Finite Group Databasebeta

← C2×#11749375 #14429454

Subgroups — C2×#11749375 #14429454

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#216C211yesmaximal, characteristic, complemented
2C2×C3×#4088C211yesmaximal, characteristic
3C2×#91307C211yesmaximal, characteristic
4C2×#91283C211yesmaximal, characteristic
5C2×#91120C211yesmaximal, characteristic, complemented
6#11749375C218yesmaximal, direct product factor
7C2×#90993C211yesmaximal, characteristic, complemented
8C2×#90962C211yesmaximal, characteristic, complemented
9C2×#65481—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×C5×#216—21no—
16C2×C5×#216—22no—
17C2×C5×#216—21no—
18C2×C5×#216C2214yescomplemented
19C22×C5×C3⋊C8C2211yescharacteristic
20C2×C3×#689—21no—
21C3×#4088—22no—
22C3×#4088C2214yes—
23C2×C3×#688—21no—
24C2×C3×#681C2211yescharacteristic
25C2×#6661—21no—
26#91307—22no—
27#91307C2214yes—
28C2×#6655—21no—
29C2×#6649—21no—
30#91283—22no—
31#91283C2214yes—
32C2×D5×C3⋊C8—21no—
33#91120C2214yescomplemented
34#90993C2214yescomplemented
35#90962C2214yescomplemented
36C2×#5204—51nomaximal, Hall
37C22×C5×Q16—31no—
38C2×#4088—31no—
39C2×#4088D311yescharacteristic
40C2×#4047—31no—
41C2×#3968—31no—
42C2×#3968—31no—
43#65481—38no—
44C2×#3951—31no—
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8C2312yes—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C5×Dic3—21no—
54C2×C5×Dic6—21no—
55C2×C5×Dic6—21no—
56C2×C5×Dic6—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6C2312yes—
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#6710—21no—
69#6710—21no—
70#6710C2312yes—
71#6710C2312yes—
72C2×C3⋊#168—21no—
73C2×C3⋊#168—21no—
74C5×#216—24no—
75C5×#216—24no—
76C2×C5×C3⋊C8D411yescharacteristic
77C2×C5×C3⋊C8D412yes—
78C2×C5×C3⋊C8D411yescharacteristic
79C2×C5×C3⋊C8C2312yes—
80C3×#689—24no—
81C3×#688—24no—
82C3×#681—21no—
83C3×#681C2312yes—
84C2×C3×#168—21no—
85#6661—24no—
86#6655—24no—
87#6649—24no—
88D5×C3⋊C8—24no—
89C2×C3×#137—51no—
90C2×#951—51no—
91C2×#948—51no—
92C22×#216D511yescharacteristic, complemented
93C2×#836—51no—
94#5204—58no—
95C2×#824—51no—
96C2×#822—51no—
97C22×C5×Q8—31no—
98C22×C5×Q8C2×D311yescharacteristic
99C2×#709C2×D311yescharacteristic
100C2×C5×Q16—34no—
101C2×C5×Q16—61no—
102C2×C5×Q16—61no—
103C2×C5×Q16—62no—
104C22×C5×C8—31no—
105C2×#689—21no—
106C2×#689—61no—
107#4088—22no—
108#4088—34no—
109#4088—62no—
110#4088C2×D314yes—
111C2×#688—21no—
112C2×#688—61no—
113C2×#681—31no—
114C2×#681—31no—
115C2×#681C2×D311yescharacteristic
116#4047—34no—
117#4047—62no—
118C2×#676—61no—
119C2×C8×D5—61no—
120#3968—34no—
121#3968—34no—
122#3951—34no—
123C2×#473—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×C3×D5—21no—
126C3×C5×Q8—22no—
127C3×C5×Q8—22no—
128C3×C5×Q8—41no—
129C3×C5×Q8—41no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—41no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5#4111yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×C5×Dic3—22no—
