Finite Group Databasebeta

← C2×C5×#548⋊C3 #14511332

Subgroups — C2×C5×#548⋊C3 #14511332

Order 1920.

850 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C22×C5×#41⋊C3C211yesmaximal, characteristic, complemented
2C23×C5×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3C5×#548⋊C3C214yesmaximal, direct product factor
4C2×C4×C5×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
5C2×C5×#548C311yesmaximal, characteristic, complemented, Hall
6C2×C5×#41⋊C3—22no—
7C2×C5×#41⋊C3C2212yescomplemented
8C22×C5×SL(2,𝔽3)—22no—
9C22×C5×SL(2,𝔽3)C2211yescharacteristic
10C22×C5×SL(2,𝔽3)C2212yescomplemented
11C2×C3×C5×C22⋊C4—41nomaximal
12C4×C5×SL(2,𝔽3)C2212yescomplemented
13C2×#548⋊C3C511yesmaximal, characteristic, direct product factor, Hall
14C22×C5×#41C2×C311yescharacteristic, complemented
15C23×C5×Q8C2×C311yescharacteristic
16C5×#548—34no—
17C5×#548C2×C314yescomplemented
18C2×C5×#124—31no—
19C2×C5×C22⋊Q8—31no—
20C2×C5×#121—31no—
21C2×C4×C5×Q8C2×C311yescharacteristic, complemented
22C2×C4×C5×D4—31no—
23C24×C3×C5—41no—
24C22×C3×C4×C5—41no—
25C22×C3×C4×C5—41no—
26C5×#41⋊C3—22no—
27C2×C5×SL(2,𝔽3)—22no—
28C2×C5×SL(2,𝔽3)D412yescomplemented
29C2×C5×SL(2,𝔽3)C2311yescharacteristic
30C3×C5×C22⋊C4—44no—
31C22×#41⋊C3C2×C511yescharacteristic, complemented
32C23×SL(2,𝔽3)C2×C511yescharacteristic, complemented
33#548⋊C3C2×C514yesdirect product factor
34C2×C4×SL(2,𝔽3)C2×C511yescharacteristic, complemented
35C2×C5×#41—22no—
36C2×C5×#41—32no—
37C2×C5×#41—62no—
38C2×C5×#41C22×C312yescomplemented
39C22×C5×Q8—22no—
40C22×C5×Q8—31no—
41C22×C5×Q8—32no—
42C22×C5×Q8—62no—
43C22×C5×Q8C22×C312yes—
44C22×C5×Q8C22×C311yescharacteristic
45C22×C5×D4—31no—
46C22×C5×D4—31no—
47C23×C4×C5—31no—
48C23×C4×C5—31no—
49C5×#124—34no—
50C5×#124—34no—
51C5×C22⋊Q8—34no—
52C5×C22⋊Q8—34no—
53C5×#121—34no—
54C5×#121—34no—
55C4×C5×Q8—32no—
56C4×C5×Q8C22×C312yescomplemented
57C4×C5×D4—34no—
58C4×C5×D4—34no—
59C2×C5×C4⋊C4—31no—
60C2×C5×C4⋊C4—31no—
61C2×C5×C22⋊C4—32no—
62C2×C5×C22⋊C4—31no—
63C2×C5×C22⋊C4A411yescharacteristic
64C2×C42×C5—31no—
65C2×#548C3×C511yescharacteristic, complemented, Sylow
66C23×C3×C5—41no—
67C23×C3×C5—44no—
68C23×C3×C5—42no—
69C23×C3×C5—82no—
70C23×C3×C5—82no—
71C2×C3×C4×C5—42no—
72C2×C3×C4×C5—42no—
73C2×C3×C4×C5—82no—
74C2×C3×C4×C5—82no—
75C5×SL(2,𝔽3)C2×D411yescharacteristic, complemented
76C2×#41⋊C3—22no—
77C2×#41⋊C3C22×C512yescomplemented
78C22×SL(2,𝔽3)—22no—
79C22×SL(2,𝔽3)C22×C511yescharacteristic
80C22×SL(2,𝔽3)C22×C512yescomplemented
81C2×C3×C22⋊C4—41no—
