Finite Group Databasebeta

← C2×#11749443 #14417964

Subgroups — C2×#11749443 #14417964

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91837C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic
3C2×#91288C211yesmaximal, characteristic, complemented
4C2×C3×#3969C211yesmaximal, characteristic, complemented
5#11749443C218yesmaximal, direct product factor
6C2×#90993C211yesmaximal, characteristic, complemented
7C2×#90979C211yesmaximal, characteristic, complemented
8C2×#90952C211yesmaximal, characteristic, complemented
9C2×#65486—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C2×C5×#235C2211yescharacteristic
12#91837—22no—
13#91837C2214yescomplemented
14C2×#6710—21no—
15C2×#6710C2211yescharacteristic
16C22×C3⋊#168—21no—
17C22×C3⋊#168C2211yescharacteristic
18C5×#950C414yescomplemented
19C5×#950C2214yes—
20C2×C5×#216C411yescharacteristic, complemented
21C2×C5×#215C411yescharacteristic, complemented
22C2×C5×#214C411yescharacteristic, complemented
23C2×C5×#213C411yescharacteristic, complemented
24C22×C5×C3⋊C8C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×#681C2211yescharacteristic
27C2×#6650—21no—
28#91288—22no—
29#91288C2214yescomplemented
30C2×D3×#168—21no—
31C3×#3969C2214yescomplemented
32#90993C2214yescomplemented
33#90979C2214yescomplemented
34#90952C2214yescomplemented
35C2×#4823—51nomaximal, Hall
36C2×C5×#135—31no—
37C2×#4094—31no—
38C2×#4094—31no—
39C2×#3969—31no—
40C2×#3969D311yescharacteristic, complemented
41#65486—38no—
42C2×#3951—31no—
43C2×#3947—31no—
44C3×C5×#41—21no—
45C3×C5×#41—21no—
46C3×C5×#41C2×C412yes—
47C3×C5×#41C2312yes—
48C2×C3×C5×Q8C2×C411yescharacteristic
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4C2×C411yescharacteristic
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C2×C5×#67—21no—
54C5×#235—21no—
55C5×#235—21no—
56C5×#235C2×C412yes—
57C5×#235C2312yes—
58C2×C5×D12C2×C411yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C5×Dic6C2×C411yescharacteristic
61C22×C3×Dic5—21no—
62#6710—21no—
63#6710—24no—
64#6710C2312yes—
65C2×C3⋊#168—21no—
66C2×C3⋊#168—24no—
67C2×C3⋊#168D411yescharacteristic
68C2×C3⋊#168D412yes—
69C2×C3⋊#168D411yescharacteristic
70C2×C3⋊#168C2312yes—
71C5×#216C2×C414yescomplemented
72C5×#215C2×C414yescomplemented
73C5×#214C2×C414yescomplemented
74C5×#213C2×C414yescomplemented
75C2×C5×C3⋊C8C2×C411yescharacteristic
76C2×C5×C3⋊C8C2×C411yescharacteristic
77C2×C5×C3⋊C8C2×C412yes—
78C2×C5×C3⋊C8C2312yes—
79C3×C4×Dic5—21no—
80C3×C4×Dic5C2312yes—
81C3×#681—21no—
82C3×#681C2312yes—
83C2×C3×#168—21no—
84#6650—24no—
85D3×#168—24no—
86C2×#950D511yescharacteristic
87C2×#948—51no—
88C2×#907—51no—
89C2×C3×#104—51no—
90C2×#822—51no—
91C2×#805—51no—
92C2×#803—51no—
93#4823—58no—
94C2×C5×#41—31no—
95C2×C5×#41C2×D311yescharacteristic
96C5×#135—34no—
97C5×#135—34no—
98C2×C5×Q16—31no—
99C2×C5×SD16—31no—
100C2×C5×SD16—31no—
101C2×C5×D8—31no—
102C22×C5×C8—31no—
103#4094—34no—
104#4094—34no—
105#4094—62no—
106#4094—62no—
107C2×C4×Dic5C2×D311yescharacteristic
108C2×#681—31no—
109C2×#681—61no—
110C2×#681—61no—
111C2×#681C2×D311yescharacteristic
112C22×#168—31no—
113C22×#168—61no—
114C22×#168—61no—
115#3969—34no—
116#3969C2×D314yescomplemented
117#3951—34no—
118#3947—34no—
119C2×#444—151noSylow
120C23×C3×C5—21no—
121C23×C3×C5#4111yescharacteristic
