Finite Group Databasebeta

← C2×#11749131 #14429324

Subgroups — C2×#11749131 #14429324

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
1C22×#6716C211yesmaximal, characteristic, complemented
2C2×C3×#4078C211yesmaximal, characteristic
3C2×#91313C211yesmaximal, characteristic, complemented
4C2×#91284C211yesmaximal, characteristic, complemented
5C2×C5×#833C211yesmaximal, characteristic, complemented
6#11749131C218yesmaximal, direct product factor
7C2×#90992C211yesmaximal, characteristic, complemented
8C2×#90963C211yesmaximal, characteristic, complemented
9C2×#65037—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×#6716—21no—
14C2×#6716—22no—
15C2×#6716—21no—
16C2×#6716C2214yescomplemented
17C22×C3⋊#168C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×#687—21no—
21C3×#4078—22no—
22C3×#4078C2214yes—
23C2×C3×#686—21no—
24C2×C3×#681C2211yescharacteristic
25C2×#6662—21no—
26#91313—22no—
27#91313C2214yescomplemented
28C2×#6657—21no—
29C2×#6649—21no—
30#91284—22no—
31#91284C2214yescomplemented
32C2×D5×C3⋊C8—21no—
33C5×#833C2214yescomplemented
34#90992C2214yescomplemented
35#90963C2214yescomplemented
36C2×#5200—51nomaximal, Hall
37C22×#687—31no—
38C2×#4078D311yescharacteristic
39C2×#4055—31no—
40C2×#4053—31no—
41C2×C5×#100—31no—
42C2×#3956—31no—
43C2×#3954—31no—
44#65037—38no—
45C24×C3×C5—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15—21no—
54C2×Dic30—21no—
55C2×Dic30—21no—
56C2×Dic30—21no—
57C2×Dic30—21no—
58C2×Dic30—21no—
59C2×Dic30C2312yes—
60C2×C3×C22⋊D5—21no—
61C3×#709—21no—
62C3×#709—21no—
63C3×#709D412yes—
64C3×#709C2312yes—
65C2×C3×D20D411yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10D411yescharacteristic
68#6716—24no—
69#6716—24no—
70C2×C3⋊#168D411yescharacteristic
71C2×C3⋊#168D412yes—
72C2×C3⋊#168D411yescharacteristic
73C2×C3⋊#168C2312yes—
74C5×#208—21no—
75C5×#208—21no—
76C5×#208C2312yes—
77C5×#208C2312yes—
78C2×C5×C3⋊C8—21no—
79C2×C5×C3⋊C8—21no—
80C3×#687—24no—
81C3×#686—24no—
82C3×#681—21no—
83C3×#681C2312yes—
84C2×C3×#168—21no—
85#6662—24no—
86#6657—24no—
87#6649—24no—
88D5×C3⋊C8—24no—
89C2×C3×AGL(1,ℤ/8)—51no—
90C2×#951—51no—
91C2×#948—51no—
92C22×#214—51no—
93C2×#833D511yescharacteristic, complemented
94#5200—58no—
95C2×#824—51no—
96C2×#822—51no—
97C22×C5×D4C2×D311yescharacteristic
98C2×#709C2×D311yescharacteristic
99C22×Dic10—31no—
100C2×C5×M16—31no—
101C2×C5×M16—31no—
102C2×#687—21no—
103C2×#687—34no—
104C2×#687—61no—
105C2×#687—61no—
106C2×#687—62no—
107#4078—22no—
108#4078C2×D314yes—
109C2×#686—21no—
110C2×#681C2×D311yescharacteristic
111C22×#168—31no—
112#4055—34no—
113#4055—62no—
114#4053—34no—
115#4053—62no—
116C2×Dic20—61no—
117C2×#677—61no—
118C2×#676—61no—
119C2×C8×D5—61no—
120C5×#100—34no—
121#3956—34no—
122#3954—34no—
123C2×#471—151noSylow
124C23×C3×C5—22no—
125C23×C3×C5—41no—
126C23×C3×C5—41no—
127C23×C3×C5—82no—
128C23×C3×C5#4111yescharacteristic
129C22×C3×D5—21no—
130C3×C5×D4—22no—
131C3×C5×D4—22no—
132C3×C5×D4—41no—
133C3×C5×D4—41no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5#4111yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—22no—
141C2×Dic15—41no—
142C2×Dic15—41no—
143Dic30—22no—
144Dic30—22no—
145Dic30—41no—
146Dic30—41no—
147C3×C22⋊D5—22no—
148C3×C22⋊D5—22no—
149C2×C3×Dic5—21no—
150C3×D20—21no—
151C3×D20C2×D412yes—
152C3×C4×D5—22no—
153C3×C4×D5—22no—
154C3×Dic10—21no—
155C3×Dic10C2×D412yes—
156C3⋊#168C2×D412yes—
157C3⋊#168C2×D412yes—
158C3×#168—22no—
159C5×C3⋊C8—22no—
160C5×C3⋊C8—22no—
161C2×C3×#41—51no—
162C22×C3×D4C2×D511yescharacteristic
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—54no—
172#948—102no—
173C2×#216—101no—
174C2×#214—54no—
175C2×#214—101no—
176C2×#214—101no—
177C2×#214—101no—
178C2×#214—102no—
179C2×#208—101no—
