Finite Group Databasebeta

← C2×#11748126 #14423395

Subgroups — C2×#11748126 #14423395

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
2C22×C3×Dic20C211yesmaximal, characteristic, complemented
3C2×#91390C211yesmaximal, characteristic
4C22×#6661C211yesmaximal, characteristic, complemented
5C2×#91104C211yesmaximal, characteristic
6C2×C5×#816C211yesmaximal, characteristic, complemented
7C2×#90970C211yesmaximal, characteristic, complemented
8#11748126C218yesmaximal, direct product factor
9C2×#65097—31nomaximal, Hall
10C22×C4×D15C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×#1204—21no—
15C22×#1200—21no—
16C2×D15⋊Q8—22no—
17C2×D15⋊Q8—24no—
18C2×D15⋊Q8—24no—
19C2×D15⋊Q8C2214yes—
20C22×C3×C5×C8C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic20—24no—
24C2×C3×Dic20C2214yescomplemented
25C2×Dic3⋊Dic5—21no—
26C2×#6667—21no—
27#91390—22no—
28#91390C2214yes—
29C2×#6661—24no—
30C2×#6661C2214yescomplemented
31#91104C2214yes—
32C5×#816C2214yescomplemented
33#90970C2214yescomplemented
34C2×#5186—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×#689—31no—
37C22×Dic20D311yescharacteristic, complemented
38C2×#4043—31no—
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65097—38no—
43C23×D15D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15D411yescharacteristic
46C2×C4×D15—22no—
47C2×C4×D15—22no—
48C2×C4×D15D412yes—
49C2×C4×D15C2312yes—
50C22×C5×Dic3—21no—
51C22×C5×Dic3—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6—22no—
54C2×C5×Dic6D414yes—
55C2×C5×Dic6C2312yes—
56C22×C3×Dic5—21no—
57C22×C3×Dic5—21no—
58C2×C3×Dic10—21no—
59C2×C3×Dic10—22no—
60C2×C3×Dic10—22no—
61C2×C3×Dic10—22no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10D414yes—
64C2×C3×Dic10C2312yes—
65C2×C3×Dic10C2312yes—
66C2×#1204—28no—
67C2×#1204—24no—
68C2×#1200—28no—
69C2×#1200—24no—
70D15⋊Q8—216no—
71D15⋊Q8—28no—
72D15⋊Q8—28no—
73C2×C3×C5×C8—22no—
74C2×C3×C5×C8C2312yes—
75C2×C3⋊#168—22no—
76C2×C3⋊#168C2312yes—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C3×Dic20—28no—
80Dic3⋊Dic5—24no—
81#6667—24no—
82#6661—28no—
83C22×D3×Q8—51no—
84C22×C3×Q16—51no—
85C2×#946—51no—
86C22×#216—51no—
87C2×#835—51no—
88#5186—58no—
89C2×(C2×D3)⋊C8—51no—
90C2×#816D511yescharacteristic, complemented
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—61no—
99C22×Dic10C2×D311yescharacteristic
100C22×Dic10C2×D311yescharacteristic
101C22×C5×C8C2×D311yescharacteristic
102C2×C5×C4⋊C4—31no—
103C2×#689—34no—
104C2×#689—64no—
105C2×#685—61no—
106C2×C4⋊Dic5—61no—
107C22×#168—31no—
108C2×Dic20—24no—
109C2×Dic20C2×D314yescomplemented
110#4043—34no—
111#4043—62no—
112C5×#103—34no—
113#3952—34no—
114#3942—34no—
115C2×#451—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15Q1614yescomplemented
120C22×D15C2×D412yes—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D412yes—
123C2×C3×C4×C5C2×D412yes—
124C2×C3×C4×C5C2411yescharacteristic
125C2×Dic15—22no—
126C2×Dic15C2×D412yes—
127C4×D15—24no—
128C4×D15—22no—
129C4×D15—22no—
130C2×C5×Dic3—24no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—42no—
134C5×Dic6—24no—
135C5×Dic6—22no—
136C5×Dic6C2×D414yes—
137C2×C3×Dic5—24no—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—42no—
141C3×Dic10—24no—
142C3×Dic10—22no—
143C3×Dic10—22no—
144C3×Dic10—22no—
145C3×Dic10—42no—
146C3×Dic10C2×D414yes—
147#1204—216no—
148#1200—216no—
149C3×C5×C8—22no—
150C3⋊#168—22no—
151C22×C3×Q8—51no—
152C22×C3×Q8—51no—
153C2×D3×Q8—54no—
154C2×D3×Q8—102no—
155C2×D3×Q8—104no—
156C2×D3×Q8—104no—
157C22×C4×D3—51no—
158C22×C4×D3—101no—
159C22×Dic6—101no—
