Finite Group Databasebeta

← C3×#91277 #13086426

Subgroups — C3×#91277 #13086426

Order 1440.

270 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 76 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×#6766C212yesmaximal, complemented
2C3×C8×D15C211yesmaximal, characteristic, complemented
3C3×C5×Dic12C211yesmaximal, characteristic, complemented
4C32×D40C211yesmaximal, characteristic, complemented
5C3×#6655C212yesmaximal, complemented
6C3×#4065—31nomaximal
7#91277C311yesmaximal, characteristic, direct product factor
8C3×C4×D15C2211yescharacteristic
9C3×C5×Dic6C2212yes—
10C32×D20C2212yes—
11C3×#1202—22no—
12C3×D5×Dic3—22no—
13C32×C5×C8C2211yescharacteristic
14C3×C3⋊#168C2211yescharacteristic
15C3×#912—51nomaximal, Hall
16C3×#713—32no—
17#6766C2×C312yescomplemented
18C3×C5×Q16—31no—
19C8×D15C2×C311yescharacteristic, complemented
20C5×Dic12C2×C311yescharacteristic, complemented
21C3×#688—32no—
22C3×D40—21no—
23C3×D40D311yescharacteristic, complemented
24C3×D40C2×C311yescharacteristic, complemented
25C3×C8×D5—31no—
26#6655C2×C312yescomplemented
27C2×C3×D15D411yescharacteristic
28C2×C32×D5—22no—
29C32×C4×C5C2311yescharacteristic
30C3×Dic15D411yescharacteristic
31C3×C5×Dic3—22no—
32#4065—31noHall
33C3×#237—52no—
34C32×D8—51no—
35C3×#214—52no—
36C3×Dic12D511yescharacteristic, complemented
37C3×D3×C8—51no—
38C3×C5×Q8—32no—
39C4×D15C22×C311yescharacteristic
40C5×Dic6C22×C312yes—
41C3×D20—22no—
42C3×D20—62no—
43C3×D20C2×D312yes—
44C3×D20C22×C312yes—
45C3×C4×D5—31no—
46C3×C4×D5—62no—
47#1202—22no—
48D5×Dic3—22no—
49C3×C5×C8—21no—
50C3×C5×C8C2×D311yescharacteristic
51C3×C5×C8C22×C311yescharacteristic
52C3⋊#168C22×C311yescharacteristic
53C3×#168—31no—
54C3×#135—151no—
55#912—51no—
56C2×C32×C5C2×D411yescharacteristic
57C3×D15—21no—
58C32×D5—42no—
59#713—32no—
60C5×Q16—31no—
61#688—32no—
62D40C3×D311yescharacteristic, complemented
63C8×D5—31no—
64C32×D4—52no—
65C3×#67—102no—
66C2×C3×Dic3—102no—
67C3×C4×D3—51no—
68C3×Dic6C2×D512yes—
69C32×C8C2×D511yescharacteristic
70C3×C3⋊C8—51no—
71C2×D15C3×D411yescharacteristic
72C2×C3×D5—22no—
73C2×C3×D5—22no—
74C2×C3×D5—31no—
75C2×C3×D5—42no—
76C3×C4×C5—21no—
77C3×C4×C5—62no—
78C3×C4×C5C22×D311yescharacteristic
79C3×C4×C5C23×C311yescharacteristic
80Dic15C3×D411yescharacteristic
81C3×Dic5—31no—
82C5×Dic3—22no—
83C3×#41—152no—
84#237—52no—
85C3×Q16—31no—
86C3×SD16—152no—
87C3×D8—51no—
88C3×D8—51no—
89C3×D8—101no—
90C2×C3×C8—151no—
91#214—52no—
92Dic12C3×D511yescharacteristic, complemented
93D3×C8—51no—
94C32×C5#13511yescharacteristic, complemented, Hall
95C5×Q8—32no—
96D20—62no—
97D20C2×C3×D312yes—
98C4×D5—31no—
99C4×D5—62no—
100C5×C8C2×C3×D311yescharacteristic
101#168—31no—
102C22×C32—102no—
103C2×C3×D3—51no—
104C32×C4C22×D511yescharacteristic
105C3×Dic3—22no—
106C3×Dic3—51no—
107#135—151noSylow
