Finite Group Databasebeta

← C2×#11756458 #14495379

Subgroups — C2×#11756458 #14495379

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2#11756458C2116yesmaximal, direct product factor
3C2×#91787C212yesmaximal, complemented
4C2×#91787C212yesmaximal, complemented
5C2×#91786C212yesmaximal, complemented
6C2×#91785C212yesmaximal, complemented
7C2×#91783C212yesmaximal
8C2×#91777C212yesmaximal, complemented
9C2×#91764C211yesmaximal, characteristic
10C2×#91759C211yesmaximal, characteristic, complemented
11C2×#66033—31nomaximal, Hall
12C22×D60C2211yescharacteristic
13C22×C4×D15C2212yes—
14C22×Dic30C2211yescharacteristic
15C22×Dic30C2212yes—
16C3×C5×#125C2218yescomplemented
17C2×C3×C5×C4⋊C4C2212yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2212yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×#6714C2212yes—
23C2×#6714C2212yes—
24C2×#6714C2212yes—
25C2×#6714C2212yes—
26C2×#6714C2212yes—
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2212yes—
30C2×#6712C2212yes—
31C2×#6712C2212yes—
32C2×#6712C2212yes—
33C2×C4×Dic15C2212yes—
34#91787C22116yescomplemented
35#91787C22116yescomplemented
36#91786C22116yescomplemented
37#91785C22116yescomplemented
38#91783C22116yes—
39#91777C22116yescomplemented
40#91764C2218yes—
41#91759C2218yescomplemented
42C2×#5699—51nomaximal, Hall
43C2×C5×#125D311yescharacteristic, complemented
44#66033—316no—
45C2×#4044—32no—
46C2×#4044—32no—
47C2×#4043—32no—
48C2×#4042—32no—
49C2×#4040—32no—
50C2×#4034—32no—
51C2×#4021—31no—
52C2×#4016—31no—
53C23×D15C2312yes—
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C22×Dic15C2312yes—
62C2×D60—42no—
63C2×D60C2314yes—
64C2×C4×D15—44no—
65C2×C4×D15C2318yes—
66C2×Dic30—42no—
67C2×Dic30—44no—
68C2×Dic30C2314yes—
69C2×Dic30C2318yes—
70C3×C5×C4⋊C4C2318yes—
71C3×C5×C4⋊C4C2314yes—
72C3×C5×C4⋊C4C2318yes—
73C3×C5×C4⋊C4C2314yes—
74C3×C42×C5C2314yes—
75#6714C2318yes—
76#6714C2318yes—
77#6714C2318yes—
78#6714C2318yes—
79#6714C2318yes—
80C4⋊Dic15C2314yes—
81C4⋊Dic15C2314yes—
82C4⋊Dic15C2318yes—
83#6712C2318yes—
84#6712C2318yes—
85#6712C2318yes—
86C4×Dic15C2318yes—
87C2×C3×#125D511yescharacteristic, complemented
88#5699—516no—
89C2×#898—52no—
90C2×#898—52no—
91C2×#897—52no—
92C2×#896—52no—
93C2×#894—52no—
94C2×#888—52no—
95C2×#875—51no—
96C2×#870—51no—
97C22×D20—31no—
98C22×C4×D5—32no—
99C22×Dic10—31no—
100C22×Dic10—32no—
101C5×#125C2×D318yescomplemented
102C2×C5×C4⋊C4C2×D312yes—
103C2×C5×C4⋊C4C2×D311yescharacteristic
104C2×C5×C4⋊C4C2×D312yes—
105C2×C5×C4⋊C4C2×D311yescharacteristic
106C2×C42×C5C2×D311yescharacteristic
107C2×#685—32no—
108C2×#685—32no—
109C2×#685—32no—
110C2×#685—32no—
111C2×#685—32no—
112C2×C4⋊Dic5—31no—
113C2×C4⋊Dic5—31no—
114C2×C4⋊Dic5—32no—
115C2×#683—32no—
116C2×#683—32no—
117C2×#683—32no—
118C2×C4×Dic5—32no—
119#4044—316no—
120#4044—316no—
121#4043—316no—
122#4042—316no—
