Finite Group Databasebeta

← C2×#11754444 #14478928

Subgroups — C2×#11754444 #14478928

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C22×C4×Dic15C211yesmaximal, characteristic, complemented
3C2×C5×#926C211yesmaximal, characteristic, complemented
4C2×#91559C214yesmaximal, complemented
5#11754444C2116yesmaximal, direct product factor
6C2×#91434C212yesmaximal, complemented
7C2×C4×D5×Dic3C212yesmaximal, complemented
8C2×#91357C212yesmaximal, complemented
9C2×#91331C212yesmaximal, complemented
10C2×#65856—31nomaximal, Hall
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2212yes—
13C22×C3×C22⋊D5C2212yes—
14C2×C3×#709C4116yescomplemented
15C2×C3×#709C2218yes—
16C22×C3×D20C2211yescharacteristic
17C22×C3×C4×D5C2212yes—
18C22×C3×Dic10C2211yescharacteristic
19C22×D5×Dic3C2214yes—
20C2×C4×Dic15C2211yescharacteristic
21C2×C4×Dic15C2212yes—
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2218yescomplemented
24C2×C5×#217C2212yes—
25C5×#926C2218yescomplemented
26C2×C5×C4⋊Dic3C2212yes—
27C2×C4×C5×Dic3C2212yes—
28#91559C22132yescomplemented
29C2×#6668C2214yes—
30C2×#6665C2214yes—
31C2×Dic3×Dic5C2214yes—
32#91434C22116yescomplemented
33C4×D5×Dic3C22116yescomplemented
34#91357C22116yescomplemented
35#91331C22116yescomplemented
36C2×Dic3×#41—51nomaximal, Hall
37C22×#709D311yescharacteristic
38C2×C5×#117—31no—
39C22×C4×Dic5—31no—
40#65856—316no—
41C2×#4039—32no—
42C2×#4033—32no—
43C2×#4027—34no—
44C2×#4018—32no—
45C2×C42×D5—32no—
46C24×C3×C5C2311yescharacteristic
47C23×C3×D5C2312yes—
48C22×C3×C4×C5C2×C418yescomplemented
49C22×C3×C4×C5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2314yes—
52C22×Dic15—28no—
53C22×Dic15C2312yes—
54C22×Dic15C2318yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3C2314yes—
57C2×C3×C22⋊D5C2×C4116yescomplemented
58C2×C3×C22⋊D5C2318yes—
59C22×C3×Dic5C2312yes—
60C3×#709C2×C4164yescomplemented
61C2×C3×D20C2×C418yescomplemented
62C2×C3×D20C2314yes—
63C2×C3×C4×D5C2×C4116yescomplemented
64C2×C3×C4×D5C2318yes—
65C2×C3×Dic10C2×C418yescomplemented
66C2×C3×Dic10C2314yes—
67C2×D5×Dic3—216no—
68C2×D5×Dic3C23116yes—
69C4×Dic15C2318yes—
70C4×Dic15C2314yes—
71C4×Dic15C2314yes—
72C5×#217C2318yes—
73C5×C4⋊Dic3C2318yes—
74C4×C5×Dic3C2318yes—
75#6668C23116yes—
76#6665C23116yes—
77Dic3×Dic5C23116yes—
78C22×C3×#41—51no—
79Dic3×#41—516no—
80C2×Q8×Dic3—52no—
81C2×D4×Dic3—54no—
82C2×D4×Dic3—52no—
83C2×#926—52no—
84C2×#926D511yescharacteristic, complemented
85C22×C4×Dic3—51no—
86C22×C4×Dic3—52no—
