Finite Group Databasebeta

← C2×#11753334 #14481263

Subgroups — C2×#11753334 #14481263

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91786C211yesmaximal, characteristic
2C2×C5×#887C211yesmaximal, characteristic, complemented
3C2×C3×#4036C211yesmaximal, characteristic, complemented
4C2×#91386C211yesmaximal, characteristic
5C2×#91383C211yesmaximal, characteristic
6C2×#91381C212yesmaximal, complemented
7C2×#91380C212yesmaximal
8C2×#91376C211yesmaximal, characteristic, complemented
9C2×#91345C212yesmaximal
10C2×#91340C211yesmaximal, characteristic, complemented
11C2×#91334C212yesmaximal, complemented
12#11753334C2116yesmaximal, direct product factor
13C2×#65917—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C22×C5×Dic6C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×#6714C2212yes—
19C2×C4⋊Dic15C2212yes—
20#91786C2218yes—
21C2×C5×Dic3⋊C4C2212yes—
22C2×C4×C5×Dic3C2212yes—
23C2×C4×C5×Dic3C2211yescharacteristic
24C5×#887C2218yescomplemented
25C2×C3×C4⋊Dic5C2212yes—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×#683C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C3×#4036C2218yescomplemented
30C2×#6669C2212yes—
31C2×#6669C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6668C2212yes—
34C2×#6668C2212yes—
35C2×#6668C2212yes—
36C2×#6667C2211yescharacteristic
37C2×#6667C2212yes—
38C2×#6667C2211yescharacteristic
39C2×Dic3×Dic5C2212yes—
40#91386C2218yes—
41#91383C2218yes—
42#91381C22116yescomplemented
43#91380C22116yes—
44#91376C2218yescomplemented
45#91345C22116yes—
46#91340C2218yescomplemented
47#91334C22116yescomplemented
48C2×#5698—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4092—31no—
51C2×#4090—31no—
52#65917—316no—
53C2×#4044—32no—
54C2×#4043—31no—
55C2×#4036D311yescharacteristic, complemented
56C2×#4035—32no—
57C2×#4022—32no—
58C2×#4018—31no—
59C2×#4016—32no—
60C2×C4×Dic10—31no—
61C23×D15C2311yescharacteristic
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2312yes—
65C22×Dic15C2311yescharacteristic
66C2×C4×D15—24no—
67C2×C4×D15C2314yes—
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C22×C3×Dic5C2312yes—
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C3×C5×C4⋊C4C2314yes—
79#6714C2318yes—
80C4⋊Dic15C2318yes—
81C5×Dic3⋊C4C2318yes—
82C4×C5×Dic3C2314yes—
83C4×C5×Dic3C2318yes—
84C3×C4⋊Dic5C2314yes—
85C3×C4⋊Dic5C2318yes—
86C3×#683C2318yes—
87C3×C4×Dic5C2314yes—
88#6669C2314yes—
89#6669C2318yes—
90#6669C2314yes—
91#6668C2318yes—
92#6668C2318yes—
93#6668C2318yes—
94#6667C2314yes—
95#6667C2318yes—
96#6667C2314yes—
97Dic3×Dic5C2318yes—
98C2×C3×#125—51no—
99#5698—516no—
100C2×#898—52no—
101C2×#898—52no—
102C2×#897—51no—
103C2×#897—51no—
104C2×#890—52no—
105C2×#890—52no—
106C2×#887—51no—
107C2×#887D511yescharacteristic, complemented
108C2×#872—51no—
109C2×#869—51no—
110C22×C5×Q8—31no—
111C22×C4×D5—31no—
112C22×Dic10—31no—
113C4×C5×Q8—38no—
114C2×C5×C4⋊C4—32no—
115C2×C5×C4⋊C4C2×D311yescharacteristic
116C2×C42×C5—31no—
117C2×C42×C5—32no—
118#4092—38no—
119#4090—38no—
120C2×#685—32no—
121C2×#685—31no—
122C2×#685—31no—
123C2×#685—32no—
