Finite Group Databasebeta

← C2×#11749441 #14417961

Subgroups — C2×#11749441 #14417961

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×C3×#4096C211yesmaximal, characteristic
3C2×#91284C211yesmaximal, characteristic, complemented
4C2×C5×#837C211yesmaximal, characteristic, complemented
5#11749441C218yesmaximal, direct product factor
6C2×#90991C211yesmaximal, characteristic, complemented
7C2×#90977C211yesmaximal, characteristic, complemented
8C2×#90953C211yesmaximal, characteristic, complemented
9C2×#65112—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C2×C3×#709C2211yescharacteristic
12#91837—22no—
13#91837C2214yescomplemented
14C2×#6710—21no—
15C2×#6710C2211yescharacteristic
16C22×C3⋊#168—21no—
17C22×C3⋊#168C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C3×#4096C414yescomplemented
21C3×#4096C2214yes—
22C2×C3×#689C411yescharacteristic, complemented
23C2×C3×#688C411yescharacteristic, complemented
24C2×C3×#687C411yescharacteristic, complemented
25C2×C3×#686C411yescharacteristic, complemented
26C22×C3×#168C2211yescharacteristic
27C2×#6649—21no—
28#91284—22no—
29#91284C2214yescomplemented
30C2×D5×C3⋊C8—21no—
31C5×#837C2214yescomplemented
32#90991C2214yescomplemented
33#90977C2214yescomplemented
34#90953C2214yescomplemented
35C2×#5197—51nomaximal, Hall
36C2×#4096D311yescharacteristic
37C2×#4094—31no—
38C2×#4053—31no—
39C2×C5×#104—31no—
40C2×#3954—31no—
41C2×#3937—31no—
42C2×#3935—31no—
43#65112—38no—
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
53C22×C5×Dic3—21no—
54C2×C3×C22⋊D5—21no—
55C3×#709—21no—
56C3×#709—21no—
57C3×#709C2×C412yes—
58C3×#709C2312yes—
59C2×C3×D20C2×C411yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10C2×C411yescharacteristic
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—
71C4×C5×Dic3—21no—
72C4×C5×Dic3C2312yes—
73C5×#208—21no—
74C5×#208C2312yes—
75C2×C5×C3⋊C8—21no—
76C3×#689C2×C414yescomplemented
77C3×#688C2×C414yescomplemented
78C3×#687C2×C414yescomplemented
79C3×#686C2×C414yescomplemented
80C2×C3×#168C2×C411yescharacteristic
81C2×C3×#168C2×C411yescharacteristic
82C2×C3×#168C2×C412yes—
83C2×C3×#168C2312yes—
84#6649—24no—
85D5×C3⋊C8—24no—
86C2×C3×#135—51no—
87C2×#948—51no—
88C2×#948—51no—
89C2×#837—51no—
90C2×#837D511yescharacteristic, complemented
91#5197—58no—
92C2×#819—51no—
93C2×#815—51no—
94C2×C5×#41C2×D311yescharacteristic
95C2×#709C2×D311yescharacteristic
96C2×C5×M16—31no—
97C2×C42×C5—31no—
98#4096Dic314yescomplemented
99#4096C2×D314yes—
100#4094—34no—
101#4094—62no—
102C2×#689Dic311yescharacteristic, complemented
103C2×#688Dic311yescharacteristic, complemented
104C2×#687Dic311yescharacteristic, complemented
105C2×#686Dic311yescharacteristic, complemented
106C2×#681—31no—
107C2×#681—61no—
108C22×#168—31no—
109C22×#168—61no—
110C22×#168C2×D311yescharacteristic
111#4053—34no—
112#4053—62no—
113C2×#676—61no—
114C2×C8×D5—61no—
115C5×#104—34no—
116#3954—34no—
117#3937—34no—
118#3935—34no—
119C2×#444—151noSylow
120C23×C3×C5—21no—
121C23×C3×C5#4111yescharacteristic
