Finite Group Databasebeta

← C2×#11749455 #14429467

Subgroups — C2×#11749455 #14429467

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
1C2×#91837C211yesmaximal, characteristic
2C2×C5×#951C211yesmaximal, characteristic
3C2×C3×#4097C211yesmaximal, characteristic
4C22×#6661C211yesmaximal, characteristic, complemented
5#11749455C218yesmaximal, direct product factor
6C2×#90992C211yesmaximal, characteristic, complemented
7C2×#90962C211yesmaximal, characteristic, complemented
8C2×#90961C211yesmaximal, characteristic, complemented
9C2×#65493—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13#91837—22no—
14#91837C2214yes—
15C2×#6710—21no—
16C2×#6710C2211yescharacteristic
17C22×C3⋊#168—21no—
18C22×C3⋊#168C2211yescharacteristic
19C5×#951—22no—
20C5×#951C2214yes—
21C2×C5×#216—21no—
22C2×C5×#214—21no—
23C2×C5×#208C2211yescharacteristic
24C3×#4097—22no—
25C3×#4097C2214yes—
26C2×C3×#689—21no—
27C2×C3×#687—21no—
28C2×C3×#681C2211yescharacteristic
29C2×#6661—21no—
30C2×#6661—21no—
31C2×#6661—22no—
32C2×#6661C2214yescomplemented
33#90992C2214yescomplemented
34#90962C2214yescomplemented
35#90961C2214yescomplemented
36C2×#5204—51nomaximal, Hall
37C2×C5×#137—31no—
38C2×#4097D311yescharacteristic
39C2×#4094—31no—
40C22×#689—31no—
41C2×#3968—31no—
42#65493—38no—
43C2×#3956—31no—
44C2×#3954—31no—
45C3×C5×#41—21no—
46C3×C5×#41—21no—
47C3×C5×#41D412yes—
48C3×C5×#41C2312yes—
49C2×C3×C5×Q8D411yescharacteristic
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4D411yescharacteristic
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C5×Dic3—21no—
55C2×C5×Dic6—21no—
56C2×C5×Dic6—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6—21no—
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5—21no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—21no—
67C2×C3×Dic10C2312yes—
68#6710—21no—
69#6710—24no—
70#6710C2312yes—
71C2×C3⋊#168—21no—
72C2×C3⋊#168—24no—
73C2×C3⋊#168D411yescharacteristic
74C2×C3⋊#168D411yescharacteristic
75C2×C3⋊#168D412yes—
76C2×C3⋊#168C2312yes—
77C5×#216—24no—
78C5×#214—24no—
79C5×#208—21no—
80C5×#208C2312yes—
81C2×C5×C3⋊C8—21no—
82C3×#689—24no—
83C3×#687—24no—
84C3×#681—21no—
85C3×#681C2312yes—
86C2×C3×#168—21no—
87#6661—24no—
88#6661—24no—
89C2×C3×#137—51no—
90C2×#951D511yescharacteristic
91C2×#948—51no—
92C22×#216—51no—
93C2×#836—51no—
94#5204—58no—
95C2×#824—51no—
96C2×#822—51no—
97C2×C5×#41C2×D311yescharacteristic
98C22×C5×Q8—31no—
99C22×Dic10C2×D311yescharacteristic
100C5×#137—34no—
101C5×#137—62no—
102C2×C5×Q16—61no—
103C2×C5×SD16—61no—
104C2×C5×M16—31no—
105#4097—22no—
106#4097C2×D314yes—
107#4094—34no—
108#4094—62no—
109C2×#689—21no—
110C2×#689—34no—
111C2×#689—61no—
112C2×#689—61no—
113C2×#689—62no—
114C2×#687—21no—
115C2×#681—31no—
116C2×#681—61no—
117C2×#681C2×D311yescharacteristic
118C22×#168—31no—
119C22×#168—61no—
120#3968—34no—
121#3956—34no—
