Finite Group Databasebeta

← D5×AGL(1,ℤ/8) #66106

Subgroups — D5×AGL(1,ℤ/8) #66106

Order 320.

298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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
1D5×#41C211yesmaximal, characteristic, complemented
2C2×D4×D5C211yesmaximal, characteristic, complemented
3C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4#4095C211yesmaximal, characteristic, complemented
5#4078C211yesmaximal, characteristic, complemented
6#4060C212yesmaximal, complemented
7D5×SD16C212yesmaximal, complemented
8#4057C212yesmaximal, complemented
9D5×D8C212yesmaximal, complemented
10#4054C211yesmaximal, characteristic, complemented
11D5×M16C211yesmaximal, characteristic, complemented
12C23×D5—21no—
13C5×#41C2211yescharacteristic, complemented
14C2×C5×D4C2211yescharacteristic, complemented
15C2×C22⋊D5—21no—
16#713C2211yescharacteristic, complemented
17Q8×D5C2211yescharacteristic, complemented
18#711—21no—
19#711C2211yescharacteristic, complemented
20D4×D5—21no—
21D4×D5—21no—
22D4×D5—21no—
23D4×D5C2212yes—
24D4×D5C2212yescomplemented
25D4×D5C2211yescharacteristic, complemented
26#709—21no—
27#709C2211yescharacteristic, complemented
28C2×D20C2211yescharacteristic, complemented
29C2×C4×D5—21no—
30C2×C4×D5C2211yescharacteristic
31C5×SD16C2212yescomplemented
32C5×D8C2212yescomplemented
33C5×M16C2211yescharacteristic, complemented
34#688C2212yescomplemented
35#687C2212yescomplemented
36#686C2212yescomplemented
37#686C2212yescomplemented
38#681C2211yescharacteristic, complemented
39D40C2212yescomplemented
40#677C2212yescomplemented
41#676C2212yescomplemented
42C8×D5C2212yescomplemented
43C2×AGL(1,ℤ/8)—51nomaximal, Sylow
44C23×C5—21no—
45C22×D5—21no—
46C22×D5—21no—
47C22×D5—22no—
48C22×D5—22no—
49C22×D5—44no—
50C22×D5D411yescharacteristic
51C5×Q8C2311yescharacteristic, complemented
52C5×D4—21no—
53C5×D4—21no—
54C5×D4C2312yes—
55C5×D4C2311yescharacteristic, complemented
56C2×C4×C5—21no—
57C2×C4×C5C2311yescharacteristic
58C22⋊D5—21no—
59C22⋊D5—21no—
60C22⋊D5—21no—
61C22⋊D5—22no—
62C22⋊D5—22no—
63C2×Dic5—21no—
64C2×Dic5D411yescharacteristic
65D20—21no—
66D20—21no—
67D20C2312yes—
68D20C2311yescharacteristic, complemented
69C4×D5—21no—
70C4×D5—21no—
71C4×D5—21no—
72C4×D5D411yescharacteristic
73C4×D5D411yescharacteristic
74C4×D5C2311yescharacteristic
75C4×D5C2311yescharacteristic
76Dic10—21no—
77Dic10C2311yescharacteristic, complemented
78C5×C8C2312yescomplemented
79#168C2312yescomplemented
80C2×#41—51no—
81C22×D4—51no—
82AGL(1,ℤ/8)—51no—
83AGL(1,ℤ/8)—51no—
84AGL(1,ℤ/8)—52no—
85AGL(1,ℤ/8)—52no—
86AGL(1,ℤ/8)—51no—
87AGL(1,ℤ/8)D511yescharacteristic, direct product factor
88C2×SD16—52no—
89C2×D8—52no—
90C2×M16—51no—
91C22×C5—21no—
92C22×C5—22no—
93C22×C5—42no—
94C22×C5C2×D411yescharacteristic
95C2×D5—22no—
96C2×D5—21no—
97C2×D5—22no—
98C2×D5—44no—
99C2×D5—42no—
100C2×D5—42no—
101C2×D5—44no—
102C2×D5C2×D411yescharacteristic
103C2×D5C2×D411yescharacteristic
104C4×C5—21no—
105C4×C5C2×D411yescharacteristic
106C4×C5C2411yescharacteristic
107Dic5—21no—
108Dic5C2×D411yescharacteristic
109Dic5C2×D411yescharacteristic
110C24—101no—
111#41—51no—
112#41—51no—
113#41—51no—
114#41—101no—
115#41—101no—
116#41C2×D511yescharacteristic, complemented