123#4040—316no—
124#4034—316no—
125#4021—38no—
126#4016—38no—
127C2×#563—151noSylow
128C23×C3×C5C2411yescharacteristic
129C22×D15—24no—
130C22×D15—24no—
131C22×D15—24no—
132C22×D15C2414yes—
133C2×C3×C4×C5—24no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—24no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2414yes—
139C2×C3×C4×C5C2412yes—
140C2×C3×C4×C5C2412yes—
141C2×C3×C4×C5C2414yes—
142C2×C3×C4×C5C2412yes—
143C2×Dic15—24no—
144C2×Dic15—24no—
145C2×Dic15—24no—
146C2×Dic15C2414yes—
147C2×Dic15C2414yes—
148C2×Dic15C2414yes—
149D60—44no—
150C4×D15—48no—
151Dic30—44no—
152Dic30—48no—
153C22×D12—51no—
154C22×C4×D3—52no—
155C22×Dic6—51no—
156C22×Dic6—52no—
157C3×#125C2×D518yescomplemented
158C2×C3×C4⋊C4C2×D512yes—
159C2×C3×C4⋊C4C2×D511yescharacteristic
160C2×C3×C4⋊C4C2×D512yes—
161C2×C3×C4⋊C4C2×D511yescharacteristic
162C2×C3×C42C2×D511yescharacteristic
163C2×(C2×D3)⋊C4—52no—
164C2×(C2×D3)⋊C4—52no—
165C2×(C2×D3)⋊C4—52no—
166C2×(C2×D3)⋊C4—52no—
167C2×(C2×D3)⋊C4—52no—
168C2×C4⋊Dic3—51no—
169C2×C4⋊Dic3—51no—
170C2×C4⋊Dic3—52no—
171C2×Dic3⋊C4—52no—
172C2×Dic3⋊C4—52no—
173C2×Dic3⋊C4—52no—
174C2×C4×Dic3—52no—
175#898—516no—
176#898—516no—
177#897—516no—
178#896—516no—
179#894—516no—
180#888—516no—
181#875—58no—
182#870—58no—
183C23×D5—32no—
184C22×C4×C5C22×D311yescharacteristic
185C22×C4×C5C22×D311yescharacteristic
186C22×C4×C5C22×D311yescharacteristic
187C22×C4×C5C22×D312yes—
188C22×C4×C5C22×D312yes—
189C22×Dic5—32no—
190C22×Dic5—32no—
191C22×Dic5—32no—
192C2×D20—34no—
193C2×D20—122no—
194C2×C4×D5—38no—
195C2×C4×D5—124no—
196C2×Dic10—34no—
197C2×Dic10—38no—
198C2×Dic10—122no—
199C2×Dic10—124no—
200C5×C4⋊C4C22×D318yes—
201C5×C4⋊C4C22×D314yes—
202C5×C4⋊C4C22×D318yes—
203C5×C4⋊C4C22×D314yes—
204C42×C5C22×D314yes—
205#685—38no—
206#685—38no—
207#685—38no—
208#685—38no—
209#685—38no—
210C4⋊Dic5—34no—
211C4⋊Dic5—34no—
212C4⋊Dic5—38no—
213#683—38no—
214#683—38no—
215#683—38no—
216C4×Dic5—38no—
217#563—1516no—
218C2×C4⋊Q8—152no—
219C2×#126—152no—
220C2×#126—152no—
221C2×#125—151no—
222C2×#125D1511yescharacteristic, complemented
223C2×#124—151no—
224C2×#123—152no—
225C2×C22⋊Q8—152no—
226C2×C22⋊Q8—152no—
227C22×C3×C5H(5,𝔽2)12yes—
228C22×C3×C52−1+412yes—
229C22×C3×C52−1+412yes—
230C22×C3×C5C2511yescharacteristic
231C2×D15—24no—
232C2×D15—24no—
233C2×D15—24no—
234C2×D15—48no—
235C3×C4×C5—24no—
236C3×C4×C5—22no—
237C3×C4×C5—22no—
238C3×C4×C5—24no—
239C3×C4×C5—22no—
240Dic15—24no—
241Dic15—24no—
242Dic15—24no—
243C23×D3—52no—
244C22×C3×C4C22×D512yes—
245C22×C3×C4C22×D511yescharacteristic
246C22×C3×C4C22×D511yescharacteristic
247C22×C3×C4C22×D512yes—
248C22×C3×C4C22×D511yescharacteristic
249C22×Dic3—52no—
250C22×Dic3—52no—
251C22×Dic3—52no—
252C2×D12—54no—
253C2×D12—202no—
254C2×C4×D3—58no—
255C2×C4×D3—204no—
256C2×Dic6—54no—
257C2×Dic6—58no—
258C2×Dic6—202no—
