Finite Group Databasebeta

← C2×#11747496 #14423398

Subgroups — C2×#11747496 #14423398

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×D15⋊Q8C211yesmaximal, characteristic
2C2×#91786C211yesmaximal, characteristic
3C22×#6663C211yesmaximal, characteristic, complemented
4C22×#6662C211yesmaximal, characteristic, complemented
5C2×C5×#810C211yesmaximal, characteristic, complemented
6C2×C3×#3942C211yesmaximal, characteristic, complemented
7C2×#90957C211yesmaximal, characteristic
8#11747496C218yesmaximal, direct product factor
9C2×#65097—31nomaximal, Hall
10C22×C4×D15C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×#1204—21no—
15C22×#1200—21no—
16C2×D15⋊Q8—22no—
17C2×D15⋊Q8—24no—
18C2×D15⋊Q8—24no—
19C2×D15⋊Q8C2214yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6714—21no—
22C2×C4⋊Dic15—21no—
23#91786—22no—
24#91786C2214yes—
25C22×C5×C3⋊C8C2211yescharacteristic
26C22×C3×#168C2211yescharacteristic
27C2×#6663—24no—
28C2×#6663C2214yescomplemented
29C2×#6662—24no—
30C2×#6662C2214yescomplemented
31C5×#810C2214yescomplemented
32C3×#3942C2214yescomplemented
33#90957C2214yes—
34C2×#4809—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×#689—31no—
37C22×Dic20—31no—
38C2×#4043—31no—
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3942D311yescharacteristic, complemented
42#65097—38no—
43C23×D15D411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C22×Dic15D411yescharacteristic
48C2×C4×D15—22no—
49C2×C4×D15—22no—
50C2×C4×D15D412yes—
51C2×C4×D15C2312yes—
52C2×Dic30—22no—
53C2×Dic30—22no—
54C2×Dic30—21no—
55C2×Dic30C2312yes—
56C22×C5×Dic3—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—22no—
59C2×C5×Dic6D414yes—
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5—21no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—22no—
64C2×C3×Dic10D414yes—
65C2×C3×Dic10C2312yes—
66C2×#1204—28no—
67C2×#1204—24no—
68C2×#1200—28no—
69C2×#1200—24no—
70D15⋊Q8—216no—
71D15⋊Q8—28no—
72D15⋊Q8—28no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75#6714—24no—
76C4⋊Dic15—24no—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2312yes—
79C2×C3×#168—22no—
80C2×C3×#168C2312yes—
81#6663—28no—
82#6662—28no—
83C22×D3×Q8—51no—
84C22×#216—51no—
85C22×Dic12—51no—
86C2×#897—51no—
87C2×C3×#103—51no—
88C2×(C2×D3)⋊C8—51no—
89C2×#810D511yescharacteristic, complemented
90#4809—58no—
91C22×C5×Q8—31no—
92C2×Q8×D5—34no—
93C2×Q8×D5—62no—
94C2×Q8×D5—64no—
95C2×Q8×D5—64no—
96C22×C4×D5—31no—
97C22×C4×D5—61no—
98C22×Dic10—31no—
99C22×Dic10—61no—
100C22×Dic10C2×D311yescharacteristic
101C22×C5×C8—31no—
102C2×C5×C4⋊C4C2×D311yescharacteristic
103C2×#689—34no—
104C2×#689—64no—
105C2×#685—61no—
106C2×C4⋊Dic5—61no—
107C22×#168C2×D311yescharacteristic
108C2×Dic20—34no—
109C2×Dic20—64no—
110#4043—34no—
111#4043—62no—
112C5×#103—34no—
113#3952—34no—
114#3942C2×D314yescomplemented
115C2×#451—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15Q1614yescomplemented
120C22×D15C2×D412yes—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—42no—
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D412yes—
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2411yescharacteristic
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—42no—
130C2×Dic15C2×D412yes—
131C4×D15—24no—
132C4×D15—22no—
133C4×D15—22no—
134Dic30—22no—
135Dic30—22no—
136Dic30—42no—
137C2×C5×Dic3—24no—
138C2×C5×Dic3—22no—
139C5×Dic6—24no—
140C5×Dic6—22no—