122C22×C3×D5—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
138C2×C5×Dic3—22no—
139C2×C5×Dic3—42no—
140C3×C22⋊D5—22no—
141C3×C22⋊D5—22no—
142C2×C3×Dic5—21no—
143C3×D20—21no—
144C3×D20C22×C412yes—
145C3×C4×D5—22no—
146C3×C4×D5—22no—
147C3×Dic10—21no—
148C3×Dic10C22×C412yes—
149C3⋊#168—22no—
150C3⋊#168C2×D412yes—
151C3⋊#168C2×D412yes—
152C3×#168C22×C412yes—
153C3×#168C22×C412yes—
154C5×C3⋊C8—22no—
155C2×C3×#41—51no—
156C2×C3×#41C2×D511yescharacteristic
157C3×#135—54no—
158C3×#135—54no—
159C2×C3×Q16—51no—
160C2×C3×SD16—51no—
161C2×C3×SD16—51no—
162C2×C3×D8—51no—
163C22×C3×C8—51no—
164#948—54no—
165#948—54no—
166#948—102no—
167#948—102no—
168C2×C4×Dic3C2×D511yescharacteristic
169C2×#208—51no—
170C2×#208—101no—
171C2×#208—101no—
172C2×#208C2×D511yescharacteristic
173C22×C3⋊C8—51no—
174C22×C3⋊C8—101no—
175C22×C3⋊C8—101no—
176#837—54no—
177#837C2×D514yescomplemented
178#819—54no—
179#815—54no—
180C5×#41—21no—
181C5×#41—21no—
182C5×#41C2×Dic312yes—
183C5×#41C22×D312yes—
184C2×C5×Q8C2×Dic311yescharacteristic
185C2×C5×D4—21no—
186C2×C5×D4C2×Dic311yescharacteristic
187C22×C4×C5—21no—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—21no—
191#709—21no—
192#709—21no—
193#709C2×Dic312yes—
194#709C22×D312yes—
195C2×D20C2×Dic311yescharacteristic
196C2×C4×D5—21no—
197C2×Dic10C2×Dic311yescharacteristic
198C5×M16—32no—
199C5×M16—61no—
200C2×C5×C8—61no—
201C42×C5—32no—
202C42×C5—61no—
203#689C2×Dic314yescomplemented
204#688C2×Dic314yescomplemented
205#687C2×Dic314yescomplemented
206#686C2×Dic314yescomplemented
207#681—32no—
208#681—64no—
209#681—61no—
210C2×#168—31no—
211C2×#168—31no—
212C2×#168—32no—
213C2×#168—32no—
214C2×#168—64no—
215C2×#168—61no—
216C2×#168C2×Dic312yes—
217C2×#168C2×Dic311yescharacteristic
218C2×#168C2×Dic311yescharacteristic
219C2×#168C22×D312yes—
220#676—64no—
221C8×D5—64no—
222C2×#135—51no—
223C2×#131—151no—
224C2×#131—151no—
225#444—158no—
226C2×#108—151no—
227C2×#104—31no—
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×C3×D5—22no—
237C2×C3×D5—42no—
238C3×C4×C5—22no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×D411yescharacteristic
243C3×Dic5—22no—
244C5×Dic3—42no—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—52no—
248C3×#41—52no—
249C3×#41—101no—
250C3×#41—101no—
251C3×#41C4×D512yes—
252C3×#41C22×D512yes—
253C2×C3×Q8—51no—
254C2×C3×Q8C4×D511yescharacteristic
255C2×C3×D4—21no—
256C2×C3×D4—51no—
257C2×C3×D4—101no—
258C2×C3×D4C4×D511yescharacteristic
259C22×C3×C4—21no—
260C22×C3×C4—101no—
261C22×C3×C4C22×D511yescharacteristic
262C22×Dic3—21no—
263C3×Q16—54no—
264C3×SD16—54no—
265C3×SD16—54no—
266C3×D8—54no—
267C2×C3×C8—51no—
268C2×C3×C8—51no—
269C2×C3×C8—52no—
270C2×C3×C8—52no—
271C4×Dic3—21no—
272C4×Dic3C22×D512yes—
273#208—21no—
274#208—52no—
275#208—104no—
276#208—104no—
277#208—101no—
278#208C22×D512yes—
279C2×C3⋊C8—21no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—52no—
284C2×C3⋊C8—104no—
285C2×C3⋊C8—104no—
286C2×C3⋊C8—101no—
287C23×C5—21no—
288C23×C5#23711yescharacteristic
289C22×D5—21no—
290C5×Q8—21no—
291C5×Q8C22×Dic312yes—
