Finite Group Databasebeta

← C13×#10387 #15696726

Subgroups — C13×#10387 #15696726

Order 3328.

414 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2607C211yesmaximal, characteristic
2C13×#1826C212yesmaximal
3C13×#1820C211yesmaximal, characteristic
4C13×#1306C211yesmaximal, characteristic
5C13×#1284C212yesmaximal
6C2×C13×#117C2211yescharacteristic
7C13×#407C2212yes—
8C13×#399—21no—
9C13×#393—21no—
10C13×#391—22no—
11C13×#387—22no—
12C13×#381C2211yescharacteristic
13C13×#381C2211yescharacteristic
14C4×C13×C22⋊C4C2212yes—
15C13×#342—21no—
16C13×#342—21no—
17C13×#339—22no—
18C13×#339—22no—
19C22×Q8×C13—21no—
20C23×C4×C13C2311yescharacteristic
21C2×C13×M16—22no—
22C13×#117—22no—
23C13×#117—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4Q812yescomplemented
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—21no—
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13D412yes—
34C2×C42×C13D412yes—
35C13×C22⋊C8—22no—
36C13×C22⋊C8—22no—
37C13×#95—21no—
38C13×#95—22no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95—22no—
43#10387C1311yesmaximal, characteristic, direct product factor, Sylow
44C24×C13C2×D411yescharacteristic
45C2×Q8×C13—44no—
46C2×Q8×C13—81no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13C2×D412yes—
56C22×C4×C13C2×Q811yescharacteristic
57C22×C4×C13#4112yes—
58C22×C4×C13#4111yescharacteristic
59C13×M16—42no—
60C13×M16—42no—
61C2×C8×C13—42no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—44no—
64C13×C4⋊C4—81no—
65C13×C22⋊C4—44no—
66C13×C22⋊C4—41no—
67C13×C22⋊C4—41no—
68C13×C22⋊C4—41no—
69C13×C22⋊C4—41no—
70C13×C22⋊C4—41no—
71C13×C22⋊C4—41no—
72C42×C13—42no—
73C42×C13—42no—
74C42×C13—42no—
75#2607C2×C1311yescharacteristic
76#1826C2×C1312yes—
77#1820C2×C1311yescharacteristic
78#1306C2×C1311yescharacteristic
79#1284C2×C1312yes—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—42no—
83C23×C13#12011yescharacteristic
84C23×C13C22⋊Q811yescharacteristic
85C23×C13#12411yescharacteristic
86Q8×C13—84no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—24no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
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—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—82no—
104C2×C4×C13—81no—
105C2×C4×C13—82no—
106C2×C4×C13C22⋊Q812yes—
107C2×C4×C13#12412yes—
108C8×C13—82no—
109C2×#117C22×C1311yescharacteristic
110#407C22×C1312yes—
111#399—21no—
112#393—21no—
113#391—22no—
114#387—22no—
115#381C22×C1311yescharacteristic
116#381C22×C1311yescharacteristic
117C4×C22⋊C4C22×C1312yes—
118#342—21no—
119#342—21no—
120#339—22no—
121#339—22no—
122C22×C13—22no—
123C22×C13—21no—
124C22×C13—21no—
125C22×C13—22no—
126C22×C13—22no—
127C22×C13—81no—
128C22×C13—81no—
129C22×C13#39311yescharacteristic
130C22×C13#45811yescharacteristic
131C22×C13#45811yescharacteristic
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—44no—
135C4×C13—82no—
136C4×C13—81no—
137C4×C13—81no—
138C4×C13—82no—
139C4×C13—161no—
140C22×Q8—21no—
141C23×C4C23×C1311yescharacteristic
142C2×M16—22no—
143#117—22no—
144#117—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4Q8×C1312yescomplemented
148C2×C22⋊C4—21no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4D4×C1311yescharacteristic
152C2×C22⋊C4D4×C1311yescharacteristic
153C2×C42—21no—
154C2×C42D4×C1312yes—
155C2×C42D4×C1312yes—
156C22⋊C8—22no—
157C22⋊C8—22no—
158#95—21no—
159#95—22no—
160#95—21no—
161#95—22no—
162#95—22no—
163#95—22no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13—41no—
167C2×C13—41no—
168C2×C13#203011yescharacteristic
169C2×C13#203112yes—
170C24C2×D4×C1311yescharacteristic
171C2×Q8—44no—
172C2×Q8—81no—
173C22×C4—22no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4C2×D4×C1312yes—
182C22×C4C2×Q8×C1311yescharacteristic
183C22×C4C13×#4112yes—
184C22×C4C13×#4111yescharacteristic
185M16—42no—
186M16—42no—
187C2×C8—42no—
188C4⋊C4—24no—
189C4⋊C4—44no—
190C4⋊C4—81no—
191C22⋊C4—44no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—41no—
195C22⋊C4—41no—
196C22⋊C4—41no—
197C22⋊C4—41no—
198C42—42no—
199C42—42no—
200C42—42no—
201C13#1038711yescharacteristic, direct product factor, Sylow
202C23—21no—
203C23—21no—
204C23—42no—
205C23C13×#12011yescharacteristic
206C23C13×C22⋊Q811yescharacteristic
207C23C13×#12411yescharacteristic
208Q8—84no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—82no—
226C2×C4—81no—
227C2×C4—82no—
228C2×C4C13×C22⋊Q812yes—
229C2×C4C13×#12412yes—
230C8—82no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22C13×#39311yescharacteristic
239C22C13×#45811yescharacteristic
240C22C13×#45811yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—82no—
245C4—81no—
246C4—81no—
247C4—82no—
248C4—161no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2C13×#203011yescharacteristic
254C2C13×#203112yes—
subgroupG/H
center, socleC22×C13#393
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
26. C2×C13×C4⋊C4Q8semidirect
43. #10387C13direct (N × H)
147. C2×C4⋊C4Q8×C13semidirect
201. C13#10387direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26072
C13×#18262
C13×#18202
C13×#13062
C13×#12842
#1038713