87C23×C4×C5C2×D311yescharacteristic
88C22×C22⋊D5C2×D312yes—
89C23×Dic5—32no—
90C2×#709Dic3116yescomplemented
91C2×#709C2×D318yes—
92C22×D20C2×D311yescharacteristic
93C22×C4×D5—34no—
94C22×C4×D5C2×D312yes—
95C22×Dic10C2×D311yescharacteristic
96C5×#117—38no—
97C2×C5×C4⋊C4—32no—
98C2×C5×C22⋊C4—32no—
99C2×C42×C5—32no—
100C2×#685—34no—
101C2×#683—34no—
102C2×C4×Dic5—31no—
103C2×C4×Dic5—31no—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—38no—
106C2×C4×Dic5—34no—
107#4039—316no—
108#4033—316no—
109#4027—332no—
110#4018—316no—
111C42×D5—316no—
112C2×C4×#41—151noSylow
113C23×C3×C5—24no—
114C23×C3×C5C22×C414yes—
115C23×C3×C5C2412yes—
116C23×C3×C5C2411yescharacteristic
117C22×C3×D5—28no—
118C22×C3×D5C22×C418yes—
119C22×C3×D5C2414yes—
120C2×C3×C4×C5C22×C414yes—
121C2×C3×C4×C5C22×C414yes—
122C2×C3×C4×C5C22×C4116yescomplemented
123C2×C3×C4×C5C2412yes—
124C2×C3×C4×C5C2412yes—
125C2×Dic15—24no—
126C2×Dic15—216no—
127C2×Dic15#4118yescomplemented
128C2×Dic15C2414yes—
129C2×Dic15C2414yes—
130C2×C5×Dic3—28no—
131C2×C5×Dic3C2418yes—
132C3×C22⋊D5C22×C4132yescomplemented
133C2×C3×Dic5C22×C418yes—
134C2×C3×Dic5C2414yes—
135C3×D20C22×C4116yescomplemented
136C3×C4×D5C22×C4132yescomplemented
137C3×Dic10C22×C4116yescomplemented
138D5×Dic3—232no—
139C2×C3×#41—516no—
140C2×C3×#41—58no—
141C22×C3×Q8—51no—
142C22×C3×D4—52no—
143C22×C3×D4—51no—
144C23×C3×C4—52no—
145C23×C3×C4C2×D511yescharacteristic
146C23×Dic3—52no—
147C23×Dic3—54no—
148C2×#217—54no—
149C2×#217C2×D512yes—
150Q8×Dic3—516no—
151D4×Dic3—532no—
152D4×Dic3—516no—
153#926—516no—
154#926C2×D518yescomplemented
155C2×C4⋊Dic3—54no—
156C2×C4⋊Dic3C2×D512yes—
157C2×C4×Dic3—51no—
158C2×C4×Dic3—51no—
159C2×C4×Dic3—52no—
160C2×C4×Dic3—58no—
161C2×C4×Dic3—54no—
162C2×C4×Dic3—516no—
163C2×C4×Dic3C2×D512yes—
164C24×C5C22×D311yescharacteristic
165C23×D5C22×D312yes—
166C22×C4×C5—34no—
167C22×C4×C5C2×Dic318yescomplemented
168C22×C4×C5C22×D311yescharacteristic
169C22×C4×C5C22×D314yes—
170C22×C4×C5C22×D311yescharacteristic
171C2×C22⋊D5C2×Dic3116yescomplemented
172C2×C22⋊D5C22×D318yes—
173C22×Dic5—32no—
174C22×Dic5—38no—
175C22×Dic5—32no—
176C22×Dic5—68no—
177C22×Dic5C22×D312yes—
178#709C2×Dic3164yescomplemented
179C2×D20C2×Dic318yescomplemented
180C2×D20C22×D314yes—
181C2×C4×D5—316no—
182C2×C4×D5—616no—
183C2×C4×D5C2×Dic3116yescomplemented
184C2×C4×D5C22×D318yes—
185C2×Dic10C2×Dic318yescomplemented
186C2×Dic10C22×D314yes—
187C5×C4⋊C4—38no—
188C5×C22⋊C4—38no—
189C42×C5—38no—