140C2×C5×Dic3—41no—
141C2×C5×Dic3—41no—
142C5×Dic6—22no—
143C5×Dic6—22no—
144C5×Dic6—41no—
145C5×Dic6—41no—
146C3×C22⋊D5—22no—
147C3×C22⋊D5—22no—
148C2×C3×Dic5—21no—
149C3×D20—21no—
150C3×D20C2×D412yes—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153C3×Dic10—21no—
154C3×Dic10C2×D412yes—
155C3⋊#168—22no—
156C3⋊#168—22no—
157C3×#168—22no—
158C5×C3⋊C8C2×D412yes—
159C5×C3⋊C8C2×D412yes—
160C2×C3×#41—51no—
161C22×C3×Q8C2×D511yescharacteristic
162C22×Dic6C2×D511yescharacteristic
163C3×#137—54no—
164C3×#137—102no—
165C2×C3×Q16—101no—
166C2×C3×SD16—101no—
167C2×C3×M16—51no—
168#951—54no—
169#951—102no—
170#948—54no—
171#948—102no—
172C2×#216—21no—
173C2×#216—21no—
174C2×#216—22no—
175C2×#216—101no—
176C2×#216C2×D514yescomplemented
177C2×#214—101no—
178C2×#208—51no—
179C2×#208—51no—
180C2×#208—101no—
181C22×C3⋊C8—101no—
182C22×C3⋊C8C2×D511yescharacteristic
183#836—54no—
184#824—54no—
185#822—54no—
186C2×C5×Q8—21no—
187C2×C5×Q8—21no—
188C2×C5×Q8—21no—
189C2×C5×Q8—21no—
190C2×C5×Q8—21no—
191C2×C5×Q8—32no—
192C2×C5×Q8—61no—
193C2×C5×Q8—61no—
194C2×C5×Q8—61no—
195C2×C5×Q8—61no—
196C2×C5×Q8—61no—
197C2×C5×Q8C22×D312yes—
198C22×C4×C5—21no—
199C22×C4×C5—61no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—21no—
202#709—21no—
203#709—21no—
204#709#6712yes—
205#709C22×D312yes—
206C2×D20#6711yescharacteristic
207C2×C4×D5—21no—
208C2×Dic10#6711yescharacteristic
209C5×Q16—64no—
210C5×Q16—64no—
211C2×C5×C8—31no—
212C2×C5×C8—31no—
213C2×C5×C8—32no—
214C2×C5×C8—32no—
215#689—24no—
216#689—64no—
217#688—24no—
218#688—64no—
219#681—21no—
220#681—32no—
221#681—32no—
222#681—61no—
223#681—61no—
224#681C22×D312yes—
225C2×#168—21no—
226C2×#168—61no—
227C2×#168—61no—
228#676—64no—
229C8×D5—64no—
230C2×#137—51no—
231C2×#137—151no—
232C22×Q16—31no—
233C2×#131—151no—
234#473—158no—
235C2×#108—151no—
236C2×#101—151no—
237C2×#101—151no—
238C22×C3×C5—22no—
239C22×C3×C5#12111yescharacteristic
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C2×C3×D5—22no—
243C2×C3×D5—42no—
244C3×C4×C5—42no—
245C3×C4×C5#12111yescharacteristic
246C3×C4×C5#12111yescharacteristic
247C3×C4×C5C22×D411yescharacteristic
248C3×C4×C5C22×D411yescharacteristic
249C3×Dic5—22no—
250C5×Dic3—42no—
251C3×#41—52no—
252C3×#41—52no—
253C3×#41—101no—
254C3×#41—101no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8—51no—
261C2×C3×Q8C22×D512yes—
262C2×C3×D4—51no—
263C2×C3×D4—101no—
264C22×C3×C4—21no—
265C22×C3×C4—101no—
266C22×C3×C4C22×D511yescharacteristic
267C22×Dic3—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6C22×D512yes—
274C3×Q16—104no—
275C3×SD16—104no—
276C3×M16—52no—
277C3×M16—101no—
278C2×C3×C8—101no—
279#216—24no—
280#216—24no—
281#216—104no—
282#214—104no—
283#208—52no—
284#208—52no—
285#208—101no—
286#208—101no—
287#208—104no—
288C2×C3⋊C8—101no—
289C2×C3⋊C8—101no—
290C2×C3⋊C8—104no—
291C2×C3⋊C8C22⋊D511yescharacteristic
