Finite Group Databasebeta

← C2×#11755148 #14495399

Subgroups — C2×#11755148 #14495399

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91836C211yesmaximal, characteristic
2C2×C5×#944C211yesmaximal, characteristic, complemented
3C2×C3×#4090C211yesmaximal, characteristic, complemented
4#11755148C2116yesmaximal, direct product factor
5C2×#91433C212yesmaximal
6C2×#91424C212yesmaximal, complemented
7C2×#91411C212yesmaximal, complemented
8C2×#91387C212yesmaximal, complemented
9C2×#91382C212yesmaximal, complemented
10C2×#91380C212yesmaximal, complemented
11C2×#66069—31nomaximal, Hall
12C22×C3×C5×Q8C2211yescharacteristic
13C22×D60C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C22×#1200C2212yes—
17#91836C2218yes—
18C2×#6714C2212yes—
19C2×#6714C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21C5×#944C2218yescomplemented
22C2×C5×Dic3⋊C4C2212yes—
23C2×C5×Dic3⋊C4C2212yes—
24C2×C4×C5×Dic3C2211yescharacteristic
25C3×#4090C2218yescomplemented
26C2×C3×#683C2212yes—
27C2×C3×#683C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×Dic3⋊Dic5C2212yes—
30C2×#6669C2212yes—
31C2×#6669C2212yes—
32C2×#6668C2212yes—
33C2×#6667C2212yes—
34C2×#6667C2212yes—
35C2×#6667C2212yes—
36#91433C22116yes—
37#91424C22116yescomplemented
38#91411C22116yescomplemented
39#91387C22116yescomplemented
40#91382C22116yescomplemented
41#91380C22116yescomplemented
42C2×#5735—51nomaximal, Hall
43C2×C5×C4⋊Q8—31no—
44C2×#4093—31no—
45C2×#4092—32no—
46C2×#4090D311yescharacteristic, complemented
47#66069—316no—
48C2×#4044—32no—
49C2×#4042—32no—
50C2×#4040—32no—
51C2×#4035—32no—
52C2×#4022—32no—
53C23×D15C2312yes—
54C2×C3×C5×Q8—42no—
55C2×C3×C5×Q8C2314yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C2×D60—42no—
61C2×D60C2314yes—
62C22×C5×Dic3C2312yes—
63C22×C5×Dic3C2312yes—
64C2×C5×Dic6—42no—
65C2×C5×Dic6C2314yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C2×C3×Dic10—42no—
69C2×C3×Dic10C2314yes—
70C2×#1200—44no—
71C2×#1200C2318yes—
72#6714C2318yes—
73#6714C2318yes—
74C4×Dic15C2314yes—
75C5×Dic3⋊C4C2318yes—
76C5×Dic3⋊C4C2318yes—
77C4×C5×Dic3C2314yes—
78C3×#683C2318yes—
79C3×#683C2318yes—
80C3×C4×Dic5C2314yes—
81Dic3⋊Dic5C2318yes—
82#6669C2318yes—
83#6669C2318yes—
84#6668C2318yes—
85#6667C2318yes—
86#6667C2318yes—
87#6667C2318yes—
88C2×C3×C4⋊Q8—51no—
89C2×#947—51no—
90C2×#946—52no—
91C2×#944D511yescharacteristic, complemented
92#5735—516no—
93C2×#898—52no—
94C2×#896—52no—
95C2×#894—52no—
96C2×#889—52no—
97C2×#876—52no—
98C22×C5×Q8—31no—
99C22×C5×Q8C2×D311yescharacteristic
100C22×D20—31no—
101C22×C4×D5—32no—
102C22×Dic10C2×D311yescharacteristic
103C5×C4⋊Q8—38no—
104C2×C5×C4⋊C4—32no—
105C2×C5×C4⋊C4—32no—
106C2×C42×C5—31no—
107#4093—38no—
108#4092—316no—
