Finite Group Databasebeta

← C2×#11749308 #14423380

Subgroups — C2×#11749308 #14423380

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D15C211yesmaximal, characteristic
2C22×C5×#216C211yesmaximal, characteristic, complemented
3C2×#91383C211yesmaximal, characteristic
4C22×#6663C211yesmaximal, characteristic, complemented
5C2×C3×#3967C211yesmaximal, characteristic, complemented
6#11749308C218yesmaximal, direct product factor
7C2×#90974C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic
9C2×#65475—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×Q8×D15—24no—
12C2×Q8×D15—22no—
13C2×Q8×D15—24no—
14C2×Q8×D15C2214yes—
15C22×C4×D15—21no—
16C22×C4×D15C2211yescharacteristic
17C22×Dic30—21no—
18C22×Dic30C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C2×C5×#216—24no—
21C2×C5×#216C2214yescomplemented
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25C2×#6668—21no—
26C2×#6667—21no—
27#91383—22no—
28#91383C2214yes—
29C2×#6663—24no—
30C2×#6663C2214yescomplemented
31C3×#3967C2214yescomplemented
32#90974C2214yescomplemented
33#90957C2214yes—
34C2×#4809—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×C5×Q16—31no—
37C2×#4092—31no—
38C22×#689—31no—
39C2×#3967D311yescharacteristic, complemented
40#65475—38no—
41C2×#3952—31no—
42C2×#3948—31no—
43C23×D15D411yescharacteristic
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8D414yes—
47C2×C3×C5×Q8C2312yes—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—21no—
51C22×Dic15D411yescharacteristic
52Q8×D15—216no—
53Q8×D15—28no—
54Q8×D15—28no—
55C2×C4×D15—28no—
56C2×C4×D15—24no—
57C2×C4×D15—22no—
58C2×C4×D15—22no—
59C2×C4×D15D412yes—
60C2×C4×D15C2312yes—
61C2×Dic30—28no—
62C2×Dic30—21no—
63C2×Dic30—22no—
64C2×Dic30—24no—
65C2×Dic30D414yes—
66C2×Dic30C2312yes—
67C22×C5×Dic3—21no—
68C2×C5×Dic6—22no—
69C2×C5×Dic6—22no—
70C2×C5×Dic6—21no—
71C2×C5×Dic6C2312yes—
72C22×C3×Dic5—21no—
73C5×#216—28no—
74C2×C5×C3⋊C8—22no—
75C2×C5×C3⋊C8C2312yes—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5C2312yes—
78C2×C3×#168—22no—
79C2×C3×#168C2312yes—
80#6668—24no—
81#6667—24no—
82#6663—28no—
83C22×D3×Q8—51no—
84C22×#216D511yescharacteristic, complemented
85C22×Dic12—51no—
86C2×#897—51no—
87C2×C3×#103—51no—
88C2×(C2×D3)⋊C8—51no—
89C2×#810—51no—
90#4809—58no—
91C22×C5×Q8—31no—
92C22×C5×Q8C2×D311yescharacteristic
93C2×Q8×D5—34no—
94C2×Q8×D5—64no—
95C2×Q8×D5—62no—
96C2×Q8×D5—64no—
97C22×C4×D5—31no—
98C22×C4×D5—61no—
99C22×Dic10—31no—
100C22×Dic10—61no—
101C2×C5×Q16—34no—
102C2×C5×Q16—64no—
103C22×C5×C8—31no—
104#4092—34no—
105#4092—62no—
106C2×#689—34no—
107C2×#689—64no—
108C2×#685—61no—
109C2×C4⋊Dic5C2×D311yescharacteristic
110C2×#683—61no—
111C22×#168C2×D311yescharacteristic
112#3967C2×D314yescomplemented
113#3952—34no—
114#3948—34no—
115C2×#451—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15Q1614yescomplemented
120C22×D15C2×D412yes—
121C3×C5×Q8—24no—
122C3×C5×Q8—22no—
