Finite Group Databasebeta

← C2×#11751153 #14428037

Subgroups — C2×#11751153 #14428037

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic
2C22×#6718C211yesmaximal, characteristic, complemented
3C2×#91813C211yesmaximal, characteristic
4C22×#6710C211yesmaximal, characteristic
5C2×#91119C211yesmaximal, characteristic, complemented
6#11751153C218yesmaximal, direct product factor
7C2×#91094C211yesmaximal, characteristic, complemented
8C2×#91092C211yesmaximal, characteristic, complemented
9C2×#65341—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C3×C5×C22⋊Q8—22no—
14C3×C5×C22⋊Q8C2214yes—
15C2×C3×C5×C4⋊C4—21no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C22⋊C4—21no—
18C2×#6719—21no—
19C2×#6718—24no—
20C2×#6718C2214yescomplemented
21C2×C4⋊Dic15C2211yescharacteristic
22#91813—22no—
23#91813C2214yes—
24C2×#6712—21no—
25C2×#6710—24no—
26C2×#6710C2214yes—
27C22×C3⋊#168C2211yescharacteristic
28C22×C3⋊#168C2211yescharacteristic
29#91119C2214yescomplemented
30#91094C2214yescomplemented
31#91092C2214yescomplemented
32C2×#5052—51nomaximal, Hall
33C2×C5×C22⋊Q8D311yescharacteristic
34C22×#689—31no—
35C2×#4070—31no—
36C22×#681—31no—
37C2×#3967—31no—
38#65341—38no—
39C2×#3942—31no—
40C2×#3940—31no—
41C24×C3×C5D411yescharacteristic
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8—22no—
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8C2312yes—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5D411yescharacteristic
51C22×C3×C4×C5D412yes—
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15—21no—
55C22×Dic15—21no—
56C2×Dic30—22no—
57C2×Dic30—22no—
58C2×Dic30—21no—
59C2×Dic30C2312yes—
60C3×C5×C4⋊C4—24no—
61C3×C5×C4⋊C4—21no—
62C3×C5×C4⋊C4C2312yes—
63C3×C5×C22⋊C4—24no—
64#6719—24no—
65#6718—28no—
66C4⋊Dic15—21no—
67C4⋊Dic15C2312yes—
68#6712—24no—
69#6710—28no—
70C2×C3⋊#168—22no—
71C2×C3⋊#168D414yes—
72C2×C3⋊#168C2312yes—
73C2×C3⋊#168C2312yes—
74C2×C3×C22⋊Q8D511yescharacteristic
75C22×#216—51no—
76C2×#924—51no—
77C22×#208—51no—
78C2×#835—51no—
79#5052—58no—
80C2×#810—51no—
81C2×#808—51no—
82C22×C5×Q8C2×D311yescharacteristic
83C23×C4×C5C2×D311yescharacteristic
84C22×Dic10—31no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8C2×D314yes—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4C2×D311yescharacteristic
89C2×C5×C22⋊C4—21no—
90C2×C22⋊Dic5—61no—
91C2×#689—34no—
92C2×#689—64no—
93C2×C4⋊Dic5—31no—
94#4070—34no—
95#4070—62no—
96C2×#683—61no—
97C2×#681—34no—
98C2×#681—64no—
99C22×#168—31no—
100C22×#168—31no—
101#3967—34no—
102#3942—34no—
103#3940—34no—
104C2×#470—151noSylow
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5—22no—
108C23×C3×C5C2×D412yes—
109C23×C3×C5C2×D411yescharacteristic
110C3×C5×Q8—22no—
111C3×C5×Q8—22no—
112C3×C5×Q8—42no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—24no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—42no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5C2×D412yes—
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D412yes—
124C2×C3×C4×C5#4112yes—
125C2×C3×C4×C5C2411yescharacteristic
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—42no—
129C2×Dic15—42no—
130Dic30—22no—
131Dic30—22no—
132Dic30—42no—
133C3⋊#168—22no—
134C3⋊#168C2×D414yes—
135C22×C3×Q8C2×D511yescharacteristic
136C23×C3×C4C2×D511yescharacteristic
137C22×Dic6—51no—
138C3×C22⋊Q8—22no—
139C3×C22⋊Q8C2×D514yes—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4C2×D511yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×#217—101no—
144C2×#216—54no—
145C2×#216—104no—
146C2×C4⋊Dic3—51no—