82C4×SL(2,𝔽3)C22×C512yescomplemented
83C24×C5—31no—
84C24×C5C2×A411yescharacteristic
85C5×#41—22no—
86C5×#41—64no—
87C5×#41—64no—
88C5×#41—62no—
89C2×C5×Q8—22no—
90C2×C5×Q8—32no—
91C2×C5×Q8—31no—
92C2×C5×Q8—32no—
93C2×C5×Q8—32no—
94C2×C5×Q8—62no—
95C2×C5×Q8—62no—
96C2×C5×Q8—64no—
97C2×C5×Q8—62no—
98C2×C5×Q8—64no—
99C2×C5×Q8C3×D412yes—
100C2×C5×Q8C23×C311yescharacteristic
101C2×C5×D4—32no—
102C2×C5×D4—32no—
103C2×C5×D4—34no—
104C2×C5×D4—62no—
105C2×C5×D4—62no—
106C2×C5×D4—64no—
107C22×C4×C5—31no—
108C22×C4×C5—32no—
109C22×C4×C5—32no—
110C22×C4×C5—31no—
111C22×C4×C5—31no—
112C22×C4×C5—32no—
113C22×C4×C5—32no—
114C22×C4×C5—62no—
115C22×C4×C5—62no—
116C22×C4×C5—62no—
117C22×C4×C5—62no—
118C22×C4×C5C2×A411yescharacteristic
119C22×C4×C5C2×A411yescharacteristic
120C5×C4⋊C4—32no—
121C5×C4⋊C4—32no—
122C5×C4⋊C4—34no—
123C5×C22⋊C4—38no—
124C5×C22⋊C4—34no—
125C5×C22⋊C4C2×A414yes—
126C42×C5—32no—
127C42×C5—32no—
128C22×#41C2×C3×C511yescharacteristic, complemented
129C23×Q8C2×C3×C511yescharacteristic
130#548—34no—
131#548C2×C3×C514yescomplemented
132C2×#124—31no—
133C2×C22⋊Q8—31no—
134C2×#121—31no—
135C2×C4×Q8C2×C3×C511yescharacteristic, complemented
136C2×C4×D4—31no—
137C22×C3×C5—42no—
138C22×C3×C5—42no—
139C22×C3×C5—44no—
140C22×C3×C5—42no—
141C22×C3×C5—41no—
142C22×C3×C5—82no—
143C22×C3×C5—82no—
144C22×C3×C5—88no—
145C3×C4×C5—82no—
146C3×C4×C5—82no—
147C24×C3—41no—
148C22×C3×C4—41no—
149C22×C3×C4—41no—
150#41⋊C3—22no—
151C2×SL(2,𝔽3)—22no—
152C2×SL(2,𝔽3)C5×D412yescomplemented
153C2×SL(2,𝔽3)C23×C511yescharacteristic
154C3×C22⋊C4—44no—
155C23×C5—22no—
156C23×C5—22no—
157C23×C5—32no—
158C23×C5—62no—
159C23×C5—62no—
160C23×C5—62no—
161C23×C5#41⋊C314yescomplemented
162C23×C5C22×A412yes—
163C23×C5C22×A411yescharacteristic
164C5×Q8—32no—
165C5×Q8—31no—
166C5×Q8—32no—
167C5×Q8—62no—
168C5×Q8—62no—
169C5×Q8—64no—
170C5×Q8C2×C3×D411yescharacteristic
171C5×D4—62no—
172C5×D4—62no—
173C5×D4—64no—
174C5×D4—68no—
175C2×C4×C5—22no—
176C2×C4×C5—22no—
177C2×C4×C5—32no—
178C2×C4×C5—32no—
179C2×C4×C5—31no—
180C2×C4×C5—31no—
181C2×C4×C5—32no—
182C2×C4×C5—32no—
183C2×C4×C5—62no—
184C2×C4×C5—64no—
185C2×C4×C5—62no—
186C2×C4×C5—62no—
187C2×C4×C5—64no—
188C2×C4×C5—62no—
189C2×C4×C5—62no—
190C2×C4×C5—62no—
191C2×C4×C5C22×A412yes—
192C2×C4×C5C22×A412yes—
193C2×#41—22no—
194C2×#41—32no—
195C2×#41—62no—
196C2×#41C22×C3×C512yescomplemented
197C22×Q8—22no—
198C22×Q8—31no—
199C22×Q8—32no—
200C22×Q8—62no—
201C22×Q8C22×C3×C512yes—
202C22×Q8C22×C3×C511yescharacteristic
203C22×D4—31no—
204C22×D4—31no—
205C23×C4—31no—
