Finite Group Databasebeta

← C2×#11755216 #14495400

Subgroups — C2×#11755216 #14495400

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×#91833C211yesmaximal, characteristic, complemented
2C2×C5×#947C211yesmaximal, characteristic
3C2×C3×#4090C211yesmaximal, characteristic, complemented
4#11755216C2116yesmaximal, direct product factor
5C2×#91432C212yesmaximal, complemented
6C2×#91423C212yesmaximal
7C2×#91410C212yesmaximal, complemented
8C2×#91379C212yesmaximal, complemented
9C2×#91372C212yesmaximal, complemented
10C2×#91367C212yesmaximal, complemented
11C2×#66006—31nomaximal, Hall
12C22×C3×C5×Q8C2211yescharacteristic
13C22×Dic30C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17#91833C2218yescomplemented
18C2×#6712C2212yes—
19C2×#6712C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21C5×#947C2218yes—
22C2×C5×(C2×D3)⋊C4C2212yes—
23C2×C5×(C2×D3)⋊C4C2212yes—
24C2×C4×C5×Dic3C2211yescharacteristic
25C3×#4090C2218yescomplemented
26C2×C3×#683C2212yes—
27C2×C3×#683C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×Dic3⋊Dic5C2212yes—
30C2×Dic3⋊Dic5C2212yes—
31C2×#6669C2212yes—
32C2×#6668C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35C2×(C2×D3)⋊Dic5C2212yes—
36#91432C22116yescomplemented
37#91423C22116yes—
38#91410C22116yescomplemented
39#91379C22116yescomplemented
40#91372C22116yescomplemented
41#91367C22116yescomplemented
42C2×#5735—51nomaximal, Hall
43C2×C5×#124—31no—
44C2×#4090—31no—
45C2×#4090D311yescharacteristic, complemented
46C2×#4081—32no—
47#66006—316no—
48C2×#4025—32no—
49C2×#4025—32no—
50C2×#4024—32no—
51C2×#4024—32no—
52C2×#4016—32no—
53C23×C5×D3C2312yes—
54C2×C3×C5×Q8—42no—
55C2×C3×C5×Q8C2314yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C2×Dic30—42no—
62C2×Dic30C2314yes—
63C22×C5×Dic3C2312yes—
64C2×C5×D12—42no—
65C2×C5×D12C2314yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C2×C3×Dic10—42no—
69C2×C3×Dic10C2314yes—
70C2×D3×Dic5—44no—
71C2×D3×Dic5C2318yes—
72#6712C2318yes—
73#6712C2318yes—
74C4×Dic15C2314yes—
75C5×(C2×D3)⋊C4C2318yes—
76C5×(C2×D3)⋊C4C2318yes—
77C4×C5×Dic3C2314yes—
78C3×#683C2318yes—
79C3×#683C2318yes—
80C3×C4×Dic5C2314yes—
81Dic3⋊Dic5C2318yes—
82Dic3⋊Dic5C2318yes—
83#6669C2318yes—
84#6668C2318yes—
85(C2×D3)⋊Dic5C2318yes—
86(C2×D3)⋊Dic5C2318yes—
87(C2×D3)⋊Dic5C2318yes—
88C2×C3×C4⋊Q8—51no—
89C2×#947D511yescharacteristic
90C2×#946—52no—
91C2×#944—51no—
92#5735—516no—
93C2×#898—52no—
94C2×#896—52no—
95C2×#894—52no—
96C2×#889—52no—
97C2×#876—52no—
98C22×C5×Q8C2×D311yescharacteristic
99C22×C5×D4—31no—
100C23×Dic5—32no—
101C22×Dic10—31no—
102C22×Dic10C2×D311yescharacteristic
103C5×#124—38no—
104C2×C5×C22⋊C4—32no—
105C2×C5×C22⋊C4—32no—
106C2×C42×C5—31no—
107C2×C22⋊Dic5—32no—
108C2×C22⋊Dic5—32no—
109C2×C22⋊Dic5—32no—
110#4090—38no—
111#4090C2×D318yescomplemented
112#4081—316no—
113C2×C4⋊Dic5—32no—
114C2×C4⋊Dic5—32no—
115C2×#683—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#4025—316no—
124#4025—316no—
125#4024—316no—
126#4024—316no—
127#4016—316no—
128C2×#563—151noSylow
129C23×C3×C5C2411yescharacteristic
130C22×C5×D3—24no—
131C22×C5×D3—28no—
132C22×C5×D3C2414yes—
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×Dic15—24no—
142C2×Dic15C2414yes—
143C2×Dic15C2414yes—
144Dic30—44no—
145C2×C5×Dic3—24no—