147#924—54no—
148#924—102no—
149C2×Dic3⋊C4—101no—
150C2×#208—54no—
151C2×#208—104no—
152C22×C3⋊C8—51no—
153C22×C3⋊C8—51no—
154#835—54no—
155#810—54no—
156#808—54no—
157C24×C5#6711yescharacteristic
158C2×C5×Q8—21no—
159C2×C5×Q8—22no—
160C2×C5×Q8—22no—
161C2×C5×Q8C22×D312yes—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5#6711yescharacteristic
167C22×C4×C5#6712yes—
168C22×C4×C5C22×D312yes—
169C22×C4×C5C22×D311yescharacteristic
170C22×Dic5—61no—
171C22×Dic5—61no—
172C2×Dic10—32no—
173C2×Dic10—62no—
174C2×Dic10—62no—
175C2×Dic10—61no—
176C5×C4⋊C4—24no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4C22×D312yes—
179C5×C22⋊C4—24no—
180C22⋊Dic5—64no—
181#689—68no—
182C4⋊Dic5—32no—
183C4⋊Dic5—61no—
184#683—64no—
185#681—68no—
186C2×#168—34no—
187C2×#168—32no—
188C2×#168—32no—
189C2×#168—62no—
190C22×Q16—151no—
191C22×M16—151no—
192C2×C22⋊Q8—151no—
193C2×C22⋊Q8D1511yescharacteristic
194#470—158no—
195C2×#106—151no—
196C2×#103—151no—
197C2×#103—151no—
198C22×C3×C5—22no—
199C22×C3×C5—22no—
200C22×C3×C5—22no—
201C22×C3×C5—44no—
202C22×C3×C5#12112yes—
203C22×C3×C5#13712yes—
204C22×C3×C5#13712yes—
205C22×C3×C5C22×D411yescharacteristic
206C3×C4×C5—22no—
207C3×C4×C5—42no—
208C3×C4×C5—42no—
209C3×C4×C5#12112yes—
210C3×C4×C5C22×D411yescharacteristic
211C3×C4×C5C2×#4111yescharacteristic
212Dic15—42no—
213Dic15—42no—
214C24×C3C22⋊D511yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—22no—
217C2×C3×Q8—22no—
218C2×C3×Q8C22×D512yes—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4C22⋊D511yescharacteristic
224C22×C3×C4C22⋊D512yes—
225C22×C3×C4C22×D512yes—
226C22×C3×C4C22×D511yescharacteristic
227C22×Dic3—101no—
228C22×Dic3—101no—
229C2×Dic6—52no—
230C2×Dic6—102no—
231C2×Dic6—102no—
232C2×Dic6—101no—
233C3×C4⋊C4—24no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4C22×D512yes—
236C3×C22⋊C4—24no—
237#217—104no—
238#216—108no—
239C4⋊Dic3—52no—
240C4⋊Dic3—101no—
241Dic3⋊C4—104no—
242#208—108no—
243C2×C3⋊C8—54no—
244C2×C3⋊C8—52no—
245C2×C3⋊C8—52no—
246C2×C3⋊C8—102no—
247C23×C5—22no—
248C23×C5—22no—
249C23×C5—22no—
250C23×C5C2×#6712yes—
251C23×C5C2×#6711yescharacteristic
252C5×Q8—22no—
253C5×Q8—22no—
254C5×Q8—42no—
255C2×C4×C5—22no—
256C2×C4×C5—24no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5D3×D412yes—
264C2×C4×C5#23712yes—
265C2×C4×C5C2×#6712yes—
266C2×C4×C5C2×#6711yescharacteristic
267C2×C4×C5C23×D311yescharacteristic
268C2×Dic5—62no—
269C2×Dic5—62no—
270C2×Dic5—122no—
271C2×Dic5—122no—
272Dic10—62no—
273Dic10—62no—
274Dic10—122no—
275#168—34no—
276#168—62no—
277C22×Q8—151no—
278C22×Q8C2×D1511yescharacteristic
279C23×C4C2×D1511yescharacteristic
280C2×Q16—154no—
281C2×Q16—304no—
282C2×M16—154no—
283C2×M16—304no—
284C22×C8—151no—
285C22×C8—151no—
286C22⋊Q8—22no—
287C22⋊Q8—154no—
288C22⋊Q8—302no—
289C22⋊Q8C2×D1514yes—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—151no—
292C2×C4⋊C4—301no—
293C2×C4⋊C4C2×D1511yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—301no—
296#106—154no—
297#103—154no—
298#103—154no—
299C2×C3×C5—42no—
300C2×C3×C5#47014yescomplemented
301C2×C3×C5C2×#12111yescharacteristic
302C2×C3×C5C2×#13711yescharacteristic
303C2×C3×C5C2×#13711yescharacteristic
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3C2×C22⋊D512yes—
308C23×C3C2×C22⋊D511yescharacteristic
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—42no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4D4×D512yes—
321C2×C3×C4#71112yes—
322C2×C3×C4C2×C22⋊D512yes—
323C2×C3×C4C2×C22⋊D511yescharacteristic
324C2×C3×C4C23×D511yescharacteristic