122C22×C5×D3—21no—
123C3×C5×Q8—21no—
124C3×C5×Q8C22×C412yes—
125C3×C5×D4—22no—
126C3×C5×D4—22no—
127C3×C5×D4—21no—
128C3×C5×D4C22×C412yes—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C22×C411yescharacteristic
133C2×C3×C4×C5C22×C411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5#4111yescharacteristic
137C2×C3×C4×C5C2411yescharacteristic
138C5×#67—22no—
139C5×#67—22no—
140C2×C5×Dic3—21no—
141C5×D12—21no—
142C5×D12C22×C412yes—
143C4×C5×D3—22no—
144C4×C5×D3—22no—
145C5×Dic6—21no—
146C5×Dic6C22×C412yes—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—42no—
149C3⋊#168—22no—
150C3⋊#168C2×D412yes—
151C3⋊#168C2×D412yes—
152C3×#168—22no—
153C5×C3⋊C8C22×C412yes—
154C5×C3⋊C8C22×C412yes—
155C2×C3×#41C2×D511yescharacteristic
156C2×#235C2×D511yescharacteristic
157C2×C3×M16—51no—
158C2×C3×C42—51no—
159#950Dic514yescomplemented
160#950C2×D514yes—
161#948—54no—
162#948—102no—
163C2×#216Dic511yescharacteristic, complemented
164C2×#215Dic511yescharacteristic, complemented
165C2×#214Dic511yescharacteristic, complemented
166C2×#213Dic511yescharacteristic, complemented
167C2×#208—51no—
168C2×#208—101no—
169C22×C3⋊C8—51no—
170C22×C3⋊C8—101no—
171C22×C3⋊C8C2×D511yescharacteristic
172#907—54no—
173#907—102no—
174C2×ΓL(1,𝔽25)—101no—
175C2×D3×C8—101no—
176C3×#104—54no—
177#822—54no—
178#805—54no—
179#803—54no—
180C5×#41—21no—
181C5×#41—21no—
182C5×#41—32no—
183C5×#41—32no—
184C5×#41—61no—
185C5×#41—61no—
186C5×#41C4×D312yes—
187C5×#41C22×D312yes—
188C2×C5×Q8—31no—
189C2×C5×Q8C4×D311yescharacteristic
190C2×C5×D4—21no—
191C2×C5×D4—31no—
192C2×C5×D4—61no—
193C2×C5×D4C4×D311yescharacteristic
194C22×C4×C5—21no—
195C22×C4×C5—61no—
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—21no—
198C5×Q16—34no—
199C5×SD16—34no—
200C5×SD16—34no—
201C5×D8—34no—
202C2×C5×C8—31no—
203C2×C5×C8—31no—
204C2×C5×C8—32no—
205C2×C5×C8—32no—
206C4×Dic5—21no—
207C4×Dic5C22×D312yes—
208#681—21no—
209#681—32no—
210#681—64no—
211#681—64no—
212#681—61no—
213#681C22×D312yes—
214C2×#168—21no—
215C2×#168—31no—
216C2×#168—31no—
217C2×#168—32no—
218C2×#168—32no—
219C2×#168—64no—
220C2×#168—64no—
221C2×#168—61no—
222C2×#135—31no—
223C2×#131—151no—
224C2×#131—151no—
225#444—158no—
226C2×#108—151no—
227C2×#104—51no—
228C2×#104—151no—
229C2×#97—151no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—42no—
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5C4×D411yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C2×C5×D3—22no—
237C2×C5×D3—42no—
238C3×C4×C5—22no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×D411yescharacteristic
243C3×Dic5—42no—
244C5×Dic3—22no—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41C2×Dic512yes—
248C3×#41C22×D512yes—
249C2×C3×Q8C2×Dic511yescharacteristic
250C2×C3×D4—21no—
251C2×C3×D4C2×Dic511yescharacteristic
252C22×C3×C4—21no—
253C22×C3×C4—101no—
254C22×C3×C4C22×D511yescharacteristic
255C2×#67—21no—
256#235—21no—
257#235—21no—
258#235C2×Dic512yes—
259#235C22×D512yes—
260C2×D12C2×Dic511yescharacteristic
261C2×C4×D3—21no—
262C2×Dic6C2×Dic511yescharacteristic
263C3×M16—52no—
264C3×M16—101no—
265C2×C3×C8—101no—
266C3×C42—52no—
267C3×C42—101no—
268#216C2×Dic514yescomplemented
269#215C2×Dic514yescomplemented
270#214C2×Dic514yescomplemented
271#213C2×Dic514yescomplemented