122#3954—34no—
123C2×#473—151noSylow
124C23×C3×C5—21no—
125C23×C3×C5#4111yescharacteristic
126C3×C5×Q8—21no—
127C3×C5×Q8C2×D412yes—
128C3×C5×D4—22no—
129C3×C5×D4—22no—
130C3×C5×D4—21no—
131C3×C5×D4C2×D412yes—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4111yescharacteristic
140C2×C3×C4×C5C2411yescharacteristic
141C2×C5×Dic3—22no—
142C2×C5×Dic3—41no—
143C2×C5×Dic3—41no—
144C5×Dic6—22no—
145C5×Dic6—22no—
146C5×Dic6—41no—
147C5×Dic6—41no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—41no—
150C2×C3×Dic5—41no—
151C3×Dic10—22no—
152C3×Dic10—22no—
153C3×Dic10—41no—
154C3×Dic10—41no—
155C3⋊#168—22no—
156C3⋊#168C2×D412yes—
157C3⋊#168C2×D412yes—
158C3×#168—22no—
159C5×C3⋊C8—22no—
160C2×C3×#41C2×D511yescharacteristic
161C22×C3×Q8—51no—
162C22×Dic6C2×D511yescharacteristic
163C3×#137—54no—
164C3×#137—102no—
165C2×C3×Q16—101no—
166C2×C3×SD16—101no—
167C2×C3×M16—51no—
168#951—22no—
169#951C2×D514yes—
170#948—54no—
171#948—102no—
172C2×#216—21no—
173C2×#216—54no—
174C2×#216—101no—
175C2×#216—101no—
176C2×#216—102no—
177C2×#214—21no—
178C2×#208—51no—
179C2×#208—101no—
180C2×#208C2×D511yescharacteristic
181C22×C3⋊C8—51no—
182C22×C3⋊C8—101no—
183#836—54no—
184#824—54no—
185#822—54no—
186C5×#41—21no—
187C5×#41—21no—
188C5×#41#6712yes—
189C5×#41C22×D312yes—
190C2×C5×Q8—32no—
191C2×C5×Q8—61no—
192C2×C5×Q8—61no—
193C2×C5×Q8—61no—
194C2×C5×Q8—61no—
195C2×C5×Q8—61no—
196C2×C5×Q8#6711yescharacteristic
197C2×C5×D4—21no—
198C2×C5×D4#6711yescharacteristic
199C22×C4×C5—21no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—21no—
203C2×Dic10—21no—
204C2×Dic10—21no—
205C2×Dic10—21no—
206C2×Dic10—21no—
207C2×Dic10—21no—
208C2×Dic10C22×D312yes—
209C5×Q16—64no—
210C5×SD16—64no—
211C5×M16—32no—
212C5×M16—61no—
213C2×C5×C8—61no—
214#689—24no—
215#689—64no—
216#689—64no—
217#687—24no—
218#681—21no—
219#681—32no—
220#681—64no—
221#681—61no—
222#681C22×D312yes—
223C2×#168—21no—
224C2×#168—31no—
225C2×#168—31no—
226C2×#168—32no—
227C2×#168—32no—
228C2×#168—64no—
229C2×#168—61no—
230C2×#137—31no—
231C2×#137—51no—
232C22×Q16—151no—
233C2×#131—151no—
234#473—158no—
235C2×#108—151no—
236C2×#101—151no—
237C2×#101—151no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—42no—
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5#12111yescharacteristic
243C22×C3×C5C2×#4111yescharacteristic
244C3×C4×C5—22no—
245C3×C4×C5#12111yescharacteristic
246C3×C4×C5#12111yescharacteristic
247C3×C4×C5C22×D411yescharacteristic
248C3×C4×C5C22×D411yescharacteristic
249C3×Dic5—42no—
250C5×Dic3—42no—
251C3×#41—21no—
252C3×#41—21no—
253C3×#41C22⋊D512yes—
254C3×#41C22×D512yes—
255C2×C3×Q8—52no—
256C2×C3×Q8—101no—
257C2×C3×Q8—101no—
258C2×C3×Q8—101no—
259C2×C3×Q8—101no—
260C2×C3×Q8—101no—
261C2×C3×Q8C22⋊D511yescharacteristic
262C2×C3×D4—21no—
263C2×C3×D4C22⋊D511yescharacteristic