124C2×C4⋊Dic5—32no—
125C2×C4⋊Dic5C2×D311yescharacteristic
126C2×C4⋊Dic5C2×D312yes—
127C2×#683—32no—
128C2×#683—31no—
129C2×#683—32no—
130C2×#683—32no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683C2×D312yes—
134C2×C4×Dic5—32no—
135C2×C4×Dic5C2×D311yescharacteristic
136#4044—316no—
137#4043—38no—
138#4036C2×D318yescomplemented
139#4035—316no—
140#4022—316no—
141#4018—38no—
142#4016—316no—
143C4×Dic10—38no—
144C2×#541—151noSylow
145C23×C3×C5C2411yescharacteristic
146C22×D15—22no—
147C22×D15—22no—
148C22×D15—22no—
149C22×D15C2412yes—
150C2×C3×C4×C5—24no—
151C2×C3×C4×C5#4114yes—
152C2×C3×C4×C5C2414yes—
153C2×C3×C4×C5C2412yes—
154C2×Dic15—24no—
155C2×Dic15—22no—
156C2×Dic15C2414yes—
157C2×Dic15C2412yes—
158C4×D15—28no—
159Dic30—28no—
160C2×C5×Dic3—24no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3C2412yes—
164C2×C5×Dic3C2414yes—
165C2×C5×Dic3C2412yes—
166C5×Dic6—28no—
167C2×C3×Dic5—24no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5C2414yes—
171C2×C3×Dic5C2412yes—
172C2×C3×Dic5C2412yes—
173C22×C4×D3—51no—
174C22×Dic6—51no—
175C22×Dic6C2×D511yescharacteristic
176C3×#125—58no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C4⋊C4—52no—
179C2×C3×C4⋊C4—52no—
180C2×C3×C4⋊C4C2×D511yescharacteristic
181C2×C3×C42—51no—
182C2×(C2×D3)⋊C4—52no—
183C2×(C2×D3)⋊C4—51no—
184C2×(C2×D3)⋊C4—51no—
185C2×(C2×D3)⋊C4—52no—
186C2×C4⋊Dic3—52no—
187C2×C4⋊Dic3—52no—
188C2×C4⋊Dic3—52no—
189C2×C4⋊Dic3—52no—
190C2×Dic3⋊C4—51no—
191C2×Dic3⋊C4—51no—
192C2×Dic3⋊C4—52no—
193C2×Dic3⋊C4C2×D512yes—
194C2×C4×Dic3—52no—
195C2×C4×Dic3C2×D511yescharacteristic
196C2×C4×Dic3C2×D512yes—
197#898—516no—
198#898—516no—
199#897—58no—
200#897—58no—
201#890—516no—
202#890—516no—
203#887—58no—
204#887C2×D518yescomplemented
205#872—58no—
206#869—58no—
207C23×D5—31no—
208C2×C5×Q8—34no—
209C2×C5×Q8—64no—
210C22×C4×C5—31no—
211C22×C4×C5—31no—
212C22×C4×C5—32no—
213C22×C4×C5C22×D312yes—
214C22×C4×C5C22×D311yescharacteristic
215C22×Dic5—32no—
216C22×Dic5—31no—
217C22×Dic5C22×D312yes—
218C22×Dic5C22×D311yescharacteristic
219C22×Dic5C22×D311yescharacteristic
220C2×C4×D5—34no—
221C2×C4×D5—64no—
222C2×Dic10—34no—
223C2×Dic10—64no—
224C5×C4⋊C4—38no—
225C5×C4⋊C4C22×D314yes—
226C42×C5—34no—
227C42×C5—38no—
228#685—38no—
229#685—34no—
230#685—34no—
231#685—38no—
232C4⋊Dic5—38no—
233C4⋊Dic5C22×D314yes—
234C4⋊Dic5C22×D318yes—
235#683—38no—
236#683—38no—
237#683—38no—
238#683—38no—
239#683—34no—
240#683—34no—
241#683C22×D318yes—
242C4×Dic5—38no—
243C4×Dic5C22×D314yes—
244#541—1516no—
245C2×C4⋊Q8—151no—
246C2×#126—152no—
247C2×#126—152no—
248C2×#125—51no—
249C2×#125—152no—
250C2×#125—152no—
251C2×C22⋊Q8—151no—
252C2×C22⋊Q8—151no—
253C2×C4×Q8—31no—
254C2×C4×Q8—151no—
255C2×#117—151no—
256C22×C3×C5C2×#4112yes—
257C22×C3×C52−1+412yes—
258C22×C3×C52−1+412yes—
259C22×C3×C5C2511yescharacteristic
260C2×D15—22no—
261C2×D15—22no—
262C2×D15—22no—
263C2×D15—44no—
264C3×C4×C5—24no—
265C3×C4×C5C2×#4114yes—
266Dic15—24no—
267Dic15—22no—
268C3×Dic5—24no—
269C3×Dic5—22no—
270C3×Dic5—22no—
271C5×Dic3—24no—
272C5×Dic3—22no—
273C5×Dic3—22no—
274C23×D3—51no—