190#685—316no—
191#683—316no—
192C4×Dic5—34no—
193C4×Dic5—34no—
194C4×Dic5—38no—
195C4×Dic5—316no—
196C22×#41—51no—
197C4×#41—1516no—
198C2×C4×Q8—152no—
199C2×C4×D4—154no—
200C2×C4×D4—152no—
201C2×#117—31no—
202C2×#117—152no—
203C22×C42—152no—
204C22×C42—151no—
205C22×C3×C5—28no—
206C22×C3×C5—24no—
207C22×C3×C5C23×C414yes—
208C22×C3×C5C23×C412yes—
209C22×C3×C5C2×#4114yes—
210C22×C3×C5C2511yescharacteristic
211C2×C3×D5—216no—
212C2×C3×D5—28no—
213C2×C3×D5C23×C418yes—
214C3×C4×C5C23×C414yes—
215C3×C4×C5C23×C414yes—
216Dic15—24no—
217Dic15C2×#4118yescomplemented
218C3×Dic5C23×C418yes—
219C5×Dic3—28no—
220C24×C3—52no—
221C24×C3C22×D511yescharacteristic
222C3×#41—564no—
223C2×C3×Q8—58no—
224C2×C3×Q8—54no—
225C2×C3×D4—516no—
226C2×C3×D4—58no—
227C2×C3×D4—58no—
228C2×C3×D4—54no—
229C22×C3×C4—52no—
230C22×C3×C4—516no—
231C22×C3×C4—58no—
232C22×C3×C4C4×D518yescomplemented
233C22×C3×C4C22×D511yescharacteristic
234C22×C3×C4C22×D514yes—
235C22×C3×C4C22×D511yescharacteristic
236C22×Dic3—52no—
237C22×Dic3—52no—
238C22×Dic3—58no—
239C22×Dic3—516no—
240C22×Dic3—1016no—
241C22×Dic3—108no—
242C22×Dic3C22×D514yes—
243#217—516no—
244#217C22×D518yes—
245C4⋊Dic3—516no—
246C4⋊Dic3C22×D518yes—
247C4×Dic3—54no—
248C4×Dic3—54no—
249C4×Dic3—58no—
250C4×Dic3—516no—
251C4×Dic3C22×D518yes—
252C23×C5—24no—
253C23×C5C22×Dic314yes—
254C23×C5C23×D312yes—
255C23×C5C23×D311yescharacteristic
256C22×D5—28no—
257C22×D5C22×Dic318yes—
258C22×D5C23×D314yes—
259C2×C4×C5—38no—
260C2×C4×C5—68no—
261C2×C4×C5C22×Dic314yes—
262C2×C4×C5C22×Dic314yes—
263C2×C4×C5C22×Dic3116yescomplemented
264C2×C4×C5C23×D312yes—
265C2×C4×C5C23×D312yes—
266C22⋊D5C22×Dic3132yescomplemented
267C2×Dic5—38no—
268C2×Dic5—34no—
269C2×Dic5—34no—
270C2×Dic5—616no—
271C2×Dic5—64no—
272C2×Dic5C22×Dic318yes—
273C2×Dic5C23×D314yes—
274D20C22×Dic3116yescomplemented
275C4×D5—632no—
276C4×D5C22×Dic3132yescomplemented
277Dic10C22×Dic3116yescomplemented
278C2×#41—516no—
279C2×#41—58no—
280C22×Q8—51no—
281C22×D4—52no—
282C22×D4—51no—
283C23×C4—52no—
284C23×C4—154no—
285C23×C4—152no—
286C23×C4D3×D511yescharacteristic
287C4×Q8—1516no—
288C4×D4—1532no—
289C4×D4—1516no—
290#117—38no—
291#117—1516no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—154no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—154no—
296C2×C42—32no—
297C2×C42—1516no—
298C2×C42—154no—
299C2×C42—152no—
300C2×C42—158no—
301C2×C42—151no—
302C2×C42—151no—
303C2×C3×C5—24no—
304C2×C3×C5C4×#4114yescomplemented