146C2×C5×Dic3C2414yes—
147C5×D12—44no—
148C2×C3×Dic5—24no—
149C2×C3×Dic5—24no—
150C2×C3×Dic5C2414yes—
151C2×C3×Dic5C2414yes—
152C3×Dic10—44no—
153D3×Dic5—48no—
154C22×C3×Q8—51no—
155C22×C3×Q8C2×D511yescharacteristic
156C22×D12C2×D511yescharacteristic
157C22×C4×D3—52no—
158C22×Dic6—51no—
159C3×C4⋊Q8—58no—
160C2×C3×C4⋊C4—52no—
161C2×C3×C4⋊C4—52no—
162C2×C3×C42—51no—
163#947C2×D518yes—
164#946—516no—
165#944—58no—
166C2×(C2×D3)⋊C4—52no—
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4C2×D512yes—
170C2×(C2×D3)⋊C4C2×D512yes—
171C2×C4⋊Dic3—52no—
172C2×Dic3⋊C4—52no—
173C2×Dic3⋊C4—52no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—52no—
177C2×C4×Dic3—51no—
178C2×C4×Dic3C2×D511yescharacteristic
179#898—516no—
180#896—516no—
181#894—516no—
182#889—516no—
183#876—516no—
184C24×C5—32no—
185C2×C5×Q8—42no—
186C2×C5×Q8C22×D314yes—
187C2×C5×D4—34no—
188C2×C5×D4—122no—
189C22×C4×C5—32no—
190C22×C4×C5C22×D311yescharacteristic
191C22×C4×C5C22×D311yescharacteristic
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—32no—
194C22×Dic5—32no—
195C22×Dic5—38no—
196C22×Dic5—124no—
197C22×Dic5C22×D312yes—
198C22×Dic5C22×D312yes—
199C2×Dic10—34no—
200C2×Dic10—42no—
201C2×Dic10—122no—
202C2×Dic10C22×D314yes—
203C5×C22⋊C4—38no—
204C5×C22⋊C4—38no—
205C42×C5—34no—
206C22⋊Dic5—38no—
207C22⋊Dic5—38no—
208C22⋊Dic5—38no—
209C4⋊Dic5—38no—
210C4⋊Dic5—38no—
211#683—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—51no—
221C2×C4⋊Q8—151no—
222C2×#126—152no—
223C2×#126—152no—
224C2×#125—152no—
225C2×#124—31no—
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×C5×D3—24no—
233C2×C5×D3—28no—
234C2×C5×D3—48no—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237C3×C4×C5—22no—
238Dic15—24no—
239Dic15—24no—
240C3×Dic5—24no—
241C3×Dic5—24no—
242C5×Dic3—24no—
243C23×D3C22×D512yes—
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×Dic3—52no—
255C22×Dic3C22×D512yes—
256C2×D12—42no—
257C2×D12C22×D514yes—
258C2×C4×D3—58no—
259C2×C4×D3—204no—
260C2×Dic6—54no—
261C2×Dic6—202no—
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)⋊C4C22×D518yes—
269(C2×D3)⋊C4C22×D518yes—
270C4⋊Dic3—58no—
271Dic3⋊C4—58no—
272Dic3⋊C4—58no—
273Dic3⋊C4—58no—
274Dic3⋊C4—58no—
275Dic3⋊C4—58no—
276C4×Dic3—54no—
277C4×Dic3C22×D514yes—
278C23×C5—34no—
279C23×C5—64no—
280C23×C5—68no—
281C23×C5C23×D311yescharacteristic
282C5×Q8—44no—
283C5×D4—124no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—34no—
288C2×C4×C5—64no—
289C2×C4×C5C23×D312yes—
290C2×C4×C5C23×D312yes—
291C2×C4×C5C23×D312yes—
292C2×Dic5—24no—
293C2×Dic5—24no—
294C2×Dic5—34no—
295C2×Dic5—34no—
296C2×Dic5—64no—
297C2×Dic5—64no—
298C2×Dic5—128no—
299C2×Dic5C23×D314yes—
300C2×Dic5C23×D314yes—
301Dic10—44no—
302Dic10—124no—
303C22×Q8—51no—
304C22×Q8—151no—
305C22×Q8D3×D511yescharacteristic
306C22×D4—31no—
307C23×C4—152no—
308C4⋊Q8—58no—
309C4⋊Q8—158no—
310#126—1516no—
311#126—1516no—
312#125—1516no—
313#124—38no—
314#123—1516no—
315C22⋊Q8—1516no—
316C22⋊Q8—1516no—
317C2×C4⋊C4—52no—
318C2×C4⋊C4—52no—
319C2×C4⋊C4—152no—
320C2×C4⋊C4—152no—
321C2×C4⋊C4—152no—
322C2×C4⋊C4—152no—
323C2×C4⋊C4—152no—
324C2×C4⋊C4—152no—
325C2×C22⋊C4—32no—
326C2×C22⋊C4—32no—
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—
336C5×D3—44no—