292C5×D4—22no—
293C5×D4—22no—
294C5×D4—21no—
295C5×D4C22×Dic312yes—
296C2×C4×C5—21no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—62no—
300C2×C4×C5—122no—
301C2×C4×C5D3×D411yescharacteristic
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5#23711yescharacteristic
304C2×C4×C5C22×Dic311yescharacteristic
305C2×C4×C5C22×Dic311yescharacteristic
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—22no—
308C22⋊D5—22no—
309C2×Dic5—21no—
310D20—21no—
311D20C22×Dic312yes—
312C4×D5—22no—
313C4×D5—22no—
314Dic10—21no—
315Dic10C22×Dic312yes—
316C5×C8—62no—
317#168—32no—
318#168—32no—
319#168—62no—
320#168C22×Dic312yes—
321#168C22×Dic312yes—
322C2×#41—51no—
323C2×#41D3×D511yescharacteristic
324#135—54no—
325#135—54no—
326C2×Q16—51no—
327C2×SD16—51no—
328C2×SD16—51no—
329C2×D8—51no—
330#131—154no—
331#131—154no—
332#131—302no—
333#131—302no—
334C2×M16—31no—
335C2×M16—151no—
336C2×M16—301no—
337C2×M16—301no—
338C22×C8—51no—
339C22×C8—151no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42—31no—
343#108—154no—
344#104—34no—
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
352C3×D5—42no—
353C23×C3—21no—
354C23×C3—101no—
355C23×C3#71111yescharacteristic
356C3×Q8—21no—
357C3×Q8—52no—
358C3×Q8—101no—
359C3×Q8C2×C4×D512yes—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—21no—
363C3×D4—52no—
364C3×D4—102no—
365C3×D4—102no—
366C3×D4—101no—
367C3×D4C2×C4×D512yes—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—101no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4C2×C4×D511yescharacteristic
375C2×C3×C4C2×C4×D511yescharacteristic
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4#71111yescharacteristic
379C2×C3×C4C23×D511yescharacteristic
380C2×Dic3—22no—
381C2×Dic3—42no—
382C3×C8—52no—
383C3×C8—52no—
384C3⋊C8—22no—
385C3⋊C8—52no—
386C3⋊C8—52no—
387C3⋊C8—102no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—42no—
391C22×C5D4×Dic311yescharacteristic
392C22×C5D4×Dic311yescharacteristic
393C22×C5C2×#23711yescharacteristic
394C2×D5—22no—
395C2×D5—42no—
396C4×C5—22no—
397C4×C5—122no—
398C4×C5D4×Dic311yescharacteristic
399C4×C5D4×Dic311yescharacteristic
400C4×C5C2×D3×D411yescharacteristic
401C4×C5C23×Dic311yescharacteristic
402Dic5—22no—
403#41—21no—
404#41—21no—
405#41—52no—
406#41—52no—
407#41—101no—
408#41—101no—
409#41D5×Dic312yes—
410#41C2×D3×D512yes—
411C2×Q8—51no—
412C2×Q8D5×Dic311yescharacteristic
413C2×D4—21no—
414C2×D4—51no—
415C2×D4—101no—
416C2×D4D5×Dic311yescharacteristic
417C22×C4—21no—
418C22×C4—61no—
419C22×C4—101no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—54no—
422SD16—54no—
423SD16—54no—
424D8—54no—
425M16—32no—
426M16—61no—
427M16—152no—
428M16—304no—
429M16—304no—
430M16—301no—
431C2×C8—51no—
432C2×C8—51no—
433C2×C8—52no—
434C2×C8—52no—
435C2×C8—61no—
436C2×C8—152no—
437C2×C8—151no—
438C2×C8—151no—
439C2×C8—152no—
440C2×C8—304no—
441C2×C8—304no—
442C2×C8—301no—
443C42—32no—
444C42—61no—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—42no—
449C22×C3—102no—
450C22×C3—202no—
451C22×C3#402711yescharacteristic
