Finite Group Databasebeta

← #11755443

Subgroups — #11755443

Order 960.

520 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 120 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#91842C211yesmaximal, characteristic, complemented
2C5×#953C211yesmaximal, characteristic, complemented
3C3×#4099C211yesmaximal, characteristic, complemented
4#91577C213yesmaximal, complemented
5#91534C213yesmaximal, complemented
6#91526C213yesmaximal, complemented
7#91525C213yesmaximal, complemented
8#65928—31nomaximal, Hall
9C24×C3×C5C2211yescharacteristic, complemented
10C22×D3×D5C2211yescharacteristic, complemented
11C2×#1220C2213yes—
12C2×C5×#67C2213yes—
13C2×C3×C22⋊D5C2213yes—
14C2×#1204C2213yescomplemented
15#6719C2213yescomplemented
16C5×#217C2213yescomplemented
17C3×C22⋊Dic5C2213yescomplemented
18#6667C2213yescomplemented
19(C2×D3)⋊Dic5C2213yescomplemented
20#6665C2213yescomplemented
21Dic3×Dic5C2213yescomplemented
22#5594—51nomaximal, Hall
23C5×#120—31no—
24#4099—31no—
25#4099D311yescharacteristic, complemented
26#4083—33no—
27#4082—33no—
28#4031—33no—
29#4031—33no—
30C23×C3×C5—43no—
31C23×C3×C5C2313yes—
32C22×D15C2311yescharacteristic
33C22×C5×D3C2311yescharacteristic
34C22×C3×D5C2311yescharacteristic
35C2×D3×D5—43no—
36#1220—43no—
37C2×Dic15C2313yes—
38C5×#67—43no—
39C2×C5×Dic3C2313yes—
40C3×C22⋊D5—43no—
41C2×C3×Dic5C2313yes—
42#1204—43no—
43C3×#120—51no—
44#953—51no—
45#953D511yescharacteristic, complemented
46#937—53no—
47#936—53no—
48#885—53no—
49#885—53no—
50C24×C5C2×D311yescharacteristic, complemented
51C23×D5—31no—
52C2×C5×D4—33no—
53C2×C22⋊D5—33no—
54C2×C22⋊D5C2×D313yes—
55C2×Dic10—33no—
56C5×C22⋊C4—33no—
57C22⋊Dic5—33no—
58C22⋊Dic5—33no—
59C22⋊Dic5C2×D313yescomplemented
60#685—33no—
61#685—33no—
62C4×Dic5—33no—
63H(3,𝔽4)—151noSylow
64C22×C3×C5—23no—
65C22×C3×C5—23no—
66C22×C3×C5—23no—
67C22×C3×C5—44no—
68C22×C3×C5C2411yescharacteristic
69C2×D15—23no—
70C2×C5×D3—23no—
71C2×C3×D5—23no—
72D3×D5—44no—
73Dic15—23no—
74C3×Dic5—23no—
75C5×Dic3—23no—
76C24×C3C2×D511yescharacteristic, complemented
77C23×D3—51no—
78C2×C3×D4—53no—
79C2×#67—53no—
80C2×#67C2×D513yes—
81C2×Dic6—53no—
82C3×C22⋊C4—53no—
83#217—53no—
84#217—53no—
85#217C2×D513yescomplemented
86(C2×D3)⋊C4—53no—
87(C2×D3)⋊C4—53no—
88C4×Dic3—53no—
89C23×C5—31no—
90C23×C5—43no—
91C23×C5C22×D313yes—
92C22×D5—31no—
93C22×D5—123no—
94C22×D5C22×D311yescharacteristic
95C5×D4—123no—
96C2×C4×C5—33no—
97C22⋊D5—43no—
98C22⋊D5—123no—
99C2×Dic5—33no—
100C2×Dic5C22×D313yes—
101Dic10—123no—
102#124—153no—
103#124—153no—
104#124—153no—
105#120—31no—
106#120—51no—
107#120—153no—
108#120—151no—
109C2×C3×C5—43no—
110C2×C3×C5H(5,𝔽2)13yes—
111D15—41no—