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—104no—
281#216—104no—
282#214—24no—
283#208—21no—
284#208—52no—
285#208—104no—
286#208—101no—
287#208C22×D512yes—
288C2×C3⋊C8—21no—
289C2×C3⋊C8—51no—
290C2×C3⋊C8—51no—
291C2×C3⋊C8—52no—
292C2×C3⋊C8—52no—
293C2×C3⋊C8—104no—
294C2×C3⋊C8—101no—
295C23×C5—21no—
296C23×C5#23711yescharacteristic
297C5×Q8—21no—
298C5×Q8—62no—
299C5×Q8—62no—
300C5×Q8—121no—
301C5×Q8—121no—
302C5×Q8C2×#6712yes—
303C5×D4—22no—
304C5×D4—22no—
305C5×D4—21no—
306C5×D4C2×#6712yes—
307C2×C4×C5—21no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—62no—
311C2×C4×C5—121no—
312C2×C4×C5—121no—
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5#23711yescharacteristic
316C2×C4×C5C2×#6711yescharacteristic
317C2×C4×C5C2×#6711yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C2×Dic5—22no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322Dic10—22no—
323Dic10—22no—
324Dic10—41no—
325Dic10—41no—
326C5×C8—62no—
327#168—22no—
328#168—32no—
329#168—32no—
330#168—62no—
331C2×#41D3×D511yescharacteristic
332C22×Q8—31no—
333C22×Q8—51no—
334#137—34no—
335#137—54no—
336#137—62no—
337#137—102no—
338C2×Q16—61no—
339C2×Q16—101no—
340C2×Q16—154no—
341C2×Q16—301no—
342C2×Q16—301no—
343C2×Q16—302no—
344C2×SD16—61no—
345C2×SD16—101no—
346#131—154no—
347#131—302no—
348C2×M16—31no—
349C2×M16—51no—
350C2×M16—151no—
351C2×M16—301no—
352C22×C8—151no—
353C22×C8—301no—
354#108—154no—
355#101—154no—
356#101—154no—
357C2×C3×C5—21no—
358C2×C3×C5—21no—
359C2×C3×C5—42no—
360C2×C3×C5#47312yescomplemented
361C2×C3×C5C2×#12111yescharacteristic
362C23×C3—21no—
363C23×C3#71111yescharacteristic
364C3×Q8—21no—
365C3×Q8—102no—
366C3×Q8—102no—
367C3×Q8—201no—
368C3×Q8—201no—
369C3×Q8C2×C22⋊D512yes—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—21no—
373C3×D4C2×C22⋊D512yes—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—102no—
378C2×C3×C4—201no—
379C2×C3×C4—201no—
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—22no—
395C3⋊C8—52no—
396C3⋊C8—52no—
397C3⋊C8—102no—
398C22×C5—22no—
399C22×C5—22no—
400C22×C5—42no—
401C22×C5#93911yescharacteristic
402C22×C5#93911yescharacteristic
403C22×C5C2×#23711yescharacteristic
404C4×C5—22no—
405C4×C5—122no—
406C4×C5#93911yescharacteristic
407C4×C5#93911yescharacteristic
408C4×C5C2×D3×D411yescharacteristic
409C4×C5C22×#6711yescharacteristic
410Dic5—42no—
411#41—21no—
412#41—21no—
413#41#120112yes—
414#41C2×D3×D512yes—
415C2×Q8—32no—
416C2×Q8—52no—
417C2×Q8—61no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×Q8—61no—
421C2×Q8—61no—
422C2×Q8—101no—
423C2×Q8—101no—
424C2×Q8—101no—
425C2×Q8—101no—
426C2×Q8—101no—
427C2×Q8#120111yescharacteristic
428C2×D4—21no—
429C2×D4#120111yescharacteristic
430C22×C4—21no—
431C22×C4—61no—
432C22×C4—101no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—64no—
435Q16—104no—
436Q16—304no—
437Q16—304no—
438SD16—64no—