123C3×C5×Q8C2×D414yes—
124C2×C3×C4×C5—24no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2411yescharacteristic
130C2×Dic15—22no—
131C2×Dic15—24no—
132C2×Dic15—22no—
133C2×Dic15C2×D412yes—
134C4×D15—216no—
135C4×D15—24no—
136C4×D15—22no—
137C4×D15—22no—
138Dic30—216no—
139Dic30—24no—
140Dic30—22no—
141Dic30C2×D414yes—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—42no—
144C5×Dic6—22no—
145C5×Dic6—22no—
146C5×Dic6—42no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—42no—
149C3×#168—22no—
150C5×C3⋊C8—22no—
151C22×C3×Q8C2×D511yescharacteristic
152C2×D3×Q8—54no—
153C2×D3×Q8—104no—
154C2×D3×Q8—102no—
155C2×D3×Q8—104no—
156C22×C4×D3—51no—
157C22×C4×D3—101no—
158C22×Dic6—51no—
159C22×Dic6—101no—
160C22×Dic6C2×D511yescharacteristic
161C22×C3×C8—51no—
162C2×C3×C4⋊C4—51no—
163C2×#216—24no—
164C2×#216C2×D514yescomplemented
165C2×(C2×D3)⋊C4—101no—
166C2×C4⋊Dic3—101no—
167C22×C3⋊C8C2×D511yescharacteristic
168C2×Dic12—54no—
169C2×Dic12—104no—
170#897—54no—
171#897—102no—
172C3×#103—54no—
173(C2×D3)⋊C8—54no—
174#810—54no—
175C23×D5—31no—
176C2×C5×Q8—22no—
177C2×C5×Q8—21no—
178C2×C5×Q8—32no—
179C2×C5×Q8—61no—
180C2×C5×Q8—62no—
181C2×C5×Q8—62no—
182C2×C5×Q8D1214yes—
183C2×C5×Q8C22×D312yes—
184C22×C4×C5—21no—
185C22×C4×C5—61no—
186C22×C4×C5C22×D311yescharacteristic
187C22×Dic5—21no—
188C22×Dic5—31no—
189C22×Dic5—61no—
190Q8×D5—68no—
191Q8×D5—616no—
192Q8×D5—68no—
193C2×C4×D5—32no—
194C2×C4×D5—32no—
195C2×C4×D5—64no—
196C2×C4×D5—68no—
197C2×C4×D5—62no—
198C2×C4×D5—62no—
199C2×Dic10—34no—
200C2×Dic10—32no—
201C2×Dic10—64no—
202C2×Dic10—68no—
203C2×Dic10—62no—
204C2×Dic10—61no—
205C5×Q16—68no—
206C2×C5×C8—32no—
207C2×C5×C8—62no—
208#689—68no—
209#685—64no—
210C4⋊Dic5—21no—
211C4⋊Dic5C22×D312yes—
212#683—64no—
213C2×#168—22no—
214C2×#168C22×D312yes—
215C23×Q8—151no—
216C22×Q16—31no—
217C22×Q16—151no—
218C2×C22⋊Q8—151no—
219#451—158no—
220C2×#103—51no—
221C2×#103—151no—
222C2×C22⋊C8—151no—
223C22×C3×C5#12012yes—
224C22×C3×C5C2×Q1612yes—
225C22×C3×C5#13712yes—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—22no—
229C2×D15—28no—
230C2×D15C2×Q1614yescomplemented
231C3×C4×C5—24no—
232C3×C4×C5#12012yes—
233C3×C4×C5C22×D411yescharacteristic
234C3×C4×C5C22×D411yescharacteristic
235Dic15—22no—
236Dic15—24no—
237C3×Dic5—42no—
238C5×Dic3—42no—
239C23×D3—51no—
240C2×C3×Q8—21no—
241C2×C3×Q8—22no—
242C2×C3×Q8C22⋊D514yes—
243C2×C3×Q8C22×D512yes—
244C22×C3×C4—21no—
245C22×C3×C4—101no—
246C22×C3×C4C22×D511yescharacteristic
247C22×Dic3—21no—
248C22×Dic3—51no—
249C22×Dic3—101no—
250D3×Q8—108no—
251D3×Q8—1016no—
252D3×Q8—108no—
253C2×C4×D3—52no—
254C2×C4×D3—52no—
255C2×C4×D3—104no—
256C2×C4×D3—108no—
257C2×C4×D3—102no—
258C2×C4×D3—102no—
259C2×Dic6—22no—
260C2×Dic6—22no—
261C2×Dic6—21no—
262C2×Dic6—54no—
263C2×Dic6—52no—
264C2×Dic6—104no—
265C2×Dic6—108no—
266C2×Dic6—101no—
267C2×Dic6—102no—
268C2×Dic6C22×D512yes—
269C2×C3×C8—52no—
