Finite Group Databasebeta

← #66096

Subgroups — #66096

Order 320.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#4147C211yesmaximal, characteristic, complemented
2#4144C211yesmaximal, characteristic, complemented
3C2×C5×SD16C211yesmaximal, characteristic, complemented
4#4088C211yesmaximal, characteristic, complemented
5#4078C211yesmaximal, characteristic, complemented
6#4062C212yesmaximal, complemented
7#4061C212yesmaximal, complemented
8#4060C212yesmaximal, complemented
9D5×SD16C212yesmaximal, complemented
10#4050C211yesmaximal, characteristic, complemented
11#4047C211yesmaximal, characteristic, complemented
12C2×C5×Q8C2211yescharacteristic, complemented
13C2×C5×D4C2211yescharacteristic
14C2×C22⋊D5—22no—
15#713—21no—
16#713C2212yescomplemented
17Q8×D5—21no—
18Q8×D5C2212yescomplemented
19#711—21no—
20#711C2212yes—
21D4×D5—21no—
22D4×D5C2212yes—
23#709—22no—
24#709C2211yescharacteristic
25#709C2211yescharacteristic
26#709C2211yescharacteristic, complemented
27C5×SD16C2212yescomplemented
28C5×SD16C2212yescomplemented
29C2×C5×C8C2211yescharacteristic, complemented
30#689C2212yescomplemented
31#688C2212yescomplemented
32#687C2212yescomplemented
33#686C2212yescomplemented
34#681C2211yescharacteristic, complemented
35Dic20C2211yescharacteristic, complemented
36D40C2211yescharacteristic, complemented
37#677C2211yescharacteristic, complemented
38#677C2211yescharacteristic, complemented
39#676C2212yescomplemented
40C8×D5C2212yescomplemented
41#577—51nomaximal, Sylow
42C23×C5—21no—
43C22×D5—22no—
44C5×Q8—21no—
45C5×Q8C2312yes—
46C5×D4—21no—
47C5×D4C2312yes—
48C2×C4×C5—21no—
49C2×C4×C5C2311yescharacteristic
50C22⋊D5—21no—
51C22⋊D5—21no—
52C22⋊D5—22no—
53C22⋊D5—22no—
54C22⋊D5D412yes—
55C2×Dic5—22no—
56D20—22no—
57D20D411yescharacteristic
58D20C2311yescharacteristic
59D20C2311yescharacteristic
60C4×D5—22no—
61C4×D5—21no—
62C4×D5—21no—
63C4×D5—22no—
64C4×D5C2312yes—
65Dic10—22no—
66Dic10D411yescharacteristic
67Dic10C2311yescharacteristic
68Dic10C2311yescharacteristic
69C5×C8C2311yescharacteristic
70C5×C8C2311yescharacteristic
71#168C2312yes—
722−1+4—51no—
73H(5,𝔽2)—51no—
74#137—51no—
75#137—52no—
76AGL(1,ℤ/8)—51no—
77AGL(1,ℤ/8)—52no—
78#135—52no—
79#135—51no—
80C2×SD16—52no—
81C2×SD16D511yescharacteristic, complemented
82#131—51no—
83C22×C5—22no—
84C22×C5—81no—
85C22×C5C2×D411yescharacteristic
86C2×D5—21no—
87C2×D5—21no—
88C2×D5—82no—
89C2×D5C2×D412yes—
90C4×C5—22no—
91C4×C5C2×D411yescharacteristic
92C4×C5C2411yescharacteristic
93Dic5—21no—
94Dic5—21no—
95Dic5C2×D412yes—
96#41—51no—
97#41—52no—
98#41—52no—
99#41—51no—
100#41—51no—
101#41—102no—
102#41—101no—
103#41—101no—
104C2×Q8—52no—
105C2×Q8—101no—
106C2×Q8C2×D511yescharacteristic, complemented
107C2×D4—52no—
108C2×D4—101no—
109C2×D4—102no—
110C2×D4C2×D511yescharacteristic
111Q16—52no—
112Q16—51no—
113SD16—52no—
114SD16—52no—
115SD16—51no—
116SD16—51no—
117SD16C2×D512yescomplemented
118SD16C2×D512yescomplemented
119D8—52no—
120D8—51no—
121M16—51no—
122M16—52no—
123C2×C8—52no—
124C2×C8C2×D511yescharacteristic, complemented
125C2×C5—21no—
126C2×C5—42no—
127C2×C5C22×D411yescharacteristic
128D5—22no—
129D5—41no—
130D5—41no—
131C23—21no—
132C23—102no—
133Q8—21no—
134Q8—51no—
135Q8—51no—
136Q8—51no—
137Q8—102no—
138Q8C22×D512yes—
139D4—21no—
140D4—52no—
141D4—51no—
142D4—51no—
143D4—51no—
144D4—102no—
145D4—102no—
146D4—102no—
147D4—101no—
148D4—101no—
149D4C22×D512yes—
150C2×C4—21no—
151C2×C4—52no—
152C2×C4—102no—
153C2×C4—102no—
154C2×C4—102no—
155C2×C4—101no—
156C2×C4—101no—
157C2×C4C22×D511yescharacteristic
158C8—52no—
159C8C22×D511yescharacteristic
160C8C22×D511yescharacteristic
161C5#57711yescharacteristic, complemented, Sylow
162C22—22no—
163C22—52no—
164C22—81no—
165C22—101no—
166C22—101no—
167C22—402no—
168C22D4×D511yescharacteristic
169C4—22no—
170C4—52no—
171C4—101no—
172C4—101no—
173C4D4×D511yescharacteristic
174C4C23×D511yescharacteristic
175C2—21no—
176C2—42no—
177C2—102no—
178C2—201no—
179C2—201no—
180C2C2×D4×D511yescharacteristic
subgroupG/H
centerC2C2×D4×D5
commutator, cosocleC4×C5C24
FrattiniC4C23×D5
FittingC2×C5×SD16C2
socleC2×C5C22×D4
hypercenterC2×SD16D5
hypocenterC5#577
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #4147C2semidirect
2. #4144C2semidirect
3. C2×C5×SD16C2semidirect
4. #4088C2semidirect
5. #4078C2semidirect
6. #4062C2semidirect
7. #4061C2semidirect
8. #4060C2semidirect
9. D5×SD16C2semidirect
10. #4050C2semidirect
11. #4047C2semidirect
12. C2×C5×Q8C22semidirect
16. #713C22semidirect
18. Q8×D5C22semidirect
26. #709C22semidirect
27. C5×SD16C22semidirect
28. C5×SD16C22semidirect
29. C2×C5×C8C22semidirect
30. #689C22semidirect
31. #688C22semidirect
32. #687C22semidirect
33. #686C22semidirect
34. #681C22semidirect
35. Dic20C22semidirect
36. D40C22semidirect
37. #677C22semidirect
38. #677C22semidirect
39. #676C22semidirect
40. C8×D5C22semidirect
81. C2×SD16D5semidirect
106. C2×Q8C2×D5semidirect
117. SD16C2×D5semidirect
118. SD16C2×D5semidirect
124. C2×C8C2×D5semidirect
161. C5#577semidirect

Maximal subgroups

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

subgroupindex
#41472
#41442
C2×C5×SD162
#40882
#40782
#40622
#40612
#40602
D5×SD162
#40502
#40472
#5775