206C23×C4—31no—
207#124—34no—
208#124—34no—
209C22⋊Q8—34no—
210C22⋊Q8—34no—
211#121—34no—
212#121—34no—
213C4×Q8—32no—
214C4×Q8C22×C3×C512yescomplemented
215C4×D4—34no—
216C4×D4—34no—
217C2×C4⋊C4—31no—
218C2×C4⋊C4—31no—
219C2×C22⋊C4—32no—
220C2×C22⋊C4—31no—
221C2×C22⋊C4C5×A411yescharacteristic
222C2×C42—31no—
223C2×C3×C5—41no—
224C2×C3×C5—41no—
225C2×C3×C5—41no—
226C2×C3×C5—44no—
227C2×C3×C5—84no—
228C23×C3—44no—
229C23×C3—41no—
230C23×C3—42no—
231C23×C3—82no—
232C23×C3—82no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—82no—
236C2×C3×C4—82no—
237SL(2,𝔽3)C2×C5×D411yescharacteristic, complemented
238C22×C5—22no—
239C22×C5—22no—
240C22×C5—28no—
241C22×C5—62no—
242C22×C5—62no—
243C22×C5—62no—
244C22×C5—124no—
245C22×C5D4×A412yes—
246C22×C5C2×#41⋊C312yes—
247C22×C5C2×#41⋊C314yescomplemented
248C22×C52−1+4⋊C312yes—
249C22×C5C23×A411yescharacteristic
250C4×C5—22no—
251C4×C5—22no—
252C4×C5—31no—
253C4×C5—32no—
254C4×C5—31no—
255C4×C5—62no—
256C4×C5—62no—
257C24—31no—
258C24C2×C5×A411yescharacteristic
259#41—22no—
260#41—64no—
261#41—64no—
262#41—62no—
263C2×Q8—22no—
264C2×Q8—32no—
265C2×Q8—31no—
266C2×Q8—32no—
267C2×Q8—32no—
268C2×Q8—62no—
269C2×Q8—62no—
270C2×Q8—64no—
271C2×Q8—62no—
272C2×Q8—64no—
273C2×Q8C3×C5×D412yes—
274C2×Q8C23×C3×C511yescharacteristic
275C2×D4—32no—
276C2×D4—32no—
277C2×D4—34no—
278C2×D4—62no—
279C2×D4—62no—
280C2×D4—64no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—31no—
284C22×C4—32no—
285C22×C4—32no—
286C22×C4—32no—
287C22×C4—32no—
288C22×C4—62no—
289C22×C4—62no—
290C22×C4—62no—
291C22×C4—62no—
292C22×C4C2×C5×A411yescharacteristic
293C22×C4C2×C5×A411yescharacteristic
294C4⋊C4—32no—
295C4⋊C4—32no—
296C4⋊C4—34no—
297C22⋊C4—38no—
298C22⋊C4—34no—
299C22⋊C4C2×C5×A414yes—
300C42—32no—
301C42—32no—
302C3×C5—41noHall
303C22×C3—42no—
304C22×C3—42no—
305C22×C3—44no—
306C22×C3—42no—
307C22×C3—41no—
308C22×C3—82no—
309C22×C3—88no—
310C22×C3—82no—
311C3×C4—82no—
312C3×C4—82no—
313C2×C5—24no—
314C2×C5—122no—
315C2×C5#548⋊C314yesdirect product factor
316C2×C5C2×D4×A411yescharacteristic
317C2×C5C22×#41⋊C311yescharacteristic
318C2×C5C2×2−1+4⋊C311yescharacteristic
319C23—22no—
320C23—22no—
321C23—32no—
322C23—62no—
323C23—62no—
324C23—62no—
325C23C5×#41⋊C314yescomplemented
326C23C22×C5×A412yes—
327C23C22×C5×A411yescharacteristic
328Q8—32no—
329Q8—31no—
330Q8—32no—
331Q8—62no—
332Q8—62no—
333Q8—64no—
334Q8C2×C3×C5×D411yescharacteristic
335D4—62no—
336D4—62no—
337D4—64no—
338D4—68no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—32no—