292C2×C3⋊C8C22⋊D511yescharacteristic
293C2×C3⋊C8C22⋊D512yes—
294C2×C3⋊C8C22×D512yes—
295C23×C5#23711yescharacteristic
296C22×D5—21no—
297C5×Q8—22no—
298C5×Q8—22no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×Q8—62no—
302C5×Q8—62no—
303C5×Q8—121no—
304C5×Q8—121no—
305C2×C4×C5—22no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—62no—
309C2×C4×C5—121no—
310C2×C4×C5—121no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5#23711yescharacteristic
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C2×#6711yescharacteristic
316C2×C4×C5C23×D311yescharacteristic
317C22⋊D5—22no—
318C22⋊D5—22no—
319C2×Dic5—21no—
320D20—21no—
321D20C2×#6712yes—
322C4×D5—22no—
323C4×D5—22no—
324Dic10—21no—
325Dic10C2×#6712yes—
326C5×C8—32no—
327C5×C8—32no—
328#168—22no—
329#168—62no—
330#168—62no—
331C2×#41—51no—
332C22×Q8—31no—
333C22×Q8D3×D511yescharacteristic
334#137—54no—
335#137—102no—
336#137—154no—
337#137—302no—
338C2×Q16—34no—
339C2×Q16—61no—
340C2×Q16—61no—
341C2×Q16—62no—
342C2×Q16—101no—
343C2×Q16—301no—
344C2×SD16—101no—
345C2×SD16—301no—
346#131—154no—
347#131—302no—
348C2×M16—51no—
349C2×M16—151no—
350C2×M16—151no—
351C2×M16—301no—
352C22×C8—31no—
353C22×C8—301no—
354#108—154no—
355#101—154no—
356#101—154no—
357C2×C3×C5—21no—
358C2×C3×C5—21no—
359C2×C3×C5#47312yescomplemented
360C2×C3×C5C2×#12111yescharacteristic
361C3×D5—42no—
362C23×C3—101no—
363C23×C3#71111yescharacteristic
364C3×Q8—22no—
365C3×Q8—22no—
366C3×Q8—41no—
367C3×Q8—41no—
368C3×Q8—52no—
369C3×Q8—101no—
370C3×D4—52no—
371C3×D4—102no—
372C3×D4—102no—
373C3×D4—101no—
374C2×C3×C4—22no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—101no—
378C2×C3×C4—102no—
379C2×C3×C4—102no—
380C2×C3×C4D4×D511yescharacteristic
381C2×C3×C4D4×D511yescharacteristic
382C2×C3×C4#71111yescharacteristic
383C2×C3×C4C2×C22⋊D511yescharacteristic
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386C2×Dic3—22no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389Dic6—22no—
390Dic6—22no—
391Dic6—41no—
392Dic6—41no—
393C3×C8—102no—
394C3⋊C8—102no—
395C3⋊C8—102no—
396C3⋊C8C2×C22⋊D512yes—
397C3⋊C8C2×C22⋊D512yes—
398C22×C5—22no—
399C22×C5#93911yescharacteristic
400C22×C5#93911yescharacteristic
401C22×C5C2×#23711yescharacteristic
402C2×D5—22no—
403C2×D5—42no—
404C4×C5—42no—
405C4×C5—122no—
406C4×C5#93911yescharacteristic
407C4×C5#93911yescharacteristic
408C4×C5C2×D3×D411yescharacteristic
409C4×C5C22×#6711yescharacteristic
410Dic5—22no—
411#41—52no—
412#41—52no—
413#41—101no—
414#41—101no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—32no—
421C2×Q8—51no—
422C2×Q8—61no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×Q8—61no—
426C2×Q8—61no—
427C2×Q8C2×D3×D512yes—
428C2×D4—51no—
429C2×D4—101no—
430C22×C4—21no—
431C22×C4—61no—
432C22×C4—101no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—64no—
435Q16—64no—
436Q16—104no—
437Q16—304no—
438SD16—104no—