108C2×C3×C5—21no—
109C2×C3×C5D3×D411yescharacteristic
110C2×C3×C5C2×C3×D411yescharacteristic
111D15—21no—
112C3×D5—42no—
113C3×D5—42no—
114C3×D5—61no—
115C3×D5—82no—
116C3×Q8—32no—
117C3×D4—52no—
118C3×D4—52no—
119C3×D4—102no—
120C3×D4—302no—
121C2×C3×C4—151no—
122C2×C3×C4—302no—
123#67—102no—
124C2×Dic3—102no—
125C4×D3—51no—
126Dic6C2×C3×D512yes—
127C3×C8—21no—
128C3×C8—151no—
129C3×C8D3×D511yescharacteristic
130C3×C8C2×C3×D511yescharacteristic
131C3⋊C8—51no—
132C2×D5—22no—
133C2×D5—31no—
134C4×C5—62no—
135C4×C5C22×C3×D311yescharacteristic
136Dic5—31no—
137C2×C32—202no—
138C2×C32D4×D511yescharacteristic
139C3×D3—101no—
140#41—152no—
141Q16—31no—
142SD16—152no—
143D8—51no—
144C2×C8—151no—
145C3×C5—21no—
146C3×C5#91211yescharacteristic, complemented
147C3×C5C3×#13511yescharacteristic, complemented
148C22×C3—102no—
149C22×C3—102no—
150C22×C3—151no—
151C22×C3—202no—
152C2×D3—51no—
153C3×C4—21no—
154C3×C4—62no—
155C3×C4—151no—
156C3×C4C2×D3×D511yescharacteristic
157C3×C4C22×C3×D511yescharacteristic
158Dic3—22no—
159Dic3—51no—
160C2×C5C3×D3×D411yescharacteristic
161D5—42no—
162D5—61no—
163C32#406511yescharacteristic, complemented, Sylow
164Q8—32no—
165D4—52no—
166D4—302no—
167C2×C4—151no—
168C2×C4—302no—
169C8—151no—
170C8C3×D3×D511yescharacteristic
171C2×C3—21no—
172C2×C3—202no—
173C2×C3—202no—
174C2×C3—301no—
175C2×C3—402no—
176C2×C3#677711yescharacteristic
177C2×C3C3×D4×D511yescharacteristic
178D3—101no—
179C5C3×#91211yescharacteristic, complemented, Sylow
180C22—102no—
181C22—151no—
182C4—62no—
183C4—151no—
184C4C2×C3×D3×D511yescharacteristic
185C3—21no—
186C3#9127711yescharacteristic, direct product factor
187C3C3×#406511yescharacteristic, complemented
188C2—202no—
189C2—301no—
190C2C3×#677711yescharacteristic
subgroupG/H
centerC2×C3#6777
commutator, cosocleC3×C4×C5C23×C3
FrattiniC4C2×C3×D3×D5
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
hypercenterC3×C8D3×D5
hypocenterC3×C5C3×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

Complements

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

NH ≅ G/Ntype
1. C3×#6766C2semidirect
2. C3×C8×D15C2semidirect
3. C3×C5×Dic12C2semidirect
4. C32×D40C2semidirect
5. C3×#6655C2semidirect
7. #91277C3direct (N × H)
17. #6766C2×C3semidirect
19. C8×D15C2×C3semidirect
20. C5×Dic12C2×C3semidirect
23. C3×D40D3semidirect
24. C3×D40C2×C3semidirect
26. #6655C2×C3semidirect
36. C3×Dic12D5semidirect
62. D40C3×D3semidirect
92. Dic12C3×D5semidirect
94. C32×C5#135semidirect
146. C3×C5#912semidirect
147. C3×C5C3×#135semidirect
163. C32#4065semidirect
179. C5C3×#912semidirect
186. C3#91277direct (N × H)
187. C3C3×#4065semidirect

Maximal subgroups

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

subgroupindex
C3×#67662
C3×C8×D152
C3×C5×Dic122
C32×D402
C3×#66552
C3×#40653
#912773
C3×#9125