Finite Group Databasebeta

← #11756478

Subgroups — #11756478

Order 960.

480 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 139 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×C5×#127C211yesmaximal, characteristic, complemented
2#91828C214yesmaximal, complemented
3#91827C212yesmaximal, complemented
4#91824C214yesmaximal, complemented
5D4×Dic15C212yesmaximal, complemented
6#91761C211yesmaximal, characteristic, complemented
7#91759C211yesmaximal, characteristic, complemented
8#66053—31nomaximal, Hall
9C2×C3×C5×D4C2212yes—
10C2×C3×C5×D4C2214yes—
11C2×#1220C2214yes—
12C22×Dic15C2214yes—
13C2×C4×D15C2211yescharacteristic
14C3×C42×C5C2211yescharacteristic
15#6719C2214yes—
16#6719C2214yes—
17#6714C2212yes—
18C4⋊Dic15C2212yes—
19#6712C2214yes—
20#6712C2212yes—
21C4×Dic15C2211yescharacteristic
22#5719—51nomaximal, Hall
23C5×#127D311yescharacteristic, complemented
24#4085—34no—
25#4084—32no—
26#4081—34no—
27D4×Dic5—32no—
28#4018—31no—
29#4016—31no—
30C23×C3×C5C2314yes—
31C22×D15C2311yescharacteristic
32C3×C5×D4—24no—
33C3×C5×D4—44no—
34C2×C3×C4×C5C2312yes—
35C2×C3×C4×C5C2311yescharacteristic
36#1220—44no—
37C2×Dic15—44no—
38C2×Dic15C2312yes—
39C2×Dic15C2314yes—
40C2×Dic15C2311yescharacteristic
41C4×D15—22no—
42C3×#127D511yescharacteristic, complemented
43#939—54no—
44#938—52no—
45#935—54no—
46D4×Dic3—52no—
47#872—51no—
48#870—51no—
49C2×C5×D4C2×D312yes—
50C2×C5×D4C2×D314yes—
51C2×C22⋊D5—34no—
52C22×Dic5—34no—
53C2×C4×D5—31no—
54C42×C5C2×D311yescharacteristic
55C22⋊Dic5—34no—
56C22⋊Dic5—34no—
57#685—32no—
58C4⋊Dic5—32no—
59#683—34no—
60#683—32no—
61C4×Dic5—31no—
62#540—151noSylow
63C22×C3×C5—24no—
64C22×C3×C5—24no—
65C22×C3×C5—24no—
66C22×C3×C5C2411yescharacteristic
67C2×D15—21no—
68C2×D15—22no—
69C3×C4×C5—22no—
70C3×C4×C5#4112yes—
71Dic15—21no—
72Dic15—22no—
73Dic15—24no—
74C2×C3×D4C2×D512yes—
75C2×C3×D4C2×D514yes—
76C2×#67—54no—
77C22×Dic3—54no—
78C2×C4×D3—51no—
79C3×C42C2×D511yescharacteristic
80#217—54no—
81#217—54no—
82(C2×D3)⋊C4—52no—
83C4⋊Dic3—52no—
84Dic3⋊C4—54no—
85Dic3⋊C4—52no—
86C4×Dic3—51no—
87C23×C5C22×D314yes—
88C22×D5—31no—
89C5×D4—24no—
90C5×D4—44no—
91C2×C4×C5C22×D312yes—
92C2×C4×C5C22×D311yescharacteristic
93C22⋊D5—124no—
94C2×Dic5—32no—
95C2×Dic5—34no—
96C2×Dic5—31no—
97C2×Dic5—124no—
98C4×D5—62no—
99#127D1511yescharacteristic, complemented
100#125—151no—
101#123—154no—
102#121—152no—
103#121—154no—
104C4×D4—152no—
105#117—151no—
106C2×C3×C5—44no—
107C2×C3×C5C2×#4111yescharacteristic
108C2×C3×C5H(5,𝔽2)12yes—
109D15—41no—
110C23×C3C22×D514yes—
111C22×D3—51no—
112C3×D4—24no—
113C3×D4—44no—
114C2×C3×C4C22×D512yes—
115C2×C3×C4C22×D511yescharacteristic
116#67—204no—
117C2×Dic3—52no—
118C2×Dic3—54no—
119C2×Dic3—51no—
120C2×Dic3—204no—
121C4×D3—102no—
122C22×C5—24no—
123C22×C5—24no—
124C22×C5—24no—
125C22×C5C23×D311yescharacteristic
126C2×D5—61no—
127C2×D5—62no—
128C4×C5—22no—
129C4×C5#23712yes—
130Dic5—61no—
131Dic5—62no—
132Dic5—64no—
133C2×D4—154no—
134C2×D4C2×D1512yes—
135C2×D4C2×D1514yes—
136C22×C4—154no—
137C22×C4—151no—
138C4⋊C4—152no—
139C4⋊C4—152no—
140C4⋊C4—154no—
141C22⋊C4—154no—
142C22⋊C4—154no—
143C22⋊C4—152no—
144C42—151no—
145C42C2×D1511yescharacteristic
146C3×C5#54011yescharacteristic, complemented, Hall
147C22×C3—24no—
148C22×C3—24no—
149C22×C3—24no—
150C22×C3C23×D511yescharacteristic
151C2×D3—101no—
152C2×D3—102no—
153C3×C4—22no—
154C3×C4#71112yes—
155Dic3—101no—
156Dic3—102no—
157Dic3—104no—
158C2×C5—44no—
159C2×C5C2×#23711yescharacteristic
160C2×C5#100412yes—
161D5—121no—
162C23—151no—
163C23C22×D1514yes—
164D4—24no—
165D4—44no—
166D4—604no—
167C2×C4—152no—
168C2×C4—151no—
169C2×C4—154no—
170C2×C4—302no—
171C2×C4—604no—
172C2×C4C22×D1512yes—
173C2×C4C22×D1511yescharacteristic
174C2×C3—44no—
175C2×C3C2×#71111yescharacteristic
176C2×C3#414412yes—
177D3—201no—
178C5#571911yescharacteristic, complemented, Sylow
179C22—24no—
180C22—24no—
181C22—24no—
182C22—301no—
183C22—302no—
184C22C23×D1511yescharacteristic
185C4—22no—
186C4—301no—
187C4—302no—
188C4—304no—
189C4#681912yes—
190C3#6605311yescharacteristic, complemented, Sylow
191C2—44no—
192C2—601no—
193C2C2×#681911yescharacteristic
194C2#9209512yes—
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#127C2
hypercenter#127D15
hypocenterC3×C5#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×C5×#127C2semidirect
2. #91828C2semidirect
3. #91827C2semidirect
4. #91824C2semidirect
5. D4×Dic15C2semidirect
6. #91761C2semidirect
7. #91759C2semidirect
23. C5×#127D3semidirect
42. C3×#127D5semidirect
99. #127D15semidirect
146. C3×C5#540semidirect
178. C5#5719semidirect
190. C3#66053semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1272
#918282
#918272
#918242
D4×Dic152
#917612
#917592
#660533
#57195