Finite Group Databasebeta

← C13×#12247 #15698586

Subgroups — C13×#12247 #15698586

Order 3328.

394 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2582C211yesmaximal, characteristic
2C13×#2060C211yesmaximal, characteristic
3C13×#1611C212yesmaximal
4C13×#1346C212yesmaximal
5C13×#1325C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C2×C4×Q8×C13—21no—
8C13×#483—22no—
9C13×#428—21no—
10C13×#398—21no—
11C13×#398C2212yes—
12C13×#391—22no—
13C13×#389—22no—
14C13×#384C2211yescharacteristic
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17C13×#328—22no—
18C13×#324C2212yes—
19C22×Q8×C13—21no—
20C2×C13×M16—21no—
21C13×C4⋊Q8—41no—
22C13×#125—41no—
23C13×C22⋊Q8—22no—
24C4×Q8×C13—42no—
25C4×Q8×C13—42no—
26C13×#117—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D412yes—
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C42×C13—22no—
35C2×C42×C13D411yescharacteristic
36C13×#107—41no—
37C13×#106—41no—
38C13×#106—42no—
39C13×#103—42no—
40C13×C22⋊C8—22no—
41C13×#95—22no—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95D412yes—
45#12247C1311yesmaximal, characteristic, direct product factor, Sylow
46C2×Q8×C13—24no—
47C2×Q8×C13—22no—
48C2×Q8×C13—42no—
49C2×Q8×C13—42no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D412yes—
56C13×M16—22no—
57C13×M16—41no—
58C2×C8×C13—41no—
59C2×C8×C13—42no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—21no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—44no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—81no—
72C13×C22⋊C4—41no—
73C42×C13—21no—
74C42×C13—44no—
75C42×C13—41no—
76C42×C13SD1612yes—
77#2582C2×C1311yescharacteristic
78#2060C2×C1311yescharacteristic
79#1611C2×C1312yes—
80#1346C2×C1312yes—
81#1325C2×C1311yescharacteristic
82C23×C13#12011yescharacteristic
83Q8×C13—48no—
84Q8×C13—82no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—24no—
91C2×C4×C13—22no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13C2×SD1611yescharacteristic
103C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
104C8×C13—42no—
105C8×C13—82no—
106#544C22×C1311yescharacteristic
107C2×C4×Q8—21no—
108#483—22no—
109#428—21no—
110#398—21no—
111#398C22×C1312yes—
112#391—22no—
113#389—22no—
114#384C22×C1311yescharacteristic
115#343C22×C1311yescharacteristic
116#339—21no—
117#328—22no—
118#324C22×C1312yes—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#45011yescharacteristic
122C22×C13#45611yescharacteristic
123C22×C13B(4,𝔽2)11yescharacteristic
124C4×C13—24no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—44no—
128C4×C13—42no—
129C4×C13—82no—
130C4×C13—81no—
131C4×C13—81no—
132C4×C13—81no—
133C22×Q8—21no—
134C2×M16—21no—
135C4⋊Q8—41no—
136#125—41no—
137C22⋊Q8—22no—
138C4×Q8—42no—
139C4×Q8—42no—
140#117—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4D4×C1311yescharacteristic
146C2×C4⋊C4D4×C1312yes—
147C2×C4⋊C4C23×C1311yescharacteristic
148C2×C42—22no—
149C2×C42D4×C1311yescharacteristic
150#107—41no—
151#106—41no—
152#106—42no—
153#103—42no—
154C22⋊C8—22no—
155#95—22no—
156#95—21no—
157#95—22no—
158#95D4×C1312yes—
159C2×C13—21no—
160C2×C13—21no—
161C2×C13#160411yescharacteristic
162C2×C13#219811yescharacteristic
163C2×C13#220511yescharacteristic
164C2×Q8—24no—
165C2×Q8—22no—
166C2×Q8—42no—
167C2×Q8—42no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4C2×D4×C1311yescharacteristic
173C22×C4C2×D4×C1312yes—
174M16—22no—
175M16—41no—
176C2×C8—41no—
177C2×C8—42no—
178C4⋊C4—21no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—44no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—81no—
190C22⋊C4—41no—
191C42—21no—
192C42—44no—
193C42—41no—
194C42C13×SD1612yes—
195C13#1224711yescharacteristic, direct product factor, Sylow
196C23C13×#12011yescharacteristic
197Q8—48no—
198Q8—82no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4C2×C13×SD1611yescharacteristic
217C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
218C8—42no—
219C8—82no—
220C22—21no—
221C22—21no—
222C22C13×#45011yescharacteristic
223C22C13×#45611yescharacteristic
224C22C13×B(4,𝔽2)11yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—42no—
230C4—82no—
231C4—81no—
232C4—81no—
233C4—81no—
234C2—21no—
235C2—21no—
236C2C13×#160411yescharacteristic
237C2C13×#219811yescharacteristic
238C2C13×#220511yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC23×C13#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
45. #12247C13direct (N × H)
195. C13#12247direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25822
C13×#20602
C13×#16112
C13×#13462
C13×#13252
#1224713