259C2×Dic6—204no—
260C3×C4⋊C4C22×D518yes—
261C3×C4⋊C4C22×D514yes—
262C3×C4⋊C4C22×D518yes—
263C3×C4⋊C4C22×D514yes—
264C3×C42C22×D514yes—
265(C2×D3)⋊C4—58no—
266(C2×D3)⋊C4—58no—
267(C2×D3)⋊C4—58no—
268(C2×D3)⋊C4—58no—
269(C2×D3)⋊C4—58no—
270C4⋊Dic3—54no—
271C4⋊Dic3—54no—
272C4⋊Dic3—58no—
273Dic3⋊C4—58no—
274Dic3⋊C4—58no—
275Dic3⋊C4—58no—
276C4×Dic3—58no—
277C23×C5C23×D311yescharacteristic
278C22×D5—34no—
279C22×D5—64no—
280C22×D5—64no—
281C22×D5—64no—
282C2×C4×C5—22no—
283C2×C4×C5—24no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—24no—
287C2×C4×C5C23×D314yes—
288C2×C4×C5C23×D312yes—
289C2×C4×C5C23×D312yes—
290C2×C4×C5C23×D314yes—
291C2×C4×C5C23×D312yes—
292C2×Dic5—34no—
293C2×Dic5—34no—
294C2×Dic5—34no—
295C2×Dic5—64no—
296C2×Dic5—64no—
297C2×Dic5—64no—
298D20—124no—
299C4×D5—128no—
300Dic10—124no—
301Dic10—128no—
302C22×Q8—152no—
303C22×Q8—151no—
304C22×D4—151no—
305C23×C4—152no—
306C4⋊Q8—1516no—
307#126—1516no—
308#126—1516no—
309#125—158no—
310#125C2×D1518yescomplemented
311#124—158no—
312#123—1516no—
313C22⋊Q8—1516no—
314C22⋊Q8—1516no—
315C2×C4⋊C4—151no—
316C2×C4⋊C4—152no—
317C2×C4⋊C4—152no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—152no—
320C2×C4⋊C4—151no—
321C2×C4⋊C4C2×D1511yescharacteristic
322C2×C4⋊C4C2×D1512yes—
323C2×C4⋊C4C2×D1512yes—
324C2×C4⋊C4C2×D1511yescharacteristic
325C2×C22⋊C4—152no—
326C2×C22⋊C4—152no—
327C2×C22⋊C4—152no—
328C2×C22⋊C4—152no—
329C2×C22⋊C4—152no—
330C2×C42—152no—
331C2×C42C2×D1511yescharacteristic
332C2×C3×C5#56314yescomplemented
333C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
334C2×C3×C5C2×2−1+411yescharacteristic
335C2×C3×C5C2×2−1+411yescharacteristic
336D15—44no—
337C23×C3C23×D511yescharacteristic
338C22×D3—54no—
339C22×D3—104no—
340C22×D3—104no—
341C22×D3—104no—
342C2×C3×C4—22no—
343C2×C3×C4—24no—
344C2×C3×C4—22no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4C23×D514yes—
348C2×C3×C4C23×D512yes—
349C2×C3×C4C23×D512yes—
350C2×C3×C4C23×D514yes—
351C2×C3×C4C23×D512yes—
352C2×Dic3—54no—
353C2×Dic3—54no—
354C2×Dic3—54no—
355C2×Dic3—104no—
356C2×Dic3—104no—
357C2×Dic3—104no—
358D12—204no—
359C4×D3—208no—
360Dic6—204no—
361Dic6—208no—
362C22×C5#100712yes—
363C22×C5#100912yes—
364C22×C5#101012yes—
365C22×C5C24×D311yescharacteristic
366C2×D5—64no—
367C2×D5—64no—
368C2×D5—64no—
369C2×D5—128no—
370C4×C5—22no—
371C4×C5—24no—
372C4×C5—22no—
373C4×C5—24no—
374C4×C5—22no—
375Dic5—64no—
376Dic5—64no—
377Dic5—64no—
378C24—152no—
379C2×Q8—158no—
380C2×Q8—154no—
381C2×Q8—604no—
382C2×Q8—602no—
383C2×D4—154no—
384C2×D4—602no—
385C22×C4—152no—
386C22×C4—152no—
387C22×C4—152no—
388C22×C4—158no—
389C22×C4—604no—
390C22×C4C22×D1512yes—
391C22×C4C22×D1511yescharacteristic
392C22×C4C22×D1511yescharacteristic
393C22×C4C22×D1511yescharacteristic
394C22×C4C22×D1512yes—
395C4⋊C4—154no—
396C4⋊C4—158no—