270C2×C3×C8—102no—
271C3×C4⋊C4—52no—
272C3×C4⋊C4—101no—
273#216—28no—
274(C2×D3)⋊C4—104no—
275C4⋊Dic3—104no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8C22×D512yes—
278Dic12—108no—
279C23×C5D3×D411yescharacteristic
280C22×D5—34no—
281C22×D5—32no—
282C22×D5—62no—
283C22×D5—62no—
284C5×Q8—24no—
285C5×Q8—22no—
286C5×Q8—62no—
287C5×Q8—62no—
288C5×Q8—122no—
289C5×Q8C2×D1214yes—
290C2×C4×C5—24no—
291C2×C4×C5—22no—
292C2×C4×C5—62no—
293C2×C4×C5—122no—
294C2×C4×C5C2×D1212yes—
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×D412yes—
297C2×C4×C5C23×D311yescharacteristic
298C2×Dic5—22no—
299C2×Dic5—32no—
300C2×Dic5—42no—
301C2×Dic5—64no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C4×D5—616no—
305C4×D5—64no—
306C4×D5—62no—
307C4×D5—62no—
308Dic10—34no—
309Dic10—616no—
310Dic10—64no—
311Dic10—62no—
312C5×C8—62no—
313#168—22no—
314C22×Q8—31no—
315C22×Q8—154no—
316C22×Q8—151no—
317C22×Q8—301no—
318C22×Q8—302no—
319C22×Q8—304no—
320C22×Q8—304no—
321C22×Q8D3×D511yescharacteristic
322C23×C4—151no—
323C23×C4—301no—
324C2×Q16—34no—
325C2×Q16—64no—
326C2×Q16—154no—
327C2×Q16—304no—
328C22×C8—31no—
329C22×C8—51no—
330C22⋊Q8—154no—
331C22⋊Q8—302no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—301no—
334C2×C22⋊C4—301no—
335#103—54no—
336#103—154no—
337C22⋊C8—154no—
338C2×C3×C5#45114yescomplemented
339C2×C3×C5C2×#12011yescharacteristic
340C2×C3×C5C22×Q1611yescharacteristic
341C2×C3×C5C2×#13711yescharacteristic
342D15—24no—
343C23×C3D4×D511yescharacteristic
344C22×D3—52no—
345C22×D3—54no—
346C22×D3—102no—
347C22×D3—102no—
348C3×Q8—22no—
349C3×Q8—24no—
350C3×Q8C2×C22⋊D514yes—
351C2×C3×C4—22no—
352C2×C3×C4—24no—
353C2×C3×C4—102no—
354C2×C3×C4—202no—
355C2×C3×C4D4×D512yes—
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4C2×C22⋊D512yes—
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—22no—
360C2×Dic3—42no—
361C2×Dic3—52no—
362C2×Dic3—102no—
363C2×Dic3—104no—
364C2×Dic3—102no—
365C4×D3—1016no—
366C4×D3—102no—
367C4×D3—102no—
368C4×D3—104no—
369Dic6—22no—
370Dic6—22no—
371Dic6—42no—
372Dic6—54no—
373Dic6—1016no—
374Dic6—102no—
375Dic6—104no—
376C3×C8—102no—
377C3⋊C8—22no—
378C22×C5#88212yes—
379C22×C5#91512yes—
380C22×C5D3×Q1612yes—
381C22×C5C2×D3×D411yescharacteristic
382C2×D5—34no—
383C2×D5—62no—
384C2×D5—62no—
385C2×D5—68no—
386C4×C5—24no—
387C4×C5—122no—
388C4×C5#88212yes—
389C4×C5C22×D1211yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—42no—
392Dic5—64no—
393Dic5—62no—
394C24—151no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—32no—
398C2×Q8—61no—
399C2×Q8—62no—
400C2×Q8—62no—
401C2×Q8—154no—
402C2×Q8—152no—
403C2×Q8—304no—
404C2×Q8—308no—
405C2×Q8—308no—
406C2×Q8—3016no—
407C2×Q8—308no—
408C2×Q8—302no—
409C2×Q8—301no—
410C2×Q8#120314yes—
411C2×Q8C2×D3×D512yes—
412C22×C4—21no—
413C22×C4—61no—
414C22×C4—101no—
415C22×C4—151no—
416C22×C4—152no—
417C22×C4—152no—
418C22×C4—304no—
