Finite Group Databasebeta

← D15×SD32 #11751014

Subgroups — D15×SD32 #11751014

Order 960.

180 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 49 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
1Q16×D15C211yesmaximal, characteristic, complemented
2D8×D15C211yesmaximal, characteristic
3C3×C5×SD32C211yesmaximal, characteristic, complemented
4#91112C211yesmaximal, characteristic, complemented
5#91111C211yesmaximal, characteristic, complemented
6#91084C211yesmaximal, characteristic, complemented
7C16×D15C211yesmaximal, characteristic, complemented
8D5×SD32—31nomaximal, Hall
9Q8×D15—21no—
10D4×D15—21no—
11C3×C5×Q16C2211yescharacteristic, complemented
12C3×C5×D8C2211yescharacteristic
13#6718—21no—
14#6715—21no—
15Dic60C2211yescharacteristic, complemented
16D120C2211yescharacteristic
17C8×D15C2211yescharacteristic
18C3×C5×C16C2211yescharacteristic, complemented
19C3⋊#672C2211yescharacteristic, complemented
20D3×SD32—51nomaximal, Hall
21D5×Q16—31no—
22D5×D8—31no—
23C5×SD32D311yescharacteristic, complemented
24#3960—31no—
25#3959—31no—
26#3932—31no—
27D5×C16—31no—
28C22×D15—41no—
29C3×C5×Q8—21no—
30C3×C5×D4—21no—
31#1220—41no—
32D60—21no—
33C4×D15—41no—
34C4×D15D411yescharacteristic
35Dic30—21no—
36Dic30—41no—
37C3×C5×C8C2311yescharacteristic
38C3⋊#168D411yescharacteristic
39D3×Q16—51no—
40D3×D8—51no—
41C3×SD32D511yescharacteristic, complemented
42#828—51no—
43#827—51no—
44#800—51no—
45D3×C16—51no—
46Q8×D5—61no—
47D4×D5—61no—
48C5×Q16C2×D311yescharacteristic, complemented
49C5×D8C2×D311yescharacteristic
50#689—61no—
51#686—61no—
52Dic20—31no—
53D40—31no—
54C8×D5—31no—
55C5×C16C2×D311yescharacteristic, complemented
56#672—31no—
57C2×SD32—151noSylow
58C22×C3×C5—41no—
59C2×D15—41no—
60C2×D15—82no—
61C2×D15D811yescharacteristic
62C3×C4×C5—41no—
63C3×C4×C5C2×D411yescharacteristic
64Dic15—41no—
65Dic15D811yescharacteristic
66D3×Q8—101no—
67D3×D4—101no—
68C3×Q16C2×D511yescharacteristic, complemented
69C3×D8C2×D511yescharacteristic
70#216—101no—
71#213—101no—
72Dic12—51no—
73D24—51no—
74D3×C8—51no—
75C3×C16C2×D511yescharacteristic, complemented
76C3⋊C16—51no—
77C22×D5—121no—
78C5×Q8—21no—
79C5×D4—21no—
80C22⋊D5—121no—
81D20—61no—
82C4×D5—31no—
83C4×D5—121no—
84Dic10—61no—
85Dic10—121no—
86C5×C8C22×D311yescharacteristic
87#168—31no—
88C2×Q16—151no—
89C2×D8—151no—
90SD32—151no—
91SD32—151no—
92SD32—151no—
93SD32D1511yescharacteristic, direct product factor
94C2×C16—151no—
95C2×C3×C5—81no—
96C2×C3×C5C2×D811yescharacteristic
97D15—81no—
98D15SD3212yesdirect product factor
99C22×D3—201no—
100C3×Q8—21no—
101C3×D4—21no—
102#67—201no—
103D12—101no—
104C4×D3—51no—
105C4×D3—201no—
106Dic6—101no—
107Dic6—201no—
108C3×C8C22×D511yescharacteristic
109C3⋊C8—51no—
110C22×C5—41no—
111C2×D5—31no—
112C2×D5—121no—
113C2×D5—242no—
114C4×C5—41no—
115C4×C5D3×D411yescharacteristic
116Dic5—31no—
117Dic5—121no—
118C2×Q8—301no—
119C2×D4—301no—
120Q16—151no—
121Q16—301no—
122Q16C2×D1511yescharacteristic, complemented
123D8—151no—
124D8—301no—
125D8C2×D1511yescharacteristic
126C2×C8—151no—
127C16—151no—
128C16C2×D1511yescharacteristic, complemented
129C3×C5C2×SD3211yescharacteristic, complemented, Hall
130C22×C3—41no—
131C2×D3—51no—
132C2×D3—201no—
133C2×D3—402no—
134C3×C4—41no—
135C3×C4D4×D511yescharacteristic
136Dic3—51no—
137Dic3—201no—
138C2×C5—81no—
139C2×C5D3×D811yescharacteristic
140D5—32no—
141D5—241no—
142C23—601no—
143Q8—21no—
144Q8—301no—
145Q8—601no—
146D4—21no—
147D4—301no—
148D4—601no—
149C2×C4—151no—
150C2×C4—601no—
151C8—151no—
152C8C22×D1511yescharacteristic
153C2×C3—81no—
154C2×C3D5×D811yescharacteristic
155D3—52no—
156D3—401no—
157C5D3×SD3211yescharacteristic, complemented, Sylow
158C22—41no—
159C22—151no—
160C22—601no—
161C22—1202no—
162C4—41no—
163C4—151no—
164C4—601no—
165C4D4×D1511yescharacteristic
166C3D5×SD3211yescharacteristic, complemented, Sylow
167C2—81no—
168C2—152no—
169C2—1201no—
170C2D8×D1511yescharacteristic
subgroupG/H
centerC2D8×D15
commutator, cosocleC3×C5×C8C23
FrattiniC8C22×D15
FittingC3×C5×SD32C2
socleC2×C3×C5C2×D8
prime radicalD8×D15C2
hypercenterSD32D15
hypocenterC3×C5C2×SD32
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. Q16×D15C2semidirect
3. C3×C5×SD32C2semidirect
4. #91112C2semidirect
5. #91111C2semidirect
6. #91084C2semidirect
7. C16×D15C2semidirect
11. C3×C5×Q16C22semidirect
15. Dic60C22semidirect
18. C3×C5×C16C22semidirect
19. C3⋊#672C22semidirect
23. C5×SD32D3semidirect
41. C3×SD32D5semidirect
48. C5×Q16C2×D3semidirect
55. C5×C16C2×D3semidirect
68. C3×Q16C2×D5semidirect
75. C3×C16C2×D5semidirect
93. SD32D15direct (N × H)
98. D15SD32direct (N × H)
122. Q16C2×D15semidirect
128. C16C2×D15semidirect
129. C3×C5C2×SD32semidirect
157. C5D3×SD32semidirect
166. C3D5×SD32semidirect

Maximal subgroups

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

subgroupindex
Q16×D152
D8×D152
C3×C5×SD322
#911122
#911112
#910842
C16×D152
D5×SD323
D3×SD325