Finite Group Databasebeta

← D3×D5×#10597245 #49137535

Subgroups — D3×D5×#10597245 #49137535

Order 36300.

232 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D15×#10597245C211yesmaximal, characteristic, complemented
2C5×D3×#10597245C211yesmaximal, characteristic, complemented
3C3×D5×#10597245C211yesmaximal, characteristic, complemented
4C2×D5×#10597245—31nomaximal, Hall
5C3×C5×#10597245C2211yescharacteristic, complemented, Hall
6D3×D5×C112C511yesmaximal, characteristic, complemented
7C2×D3×#10597245—51nomaximal
8C2×C5×#10597245—31no—
9D5×#10597245—31no—
10D5×#10597245D311yescharacteristic, direct product factor
11C112×D15C2×C511yescharacteristic, complemented
12C5×D3×C112C2×C511yescharacteristic, complemented
13C3×D5×C112C2×C511yescharacteristic, complemented
14C2×C3×#10597245—51no—
15D3×#10597245—22no—
16D3×#10597245—51no—
17D3×#10597245D511yescharacteristic, direct product factor
18D3×D5×C11⋊C5—112nomaximal
19C5×#10597245C2×D311yescharacteristic, complemented, Hall
20C2×D5×C112—31no—
21C22×#10597245—151no—
22C3×C5×C112C22×C511yescharacteristic, complemented
23C3×#10597245—22no—
24C3×#10597245C2×D511yescharacteristic, complemented
25D15×C11⋊C5—112no—
26C5×D3×C11⋊C5—112no—
27C3×D5×C11⋊C5—112no—
28C2×D3×C112—51noHall
29C2×C5×C112—31no—
30D5×C112—31no—
31D5×C112C5×D311yescharacteristic, complemented
32C2×#10597245—31no—
33C2×#10597245—51no—
34C2×#10597245—62no—
35C2×#10597245—151no—
36C2×D5×C11⋊C5—332no—
37C3×C5×C11⋊C5—112no—
38C2×C3×C112—51no—
39D3×C112—51no—
40D3×C112C5×D511yescharacteristic, complemented
41D3×D5×C11—52no—
42D3×D5×C11C11⋊C512yescomplemented
43C2×D3×C11⋊C5—552no—
44C5×C112C2×C5×D311yescharacteristic, complemented
45#10597245—22no—
46#10597245D3×D511yescharacteristic, direct product factor
47C2×C5×C11⋊C5—332no—
48D5×C11⋊C5—112no—
49D5×C11⋊C5—332no—
50C22×C112—151noHall
51C3×C112C2×C5×D511yescharacteristic, complemented, Hall
52C11×D15—52no—
53C11×D15C2×C11⋊C512yescomplemented
54C5×D3×C11—52no—
55C5×D3×C11C2×C11⋊C512yescomplemented
56C3×D5×C11—52no—
57C3×D5×C11C2×C11⋊C512yescomplemented
58C2×C3×C11⋊C5—552no—
59D3×C11⋊C5—112no—
60D3×C11⋊C5—224no—
61D3×C11⋊C5—552no—
62C5×D3×D5—1211noHall
63C5×C11⋊C5—112no—
64C2×C112—31no—
65C2×C112—51no—
66C2×C112—151no—
67C2×D5×C11—32no—
68C2×D5×C11—152no—
69C22×C11⋊C5—1652no—
70C3×C5×C11—52no—
71C3×C5×C11C22×C11⋊C512yescomplemented
72C3×C11⋊C5—112no—
73C3×C11⋊C5—224no—
74C5×D15—1211no—
75C52×D3—1211no—
76C3×C5×D5—1211no—
77C2×D3×C11—52no—
78C2×D3×C11—252no—
79C112C5×D3×D511yescharacteristic, complemented, Sylow
80C2×C5×C11—32no—
81C2×C5×C11—152no—
82D5×C11—32no—
83D5×C11—52no—
84D5×C11—152no—
85D5×C11D3×C11⋊C512yescomplemented
86C2×C11⋊C5—332no—
87C2×C11⋊C5—552no—
88C2×C11⋊C5—664no—
89C2×C11⋊C5—1652no—
90C2×C5×D5—3631noHall
91C3×C52—1211noHall
92C2×C3×C11—52no—
93C2×C3×C11—252no—
94D3×C11—52no—