180C2×#208C2×D511yescharacteristic
181C2×#208C2×D511yescharacteristic
182C22×C3⋊C8—51no—
183C22×C3⋊C8—101no—
184#833C2×D514yescomplemented
185#824—54no—
186#822—54no—
187C24×C5—21no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—21no—
193C2×C5×D4C22×D312yes—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—21no—
196C22×Dic5—61no—
197#709—21no—
198#709—21no—
199#709#6712yes—
200#709C22×D312yes—
201C2×D20#6711yescharacteristic
202C2×C4×D5—21no—
203C2×Dic10—32no—
204C2×Dic10—61no—
205C2×Dic10—61no—
206C2×Dic10—61no—
207C2×Dic10—61no—
208C2×Dic10—61no—
209C2×Dic10#6711yescharacteristic
210C5×M16—32no—
211C5×M16—32no—
212C5×M16—61no—
213C5×M16—61no—
214C2×C5×C8—61no—
215C2×C5×C8—61no—
216#687—24no—
217#687—64no—
218#687—64no—
219#686—24no—
220#681—21no—
221#681C22×D312yes—
222C2×#168—21no—
223C2×#168—31no—
224C2×#168—31no—
225C2×#168—32no—
226C2×#168—32no—
227Dic20—64no—
228#677—64no—
229#676—64no—
230C8×D5—64no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—51no—
233C22×SD16—151no—
234C2×#131—151no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—31no—
239C22×C3×C5—22no—
240C22×C3×C5—42no—
241C22×C3×C5—82no—
242C22×C3×C5—82no—
243C22×C3×C5—82no—
244C22×C3×C5#12111yescharacteristic
245C22×C3×C5#12111yescharacteristic
246C22×C3×C5C2×#4111yescharacteristic
247C2×C3×D5—22no—
248C2×C3×D5—42no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253Dic15—42no—
254C3×Dic5—22no—
255C24×C3—21no—
256C3×#41—52no—
257C3×#41—52no—
258C3×#41—101no—
259C3×#41—101no—
260C2×C3×Q8—51no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—51no—
267C2×C3×D4—101no—
268C2×C3×D4C22×D512yes—
269C22×C3×C4—101no—
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—21no—
289#208—104no—
290#208C22×D512yes—
291#208C22×D512yes—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—51no—
295C2×C3⋊C8—51no—
296C2×C3⋊C8—52no—
297C2×C3⋊C8—52no—
298C2×C3⋊C8—104no—
299C23×C5—22no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—82no—
303C23×C5#23711yescharacteristic
304C22×D5—21no—
305C5×D4—22no—
306C5×D4—22no—
307C5×D4—41no—
308C5×D4—41no—
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5D3×D411yescharacteristic
311C2×C4×C5#23711yescharacteristic
312C2×C4×C5C2×#6711yescharacteristic
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—22no—
316C22⋊D5—22no—
317C2×Dic5—21no—
318C2×Dic5—62no—
319C2×Dic5—121no—
320C2×Dic5—121no—
321D20—21no—
322D20C2×#6712yes—
323C4×D5—22no—
324C4×D5—22no—
325Dic10—21no—
326Dic10—62no—
327Dic10—62no—
328Dic10—121no—
329Dic10—121no—
330Dic10C2×#6712yes—
331C5×C8—62no—
332C5×C8—62no—
333#168—22no—
334#168—32no—
335#168—32no—
336C2×#41—51no—
337C22×Q8—151no—
338C22×D4D3×D511yescharacteristic
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—301no—
349C2×SD16—302no—
350C2×D8—101no—
351#131—154no—
352#131—302no—
353C2×M16—31no—
354C2×M16—31no—
355C2×M16—51no—
356C2×M16—301no—
357C22×C8—151no—
358C22×C8—301no—
359#108—154no—
360#101—154no—
361#100—34no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—82no—
365C2×C3×C5#47112yescomplemented
366C2×C3×C5C2×#12111yescharacteristic
367C3×D5—42no—
368C23×C3—22no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—82no—
372C23×C3—101no—
373C23×C3#70911yescharacteristic
374C3×Q8—52no—
375C3×Q8—101no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—41no—
379C3×D4—41no—
380C3×D4—52no—
381C3×D4—102no—
382C3×D4—102no—
383C3×D4—101no—
384C2×C3×C4—101no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4#70911yescharacteristic
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4D4×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—22no—
403C3⋊C8—52no—
404C3⋊C8—52no—
405C22×C5—22no—
406C22×C5—42no—
407C22×C5—82no—
408C22×C5—82no—
409C22×C5—82no—
