Finite Group Databasebeta

← C13×#1595 #13110653

Subgroups — C13×#1595 #13110653

Order 1664.

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

normal subgroups only

This group has 368 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×#534C211yesmaximal, characteristic, complemented
2C13×#447C212yesmaximal, complemented
3C13×#392C211yesmaximal, characteristic, complemented
4C13×#327C212yesmaximal, complemented
5C13×#323C211yesmaximal, characteristic, complemented
6C22×D4×C13—21no—
7C22×D4×C13—21no—
8C22×D4×C13C2211yescharacteristic, complemented
9C2×C13×D8—22no—
10C13×#123—22no—
11C13×#121—21no—
12C13×#121C2212yes—
13C13×#120—22no—
14C2×C13×C22⋊C4—21no—
15C2×C13×C22⋊C4C2211yescharacteristic
16C13×#102—22no—
17C13×C22⋊C8C2212yescomplemented
18C13×#95C2211yescharacteristic, complemented
19C24×C13—21no—
20C24×C13—21no—
21C24×C13D411yescharacteristic
22C2×D4×C13—22no—
23C2×D4×C13—22no—
24C2×D4×C13—21no—
25C2×D4×C13—22no—
26C2×D4×C13—42no—
27C2×D4×C13—42no—
28C2×D4×C13—42no—
29C2×D4×C13—42no—
30C2×D4×C13—42no—
31C2×D4×C13—42no—
32C2×D4×C13D412yescomplemented
33C22×C4×C13—21no—
34C22×C4×C13—21no—
35C22×C4×C13D411yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C13×D8—44no—
38C2×C8×C13—22no—
39C13×C4⋊C4—21no—
40C13×C4⋊C4D412yescomplemented
41C13×C22⋊C4—22no—
42C13×C22⋊C4—22no—
43C13×C22⋊C4—22no—
44C13×C22⋊C4—42no—
45#1595C1311yesmaximal, characteristic, direct product factor, Sylow
46C23×C13—21no—
47C23×C13—21no—
48C23×C13—22no—
49C23×C13—22no—
50C23×C13—41no—
51C23×C13—41no—
52C23×C13—41no—
53C23×C13—41no—
54C23×C13—41no—
55C23×C13—42no—
56C23×C13—41no—
57C23×C13—41no—
58C23×C13—41no—
59C23×C13—81no—
60C23×C13—81no—
61C23×C13D812yescomplemented
62C23×C13C2×D411yescharacteristic
63D4×C13—24no—
64D4×C13—42no—
65D4×C13—42no—
66D4×C13—44no—
67D4×C13—48no—
68D4×C13—42no—
69D4×C13—42no—
70D4×C13—81no—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—41no—
75C2×C4×C13—41no—
76C2×C4×C13—42no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13C2×D412yes—
80C8×C13—42no—
81#534C2×C1311yescharacteristic, complemented
82#447C2×C1312yescomplemented
83#392C2×C1311yescharacteristic, complemented
84#327C2×C1312yescomplemented
85#323C2×C1311yescharacteristic, complemented
86C22×C13—21no—
87C22×C13—21no—
88C22×C13—22no—
89C22×C13—42no—
90C22×C13—42no—
91C22×C13—42no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13—42no—
95C22×C13—42no—
96C22×C13—42no—
97C22×C13—42no—
98C22×C13—81no—
99C22×C13—81no—
100C22×C13—81no—
101C22×C13—84no—
102C22×C13—81no—
103C22×C13—81no—
104C22×C13#12011yescharacteristic
105C22×C13C2×D811yescharacteristic
106C22×C13AGL(1,ℤ/8)11yescharacteristic
107C4×C13—22no—
108C4×C13—42no—
109C4×C13—42no—
110C4×C13—41no—
111C22×D4—21no—
112C22×D4—21no—
113C22×D4C22×C1311yescharacteristic, complemented
114C2×D8—22no—
115#123—22no—
116#121—21no—
117#121C22×C1312yes—
118#120—22no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4C22×C1311yescharacteristic
121#102—22no—
122C22⋊C8C22×C1312yescomplemented
123#95C22×C1311yescharacteristic, complemented
124C2×C13—21no—
125C2×C13—21no—
126C2×C13—42no—
127C2×C13—82no—
128C2×C13—82no—
129C2×C13#44711yescharacteristic
130C2×C13#45311yescharacteristic
131C2×C13B(4,𝔽2)11yescharacteristic
132C24—21no—
133C24—21no—
134C24D4×C1311yescharacteristic
135C2×D4—22no—
136C2×D4—22no—
137C2×D4—21no—
138C2×D4—22no—
139C2×D4—42no—
140C2×D4—42no—
141C2×D4—42no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4D4×C1312yescomplemented
146C22×C4—21no—
147C22×C4—21no—
148C22×C4D4×C1311yescharacteristic
149C22×C4C23×C1311yescharacteristic
150D8—44no—
151C2×C8—22no—
152C4⋊C4—21no—
153C4⋊C4D4×C1312yescomplemented
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—42no—
158C13#159511yescharacteristic, direct product factor, Sylow
159C23—21no—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—41no—
164C23—41no—
165C23—41no—
166C23—41no—
167C23—41no—
168C23—42no—
169C23—41no—
170C23—41no—
171C23—41no—
172C23—81no—
173C23—81no—
174C23C13×D812yescomplemented
175C23C2×D4×C1311yescharacteristic
176D4—24no—
177D4—42no—
178D4—42no—
179D4—44no—
180D4—48no—
181D4—42no—
182D4—42no—
183D4—81no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4C2×D4×C1312yes—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—41no—
201C22—41no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—81no—
207C22—81no—
208C22—81no—
209C22—84no—
210C22—81no—
211C22—81no—
212C22C13×#12011yescharacteristic
213C22C2×C13×D811yescharacteristic
214C22C13×AGL(1,ℤ/8)11yescharacteristic
215C4—22no—
216C4—42no—
217C4—42no—
218C4—41no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—82no—
223C2—82no—
224C2C13×#44711yescharacteristic
225C2C13×#45311yescharacteristic
226C2C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13#120
commutator, Frattini, cosocleC22×C4C23×C13
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×#534C2semidirect
2. C13×#447C2semidirect
3. C13×#392C2semidirect
4. C13×#327C2semidirect
5. C13×#323C2semidirect
8. C22×D4×C13C22semidirect
17. C13×C22⋊C8C22semidirect
18. C13×#95C22semidirect
32. C2×D4×C13D4semidirect
40. C13×C4⋊C4D4semidirect
45. #1595C13direct (N × H)
61. C23×C13D8semidirect
81. #534C2×C13semidirect
82. #447C2×C13semidirect
83. #392C2×C13semidirect
84. #327C2×C13semidirect
85. #323C2×C13semidirect
113. C22×D4C22×C13semidirect
122. C22⋊C8C22×C13semidirect
123. #95C22×C13semidirect
145. C2×D4D4×C13semidirect
153. C4⋊C4D4×C13semidirect
158. C13#1595direct (N × H)
174. C23C13×D8semidirect

Maximal subgroups

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

subgroupindex
C13×#5342
C13×#4472
C13×#3922
C13×#3272
C13×#3232
#159513