419C22×C4—308no—
420C22×C4—301no—
421C22×C4—302no—
422C22×C4—302no—
423C22×C4C2×D3×D511yescharacteristic
424Q16—68no—
425Q16—308no—
426C2×C8—32no—
427C2×C8—52no—
428C2×C8—62no—
429C2×C8—102no—
430C4⋊C4—52no—
431C4⋊C4—101no—
432C4⋊C4—304no—
433C22⋊C4—304no—
434C3×C5C2×#45111yescharacteristic, complemented, Hall
435C22×C3D5×Q1612yes—
436C22×C3#406412yes—
437C22×C3#408312yes—
438C22×C3C2×D4×D511yescharacteristic
439C2×D3—54no—
440C2×D3—102no—
441C2×D3—102no—
442C2×D3—108no—
443C3×C4—24no—
444C3×C4—202no—
445C3×C4#408312yes—
446C3×C4C2×D4×D511yescharacteristic
447C3×C4C22×C22⋊D511yescharacteristic
448Dic3—42no—
449Dic3—104no—
450Dic3—102no—
451C2×C5#480914yescomplemented
452C2×C5C2×#88211yescharacteristic
453C2×C5C2×#91511yescharacteristic
454C2×C5C2×D3×Q1611yescharacteristic
455D5—64no—
456C23—154no—
457C23—152no—
458C23—302no—
459C23—302no—
460C23#679011yescharacteristic
461Q8—22no—
462Q8—24no—
463Q8—62no—
464Q8—62no—
465Q8—122no—
466Q8—154no—
467Q8—3016no—
468Q8—302no—
469Q8—304no—
470Q8C2×#120314yes—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—62no—
474C2×C4—102no—
475C2×C4—122no—
476C2×C4—152no—
477C2×C4—202no—
478C2×C4—3016no—
479C2×C4—302no—
480C2×C4—302no—
481C2×C4—304no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—304no—
485C2×C4C2×#120312yes—
486C2×C4#679012yes—
487C2×C4#679011yescharacteristic
488C2×C4C22×D3×D511yescharacteristic
489C8—62no—
490C8—102no—
491C2×C3#6547514yescomplemented
492C2×C3C2×D5×Q1611yescharacteristic
493C2×C3C2×#406411yescharacteristic
494C2×C3C2×#408311yescharacteristic
495D3—104no—
496C5C2×#480911yescharacteristic, complemented, Sylow
497C22—154no—
498C22—302no—
499C22—302no—
500C22—308no—
501C22#9151112yes—
502C22#9152212yes—
503C22#9157312yes—
504C22C2×#679011yescharacteristic
505C4—24no—
506C4—122no—
507C4—202no—
508C4—302no—
509C4—304no—
510C4#9157312yes—
511C4C22×#120311yescharacteristic
512C4C2×#679011yescharacteristic
513C3C2×#6547511yescharacteristic, complemented, Sylow
514C2—304no—
515C2#1174930814yesdirect product factor
516C2C2×#9151111yescharacteristic
517C2C2×#9152211yescharacteristic
518C2C2×#9157311yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C5×#216C2semidirect
4. C22×#6663C2semidirect
5. C2×C3×#3967C2semidirect
6. #11749308C2direct (N × H)
7. C2×#90974C2semidirect
21. C2×C5×#216C22semidirect
30. C2×#6663C22semidirect
31. C3×#3967C22semidirect
32. #90974C22semidirect
39. C2×#3967D3semidirect
84. C22×#216D5semidirect
112. #3967C2×D3semidirect
119. C22×D15Q16semidirect
164. C2×#216C2×D5semidirect
230. C2×D15C2×Q16semidirect
338. C2×C3×C5#451semidirect
434. C3×C5C2×#451semidirect
451. C2×C5#4809semidirect
491. C2×C3#65475semidirect
496. C5C2×#4809semidirect
513. C3C2×#65475semidirect
515. C2#11749308direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C22×C5×#2162
C2×#913832
C22×#66632
C2×C3×#39672
#117493082
C2×#909742
C2×#909572
C2×#654753
C2×#48095