117C2×Q8—51no—
118C2×D4—52no—
119C2×D4—52no—
120C2×D4—51no—
121C2×D4—51no—
122C2×D4—101no—
123C2×D4—101no—
124C2×D4—101no—
125C2×D4—101no—
126C2×D4C2×D511yescharacteristic, complemented
127C22×C4—51no—
128C22×C4—101no—
129SD16—52no—
130SD16—52no—
131SD16—52no—
132SD16C2×D512yescomplemented
133D8—52no—
134D8—52no—
135D8—52no—
136D8C2×D512yescomplemented
137M16—51no—
138M16—52no—
139M16C2×D511yescharacteristic, complemented
140C2×C8—52no—
141C2×C5—21no—
142C2×C5—42no—
143C2×C5—41no—
144C2×C5C22×D411yescharacteristic
145D5—21no—
146D5—41no—
147D5—42no—
148D5AGL(1,ℤ/8)12yesdirect product factor
149C23—21no—
150C23—51no—
151C23—101no—
152C23—102no—
153C23—102no—
154C23—101no—
155C23—204no—
156Q8—51no—
157Q8—101no—
158Q8C22×D511yescharacteristic, complemented
159D4—21no—
160D4—21no—
161D4—51no—
162D4—52no—
163D4—101no—
164D4—102no—
165D4—102no—
166D4—101no—
167D4—101no—
168D4—101no—
169D4—101no—
170D4C22×D512yes—
171D4C22×D511yescharacteristic, complemented
172C2×C4—21no—
173C2×C4—51no—
174C2×C4—51no—
175C2×C4—51no—
176C2×C4—51no—
177C2×C4—51no—
178C2×C4—101no—
179C2×C4—101no—
180C2×C4—101no—
181C2×C4—101no—
182C2×C4C22×D511yescharacteristic
183C8—52no—
184C8C22×D512yescomplemented
185C5C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
186C22—21no—
187C22—22no—
188C22—42no—
189C22—51no—
190C22—51no—
191C22—102no—
192C22—101no—
193C22—102no—
194C22—202no—
195C22—204no—
196C22—202no—
197C22—204no—
198C22D4×D511yescharacteristic
199C4—21no—
200C4—51no—
201C4—51no—
202C4—101no—
203C4D4×D511yescharacteristic
204C4C23×D511yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—52no—
209C2—101no—
210C2—202no—
211C2—201no—
212C2C2×D4×D511yescharacteristic
subgroupG/H
centerC2C2×D4×D5
commutator, cosocleC4×C5C24
FrattiniC4C23×D5
FittingC5×AGL(1,ℤ/8)C2
socleC2×C5C22×D4
hypercenterAGL(1,ℤ/8)D5
hypocenterC5C2×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. D5×#41C2semidirect
2. C2×D4×D5C2semidirect
3. C5×AGL(1,ℤ/8)C2semidirect
4. #4095C2semidirect
5. #4078C2semidirect
6. #4060C2semidirect
7. D5×SD16C2semidirect
8. #4057C2semidirect
9. D5×D8C2semidirect
10. #4054C2semidirect
11. D5×M16C2semidirect
13. C5×#41C22semidirect
14. C2×C5×D4C22semidirect
16. #713C22semidirect
17. Q8×D5C22semidirect
19. #711C22semidirect
24. D4×D5C22semidirect
25. D4×D5C22semidirect
27. #709C22semidirect
28. C2×D20C22semidirect
31. C5×SD16C22semidirect
32. C5×D8C22semidirect
33. C5×M16C22semidirect
34. #688C22semidirect
35. #687C22semidirect
36. #686C22semidirect
37. #686C22semidirect
38. #681C22semidirect
39. D40C22semidirect
40. #677C22semidirect
41. #676C22semidirect
42. C8×D5C22semidirect
51. C5×Q8C23semidirect
55. C5×D4C23semidirect
68. D20C23semidirect
77. Dic10C23semidirect
78. C5×C8C23semidirect
79. #168C23semidirect
87. AGL(1,ℤ/8)D5direct (N × H)
116. #41C2×D5semidirect
126. C2×D4C2×D5semidirect
132. SD16C2×D5semidirect
136. D8C2×D5semidirect
139. M16C2×D5semidirect
148. D5AGL(1,ℤ/8)direct (N × H)
158. Q8C22×D5semidirect
171. D4C22×D5semidirect
184. C8C22×D5semidirect
185. C5C2×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
D5×#412
C2×D4×D52
C5×AGL(1,ℤ/8)2
#40952
#40782
#40602
D5×SD162
#40572
D5×D82
#40542
D5×M162
C2×AGL(1,ℤ/8)5