272#208—52no—
273#208—104no—
274#208—101no—
275C2×C3⋊C8—51no—
276C2×C3⋊C8—51no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—52no—
279C2×C3⋊C8—104no—
280C2×C3⋊C8—101no—
281C2×C3⋊C8C2×Dic511yescharacteristic
282C2×C3⋊C8C2×Dic511yescharacteristic
283C2×C3⋊C8C2×Dic512yes—
284C2×C3⋊C8C22×D512yes—
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
287C23×C5—21no—
288C23×C5—61no—
289C23×C5#23711yescharacteristic
290C5×Q8—21no—
291C5×Q8—32no—
292C5×Q8—61no—
293C5×Q8C2×C4×D312yes—
294C5×D4—22no—
295C5×D4—22no—
296C5×D4—21no—
297C5×D4—32no—
298C5×D4—62no—
299C5×D4—62no—
300C5×D4—61no—
301C5×D4C2×C4×D312yes—
302C2×C4×C5—21no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—61no—
306C2×C4×C5—62no—
307C2×C4×C5—62no—
308C2×C4×C5C2×C4×D311yescharacteristic
309C2×C4×C5C2×C4×D311yescharacteristic
310C2×C4×C5D3×D411yescharacteristic
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5#23711yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C2×Dic5—22no—
315C2×Dic5—42no—
316C5×C8—32no—
317C5×C8—32no—
318#168—22no—
319#168—32no—
320#168—32no—
321#168—62no—
322C2×#41—31no—
323C2×#41D3×D511yescharacteristic
324#135—34no—
325#135—34no—
326C2×Q16—31no—
327C2×SD16—31no—
328C2×SD16—31no—
329C2×D8—31no—
330#131—154no—
331#131—154no—
332#131—302no—
333#131—302no—
334C2×M16—51no—
335C2×M16—151no—
336C2×M16—301no—
337C2×M16—301no—
338C22×C8—31no—
339C22×C8—151no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42—51no—
343#108—154no—
344#104—54no—
345#104—154no—
346#97—154no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5—42no—
350C2×C3×C5#44412yescomplemented
351C2×C3×C5C2×C4×D411yescharacteristic
352C5×D3—42no—
353C23×C3—21no—
354C23×C3#71111yescharacteristic
355C22×D3—21no—
356C3×Q8—21no—
357C3×Q8C22×Dic512yes—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4C22×Dic512yes—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—102no—
366C2×C3×C4—202no—
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4#71111yescharacteristic
370C2×C3×C4C22×Dic511yescharacteristic
371C2×C3×C4C22×Dic511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—22no—
374#67—22no—
375C2×Dic3—21no—
376D12—21no—
377D12C22×Dic512yes—
378C4×D3—22no—
379C4×D3—22no—
380Dic6—21no—
381Dic6C22×Dic512yes—
382C3×C8—102no—
383C3⋊C8—52no—
384C3⋊C8—52no—
385C3⋊C8—102no—
386C3⋊C8C22×Dic512yes—
387C3⋊C8C22×Dic512yes—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—42no—
391C22×C5—62no—
392C22×C5—122no—
393C22×C5#67⋊C411yescharacteristic
394C22×C5#67⋊C411yescharacteristic
395C22×C5C2×#23711yescharacteristic
396C4×C5—22no—
397C4×C5—62no—
398C4×C5#67⋊C411yescharacteristic
399C4×C5#67⋊C411yescharacteristic
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C2×D3×D411yescharacteristic
402Dic5—42no—
403#41—21no—
404#41—21no—
405#41—32no—
406#41—32no—
407#41—61no—
408#41—61no—
409#41D3×Dic512yes—
410#41C2×D3×D512yes—
411C2×Q8—31no—
412C2×Q8D3×Dic511yescharacteristic
413C2×D4—21no—
414C2×D4—31no—
415C2×D4—61no—
416C2×D4D3×Dic511yescharacteristic
417C22×C4—21no—
418C22×C4—61no—
419C22×C4—101no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—34no—
422SD16—34no—
423SD16—34no—
424D8—34no—
425M16—52no—
426M16—101no—
427M16—152no—
428M16—304no—
429M16—304no—
430M16—301no—
431C2×C8—31no—
432C2×C8—31no—
433C2×C8—32no—
