407C2×Q8—308no—
408C2×Q8—308no—
409C2×Q8—3016no—
410C2×Q8—302no—
411C2×Q8—301no—
412C22×C4—21no—
413C22×C4—51no—
414C22×C4—52no—
415C22×C4—52no—
416C22×C4—61no—
417C22×C4—102no—
418C22×C4—102no—
419C22×C4—101no—
420C22×C4—304no—
421C22×C4—308no—
422C22×C4—301no—
423C22×C4C2×D3×D511yescharacteristic
424Q16—308no—
425Q16—308no—
426C2×C8—32no—
427C2×C8—62no—
428C2×C8—152no—
429C2×C8—302no—
430C4⋊C4—21no—
431C4⋊C4—104no—
432C4⋊C4C2×D3×D512yes—
433C22⋊C4—104no—
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—42no—
444C3×C4—102no—
445C3×C4—202no—
446C3×C4#402812yes—
447C3×C4C22×D2011yescharacteristic
448C3×C4C2×D4×D511yescharacteristic
449Dic3—24no—
450Dic3—104no—
451C2×C5#505014yescomplemented
452C2×C5C2×#93711yescharacteristic
453C2×C5C22×#21611yescharacteristic
454C2×C5C2×#95111yescharacteristic
455D5—24no—
456C23—54no—
457C23—52no—
458C23—102no—
459C23—102no—
460C23D5×#6711yescharacteristic
461Q8—34no—
462Q8—64no—
463Q8—62no—
464Q8—102no—
465Q8—102no—
466Q8—154no—
467Q8—202no—
468Q8—3016no—
469Q8—304no—
470Q8—302no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—52no—
474C2×C4—64no—
475C2×C4—62no—
476C2×C4—102no—
477C2×C4—104no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—102no—
481C2×C4—202no—
482C2×C4—3016no—
483C2×C4—304no—
484C2×C4—302no—
485C2×C4D3×D2012yes—
486C2×C4#677712yes—
487C2×C4D5×#6711yescharacteristic
488C2×C4C22×D3×D511yescharacteristic
489C8—62no—
490C8—302no—
491C2×C3—104no—
492C2×C3#6509714yescomplemented
493C2×C3C2×#402811yescharacteristic
494C2×C3C2×#406111yescharacteristic
495C2×C3C2×D5×Q1611yescharacteristic
496C5C2×#505011yescharacteristic, complemented, Sylow
497C22—54no—
498C22—102no—
499C22—108no—
500C22—102no—
501C22#9147412yes—
502C22#9148412yes—
503C22D5×#21612yes—
504C22C2×D5×#6711yescharacteristic
505C4—42no—
506C4—64no—
507C4—102no—
508C4—202no—
509C4—304no—
510C4#9147412yes—
511C4C2×D3×D2011yescharacteristic
512C4C2×#677711yescharacteristic
513C3C2×#6509711yescharacteristic, complemented, Sylow
514C2—104no—
515C2#1174749214yesdirect product factor
516C2C2×#9147411yescharacteristic
517C2C2×#9148411yescharacteristic
518C2C2×D5×#21611yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#6662C2semidirect
4. C22×#6661C2semidirect
5. C2×#91094C2semidirect
6. C2×C5×#810C2semidirect
8. #11747492C2direct (N × H)
28. C2×#6662C22semidirect
30. C2×#6661C22semidirect
31. #91094C22semidirect
32. C5×#810C22semidirect
90. C2×#810D5semidirect
119. C22×C3×D5Q16semidirect
174. #810C2×D5semidirect
230. C2×C3×D5C2×Q16semidirect
282. C22×D5#216semidirect
338. C2×C3×C5#451semidirect
385. C2×D5C2×#216semidirect
434. C3×C5C2×#451semidirect
451. C2×C5#5050semidirect
492. C2×C3#65097semidirect
496. C5C2×#5050semidirect
513. C3C2×#65097semidirect
515. C2#11747492direct (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
C2×C3×#40432
C22×#66622
C22×#66612
C2×#910942
C2×C5×#8102
C2×#909552
#117474922
C2×#650973
C2×#50505