109#4090C2×D318yescomplemented
110C2×#685—32no—
111C2×#685—32no—
112C2×#685—32no—
113C2×#685—32no—
114C2×#685—32no—
115C2×C4⋊Dic5—32no—
116C2×#683—32no—
117C2×#683—32no—
118C2×#683—32no—
119C2×#683C2×D312yes—
120C2×#683C2×D312yes—
121C2×C4×Dic5—31no—
122C2×C4×Dic5C2×D311yescharacteristic
123#4044—316no—
124#4042—316no—
125#4040—316no—
126#4035—316no—
127#4022—316no—
128C2×#563—151noSylow
129C23×C3×C5C2411yescharacteristic
130C22×D15—24no—
131C22×D15—28no—
132C22×D15C2414yes—
133C3×C5×Q8—44no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5C2412yes—
138C2×C3×C4×C5C2412yes—
139C2×C3×C4×C5C2412yes—
140C2×Dic15—24no—
141C2×Dic15C2414yes—
142D60—44no—
143C2×C5×Dic3—24no—
144C2×C5×Dic3—24no—
145C2×C5×Dic3C2414yes—
146C2×C5×Dic3C2414yes—
147C5×Dic6—44no—
148C2×C3×Dic5—24no—
149C2×C3×Dic5—24no—
150C2×C3×Dic5C2414yes—
151C2×C3×Dic5C2414yes—
152C3×Dic10—44no—
153#1200—48no—
154C22×C3×Q8—51no—
155C22×C3×Q8C2×D511yescharacteristic
156C22×D12—51no—
157C22×C4×D3—52no—
158C22×Dic6C2×D511yescharacteristic
159C3×C4⋊Q8—58no—
160C2×C3×C4⋊C4—52no—
161C2×C3×C4⋊C4—52no—
162C2×C3×C42—51no—
163#947—58no—
164#946—516no—
165#944C2×D518yescomplemented
166C2×(C2×D3)⋊C4—52no—
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4—52no—
171C2×C4⋊Dic3—52no—
172C2×Dic3⋊C4—52no—
173C2×Dic3⋊C4—52no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4C2×D512yes—
176C2×Dic3⋊C4C2×D512yes—
177C2×C4×Dic3—51no—
178C2×C4×Dic3C2×D511yescharacteristic
179#898—516no—
180#896—516no—
181#894—516no—
182#889—516no—
183#876—516no—
184C23×D5—32no—
185C2×C5×Q8—34no—
186C2×C5×Q8—42no—
187C2×C5×Q8—122no—
188C2×C5×Q8C22×D314yes—
189C22×C4×C5—32no—
190C22×C4×C5—32no—
191C22×C4×C5C22×D311yescharacteristic
192C22×C4×C5C22×D311yescharacteristic
193C22×C4×C5C22×D311yescharacteristic
194C22×Dic5—32no—
195C22×Dic5C22×D312yes—
196C22×Dic5C22×D312yes—
197C2×D20—34no—
198C2×D20—122no—
199C2×C4×D5—38no—
200C2×C4×D5—124no—
201C2×Dic10—42no—
202C2×Dic10C22×D314yes—
203C5×C4⋊C4—38no—
204C5×C4⋊C4—38no—
205C42×C5—34no—
206#685—38no—
207#685—38no—
208#685—38no—
209#685—38no—
210#685—38no—
211C4⋊Dic5—38no—
212#683—38no—
213#683—38no—
214#683—38no—
215#683C22×D318yes—
216#683C22×D318yes—
217C4×Dic5—34no—
218C4×Dic5C22×D314yes—
219#563—1516no—
220C2×C4⋊Q8—31no—
221C2×C4⋊Q8—51no—
222C2×#126—152no—
223C2×#126—152no—
224C2×#125—152no—
225C2×#124—151no—
226C2×#123—152no—
227C2×C22⋊Q8—152no—
228C2×C22⋊Q8—152no—
229C22×C3×C5H(5,𝔽2)12yes—
230C22×C3×C52−1+414yes—
231C22×C3×C5C2511yescharacteristic
232C2×D15—24no—
233C2×D15—28no—
234C2×D15—48no—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237C3×C4×C5—22no—
238Dic15—24no—
239C3×Dic5—24no—
240C3×Dic5—24no—
241C5×Dic3—24no—
242C5×Dic3—24no—
243C23×D3—52no—
244C2×C3×Q8—42no—