434C2×C8—32no—
435C2×C8—101no—
436C2×C8—152no—
437C2×C8—151no—
438C2×C8—151no—
439C2×C8—152no—
440C2×C8—304no—
441C2×C8—304no—
442C2×C8—301no—
443C42—52no—
444C42—101no—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—42no—
449C22×C3D4×Dic511yescharacteristic
450C22×C3D4×Dic511yescharacteristic
451C22×C3C2×#71111yescharacteristic
452C2×D3—22no—
453C2×D3—42no—
454C3×C4—22no—
455C3×C4—202no—
456C3×C4D4×Dic511yescharacteristic
457C3×C4D4×Dic511yescharacteristic
458C3×C4C2×D4×D511yescharacteristic
459C3×C4C23×Dic511yescharacteristic
460Dic3—22no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—42no—
464C2×C5—122no—
465C2×C5#482312yescomplemented
466C2×C5C2×#67⋊C411yescharacteristic
467C23—21no—
468C23—61no—
469C23#678011yescharacteristic
470Q8—21no—
471Q8—32no—
472Q8—61no—
473Q8C2×D3×Dic512yes—
474D4—22no—
475D4—22no—
476D4—21no—
477D4—32no—
478D4—62no—
479D4—62no—
480D4—61no—
481D4C2×D3×Dic512yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—102no—
489C2×C4—202no—
490C2×C4#678011yescharacteristic
491C2×C4C2×D3×Dic511yescharacteristic
492C2×C4C2×D3×Dic511yescharacteristic
493C2×C4#679011yescharacteristic
494C2×C4#679011yescharacteristic
495C2×C4C22×D3×D511yescharacteristic
496C8—32no—
497C8—32no—
498C8—102no—
499C8—152no—
500C8—152no—
501C8—302no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3#6548612yescomplemented
506C2×C3C2×D4×Dic511yescharacteristic
507D3—42no—
508C5C2×#482311yescharacteristic, complemented, Sylow
509C22—22no—
510C22—22no—
511C22—42no—
512C22—62no—
513C22—122no—
514C22#67⋊Dic511yescharacteristic
515C22#67⋊Dic511yescharacteristic
516C22C2×#678011yescharacteristic
517C4—22no—
518C4—62no—
519C4—202no—
520C4#67⋊Dic511yescharacteristic
521C4#67⋊Dic511yescharacteristic
522C4C22×D3×Dic511yescharacteristic
523C4C2×#679011yescharacteristic
524C3C2×#6548611yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—42no—
528C2—122no—
529C2#1174944312yesdirect product factor
530C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#950C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91837C2semidirect
3. C2×#91288C2semidirect
4. C2×C3×#3969C2semidirect
5. #11749443C2direct (N × H)
6. C2×#90993C2semidirect
7. C2×#90979C2semidirect
8. C2×#90952C2semidirect
13. #91837C22semidirect
18. C5×#950C4semidirect
20. C2×C5×#216C4semidirect
21. C2×C5×#215C4semidirect
22. C2×C5×#214C4semidirect
23. C2×C5×#213C4semidirect
29. #91288C22semidirect
31. C3×#3969C22semidirect
32. #90993C22semidirect
33. #90979C22semidirect
34. #90952C22semidirect
40. C2×#3969D3semidirect
71. C5×#216C2×C4semidirect
72. C5×#215C2×C4semidirect
73. C5×#214C2×C4semidirect
74. C5×#213C2×C4semidirect
116. #3969C2×D3semidirect
159. #950Dic5semidirect
163. C2×#216Dic5semidirect
164. C2×#215Dic5semidirect
165. C2×#214Dic5semidirect
166. C2×#213Dic5semidirect
268. #216C2×Dic5semidirect
269. #215C2×Dic5semidirect
270. #214C2×Dic5semidirect
271. #213C2×Dic5semidirect
350. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
465. C2×C5#4823semidirect
505. C2×C3#65486semidirect
508. C5C2×#4823semidirect
524. C3C2×#65486semidirect
529. C2#11749443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918372
C2×C5×#9502
C2×#912882
C2×C3×#39692
#117494432
C2×#909932
C2×#909792
C2×#909522
C2×#654863
C2×#48235