Finite Group Databasebeta

← C13×#1535 #13110593

Subgroups — C13×#1535 #13110593

Order 1664.

200 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 84 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×#529C211yesmaximal, characteristic
2C13×#432C211yesmaximal, characteristic, complemented
3C13×#432C211yesmaximal, characteristic, complemented
4C13×#330C212yesmaximal, complemented
5C13×#329C212yesmaximal, complemented
6C13×#126—21no—
7C13×#125C2211yescharacteristic
8C13×#124C2211yescharacteristic
9C13×#123—21no—
10C13×C22⋊Q8C411yescharacteristic
11C13×#121C411yescharacteristic
12C4×Q8×C13C411yescharacteristic
13C4×D4×C13—21no—
14C4×D4×C13C411yescharacteristic
15C13×#117—21no—
16C2×C42×C13C2211yescharacteristic
17C13×C4⋊C8—21no—
18C13×C4⋊C8—21no—
19C13×C22⋊C8—21no—
20C13×C22⋊C8—21no—
21C13×#97C2212yes—
22C13×#97C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24C2×D4×C13—21no—
25C2×D4×C13C2×C411yescharacteristic
26C22×C4×C13—21no—
27C22×C4×C13C2×C411yescharacteristic
28C22×C4×C13D411yescharacteristic
29C22×C4×C13D411yescharacteristic
30C2×C8×C13—22no—
31C2×C8×C13—22no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4C2×C411yescharacteristic
37C13×C4⋊C4C2×C411yescharacteristic
38C13×C22⋊C4—21no—
39C13×C22⋊C4—21no—
40C13×C22⋊C4—21no—
41C13×C22⋊C4—21no—
42C13×C22⋊C4—21no—
43C42×C13—21no—
44C42×C13C2×C411yescharacteristic
45C42×C13D411yescharacteristic
46C42×C13D411yescharacteristic
47C42×C13C2311yescharacteristic
48#1535C1311yesmaximal, characteristic, direct product factor, Sylow
49C23×C13—21no—
50C23×C13C22⋊C411yescharacteristic
51Q8×C13—41no—
52D4×C13—41no—
53D4×C13—42no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13—42no—
61C2×C4×C13C22⋊C411yescharacteristic
62C2×C4×C13C22⋊C411yescharacteristic
63C2×C4×C13C22⋊C411yescharacteristic
64C2×C4×C13C22×C411yescharacteristic
65C2×C4×C13C2×D411yescharacteristic
66C2×C4×C13C2×D411yescharacteristic
67C8×C13—42no—
68C8×C13—42no—
69#529C2×C1311yescharacteristic
70#432C2×C1311yescharacteristic, complemented
71#432C2×C1311yescharacteristic, complemented
72#330C2×C1312yescomplemented
73#329C2×C1312yescomplemented
74C22×C13—21no—
75C22×C13—21no—
76C22×C13—21no—
77C22×C13—41no—
78C22×C13—41no—
79C22×C13—41no—
80C22×C13C2×C22⋊C411yescharacteristic
81C4×C13—21no—
82C4×C13—21no—
83C4×C13—21no—
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—21no—
87C4×C13—41no—
88C4×C13—41no—
89C4×C13—41no—
90#126—21no—
91#125C22×C1311yescharacteristic
92#124C22×C1311yescharacteristic
93#123—21no—
94C22⋊Q8C4×C1311yescharacteristic
95#121C4×C1311yescharacteristic
96C4×Q8C4×C1311yescharacteristic
97C4×D4—21no—
98C4×D4C4×C1311yescharacteristic
99#117—21no—
100C2×C42C22×C1311yescharacteristic
101C4⋊C8—21no—
102C4⋊C8—21no—
103C22⋊C8—21no—
104C22⋊C8—21no—
105#97C22×C1312yes—
106#97C22×C1312yes—
107C2×C13—41no—
108C2×C13—81no—
109C2×C13#41311yescharacteristic
110C2×C13#42111yescharacteristic
111C2×C13#42111yescharacteristic
112C2×Q8C2×C4×C1311yescharacteristic
113C2×D4—21no—
114C2×D4C2×C4×C1311yescharacteristic
115C22×C4—21no—
116C22×C4C2×C4×C1311yescharacteristic
117C22×C4D4×C1311yescharacteristic
118C22×C4D4×C1311yescharacteristic
119C2×C8—22no—
120C2×C8—22no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4C2×C4×C1311yescharacteristic
126C4⋊C4C2×C4×C1311yescharacteristic
127C22⋊C4—21no—
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C42—21no—
133C42C2×C4×C1311yescharacteristic
134C42D4×C1311yescharacteristic
135C42D4×C1311yescharacteristic
136C42C23×C1311yescharacteristic
137C13#153511yescharacteristic, direct product factor, Sylow
138C23—21no—
139C23C13×C22⋊C411yescharacteristic
140Q8—41no—
141D4—41no—
142D4—42no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4C13×C22⋊C411yescharacteristic
151C2×C4C13×C22⋊C411yescharacteristic
152C2×C4C13×C22⋊C411yescharacteristic
153C2×C4C22×C4×C1311yescharacteristic
154C2×C4C2×D4×C1311yescharacteristic
155C2×C4C2×D4×C1311yescharacteristic
156C8—42no—
157C8—42no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22C2×C13×C22⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—41no—
174C2—41no—
175C2—81no—
176C2C13×#41311yescharacteristic
177C2C13×#42111yescharacteristic
178C2C13×#42111yescharacteristic
subgroupG/H
center, socleC22×C13C2×C22⋊C4
commutatorC2×C4C22×C4×C13
Frattini, cosocleC42C23×C13
prime radicalC13×#121C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#432C2semidirect
3. C13×#432C2semidirect
4. C13×#330C2semidirect
5. C13×#329C2semidirect
48. #1535C13direct (N × H)
70. #432C2×C13semidirect
71. #432C2×C13semidirect
72. #330C2×C13semidirect
73. #329C2×C13semidirect
137. C13#1535direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5292
C13×#4322
C13×#3302
C13×#3292
#153513