Finite Group Databasebeta

← #11747415

Subgroups — #11747415

Order 960.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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×#4039C211yesmaximal, characteristic
2#91468C211yesmaximal, characteristic, complemented
3#91092C211yesmaximal, characteristic, complemented
4C5×#808C211yesmaximal, characteristic, complemented
5#90982C211yesmaximal, characteristic, complemented
6#90965C211yesmaximal, characteristic
7#90964C211yesmaximal, characteristic
8#65159—31nomaximal, Hall
9C2×C3×D20C2211yescharacteristic
10C2×C3×C4×D5—21no—
11C2×#1204—21no—
12C3×C5×C4⋊C4C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#685—21no—
18C3×C4×Dic5C2211yescharacteristic
19#6668—21no—
20#5008—51nomaximal, Hall
21#4039D311yescharacteristic
22#4034—31no—
23C5×#106—31no—
24#3953—31no—
25#3946—31no—
26#3941—31no—
27#3940—31no—
28C22×C3×D5—21no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5C2311yescharacteristic
31C2×Dic15—21no—
32C2×C5×Dic3—21no—
33C2×C3×Dic5D411yescharacteristic
34C2×C3×Dic5D411yescharacteristic
35C3×D20—21no—
36C3×D20Q812yescomplemented
37C3×C4×D5—42no—
38#1204—42no—
39C3⋊#168—21no—
40C5×C3⋊C8—21no—
41C3×C4×D4—51no—
42#869—51no—
43#832—51no—
44#832—51no—
45#808—51no—
46#808D511yescharacteristic, complemented
47C4⋊(C3⋊C8)—51no—
48C2×D20C2×D311yescharacteristic
49C2×C4×D5—21no—
50C2×Dic10—61no—
51C2×C5×C8—31no—
52C5×C4⋊C4—31no—
53C5×C4⋊C4C2×D311yescharacteristic
54#685—21no—
55C4⋊Dic5—31no—
56#683—61no—
57C4×Dic5C2×D311yescharacteristic
58C2×#168—31no—
59#476—151noSylow
60C22×C3×C5C2×D411yescharacteristic
61C2×C3×D5—22no—
62C2×C3×D5—41no—
63C2×C3×D5—41no—
64C3×C4×C5—41no—
65C3×C4×C5C2×Q811yescharacteristic
66C3×C4×C5#4111yescharacteristic
67Dic15—41no—
68C3×Dic5—21no—
69C3×Dic5SD1612yes—
70C5×Dic3—41no—
71C2×C3×D4—51no—
72C22×C3×C4—101no—
73C2×Dic6—101no—
74C3×C4⋊C4C2×D511yescharacteristic
75C3×C22⋊C4—101no—
76C3×C42—51no—
77C4⋊Dic3—51no—
78C4⋊Dic3—101no—
79C4⋊Dic3C2×D511yescharacteristic
80C2×C3⋊C8—51no—
81C2×C3⋊C8C2×D511yescharacteristic
82C22×D5—21no—
83C2×C4×C5—21no—
84C2×C4×C5—61no—
85C2×C4×C5C22×D311yescharacteristic
86C2×Dic5—61no—
87C2×Dic5#6711yescharacteristic
88C2×Dic5#6711yescharacteristic
89D20—21no—
90D20Dic612yescomplemented
91C4×D5—42no—
92Dic10—122no—
93C5×C8—61no—
94#168—61no—
95C4⋊Q8—151no—
96C4×D4—51no—
97#106—31no—
98#106—151no—
99C4⋊C8—151no—
100#102—151no—
101#102—151no—
102C2×C3×C5C22⋊Q811yescharacteristic
103C2×C3×C5C2×SD1611yescharacteristic
104C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
105C3×D5—42no—
106C23×C3—101no—
107C3×D4—52no—
108C3×D4—101no—
109C2×C3×C4—21no—
110C2×C3×C4—51no—
111C2×C3×C4—51no—
112C2×C3×C4—202no—
113C2×C3×C4C22×D511yescharacteristic
114C2×Dic3—21no—
115C2×Dic3—101no—
116Dic6—202no—
117C3⋊C8—21no—
118C3⋊C8—101no—
119C22×C5C2×#6711yescharacteristic
120C2×D5—22no—
121C2×D5—41no—
122C2×D5—41no—
123C4×C5—41no—
124C4×C5—121no—
125C4×C5C2×Dic611yescharacteristic
126C4×C5#23511yescharacteristic
127Dic5—21no—
128Dic5—121no—
129Dic5#21412yes—
130C2×Q8—301no—
131C2×D4—51no—
132C22×C4—101no—
133C2×C8—31no—
134C2×C8—151no—
135C4⋊C4—31no—
136C4⋊C4—151no—
137C4⋊C4—301no—
138C4⋊C4D3×D511yescharacteristic
139C22⋊C4—101no—
140C42—51no—
141C3×C5#47611yescharacteristic, complemented, Hall
142C22×C3—102no—
143C22×C3—201no—
144C22×C3—201no—
145C22×C3D4×D511yescharacteristic
146C3×C4—41no—
147C3×C4—52no—
148C3×C4—101no—
149C3×C4#70911yescharacteristic
150C3×C4Q8×D511yescharacteristic
151Dic3—41no—
152Dic3—201no—
153C2×C5#92411yescharacteristic
154C2×C5C2×#21411yescharacteristic
155C2×C5#94911yescharacteristic
156D5—42no—
157C23—101no—
158Q8—602no—
159D4—52no—
160D4—101no—
161C2×C4—21no—
162C2×C4—51no—
163C2×C4—51no—
164C2×C4—61no—
165C2×C4—202no—
166C2×C4—301no—
167C2×C4C2×D3×D511yescharacteristic
168C8—61no—
169C8—301no—
170C2×C3—202no—
171C2×C3#404211yescharacteristic
172C2×C3D5×SD1611yescharacteristic
173C2×C3#406011yescharacteristic
174C5#500811yescharacteristic, complemented, Sylow
175C22—102no—
176C22—201no—
177C22—201no—
178C22D5×#6711yescharacteristic
179C4—41no—
180C4—52no—
181C4—101no—
182C4—121no—
183C4—601no—
184C4D5×Dic611yescharacteristic
185C4#677111yescharacteristic
186C3#6515911yescharacteristic, complemented, Sylow
187C2—202no—
188C2#9134911yescharacteristic
189C2D5×#21411yescharacteristic
190C2#9150211yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC2×C3×D20C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#476
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #91468C2semidirect
3. #91092C2semidirect
4. C5×#808C2semidirect
5. #90982C2semidirect
36. C3×D20Q8semidirect
46. #808D5semidirect
90. D20Dic6semidirect
141. C3×C5#476semidirect
174. C5#5008semidirect
186. C3#65159semidirect

Maximal subgroups

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

subgroupindex
C3×#40392
#914682
#910922
C5×#8082
#909822
#909652
#909642
#651593
#50085