325C2×Dic3—102no—
326C2×Dic3—102no—
327C2×Dic3—202no—
328C2×Dic3—202no—
329Dic6—102no—
330Dic6—102no—
331Dic6—202no—
332C3⋊C8—54no—
333C3⋊C8—102no—
334C22×C5—22no—
335C22×C5—22no—
336C22×C5—22no—
337C22×C5—44no—
338C22×C5#93912yes—
339C22×C5#94212yes—
340C22×C5#95112yes—
341C22×C5C22×#6711yescharacteristic
342C4×C5—22no—
343C4×C5—42no—
344C4×C5—42no—
345C4×C5#93912yes—
346C4×C5C2×D3×D411yescharacteristic
347C4×C5C2×#23711yescharacteristic
348Dic5—122no—
349Dic5—122no—
350C24#122011yescharacteristic
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—152no—
355C2×Q8—301no—
356C2×Q8—302no—
357C2×Q8—302no—
358C2×Q8C22×D1512yes—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—301no—
364C22×C4—301no—
365C22×C4#122012yes—
366C22×C4#122011yescharacteristic
367C22×C4C22×D1512yes—
368C22×C4C22×D1511yescharacteristic
369Q16—308no—
370M16—308no—
371C2×C8—154no—
372C2×C8—152no—
373C2×C8—152no—
374C2×C8—302no—
375C4⋊C4—24no—
376C4⋊C4—21no—
377C4⋊C4—152no—
378C4⋊C4—301no—
379C4⋊C4—304no—
380C4⋊C4C22×D1512yes—
381C22⋊C4—24no—
382C22⋊C4—304no—
383C3×C5C2×#47011yescharacteristic, complemented, Hall
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—44no—
388C22×C3#408512yes—
389C22×C3#408812yes—
390C22×C3#409712yes—
391C22×C3C22×C22⋊D511yescharacteristic
392C3×C4—22no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4#408512yes—
396C3×C4C2×D4×D511yescharacteristic
397C3×C4C2×#71111yescharacteristic
398Dic3—202no—
399Dic3—202no—
400C2×C5—42no—
401C2×C5#505214yescomplemented
402C2×C5C2×#93911yescharacteristic
403C2×C5C2×#94211yescharacteristic
404C2×C5C2×#95111yescharacteristic
405C23—22no—
406C23—22no—
407C23—22no—
408C23C2×#122012yes—
409C23C2×#122011yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—42no—
413Q8—302no—
414Q8—302no—
415Q8—602no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—302no—
425C2×C4—302no—
426C2×C4—602no—
427C2×C4—602no—
428C2×C4D4×D1512yes—
429C2×C4#681912yes—
430C2×C4C2×#122012yes—
431C2×C4C2×#122011yescharacteristic
432C2×C4C23×D1511yescharacteristic
433C8—154no—
434C8—302no—
435C2×C3—42no—
436C2×C3#6534114yescomplemented
437C2×C3C2×#408511yescharacteristic
438C2×C3C2×#408811yescharacteristic
439C2×C3C2×#409711yescharacteristic
440C5C2×#505211yescharacteristic, complemented, Sylow
441C22—22no—
442C22—22no—
443C22—22no—
444C22—44no—
445C22#9182812yes—
446C22#9183112yes—
447C22#9184012yes—
448C22C22×#122011yescharacteristic
449C4—22no—
450C4—42no—
451C4—42no—
452C4—602no—
453C4—602no—
454C4#9182812yes—
455C4C2×D4×D1511yescharacteristic
456C4C2×#681911yescharacteristic
457C3C2×#6534111yescharacteristic, complemented, Sylow
458C2—42no—
459C2#1175115314yesdirect product factor
460C2C2×#9182811yescharacteristic
461C2C2×#9183111yescharacteristic
462C2C2×#9184011yescharacteristic
subgroupG/H
centerC23C2×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
hypercenterC2×C22⋊Q8D15
hypocenterC3×C5C2×#470
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#6718C2semidirect
5. C2×#91119C2semidirect
6. #11751153C2direct (N × H)
7. C2×#91094C2semidirect
8. C2×#91092C2semidirect
20. C2×#6718C22semidirect
29. #91119C22semidirect
30. #91094C22semidirect
31. #91092C22semidirect
300. C2×C3×C5#470semidirect
383. C3×C5C2×#470semidirect
401. C2×C5#5052semidirect
436. C2×C3#65341semidirect
440. C5C2×#5052semidirect
457. C3C2×#65341semidirect
459. C2#11751153direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊Q82
C22×#67182
C2×#918132
C22×#67102
C2×#911192
#117511532
C2×#910942
C2×#910922
C2×#653413
C2×#50525