Finite Group Databasebeta

← C13×#12256 #15698595

Subgroups — C13×#12256 #15698595

Order 3328.

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

normal subgroups only

This group has 442 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×#2551C211yesmaximal, characteristic
2C13×#2060C211yesmaximal, characteristic
3C13×#1605C212yesmaximal
4C13×#1354C212yesmaximal
5C13×#1325C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C2×C13×C4⋊Q8—22no—
8C13×#451—22no—
9C13×#428—21no—
10C13×#395—21no—
11C13×#395C2212yes—
12C13×#389—22no—
13C13×#384C2211yescharacteristic
14C4×C13×C4⋊C4—21no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17C13×#328—22no—
18C13×#324C2212yes—
19C22×Q8×C13—21no—
20C22×Q8×C13D412yes—
21C2×C13×Q16—42no—
22C2×C13×M16—21no—
23C13×C4⋊Q8—41no—
24C13×C4⋊Q8—48no—
25C13×#125—41no—
26C13×C22⋊Q8—22no—
27C13×#117—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C42×C13—22no—
36C2×C42×C13D411yescharacteristic
37C13×#107—41no—
38C13×#106—41no—
39C13×#103—42no—
40C13×C22⋊C8—22no—
41C13×#95—21no—
42C13×#95—22no—
43C13×#95D412yes—
44#12256C1311yesmaximal, characteristic, direct product factor, Sylow
45C2×Q8×C13—22no—
46C2×Q8×C13—44no—
47C2×Q8×C13—44no—
48C2×Q8×C13—42no—
49C2×Q8×C13—81no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—21no—
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D412yes—
56C13×Q16—84no—
57C13×M16—22no—
58C13×M16—41no—
59C2×C8×C13—41no—
60C2×C8×C13—42no—
61C13×C4⋊C4—24no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—21no—
65C13×C4⋊C4—21no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—44no—
69C13×C4⋊C4—44no—
70C13×C4⋊C4—44no—
71C13×C4⋊C4—42no—
72C13×C22⋊C4—41no—
73C42×C13—21no—
74C42×C13—44no—
75C42×C13—41no—
76C42×C13Q1612yescomplemented
77#2551C2×C1311yescharacteristic
78#2060C2×C1311yescharacteristic
79#1605C2×C1312yes—
80#1354C2×C1312yes—
81#1325C2×C1311yescharacteristic
82C23×C13#12011yescharacteristic
83Q8×C13—44no—
84Q8×C13—82no—
85Q8×C13—84no—
86Q8×C13—82no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—24no—
93C2×C4×C13—24no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13C2×Q1611yescharacteristic
105C2×C4×C13#13711yescharacteristic
106C8×C13—42no—
107C8×C13—82no—
108#544C22×C1311yescharacteristic
109C2×C4⋊Q8—22no—
110#451—22no—
111#428—21no—
112#395—21no—
113#395C22×C1312yes—
114#389—22no—
115#384C22×C1311yescharacteristic
116C4×C4⋊C4—21no—
117#343C22×C1311yescharacteristic
118#339—21no—
119#328—22no—
120#324C22×C1312yes—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#45111yescharacteristic
124C22×C13#45611yescharacteristic
125C22×C13B(4,𝔽2)11yescharacteristic
126C4×C13—24no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—44no—
130C4×C13—42no—
131C4×C13—44no—
132C4×C13—81no—
133C4×C13—81no—
134C4×C13—81no—
135C22×Q8—21no—
136C22×Q8D4×C1312yes—
137C2×Q16—42no—
138C2×M16—21no—
139C4⋊Q8—41no—
140C4⋊Q8—48no—
141#125—41no—
142C22⋊Q8—22no—
143#117—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4D4×C1311yescharacteristic
150C2×C4⋊C4C23×C1311yescharacteristic
151C2×C42—22no—
152C2×C42D4×C1311yescharacteristic
153#107—41no—
154#106—41no—
155#103—42no—
156C22⋊C8—22no—
157#95—21no—
158#95—22no—
159#95D4×C1312yes—
160C2×C13—21no—
161C2×C13—21no—
162C2×C13#160511yescharacteristic
163C2×C13#219611yescharacteristic
164C2×C13#220511yescharacteristic
165C2×Q8—22no—
166C2×Q8—44no—
167C2×Q8—44no—
168C2×Q8—42no—
169C2×Q8—81no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4C2×D4×C1311yescharacteristic
175C22×C4C2×D4×C1312yes—
176Q16—84no—
177M16—22no—
178M16—41no—
179C2×C8—41no—
180C2×C8—42no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—44no—
189C4⋊C4—44no—
190C4⋊C4—44no—
191C4⋊C4—42no—
192C22⋊C4—41no—
193C42—21no—
194C42—44no—
195C42—41no—
196C42C13×Q1612yescomplemented
197C13#1225611yescharacteristic, direct product factor, Sylow
198C23C13×#12011yescharacteristic
199Q8—44no—
200Q8—82no—
201Q8—84no—
202Q8—82no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—24no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4C2×C13×Q1611yescharacteristic
221C2×C4C13×#13711yescharacteristic
222C8—42no—
223C8—82no—
224C22—21no—
225C22—21no—
226C22C13×#45111yescharacteristic
227C22C13×#45611yescharacteristic
228C22C13×B(4,𝔽2)11yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—44no—
233C4—42no—
234C4—44no—
235C4—81no—
236C4—81no—
237C4—81no—
238C2—21no—
239C2—21no—
240C2C13×#160511yescharacteristic
241C2C13×#219611yescharacteristic
242C2C13×#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
44. #12256C13direct (N × H)
76. C42×C13Q16semidirect
196. C42C13×Q16semidirect
197. C13#12256direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25512
C13×#20602
C13×#16052
C13×#13542
C13×#13252
#1225613