Finite Group Databasebeta

← C13×#7237 #15693576

Subgroups — C13×#7237 #15693576

Order 3328.

376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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×#1954C211yesmaximal, characteristic
2C13×#1799C212yesmaximal
3C2×C4×D4×C13C2211yescharacteristic
4C2×C13×C4⋊C8C411yescharacteristic, complemented
5C2×C13×#99—22no—
6C2×C13×C22⋊C8—22no—
7C2×C4×C8×C13C411yescharacteristic, complemented
8C13×#380—22no—
9C13×#342C414yescomplemented
10C22×D4×C13D411yescharacteristic
11C23×C4×C13D412yes—
12C22×C8×C13—21no—
13C22×C8×C13—21no—
14C4×D4×C13—41no—
15C4×D4×C13—41no—
16C2×C13×C4⋊C4—42no—
17C2×C13×C4⋊C4Q811yescharacteristic
18C2×C13×C22⋊C4—24no—
19C2×C13×C22⋊C4C2×C412yes—
20C2×C42×C13C2×C411yescharacteristic
21C13×C4⋊C8—41no—
22C13×#99—42no—
23C13×#99—42no—
24C13×C22⋊C8—44no—
25C4×C8×C13—41no—
26C13×#95—42no—
27#7237C1311yesmaximal, characteristic, direct product factor, Sylow
28C24×C13C22⋊C412yes—
29C2×D4×C13—41no—
30C2×D4×C13—41no—
31C2×D4×C13D811yescharacteristic
32C2×D4×C13SD1612yes—
33C2×D4×C13Q1611yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—42no—
37C22×C4×C13—42no—
38C22×C4×C13—44no—
39C22×C4×C13C4211yescharacteristic
40C22×C4×C13C22⋊C411yescharacteristic
41C22×C4×C13C4⋊C411yescharacteristic
42C22×C4×C13C4⋊C412yes—
43C2×C8×C13—22no—
44C2×C8×C13—41no—
45C2×C8×C13—41no—
46C2×C8×C13—42no—
47C2×C8×C13—41no—
48C13×C4⋊C4—41no—
49C13×C4⋊C4—82no—
50C13×C4⋊C4—82no—
51C13×C22⋊C4—42no—
52C13×C22⋊C4—44no—
53C13×C22⋊C4—44no—
54C42×C13—21no—
55C42×C13—21no—
56#1954C2×C1311yescharacteristic
57#1799C2×C1312yes—
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—42no—
61C23×C13—42no—
62C23×C13#9511yescharacteristic
63C23×C13#10212yes—
64C23×C13#10312yes—
65D4×C13—41no—
66D4×C13—42no—
67D4×C13—41no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—42no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13—41no—
78C2×C4×C13—82no—
79C2×C4×C13—84no—
80C2×C4×C13—84no—
81C2×C4×C13—84no—
82C2×C4×C13#9911yescharacteristic
83C2×C4×C13#9911yescharacteristic
84C2×C4×C13#10611yescharacteristic
85C2×C4×C13#10711yescharacteristic
86C8×C13—42no—
87C8×C13—81no—
88C2×C4×D4C22×C1311yescharacteristic
89C2×C4⋊C8C4×C1311yescharacteristic, complemented
90C2×#99—22no—
91C2×C22⋊C8—22no—
92C2×C4×C8C4×C1311yescharacteristic, complemented
93#380—22no—
94#342C4×C1314yescomplemented
95C22×C13—21no—
96C22×C13—21no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—82no—
104C22×C13H(3,ℤ/4)11yescharacteristic
105C22×C13#34011yescharacteristic
106C22×C13#34211yescharacteristic
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—41no—
111C4×C13—42no—
112C4×C13—164no—
113C4×C13#35311yescharacteristic
114C4×C13#35411yescharacteristic
115C22×D4D4×C1311yescharacteristic
116C23×C4D4×C1312yes—
117C22×C8—21no—
118C22×C8—21no—
119C4×D4—41no—
120C4×D4—41no—
121C2×C4⋊C4—42no—
122C2×C4⋊C4Q8×C1311yescharacteristic
123C2×C22⋊C4—24no—
124C2×C22⋊C4C2×C4×C1312yes—
125C2×C42C2×C4×C1311yescharacteristic
126C4⋊C8—41no—
127#99—42no—
128#99—42no—
129C22⋊C8—44no—
130C4×C8—41no—
131#95—42no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13—42no—
135C2×C13—42no—
136C2×C13#128911yescharacteristic
137C2×C13#139111yescharacteristic
138C2×C13#139311yescharacteristic
139C24C13×C22⋊C412yes—
140C2×D4—41no—
141C2×D4—41no—
142C2×D4C13×D811yescharacteristic
143C2×D4C13×SD1612yes—
144C2×D4C13×Q1611yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—44no—
150C22×C4C42×C1311yescharacteristic
151C22×C4C13×C22⋊C411yescharacteristic
152C22×C4C13×C4⋊C411yescharacteristic
153C22×C4C13×C4⋊C412yes—
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—42no—
158C2×C8—41no—
159C4⋊C4—41no—
160C4⋊C4—82no—
161C4⋊C4—82no—
162C22⋊C4—42no—
163C22⋊C4—44no—
164C22⋊C4—44no—
165C42—21no—
166C42—21no—
167C13#723711yescharacteristic, direct product factor, Sylow
168C23—22no—
169C23—22no—
170C23—42no—
171C23—42no—
172C23C13×#9511yescharacteristic
173C23C13×#10212yes—
174C23C13×#10312yes—
175D4—41no—
176D4—42no—
177D4—41no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—82no—
189C2×C4—84no—
190C2×C4—84no—
191C2×C4—84no—
192C2×C4C13×#9911yescharacteristic
193C2×C4C13×#9911yescharacteristic
194C2×C4C13×#10611yescharacteristic
195C2×C4C13×#10711yescharacteristic
196C8—42no—
197C8—81no—
198C22—21no—
199C22—21no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—82no—
207C22C13×H(3,ℤ/4)11yescharacteristic
208C22C13×#34011yescharacteristic
209C22C13×#34211yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—42no—
215C4—164no—
216C4C13×#35311yescharacteristic
217C4C13×#35411yescharacteristic
218C2—21no—
219C2—21no—
220C2—42no—
221C2—42no—
222C2C13×#128911yescharacteristic
223C2C13×#139111yescharacteristic
224C2C13×#139311yescharacteristic
subgroupG/H
center, socleC22×C13#342
commutatorC22×C4C42×C13
Frattini, cosocleC2×C4×D4C22×C13
prime radicalC22×D4×C13D4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C13×C4⋊C8C4semidirect
7. C2×C4×C8×C13C4semidirect
9. C13×#342C4semidirect
27. #7237C13direct (N × H)
89. C2×C4⋊C8C4×C13semidirect
92. C2×C4×C8C4×C13semidirect
94. #342C4×C13semidirect
167. C13#7237direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#19542
C13×#17992
#723713