Finite Group Databasebeta

← C2×#11749449 #14429333

Subgroups — C2×#11749449 #14429333

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91840C211yesmaximal, characteristic, complemented
2C2×C5×#948C211yesmaximal, characteristic, complemented
3C2×C3×#4095C211yesmaximal, characteristic
4C22×#6657C211yesmaximal, characteristic, complemented
5#11749449C218yesmaximal, direct product factor
6C2×#90993C211yesmaximal, characteristic, complemented
7C2×#90963C211yesmaximal, characteristic, complemented
8C2×#90958C211yesmaximal, characteristic, complemented
9C2×#65430—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C3×D20C2211yescharacteristic
13#91840—22no—
14#91840C2214yescomplemented
15C2×#6718—21no—
16C2×#6716—21no—
17C2×#6710C2211yescharacteristic
18C5×#948—22no—
19C5×#948C2214yescomplemented
20C2×C5×#208—21no—
21C2×C5×#208C2211yescharacteristic
22C22×C5×C3⋊C8—21no—
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4095—22no—
25C3×#4095C2214yes—
26C2×C3×#688—21no—
27C2×C3×#686—21no—
28C2×C3×#681C2211yescharacteristic
29C2×#6657—21no—
30C2×#6657—21no—
31C2×#6657—22no—
32C2×#6657C2214yescomplemented
33#90993C2214yescomplemented
34#90963C2214yescomplemented
35#90958C2214yescomplemented
36C2×#5200—51nomaximal, Hall
37C2×C5×#131—31no—
38C2×#4097—31no—
39C2×#4095D311yescharacteristic
40C22×#677—31no—
41#65430—38no—
42C2×#3956—31no—
43C2×#3955—31no—
44C2×#3951—31no—
45C23×C3×D5—21no—
46C3×C5×#41—21no—
47C3×C5×#41—21no—
48C3×C5×#41D412yes—
49C3×C5×#41C2312yes—
50C2×C3×C5×Q8D411yescharacteristic
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4D411yescharacteristic
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—21no—
56C2×Dic30—21no—
57C2×Dic30—21no—
58C2×Dic30—21no—
59C2×Dic30—21no—
60C2×Dic30—21no—
61C2×Dic30C2312yes—
62C2×C3×D20—21no—
63C2×C3×D20—21no—
64C2×C3×D20—21no—
65C2×C3×D20—21no—
66C2×C3×D20—21no—
67C2×C3×D20C2312yes—
68#6718—24no—
69#6716—24no—
70#6710—21no—
71#6710C2312yes—
72C2×C3⋊#168—21no—
73C5×#208—21no—
74C5×#208—24no—
75C5×#208C2312yes—
76C2×C5×C3⋊C8—21no—
77C2×C5×C3⋊C8—24no—
78C2×C5×C3⋊C8D411yescharacteristic
79C2×C5×C3⋊C8D411yescharacteristic
80C2×C5×C3⋊C8D412yes—
81C2×C5×C3⋊C8C2312yes—
82C3×#688—24no—
83C3×#686—24no—
84C3×#681—21no—
85C3×#681C2312yes—
86C2×C3×#168—21no—
87#6657—24no—
88#6657—24no—
89C2×C3×AGL(1,ℤ/8)—51no—
90C2×#951—51no—
91C2×#948D511yescharacteristic, complemented
92C22×#214—51no—
93C2×#833—51no—
94#5200—58no—
95C2×#824—51no—
96C2×#822—51no—
97C2×C5×#41C2×D311yescharacteristic
98C22×D20C2×D311yescharacteristic
99C22×Dic10—31no—
100C5×#131—34no—
101C5×#131—62no—
102C2×C5×M16—31no—
103C2×C5×M16—61no—
104C22×C5×C8—31no—
105C22×C5×C8—61no—
106#4097—34no—
107#4097—62no—
108#4095—22no—
109#4095C2×D314yes—
110C2×#689—61no—
111C2×#688—21no—
112C2×#687—61no—
113C2×#686—21no—
114C2×#681—31no—
115C2×#681C2×D311yescharacteristic
116C2×#677—34no—
117C2×#677—61no—
118C2×#677—61no—
119C2×#677—62no—
120#3956—34no—
121#3955—34no—
122#3951—34no—
123C2×#471—151noSylow
124C23×C3×C5—21no—
125C23×C3×C5#4111yescharacteristic
126C22×C3×D5—22no—
127C22×C3×D5—41no—