305C2×C3×C5C24×C411yescharacteristic
306C2×C3×C5C22×#4112yes—
307C3×D5—28no—
308C23×C3—24no—
309C23×C3—58no—
310C23×C3—54no—
311C23×C3—108no—
312C23×C3C2×C4×D514yes—
313C23×C3C23×D512yes—
314C23×C3C23×D511yescharacteristic
315C3×Q8—516no—
316C3×D4—532no—
317C3×D4—516no—
318C2×C3×C4—58no—
319C2×C3×C4—54no—
320C2×C3×C4—532no—
321C2×C3×C4C2×C4×D514yes—
322C2×C3×C4C2×C4×D514yes—
323C2×C3×C4C2×C4×D5116yescomplemented
324C2×C3×C4C23×D512yes—
325C2×C3×C4C23×D512yes—
326C2×Dic3—28no—
327C2×Dic3—58no—
328C2×Dic3—54no—
329C2×Dic3—54no—
330C2×Dic3—1032no—
331C2×Dic3—1016no—
332C2×Dic3—104no—
333C2×Dic3C23×D518yes—
334C22×C5—24no—
335C22×C5—28no—
336C22×C5D3×#4114yes—
337C22×C5C23×Dic314yes—
338C22×C5C23×Dic312yes—
339C22×C5C24×D311yescharacteristic
340C2×D5—28no—
341C2×D5—216no—
342C2×D5C23×Dic318yes—
343C4×C5—68no—
344C4×C5C23×Dic314yes—
345C4×C5C23×Dic314yes—
346Dic5—38no—
347Dic5—64no—
348Dic5C23×Dic318yes—
349C24—52no—
350C24C2×D3×D511yescharacteristic
351#41—564no—
352C2×Q8—58no—
353C2×Q8—54no—
354C2×D4—516no—
355C2×D4—58no—
356C2×D4—58no—
357C2×D4—54no—
358C22×C4—34no—
359C22×C4—52no—
360C22×C4—516no—
361C22×C4—58no—
362C22×C4—1516no—
363C22×C4—152no—
364C22×C4—152no—
365C22×C4—158no—
366C22×C4—3016no—
367C22×C4—308no—
368C22×C4D5×Dic318yescomplemented
369C22×C4C2×D3×D511yescharacteristic
370C22×C4C2×D3×D514yes—
371C22×C4C2×D3×D511yescharacteristic
372C4⋊C4—38no—
373C4⋊C4—1516no—
374C22⋊C4—38no—
375C22⋊C4—1516no—
376C42—38no—
377C42—1516no—
378C42—154no—
379C42—154no—
380C42—158no—
381C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
382C22×C3—28no—
383C22×C3—24no—
384C22×C3—58no—
385C22×C3—1016no—
386C22×C3—108no—
387C22×C3C22×C4×D514yes—
388C22×C3C22×C4×D512yes—
389C22×C3D5×#4114yes—
390C22×C3C24×D511yescharacteristic
391C3×C4—58no—
392C3×C4C22×C4×D514yes—
393C3×C4C22×C4×D514yes—
394Dic3—28no—
395Dic3—58no—
396Dic3—104no—
397C2×C5—24no—
398C2×C5Dic3×#4114yescomplemented
399C2×C5C2×D3×#4112yes—
400C2×C5C24×Dic311yescharacteristic
401D5—28no—
402C23—24no—
403C23—58no—
404C23—54no—
405C23—108no—
406C23C2×D5×Dic314yes—
407C23C22×D3×D512yes—
408C23C22×D3×D511yescharacteristic
409Q8—516no—
410D4—532no—
411D4—516no—
412C2×C4—38no—
413C2×C4—58no—
414C2×C4—54no—
415C2×C4—532no—
416C2×C4—68no—
417C2×C4—158no—
418C2×C4—154no—
419C2×C4—154no—
420C2×C4—3032no—
421C2×C4—3016no—
422C2×C4—304no—
423C2×C4C2×D5×Dic314yes—
424C2×C4C2×D5×Dic314yes—
425C2×C4C2×D5×Dic3116yescomplemented
426C2×C4C22×D3×D512yes—