410C22×C5#93911yescharacteristic
411C22×C5#93911yescharacteristic
412C22×C5C2×#23711yescharacteristic
413C2×D5—22no—
414C2×D5—42no—
415C4×C5#93911yescharacteristic
416C4×C5#93911yescharacteristic
417C4×C5C2×D3×D411yescharacteristic
418C4×C5C22×#6711yescharacteristic
419Dic5—22no—
420Dic5—122no—
421C24—21no—
422#41—52no—
423#41—52no—
424#41—101no—
425#41—101no—
426C2×Q8—51no—
427C2×Q8—152no—
428C2×Q8—301no—
429C2×Q8—301no—
430C2×Q8—301no—
431C2×Q8—301no—
432C2×Q8—301no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—51no—
439C2×D4—101no—
440C2×D4C2×D3×D512yes—
441C22×C4—101no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—104no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—104no—
450M16—32no—
451M16—32no—
452M16—52no—
453M16—61no—
454M16—61no—
455M16—101no—
456M16—304no—
457C2×C8—61no—
458C2×C8—61no—
459C2×C8—101no—
460C2×C8—151no—
461C2×C8—151no—
462C2×C8—152no—
463C2×C8—152no—
464C2×C8—304no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—42no—
468C22×C3—82no—
469C22×C3—82no—
470C22×C3—82no—
471C22×C3—102no—
472C22×C3—202no—
473C22×C3#403011yescharacteristic
474C22×C3#403011yescharacteristic
475C22×C3C2×#70911yescharacteristic
476C3×C4—102no—
477C3×C4#403011yescharacteristic
478C3×C4#403011yescharacteristic
479C3×C4C2×D4×D511yescharacteristic
480C3×C4C2×D4×D511yescharacteristic
481Dic3—202no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—82no—
485C2×C5#520012yescomplemented
486C2×C5C2×#93911yescharacteristic
487D5—42no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—82no—
492C23—101no—
493C23#677911yescharacteristic
494Q8—52no—
495Q8—101no—
496Q8—302no—
497Q8—302no—
498Q8—601no—
499Q8—601no—
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504D4—52no—
505D4—102no—
506D4—102no—
507D4—101no—
508C2×C4—101no—
509C2×C4—102no—
510C2×C4—102no—
511C2×C4—302no—
512C2×C4—601no—
513C2×C4—601no—
514C2×C4#677911yescharacteristic
515C2×C4D5×#6711yescharacteristic
516C2×C4D5×#6711yescharacteristic
517C2×C4#679011yescharacteristic
518C2×C4#679011yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—62no—
521C8—62no—
522C8—102no—
523C8—152no—
524C8—152no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—82no—
528C2×C3—202no—
529C2×C3#6503712yescomplemented
530C2×C3C2×#403011yescharacteristic
531C5C2×#520011yescharacteristic, complemented, Sylow
532C22—22no—
533C22—42no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22—102no—
538C22—202no—
539C22#9155011yescharacteristic
540C22#9155011yescharacteristic
541C22C2×#677911yescharacteristic
542C4—102no—
543C4—602no—
544C4#9155011yescharacteristic
545C4#9155011yescharacteristic
546C4C2×D5×#6711yescharacteristic
547C4C2×#679011yescharacteristic
548C3C2×#6503711yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—82no—
552C2—202no—
553C2#1174913112yesdirect product factor
554C2C2×#9155011yescharacteristic
subgroupG/H
centerC22#91550
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5#121
prime radicalC2×C3×#4078C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6716C2semidirect
3. C2×#91313C2semidirect
4. C2×#91284C2semidirect
5. C2×C5×#833C2semidirect
6. #11749131C2direct (N × H)
7. C2×#90992C2semidirect
8. C2×#90963C2semidirect
16. C2×#6716C22semidirect
27. #91313C22semidirect
31. #91284C22semidirect
33. C5×#833C22semidirect
34. #90992C22semidirect
35. #90963C22semidirect
93. C2×#833D5semidirect
184. #833C2×D5semidirect
365. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
485. C2×C5#5200semidirect
529. C2×C3#65037semidirect
531. C5C2×#5200semidirect
548. C3C2×#65037semidirect
553. C2#11749131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67162
C2×C3×#40782
C2×#913132
C2×#912842
C2×C5×#8332
#117491312
C2×#909922
C2×#909632
C2×#650373
C2×#52005