Finite Group Databasebeta

← D5×C3⋊#11925894 #49137514

Subgroups — D5×C3⋊#11925894 #49137514

Order 36300.

232 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 38 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
1C3⋊(C5⋊#11925894)C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925894C211yesmaximal, characteristic, complemented
3C3×D5×#10597244C211yesmaximal, characteristic, complemented
4D5×#11925894—31nomaximal, Hall
5C3×C5×#10597244C2211yescharacteristic, complemented, Hall
6D5×C3⋊(C11⋊D11)C511yesmaximal, characteristic, complemented
7C2×C3⋊#11925894—51nomaximal
8D5×#10597244D311yescharacteristic, complemented
9C5⋊#11925894—31no—
10C5×#11925894—31no—
11C3⋊(C5⋊(C11⋊D11))C2×C511yescharacteristic, complemented
12C5×C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
13C3×D5×C112C2×C511yescharacteristic, complemented
14C2×C3×#10597244—51no—
15C3⋊#11925894—22no—
16C3⋊#11925894—51no—
17C3⋊#11925894D511yescharacteristic, direct product factor
18D5×C3⋊AGL(1,𝔽11)—112nomaximal
19C5×#10597244C2×D311yescharacteristic, complemented, Hall
20D5×C11⋊D11—31no—
21C2×#11925894—151no—
22C3×C5×C112C22×C511yescharacteristic, complemented
23C3×#10597244—22no—
24C3×#10597244C2×D511yescharacteristic, complemented
25C3⋊(C5⋊AGL(1,𝔽11))—112no—
26C5×C3⋊AGL(1,𝔽11)—112no—
27C3×D5×C11⋊C5—222no—
28C2×C3⋊(C11⋊D11)—51noHall
29C5⋊(C11⋊D11)—31no—
30D5×C112C5×D311yescharacteristic, complemented
31C5×C11⋊D11—31no—
32C2×#10597244—51no—
33#11925894—31no—
34#11925894—62no—
35#11925894—151no—
36D5×AGL(1,𝔽11)—332no—
37C3×C5×C11⋊C5—222no—
38C2×C3×C112—51no—
39C3⋊(C11⋊D11)—51no—
40C3⋊(C11⋊D11)C5×D511yescharacteristic, complemented
41D5×D33—112no—
42D5×D33—552no—
43C2×C3⋊AGL(1,𝔽11)—552no—
44C5×C112C2×C5×D311yescharacteristic, complemented
45#10597244—22no—
46#10597244D3×D511yescharacteristic, complemented
47C5⋊AGL(1,𝔽11)—332no—
48D5×C11⋊C5—222no—
49C5×AGL(1,𝔽11)—332no—
50C2×C11⋊D11—151noHall
51C3×C112C2×C5×D511yescharacteristic, complemented, Hall
52D165—112no—
53D165—552no—
54C5×D33—112no—
55C5×D33—552no—
56C3×D5×C11—52no—
57C3×D5×C11AGL(1,𝔽11)12yescomplemented
58C2×C3×C11⋊C5—1102no—
59C3⋊AGL(1,𝔽11)—112no—
60C3⋊AGL(1,𝔽11)—224no—
61C3⋊AGL(1,𝔽11)—552no—
62C5×D3×D5—1211noHall
63C5×C11⋊C5—222no—
64C2×C112—51no—
65C11⋊D11—31no—
66C11⋊D11—151no—
67D5×D11—332no—
68D5×D11—1652no—
69C2×AGL(1,𝔽11)—1652no—
70C3×C5×C11—52no—
71C3×C5×C11C2×AGL(1,𝔽11)12yescomplemented
72C3×C11⋊C5—222no—
73C3×C11⋊C5—444no—
74C5×D15—1211no—
75C52×D3—1211no—
76C3×C5×D5—2421no—
77C2×D33—2752no—
78C2×D33—552no—
79C112C5×D3×D511yescharacteristic, complemented, Sylow
80D55—332no—
81D55—1652no—
82C5×D11—332no—
83C5×D11—1652no—
84D5×C11—52no—