128C22×C3×D5—41no—
129C22×C3×D5—82no—
130C3×C5×Q8—21no—
131C3×C5×Q8C2×D412yes—
132C3×C5×D4—22no—
133C3×C5×D4—22no—
134C3×C5×D4—21no—
135C3×C5×D4C2×D412yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4111yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—22no—
146C2×Dic15—41no—
147C2×Dic15—41no—
148Dic30—22no—
149Dic30—22no—
150Dic30—41no—
151Dic30—41no—
152C3×D20—22no—
153C3×D20—22no—
154C3×D20—41no—
155C3×D20—41no—
156C3⋊#168—22no—
157C3×#168—22no—
158C5×C3⋊C8—22no—
159C5×C3⋊C8C2×D412yes—
160C5×C3⋊C8C2×D412yes—
161C2×C3×#41C2×D511yescharacteristic
162C22×C3×D4—51no—
163C22×Dic6—51no—
164C3×AGL(1,ℤ/8)—54no—
165C3×AGL(1,ℤ/8)—102no—
166C2×C3×SD16—101no—
167C2×C3×D8—101no—
168C2×C3×M16—51no—
169#951—54no—
170#951—102no—
171#948—22no—
172#948C2×D514yescomplemented
173C2×#216—101no—
174C2×#214—54no—
175C2×#214—101no—
176C2×#214—101no—
177C2×#214—101no—
178C2×#214—102no—
179C2×#208—21no—
180C2×#208—51no—
181C2×#208C2×D511yescharacteristic
182C22×C3⋊C8—21no—
183C22×C3⋊C8C2×D511yescharacteristic
184#833—54no—
185#824—54no—
186#822—54no—
187C23×D5—21no—
188C5×#41—21no—
189C5×#41—21no—
190C5×#41#6712yes—
191C5×#41C22×D312yes—
192C2×C5×Q8#6711yescharacteristic
193C2×C5×D4—21no—
194C2×C5×D4#6711yescharacteristic
195C22×C4×C5—21no—
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—61no—
198C2×D20—21no—
199C2×D20—21no—
200C2×D20—21no—
201C2×D20—21no—
202C2×D20—21no—
203C2×D20C22×D312yes—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—61no—
207C2×Dic10—61no—
208C2×Dic10—61no—
209C2×Dic10—61no—
210C5×M16—32no—
211C5×M16—64no—
212C5×M16—61no—
213C2×C5×C8—31no—
214C2×C5×C8—31no—
215C2×C5×C8—32no—
216C2×C5×C8—32no—
217C2×C5×C8—64no—
218C2×C5×C8—61no—
219#689—64no—
220#688—24no—
221#687—64no—
222#686—24no—
223#681—21no—
224#681—32no—
225#681—61no—
226#681C22×D312yes—
227C2×#168—21no—
228C2×#168—61no—
229#677—64no—
230#677—64no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—51no—
233C22×SD16—151no—
234C2×#131—31no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—42no—
242C22×C3×C5#12111yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C2×C3×D5—42no—
246C2×C3×D5—82no—
247C2×C3×D5—82no—
248C2×C3×D5—82no—
249C3×C4×C5—22no—
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5#12111yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253C3×C4×C5C22×D411yescharacteristic
254Dic15—42no—
255C24×C3—101no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41D2012yes—
259C3×#41C22×D512yes—
260C2×C3×Q8D2011yescharacteristic
261C2×C3×D4—21no—
262C2×C3×D4—52no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×C3×D4—101no—
266C2×C3×D4—101no—
267C2×C3×D4—101no—
268C2×C3×D4D2011yescharacteristic
269C22×C3×C4—21no—
270C22×C3×C4C22×D511yescharacteristic
271C22×Dic3—101no—
272C2×Dic6—52no—
273C2×Dic6—101no—
274C2×Dic6—101no—
275C2×Dic6—101no—
276C2×Dic6—101no—
277C2×Dic6—101no—
278C3×SD16—104no—
279C3×D8—104no—
280C3×M16—52no—
281C3×M16—101no—
282C2×C3×C8—101no—
283#216—104no—
284#214—104no—
285#214—104no—
286#214—104no—
287#208—21no—
288#208—24no—
289#208—52no—
290#208—101no—
