Finite Group Databasebeta

← C13×#12971 #15699310

Subgroups — C13×#12971 #15699310

Order 3328.

424 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2381C211yesmaximal, characteristic
2C2×C13×#356C211yesmaximal, characteristic
3C13×#1886C211yesmaximal, characteristic
4C13×#1857C212yesmaximal
5C13×#1394C212yesmaximal
6C2×C13×C4⋊Q8C2211yescharacteristic
7C13×#519C2211yescharacteristic
8C13×#428—22no—
9C13×#419—21no—
10C2×C13×#101C2211yescharacteristic
11C2×C13×#101C2212yes—
12C13×#391—21no—
13C13×#391C2212yes—
14C13×#387—22no—
15C13×#387—22no—
16C13×#383—21no—
17C13×#356C414yescomplemented
18C13×#339—22no—
19C13×#339—21no—
20C22×Q8×C13D411yescharacteristic
21C22×Q8×C13C2311yescharacteristic
22C2×C13×M16—22no—
23C2×C13×M16—21no—
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8C2×C412yes—
26C13×C4⋊Q8Q812yes—
27C4×Q8×C13—42no—
28C13×#117—21no—
29C13×#117—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D412yes—
33C2×C42×C13—21no—
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D412yes—
36C13×#107—42no—
37C13×#106—42no—
38C13×#103—42no—
39C13×#101—22no—
40C13×#101—22no—
41C13×#101C2×C414yes—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95—21no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95—22no—
48#12971C1311yesmaximal, characteristic, direct product factor, Sylow
49C2×Q8×C13—21no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13C4⋊C412yes—
55C2×Q8×C13C22×C411yescharacteristic
56C2×Q8×C13C2×Q811yescharacteristic
57C2×Q8×C13#4112yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D412yes—
64C13×M16—24no—
65C13×M16—42no—
66C13×M16—41no—
67C13×M16—41no—
68C2×C8×C13—42no—
69C2×C8×C13—41no—
70C13×C4⋊C4—24no—
71C13×C4⋊C4—24no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—81no—
77C13×C22⋊C4—41no—
78C42×C13—21no—
79C42×C13—42no—
80C42×C13—42no—
81C42×C13—41no—
82C42×C13—81no—
83C42×C13C4⋊C412yes—
84#2381C2×C1311yescharacteristic
85C2×#356C2×C1311yescharacteristic
86#1886C2×C1311yescharacteristic
87#1857C2×C1312yes—
88#1394C2×C1312yes—
89C23×C13#12011yescharacteristic
90Q8×C13—41no—
91Q8×C13—41no—
92Q8×C13—42no—
93Q8×C13—42no—
94Q8×C13—81no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—44no—
105C2×C4×C13—44no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13C2×C4⋊C411yescharacteristic
110C2×C4×C13C4×D412yes—
111C2×C4×C13C22⋊Q812yes—
112C2×C4×C13#12311yescharacteristic
113C8×C13—44no—
114C8×C13—81no—
115C2×C4⋊Q8C22×C1311yescharacteristic
116#519C22×C1311yescharacteristic
117#428—22no—
118#419—21no—
119C2×#101C22×C1311yescharacteristic
120C2×#101C22×C1312yes—
121#391—21no—
122#391C22×C1312yes—
123#387—22no—
124#387—22no—
125#383—21no—
126#356C4×C1314yescomplemented
127#339—22no—
128#339—21no—
129C22×C13—22no—
130C22×C13#38511yescharacteristic
131C22×C13B(4,𝔽2)11yescharacteristic
132C22×C13#45811yescharacteristic
133C4×C13—22no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—42no—
138C4×C13—42no—
139C4×C13—82no—
140C4×C13—82no—
141C4×C13—82no—
142C22×Q8D4×C1311yescharacteristic
143C22×Q8C23×C1311yescharacteristic
144C2×M16—22no—
145C2×M16—21no—
146C4⋊Q8—22no—
147C4⋊Q8C2×C4×C1312yes—
148C4⋊Q8Q8×C1312yes—
149C4×Q8—42no—
150#117—21no—
151#117—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4D4×C1312yes—
155C2×C42—21no—
156C2×C42D4×C1311yescharacteristic
157C2×C42D4×C1312yes—
158#107—42no—
159#106—42no—
160#103—42no—
161#101—22no—
162#101—22no—
163#101C2×C4×C1314yes—
164#95—21no—
165#95—22no—
166#95—21no—
167#95—22no—
168#95—22no—
169#95—22no—
170C2×C13—21no—
171C2×C13—21no—
172C2×C13#186711yescharacteristic
173C2×C13#220312yes—
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C13×C4⋊C412yes—
180C2×Q8C22×C4×C1311yescharacteristic
181C2×Q8C2×Q8×C1311yescharacteristic
182C2×Q8C13×#4112yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C2×D4×C1311yescharacteristic
188C22×C4C2×D4×C1312yes—
189M16—24no—
190M16—42no—
191M16—41no—
192M16—41no—
193C2×C8—42no—
194C2×C8—41no—
195C4⋊C4—24no—
196C4⋊C4—24no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—81no—
202C22⋊C4—41no—
203C42—21no—
204C42—42no—
205C42—42no—
206C42—41no—
207C42—81no—
208C42C13×C4⋊C412yes—
209C13#1297111yescharacteristic, direct product factor, Sylow
210C23C13×#12011yescharacteristic
211Q8—41no—
212Q8—41no—
213Q8—42no—
214Q8—42no—
215Q8—81no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4C2×C13×C4⋊C411yescharacteristic
231C2×C4C4×D4×C1312yes—
232C2×C4C13×C22⋊Q812yes—
233C2×C4C13×#12311yescharacteristic
234C8—44no—
235C8—81no—
236C22—22no—
237C22C13×#38511yescharacteristic
238C22C13×B(4,𝔽2)11yescharacteristic
239C22C13×#45811yescharacteristic
240C4—22no—
241C4—21no—
242C4—21no—
243C4—22no—
244C4—42no—
245C4—42no—
246C4—82no—
247C4—82no—
248C4—82no—
249C2—21no—
250C2—21no—
251C2C13×#186711yescharacteristic
252C2C13×#220312yes—
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutatorC2×Q8C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC23×C13#120
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
17. C13×#356C4semidirect
48. #12971C13direct (N × H)
126. #356C4×C13semidirect
209. C13#12971direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23812
C2×C13×#3562
C13×#18862
C13×#18572
C13×#13942
#1297113