Finite Group Databasebeta

← C3×#65350 #11749958

Subgroups — C3×#65350 #11749958

Order 960.

304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4144C211yesmaximal, characteristic
2C3×C5×#124C211yesmaximal, characteristic, complemented
3C3×#4088C212yesmaximal, complemented
4C3×#3965C211yesmaximal, characteristic, complemented
5C3×#3937C212yesmaximal, complemented
6#65350C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q8C2211yescharacteristic, complemented
8C2×C3×C5×D4C2211yescharacteristic
9C2×C3×C22⋊D5—22no—
10C3×#711—22no—
11C3×D4×D5—22no—
12C3×#709C2212yes—
13C3×C5×C22⋊C4—22no—
14C3×C42×C5C2211yescharacteristic, complemented
15C3×#689—22no—
16C3×#688—22no—
17C3×#681C2212yescomplemented
18C3×#455—51nomaximal, Hall
19#4144C2×C311yescharacteristic
20C5×#124C2×C311yescharacteristic, complemented
21#4088C2×C312yescomplemented
22#3965C2×C311yescharacteristic, complemented
23#3937C2×C312yescomplemented
24C23×C3×C5D412yes—
25C22×C3×D5—22no—
26C3×C5×Q8—22no—
27C3×C5×D4—22no—
28C2×C3×C4×C5—21no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5C2311yescharacteristic
31C3×C22⋊D5—24no—
32C3×C22⋊D5—22no—
33C2×C3×Dic5—22no—
34C3×D20D412yes—
35C3×C4×D5—22no—
36C3×Dic10D412yes—
37C3×#168—22no—
38C3×H(5,𝔽2)—51no—
39C3×#137—52no—
40C3×#124D511yescharacteristic, complemented
41C3×#104—52no—
42C3×#100—51no—
43C2×C5×Q8C22×C311yescharacteristic, complemented
44C2×C5×D4C22×C311yescharacteristic
45C2×C22⋊D5—22no—
46#711—22no—
47D4×D5—22no—
48#709C22×C312yes—
49C5×C22⋊C4—22no—
50C42×C5C22×C311yescharacteristic, complemented
51#689—22no—
52#688—22no—
53#681C22×C312yescomplemented
54#455—51noSylow
55C22×C3×C5—22no—
56C22×C3×C5—42no—
57C22×C3×C5C2×D411yescharacteristic
58C2×C3×D5—22no—
59C2×C3×D5—82no—
60C3×C4×C5—41no—
61C3×C4×C5—41no—
62C3×C4×C5C2×D412yes—
63C3×Dic5—22no—
64C3×#41—52no—
65C3×#41—102no—
66C2×C3×Q8C2×D511yescharacteristic, complemented
67C2×C3×D4—102no—
68C2×C3×D4—102no—
69C2×C3×D4C2×D511yescharacteristic
70C3×Q16—102no—
71C3×SD16—102no—
72C3×M16—52no—
73C3×C22⋊C4—22no—
74C3×C42C2×D511yescharacteristic, complemented
75C23×C5C3×D412yes—
76C22×D5—22no—
77C5×Q8—22no—
78C5×D4—22no—
79C2×C4×C5—21no—
80C2×C4×C5—21no—
81C2×C4×C5C23×C311yescharacteristic
82C22⋊D5—24no—
83C22⋊D5—22no—
84C2×Dic5—22no—
85D20C3×D412yes—
86C4×D5—22no—
87Dic10C3×D412yes—
88#168—22no—
89H(5,𝔽2)—51no—
90#137—52no—
91#124C3×D511yescharacteristic, complemented
92#104—52no—
93#100—51no—
94C2×C3×C5—21no—
95C2×C3×C5—42no—
96C2×C3×C5#12011yescharacteristic
97C3×D5—42no—
98C23×C3—102no—
99C23×C3C22⋊D512yes—
100C3×Q8—22no—
101C3×Q8—52no—
102C3×D4—22no—
103C3×D4—52no—
104C3×D4—104no—
105C3×D4—102no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—102no—
109C2×C3×C4—102no—
110C2×C3×C4C22×D511yescharacteristic
111C3×C8—102no—
112C22×C5—22no—
113C22×C5—42no—
114C22×C5C2×C3×D411yescharacteristic
115C2×D5—22no—
116C2×D5—82no—
117C4×C5—41no—
118C4×C5—41no—
119C4×C5C2×C3×D412yes—
120Dic5—22no—
121#41—52no—
122#41—102no—
123C2×Q8C2×C3×D511yescharacteristic, complemented
124C2×D4—102no—
125C2×D4—102no—
126C2×D4C2×C3×D511yescharacteristic
127Q16—102no—
128SD16—102no—
129M16—52no—
130C22⋊C4—22no—
131C42C2×C3×D511yescharacteristic, complemented
132C3×C5#45511yescharacteristic, complemented, Hall
133C22×C3—22no—
134C22×C3—42no—
135C22×C3—102no—
136C22×C3—402no—
137C22×C3C2×C22⋊D511yescharacteristic
138C3×C4—41no—
139C3×C4—41no—
140C3×C4—102no—
141C3×C4D4×D512yes—
142C2×C5—21no—
143C2×C5—42no—
144C2×C5C3×#12011yescharacteristic
145D5—42no—
146C23—102no—
147C23C3×C22⋊D512yes—
148Q8—22no—
149Q8—52no—
150D4—22no—
151D4—52no—
152D4—104no—
153D4—102no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—102no—
157C2×C4—102no—
158C2×C4C22×C3×D511yescharacteristic
159C8—102no—
160C2×C3—21no—
161C2×C3—42no—
162C2×C3—202no—
163C2×C3#408311yescharacteristic
164C5C3×#45511yescharacteristic, complemented, Sylow
165C22—22no—
166C22—42no—
167C22—102no—
168C22—402no—
169C22C2×C3×C22⋊D511yescharacteristic
170C4—41no—
171C4—41no—
172C4—102no—
173C4C3×D4×D512yes—
174C3#6535011yescharacteristic, direct product factor, Sylow
175C2—21no—
176C2—42no—
177C2—202no—
178C2C3×#408311yescharacteristic
subgroupG/H
centerC2×C3#4083
commutator, cosocleC2×C4×C5C23×C3
FrattiniC2×C4C22×C3×D5
FittingC3×C5×#124C2
socleC2×C3×C5#120
prime radicalC3×#4144C2
hypercenterC3×#124D5
hypocenterC5C3×#455
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#124

Complements

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

NH ≅ G/Ntype
2. C3×C5×#124C2semidirect
3. C3×#4088C2semidirect
4. C3×#3965C2semidirect
5. C3×#3937C2semidirect
6. #65350C3direct (N × H)
7. C2×C3×C5×Q8C22semidirect
14. C3×C42×C5C22semidirect
17. C3×#681C22semidirect
20. C5×#124C2×C3semidirect
21. #4088C2×C3semidirect
22. #3965C2×C3semidirect
23. #3937C2×C3semidirect
40. C3×#124D5semidirect
43. C2×C5×Q8C22×C3semidirect
50. C42×C5C22×C3semidirect
53. #681C22×C3semidirect
66. C2×C3×Q8C2×D5semidirect
74. C3×C42C2×D5semidirect
91. #124C3×D5semidirect
123. C2×Q8C2×C3×D5semidirect
131. C42C2×C3×D5semidirect
132. C3×C5#455semidirect
164. C5C3×#455semidirect
174. C3#65350direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#41442
C3×C5×#1242
C3×#40882
C3×#39652
C3×#39372
#653503
C3×#4555