Finite Group Databasebeta

← C13×#1616 #13110674

Subgroups — C13×#1616 #13110674

Order 1664.

246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C13×#537C211yesmaximal, characteristic
2C13×#481C212yesmaximal, complemented
3C13×#400C211yesmaximal, characteristic, complemented
4C13×#327C212yesmaximal, complemented
5C13×#324C211yesmaximal, characteristic, complemented
6C2×C13×#41—21no—
7C13×C22⋊Q8—22no—
8C13×#121—22no—
9C13×#121—21no—
10C13×#121C2212yes—
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C13×#106—22no—
14C13×#102—22no—
15C13×C22⋊C8C2212yes—
16C13×#95—21no—
17C13×#95—21no—
18C13×#95C2211yescharacteristic
19C13×#41—42no—
20C13×#41—42no—
21C2×Q8×C13—21no—
22C2×D4×C13—21no—
23C2×D4×C13—22no—
24C2×D4×C13—21no—
25C2×D4×C13D412yes—
26C22×C4×C13—22no—
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13D411yescharacteristic
30C22×C4×C13D411yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C2×C8×C13—22no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—22no—
35C13×C4⋊C4—22no—
36C13×C4⋊C4D412yes—
37C13×C22⋊C4—22no—
38C13×C22⋊C4—22no—
39#1616C1311yesmaximal, characteristic, direct product factor, Sylow
40C23×C13—22no—
41C23×C13C2×D411yescharacteristic
42Q8×C13—42no—
43D4×C13—42no—
44D4×C13—42no—
45D4×C13—42no—
46D4×C13—42no—
47D4×C13—81no—
48C2×C4×C13—21no—
49C2×C4×C13—21no—
50C2×C4×C13—21no—
51C2×C4×C13—22no—
52C2×C4×C13—41no—
53C2×C4×C13—44no—
54C2×C4×C13—41no—
55C2×C4×C13—41no—
56C2×C4×C13—41no—
57C2×C4×C13—42no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13SD1612yes—
61C2×C4×C13C2×D412yes—
62C8×C13—42no—
63#537C2×C1311yescharacteristic
64#481C2×C1312yescomplemented
65#400C2×C1311yescharacteristic, complemented
66#327C2×C1312yescomplemented
67#324C2×C1311yescharacteristic, complemented
68C22×C13—21no—
69C22×C13—21no—
70C22×C13—42no—
71C22×C13—42no—
72C22×C13—42no—
73C22×C13#12011yescharacteristic
74C22×C13C2×SD1611yescharacteristic
75C22×C13AGL(1,ℤ/8)11yescharacteristic
76C4×C13—22no—
77C4×C13—22no—
78C4×C13—42no—
79C4×C13—41no—
80C4×C13—81no—
81C4×C13—81no—
82C2×#41—21no—
83C22⋊Q8—22no—
84#121—22no—
85#121—21no—
86#121C22×C1312yes—
87C2×C4⋊C4C22×C1311yescharacteristic
88C2×C4⋊C4C22×C1311yescharacteristic
89#106—22no—
90#102—22no—
91C22⋊C8C22×C1312yes—
92#95—21no—
93#95—21no—
94#95C22×C1311yescharacteristic
95C2×C13—21no—
96C2×C13—21no—
97C2×C13—82no—
98C2×C13#45011yescharacteristic
99C2×C13#45411yescharacteristic
100C2×C13#45811yescharacteristic
101#41—42no—
102#41—42no—
103C2×Q8—21no—
104C2×D4—21no—
105C2×D4—22no—
106C2×D4—21no—
107C2×D4D4×C1312yes—
108C22×C4—22no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4D4×C1311yescharacteristic
112C22×C4D4×C1311yescharacteristic
113C22×C4C23×C1311yescharacteristic
114C2×C8—22no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4D4×C1312yes—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C13#161611yescharacteristic, direct product factor, Sylow
122C23—22no—
123C23C2×D4×C1311yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4C13×SD1612yes—
143C2×C4C2×D4×C1312yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22C13×#12011yescharacteristic
151C22C2×C13×SD1611yescharacteristic
152C22C13×AGL(1,ℤ/8)11yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—41no—
157C4—81no—
158C4—81no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2C13×#45011yescharacteristic
163C2C13×#45411yescharacteristic
164C2C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13#120
commutator, Frattini, cosocleC22×C4C23×C13
prime radicalC13×#537C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#481C2semidirect
3. C13×#400C2semidirect
4. C13×#327C2semidirect
5. C13×#324C2semidirect
39. #1616C13direct (N × H)
64. #481C2×C13semidirect
65. #400C2×C13semidirect
66. #327C2×C13semidirect
67. #324C2×C13semidirect
121. C13#1616direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5372
C13×#4812
C13×#4002
C13×#3272
C13×#3242
#161613