Finite Group Databasebeta

← C2×#11748269 #14478351

Subgroups — C2×#11748269 #14478351

Order 1920.

800 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91801C211yesmaximal, characteristic, complemented
2C2×#91256C211yesmaximal, characteristic, complemented
3C2×C5×#826C211yesmaximal, characteristic, complemented
4C2×C3×#3958C211yesmaximal, characteristic, complemented
5#11748269C218yesmaximal, direct product factor
6C2×#90944C211yesmaximal, characteristic, complemented
7C2×#90942C211yesmaximal, characteristic, complemented
8C2×#90936C211yesmaximal, characteristic, complemented
9C2×#65200—31nomaximal, Hall
10C2×#6819—21no—
11C2×#6777—21no—
12C2×C3×C5×D8C2211yescharacteristic, complemented
13C2×#6716—21no—
14#91801—22no—
15#91801C2214yescomplemented
16C2×Dic60C2211yescharacteristic, complemented
17C2×C8×D15C2211yescharacteristic
18C2×C5×D24C2211yescharacteristic
19C2×C3×D40C2211yescharacteristic
20C2×#6652—21no—
21#91256—22no—
22#91256C2214yescomplemented
23C5×#826C2214yescomplemented
24C2×C5×C3⋊C16C2211yescharacteristic, complemented
25C3×#3958C2214yescomplemented
26C2×C3×#672C2211yescharacteristic, complemented
27#90944C2214yescomplemented
28#90942C2214yescomplemented
29#90936C2214yescomplemented
30C2×#4911—51nomaximal, Hall
31C2×#4058—31no—
32C2×D5×D8—31no—
33C2×C5×D16—31no—
34C2×#3959—31no—
35C2×#3958D311yescharacteristic, complemented
36#65200—38no—
37C2×#3932—31no—
38C2×#3930—31no—
39C22×D3×D5—41no—
40C2×C3×C5×D4—21no—
41C2×#1220—41no—
42C22×Dic15—41no—
43#6819—24no—
44#6819—42no—
45C2×C4×D15D411yescharacteristic
46C2×Dic30—21no—
47C2×C5×D12—21no—
48C2×C3×D20—21no—
49C2×#1201—41no—
50#6777—24no—
51#6777—42no—
52C3×C5×D8—21no—
53C3×C5×D8C2312yescomplemented
54C2×C3×C5×C8C2311yescharacteristic
55#6716—24no—
56C2×C3⋊#168D411yescharacteristic
57Dic60—21no—
58Dic60C2312yescomplemented
59C8×D15D412yes—
60C8×D15C2312yes—
61C5×D24—21no—
62C5×D24C2312yes—
63C3×D40—21no—
64C3×D40C2312yes—
65#6652—24no—
66C3×#672C2312yescomplemented
67C5×C3⋊C16C2312yescomplemented
68C2×#912—51no—
69C2×D3×D8—51no—
70C2×C3×D16—51no—
71C2×#827—51no—
72C2×#826D511yescharacteristic, complemented
73#4911—58no—
74C2×#800—51no—
75C2×#798—51no—
76C2×#711—61no—
77C2×D4×D5—61no—
78C2×C5×D8—31no—
79C2×C5×D8C2×D311yescharacteristic, complemented
80C2×#687—61no—
81C2×#686—61no—
82#4058—34no—
83#4058—62no—
84D5×D8—34no—
85D5×D8—62no—
86C2×Dic20—31no—
87C2×D40C2×D311yescharacteristic
88C2×C8×D5—31no—
89C5×D16—34no—
90C2×C5×C16—31no—
91#3959—34no—
92#3958C2×D314yescomplemented
93C2×#672C2×D311yescharacteristic, complemented
94#3932—34no—
95#3930—34no—
96C2×#509—151noSylow
97C23×C3×C5—41no—
98C22×D15D811yescharacteristic
99C22×C5×D3—41no—
100C22×C3×D5—41no—
101C2×D3×D5—44no—
102C2×D3×D5—84no—
103C3×C5×D4—22no—
104C3×C5×D4—41no—
105C2×C3×C4×C5C2×D411yescharacteristic
106#1220—44no—
107C2×Dic15—41no—
108C2×Dic15—44no—
109C2×Dic15D811yescharacteristic
110C4×D15D812yes—
111C4×D15C2×D412yes—
112Dic30—22no—
113Dic30—41no—
114C5×D12—22no—
115C5×D12—41no—
116C3×D20—22no—
117C3×D20—41no—
118#1201—44no—
119C3×C5×C8C2×D411yescharacteristic
120C3×C5×C8C2411yescharacteristic
121C3⋊#168C2×D412yes—
122C2×#237—101no—
123C2×D3×D4—101no—
124C2×C3×D8—51no—
125C2×C3×D8C2×D511yescharacteristic, complemented
126C2×#214—101no—
127C2×#213—101no—
128#912—54no—
129#912—102no—
130D3×D8—54no—
131D3×D8—102no—
132C2×Dic12—51no—
133C2×D24C2×D511yescharacteristic