452C22×C3#402711yescharacteristic
453C22×C3C2×#71111yescharacteristic
454C3×C4—22no—
455C3×C4—102no—
456C3×C4#402711yescharacteristic
457C3×C4#402711yescharacteristic
458C3×C4C22×C4×D511yescharacteristic
459C3×C4C2×D4×D511yescharacteristic
460Dic3—42no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—42no—
464C2×C5#519712yescomplemented
465C2×C5C2×D4×Dic311yescharacteristic
466D5—42no—
467C23—21no—
468C23—101no—
469C23#678011yescharacteristic
470Q8—21no—
471Q8—52no—
472Q8—101no—
473Q8C2×D5×Dic312yes—
474D4—22no—
475D4—22no—
476D4—21no—
477D4—52no—
478D4—102no—
479D4—102no—
480D4—101no—
481D4C2×D5×Dic312yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—62no—
486C2×C4—101no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—122no—
490C2×C4C2×D5×Dic311yescharacteristic
491C2×C4C2×D5×Dic311yescharacteristic
492C2×C4#678011yescharacteristic
493C2×C4#679011yescharacteristic
494C2×C4#679011yescharacteristic
495C2×C4C22×D3×D511yescharacteristic
496C8—52no—
497C8—52no—
498C8—62no—
499C8—152no—
500C8—152no—
501C8—302no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3—202no—
506C2×C3#6511212yescomplemented
507C2×C3C2×#402711yescharacteristic
508C5C2×#519711yescharacteristic, complemented, Sylow
509C22—22no—
510C22—22no—
511C22—42no—
512C22—102no—
513C22—202no—
514C22#9155911yescharacteristic
515C22#9155911yescharacteristic
516C22C2×#678011yescharacteristic
517C4—22no—
518C4—102no—
519C4—122no—
520C4#9155911yescharacteristic
521C4#9155911yescharacteristic
522C4C22×D5×Dic311yescharacteristic
523C4C2×#679011yescharacteristic
524C3C2×#6511211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—42no—
528C2—202no—
529C2#1174944112yesdirect product factor
530C2C2×#9155911yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C4×D4
prime radicalC2×C3×#4096C2
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×#91284C2semidirect
4. C2×C5×#837C2semidirect
5. #11749441C2direct (N × H)
6. C2×#90991C2semidirect
7. C2×#90977C2semidirect
8. C2×#90953C2semidirect
13. #91837C22semidirect
20. C3×#4096C4semidirect
22. C2×C3×#689C4semidirect
23. C2×C3×#688C4semidirect
24. C2×C3×#687C4semidirect
25. C2×C3×#686C4semidirect
29. #91284C22semidirect
31. C5×#837C22semidirect
32. #90991C22semidirect
33. #90977C22semidirect
34. #90953C22semidirect
76. C3×#689C2×C4semidirect
77. C3×#688C2×C4semidirect
78. C3×#687C2×C4semidirect
79. C3×#686C2×C4semidirect
90. C2×#837D5semidirect
98. #4096Dic3semidirect
102. C2×#689Dic3semidirect
103. C2×#688Dic3semidirect
104. C2×#687Dic3semidirect
105. C2×#686Dic3semidirect
177. #837C2×D5semidirect
203. #689C2×Dic3semidirect
204. #688C2×Dic3semidirect
205. #687C2×Dic3semidirect
206. #686C2×Dic3semidirect
350. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
464. C2×C5#5197semidirect
506. C2×C3#65112semidirect
508. C5C2×#5197semidirect
524. C3C2×#65112semidirect
529. C2#11749441direct (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×C3×#40962
C2×#912842
C2×C5×#8372
#117494412
C2×#909912
C2×#909772
C2×#909532
C2×#651123
C2×#51975