397C4⋊C4—158no—
398C4⋊C4—158no—
399C4⋊C4—158no—
400C4⋊C4—154no—
401C4⋊C4C22×D1514yes—
402C4⋊C4C22×D1518yes—
403C4⋊C4C22×D1518yes—
404C4⋊C4C22×D1514yes—
405C22⋊C4—158no—
406C22⋊C4—158no—
407C22⋊C4—158no—
408C22⋊C4—158no—
409C22⋊C4—158no—
410C42—158no—
411C42C22×D1514yes—
412C3×C5C2×#56311yescharacteristic, complemented, Hall
413C22×C3#414712yes—
414C22×C3#414912yes—
415C22×C3#415012yes—
416C22×C3C24×D511yescharacteristic
417C2×D3—104no—
418C2×D3—104no—
419C2×D3—104no—
420C2×D3—208no—
421C3×C4—22no—
422C3×C4—24no—
423C3×C4—22no—
424C3×C4—24no—
425C3×C4—22no—
426Dic3—104no—
427Dic3—104no—
428Dic3—104no—
429C2×C5#569914yescomplemented
430C2×C5C2×#100711yescharacteristic
431C2×C5C2×#100911yescharacteristic
432C2×C5C2×#101011yescharacteristic
433D5—124no—
434C23—154no—
435C23—304no—
436C23—304no—
437C23—304no—
438C23C23×D1511yescharacteristic
439Q8—608no—
440Q8—604no—
441D4—604no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—154no—
448C2×C4—154no—
449C2×C4—154no—
450C2×C4—304no—
451C2×C4—304no—
452C2×C4—304no—
453C2×C4—608no—
454C2×C4C23×D1514yes—
455C2×C4C23×D1512yes—
456C2×C4C23×D1512yes—
457C2×C4C23×D1512yes—
458C2×C4C23×D1514yes—
459C2×C3#6603314yescomplemented
460C2×C3C2×#414711yescharacteristic
461C2×C3C2×#414911yescharacteristic
462C2×C3C2×#415011yescharacteristic
463D3—204no—
464C5C2×#569911yescharacteristic, complemented, Sylow
465C22—304no—
466C22—304no—
467C22—304no—
468C22—608no—
469C22#9209812yes—
470C22#9210012yes—
471C22#9210112yes—
472C22C24×D1511yescharacteristic
473C4—22no—
474C4—24no—
475C4—22no—
476C4—24no—
477C4—22no—
478C4—304no—
479C4—304no—
480C4—304no—
481C3C2×#6603311yescharacteristic, complemented, Sylow
482C2—604no—
483C2#1175645814yesdirect product factor
484C2C2×#9209811yescharacteristic
485C2C2×#9210011yescharacteristic
486C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×#125D15
hypocenterC3×C5C2×#563
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#125C2semidirect
2. #11756458C2direct (N × H)
3. C2×#91787C2semidirect
4. C2×#91787C2semidirect
5. C2×#91786C2semidirect
6. C2×#91785C2semidirect
8. C2×#91777C2semidirect
10. C2×#91759C2semidirect
16. C3×C5×#125C22semidirect
34. #91787C22semidirect
35. #91787C22semidirect
36. #91786C22semidirect
37. #91785C22semidirect
39. #91777C22semidirect
41. #91759C22semidirect
43. C2×C5×#125D3semidirect
87. C2×C3×#125D5semidirect
101. C5×#125C2×D3semidirect
157. C3×#125C2×D5semidirect
222. C2×#125D15semidirect
310. #125C2×D15semidirect
332. C2×C3×C5#563semidirect
412. C3×C5C2×#563semidirect
429. C2×C5#5699semidirect
459. C2×C3#66033semidirect
464. C5C2×#5699semidirect
481. C3C2×#66033semidirect
483. C2#11756458direct (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×#1252
#117564582
C2×#917872
C2×#917862
C2×#917852
C2×#917832
C2×#917772
C2×#917642
C2×#917592
C2×#660333
C2×#56995