Finite Group Databasebeta

← C2×#11751019 #14478388

Subgroups — C2×#11751019 #14478388

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91808C211yesmaximal, characteristic
2C2×Q16×D15C211yesmaximal, characteristic, complemented
3C2×C3×C5×Q32C211yesmaximal, characteristic, complemented
4C2×#91113C211yesmaximal, characteristic, complemented
5C2×#91112C211yesmaximal, characteristic, complemented
6#11751019C218yesmaximal, direct product factor
7C2×#91084C211yesmaximal, characteristic, complemented
8C2×#91082C211yesmaximal, characteristic, complemented
9C2×#65207—31nomaximal, Hall
10C2×#6821—21no—
11C2×Q8×D15—21no—
12C2×C3×C5×Q16C2211yescharacteristic
13C2×C3×C5×Q16C2211yescharacteristic
14C2×#6718—21no—
15C2×#6717—21no—
16#91808—22no—
17#91808C2214yes—
18Q16×D15—22no—
19Q16×D15C2214yescomplemented
20C2×Dic60C2211yescharacteristic
21C2×D120C2211yescharacteristic
22C2×C8×D15C2211yescharacteristic
23C3×C5×Q32C2214yescomplemented
24C2×C3×C5×C16C2211yescharacteristic
25#91113C2214yescomplemented
26#91112C2214yescomplemented
27C2×C3⋊#672C2211yescharacteristic
28#91084C2214yescomplemented
29#91082C2214yescomplemented
30C2×#4918—51nomaximal, Hall
31C2×#4065—31no—
32C2×D5×Q16—31no—
33C2×C5×Q32D311yescharacteristic, complemented
34C2×#3961—31no—
35C2×#3960—31no—
36#65207—38no—
37C2×#3932—31no—
38C2×#3930—31no—
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—21no—
41#6821—24no—
42#6821—42no—
43Q8×D15—24no—
44Q8×D15—42no—
45C2×D60—21no—
46C2×D60—41no—
47C2×C4×D15—41no—
48C2×C4×D15—41no—
49C2×C4×D15D411yescharacteristic
50C2×Dic30—21no—
51C2×Dic30—41no—
52C3×C5×Q16—21no—
53C3×C5×Q16—21no—
54C3×C5×Q16C2312yes—
55C3×C5×Q16C2312yes—
56C2×C3×C5×C8C2311yescharacteristic
57#6718—24no—
58#6717—24no—
59C2×C3⋊#168D411yescharacteristic
60Dic60—21no—
61Dic60C2312yes—
62D120—21no—
63D120C2312yes—
64C8×D15D412yes—
65C8×D15C2312yes—
66C3×C5×C16C2312yes—
67C3⋊#672C2312yes—
68C2×#919—51no—
69C2×D3×Q16—51no—
70C2×C3×Q32D511yescharacteristic, complemented
71C2×#829—51no—
72C2×#828—51no—
73#4918—58no—
74C2×#800—51no—
75C2×#798—51no—
76C2×#713—61no—
77C2×Q8×D5—61no—
78C2×C5×Q16C2×D311yescharacteristic
79C2×C5×Q16C2×D311yescharacteristic
80C2×#689—61no—
81C2×#688—61no—
82#4065—34no—
83#4065—62no—
84D5×Q16—34no—
85D5×Q16—62no—
86C2×Dic20—31no—
87C2×D40—31no—
88C2×C8×D5—31no—
89C5×Q32C2×D314yescomplemented
90C2×C5×C16C2×D311yescharacteristic
91#3961—34no—
92#3960—34no—
93C2×#672—31no—
94#3932—34no—
95#3930—34no—
96C2×#510—151noSylow
97C22×D15—41no—
98C22×D15D811yescharacteristic
99C3×C5×Q8—22no—
100C3×C5×Q8—22no—
101C3×C5×Q8—41no—
102C3×C5×Q8—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—41no—
107C2×Dic15D811yescharacteristic
108D60—22no—
109D60—44no—
110D60—41no—
111C4×D15—44no—
112C4×D15—44no—
113C4×D15D812yes—
114C4×D15C2×D412yes—
115Dic30—22no—
116Dic30—41no—
117Dic30—44no—
118C3×C5×C8C2×D411yescharacteristic
119C3×C5×C8C2411yescharacteristic
120C3⋊#168C2×D412yes—
121C2×#239—101no—
122C2×D3×Q8—101no—
123C2×C3×Q16C2×D511yescharacteristic
124C2×C3×Q16C2×D511yescharacteristic
125C2×#216—101no—
126C2×#215—101no—
127#919—54no—