245C2×C3×Q8—54no—
246C2×C3×Q8—202no—
247C2×C3×Q8C22×D514yes—
248C22×C3×C4—52no—
249C22×C3×C4—52no—
250C22×C3×C4C22×D511yescharacteristic
251C22×C3×C4C22×D511yescharacteristic
252C22×C3×C4C22×D511yescharacteristic
253C22×Dic3—52no—
254C22×Dic3C22×D512yes—
255C22×Dic3C22×D512yes—
256C2×D12—54no—
257C2×D12—202no—
258C2×C4×D3—58no—
259C2×C4×D3—204no—
260C2×Dic6—42no—
261C2×Dic6C22×D514yes—
262C3×C4⋊C4—58no—
263C3×C4⋊C4—58no—
264C3×C42—54no—
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—58no—
271Dic3⋊C4—58no—
272Dic3⋊C4—58no—
273Dic3⋊C4—58no—
274Dic3⋊C4C22×D518yes—
275Dic3⋊C4C22×D518yes—
276C4×Dic3—54no—
277C4×Dic3C22×D514yes—
278C23×C5C23×D311yescharacteristic
279C22×D5—34no—
280C22×D5—64no—
281C22×D5—68no—
282C5×Q8—44no—
283C5×Q8—124no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—34no—
288C2×C4×C5—34no—
289C2×C4×C5—64no—
290C2×C4×C5—64no—
291C2×C4×C5C23×D312yes—
292C2×C4×C5C23×D312yes—
293C2×C4×C5C23×D312yes—
294C2×Dic5—24no—
295C2×Dic5—24no—
296C2×Dic5—34no—
297C2×Dic5—64no—
298C2×Dic5C23×D314yes—
299C2×Dic5C23×D314yes—
300D20—124no—
301C4×D5—128no—
302Dic10—44no—
303C22×Q8—31no—
304C22×Q8—51no—
305C22×Q8D3×D511yescharacteristic
306C22×D4—151no—
307C23×C4—152no—
308C4⋊Q8—38no—
309C4⋊Q8—58no—
310#126—1516no—
311#126—1516no—
312#125—1516no—
313#124—158no—
314#123—1516no—
315C22⋊Q8—1516no—
316C22⋊Q8—1516no—
317C2×C4⋊C4—32no—
318C2×C4⋊C4—32no—
319C2×C4⋊C4—52no—
320C2×C4⋊C4—52no—
321C2×C4⋊C4—152no—
322C2×C4⋊C4—152no—
323C2×C4⋊C4—152no—
324C2×C4⋊C4—152no—
325C2×C22⋊C4—152no—
326C2×C22⋊C4—152no—
327C2×C22⋊C4—152no—
328C2×C22⋊C4—152no—
329C2×C22⋊C4—152no—
330C2×C42—31no—
331C2×C42—51no—
332C2×C42—151no—
333C2×C3×C5#56314yescomplemented
334C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
335C2×C3×C5C2×2−1+412yes—
336D15—44no—
337C23×C3C23×D511yescharacteristic
338C22×D3—54no—
339C22×D3—104no—
340C22×D3—108no—
341C3×Q8—44no—
342C3×Q8—204no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—54no—
347C2×C3×C4—54no—
348C2×C3×C4—104no—
349C2×C3×C4—104no—
350C2×C3×C4C23×D512yes—
351C2×C3×C4C23×D512yes—
352C2×C3×C4C23×D512yes—
353C2×Dic3—24no—
354C2×Dic3—24no—
355C2×Dic3—54no—
356C2×Dic3—104no—
357C2×Dic3C23×D514yes—
358C2×Dic3C23×D514yes—
359D12—204no—
360C4×D3—208no—
361Dic6—44no—
362C22×C5#100412yes—
363C22×C5#100714yes—
364C22×C5C24×D311yescharacteristic
365C2×D5—64no—
366C2×D5—68no—
367C2×D5—128no—
368C4×C5—22no—
369C4×C5—22no—
370C4×C5—22no—
371C4×C5—64no—
372C4×C5—64no—
373Dic5—24no—
374Dic5—24no—
375Dic5—64no—
376C24—152no—
377C2×Q8—34no—
378C2×Q8—42no—
379C2×Q8—54no—
380C2×Q8—122no—
381C2×Q8—202no—
382C2×Q8C2×D3×D514yes—
383C2×D4—154no—
384C2×D4—602no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—52no—
388C22×C4—52no—