337C23×C3C23×D511yescharacteristic
338C22×D3—24no—
339C22×D3—28no—
340C22×D3C23×D514yes—
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—54no—
355C2×Dic3—54no—
356C2×Dic3—104no—
357C2×Dic3—104no—
358C2×Dic3C23×D514yes—
359D12—44no—
360C4×D3—208no—
361Dic6—204no—
362C22×C5—64no—
363C22×C5—68no—
364C22×C5—128no—
365C22×C5#100412yes—
366C22×C5#100714yes—
367C22×C5C24×D311yescharacteristic
368C4×C5—22no—
369C4×C5—22no—
370C4×C5—22no—
371C4×C5—64no—
372Dic5—24no—
373Dic5—24no—
374Dic5—64no—
375Dic5—64no—
376C24—32no—
377C2×Q8—42no—
378C2×Q8—54no—
379C2×Q8—154no—
380C2×Q8—202no—
381C2×Q8—602no—
382C2×Q8C2×D3×D514yes—
383C2×D4—34no—
384C2×D4—122no—
385C22×C4—32no—
386C22×C4—52no—
387C22×C4—52no—
388C22×C4—158no—
389C22×C4—152no—
390C22×C4—152no—
391C22×C4—604no—
392C22×C4C2×D3×D511yescharacteristic
393C22×C4C2×D3×D511yescharacteristic
394C22×C4C2×D3×D511yescharacteristic
395C4⋊C4—58no—
396C4⋊C4—58no—
397C4⋊C4—158no—
398C4⋊C4—158no—
399C4⋊C4—158no—
400C4⋊C4—158no—
401C4⋊C4—158no—
402C4⋊C4—158no—
403C22⋊C4—38no—
404C22⋊C4—38no—
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#415014yes—
414C22×C3C24×D511yescharacteristic
415C2×D3—24no—
416C2×D3—28no—
417C2×D3—48no—
418C3×C4—22no—
419C3×C4—22no—
420C3×C4—22no—
421C3×C4—104no—
422C3×C4—104no—
423Dic3—24no—
424Dic3—104no—
425Dic3—104no—
426C2×C5—124no—
427C2×C5#573514yescomplemented
428C2×C5C2×#100411yescharacteristic
429C2×C5C2×#100712yes—
430C23—34no—
431C23—68no—
432C23—64no—
433C23C22×D3×D511yescharacteristic
434Q8—44no—
435Q8—204no—
436Q8—604no—
437D4—124no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—34no—
442C2×C4—54no—
443C2×C4—54no—
444C2×C4—64no—
445C2×C4—104no—
446C2×C4—104no—
447C2×C4—154no—
448C2×C4—154no—
449C2×C4—304no—
450C2×C4—304no—
451C2×C4—608no—
452C2×C4C22×D3×D512yes—
453C2×C4C22×D3×D512yes—
454C2×C4C22×D3×D512yes—
455C2×C3#6600614yescomplemented
456C2×C3C2×#414411yescharacteristic
457C2×C3C2×#415012yes—
458D3—44no—
459C5C2×#573511yescharacteristic, complemented, Sylow
460C22—64no—
461C22—68no—
462C22—128no—
463C22#9203014yes—
464C22#9204912yes—
465C22C23×D3×D511yescharacteristic
466C4—22no—
467C4—22no—
468C4—22no—
469C4—64no—
470C4—104no—
471C4—104no—
472C4—304no—
473C4—304no—
474C3C2×#6600611yescharacteristic, complemented, Sylow
475C2—124no—
476C2#1175521614yesdirect product factor
477C2C2×#9203012yes—
478C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
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
1. C2×#91833C2semidirect
3. C2×C3×#4090C2semidirect
4. #11755216C2direct (N × H)
5. C2×#91432C2semidirect
7. C2×#91410C2semidirect
8. C2×#91379C2semidirect
9. C2×#91372C2semidirect
10. C2×#91367C2semidirect
17. #91833C22semidirect
25. C3×#4090C22semidirect
36. #91432C22semidirect
38. #91410C22semidirect
39. #91379C22semidirect
40. #91372C22semidirect
41. #91367C22semidirect
45. C2×#4090D3semidirect
111. #4090C2×D3semidirect
333. C2×C3×C5#563semidirect
411. C3×C5C2×#563semidirect
427. C2×C5#5735semidirect
455. C2×C3#66006semidirect
459. C5C2×#5735semidirect
474. C3C2×#66006semidirect
476. C2#11755216direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918332
C2×C5×#9472
C2×C3×#40902
#117552162
C2×#914322
C2×#914232
C2×#914102
C2×#913792
C2×#913722
C2×#913672
C2×#660063
C2×#57355