Finite Group Databasebeta

← C3×#91279 #13086428

Subgroups — C3×#91279 #13086428

Order 1440.

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

normal subgroups only

This group has 266 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×#6768C212yesmaximal, complemented
2C3×C8×D15C211yesmaximal, characteristic, complemented
3C3×C5×D24C211yesmaximal, characteristic, complemented
4C32×Dic20C211yesmaximal, characteristic, complemented
5C3×#6656C212yesmaximal, complemented
6C3×#4058—31nomaximal
7#91279C311yesmaximal, characteristic, direct product factor
8C3×C4×D15C2211yescharacteristic
9C3×C5×D12C2212yes—
10C32×Dic10C2212yes—
11C3×#1203—22no—
12C3×D3×Dic5—22no—
13C32×C5×C8C2211yescharacteristic
14C3×C3⋊#168C2211yescharacteristic
15C3×#919—51nomaximal, Hall
16C3×#711—32no—
17#6768C2×C312yescomplemented
18C3×C5×D8—31no—
19C8×D15C2×C311yescharacteristic, complemented
20C5×D24C2×C311yescharacteristic, complemented
21C3×#687—32no—
22C3×Dic20—21no—
23C3×Dic20D311yescharacteristic, complemented
24C3×Dic20C2×C311yescharacteristic, complemented
25C3×C8×D5—31no—
26#6656C2×C312yescomplemented
27C2×C3×D15D411yescharacteristic
28C2×C3×C5×D3—22no—
29C32×C4×C5C2311yescharacteristic
30C3×Dic15D411yescharacteristic
31C32×Dic5—22no—
32#4058—31noHall
33C3×#239—52no—
34C32×Q16—51no—
35C3×#215—52no—
36C3×D24D511yescharacteristic, complemented
37C3×D3×C8—51no—
38C3×C5×D4—32no—
39C4×D15C22×C311yescharacteristic
40C5×D12C22×C312yes—
41C3×C22⋊D5—62no—
42C2×C3×Dic5—62no—
43C3×C4×D5—31no—
44C3×Dic10—22no—
45C3×Dic10C2×D312yes—
46C3×Dic10C22×C312yes—
47#1203—22no—
48D3×Dic5—22no—
49C3×C5×C8—21no—
50C3×C5×C8C2×D311yescharacteristic
51C3×C5×C8C22×C311yescharacteristic
52C3⋊#168C22×C311yescharacteristic
53C3×#168—31no—
54C3×#135—151no—
55#919—51no—
56C2×C32×C5C2×D411yescharacteristic
57C3×D15—21no—
58C3×C5×D3—42no—
59#711—32no—
60C5×D8—31no—
61#687—32no—
62Dic20C3×D311yescharacteristic, complemented
63C8×D5—31no—
64C32×Q8—52no—
65C3×D12—102no—
66C3×D12C2×D512yes—
67C3×C4×D3—51no—
68C3×C4×D3—102no—
69C32×C8C2×D511yescharacteristic
70C3×C3⋊C8—51no—
71C22×C3×C5—62no—
72C2×D15C3×D411yescharacteristic
73C2×C5×D3—22no—
74C2×C3×D5—31no—
75C3×C4×C5—21no—
76C3×C4×C5C22×D311yescharacteristic
77C3×C4×C5C23×C311yescharacteristic
78Dic15C3×D411yescharacteristic
79C3×Dic5—22no—
80C3×Dic5—22no—
81C3×Dic5—31no—
82C3×Dic5—42no—
83C3×#41—152no—
84#239—52no—
85C3×Q16—51no—
86C3×Q16—51no—
87C3×Q16—101no—
88C3×SD16—152no—
89C3×D8—31no—
90C2×C3×C8—151no—
91#215—52no—
92D24C3×D511yescharacteristic, complemented
93D3×C8—51no—
94C32×C5#13511yescharacteristic, complemented, Hall
95C5×D4—32no—
96C22⋊D5—62no—
97C2×Dic5—62no—
98C4×D5—31no—