389C22×C4—158no—
390C22×C4—152no—
391C22×C4—604no—
392C22×C4C2×D3×D511yescharacteristic
393C22×C4C2×D3×D511yescharacteristic
394C22×C4C2×D3×D511yescharacteristic
395C4⋊C4—38no—
396C4⋊C4—38no—
397C4⋊C4—58no—
398C4⋊C4—58no—
399C4⋊C4—158no—
400C4⋊C4—158no—
401C4⋊C4—158no—
402C4⋊C4—158no—
403C22⋊C4—158no—
404C22⋊C4—158no—
405C22⋊C4—158no—
406C22⋊C4—158no—
407C22⋊C4—158no—
408C42—34no—
409C42—54no—
410C42—154no—
411C3×C5C2×#56311yescharacteristic, complemented, Hall
412C22×C3#414412yes—
413C22×C3#414714yes—
414C22×C3C24×D511yescharacteristic
415C2×D3—104no—
416C2×D3—108no—
417C2×D3—208no—
418C3×C4—22no—
419C3×C4—22no—
420C3×C4—22no—
421C3×C4—104no—
422C3×C4—104no—
423Dic3—24no—
424Dic3—24no—
425Dic3—104no—
426C2×C5#573514yescomplemented
427C2×C5C2×#100411yescharacteristic
428C2×C5C2×#100712yes—
429D5—124no—
430C23—154no—
431C23—308no—
432C23—304no—
433C23C22×D3×D511yescharacteristic
434Q8—44no—
435Q8—124no—
436Q8—204no—
437D4—604no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—34no—
442C2×C4—34no—
443C2×C4—54no—
444C2×C4—54no—
445C2×C4—64no—
446C2×C4—64no—
447C2×C4—104no—
448C2×C4—104no—
449C2×C4—154no—
450C2×C4—304no—
451C2×C4—608no—
452C2×C4C22×D3×D512yes—
453C2×C4C22×D3×D512yes—
454C2×C4C22×D3×D512yes—
455C2×C3#6606914yescomplemented
456C2×C3C2×#414411yescharacteristic
457C2×C3C2×#414712yes—
458D3—204no—
459C5C2×#573511yescharacteristic, complemented, Sylow
460C22—304no—
461C22—308no—
462C22—608no—
463C22#9202914yes—
464C22#9204912yes—
465C22C23×D3×D511yescharacteristic
466C4—22no—
467C4—22no—
468C4—22no—
469C4—64no—
470C4—64no—
471C4—104no—
472C4—104no—
473C4—304no—
474C3C2×#6606911yescharacteristic, complemented, Sylow
475C2—604no—
476C2#1175514814yesdirect product factor
477C2C2×#9202912yes—
478C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#563
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C5×#944C2semidirect
3. C2×C3×#4090C2semidirect
4. #11755148C2direct (N × H)
6. C2×#91424C2semidirect
7. C2×#91411C2semidirect
8. C2×#91387C2semidirect
9. C2×#91382C2semidirect
10. C2×#91380C2semidirect
21. C5×#944C22semidirect
25. C3×#4090C22semidirect
37. #91424C22semidirect
38. #91411C22semidirect
39. #91387C22semidirect
40. #91382C22semidirect
41. #91380C22semidirect
46. C2×#4090D3semidirect
91. C2×#944D5semidirect
109. #4090C2×D3semidirect
165. #944C2×D5semidirect
333. C2×C3×C5#563semidirect
411. C3×C5C2×#563semidirect
426. C2×C5#5735semidirect
455. C2×C3#66069semidirect
459. C5C2×#5735semidirect
474. C3C2×#66069semidirect
476. C2#11755148direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918362
C2×C5×#9442
C2×C3×#40902
#117551482
C2×#914332
C2×#914242
C2×#914112
C2×#913872
C2×#913822
C2×#913802
C2×#660693
C2×#57355