160C22×Dic6C2×D511yescharacteristic
161C2×C3×Q16—54no—
162C2×C3×Q16—104no—
163C22×C3×C8C2×D511yescharacteristic
164#946—54no—
165#946—102no—
166C2×#216—54no—
167C2×#216—104no—
168C2×(C2×D3)⋊C4—101no—
169C2×C4⋊Dic3C2×D511yescharacteristic
170C2×Dic3⋊C4—101no—
171C22×C3⋊C8—51no—
172#835—54no—
173(C2×D3)⋊C8—54no—
174#816C2×D514yescomplemented
175C23×D5—31no—
176C2×C5×Q8—34no—
177C2×C5×Q8—32no—
178C2×C5×Q8—61no—
179C2×C5×Q8—62no—
180C22×C4×C5—61no—
181C22×C4×C5—61no—
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—31no—
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—22no—
198C2×Dic10—22no—
199C2×Dic10—21no—
200C2×Dic10—64no—
201C2×Dic10—68no—
202C2×Dic10#6714yes—
203C2×Dic10C22×D312yes—
204C2×Dic10C22×D312yes—
205C2×C5×C8—22no—
206C2×C5×C8C22×D312yes—
207C5×C4⋊C4—32no—
208C5×C4⋊C4—61no—
209#689—68no—
210#685—64no—
211C4⋊Dic5—64no—
212C2×#168—32no—
213C2×#168—62no—
214Dic20—28no—
215C23×Q8—151no—
216C22×Q16—51no—
217C22×Q16—151no—
218C2×C22⋊Q8—151no—
219#451—158no—
220C2×#103—31no—
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#12012yes—
232C3×C4×C5C22×D411yescharacteristic
233C3×C4×C5C22×D411yescharacteristic
234Dic15—22no—
235C3×Dic5—24no—
236C3×Dic5—42no—
237C5×Dic3—24no—
238C5×Dic3—42no—
239C23×D3—51no—
240C2×C3×Q8—54no—
241C2×C3×Q8—52no—
242C2×C3×Q8—52no—
243C2×C3×Q8—102no—
244C2×C3×Q8—101no—
245C2×C3×Q8—101no—
246C2×C3×Q8—102no—
247C2×C3×Q8—102no—
248C22×C3×C4—101no—
249C22×C3×C4—101no—
250C22×C3×C4C22×D511yescharacteristic
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—51no—
254D3×Q8—108no—
255D3×Q8—1016no—
256D3×Q8—108no—
257C2×C4×D3—52no—
258C2×C4×D3—52no—
259C2×C4×D3—104no—
260C2×C4×D3—108no—
261C2×C4×D3—102no—
262C2×C4×D3—102no—
263C2×Dic6—21no—
264C2×Dic6—22no—
265C2×Dic6—104no—
266C2×Dic6—108no—
267C2×Dic6D2014yes—
268C2×Dic6C22×D512yes—
269C3×Q16—108no—
270C2×C3×C8—22no—
271C2×C3×C8C22×D512yes—
272#216—108no—
273(C2×D3)⋊C4—104no—
274C4⋊Dic3—21no—
275C4⋊Dic3C22×D512yes—
276Dic3⋊C4—104no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—102no—
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—64no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5—122no—
291C2×C4×C5D3×D412yes—
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5C2×#6712yes—
294C2×C4×C5C23×D311yescharacteristic
295C2×Dic5—24no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—32no—
299C2×Dic5—42no—
300C2×Dic5—62no—
301C4×D5—616no—
302C4×D5—64no—
303C4×D5—62no—
304C4×D5—62no—
305Dic10—24no—
306Dic10—22no—
307Dic10—22no—
308Dic10—22no—
309Dic10—42no—
310Dic10—616no—
311Dic10C2×#6714yes—
312C5×C8—22no—
313#168—62no—
314C22×Q8—31no—
315C22×Q8—51no—
316C22×Q8—51no—
317C22×Q8—154no—
318C22×Q8—301no—
319C22×Q8—302no—
320C22×Q8—304no—
321C22×Q8—304no—
322C23×C4—151no—
323C23×C4—301no—
324C2×Q16—54no—
325C2×Q16—104no—
326C2×Q16—154no—
327C2×Q16—304no—
328C22×C8—151no—
329C22×C8D3×D511yescharacteristic
330C22⋊Q8—154no—
331C22⋊Q8—302no—
332C2×C4⋊C4—31no—
333C2×C4⋊C4—301no—
334C2×C22⋊C4—301no—
335#103—34no—
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—54no—
349C3×Q8—102no—
350C3×Q8—104no—
351C3×Q8—102no—
352C3×Q8—102no—
353C3×Q8—202no—
354C2×C3×C4—102no—
355C2×C3×C4—104no—
356C2×C3×C4—102no—
357C2×C3×C4—202no—
358C2×C3×C4C2×D2012yes—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4D4×D512yes—
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—22no—
363C2×Dic3—24no—
364C2×Dic3—22no—
365C2×Dic3—42no—
366C2×Dic3—52no—
367C2×Dic3—102no—
368C4×D3—1016no—
369C4×D3—102no—
370C4×D3—102no—
371C4×D3—104no—
372Dic6—22no—
373Dic6—24no—