112C3×D5—41no—
113C5×D3—41no—
114C23×C3—43no—
115C23×C3—51no—
116C23×C3C22×D513yes—
117C22×D3—51no—
118C22×D3—203no—
119C22×D3C22×D511yescharacteristic
120C3×D4—203no—
121C2×C3×C4—53no—
122#67—43no—
123#67—203no—
124C2×Dic3—53no—
125C2×Dic3C22×D513yes—
126Dic6—203no—
127C22×C5—23no—
128C22×C5—23no—
129C22×C5—23no—
130C22×C5—44no—
131C22×C5—63no—
132C22×C5C23×D311yescharacteristic
133C2×D5—23no—
134C2×D5—63no—
135C2×D5—124no—
136C4×C5—63no—
137Dic5—23no—
138Dic5—63no—
139C24—151no—
140C24D3×D511yescharacteristic, complemented
141C2×Q8—153no—
142C2×D4—33no—
143C2×D4—53no—
144C2×D4—153no—
145C22⋊C4—33no—
146C22⋊C4—53no—
147C22⋊C4—153no—
148C22⋊C4—153no—
149C22⋊C4—153no—
150C22⋊C4—153no—
151C42—153no—
152C3×C5H(3,𝔽4)11yescharacteristic, complemented, Hall
153C22×C3—23no—
154C22×C3—23no—
155C22×C3—23no—
156C22×C3—44no—
157C22×C3—103no—
158C22×C3C23×D511yescharacteristic
159C2×D3—23no—
160C2×D3—103no—
161C2×D3—204no—
162C3×C4—103no—
163Dic3—23no—
164Dic3—103no—
165C2×C5—43no—
166C2×C5—121no—
167C2×C5#100413yes—
168D5—41no—
169D5—121no—
170C23—31no—
171C23—43no—
172C23—51no—
173C23—151no—
174C23—603no—
175C23C2×D3×D513yes—
176Q8—603no—
177D4—123no—
178D4—203no—
179D4—603no—
180C2×C4—33no—
181C2×C4—53no—
182C2×C4—153no—
183C2×C3—43no—
184C2×C3—201no—
185C2×C3#414413yes—
186D3—41no—
187D3—201no—
188C5#559411yescharacteristic, complemented, Sylow
189C22—23no—
190C22—23no—
191C22—23no—
192C22—44no—
193C22—63no—
194C22—103no—
195C22—303no—
196C22—604no—
197C22C22×D3×D511yescharacteristic
198C4—63no—
199C4—103no—
200C4—303no—
201C3#6592811yescharacteristic, complemented, Sylow
202C2—43no—
203C2—121no—
204C2—201no—
205C2—601no—
206C2#9204913yes—
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC24×C3×C5C22
hypercenterC24D3×D5
hypocenterC3×C5H(3,𝔽4)
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. #91842C2semidirect
2. C5×#953C2semidirect
3. C3×#4099C2semidirect
4. #91577C2semidirect
5. #91534C2semidirect
6. #91526C2semidirect
7. #91525C2semidirect
9. C24×C3×C5C22semidirect
10. C22×D3×D5C22semidirect
14. C2×#1204C22semidirect
15. #6719C22semidirect
16. C5×#217C22semidirect
17. C3×C22⋊Dic5C22semidirect
18. #6667C22semidirect
19. (C2×D3)⋊Dic5C22semidirect
20. #6665C22semidirect
21. Dic3×Dic5C22semidirect
25. #4099D3semidirect
45. #953D5semidirect
50. C24×C5C2×D3semidirect
59. C22⋊Dic5C2×D3semidirect
76. C24×C3C2×D5semidirect
85. #217C2×D5semidirect
140. C24D3×D5semidirect
152. C3×C5H(3,𝔽4)semidirect
188. C5#5594semidirect
201. C3#65928semidirect

Maximal subgroups

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

subgroupindex
#918422
C5×#9532
C3×#40992
#915772
#915342
#915262
#915252
#659283
#55945