439SD16—104no—
440M16—32no—
441M16—52no—
442M16—61no—
443M16—101no—
444M16—152no—
445M16—304no—
446M16—301no—
447C2×C8—61no—
448C2×C8—101no—
449C2×C8—151no—
450C2×C8—151no—
451C2×C8—152no—
452C2×C8—152no—
453C2×C8—304no—
454C2×C8—301no—
455C3×C5C2×#47311yescharacteristic, complemented, Hall
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—42no—
459C22×C3#408511yescharacteristic
460C22×C3#408511yescharacteristic
461C22×C3C2×#71111yescharacteristic
462C3×C4—22no—
463C3×C4—202no—
464C3×C4#408511yescharacteristic
465C3×C4#408511yescharacteristic
466C3×C4C2×D4×D511yescharacteristic
467C3×C4C22×C22⋊D511yescharacteristic
468Dic3—42no—
469C2×C5—21no—
470C2×C5—21no—
471C2×C5—42no—
472C2×C5#520412yescomplemented
473C2×C5C2×#93911yescharacteristic
474C23—21no—
475C23#678011yescharacteristic
476Q8—21no—
477Q8—62no—
478Q8—62no—
479Q8—102no—
480Q8—102no—
481Q8—121no—
482Q8—121no—
483Q8—201no—
484Q8—201no—
485Q8C2×#120112yes—
486D4—22no—
487D4—22no—
488D4—21no—
489D4C2×#120112yes—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—62no—
494C2×C4—102no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—201no—
498C2×C4—201no—
499C2×C4#678011yescharacteristic
500C2×C4C2×#120111yescharacteristic
501C2×C4C2×#120111yescharacteristic
502C2×C4#679011yescharacteristic
503C2×C4#679011yescharacteristic
504C2×C4C22×D3×D511yescharacteristic
505C8—62no—
506C8—102no—
507C8—152no—
508C8—152no—
509C8—302no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—42no—
513C2×C3#6549312yescomplemented
514C2×C3C2×#408511yescharacteristic
515C5C2×#520411yescharacteristic, complemented, Sylow
516C22—22no—
517C22—22no—
518C22—42no—
519C22#9157111yescharacteristic
520C22#9157111yescharacteristic
521C22C2×#678011yescharacteristic
522C4—22no—
523C4—122no—
524C4—202no—
525C4#9157111yescharacteristic
526C4#9157111yescharacteristic
527C4C22×#120111yescharacteristic
528C4C2×#679011yescharacteristic
529C3C2×#6549311yescharacteristic, complemented, Sylow
530C2—21no—
531C2—21no—
532C2—42no—
533C2#1174945512yesdirect product factor
534C2C2×#9157111yescharacteristic
subgroupG/H
centerC22#91571
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5#121
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#473
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
4. C22×#6661C2semidirect
5. #11749455C2direct (N × H)
6. C2×#90992C2semidirect
7. C2×#90962C2semidirect
8. C2×#90961C2semidirect
32. C2×#6661C22semidirect
33. #90992C22semidirect
34. #90962C22semidirect
35. #90961C22semidirect
360. C2×C3×C5#473semidirect
455. C3×C5C2×#473semidirect
472. C2×C5#5204semidirect
513. C2×C3#65493semidirect
515. C5C2×#5204semidirect
529. C3C2×#65493semidirect
533. C2#11749455direct (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×#9512
C2×C3×#40972
C22×#66612
#117494552
C2×#909922
C2×#909622
C2×#909612
C2×#654933
C2×#52045