275C22×C3×C4—52no—
276C22×C3×C4—51no—
277C22×C3×C4—51no—
278C22×C3×C4C22×D512yes—
279C22×C3×C4C22×D511yescharacteristic
280C22×Dic3—52no—
281C22×Dic3—51no—
282C22×Dic3C22×D511yescharacteristic
283C22×Dic3C22×D511yescharacteristic
284C22×Dic3C22×D512yes—
285C2×C4×D3—54no—
286C2×C4×D3—104no—
287C2×Dic6—24no—
288C2×Dic6—54no—
289C2×Dic6—104no—
290C2×Dic6C22×D514yes—
291C3×C4⋊C4—58no—
292C3×C4⋊C4—54no—
293C3×C4⋊C4—58no—
294C3×C4⋊C4C22×D514yes—
295C3×C42—54no—
296(C2×D3)⋊C4—58no—
297(C2×D3)⋊C4—54no—
298(C2×D3)⋊C4—54no—
299(C2×D3)⋊C4—58no—
300C4⋊Dic3—58no—
301C4⋊Dic3—58no—
302C4⋊Dic3—58no—
303C4⋊Dic3—58no—
304Dic3⋊C4—54no—
305Dic3⋊C4—54no—
306Dic3⋊C4—58no—
307Dic3⋊C4C22×D518yes—
308C4×Dic3—58no—
309C4×Dic3C22×D514yes—
310C4×Dic3C22×D518yes—
311C23×C5C23×D311yescharacteristic
312C22×D5—32no—
313C22×D5—62no—
314C22×D5—62no—
315C22×D5—62no—
316C5×Q8—68no—
317C2×C4×C5—24no—
318C2×C4×C5—32no—
319C2×C4×C5—32no—
320C2×C4×C5—34no—
321C2×C4×C5—64no—
322C2×C4×C5—62no—
323C2×C4×C5—62no—
324C2×C4×C5#23914yes—
325C2×C4×C5C23×D314yes—
326C2×C4×C5C23×D312yes—
327C2×Dic5—22no—
328C2×Dic5—24no—
329C2×Dic5—22no—
330C2×Dic5—34no—
331C2×Dic5—32no—
332C2×Dic5—64no—
333C2×Dic5—62no—
334C2×Dic5C23×D314yes—
335C2×Dic5C23×D312yes—
336C2×Dic5C23×D312yes—
337C4×D5—68no—
338Dic10—68no—
339C22×Q8—31no—
340C22×Q8—151no—
341C23×C4—151no—
342C4⋊Q8—158no—
343#126—1516no—
344#126—1516no—
345#125—58no—
346#125—1516no—
347#125—1516no—
348C22⋊Q8—158no—
349C22⋊Q8—158no—
350C4×Q8—38no—
351C4×Q8—158no—
352#117—158no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—52no—
356C2×C4⋊C4—52no—
357C2×C4⋊C4—151no—
358C2×C4⋊C4—151no—
359C2×C4⋊C4—152no—
360C2×C4⋊C4—152no—
361C2×C4⋊C4—152no—
362C2×C4⋊C4—152no—
363C2×C4⋊C4—152no—
364C2×C4⋊C4D3×D511yescharacteristic
365C2×C22⋊C4—151no—
366C2×C22⋊C4—151no—
367C2×C22⋊C4—152no—
368C2×C22⋊C4—152no—
369C2×C42—31no—
370C2×C42—32no—
371C2×C42—51no—
372C2×C42—152no—
373C2×C3×C5#54114yescomplemented
374C2×C3×C5C22×#4111yescharacteristic
375C2×C3×C5C2×2−1+411yescharacteristic
376C2×C3×C5C2×2−1+411yescharacteristic
377D15—42no—
378C23×C3C23×D511yescharacteristic
379C22×D3—52no—
380C22×D3—102no—
381C22×D3—102no—
382C22×D3—102no—
383C2×C3×C4—24no—
384C2×C3×C4—54no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—104no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4#70914yes—
391C2×C3×C4C23×D514yes—
392C2×C3×C4C23×D512yes—
393C2×Dic3—24no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—54no—
397C2×Dic3—52no—
398C2×Dic3—104no—
399C2×Dic3—102no—
400C2×Dic3C23×D512yes—
401C2×Dic3C23×D512yes—
402C2×Dic3C23×D514yes—
403C4×D3—108no—
404Dic6—28no—
405Dic6—108no—
406C22×C5C2×#23912yes—
407C22×C5#101012yes—
408C22×C5#101012yes—
409C22×C5C24×D311yescharacteristic
410C2×D5—62no—
411C2×D5—62no—
412C2×D5—62no—
413C2×D5—124no—
414C4×C5—24no—
415C4×C5—64no—
416C4×C5—62no—
417C4×C5—62no—
418C4×C5C2×#23914yes—
419Dic5—22no—
420Dic5—24no—
421Dic5—22no—
422Dic5—64no—
423Dic5—62no—
424C24—151no—
425C2×Q8—34no—
426C2×Q8—64no—
427C2×Q8—154no—
428C2×Q8—304no—
429C22×C4—31no—
430C22×C4—31no—