427C2×C4C22×D3×D512yes—
428C2×C3—24no—
429C2×C3—108no—
430C2×C3#6585614yescomplemented
431C2×C3C23×C4×D511yescharacteristic
432C2×C3C2×D5×#4112yes—
433C5C2×Dic3×#4111yescharacteristic, complemented, Sylow
434C22—28no—
435C22—24no—
436C22—58no—
437C22—1016no—
438C22—108no—
439C22#9201614yes—
440C22C22×D5×Dic314yes—
441C22C22×D5×Dic312yes—
442C22C23×D3×D511yescharacteristic
443C4—58no—
444C4—68no—
445C4—158no—
446C4—304no—
447C4C22×D5×Dic314yes—
448C4C22×D5×Dic314yes—
449C3C2×#6585611yescharacteristic, complemented, Sylow
450C2—24no—
451C2—108no—
452C2#1175444414yesdirect product factor
453C2C2×#9201612yes—
454C2C23×D5×Dic311yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×C3×#709C2
cosocleC22×C3×C5C25
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic15C2semidirect
3. C2×C5×#926C2semidirect
4. C2×#91559C2semidirect
5. #11754444C2direct (N × H)
6. C2×#91434C2semidirect
7. C2×C4×D5×Dic3C2semidirect
8. C2×#91357C2semidirect
9. C2×#91331C2semidirect
14. C2×C3×#709C4semidirect
23. C2×C4×Dic15C22semidirect
25. C5×#926C22semidirect
28. #91559C22semidirect
32. #91434C22semidirect
33. C4×D5×Dic3C22semidirect
34. #91357C22semidirect
35. #91331C22semidirect
48. C22×C3×C4×C5C2×C4semidirect
57. C2×C3×C22⋊D5C2×C4semidirect
60. C3×#709C2×C4semidirect
61. C2×C3×D20C2×C4semidirect
63. C2×C3×C4×D5C2×C4semidirect
65. C2×C3×Dic10C2×C4semidirect
84. C2×#926D5semidirect
90. C2×#709Dic3semidirect
122. C2×C3×C4×C5C22×C4semidirect
127. C2×Dic15#41semidirect
132. C3×C22⋊D5C22×C4semidirect
135. C3×D20C22×C4semidirect
136. C3×C4×D5C22×C4semidirect
137. C3×Dic10C22×C4semidirect
154. #926C2×D5semidirect
167. C22×C4×C5C2×Dic3semidirect
171. C2×C22⋊D5C2×Dic3semidirect
178. #709C2×Dic3semidirect
179. C2×D20C2×Dic3semidirect
183. C2×C4×D5C2×Dic3semidirect
185. C2×Dic10C2×Dic3semidirect
217. Dic15C2×#41semidirect
232. C22×C3×C4C4×D5semidirect
263. C2×C4×C5C22×Dic3semidirect
266. C22⋊D5C22×Dic3semidirect
274. D20C22×Dic3semidirect
276. C4×D5C22×Dic3semidirect
277. Dic10C22×Dic3semidirect
304. C2×C3×C5C4×#41semidirect
323. C2×C3×C4C2×C4×D5semidirect
368. C22×C4D5×Dic3semidirect
381. C3×C5C2×C4×#41semidirect
398. C2×C5Dic3×#41semidirect
425. C2×C4C2×D5×Dic3semidirect
430. C2×C3#65856semidirect
433. C5C2×Dic3×#41semidirect
449. C3C2×#65856semidirect
452. C2#11754444direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C22×C4×Dic152
C2×C5×#9262
C2×#915592
#117544442
C2×#914342
C2×C4×D5×Dic32
C2×#913572
C2×#913312
C2×#658563
C2×Dic3×#415