Finite Group Databasebeta

← #13183390

Subgroups — #13183390

Order 1760.

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

normal subgroups only

This group has 292 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
1Q8×D55C211yesmaximal, characteristic, complemented
2C11×#713C211yesmaximal, characteristic, complemented
3C5×Q8×D11C211yesmaximal, characteristic, complemented
4#11724989C213yesmaximal, complemented
5#11724988C213yesmaximal, complemented
6#11724985C213yesmaximal, complemented
7D5×Dic22C213yesmaximal, complemented
8C5×Q8×C11C2211yescharacteristic
9C4×D55C2213yes—
10Dic110C2213yes—
11C11×D20C2213yes—
12C4×D5×C11C2213yes—
13C4×C5×D11C2213yes—
14C5×Dic22C2213yes—
15#89170C2213yes—
16#89169C2213yes—
17#89168C2211yescharacteristic
18#89167C2213yes—
19D5×Dic11C2216yes—
20#67043—51nomaximal, Hall
21C2×D55C2311yescharacteristic
22C2×D5×C11C2313yes—
23C2×C5×D11C2311yescharacteristic
24C4×C5×C11C2313yes—
25Dic55C2313yes—
26C5×Dic11C2313yes—
27C11×Dic5C2311yescharacteristic
28C11×#41—51no—
29Q8×D11—51no—
30Q8×D11D511yescharacteristic, complemented
31#4341—53no—
32#4341—53no—
33#4339—53no—
34C2×Dic22—53no—
35#4147—111nomaximal, Hall
36C2×C5×C11C2411yescharacteristic
37D55—21no—
38C5×D11—21no—
39D5×C11—23no—
40Q8×C11C2×D511yescharacteristic
41D4×C11—53no—
42C2×C4×C11—53no—
43C22⋊D11—53no—
44C22⋊D11—53no—
45C2×Dic11—56no—
46D44—51no—
47C4×D11—53no—
48C4×D11C2×D513yes—
49Dic22—53no—
50Dic22—53no—
51Dic22C2×D513yes—
52C2×C5×Q8—111no—
53#713—113no—
54#713D1111yescharacteristic, complemented
55Q8×D5—111no—
56Q8×D5—113no—
57#709—113no—
58#709—113no—
59C5×C112−1+411yescharacteristic, complemented, Hall
60C22×C11—53no—
61C2×D11—51no—
62C2×D11C22×D511yescharacteristic
63C4×C11—51no—
64C4×C11C22×D513yes—
65Dic11—53no—
66Dic11C22×D513yes—
67C5×Q8—113no—
68C5×Q8C2×D1111yescharacteristic
69C2×C4×C5—113no—
70C22⋊D5—113no—
71C22⋊D5—111no—
72D20—113no—
73D20C2×D1113yes—
74C4×D5—116no—
75C4×D5—113no—
76C4×D5C2×D1113yes—
77Dic10—113no—
78Dic10—113no—
792−1+4—551noSylow
80C2×C11—103no—
81C2×C11C23×D511yescharacteristic
82D11—21no—
83D11—101no—
84C22×C5—111no—
85C2×D5—111no—
86C2×D5C22×D1113yes—
87C4×C5—113no—
88C4×C5C22×D1113yes—
89Dic5—113no—
90Dic5C22×D1111yescharacteristic
91#41—51no—
92#41—553no—
93#41—553no—
94#41—553no—
95C2×Q8—111no—
96C2×Q8—553no—
97C2×Q8—551no—
98C11#414711yescharacteristic, complemented, Sylow
99C2×C5—221no—
100C2×C5C23×D1111yescharacteristic
101D5—23no—
102D5—221no—
103Q8—113no—
104Q8—553no—
105Q8—553no—
106Q8D5×D1111yescharacteristic
107D4—53no—
108D4—551no—
109D4—553no—
110D4—553no—
111C2×C4—53no—
112C2×C4—113no—
113C2×C4—556no—
114C2×C4—553no—
115C5#6704311yescharacteristic, complemented, Sylow
116C22—53no—
117C22—111no—
118C22—551no—
119C4—51no—
120C4—113no—
121C4—553no—
122C4C2×D5×D1113yes—
123C2—103no—
124C2—221no—
125C2—1101no—
126C2C22×D5×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C22×D5×D11
commutator, socle, cosocleC2×C5×C11C24
FittingC5×Q8×C11C22
hypercenterQ8D5×D11
hypocenterC5×C112−1+4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ Q8

Complements

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

NH ≅ G/Ntype
1. Q8×D55C2semidirect
2. C11×#713C2semidirect
3. C5×Q8×D11C2semidirect
4. #11724989C2semidirect
5. #11724988C2semidirect
6. #11724985C2semidirect
7. D5×Dic22C2semidirect
30. Q8×D11D5semidirect
54. #713D11semidirect
59. C5×C112−1+4semidirect
98. C11#4147semidirect
115. C5#67043semidirect

Maximal subgroups

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

subgroupindex
Q8×D552
C11×#7132
C5×Q8×D112
#117249892
#117249882
#117249852
D5×Dic222
#670435
#414711