134C2×D3×C8—51no—
135C3×D16—54no—
136C2×C3×C16—51no—
137#827—54no—
138#826C2×D514yescomplemented
139C2×C3⋊C16C2×D511yescharacteristic, complemented
140#800—54no—
141#798—54no—
142C23×D5—121no—
143C2×C5×D4—21no—
144C2×C5×D4—61no—
145C2×C22⋊D5—121no—
146C2×C22⋊D5—121no—
147C22×Dic5—121no—
148#711—64no—
149#711—122no—
150D4×D5—64no—
151D4×D5—122no—
152C2×D20—21no—
153C2×C4×D5—31no—
154C2×Dic10—61no—
155C5×D8—21no—
156C5×D8—32no—
157C5×D8—61no—
158C5×D8C22×D312yescomplemented
159C2×C5×C8C22×D311yescharacteristic
160#687—64no—
161#686—64no—
162C2×#168—31no—
163Dic20—32no—
164Dic20—61no—
165D40—21no—
166D40C22×D312yes—
167C8×D5—32no—
168C8×D5—32no—
169C5×C16—32no—
170#672C22×D312yescomplemented
171C2×#135—151no—
172C22×D8—151no—
173#509—158no—
174C2×SD32—151no—
175C2×SD32—151no—
176C2×D16—31no—
177C2×D16—51no—
178C2×M32—151no—
179C22×C3×C5—42no—
180C22×C3×C5—82no—
181C22×C3×C5C2×D811yescharacteristic
182C2×D15—22no—
183C2×D15C2×D812yes—
184C2×C5×D3—42no—
185C2×C5×D3—82no—
186C2×C3×D5—42no—
187C2×C3×D5—82no—
188D3×D5—88no—
189C3×C4×C5C2×D811yescharacteristic
190C3×C4×C5C22×D411yescharacteristic
191Dic15—42no—
192Dic15C2×D812yes—
193C23×D3—201no—
194C2×C3×D4—21no—
195C2×C3×D4—101no—
196C2×#67—201no—
197C2×#67—201no—
198C22×Dic3—201no—
199#237—104no—
200#237—202no—
201D3×D4—104no—
202D3×D4—202no—
203C2×D12—21no—
204C2×C4×D3—51no—
205C2×Dic6—101no—
206C3×D8—21no—
207C3×D8—52no—
208C3×D8—101no—
209C3×D8C22×D512yescomplemented
210C2×C3×C8C22×D511yescharacteristic
211#214—104no—
212#213—104no—
213C2×C3⋊C8—51no—
214Dic12—52no—
215Dic12—101no—
216D24—21no—
217D24C22×D512yes—
218D3×C8—52no—
219D3×C8—52no—
220C3×C16—52no—
221C3⋊C16C22×D512yescomplemented
222C23×C5—41no—
223C23×C5—121no—
224C22×D5—31no—
225C22×D5—41no—
226C22×D5—124no—
227C22×D5—244no—
228C5×D4—22no—
229C5×D4—41no—
230C5×D4—62no—
231C5×D4—121no—
232C2×C4×C5D3×D411yescharacteristic
233C22⋊D5—124no—
234C22⋊D5—124no—
235C2×Dic5—31no—
236C2×Dic5—124no—
237C2×Dic5—121no—
238D20—22no—
239D20—41no—
240C4×D5—32no—
241C4×D5—32no—
242Dic10—62no—
243Dic10—121no—
244C5×C8D3×D411yescharacteristic
245C5×C8C23×D311yescharacteristic
246#168—32no—
247C2×#41—301no—
248C22×D4—301no—
249#135—154no—
250#135—302no—
251C2×Q16—151no—
252C2×SD16—301no—
253C2×D8—31no—
254C2×D8—51no—
255C2×D8—154no—
256C2×D8—302no—
257C2×D8—301no—
258C2×D8D3×D511yescharacteristic, complemented
259C22×C8—151no—
260SD32—154no—
261SD32—154no—
262D16—34no—
263D16—54no—
264M32—154no—
265C2×C16—31no—
266C2×C16—51no—
267C2×C3×C5—82no—
268C2×C3×C5#50912yescomplemented
269C2×C3×C5C22×D811yescharacteristic
270D15—22no—
271C3×D5—82no—
272C5×D3—82no—
273C23×C3—41no—
274C23×C3—201no—
275C22×D3—41no—
276C22×D3—51no—
277C22×D3—204no—
278C22×D3—404no—
279C3×D4—22no—
280C3×D4—41no—
281C3×D4—102no—
282C3×D4—201no—
283C2×C3×C4D4×D511yescharacteristic
284#67—204no—
285#67—204no—
286C2×Dic3—51no—
287C2×Dic3—204no—
288C2×Dic3—201no—
289D12—22no—
290D12—41no—
291C4×D3—52no—
292C4×D3—52no—
293Dic6—102no—
294Dic6—201no—
295C3×C8D4×D511yescharacteristic
296C3×C8C23×D511yescharacteristic
297C3⋊C8—52no—
298C22×C5—42no—
299C22×C5—82no—
300C22×C5—122no—
301C22×C5—242no—
302C22×C5D3×D811yescharacteristic
303C2×D5—32no—
304C2×D5—42no—
305C2×D5—62no—
306C2×D5—82no—
307C2×D5—248no—
308C4×C5D3×D811yescharacteristic
309C4×C5C2×D3×D411yescharacteristic
310Dic5—32no—
311Dic5—122no—
312C24—601no—
