Finite Group Databasebeta

← C13×#1599 #13110657

Subgroups — C13×#1599 #13110657

Order 1664.

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

normal subgroups only

This group has 266 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×#544C211yesmaximal, characteristic, complemented
2C13×#450C212yesmaximal
3C13×#394C211yesmaximal, characteristic
4C13×#328C212yesmaximal, complemented
5C13×#324C211yesmaximal, characteristic, complemented
6C22×D4×C13C2211yescharacteristic
7C2×C13×SD16—22no—
8C13×C4⋊Q8—22no—
9C13×#125—22no—
10C13×C22⋊Q8—21no—
11C13×C22⋊Q8C2212yes—
12C13×#117—21no—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4—21no—
15C2×C13×C22⋊C4—21no—
16C13×#102—22no—
17C13×C22⋊C8C2212yes—
18C13×#95C2211yescharacteristic
19C24×C13—21no—
20C2×Q8×C13—21no—
21C2×Q8×C13D412yes—
22C2×D4×C13—22no—
23C2×D4×C13—42no—
24C22×C4×C13—21no—
25C22×C4×C13D411yescharacteristic
26C22×C4×C13D411yescharacteristic
27C22×C4×C13C2311yescharacteristic
28C13×SD16—44no—
29C2×C8×C13—22no—
30C13×C4⋊C4—21no—
31C13×C4⋊C4—21no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4—22no—
34C13×C4⋊C4—22no—
35C13×C4⋊C4—22no—
36C13×C4⋊C4D412yes—
37C13×C22⋊C4—22no—
38C13×C22⋊C4—42no—
39C13×C22⋊C4—42no—
40C42×C13—22no—
41#1599C1311yesmaximal, characteristic, direct product factor, Sylow
42C23×C13—22no—
43C23×C13—41no—
44C23×C13—41no—
45C23×C13—41no—
46C23×C13—41no—
47C23×C13—41no—
48C23×C13—41no—
49C23×C13C2×D411yescharacteristic
50Q8×C13—42no—
51Q8×C13—81no—
52D4×C13—24no—
53D4×C13—42no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—21no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13SD1612yescomplemented
65C2×C4×C13C2×D412yes—
66C8×C13—42no—
67#544C2×C1311yescharacteristic, complemented
68#450C2×C1312yes—
69#394C2×C1311yescharacteristic
70#328C2×C1312yescomplemented
71#324C2×C1311yescharacteristic, complemented
72C22×C13—21no—
73C22×C13—21no—
74C22×C13—42no—
75C22×C13—42no—
76C22×C13—42no—
77C22×C13—81no—
78C22×C13—81no—
79C22×C13—81no—
80C22×C13—81no—
81C22×C13#12011yescharacteristic
82C22×C13C2×SD1611yescharacteristic
83C22×C13#13711yescharacteristic
84C4×C13—22no—
85C4×C13—22no—
86C4×C13—42no—
87C4×C13—41no—
88C4×C13—42no—
89C4×C13—81no—
90C22×D4C22×C1311yescharacteristic
91C2×SD16—22no—
92C4⋊Q8—22no—
93#125—22no—
94C22⋊Q8—21no—
95C22⋊Q8C22×C1312yes—
96#117—21no—
97C2×C4⋊C4C22×C1311yescharacteristic
98C2×C22⋊C4—21no—
99C2×C22⋊C4—21no—
100#102—22no—
101C22⋊C8C22×C1312yes—
102#95C22×C1311yescharacteristic
103C2×C13—21no—
104C2×C13—21no—
105C2×C13—82no—
106C2×C13#44811yescharacteristic
107C2×C13#45411yescharacteristic
108C2×C13B(4,𝔽2)11yescharacteristic
109C24—21no—
110C2×Q8—21no—
111C2×Q8D4×C1312yes—
112C2×D4—22no—
113C2×D4—42no—
114C22×C4—21no—
115C22×C4D4×C1311yescharacteristic
116C22×C4D4×C1311yescharacteristic
117C22×C4C23×C1311yescharacteristic
118SD16—44no—
119C2×C8—22no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4D4×C1312yes—
127C22⋊C4—22no—
128C22⋊C4—42no—
129C22⋊C4—42no—
130C42—22no—
131C13#159911yescharacteristic, direct product factor, Sylow
132C23—22no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23—41no—
138C23—41no—
139C23C2×D4×C1311yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—24no—
143D4—42no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4C13×SD1612yescomplemented
155C2×C4C2×D4×C1312yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22C13×#12011yescharacteristic
167C22C2×C13×SD1611yescharacteristic
168C22C13×#13711yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—81no—
175C2—21no—
176C2—21no—
177C2—82no—
178C2C13×#44811yescharacteristic
179C2C13×#45411yescharacteristic
180C2C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13#120
commutator, Frattini, cosocleC22×C4C23×C13
prime radicalC22×D4×C13C22
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
1. C13×#544C2semidirect
4. C13×#328C2semidirect
5. C13×#324C2semidirect
41. #1599C13direct (N × H)
64. C2×C4×C13SD16semidirect
67. #544C2×C13semidirect
70. #328C2×C13semidirect
71. #324C2×C13semidirect
131. C13#1599direct (N × H)
154. C2×C4C13×SD16semidirect

Maximal subgroups

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

subgroupindex
C13×#5442
C13×#4502
C13×#3942
C13×#3282
C13×#3242
#159913