291#208C22×D512yes—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—24no—
294C2×C3⋊C8—101no—
295C2×C3⋊C8C22⋊D511yescharacteristic
296C2×C3⋊C8C22⋊D511yescharacteristic
297C2×C3⋊C8C22⋊D512yes—
298C2×C3⋊C8C22×D512yes—
299C23×C5—21no—
300C23×C5#23711yescharacteristic
301C22×D5—22no—
302C22×D5—41no—
303C22×D5—41no—
304C22×D5—82no—
305C5×Q8—21no—
306C5×Q8C2×#6712yes—
307C5×D4—22no—
308C5×D4—22no—
309C5×D4—21no—
310C5×D4C2×#6712yes—
311C2×C4×C5—21no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5#23711yescharacteristic
317C2×C4×C5C2×#6711yescharacteristic
318C2×C4×C5C2×#6711yescharacteristic
319C2×C4×C5C23×D311yescharacteristic
320C2×Dic5—62no—
321C2×Dic5—121no—
322C2×Dic5—121no—
323D20—22no—
324D20—22no—
325D20—41no—
326D20—41no—
327Dic10—62no—
328Dic10—62no—
329Dic10—121no—
330Dic10—121no—
331C5×C8—32no—
332C5×C8—32no—
333C5×C8—62no—
334#168—22no—
335#168—62no—
336C2×#41D3×D511yescharacteristic
337C22×Q8—151no—
338C22×D4—51no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—54no—
342AGL(1,ℤ/8)—102no—
343C2×Q16—301no—
344C2×SD16—101no—
345C2×SD16—154no—
346C2×SD16—301no—
347C2×SD16—301no—
348C2×SD16—302no—
349C2×SD16—301no—
350C2×D8—101no—
351#131—34no—
352#131—62no—
353C2×M16—31no—
354C2×M16—51no—
355C2×M16—61no—
356C2×M16—151no—
357C22×C8—31no—
358C22×C8—61no—
359#108—154no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—42no—
365C2×C3×C5#47112yescomplemented
366C2×C3×C5C2×#12111yescharacteristic
367C3×D5—82no—
368C23×C3—21no—
369C23×C3—102no—
370C23×C3—201no—
371C23×C3—201no—
372C23×C3—402no—
373C23×C3#70911yescharacteristic
374C3×Q8—21no—
375C3×Q8C2×D2012yes—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—21no—
379C3×D4—102no—
380C3×D4—102no—
381C3×D4—201no—
382C3×D4—201no—
383C3×D4C2×D2012yes—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4C2×D2011yescharacteristic
388C2×C3×C4C2×D2011yescharacteristic
389C2×C3×C4#70911yescharacteristic
390C2×C3×C4C2×C22⋊D511yescharacteristic
391C2×C3×C4C2×C22⋊D511yescharacteristic
392C2×C3×C4C23×D511yescharacteristic
393C2×Dic3—102no—
394C2×Dic3—201no—
395C2×Dic3—201no—
396Dic6—102no—
397Dic6—102no—
398Dic6—201no—
399Dic6—201no—
400C3×C8—102no—
401C3⋊C8—22no—
402C3⋊C8—102no—
403C3⋊C8C2×C22⋊D512yes—
404C3⋊C8C2×C22⋊D512yes—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—42no—
408C22×C5#93911yescharacteristic
409C22×C5#93911yescharacteristic
410C22×C5C2×#23711yescharacteristic
411C2×D5—42no—
412C2×D5—82no—
413C2×D5—82no—
414C2×D5—82no—
415C4×C5—22no—
416C4×C5#93911yescharacteristic
417C4×C5#93911yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419C4×C5C22×#6711yescharacteristic
420Dic5—122no—
421C24—101no—
422#41—21no—
423#41—21no—
424#41#120212yes—
425#41C2×D3×D512yes—
426C2×Q8—152no—
427C2×Q8—301no—
428C2×Q8—301no—
429C2×Q8—301no—
430C2×Q8—301no—
431C2×Q8—301no—
432C2×Q8#120211yescharacteristic
433C2×D4—21no—
434C2×D4—52no—
435C2×D4—101no—
436C2×D4—101no—
437C2×D4—101no—
438C2×D4—101no—
439C2×D4—101no—
440C2×D4#120211yescharacteristic
441C22×C4—21no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—104no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—104no—
