Finite Group Databasebeta

← D15⋊#10587723 #30655516

Subgroups — D15⋊#10587723 #30655516

Order 16380.

176 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 35 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×#63271C211yesmaximal, characteristic, complemented
2C5×C3⋊#10587723C211yesmaximal, characteristic, complemented
3C3×C5⋊#10587723C211yesmaximal, characteristic, complemented
4D15⋊D91C311yesmaximal, characteristic, complemented
5D5×#10587723—31nomaximal
6C3×C5×#63271C2211yescharacteristic, complemented, Hall
7D3×#10587723—51nomaximal, Hall
8C5⋊#10587723—21no—
9C5⋊#10587723D311yescharacteristic, complemented
10D5×#63271—31no—
11C5×#10587723—31no—
12C7×C13×D15C2×C311yescharacteristic, complemented
13C5×D273C2×C311yescharacteristic, complemented
14C3×D455C2×C311yescharacteristic, complemented
15D15⋊(D13⋊C3)—71nomaximal, Hall
16D5×D91—31noHall
17C3⋊#10587723D511yescharacteristic, complemented
18D3×#63271—51no—
19C3×#10587723—51no—
20C3×C5×C7×C13C22×C311yescharacteristic, complemented
21C5×#63271—21no—
22C5×#63271C2×D311yescharacteristic, complemented
23D15⋊AGL(1,𝔽7)—131nomaximal, Hall
24D15×C13⋊C3—141no—
25C5×C3⋊(D13⋊C3)—71no—
26C3×C5⋊(D13⋊C3)—71no—
27D3×D91—51no—
28C2×#10587723—151no—
29D455C3×D311yescharacteristic, complemented
30C7×D5×C13—31no—
31C5×D91—31no—
32C3×#63271C2×D511yescharacteristic, complemented, Hall
33D15⋊D13—71no—
34D5×D13⋊C3—211no—
35ΓL(1,𝔽8)×D15—131no—
36C5×C3⋊AGL(1,𝔽7)—131no—
37C3×C5⋊AGL(1,𝔽7)—131no—
38C3×C5×C13⋊C3—141noHall
39D273C3×D511yescharacteristic, complemented
40D3×C7×C13—51no—
41C3×D91—51no—
42C2×#63271—151no—
43#10587723—31no—
44#10587723—51no—
45#10587723—101no—
46D3×D13⋊C3—351noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48D15⋊D7—131no—
49D5×AGL(1,𝔽7)—391no—
50C13×D15AGL(1,𝔽7)11yescharacteristic, complemented
51C5×D39—71no—
52C3×D65—71no—
53C5⋊(D13⋊C3)—71no—
54C5⋊(D13⋊C3)—141no—
55D5×C13⋊C3—211no—
56C5×D13⋊C3—211no—
57C2×D91—151noHall
58C3×C5×ΓL(1,𝔽8)—131noHall
59C3×C7×C13C2×C3×D511yescharacteristic, complemented
60#63271—21no—
61#63271D3×D511yescharacteristic, complemented
62D5×D13—211noHall
63D3×AGL(1,𝔽7)—651noHall
64C3⋊(D13⋊C3)—71no—
65D3×C13⋊C3—701no—
66C3×D13⋊C3—351no—
67C7×D15D13⋊C311yescharacteristic, complemented
68C5×D21—131no—
69C3×D35—131no—
70C5⋊AGL(1,𝔽7)—131no—
71C5⋊AGL(1,𝔽7)—261no—
72D5×ΓL(1,𝔽8)—781no—
73C5×AGL(1,𝔽7)—391no—
74C3×C5×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
75C5×C13⋊C3—71no—
76C5×C13⋊C3—281no—
77C2×C7×C13—151no—
78D91—31no—
79D91—51no—
80C3×D3×D5—911noHall
81D3×D13—351no—
82C2×D13⋊C3—1051no—
83D5×D7—391noHall
84D65—71no—
85C5×D13—211no—
86D5×C13—31no—
87C3⋊AGL(1,𝔽7)—131no—
88D3×ΓL(1,𝔽8)—1301no—
89C3×AGL(1,𝔽7)—651no—
90C3×C13⋊C3—141noHall
91C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
92C5×ΓL(1,𝔽8)—261no—
93C5×ΓL(1,𝔽8)—521no—
94C7×C13C3×D3×D511yescharacteristic, complemented, Hall
95C3×D15—1821no—
96C3×C5×D3—911no—
97C32×D5—911no—
98D3×D7—651no—
99C2×AGL(1,𝔽7)—1951no—
100D39—71no—
101C3×D13—351no—
