Finite Group Databasebeta

← #11750850

Subgroups — #11750850

Order 960.

216 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#91821C211yesmaximal, characteristic, complemented
2C2×#6715C211yesmaximal, characteristic, complemented
3#91797C211yesmaximal, characteristic, complemented
4#91796C211yesmaximal, characteristic, complemented
5C3×C5×#100C211yesmaximal, characteristic, complemented
6#91107C211yesmaximal, characteristic, complemented
7#91106C211yesmaximal, characteristic, complemented
8#65038—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10#6817C2211yescharacteristic
11C2×D60C2211yescharacteristic
12C3×C5×M16C2211yescharacteristic
13C3×C5×M16C2211yescharacteristic
14#6716—21no—
15#6715—21no—
16#6715—21no—
17#6715—21no—
18#6710C2211yescharacteristic
19C2×C3⋊#168C2211yescharacteristic
20D120—21no—
21#6706—21no—
22#6705—21no—
23C8×D15—21no—
24#4749—51nomaximal, Hall
25#4078—31no—
26C2×#686—31no—
27#4054—31no—
28#4053—31no—
29C5×#100D311yescharacteristic, complemented
30#3955—31no—
31#3954—31no—
32C23×C3×C5—21no—
33C22×D15—21no—
34C3×C5×D4—21no—
35C3×C5×D4—21no—
36C2×C3×C4×C5C2311yescharacteristic
37#1220—21no—
38D60—21no—
39D60—21no—
40D60D411yescharacteristic
41C4×D15—21no—
42Dic30D411yescharacteristic
43C3×C5×C8—21no—
44C3×C5×C8—21no—
45C3⋊#168—21no—
46C3⋊#168D411yescharacteristic
47C3⋊#168D411yescharacteristic
48#932—51no—
49C2×#213—51no—
50#908—51no—
51#907—51no—
52C3×#100D511yescharacteristic, complemented
53#823—51no—
54#822—51no—
55C2×C5×D4C2×D311yescharacteristic
56#709—31no—
57C2×D20—31no—
58C5×M16C2×D311yescharacteristic
59C5×M16C2×D311yescharacteristic
60#687—61no—
61#686—61no—
62#686—61no—
63#686—61no—
64#681—31no—
65C2×#168—31no—
66D40—61no—
67#677—61no—
68#676—61no—
69C8×D5—61no—
70#472—151noSylow
71C22×C3×C5—41no—
72C22×C3×C5—81no—
73C22×C3×C5#4111yescharacteristic
74C2×D15—21no—
75C2×D15—41no—
76C2×D15—81no—
77C3×C4×C5C2×D411yescharacteristic
78C3×C4×C5C2×D411yescharacteristic
79Dic15—21no—
80C2×C3×D4C2×D511yescharacteristic
81#235—51no—
82C2×D12—51no—
83C3×M16C2×D511yescharacteristic
84C3×M16C2×D511yescharacteristic
85#214—101no—
86#213—101no—
87#213—101no—
88#213—101no—
89#208—51no—
90C2×C3⋊C8—51no—
91D24—101no—
92#204—101no—
93ΓL(1,𝔽25)—101no—
94D3×C8—101no—
95C23×C5—21no—
96C22×D5—61no—
97C5×D4—21no—
98C5×D4—21no—
99C2×C4×C5C22×D311yescharacteristic
100C22⋊D5—61no—
101D20—31no—
102D20—61no—
103D20—61no—
104C4×D5—61no—
105Dic10—31no—
106C5×C8—21no—
107C5×C8—21no—
108#168—31no—
109#168—31no—
110#168—61no—
111AGL(1,ℤ/8)—151no—
112AGL(1,ℤ/8)—151no—
113C2×D8—151no—
114#131—151no—
115#108—151no—
116#100—151no—
117#100D1511yescharacteristic, complemented
118C2×C3×C5—21no—
119C2×C3×C5—81no—
120C2×C3×C5#12111yescharacteristic
121D15—41no—
122D15—81no—
123C23×C3—21no—
124C22×D3—101no—
125C3×D4—21no—
126C3×D4—21no—
127C2×C3×C4C22×D511yescharacteristic
128#67—101no—
129D12—51no—
130D12—101no—
131D12—101no—
132C4×D3—101no—
133Dic6—51no—
134C3×C8—21no—
135C3×C8—21no—
136C3⋊C8—51no—
137C3⋊C8—51no—
138C3⋊C8—101no—
139C22×C5—41no—
140C22×C5—81no—
141C22×C5#23511yescharacteristic
142C2×D5—61no—
143C2×D5—121no—
144C2×D5—241no—
145C4×C5D3×D411yescharacteristic
146C4×C5D3×D411yescharacteristic
147Dic5—61no—
148#41—151no—
149C2×D4—151no—
150C2×D4C2×D1511yescharacteristic
151SD16—301no—
152SD16—301no—
153D8—301no—
154D8—301no—
155D8—301no—
156D8—301no—
157M16—151no—
158M16—301no—
159M16C2×D1511yescharacteristic
160M16C2×D1511yescharacteristic
161C2×C8—151no—
162C2×C8—301no—
163C3×C5#47211yescharacteristic, complemented, Hall
164C22×C3—41no—
165C22×C3—81no—
166C22×C3#70911yescharacteristic
167C2×D3—101no—
168C2×D3—201no—
169C2×D3—401no—
170C3×C4D4×D511yescharacteristic
171C3×C4D4×D511yescharacteristic
172Dic3—101no—
173C2×C5—21no—
174C2×C5—81no—
175C2×C5#88411yescharacteristic
176D5—121no—
177D5—241no—
178C23—21no—
179C23—301no—
180Q8—151no—
181D4—21no—
182D4—21no—
183D4—151no—
184D4—301no—
185D4—301no—
186D4—301no—
187C2×C4—301no—
188C2×C4C22×D1511yescharacteristic
189C8—21no—
190C8—21no—
191C8—151no—
192C8—151no—
193C8—301no—
194C2×C3—21no—
195C2×C3—81no—
196C2×C3#403011yescharacteristic
197D3—201no—
198D3—401no—
199C5#474911yescharacteristic, complemented, Sylow
200C22—41no—
201C22—81no—
202C22—301no—
203C22—601no—
204C22—1201no—
205C22#681711yescharacteristic
206C4—301no—
207C4D4×D1511yescharacteristic
208C4D4×D1511yescharacteristic
209C3#6503811yescharacteristic, complemented, Sylow
210C2—21no—
211C2—81no—
212C2—601no—
213C2—1201no—
214C2#9177311yescharacteristic
subgroupG/H
centerC2#91773
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#100C2
socleC2×C3×C5#121
hypercenter#100D15
hypocenterC3×C5#472
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #91821C2semidirect
2. C2×#6715C2semidirect
3. #91797C2semidirect
4. #91796C2semidirect
5. C3×C5×#100C2semidirect
6. #91107C2semidirect
7. #91106C2semidirect
29. C5×#100D3semidirect
52. C3×#100D5semidirect
117. #100D15semidirect
163. C3×C5#472semidirect
199. C5#4749semidirect
209. C3#65038semidirect

Maximal subgroups

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

subgroupindex
#918212
C2×#67152
#917972
#917962
C3×C5×#1002
#911072
#911062
#650383
#47495