Finite Group Databasebeta

← #11750875

Subgroups — #11750875

Order 960.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#91827C211yesmaximal, characteristic
2C4⋊C4×D15C211yesmaximal, characteristic, complemented
3C3×C5×#102C211yesmaximal, characteristic, complemented
4#91116C211yesmaximal, characteristic, complemented
5#91104C211yesmaximal, characteristic, complemented
6#91102C211yesmaximal, characteristic, complemented
7#91091C211yesmaximal, characteristic, complemented
8#65063—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10C2×#1220—21no—
11C2×C4×D15—21no—
12C2×C4×D15C2211yescharacteristic
13C2×C3×C5×C8C2211yescharacteristic
14C3×C5×C4⋊C4C2211yescharacteristic
15#6719—21no—
16C4⋊Dic15C2211yescharacteristic
17C4⋊Dic15C2211yescharacteristic
18#6712—21no—
19C2×C3⋊#168C2211yescharacteristic
20#4774—51nomaximal, Hall
21#4084—31no—
22D5×C4⋊C4—31no—
23C5×#102D311yescharacteristic, complemented
24#3964—31no—
25#3952—31no—
26#3950—31no—
27#3939—31no—
28C23×C3×C5—21no—
29C22×D15D411yescharacteristic
30C3×C5×D4—21no—
31C3×C5×D4—21no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5C2311yescharacteristic
34#1220—42no—
35C2×Dic15—21no—
36C2×Dic15—21no—
37C2×Dic15D411yescharacteristic
38C4×D15—21no—
39C4×D15—21no—
40C4×D15—42no—
41C3×C5×C8—21no—
42C3⋊#168—21no—
43#938—51no—
44D3×C4⋊C4—51no—
45C3×#102D511yescharacteristic, complemented
46#832—51no—
47(C2×D3)⋊C8—51no—
48#818—51no—
49#807—51no—
50C2×C5×D4C2×D311yescharacteristic
51C2×C22⋊D5—61no—
52C2×C4×D5—31no—
53C2×C4×D5—61no—
54C2×C5×C8C2×D311yescharacteristic
55C5×C4⋊C4C2×D311yescharacteristic
56C22⋊Dic5—61no—
57C4⋊Dic5—31no—
58C4⋊Dic5—31no—
59#683—61no—
60C2×#168—31no—
61#480—151noSylow
62C22×C3×C5—41no—
63C22×C3×C5—41no—
64C22×C3×C5—41no—
65C22×C3×C5C2×D411yescharacteristic
66C2×D15—21no—
67C2×D15—21no—
68C2×D15D812yes—
69C3×C4×C5—41no—
70C3×C4×C5#4111yescharacteristic
71C3×C4×C5#4111yescharacteristic
72Dic15—21no—
73Dic15—41no—
74Dic15—41no—
75C2×C3×D4C2×D511yescharacteristic
76C2×#67—101no—
77C2×C4×D3—51no—
78C2×C4×D3—101no—
79C2×C3×C8C2×D511yescharacteristic
80C3×C4⋊C4C2×D511yescharacteristic
81#217—101no—
82C4⋊Dic3—51no—
83C4⋊Dic3—51no—
84Dic3⋊C4—101no—
85C2×C3⋊C8—51no—
86C23×C5—21no—
87C22×D5—31no—
88C5×D4—21no—
89C5×D4—21no—
90C2×C4×C5—21no—
91C2×C4×C5C22×D311yescharacteristic
92C22⋊D5—122no—
93C2×Dic5—31no—
94C2×Dic5—61no—
95C2×Dic5—61no—
96C4×D5—61no—
97C4×D5—61no—
98C4×D5—122no—
99C5×C8—21no—
100#168—61no—
101#121—151no—
102C2×C4⋊C4—151no—
103#107—151no—
104#107—151no—
105#102—151no—
106#102D1511yescharacteristic, complemented
107C22⋊C8—151no—
108C2×C3×C5—81no—
109C2×C3×C5#12311yescharacteristic
110C2×C3×C5C2×D811yescharacteristic