431C22×C4—32no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—52no—
435C22×C4—152no—
436C22×C4—151no—
437C22×C4—154no—
438C22×C4—304no—
439C22×C4C2×D3×D512yes—
440C22×C4C2×D3×D511yescharacteristic
441C4⋊C4—38no—
442C4⋊C4—54no—
443C4⋊C4—58no—
444C4⋊C4—58no—
445C4⋊C4—154no—
446C4⋊C4—154no—
447C4⋊C4—158no—
448C4⋊C4—158no—
449C4⋊C4—158no—
450C4⋊C4—158no—
451C4⋊C4—158no—
452C4⋊C4C2×D3×D514yes—
453C22⋊C4—154no—
454C22⋊C4—154no—
455C22⋊C4—158no—
456C22⋊C4—158no—
457C42—34no—
458C42—38no—
459C42—54no—
460C42—158no—
461C3×C5C2×#54111yescharacteristic, complemented, Hall
462C22×C3C2×#70912yes—
463C22×C3#414712yes—
464C22×C3#415012yes—
465C22×C3C24×D511yescharacteristic
466C2×D3—102no—
467C2×D3—102no—
468C2×D3—102no—
469C2×D3—204no—
470C3×C4—24no—
471C3×C4—104no—
472C3×C4—102no—
473C3×C4—102no—
474C3×C4C2×#70914yes—
475Dic3—24no—
476Dic3—22no—
477Dic3—22no—
478Dic3—104no—
479Dic3—102no—
480C2×C5#569814yescomplemented
481C2×C5C22×#23911yescharacteristic
482C2×C5C2×#101011yescharacteristic
483C2×C5C2×#101011yescharacteristic
484D5—122no—
485C23—152no—
486C23—302no—
487C23—302no—
488C23—302no—
489C23C22×D3×D511yescharacteristic
490Q8—68no—
491Q8—308no—
492C2×C4—24no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—34no—
496C2×C4—52no—
497C2×C4—52no—
498C2×C4—54no—
499C2×C4—64no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—104no—
505C2×C4—154no—
506C2×C4—152no—
507C2×C4—302no—
508C2×C4—304no—
509C2×C4—308no—
510C2×C4#676914yes—
511C2×C4C22×D3×D514yes—
512C2×C4C22×D3×D512yes—
513C2×C3#6591714yescomplemented
514C2×C3C22×#70911yescharacteristic
515C2×C3C2×#414711yescharacteristic
516C2×C3C2×#415011yescharacteristic
517D3—202no—
518C5C2×#569811yescharacteristic, complemented, Sylow
519C22—302no—
520C22—302no—
521C22—302no—
522C22—604no—
523C22C2×#676912yes—
524C22#9202012yes—
525C22#9202812yes—
526C22C23×D3×D511yescharacteristic
527C4—24no—
528C4—64no—
529C4—62no—
530C4—62no—
531C4—102no—
532C4—102no—
533C4—104no—
534C4—302no—
535C4—304no—
536C4C2×#676914yes—
537C3C2×#6591711yescharacteristic, complemented, Sylow
538C2—602no—
539C2#1175333414yesdirect product factor
540C2C22×#676911yescharacteristic
541C2C2×#9202011yescharacteristic
542C2C2×#9202811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#887C2semidirect
3. C2×C3×#4036C2semidirect
6. C2×#91381C2semidirect
8. C2×#91376C2semidirect
10. C2×#91340C2semidirect
11. C2×#91334C2semidirect
12. #11753334C2direct (N × H)
24. C5×#887C22semidirect
29. C3×#4036C22semidirect
42. #91381C22semidirect
44. #91376C22semidirect
46. #91340C22semidirect
47. #91334C22semidirect
55. C2×#4036D3semidirect
107. C2×#887D5semidirect
138. #4036C2×D3semidirect
204. #887C2×D5semidirect
373. C2×C3×C5#541semidirect
461. C3×C5C2×#541semidirect
480. C2×C5#5698semidirect
513. C2×C3#65917semidirect
518. C5C2×#5698semidirect
537. C3C2×#65917semidirect
539. C2#11753334direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917862
C2×C5×#8872
C2×C3×#40362
C2×#913862
C2×#913832
C2×#913812
C2×#913802
C2×#913762
C2×#913452
C2×#913402
C2×#913342
#117533342
C2×#659173
C2×#56985