Finite Group Databasebeta

← C13×#12251 #15698590

Subgroups — C13×#12251 #15698590

Order 3328.

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

normal subgroups only

This group has 342 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×#2822C211yesmaximal, characteristic
2C13×#2061C211yesmaximal, characteristic
3C13×#1611C212yesmaximal
4C13×#1346C212yesmaximal
5C13×#1324C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C2×C13×#125—21no—
8C13×#483—22no—
9C13×#428—21no—
10C13×#400—22no—
11C13×#398—21no—
12C13×#398—22no—
13C13×#398C2212yes—
14C13×#382C2211yescharacteristic
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17C13×#328—22no—
18C13×#324C2212yes—
19C2×C13×M16—21no—
20C13×C4⋊Q8—41no—
21C13×#125—42no—
22C13×#125—41no—
23C13×#125—42no—
24C13×C22⋊Q8—22no—
25C13×#117—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D412yes—
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C42×C13D411yescharacteristic
35C13×#107—41no—
36C13×#106—41no—
37C13×#106—42no—
38C13×#103—42no—
39C13×C22⋊C8—22no—
40C13×#95—22no—
41C13×#95—21no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95D412yes—
45#12251C1311yesmaximal, characteristic, direct product factor, Sylow
46C2×Q8×C13—22no—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D412yes—
53C13×M16—22no—
54C13×M16—41no—
55C2×C8×C13—41no—
56C2×C8×C13—42no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—44no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—81no—
70C13×C22⋊C4—41no—
71C42×C13—21no—
72C42×C13—41no—
73C42×C13SD1612yes—
74#2822C2×C1311yescharacteristic
75#2061C2×C1311yescharacteristic
76#1611C2×C1312yes—
77#1346C2×C1312yes—
78#1324C2×C1311yescharacteristic
79C23×C13#12011yescharacteristic
80Q8×C13—82no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13C2×SD1611yescharacteristic
99C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
100C8×C13—42no—
101C8×C13—82no—
102#544C22×C1311yescharacteristic
103C2×#125—21no—
104#483—22no—
105#428—21no—
106#400—22no—
107#398—21no—
108#398—22no—
109#398C22×C1312yes—
110#382C22×C1311yescharacteristic
111#343C22×C1311yescharacteristic
112#339—21no—
113#328—22no—
114#324C22×C1312yes—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13#45011yescharacteristic
118C22×C13#45611yescharacteristic
119C22×C13B(4,𝔽2)11yescharacteristic
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—42no—
123C4×C13—42no—
124C4×C13—82no—
125C4×C13—82no—
126C4×C13—81no—
127C4×C13—81no—
128C4×C13—81no—
129C2×M16—21no—
130C4⋊Q8—41no—
131#125—42no—
132#125—41no—
133#125—42no—
134C22⋊Q8—22no—
135#117—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4D4×C1311yescharacteristic
142C2×C4⋊C4D4×C1312yes—
143C2×C4⋊C4C23×C1311yescharacteristic
144C2×C42D4×C1311yescharacteristic
145#107—41no—
146#106—41no—
147#106—42no—
148#103—42no—
149C22⋊C8—22no—
150#95—22no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95D4×C1312yes—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#160411yescharacteristic
158C2×C13#220111yescharacteristic
159C2×C13#220311yescharacteristic
160C2×Q8—22no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4C2×D4×C1311yescharacteristic
166C22×C4C2×D4×C1312yes—
167M16—22no—
168M16—41no—
169C2×C8—41no—
170C2×C8—42no—
171C4⋊C4—21no—
172C4⋊C4—22no—
173C4⋊C4—21no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—44no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—81no—
184C22⋊C4—41no—
185C42—21no—
186C42—41no—
187C42C13×SD1612yes—
188C13#1225111yescharacteristic, direct product factor, Sylow
189C23C13×#12011yescharacteristic
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4C2×C13×SD1611yescharacteristic
209C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
210C8—42no—
211C8—82no—
212C22—21no—
213C22—21no—
214C22C13×#45011yescharacteristic
215C22C13×#45611yescharacteristic
216C22C13×B(4,𝔽2)11yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—82no—
223C4—81no—
224C4—81no—
225C4—81no—
226C2—21no—
227C2—21no—
228C2C13×#160411yescharacteristic
229C2C13×#220111yescharacteristic
230C2C13×#220311yescharacteristic
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. #12251C13direct (N × H)
188. C13#12251direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28222
C13×#20612
C13×#16112
C13×#13462
C13×#13242
#1225113