Finite Group Databasebeta

← #66283

Subgroups — #66283

Order 320.

810 conjugacy classes of subgroups; only the 443 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 443 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×C5×#41C211yesmaximal, characteristic, complemented
2#4150C214yesmaximal, complemented
3#4149C214yesmaximal, complemented
4D5×#41C218yesmaximal, complemented
5#4147C212yesmaximal, complemented
6#4144C216yesmaximal, complemented
7C2×#709C216yesmaximal, complemented
8C5×#41C2214yescomplemented
9C5×#41C2214yescomplemented
10C2×C5×Q8C2211yescharacteristic, complemented
11C2×C5×D4C2213yescomplemented
12C22×C4×C5C2213yescomplemented
13C2×C22⋊D5C22112yescomplemented
14#713C2218yescomplemented
15Q8×D5C2218yescomplemented
16#711C22124yescomplemented
17D4×D5C22124yescomplemented
18#709C2214yescomplemented
19#709C22112yescomplemented
20#709C22112yescomplemented
21#709C22112yescomplemented
22C2×D20C2216yescomplemented
23C2×C4×D5C22112yescomplemented
24C2×Dic10C2216yescomplemented
25#585—51nomaximal, Sylow
26C23×C5C2313yes—
27C22×D5C23112yes—
28C5×Q8C2314yes—
29C5×D4C23112yes—
30C2×C4×C5C2316yes—
31C2×C4×C5C2316yes—
32C2×C4×C5C2311yescharacteristic
33C2×C4×C5C2313yes—
34C22⋊D5C2318yes—
35C22⋊D5C23124yes—
36C2×Dic5C23112yes—
37D20C2314yes—
38D20C23112yes—
39C4×D5C2318yes—
40C4×D5C23124yes—
41Dic10C2314yes—
42Dic10C23112yes—
432−1+4—54no—
442−1+4—52no—
45H(5,𝔽2)—54no—
46H(5,𝔽2)—56no—
47C2×#41—58no—
48C2×#41—56no—
49C2×#41D511yescharacteristic, complemented
50C22×C5—43no—
51C22×C5C2416yes—
52C22×C5C2411yescharacteristic
53C2×D5—412no—
54C2×D5C2418yes—
55C4×C5C2411yescharacteristic
56C4×C5C2416yes—
57C4×C5C2411yescharacteristic
58Dic5C2418yes—
59#41—58no—
60#41—524no—
61#41—512no—
62#41—54no—
63#41—512no—
64#41—512no—
65#41C2×D514yescomplemented
66#41C2×D514yescomplemented
67C2×Q8—58no—
68C2×Q8—56no—
69C2×Q8C2×D511yescharacteristic, complemented
70C2×D4—512no—
71C2×D4—524no—
72C2×D4—56no—
73C2×D4C2×D513yescomplemented
74C22×C4—512no—
75C22×C4C2×D513yescomplemented
76C2×C5—26no—
77C2×C5—21no—
78C2×C5C2511yescharacteristic
79D5—28no—
80C23—512no—
81C23C22×D513yes—
82Q8—512no—
83Q8—54no—
84Q8C22×D514yes—
85D4—524no—
86D4—58no—
87D4—512no—
88D4—54no—
89D4C22×D5112yes—
90C2×C4—512no—
91C2×C4—524no—
92C2×C4—58no—
93C2×C4C22×D516yes—
94C2×C4C22×D513yes—
95C2×C4C22×D516yes—
96C2×C4C22×D511yescharacteristic
97C5#58511yescharacteristic, complemented, Sylow
98C22—43no—
99C22—58no—
100C22—2012no—
101C22C23×D516yes—
102C22C23×D511yescharacteristic
103C4—58no—
104C4C23×D516yes—
105C4C23×D511yescharacteristic
106C4C23×D511yescharacteristic
107C2—21no—
108C2—26no—
109C2—108no—
110C2C24×D511yescharacteristic
subgroupG/H
centerC4C23×D5
commutator, socle, cosocleC2×C5C25
FrattiniC2C24×D5
FittingC2×C5×#41C2
hypercenterC2×#41D5
hypocenterC5#585
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#41C2semidirect
2. #4150C2semidirect
3. #4149C2semidirect
4. D5×#41C2semidirect
5. #4147C2semidirect
6. #4144C2semidirect
7. C2×#709C2semidirect
8. C5×#41C22semidirect
9. C5×#41C22semidirect
10. C2×C5×Q8C22semidirect
11. C2×C5×D4C22semidirect
12. C22×C4×C5C22semidirect
13. C2×C22⋊D5C22semidirect
14. #713C22semidirect
15. Q8×D5C22semidirect
16. #711C22semidirect
17. D4×D5C22semidirect
18. #709C22semidirect
19. #709C22semidirect
20. #709C22semidirect
21. #709C22semidirect
22. C2×D20C22semidirect
23. C2×C4×D5C22semidirect
24. C2×Dic10C22semidirect
49. C2×#41D5semidirect
65. #41C2×D5semidirect
66. #41C2×D5semidirect
69. C2×Q8C2×D5semidirect
73. C2×D4C2×D5semidirect
75. C22×C4C2×D5semidirect
97. C5#585semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#412
#41502
#41492
D5×#412
#41472
#41442
C2×#7092
#5855