374Dic6—1016no—
375Dic6C2×D2014yes—
376C3×C8—22no—
377C3⋊C8—102no—
378C22×C5D3×Q1612yes—
379C22×C5#91812yes—
380C22×C5#93712yes—
381C22×C5C2×D3×D411yescharacteristic
382C2×D5—34no—
383C2×D5—68no—
384C2×D5—62no—
385C2×D5—62no—
386C4×C5—64no—
387C4×C5—122no—
388C4×C5#93712yes—
389C4×C5C2×D3×D411yescharacteristic
390C4×C5C22×#6711yescharacteristic
391Dic5—24no—
392Dic5—42no—
393Dic5—62no—
394C24—151no—
395C2×Q8—34no—
396C2×Q8—32no—
397C2×Q8—54no—
398C2×Q8—52no—
399C2×Q8—52no—
400C2×Q8—61no—
401C2×Q8—62no—
402C2×Q8—102no—
403C2×Q8—101no—
404C2×Q8—101no—
405C2×Q8—102no—
406C2×Q8—102no—
407C2×Q8—304no—
408C2×Q8—308no—
409C2×Q8—308no—
410C2×Q8—308no—
411C2×Q8—3016no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—101no—
415C22×C4—101no—
416C22×C4—151no—
417C22×C4—152no—
418C22×C4—152no—
419C22×C4—304no—
420C22×C4—308no—
421C22×C4—302no—
422C22×C4—302no—
423C22×C4C2×D3×D511yescharacteristic
424Q16—108no—
425Q16—308no—
426C2×C8—22no—
427C2×C8—152no—
428C2×C8—302no—
429C2×C8C2×D3×D512yes—
430C4⋊C4—32no—
431C4⋊C4—61no—
432C4⋊C4—304no—
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—104no—
444C3×C4—202no—
445C3×C4#402812yes—
446C3×C4C22×D2011yescharacteristic
447C3×C4C2×D4×D511yescharacteristic
448Dic3—24no—
449Dic3—42no—
450Dic3—102no—
451C2×C5#518614yescomplemented
452C2×C5C2×D3×Q1611yescharacteristic
453C2×C5C2×#91811yescharacteristic
454C2×C5C2×#93711yescharacteristic
455D5—64no—
456C23—152no—
457C23—154no—
458C23—302no—
459C23—302no—
460C23#677711yescharacteristic
461Q8—34no—
462Q8—54no—
463Q8—64no—
464Q8—62no—
465Q8—104no—
466Q8—102no—
467Q8—102no—
468Q8—102no—
469Q8—202no—
470Q8—3016no—
471C2×C4—64no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—104no—
475C2×C4—102no—
476C2×C4—102no—
477C2×C4—122no—
478C2×C4—152no—
479C2×C4—202no—
480C2×C4—3016no—
481C2×C4—302no—
482C2×C4—304no—
483C2×C4—302no—
484C2×C4—302no—
485C2×C4D3×D2012yes—
486C2×C4#677711yescharacteristic
487C2×C4D5×#6712yes—
488C2×C4C22×D3×D511yescharacteristic
489C8—22no—
490C8—302no—
491C2×C3#6509714yescomplemented
492C2×C3C2×#402811yescharacteristic
493C2×C3C2×#406111yescharacteristic
494C2×C3C2×D5×Q1611yescharacteristic
495D3—104no—
496C5C2×#518611yescharacteristic, complemented, Sylow
497C22—154no—
498C22—302no—
499C22—308no—
500C22—302no—
501C22#9126412yes—
502C22#9128012yes—
503C22#9147412yes—
504C22C2×#677711yescharacteristic
505C4—64no—
506C4—104no—
507C4—122no—
508C4—202no—
509C4—302no—
510C4#9147412yes—
511C4C2×D3×D2011yescharacteristic
512C4C2×D5×#6711yescharacteristic
513C3C2×#6509711yescharacteristic, complemented, Sylow
514C2—304no—
515C2#1174812614yesdirect product factor
516C2C2×#9126411yescharacteristic
517C2C2×#9128011yescharacteristic
518C2C2×#9147411yescharacteristic
subgroupG/H
centerC23#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic20C2semidirect
4. C22×#6661C2semidirect
6. C2×C5×#816C2semidirect
7. C2×#90970C2semidirect
8. #11748126C2direct (N × H)
24. C2×C3×Dic20C22semidirect
30. C2×#6661C22semidirect
32. C5×#816C22semidirect
33. #90970C22semidirect
37. C22×Dic20D3semidirect
90. C2×#816D5semidirect
109. C2×Dic20C2×D3semidirect
119. C22×D15Q16semidirect
174. #816C2×D5semidirect
230. C2×D15C2×Q16semidirect
338. C2×C3×C5#451semidirect
434. C3×C5C2×#451semidirect
451. C2×C5#5186semidirect
491. C2×C3#65097semidirect
496. C5C2×#5186semidirect
513. C3C2×#65097semidirect
515. C2#11748126direct (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
C22×C3×Dic202
C2×#913902
C22×#66612
C2×#911042
C2×C5×#8162
C2×#909702
#117481262
C2×#650973
C2×#51865