141C5×Dic6C2×D414yes—
142C2×C3×Dic5—24no—
143C2×C3×Dic5—22no—
144C3×Dic10—24no—
145C3×Dic10—22no—
146C3×Dic10C2×D414yes—
147#1204—216no—
148#1200—216no—
149C3×#168—22no—
150C5×C3⋊C8—22no—
151C22×C3×Q8—51no—
152C2×D3×Q8—54no—
153C2×D3×Q8—102no—
154C2×D3×Q8—104no—
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⋊C4C2×D511yescharacteristic
163C2×#216—54no—
164C2×#216—104no—
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#810C2×D514yescomplemented
175C23×D5—31no—
176C2×C5×Q8—34no—
177C2×C5×Q8—32no—
178C2×C5×Q8—62no—
179C2×C5×Q8—61no—
180C22×C4×C5—21no—
181C22×C4×C5—61no—
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—21no—
184C22×Dic5—31no—
185C22×Dic5—61no—
186Q8×D5—68no—
187Q8×D5—616no—
188Q8×D5—68no—
189C2×C4×D5—32no—
190C2×C4×D5—32no—
191C2×C4×D5—64no—
192C2×C4×D5—68no—
193C2×C4×D5—62no—
194C2×C4×D5—62no—
195C2×Dic10—22no—
196C2×Dic10—21no—
197C2×Dic10—32no—
198C2×Dic10—64no—
199C2×Dic10—68no—
200C2×Dic10—62no—
201C2×Dic10—62no—
202C2×Dic10—61no—
203C2×Dic10D1214yes—
204C2×Dic10C22×D312yes—
205C2×C5×C8—32no—
206C2×C5×C8—62no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4C22×D312yes—
209#689—68no—
210#685—64no—
211C4⋊Dic5—64no—
212C2×#168—22no—
213C2×#168C22×D312yes—
214Dic20—68no—
215C23×Q8—151no—
216C22×Q16—151no—
217C22×Q16—151no—
218C2×C22⋊Q8—151no—
219#451—158no—
220C2×#103—31no—
221C2×#103—51no—
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—42no—
232C3×C4×C5#12012yes—
233C3×C4×C5C22×D411yescharacteristic
234C3×C4×C5C22×D411yescharacteristic
235Dic15—22no—
236Dic15—42no—
237C3×Dic5—24no—
238C5×Dic3—24no—
239C23×D3—51no—
240C2×C3×Q8—54no—
241C2×C3×Q8—52no—
242C2×C3×Q8—102no—
243C2×C3×Q8—101no—
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—21no—
261C2×Dic6—52no—
262C2×Dic6—104no—
263C2×Dic6—108no—
264C2×Dic6—102no—
265C2×Dic6—102no—
266C2×Dic6—101no—
267C2×Dic6D2014yes—
268C2×Dic6C22×D512yes—
269C2×C3×C8—52no—
270C2×C3×C8—102no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4C22×D512yes—
273#216—108no—
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—34no—
285C5×Q8—64no—
286C5×Q8—62no—
287C2×C4×C5—22no—
288C2×C4×C5—42no—
289C2×C4×C5—64no—
290C2×C4×C5—62no—
291C2×C4×C5C2×D1212yes—
292C2×C4×C5D3×D412yes—
293C2×C4×C5D3×D411yescharacteristic
294C2×C4×C5C23×D311yescharacteristic
295C2×Dic5—24no—
296C2×Dic5—22no—
297C2×Dic5—32no—
298C2×Dic5—62no—
299C2×Dic5—62no—
300C2×Dic5—122no—
301C4×D5—616no—
302C4×D5—64no—
303C4×D5—62no—
304C4×D5—62no—
305Dic10—24no—
306Dic10—22no—
307Dic10—616no—
308Dic10—62no—
309Dic10—62no—
310Dic10—122no—
311Dic10C2×D1214yes—
312C5×C8—62no—
313#168—22no—
314C22×Q8—31no—
315C22×Q8—51no—
316C22×Q8—154no—
317C22×Q8—151no—
318C22×Q8—301no—
319C22×Q8—302no—
320C22×Q8—304no—
321C22×Q8—304no—
322C23×C4—151no—
323C23×C4—301no—
324C2×Q16—154no—
325C2×Q16—154no—
326C2×Q16—304no—
327C2×Q16—304no—
328C22×C8—31no—
329C22×C8—51no—
330C22⋊Q8—154no—
331C22⋊Q8—302no—
332C2×C4⋊C4—301no—
333C2×C4⋊C4D3×D511yescharacteristic
334C2×C22⋊C4—301no—
335#103—34no—
336#103—54no—
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—54no—
349C3×Q8—102no—
350C3×Q8—104no—
351C2×C3×C4—22no—
352C2×C3×C4—42no—
353C2×C3×C4—102no—
354C2×C3×C4—104no—
355C2×C3×C4C2×D2012yes—
356C2×C3×C4D4×D512yes—
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—22no—
360C2×Dic3—24no—
361C2×Dic3—52no—
362C2×Dic3—102no—
363C2×Dic3—102no—
364C2×Dic3—202no—
365C4×D3—1016no—