102D3×C13—51no—
103C2×C13⋊C3—2101no—
104D13⋊C3—211no—
105D13⋊C3—351no—
106D13⋊C3—701no—
107D35—131no—
108C5×D7—391no—
109C7×D5—31no—
110C5×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
111C3×ΓL(1,𝔽8)—261noHall
112C2×C3×D5—2731no—
113D3×D5—911no—
114C2×D13—1051noHall
115C32×C5—1821noHall
116D21—131no—
117C3×D7—651no—
118D3×C7—51no—
119C2×ΓL(1,𝔽8)—3901no—
120AGL(1,𝔽7)—391no—
121AGL(1,𝔽7)—651no—
122AGL(1,𝔽7)—1301no—
123C3×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
124C13⋊C3—141no—
125C13⋊C3—281no—
126C2×C3×D3—4551noHall
127C5×C7D3×D13⋊C311yescharacteristic, complemented, Hall
128C2×C3×C5—2731no—
129D15#1058772311yescharacteristic, complemented
130C3×D5—5461no—
131C3×D5—911no—
132C3×D5—911no—
133C3×D5—1821no—
134C5×D3—911no—
135C2×D7—1951noHall
136C2×C13—151no—
137D13—211no—
138D13—351no—
139C3×C7D5×D13⋊C311yescharacteristic, complemented
140ΓL(1,𝔽8)—261no—
141ΓL(1,𝔽8)—521no—
142C2×D5—2731noHall
143C2×C32—4551no—
144C3×D3—911no—
145C3×D3—9101no—
146C3×C5—3641no—
147C3×C5—1821no—
148C3×C5C2×#1058772311yescharacteristic, complemented
149C2×C7—151no—
150D7—391no—
151D7—651no—
152C13D15⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
153C22×C3—13651no—
154C2×D3—4551no—
155C2×C5—2731no—
156D5—31no—
157D5—911no—
158C32—1821noSylow
159C7D15⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
160C2×C3—2731no—
161C2×C3—9101no—
162C2×C3—27301no—
163C2×C3—4551no—
164C2×C3—4551no—
165D3—51no—
166D3—911no—
167C5D3×#1058772311yescharacteristic, complemented, Sylow
168C22—13651noSylow
169C3—3641no—
170C3—1821no—
171C3D5×#1058772311yescharacteristic, complemented
172C2—151no—
173C2—2731no—
174C2—4551no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C13C22×C3
LCSG ▷ C3×C5×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D15×#63271C2semidirect
2. C5×C3⋊#10587723C2semidirect
3. C3×C5⋊#10587723C2semidirect
4. D15⋊D91C3semidirect
6. C3×C5×#63271C22semidirect
9. C5⋊#10587723D3semidirect
12. C7×C13×D15C2×C3semidirect
13. C5×D273C2×C3semidirect
14. C3×D455C2×C3semidirect
17. C3⋊#10587723D5semidirect
20. C3×C5×C7×C13C22×C3semidirect
22. C5×#63271C2×D3semidirect
29. D455C3×D3semidirect
32. C3×#63271C2×D5semidirect
39. D273C3×D5semidirect
47. C5×C7×C13C2×C3×D3semidirect
50. C13×D15AGL(1,𝔽7)semidirect
59. C3×C7×C13C2×C3×D5semidirect
61. #63271D3×D5semidirect
67. C7×D15D13⋊C3semidirect
74. C3×C5×C13C2×AGL(1,𝔽7)semidirect
91. C3×C5×C7C2×D13⋊C3semidirect
94. C7×C13C3×D3×D5semidirect
110. C5×C13D3×AGL(1,𝔽7)semidirect
123. C3×C13D5×AGL(1,𝔽7)semidirect
127. C5×C7D3×D13⋊C3semidirect
129. D15#10587723semidirect
139. C3×C7D5×D13⋊C3semidirect
148. C3×C5C2×#10587723semidirect
152. C13D15⋊AGL(1,𝔽7)semidirect
159. C7D15⋊(D13⋊C3)semidirect
167. C5D3×#10587723semidirect
171. C3D5×#10587723semidirect

Maximal subgroups

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

subgroupindex
D15×#632712
C5×C3⋊#105877232
C3×C5⋊#105877232
D15⋊D913
D5×#105877233
D3×#105877235
D15⋊(D13⋊C3)7
D15⋊AGL(1,𝔽7)13