Finite Group Databasebeta

← #11752773

Subgroups — #11752773

Order 960.

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

normal subgroups only

This group has 504 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#91765C211yesmaximal, characteristic, complemented
2C5×#876C211yesmaximal, characteristic, complemented
3C3×#4020C211yesmaximal, characteristic, complemented
4#91474C213yesmaximal, complemented
5#91409C213yesmaximal, complemented
6#91408C213yesmaximal, complemented
7#91407C213yesmaximal, complemented
8#66045—31nomaximal, Hall
9C22×D3×D5C2211yescharacteristic
10C2×C3×D20C2213yes—
11C2×C3×D20C2213yescomplemented
12C2×#1202C2213yes—
13C2×#1201C2213yes—
14C2×D5×Dic3C2213yescomplemented
15C3×C42×C5C2211yescharacteristic, complemented
16#6714C2213yes—
17#6712C2213yescomplemented
18C5×(C2×D3)⋊C4C2213yes—
19C5×Dic3⋊C4C2213yescomplemented
20#6665C2213yes—
21#6665C2213yescomplemented
22#5720—51nomaximal, Hall
23C5×#126—31no—
24#4041—33no—
25#4040—33no—
26#4030—33no—
27#4028—33no—
28#4022—31no—
29#4020D311yescharacteristic, complemented
30C22×D15C2311yescharacteristic
31C22×C5×D3C2311yescharacteristic
32C22×C3×D5C2311yescharacteristic
33C22×C3×D5C2313yes—
34C2×D3×D5—43no—
35C2×C3×C4×C5C2313yes—
36C2×Dic15C2313yes—
37C2×C5×Dic3C2313yes—
38C3×D20—43no—
39C3×D20—43no—
40#1202—43no—
41#1201—43no—
42D5×Dic3—43no—
43C3×#127—51no—
44#939—53no—
45#939—53no—
46#937—53no—
47#935—53no—
48#876—51no—
49#876D511yescharacteristic, complemented
50C23×D5—31no—
51C2×C22⋊D5—33no—
52C2×D20—33no—
53C2×D20C2×D313yes—
54C2×D20C2×D313yescomplemented
55C2×C4×D5—33no—
56C5×C4⋊C4—33no—
57C5×C22⋊C4—33no—
58C42×C5C2×D311yescharacteristic, complemented
59#685—33no—
60#685—33no—
61#685—33no—
62#683—33no—
63#560—151noSylow
64C22×C3×C5C2411yescharacteristic
65C2×D15—23no—
66C2×C5×D3—23no—
67C2×C3×D5—23no—
68C2×C3×D5—23no—
69C2×C3×D5—23no—
70C2×C3×D5—23no—
71D3×D5—44no—
72C3×C4×C5—23no—
73Dic15—23no—
74C5×Dic3—23no—
75C23×D3—51no—
76C2×C3×D4—53no—
77C2×C3×D4—53no—
78C2×#67—53no—
79C2×#67—53no—
80C22×Dic3—53no—
81C3×C42C2×D511yescharacteristic, complemented
82#217—53no—
83#217—53no—
84(C2×D3)⋊C4—53no—
85(C2×D3)⋊C4C2×D513yes—
86Dic3⋊C4—53no—
87Dic3⋊C4C2×D513yescomplemented
88C23×C5—31no—
89C22×D5—31no—
90C22×D5—123no—
91C22×D5C22×D311yescharacteristic
92C22×D5C22×D313yes—
93C2×C4×C5—33no—
94C2×C4×C5C22×D313yes—
95C22⋊D5—123no—
96C2×Dic5—33no—
97D20—43no—
98D20—43no—
99D20—123no—
100C4×D5—123no—
101#127—51no—
102#126—31no—
103#126—151no—
104#123—153no—
105#121—153no—
106#121—153no—
107#120—153no—
108C2×C3×C5H(5,𝔽2)13yes—
109D15—41no—
110C3×D5—41no—
111C3×D5—43no—
112C5×D3—41no—
113C23×C3—51no—
114C23×C3—53no—
115C22×D3—51no—
116C22×D3—203no—
117C22×D3C22×D511yescharacteristic
118C3×D4—203no—
119C3×D4—203no—
120C2×C3×C4C22×D513yes—
121#67—203no—
122#67—203no—
123C2×Dic3—53no—
124C2×Dic3—203no—
125C2×Dic3C22×D513yes—
126C22×C5—63no—
127C22×C5C23×D311yescharacteristic
128C2×D5—23no—
129C2×D5—23no—
130C2×D5—23no—
131C2×D5—23no—
132C2×D5—63no—
133C2×D5—124no—
134C4×C5—23no—
135C4×C5—63no—
136Dic5—63no—
137C24—151no—
138C2×D4—53no—
139C2×D4—53no—
140C2×D4—153no—
141C2×D4—153no—
142C22×C4—153no—
143C4⋊C4—33no—
144C4⋊C4—153no—
145C22⋊C4—33no—
146C22⋊C4—153no—
147C22⋊C4—153no—
148C22⋊C4—153no—
149C42D3×D511yescharacteristic, complemented
150C3×C5#56011yescharacteristic, complemented, Hall
151C22×C3—103no—
152C22×C3—103no—
153C22×C3—103no—
154C22×C3—103no—
155C22×C3C23×D511yescharacteristic
156C2×D3—23no—
157C2×D3—103no—
158C2×D3—204no—
159C3×C4—23no—
160Dic3—23no—
161Dic3—103no—
162C2×C5—121no—
163C2×C5#100413yes—
164D5—41no—
165D5—43no—
166D5—121no—
167C23—31no—
168C23—51no—
169C23—53no—
170C23—151no—
171C23—603no—
172D4—203no—
173D4—203no—
174D4—603no—
175D4—603no—
176C2×C4—33no—
177C2×C4—153no—
178C2×C4—603no—
179C2×C4C2×D3×D513yes—
180C2×C3—201no—
181C2×C3—203no—
182C2×C3#414913yes—
183D3—41no—
184D3—201no—
185C5#572011yescharacteristic, complemented, Sylow
186C22—63no—
187C22—103no—
188C22—103no—
189C22—103no—
190C22—103no—
191C22—303no—
192C22—604no—
193C22C22×D3×D511yescharacteristic
194C4—23no—
195C4—63no—
196C4—303no—
197C3#6604511yescharacteristic, complemented, Sylow
198C2—121no—
199C2—201no—
200C2—203no—
201C2—601no—
202C2#9201713yes—
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
hypercenterC42D3×D5
hypocenterC3×C5#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #91765C2semidirect
2. C5×#876C2semidirect
3. C3×#4020C2semidirect
4. #91474C2semidirect
5. #91409C2semidirect
6. #91408C2semidirect
7. #91407C2semidirect
11. C2×C3×D20C22semidirect
14. C2×D5×Dic3C22semidirect
15. C3×C42×C5C22semidirect
17. #6712C22semidirect
19. C5×Dic3⋊C4C22semidirect
21. #6665C22semidirect
29. #4020D3semidirect
49. #876D5semidirect
54. C2×D20C2×D3semidirect
58. C42×C5C2×D3semidirect
81. C3×C42C2×D5semidirect
87. Dic3⋊C4C2×D5semidirect
149. C42D3×D5semidirect
150. C3×C5#560semidirect
185. C5#5720semidirect
197. C3#66045semidirect

Maximal subgroups

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

subgroupindex
#917652
C5×#8762
C3×#40202
#914742
#914092
#914082
#914072
#660453
#57205