128#919—102no—
129D3×Q16—54no—
130D3×Q16—102no—
131C2×Dic12—51no—
132C2×D24—51no—
133C2×D3×C8—51no—
134C3×Q32C2×D514yescomplemented
135C2×C3×C16C2×D511yescharacteristic
136#829—54no—
137#828—54no—
138C2×C3⋊C16—51no—
139#800—54no—
140#798—54no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143#713—64no—
144#713—122no—
145Q8×D5—64no—
146Q8×D5—122no—
147C2×D20—61no—
148C2×D20—121no—
149C2×C4×D5—31no—
150C2×C4×D5—121no—
151C2×C4×D5—121no—
152C2×Dic10—61no—
153C2×Dic10—121no—
154C5×Q16—21no—
155C5×Q16—21no—
156C5×Q16C22×D312yes—
157C5×Q16C22×D312yes—
158C2×C5×C8C22×D311yescharacteristic
159#689—64no—
160#688—64no—
161C2×#168—31no—
162Dic20—32no—
163Dic20—61no—
164D40—32no—
165D40—61no—
166C8×D5—32no—
167C8×D5—32no—
168C5×C16C22×D312yes—
169#672—32no—
170C2×#135—151no—
171C22×Q16—151no—
172#510—158no—
173C2×Q32—151no—
174C2×Q32D1511yescharacteristic, complemented
175C2×SD32—151no—
176C2×SD32—151no—
177C2×M32—151no—
178C22×C3×C5C2×D811yescharacteristic
179C2×D15—22no—
180C2×D15—42no—
181C2×D15—82no—
182C2×D15C2×D812yes—
183C3×C4×C5—42no—
184C3×C4×C5—42no—
185C3×C4×C5C2×D811yescharacteristic
186C3×C4×C5C22×D411yescharacteristic
187Dic15—42no—
188Dic15C2×D812yes—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191#239—104no—
192#239—202no—
193D3×Q8—104no—
194D3×Q8—202no—
195C2×D12—101no—
196C2×D12—201no—
197C2×C4×D3—51no—
198C2×C4×D3—201no—
199C2×C4×D3—201no—
200C2×Dic6—101no—
201C2×Dic6—201no—
202C3×Q16—21no—
203C3×Q16—21no—
204C3×Q16C22×D512yes—
205C3×Q16C22×D512yes—
206C2×C3×C8C22×D511yescharacteristic
207#216—104no—
208#215—104no—
209C2×C3⋊C8—51no—
210Dic12—52no—
211Dic12—101no—
212D24—52no—
213D24—101no—
214D3×C8—52no—
215D3×C8—52no—
216C3×C16C22×D512yes—
217C3⋊C16—52no—
218C22×D5—31no—
219C22×D5—121no—
220C5×Q8—22no—
221C5×Q8—22no—
222C5×Q8—41no—
223C5×Q8—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5D3×D411yescharacteristic
227C2×Dic5—31no—
228C2×Dic5—121no—
229D20—62no—
230D20—124no—
231D20—121no—
232C4×D5—32no—
233C4×D5—32no—
234C4×D5—124no—
235C4×D5—124no—
236Dic10—62no—
237Dic10—124no—
238Dic10—121no—
239C5×C8D3×D411yescharacteristic
240C5×C8C23×D311yescharacteristic
241#168—32no—
242C2×#41—301no—
243C22×Q8—301no—
244#135—154no—
245#135—302no—
246C2×Q16—154no—
247C2×Q16—151no—
248C2×Q16—302no—
249C2×Q16—301no—
250C2×Q16C2×D1511yescharacteristic
251C2×Q16C2×D1511yescharacteristic
252C2×SD16—301no—
253C2×D8—151no—
254C22×C8—151no—
255Q32—154no—
256Q32C2×D1514yescomplemented
257SD32—154no—
258SD32—154no—
259M32—154no—
260C2×C16—151no—
261C2×C16C2×D1511yescharacteristic
262C2×C3×C5#51012yescomplemented
263C2×C3×C5C22×D811yescharacteristic
264D15—22no—
265D15—82no—
266C22×D3—51no—
267C22×D3—201no—
268C3×Q8—22no—
269C3×Q8—22no—
270C3×Q8—41no—
271C3×Q8—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4D4×D511yescharacteristic
275C2×Dic3—51no—
276C2×Dic3—201no—
277D12—102no—
278D12—204no—
279D12—201no—
280C4×D3—52no—
281C4×D3—52no—
282C4×D3—204no—
283C4×D3—204no—
284Dic6—102no—
285Dic6—204no—
286Dic6—201no—
287C3×C8D4×D511yescharacteristic
288C3×C8C23×D511yescharacteristic
