Finite Group Databasebeta

← #13183395

Subgroups — #13183395

Order 1760.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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#11725035C211yesmaximal, characteristic, complemented
2C11×#713C211yesmaximal, characteristic, complemented
3C5×#4343C211yesmaximal, characteristic, complemented
4#11724994C213yesmaximal, complemented
5D5×D44C213yesmaximal, complemented
6D11×D20C213yesmaximal, complemented
7#11724988C213yesmaximal, complemented
8C2×D5×D11C2216yescomplemented
9C5×Q8×C11C2211yescharacteristic, complemented
10D220C2213yescomplemented
11C4×D55C2213yescomplemented
12C11×D20C2213yescomplemented
13C4×D5×C11C2213yescomplemented
14C5×D44C2213yescomplemented
15C4×C5×D11C2213yescomplemented
16#89170C2211yescharacteristic, complemented
17#89169C2213yescomplemented
18#89168C2213yescomplemented
19#89167C2213yescomplemented
20#67042—51nomaximal, Hall
21C2×D55C2313yes—
22C2×D5×C11C2313yes—
23C2×C5×D11C2313yes—
24D5×D11—46no—
25C4×C5×C11C2313yes—
26Dic55C2311yescharacteristic
27C5×Dic11C2311yescharacteristic
28C11×Dic5C2311yescharacteristic
29C11×#41—51no—
30#4343—51no—
31#4343D511yescharacteristic, complemented
32D4×D11—53no—
33D4×D11—53no—
34#4339—53no—
35C2×D44—53no—
36#4149—111nomaximal, Hall
37C2×C5×C11C2411yescharacteristic
38D55—23no—
39C5×D11—23no—
40D5×C11—23no—
41C22×D11—56no—
42Q8×C11C2×D511yescharacteristic, complemented
43D4×C11—53no—
44C2×C4×C11—53no—
45C22⋊D11—53no—
46C22⋊D11—53no—
47D44—53no—
48D44—53no—
49D44C2×D513yescomplemented
50C4×D11—53no—
51C4×D11C2×D513yescomplemented
52Dic22—51no—
53C5×#41—111no—
54#713—111no—
55#713D1111yescharacteristic, complemented
56D4×D5—113no—
57D4×D5—113no—
58#709—113no—
59C2×D20—113no—
60C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
61C22×C11—53no—
62C2×D11—53no—
63C2×D11—206no—
64C2×D11C22×D513yes—
65C4×C11—51no—
66C4×C11C22×D513yes—
67Dic11—51no—
68Dic11C22×D511yescharacteristic
69C22×D5—116no—
70C5×Q8C2×D1111yescharacteristic, complemented
71C5×D4—113no—
72C2×C4×C5—113no—
73C22⋊D5—113no—
74C22⋊D5—113no—
75D20—113no—
76D20—113no—
77D20C2×D1113yescomplemented
78C4×D5—113no—
79C4×D5C2×D1113yescomplemented
80Dic10—111no—
81H(5,𝔽2)—551noSylow
82C2×C11—103no—
83C2×C11C23×D511yescharacteristic
84D11—23no—
85D11—103no—
86C22×C5—113no—
87C2×D5—113no—
88C2×D5—446no—
89C2×D5C22×D1113yes—
90C4×C5—111no—
91C4×C5C22×D1113yes—
92Dic5—111no—
93Dic5C22×D1111yescharacteristic
94#41—51no—
95#41—111no—
96#41—553no—
97#41—551no—
98C2×D4—553no—
99C2×D4—553no—
100C2×D4—553no—
101C11#414911yescharacteristic, complemented, Sylow
102C2×C5—223no—
103C2×C5C23×D1111yescharacteristic
104D5—23no—
105D5—223no—
106C23—556no—
107Q8—551no—
108Q8D5×D1111yescharacteristic, complemented
109D4—53no—
110D4—113no—
111D4—553no—
112D4—553no—
113D4—553no—
114D4—553no—
115C2×C4—53no—
116C2×C4—113no—
117C2×C4—553no—
118C5#6704211yescharacteristic, complemented, Sylow
119C22—53no—
120C22—113no—
121C22—553no—
122C22—2206no—
123C4—51no—
124C4—111no—
125C4—551no—
126C4C2×D5×D1113yes—
127C2—103no—
128C2—223no—
129C2—1103no—
130C2C22×D5×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C22×D5×D11
commutator, socle, cosocleC2×C5×C11C24
FittingC5×Q8×C11C22
hypercenterQ8D5×D11
hypocenterC5×C11H(5,𝔽2)
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ Q8

Complements

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

NH ≅ G/Ntype
1. #11725035C2semidirect
2. C11×#713C2semidirect
3. C5×#4343C2semidirect
4. #11724994C2semidirect
5. D5×D44C2semidirect
6. D11×D20C2semidirect
7. #11724988C2semidirect
8. C2×D5×D11C22semidirect
9. C5×Q8×C11C22semidirect
10. D220C22semidirect
11. C4×D55C22semidirect
12. C11×D20C22semidirect
13. C4×D5×C11C22semidirect
14. C5×D44C22semidirect
15. C4×C5×D11C22semidirect
16. #89170C22semidirect
17. #89169C22semidirect
18. #89168C22semidirect
19. #89167C22semidirect
31. #4343D5semidirect
42. Q8×C11C2×D5semidirect
49. D44C2×D5semidirect
51. C4×D11C2×D5semidirect
55. #713D11semidirect
60. C5×C11H(5,𝔽2)semidirect
70. C5×Q8C2×D11semidirect
77. D20C2×D11semidirect
79. C4×D5C2×D11semidirect
101. C11#4149semidirect
108. Q8D5×D11semidirect
118. C5#67042semidirect

Maximal subgroups

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

subgroupindex
#117250352
C11×#7132
C5×#43432
#117249942
D5×D442
D11×D202
#117249882
#670425
#414911