439SD16—304no—
440M16—52no—
441M16—101no—
442M16—152no—
443M16—152no—
444M16—304no—
445M16—301no—
446M16—301no—
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—32no—
450C2×C8—32no—
451C2×C8—101no—
452C2×C8—304no—
453C2×C8—301no—
454C2×C8—301no—
455C3×C5C2×#47311yescharacteristic, complemented, Hall
456C22×C3—22no—
457C22×C3—102no—
458C22×C3—202no—
459C22×C3#408411yescharacteristic
460C22×C3#408411yescharacteristic
461C22×C3C2×#71111yescharacteristic
462C3×C4—42no—
463C3×C4—102no—
464C3×C4#408411yescharacteristic
465C3×C4#408411yescharacteristic
466C3×C4C2×D4×D511yescharacteristic
467C3×C4C22×C22⋊D511yescharacteristic
468Dic3—42no—
469C2×C5—21no—
470C2×C5—21no—
471C2×C5#520412yescomplemented
472C2×C5C2×#93911yescharacteristic
473D5—42no—
474C23—101no—
475C23#678011yescharacteristic
476Q8—22no—
477Q8—22no—
478Q8—41no—
479Q8—41no—
480Q8—52no—
481Q8—62no—
482Q8—62no—
483Q8—101no—
484Q8—121no—
485Q8—121no—
486D4—52no—
487D4—102no—
488D4—102no—
489D4—101no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—62no—
494C2×C4—101no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4#678011yescharacteristic
500C2×C4D5×#6711yescharacteristic
501C2×C4D5×#6711yescharacteristic
502C2×C4D3×C22⋊D511yescharacteristic
503C2×C4D3×C22⋊D511yescharacteristic
504C2×C4C22×D3×D511yescharacteristic
505C8—32no—
506C8—32no—
507C8—102no—
508C8—302no—
509C8—302no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—202no—
513C2×C3#6548112yescomplemented
514C2×C3C2×#408411yescharacteristic
515C5C2×#520411yescharacteristic, complemented, Sylow
516C22—22no—
517C22—102no—
518C22—202no—
519C22#9154911yescharacteristic
520C22#9154911yescharacteristic
521C22C2×#678011yescharacteristic
522C4—42no—
523C4—102no—
524C4—122no—
525C4#9154911yescharacteristic
526C4#9154911yescharacteristic
527C4C2×D5×#6711yescharacteristic
528C4C2×D3×C22⋊D511yescharacteristic
529C3C2×#6548111yescharacteristic, complemented, Sylow
530C2—21no—
531C2—21no—
532C2—202no—
533C2#1174937512yesdirect product factor
534C2C2×#9154911yescharacteristic
subgroupG/H
centerC22#91549
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#121
prime radicalC2×C3×#709C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#473
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C5×#216C2semidirect
5. C2×#91120C2semidirect
6. #11749375C2direct (N × H)
7. C2×#90993C2semidirect
8. C2×#90962C2semidirect
18. C2×C5×#216C22semidirect
33. #91120C22semidirect
34. #90993C22semidirect
35. #90962C22semidirect
92. C22×#216D5semidirect
176. C2×#216C2×D5semidirect
359. C2×C3×C5#473semidirect
455. C3×C5C2×#473semidirect
471. C2×C5#5204semidirect
513. C2×C3#65481semidirect
515. C5C2×#5204semidirect
529. C3C2×#65481semidirect
533. C2#11749375direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2162
C2×C3×#40882
C2×#913072
C2×#912832
C2×#911202
#117493752
C2×#909932
C2×#909622
C2×#654813
C2×#52045