99Dic10C2×C3×D312yes—
100C5×C8C2×C3×D311yescharacteristic
101#168—31no—
102C2×C3×D3—22no—
103C2×C3×D3—51no—
104C32×C4—102no—
105C32×C4C22×D511yescharacteristic
106C3×Dic3—51no—
107#135—151noSylow
108C2×C3×C5—21no—
109C2×C3×C5—122no—
110C2×C3×C5D3×D411yescharacteristic
111C2×C3×C5C2×C3×D411yescharacteristic
112D15—21no—
113C3×D5—61no—
114C5×D3—42no—
115C3×Q8—52no—
116C3×Q8—52no—
117C3×Q8—102no—
118C3×D4—32no—
119C3×D4—302no—
120C2×C3×C4—151no—
121C2×C3×C4—302no—
122D12—102no—
123D12C2×C3×D512yes—
124C4×D3—51no—
125C4×D3—102no—
126C3×C8—21no—
127C3×C8—151no—
128C3×C8D3×D511yescharacteristic
129C3×C8C2×C3×D511yescharacteristic
130C3⋊C8—51no—
131C22×C5—62no—
132C2×D5—31no—
133C4×C5C22×C3×D311yescharacteristic
134Dic5—22no—
135Dic5—31no—
136C2×C32D4×D511yescharacteristic
137C3×D3—42no—
138C3×D3—101no—
139#41—152no—
140Q16—51no—
141SD16—152no—
142D8—31no—
143C2×C8—151no—
144C3×C5—21no—
145C3×C5#91911yescharacteristic, complemented
146C3×C5C3×#13511yescharacteristic, complemented
147C22×C3—62no—
148C22×C3—151no—
149C2×D3—22no—
150C2×D3—51no—
151C3×C4—21no—
152C3×C4—102no—
153C3×C4—102no—
154C3×C4—151no—
155C3×C4—202no—
156C3×C4C2×D3×D511yescharacteristic
157C3×C4C22×C3×D511yescharacteristic
158Dic3—51no—
159C2×C5—122no—
160C2×C5C3×D3×D411yescharacteristic
161D5—61no—
162C32#405811yescharacteristic, complemented, Sylow
163Q8—52no—
164D4—32no—
165D4—302no—
166C2×C4—151no—
167C2×C4—302no—
168C8—151no—
169C8C3×D3×D511yescharacteristic
170C2×C3—21no—
171C2×C3—122no—
172C2×C3—301no—
173C2×C3#677711yescharacteristic
174C2×C3C3×D4×D511yescharacteristic
175D3—42no—
176D3—101no—
177C5C3×#91911yescharacteristic, complemented, Sylow
178C22—62no—
179C22—151no—
180C4—102no—
181C4—151no—
182C4C2×C3×D3×D511yescharacteristic
183C3—21no—
184C3#9127911yescharacteristic, direct product factor
185C3C3×#405811yescharacteristic, complemented
186C2—122no—
187C2—301no—
188C2C3×#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×#6768C2semidirect
2. C3×C8×D15C2semidirect
3. C3×C5×D24C2semidirect
4. C32×Dic20C2semidirect
5. C3×#6656C2semidirect
7. #91279C3direct (N × H)
17. #6768C2×C3semidirect
19. C8×D15C2×C3semidirect
20. C5×D24C2×C3semidirect
23. C3×Dic20D3semidirect
24. C3×Dic20C2×C3semidirect
26. #6656C2×C3semidirect
36. C3×D24D5semidirect
62. Dic20C3×D3semidirect
92. D24C3×D5semidirect
94. C32×C5#135semidirect
145. C3×C5#919semidirect
146. C3×C5C3×#135semidirect
162. C32#4058semidirect
177. C5C3×#919semidirect
184. C3#91279direct (N × H)
185. C3C3×#4058semidirect

Maximal subgroups

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

subgroupindex
C3×#67682
C3×C8×D152
C3×C5×D242
C32×Dic202
C3×#66562
C3×#40583
#912793
C3×#9195