85D5×C11C3⋊AGL(1,𝔽11)12yescomplemented
86C2×C11⋊C5—1102no—
87AGL(1,𝔽11)—332no—
88AGL(1,𝔽11)—664no—
89AGL(1,𝔽11)—1652no—
90C2×C5×D5—3631noHall
91C3×C52—2421noHall
92C2×C3×C11—52no—
93C2×C3×C11—252no—
94D33—112no—
95D33—2752no—
96D33—552no—
97D33—552no—
98C2×C5×D3—6051no—
99D3×D5—1211no—
100C5×C11—52no—
101C5×C11C2×C3⋊AGL(1,𝔽11)12yescomplemented
102C11⋊C5—222no—
103C11⋊C5—444no—
104C2×C52—3631no—
105C5×D5—3631no—
106C5×D5—2421no—
107C2×D11—8252no—
108C2×D11—1652no—
109C3×C11—52no—
110C3×C11D5×AGL(1,𝔽11)12yescomplemented
111C2×C3×C5—12101no—
112D15—1211no—
113C3×D5#1192589411yescharacteristic, complemented
114C5×D3—6051no—
115C5×D3—1211no—
116C5×D3—1211no—
117C5×D3—2422no—
118C52—2421noSylow
119C2×C11—52no—
120C2×C11—252no—
121D11—332no—
122D11—8252no—
123D11—1652no—
124D11—1652no—
125C22×C5—18151no—
126C2×D5—3631no—
127C3×C5—4842no—
128C3×C5—2421no—
129C3×C5C2×#1192589411yescharacteristic, complemented
130C2×D3—6051noHall
131C11—52no—
132C11D5×C3⋊AGL(1,𝔽11)12yescomplemented
133C2×C5—18151no—
134C2×C5—3631no—
135C2×C5—3631no—
136C2×C5—12101no—
137C2×C5—7262no—
138D5—3631no—
139D5C3⋊#1192589411yescharacteristic, direct product factor
140C2×C3—51no—
141D3—6051no—
142D3—1211no—
143C5—4842no—
144C5—2421no—
145C5C2×C3⋊#1192589411yescharacteristic, complemented
146C22—18151noSylow
147C3D5×#1192589411yescharacteristic, complemented, Sylow
148C2—51no—
149C2—18151no—
150C2—3631no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C22×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C5⋊#11925894)C2semidirect
2. C5×C3⋊#11925894C2semidirect
3. C3×D5×#10597244C2semidirect
5. C3×C5×#10597244C22semidirect
6. D5×C3⋊(C11⋊D11)C5semidirect
8. D5×#10597244D3semidirect
11. C3⋊(C5⋊(C11⋊D11))C2×C5semidirect
12. C5×C3⋊(C11⋊D11)C2×C5semidirect
13. C3×D5×C112C2×C5semidirect
17. C3⋊#11925894D5direct (N × H)
19. C5×#10597244C2×D3semidirect
22. C3×C5×C112C22×C5semidirect
24. C3×#10597244C2×D5semidirect
30. D5×C112C5×D3semidirect
40. C3⋊(C11⋊D11)C5×D5semidirect
44. C5×C112C2×C5×D3semidirect
46. #10597244D3×D5semidirect
51. C3×C112C2×C5×D5semidirect
57. C3×D5×C11AGL(1,𝔽11)semidirect
71. C3×C5×C11C2×AGL(1,𝔽11)semidirect
79. C112C5×D3×D5semidirect
85. D5×C11C3⋊AGL(1,𝔽11)semidirect
101. C5×C11C2×C3⋊AGL(1,𝔽11)semidirect
110. C3×C11D5×AGL(1,𝔽11)semidirect
113. C3×D5#11925894semidirect
129. C3×C5C2×#11925894semidirect
132. C11D5×C3⋊AGL(1,𝔽11)semidirect
139. D5C3⋊#11925894direct (N × H)
145. C5C2×C3⋊#11925894semidirect
147. C3D5×#11925894semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊#11925894)2
C5×C3⋊#119258942
C3×D5×#105972442
D5×#119258943
D5×C3⋊(C11⋊D11)5
C2×C3⋊#119258945
D5×C3⋊AGL(1,𝔽11)11