342C2×C4—32no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—32no—
346C2×C4—32no—
347C2×C4—62no—
348C2×C4—62no—
349C2×C4—64no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—64no—
353C2×C4—62no—
354C2×C4—62no—
355C2×C4C22×C5×A412yes—
356C2×C4C22×C5×A412yes—
357C2×C3—41no—
358C2×C3—41no—
359C2×C3—41no—
360C2×C3—44no—
361C2×C3—84no—
362C5C2×#548⋊C311yescharacteristic, direct product factor, Sylow
363C22—22no—
364C22—22no—
365C22—28no—
366C22—62no—
367C22—62no—
368C22—62no—
369C22—124no—
370C22C5×D4×A412yes—
371C22C2×C5×#41⋊C312yes—
372C22C2×C5×#41⋊C314yescomplemented
373C22C5×2−1+4⋊C312yes—
374C22C23×C5×A411yescharacteristic
375C4—22no—
376C4—22no—
377C4—31no—
378C4—32no—
379C4—31no—
380C4—62no—
381C4—62no—
382C3—41noSylow
383C2—24no—
384C2—122no—
385C2C5×#548⋊C314yesdirect product factor
386C2C2×C5×D4×A411yescharacteristic
387C2C22×C5×#41⋊C311yescharacteristic
388C2C2×C5×2−1+4⋊C311yescharacteristic
subgroupG/H
center, socleC23×C5C22×A4
commutator, cosocleC2×Q8C23×C3×C5
FrattiniC22C23×C5×A4
FittingC2×C5×#548C3
hypercenterC2×C5×C22⋊C4A4
hypocenterQ8C2×C3×C5×D4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C23×C5 ◁ C2×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#41⋊C3C2semidirect
2. C23×C5×SL(2,𝔽3)C2semidirect
3. C5×#548⋊C3C2direct (N × H)
4. C2×C4×C5×SL(2,𝔽3)C2semidirect
5. C2×C5×#548C3semidirect
7. C2×C5×#41⋊C3C22semidirect
10. C22×C5×SL(2,𝔽3)C22semidirect
12. C4×C5×SL(2,𝔽3)C22semidirect
13. C2×#548⋊C3C5direct (N × H)
14. C22×C5×#41C2×C3semidirect
17. C5×#548C2×C3semidirect
21. C2×C4×C5×Q8C2×C3semidirect
28. C2×C5×SL(2,𝔽3)D4semidirect
31. C22×#41⋊C3C2×C5semidirect
32. C23×SL(2,𝔽3)C2×C5semidirect
33. #548⋊C3C2×C5direct (N × H)
34. C2×C4×SL(2,𝔽3)C2×C5semidirect
38. C2×C5×#41C22×C3semidirect
56. C4×C5×Q8C22×C3semidirect
65. C2×#548C3×C5semidirect
75. C5×SL(2,𝔽3)C2×D4semidirect
77. C2×#41⋊C3C22×C5semidirect
80. C22×SL(2,𝔽3)C22×C5semidirect
82. C4×SL(2,𝔽3)C22×C5semidirect
128. C22×#41C2×C3×C5semidirect
131. #548C2×C3×C5semidirect
135. C2×C4×Q8C2×C3×C5semidirect
152. C2×SL(2,𝔽3)C5×D4semidirect
161. C23×C5#41⋊C3semidirect
196. C2×#41C22×C3×C5semidirect
214. C4×Q8C22×C3×C5semidirect
237. SL(2,𝔽3)C2×C5×D4semidirect
247. C22×C5C2×#41⋊C3semidirect
315. C2×C5#548⋊C3direct (N × H)
325. C23C5×#41⋊C3semidirect
362. C5C2×#548⋊C3direct (N × H)
372. C22C2×C5×#41⋊C3semidirect
385. C2C5×#548⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#41⋊C32
C23×C5×SL(2,𝔽3)2
C5×#548⋊C32
C2×C4×C5×SL(2,𝔽3)2
C2×C5×#5483
C2×C3×C5×C22⋊C44
C2×#548⋊C35