Finite Group Databasebeta

← C3×#4085 #91656

Subgroups — C3×#4085 #91656

Order 480.

188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×C3×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×C3×Dic5C211yesmaximal, characteristic, complemented
5C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
6C3×#685C211yesmaximal, characteristic, complemented
7C3×#683C211yesmaximal, characteristic, complemented
8#4085C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C5C2211yescharacteristic
10C23×C3×C5C2211yescharacteristic
11C22×C3×D5C2211yescharacteristic
12C3×C5×D4—22no—
13C2×C3×C4×C5C2211yescharacteristic
14C3×C22⋊D5—22no—
15C3×C22⋊D5—22no—
16C2×C3×Dic5—22no—
17C2×C3×Dic5C2211yescharacteristic
18C2×C3×Dic5C2211yescharacteristic
19C2×C3×Dic5C2211yescharacteristic
20C3×#121—51nomaximal, Hall
21C2×C5×D4C2×C311yescharacteristic, complemented
22C2×C22⋊D5C2×C311yescharacteristic, complemented
23C2×C22⋊D5C2×C311yescharacteristic, complemented
24C22×Dic5C2×C311yescharacteristic, complemented
25C22⋊Dic5C2×C311yescharacteristic, complemented
26#685C2×C311yescharacteristic, complemented
27#683C2×C311yescharacteristic, complemented
28C22×C3×C5—21no—
29C22×C3×C5—21no—
30C22×C3×C5—21no—
31C22×C3×C5—21no—
32C22×C3×C5—21no—
33C22×C3×C5D412yescomplemented
34C22×C3×C5C2311yescharacteristic
35C2×C3×D5—21no—
36C2×C3×D5—21no—
37C2×C3×D5—21no—
38C3×C4×C5—21no—
39C3×Dic5—21no—
40C3×Dic5—21no—
41C3×Dic5D412yescomplemented
42C2×C3×D4—51no—
43C2×C3×D4—51no—
44C2×C3×D4D511yescharacteristic, complemented
45C22×C3×C4—51no—
46C3×C4⋊C4—51no—
47C3×C22⋊C4—51no—
48C3×C22⋊C4—51no—
49C23×C5C22×C311yescharacteristic
50C23×C5C22×C311yescharacteristic
51C22×D5C22×C311yescharacteristic
52C5×D4—22no—
53C2×C4×C5C22×C311yescharacteristic
54C22⋊D5—22no—
55C22⋊D5—22no—
56C2×Dic5—22no—
57C2×Dic5C22×C311yescharacteristic
58C2×Dic5C22×C311yescharacteristic
59C2×Dic5C22×C311yescharacteristic
60#121—51noSylow
61C2×C3×C5—22no—
62C2×C3×C5—41no—
63C2×C3×C5C2×D411yescharacteristic
64C2×C3×C5C2×D411yescharacteristic
65C2×C3×C5#4111yescharacteristic
66C3×D5—41no—
67C23×C3—51no—
68C23×C3C2×D511yescharacteristic
69C23×C3C2×D511yescharacteristic
70C3×D4—22no—
71C3×D4—102no—
72C3×D4—102no—
73C2×C3×C4—51no—
74C2×C3×C4—51no—
75C2×C3×C4—51no—
76C2×C3×C4—102no—
77C2×C3×C4C2×D511yescharacteristic
78C22×C5—21no—
79C22×C5—21no—
80C22×C5—21no—
81C22×C5—21no—
82C22×C5—21no—
83C22×C5C3×D412yescomplemented
84C22×C5C23×C311yescharacteristic
85C2×D5—21no—
86C2×D5—21no—
87C2×D5—21no—
88C4×C5—21no—
89Dic5—21no—
90Dic5—21no—
91Dic5C3×D412yescomplemented
92C2×D4—51no—
93C2×D4—51no—
94C2×D4C3×D511yescharacteristic, complemented
95C22×C4—51no—
96C4⋊C4—51no—
97C22⋊C4—51no—
98C22⋊C4—51no—
99C3×C5#12111yescharacteristic, complemented, Hall
100C22×C3—21no—
101C22×C3—21no—
102C22×C3—21no—
103C22×C3—21no—
104C22×C3—21no—
105C22×C3—101no—
106C22×C3—101no—
107C22×C3—101no—
108C22×C3C22⋊D512yescomplemented
109C22×C3C22×D511yescharacteristic
110C3×C4—21no—
111C3×C4—52no—
112C3×C4—101no—
113C3×C4—101no—
114C2×C5—22no—
115C2×C5—41no—
116C2×C5C2×C3×D411yescharacteristic
117C2×C5C2×C3×D411yescharacteristic
118C2×C5C3×#4111yescharacteristic
119D5—41no—
120C23—51no—
121C23C2×C3×D511yescharacteristic
122C23C2×C3×D511yescharacteristic
123D4—22no—
124D4—102no—
125D4—102no—
126C2×C4—51no—
127C2×C4—51no—
128C2×C4—51no—
129C2×C4—102no—
130C2×C4C2×C3×D511yescharacteristic
131C2×C3—22no—
132C2×C3—41no—
133C2×C3—201no—
134C2×C3D4×D511yescharacteristic
135C2×C3#71111yescharacteristic
136C2×C3C2×C22⋊D511yescharacteristic
137C5C3×#12111yescharacteristic, complemented, Sylow
138C22—21no—
139C22—21no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22—101no—
144C22—101no—
145C22—101no—
146C22C3×C22⋊D512yescomplemented
147C22C22×C3×D511yescharacteristic
148C4—21no—
149C4—52no—
150C4—101no—
151C4—101no—
152C3#408511yescharacteristic, direct product factor, Sylow
153C2—22no—
154C2—41no—
155C2—201no—
156C2C3×D4×D511yescharacteristic
157C2C3×#71111yescharacteristic
158C2C2×C3×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC22×C5C23×C3
FrattiniC22C22×C3×D5
FittingC2×C3×C5×D4C2
socleC22×C3×C5C23
hypercenterC2×C3×D4D5
hypocenterC5C3×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×D4C2semidirect
2. C2×C3×C22⋊D5C2semidirect
3. C2×C3×C22⋊D5C2semidirect
4. C22×C3×Dic5C2semidirect
5. C3×C22⋊Dic5C2semidirect
6. C3×#685C2semidirect
7. C3×#683C2semidirect
8. #4085C3direct (N × H)
21. C2×C5×D4C2×C3semidirect
22. C2×C22⋊D5C2×C3semidirect
23. C2×C22⋊D5C2×C3semidirect
24. C22×Dic5C2×C3semidirect
25. C22⋊Dic5C2×C3semidirect
26. #685C2×C3semidirect
27. #683C2×C3semidirect
33. C22×C3×C5D4semidirect
41. C3×Dic5D4semidirect
44. C2×C3×D4D5semidirect
83. C22×C5C3×D4semidirect
91. Dic5C3×D4semidirect
94. C2×D4C3×D5semidirect
99. C3×C5#121semidirect
108. C22×C3C22⋊D5semidirect
137. C5C3×#121semidirect
146. C22C3×C22⋊D5semidirect
152. C3#4085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×D42
C2×C3×C22⋊D52
C22×C3×Dic52
C3×C22⋊Dic52
C3×#6852
C3×#6832
#40853
C3×#1215