289C3⋊C8—52no—
290C22×C5D3×D811yescharacteristic
291C2×D5—32no—
292C2×D5—62no—
293C2×D5—122no—
294C2×D5—242no—
295C4×C5—42no—
296C4×C5—42no—
297C4×C5D3×D811yescharacteristic
298C4×C5C2×D3×D411yescharacteristic
299Dic5—32no—
300Dic5—122no—
301#41—304no—
302#41—602no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—304no—
306C2×Q8—301no—
307C2×Q8—601no—
308C2×Q8—602no—
309C2×D4—301no—
310C2×D4—601no—
311C22×C4—151no—
312C22×C4—601no—
313C22×C4—601no—
314Q16—21no—
315Q16—21no—
316Q16—152no—
317Q16—304no—
318Q16—301no—
319Q16C22×D1512yes—
320Q16C22×D1512yes—
321SD16—304no—
322D8—152no—
323D8—301no—
324C2×C8—151no—
325C2×C8—152no—
326C2×C8—152no—
327C2×C8C22×D1511yescharacteristic
328C16—152no—
329C16C22×D1512yes—
330C3×C5C2×#51011yescharacteristic, complemented, Hall
331C22×C3D5×D811yescharacteristic
332C2×D3—52no—
333C2×D3—102no—
334C2×D3—202no—
335C2×D3—402no—
336C3×C4—42no—
337C3×C4—42no—
338C3×C4D5×D811yescharacteristic
339C3×C4C2×D4×D511yescharacteristic
340Dic3—52no—
341Dic3—202no—
342C2×C5#491812yescomplemented
343C2×C5C2×D3×D811yescharacteristic
344D5—62no—
345D5—242no—
346C23—151no—
347C23—601no—
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352Q8—302no—
353Q8—604no—
354Q8—601no—
355D4—302no—
356D4—604no—
357D4—601no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—151no—
361C2×C4—152no—
362C2×C4—152no—
363C2×C4—604no—
364C2×C4—604no—
365C2×C4—601no—
366C2×C4D4×D1511yescharacteristic
367C8—152no—
368C8D4×D1511yescharacteristic
369C8C23×D1511yescharacteristic
370C2×C3#6520712yescomplemented
371C2×C3C2×D5×D811yescharacteristic
372D3—102no—
373D3—402no—
374C5C2×#491811yescharacteristic, complemented, Sylow
375C22—152no—
376C22—302no—
377C22—602no—
378C22—1202no—
379C22D8×D1511yescharacteristic
380C4—42no—
381C4—42no—
382C4—152no—
383C4—602no—
384C4D8×D1511yescharacteristic
385C4C2×D4×D1511yescharacteristic
386C3C2×#6520711yescharacteristic, complemented, Sylow
387C2—302no—
388C2—1202no—
389C2#1175101912yesdirect product factor
390C2C2×D8×D1511yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC3×C5×C8C24
FrattiniC8C23×D15
FittingC2×C3×C5×Q32C2
socleC22×C3×C5C2×D8
prime radicalC2×#91808C2
hypercenterC2×Q32D15
hypocenterC3×C5C2×#510
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D15C2semidirect
3. C2×C3×C5×Q32C2semidirect
4. C2×#91113C2semidirect
5. C2×#91112C2semidirect
6. #11751019C2direct (N × H)
7. C2×#91084C2semidirect
8. C2×#91082C2semidirect
19. Q16×D15C22semidirect
23. C3×C5×Q32C22semidirect
25. #91113C22semidirect
26. #91112C22semidirect
28. #91084C22semidirect
29. #91082C22semidirect
33. C2×C5×Q32D3semidirect
70. C2×C3×Q32D5semidirect
89. C5×Q32C2×D3semidirect
134. C3×Q32C2×D5semidirect
174. C2×Q32D15semidirect
256. Q32C2×D15semidirect
262. C2×C3×C5#510semidirect
330. C3×C5C2×#510semidirect
342. C2×C5#4918semidirect
370. C2×C3#65207semidirect
374. C5C2×#4918semidirect
386. C3C2×#65207semidirect
389. C2#11751019direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918082
C2×Q16×D152
C2×C3×C5×Q322
C2×#911132
C2×#911122
#117510192
C2×#910842
C2×#910822
C2×#652073
C2×#49185