313#41—304no—
314#41—602no—
315C2×Q8—301no—
316C2×D4—21no—
317C2×D4—61no—
318C2×D4—101no—
319C2×D4—304no—
320C2×D4—602no—
321C2×D4—601no—
322C2×D4—601no—
323C22×C4—151no—
324C22×C4—601no—
325Q16—152no—
326Q16—301no—
327SD16—304no—
328D8—21no—
329D8—32no—
330D8—52no—
331D8—61no—
332D8—101no—
333D8—304no—
334D8C2×D3×D512yescomplemented
335C2×C8—151no—
336C2×C8—152no—
337C2×C8—152no—
338C2×C8C2×D3×D511yescharacteristic
339C16—32no—
340C16—52no—
341C3×C5C2×#50911yescharacteristic, complemented, Hall
342C22×C3—42no—
343C22×C3—82no—
344C22×C3—202no—
345C22×C3—402no—
346C22×C3D5×D811yescharacteristic
347C2×D3—42no—
348C2×D3—52no—
349C2×D3—82no—
350C2×D3—102no—
351C2×D3—408no—
352C3×C4D5×D811yescharacteristic
353C3×C4C2×D4×D511yescharacteristic
354Dic3—52no—
355Dic3—202no—
356C2×C5—82no—
357C2×C5—242no—
358C2×C5#491112yescomplemented
359C2×C5C2×D3×D811yescharacteristic
360D5—62no—
361D5—82no—
362C23—41no—
363C23—121no—
364C23—151no—
365C23—201no—
366C23—604no—
367C23—1204no—
368Q8—302no—
369Q8—601no—
370D4—22no—
371D4—41no—
372D4—62no—
373D4—102no—
374D4—121no—
375D4—201no—
376D4—604no—
377D4—604no—
378C2×C4—151no—
379C2×C4—152no—
380C2×C4—152no—
381C2×C4—604no—
382C2×C4—601no—
383C2×C4#679011yescharacteristic
384C8—152no—
385C8#679011yescharacteristic
386C8C22×D3×D511yescharacteristic
387C2×C3—82no—
388C2×C3—402no—
389C2×C3#6520012yescomplemented
390C2×C3C2×D5×D811yescharacteristic
391D3—82no—
392D3—102no—
393C5C2×#491111yescharacteristic, complemented, Sylow
394C22—42no—
395C22—82no—
396C22—122no—
397C22—152no—
398C22—202no—
399C22—242no—
400C22—302no—
401C22—402no—
402C22—1208no—
403C22#9148111yescharacteristic
404C4—152no—
405C4—602no—
406C4#9148111yescharacteristic
407C4C2×#679011yescharacteristic
408C3C2×#6520011yescharacteristic, complemented, Sylow
409C2—82no—
410C2—242no—
411C2—302no—
412C2—402no—
413C2#1174826912yesdirect product factor
414C2C2×#9148111yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C2×D8
hypercenterC2×D8D3×D5
hypocenterC3×C5C2×#509
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#91801C2semidirect
2. C2×#91256C2semidirect
3. C2×C5×#826C2semidirect
4. C2×C3×#3958C2semidirect
5. #11748269C2direct (N × H)
6. C2×#90944C2semidirect
7. C2×#90942C2semidirect
8. C2×#90936C2semidirect
12. C2×C3×C5×D8C22semidirect
15. #91801C22semidirect
16. C2×Dic60C22semidirect
22. #91256C22semidirect
23. C5×#826C22semidirect
24. C2×C5×C3⋊C16C22semidirect
25. C3×#3958C22semidirect
26. C2×C3×#672C22semidirect
27. #90944C22semidirect
28. #90942C22semidirect
29. #90936C22semidirect
35. C2×#3958D3semidirect
53. C3×C5×D8C23semidirect
58. Dic60C23semidirect
66. C3×#672C23semidirect
67. C5×C3⋊C16C23semidirect
72. C2×#826D5semidirect
79. C2×C5×D8C2×D3semidirect
92. #3958C2×D3semidirect
93. C2×#672C2×D3semidirect
125. C2×C3×D8C2×D5semidirect
138. #826C2×D5semidirect
139. C2×C3⋊C16C2×D5semidirect
158. C5×D8C22×D3semidirect
170. #672C22×D3semidirect
209. C3×D8C22×D5semidirect
221. C3⋊C16C22×D5semidirect
258. C2×D8D3×D5semidirect
268. C2×C3×C5#509semidirect
334. D8C2×D3×D5semidirect
341. C3×C5C2×#509semidirect
358. C2×C5#4911semidirect
389. C2×C3#65200semidirect
393. C5C2×#4911semidirect
408. C3C2×#65200semidirect
413. C2#11748269direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918012
C2×#912562
C2×C5×#8262
C2×C3×#39582
#117482692
C2×#909442
C2×#909422
C2×#909362
C2×#652003
C2×#49115