111C2×C3×C5#13711yescharacteristic
112D15—22no—
113C23×C3—21no—
114C22×D3—51no—
115C3×D4—21no—
116C3×D4—21no—
117C2×C3×C4—21no—
118C2×C3×C4C22×D511yescharacteristic
119#67—202no—
120C2×Dic3—51no—
121C2×Dic3—101no—
122C2×Dic3—101no—
123C4×D3—101no—
124C4×D3—101no—
125C4×D3—202no—
126C3×C8—21no—
127C3⋊C8—101no—
128C22×C5—41no—
129C22×C5—41no—
130C22×C5—41no—
131C22×C5D3×D411yescharacteristic
132C2×D5—32no—
133C2×D5—61no—
134C2×D5—61no—
135C4×C5—41no—
136C4×C5#23511yescharacteristic
137C4×C5#23711yescharacteristic
138Dic5—61no—
139Dic5—121no—
140Dic5—121no—
141C2×D4—301no—
142C2×D4C2×D1511yescharacteristic
143C22×C4—151no—
144C22×C4—301no—
145C2×C8—151no—
146C2×C8C2×D1511yescharacteristic
147C4⋊C4—151no—
148C4⋊C4—151no—
149C4⋊C4—301no—
150C4⋊C4C2×D1511yescharacteristic
151C22⋊C4—301no—
152C3×C5#48011yescharacteristic, complemented, Hall
153C22×C3—41no—
154C22×C3—41no—
155C22×C3—41no—
156C22×C3D4×D511yescharacteristic
157C2×D3—52no—
158C2×D3—101no—
159C2×D3—101no—
160C3×C4—41no—
161C3×C4#70911yescharacteristic
162C3×C4#71111yescharacteristic
163Dic3—101no—
164Dic3—201no—
165Dic3—201no—
166C2×C5—81no—
167C2×C5#88311yescharacteristic
168C2×C5D3×D811yescharacteristic
169C2×C5#91511yescharacteristic
170D5—62no—
171C23—21no—
172C23—151no—
173D4—21no—
174D4—21no—
175D4—602no—
176C2×C4—21no—
177C2×C4—151no—
178C2×C4—301no—
179C2×C4—301no—
180C2×C4—301no—
181C2×C4—301no—
182C2×C4—602no—
183C2×C4C22×D1511yescharacteristic
184C8—21no—
185C8—301no—
186C2×C3—81no—
187C2×C3#402911yescharacteristic
188C2×C3D5×D811yescharacteristic
189C2×C3#406111yescharacteristic
190D3—102no—
191C5#477411yescharacteristic, complemented, Sylow
192C22—41no—
193C22—41no—
194C22—41no—
195C22—152no—
196C22—301no—
197C22—301no—
198C22D4×D1511yescharacteristic
199C4—41no—
200C4—301no—
201C4—601no—
202C4—601no—
203C4#681711yescharacteristic
204C4#681911yescharacteristic
205C3#6506311yescharacteristic, complemented, Sylow
206C2—81no—
207C2—302no—
208C2#9177211yescharacteristic
209C2D8×D1511yescharacteristic
210C2#9180411yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#102C2
socleC22×C3×C5C2×D4
prime radical#91827C2
hypercenter#102D15
hypocenterC3×C5#480
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×D15C2semidirect
3. C3×C5×#102C2semidirect
4. #91116C2semidirect
5. #91104C2semidirect
6. #91102C2semidirect
7. #91091C2semidirect
23. C5×#102D3semidirect
45. C3×#102D5semidirect
106. #102D15semidirect
152. C3×C5#480semidirect
191. C5#4774semidirect
205. C3#65063semidirect

Maximal subgroups

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

subgroupindex
#918272
C4⋊C4×D152
C3×C5×#1022
#911162
#911042
#911022
#910912
#650633
#47745