366C4×D3—102no—
367C4×D3—102no—
368C4×D3—104no—
369Dic6—22no—
370Dic6—24no—
371Dic6—1016no—
372Dic6—102no—
373Dic6—102no—
374Dic6—202no—
375Dic6C2×D2014yes—
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—42no—
387C4×C5—64no—
388C4×C5#88212yes—
389C4×C5C22×D1211yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—24no—
392Dic5—62no—
393Dic5—122no—
394C24—151no—
395C2×Q8—34no—
396C2×Q8—32no—
397C2×Q8—54no—
398C2×Q8—52no—
399C2×Q8—62no—
400C2×Q8—61no—
401C2×Q8—102no—
402C2×Q8—101no—
403C2×Q8—152no—
404C2×Q8—304no—
405C2×Q8—308no—
406C2×Q8—308no—
407C2×Q8—308no—
408C2×Q8—3016no—
409C2×Q8—301no—
410C2×Q8—302no—
411C2×Q8—302no—
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—302no—
421C22×C4—302no—
422C22×C4—301no—
423C22×C4C2×D3×D511yescharacteristic
424Q16—308no—
425Q16—308no—
426C2×C8—32no—
427C2×C8—52no—
428C2×C8—62no—
429C2×C8—102no—
430C4⋊C4—21no—
431C4⋊C4—304no—
432C4⋊C4C2×D3×D512yes—
433C22⋊C4—304no—
434C3×C5C2×#45111yescharacteristic, complemented, Hall
435C22×C3#402812yes—
436C22×C3#406112yes—
437C22×C3D5×Q1612yes—
438C22×C3C2×D4×D511yescharacteristic
439C2×D3—54no—
440C2×D3—102no—
441C2×D3—102no—
442C2×D3—108no—
443C3×C4—42no—
444C3×C4—104no—
445C3×C4#402812yes—
446C3×C4C22×D2011yescharacteristic
447C3×C4C2×D4×D511yescharacteristic
448Dic3—24no—
449Dic3—102no—
450Dic3—202no—
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—34no—
462Q8—54no—
463Q8—64no—
464Q8—62no—
465Q8—104no—
466Q8—102no—
467Q8—3016no—
468Q8—302no—
469Q8—302no—
470Q8—602no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—64no—
474C2×C4—62no—
475C2×C4—104no—
476C2×C4—102no—
477C2×C4—152no—
478C2×C4—3016no—
479C2×C4—302no—
480C2×C4—304no—
481C2×C4—302no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—602no—
485C2×C4D5×D1212yes—
486C2×C4D3×D2012yes—
487C2×C4#679011yescharacteristic
488C2×C4C22×D3×D511yescharacteristic
489C8—62no—
490C8—102no—
491C2×C3#6509714yescomplemented
492C2×C3C2×#402811yescharacteristic
493C2×C3C2×#406111yescharacteristic
494C2×C3C2×D5×Q1611yescharacteristic
495D3—104no—
496C5C2×#480911yescharacteristic, complemented, Sylow
497C22—154no—
498C22—302no—
499C22—308no—
500C22—302no—
501C22#9147612yes—
502C22#9148812yes—
503C22#9151112yes—
504C22C2×#679011yescharacteristic
505C4—42no—
506C4—64no—
507C4—104no—
508C4—302no—
509C4—602no—
510C4#9147612yes—
511C4C2×D5×D1211yescharacteristic
512C4C2×D3×D2011yescharacteristic
513C3C2×#6509711yescharacteristic, complemented, Sylow
514C2—304no—
515C2#1174749614yesdirect product factor
516C2C2×#9147611yescharacteristic
517C2C2×#9148811yescharacteristic
518C2C2×#9151111yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#6663C2semidirect
4. C22×#6662C2semidirect
5. C2×C5×#810C2semidirect
6. C2×C3×#3942C2semidirect
8. #11747496C2direct (N × H)
28. C2×#6663C22semidirect
30. C2×#6662C22semidirect
31. C5×#810C22semidirect
32. C3×#3942C22semidirect
41. C2×#3942D3semidirect
89. C2×#810D5semidirect
114. #3942C2×D3semidirect
119. C22×D15Q16semidirect
174. #810C2×D5semidirect
230. C2×D15C2×Q16semidirect
338. C2×C3×C5#451semidirect
434. C3×C5C2×#451semidirect
451. C2×C5#4809semidirect
491. C2×C3#65097semidirect
496. C5C2×#4809semidirect
513. C3C2×#65097semidirect
515. C2#11747496direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D15⋊Q82
C2×#917862
C22×#66632
C22×#66622
C2×C5×#8102
C2×C3×#39422
C2×#909572
#117474962
C2×#650973
C2×#48095