95D3×C11—52no—
96D3×C11—252no—
97D3×C11D5×C11⋊C512yescomplemented
98C2×C5×D3—6051no—
99D3×D5#1059724511yescharacteristic, direct product factor
100C5×C11—52no—
101C5×C11C2×D3×C11⋊C512yescomplemented
102C11⋊C5—112no—
103C11⋊C5—224no—
104C2×C52—3631no—
105C5×D5—3631no—
106C5×D5—1211no—
107C22×C11—152no—
108C22×C11—752no—
109C3×C11—52no—
110C3×C11C2×D5×C11⋊C512yescomplemented
111C2×C3×C5—6051no—
112D15C2×#1059724511yescharacteristic, complemented
113C3×D5C2×#1059724511yescharacteristic, complemented
114C5×D3—6051no—
115C5×D3—1211no—
116C5×D3—2422no—
117C5×D3C2×#1059724511yescharacteristic, complemented
118C52—1211noSylow
119C2×C11—32no—
120C2×C11—52no—
121C2×C11—152no—
122C2×C11—152no—
123C2×C11—252no—
124C2×C11—752no—
125C22×C5—18151no—
126C2×D5—31no—
127C3×C5—1211no—
128C3×C5—2422no—
129C3×C5C22×#1059724511yescharacteristic, complemented
130C2×D3—51noHall
131C11—52no—
132C11D3×D5×C11⋊C512yescomplemented
133C2×C5—31no—
134C2×C5—18151no—
135C2×C5—6051no—
136C2×C5—3631no—
137C2×C5—7262no—
138D5—31no—
139D5D3×#1059724511yescharacteristic, direct product factor
140C2×C3—51no—
141D3—51no—
142D3D5×#1059724511yescharacteristic, direct product factor
143C5—1211no—
144C5—2422no—
145C5C2×D3×#1059724511yescharacteristic, complemented
146C22—151noSylow
147C3C2×D5×#1059724511yescharacteristic, complemented, Sylow
148C2—31no—
149C2—51no—
150C2—151no—
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. D15×#10597245C2semidirect
2. C5×D3×#10597245C2semidirect
3. C3×D5×#10597245C2semidirect
5. C3×C5×#10597245C22semidirect
6. D3×D5×C112C5semidirect
10. D5×#10597245D3direct (N × H)
11. C112×D15C2×C5semidirect
12. C5×D3×C112C2×C5semidirect
13. C3×D5×C112C2×C5semidirect
17. D3×#10597245D5direct (N × H)
19. C5×#10597245C2×D3semidirect
22. C3×C5×C112C22×C5semidirect
24. C3×#10597245C2×D5semidirect
31. D5×C112C5×D3semidirect
40. D3×C112C5×D5semidirect
42. D3×D5×C11C11⋊C5semidirect
44. C5×C112C2×C5×D3semidirect
46. #10597245D3×D5direct (N × H)
51. C3×C112C2×C5×D5semidirect
53. C11×D15C2×C11⋊C5semidirect
55. C5×D3×C11C2×C11⋊C5semidirect
57. C3×D5×C11C2×C11⋊C5semidirect
71. C3×C5×C11C22×C11⋊C5semidirect
79. C112C5×D3×D5semidirect
85. D5×C11D3×C11⋊C5semidirect
97. D3×C11D5×C11⋊C5semidirect
99. D3×D5#10597245direct (N × H)
101. C5×C11C2×D3×C11⋊C5semidirect
110. C3×C11C2×D5×C11⋊C5semidirect
112. D15C2×#10597245semidirect
113. C3×D5C2×#10597245semidirect
117. C5×D3C2×#10597245semidirect
129. C3×C5C22×#10597245semidirect
132. C11D3×D5×C11⋊C5semidirect
139. D5D3×#10597245direct (N × H)
142. D3D5×#10597245direct (N × H)
145. C5C2×D3×#10597245semidirect
147. C3C2×D5×#10597245semidirect

Maximal subgroups

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

subgroupindex
D15×#105972452
C5×D3×#105972452
C3×D5×#105972452
C2×D5×#105972453
D3×D5×C1125
C2×D3×#105972455
D3×D5×C11⋊C511