450M16—32no—
451M16—52no—
452M16—64no—
453M16—61no—
454M16—101no—
455M16—152no—
456M16—301no—
457C2×C8—31no—
458C2×C8—31no—
459C2×C8—32no—
460C2×C8—32no—
461C2×C8—64no—
462C2×C8—61no—
463C2×C8—101no—
464C2×C8—301no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—42no—
469C22×C3—202no—
470C22×C3—402no—
471C22×C3—402no—
472C22×C3—402no—
473C22×C3#407611yescharacteristic
474C22×C3#407611yescharacteristic
475C22×C3C2×#70911yescharacteristic
476C3×C4—22no—
477C3×C4#407611yescharacteristic
478C3×C4#407611yescharacteristic
479C3×C4C22×D2011yescharacteristic
480C3×C4C22×C22⋊D511yescharacteristic
481Dic3—202no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—42no—
485C2×C5#520012yescomplemented
486C2×C5C2×#93911yescharacteristic
487D5—82no—
488C23—21no—
489C23—102no—
490C23—201no—
491C23—201no—
492C23—402no—
493C23#677911yescharacteristic
494Q8—21no—
495Q8—302no—
496Q8—302no—
497Q8—601no—
498Q8—601no—
499Q8C2×#120212yes—
500D4—22no—
501D4—22no—
502D4—21no—
503D4—102no—
504D4—102no—
505D4—201no—
506D4—201no—
507D4C2×#120212yes—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—302no—
512C2×C4—601no—
513C2×C4—601no—
514C2×C4#677911yescharacteristic
515C2×C4C2×#120211yescharacteristic
516C2×C4C2×#120211yescharacteristic
517C2×C4D3×C22⋊D511yescharacteristic
518C2×C4D3×C22⋊D511yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—32no—
521C8—32no—
522C8—62no—
523C8—102no—
524C8—302no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—42no—
528C2×C3—402no—
529C2×C3#6543012yescomplemented
530C2×C3C2×#407611yescharacteristic
531C5C2×#520011yescharacteristic, complemented, Sylow
532C22—22no—
533C22—22no—
534C22—42no—
535C22—202no—
536C22—402no—
537C22—402no—
538C22—402no—
539C22#9156911yescharacteristic
540C22#9156911yescharacteristic
541C22C2×#677911yescharacteristic
542C4—22no—
543C4—602no—
544C4#9156911yescharacteristic
545C4#9156911yescharacteristic
546C4C22×#120211yescharacteristic
547C4C2×D3×C22⋊D511yescharacteristic
548C3C2×#6543011yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—42no—
552C2—402no—
553C2#1174944912yesdirect product factor
554C2C2×#9156911yescharacteristic
subgroupG/H
centerC22#91569
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#121
prime radicalC2×C3×#4095C2
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91840C2semidirect
2. C2×C5×#948C2semidirect
4. C22×#6657C2semidirect
5. #11749449C2direct (N × H)
6. C2×#90993C2semidirect
7. C2×#90963C2semidirect
8. C2×#90958C2semidirect
14. #91840C22semidirect
19. C5×#948C22semidirect
32. C2×#6657C22semidirect
33. #90993C22semidirect
34. #90963C22semidirect
35. #90958C22semidirect
91. C2×#948D5semidirect
172. #948C2×D5semidirect
365. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
485. C2×C5#5200semidirect
529. C2×C3#65430semidirect
531. C5C2×#5200semidirect
548. C3C2×#65430semidirect
553. C2#11749449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918402
C2×C5×#9482
C2×C3×#40952
C22×#66572
#117494492
C2×#909932
C2×#909632
C2×#909582
C2×#654303
C2×#52005