Finite Group Databasebeta

← C13×#10523 #15696862

Subgroups — C13×#10523 #15696862

Order 3328.

382 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3249C211yesmaximal, characteristic
2C13×#1994C212yesmaximal
3C13×#1831C211yesmaximal, characteristic
4C13×#1550C212yesmaximal
5C13×#1292C211yesmaximal, characteristic
6C13×#533C2212yes—
7C13×#477—22no—
8C13×#467—22no—
9C13×#462—22no—
10C13×#423C2212yes—
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C43×C13C2211yescharacteristic
14C13×#339—22no—
15C13×#339—22no—
16C13×#336—22no—
17C13×#333—22no—
18C13×#332—22no—
19C2×C13×Q16—22no—
20C2×C13×M16—22no—
21C22×C8×C13—21no—
22C22×C8×C13D412yes—
23C13×C4⋊Q8D412yes—
24C13×C4⋊Q8D412yes—
25C13×#125—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C13×#117—22no—
31C2×C42×C13—21no—
32C2×C42×C13—21no—
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C13×#107—22no—
37C13×C4⋊C8—22no—
38C13×C4⋊C8—22no—
39C13×C4⋊C8—22no—
40C13×C4⋊C8—22no—
41C13×#103—24no—
42#10523C1311yesmaximal, characteristic, direct product factor, Sylow
43C2×Q8×C13—22no—
44C2×Q8×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C2×D411yescharacteristic
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13#4111yescharacteristic
50C13×Q16—82no—
51C13×M16—42no—
52C13×M16—42no—
53C2×C8×C13—22no—
54C2×C8×C13—42no—
55C2×C8×C13—42no—
56C2×C8×C13—41no—
57C2×C8×C13—42no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C22⋊C4—42no—
65C42×C13—21no—
66C42×C13—22no—
67C42×C13—41no—
68C42×C13—41no—
69C42×C13—42no—
70C42×C13—42no—
71C42×C13Q1612yescomplemented
72C42×C13C2×D412yes—
73C42×C13#4112yes—
74#3249C2×C1311yescharacteristic
75#1994C2×C1312yes—
76#1831C2×C1311yescharacteristic
77#1550C2×C1312yes—
78#1292C2×C1311yescharacteristic
79C23×C13#12111yescharacteristic
80Q8×C13—42no—
81Q8×C13—42no—
82Q8×C13—82no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13#12011yescharacteristic
95C2×C4×C13#12112yes—
96C2×C4×C13#12312yes—
97C2×C4×C13#12411yescharacteristic
98C2×C4×C13C2×Q1611yescharacteristic
99C2×C4×C13#13511yescharacteristic
100C2×C4×C13#13712yes—
101C8×C13—42no—
102C8×C13—81no—
103C8×C13—82no—
104#533C22×C1312yes—
105#477—22no—
106#467—22no—
107#462—22no—
108#423C22×C1312yes—
109C2×C4⋊C8C22×C1311yescharacteristic
110C2×C4⋊C8C22×C1311yescharacteristic
111C43C22×C1311yescharacteristic
112#339—22no—
113#339—22no—
114#336—22no—
115#333—22no—
116#332—22no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13#39411yescharacteristic
120C22×C13#46711yescharacteristic
121C22×C13#47011yescharacteristic
122C4×C13—22no—
123C4×C13—21no—
124C4×C13—42no—
125C4×C13—42no—
126C4×C13—82no—
127C4×C13—82no—
128C4×C13#45411yescharacteristic
129C4×C13#45511yescharacteristic
130C4×C13#46212yes—
131C4×C13#46412yes—
132C2×Q16—22no—
133C2×M16—22no—
134C22×C8—21no—
135C22×C8D4×C1312yes—
136C4⋊Q8D4×C1312yes—
137C4⋊Q8D4×C1312yes—
138#125—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143#117—22no—
144C2×C42—21no—
145C2×C42—21no—
146C2×C42D4×C1311yescharacteristic
147C2×C42D4×C1311yescharacteristic
148C2×C42C23×C1311yescharacteristic
149#107—22no—
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154#103—24no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#204011yescharacteristic
158C2×C13#205011yescharacteristic
159C2×C13#205611yescharacteristic
160C2×Q8—22no—
161C2×Q8—22no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4C2×D4×C1311yescharacteristic
165C22×C4C2×D4×C1311yescharacteristic
166C22×C4C13×#4111yescharacteristic
167Q16—82no—
168M16—42no—
169M16—42no—
170C2×C8—22no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—41no—
174C2×C8—42no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C22⋊C4—42no—
182C42—21no—
183C42—22no—
184C42—41no—
185C42—41no—
186C42—42no—
187C42—42no—
188C42C13×Q1612yescomplemented
189C42C2×D4×C1312yes—
190C42C13×#4112yes—
191C13#1052311yescharacteristic, direct product factor, Sylow
192C23C13×#12111yescharacteristic
193Q8—42no—
194Q8—42no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4C13×#12011yescharacteristic
208C2×C4C13×#12112yes—
209C2×C4C13×#12312yes—
210C2×C4C13×#12411yescharacteristic
211C2×C4C2×C13×Q1611yescharacteristic
212C2×C4C13×#13511yescharacteristic
213C2×C4C13×#13712yes—
214C8—42no—
215C8—81no—
216C8—82no—
217C22—21no—
218C22—21no—
219C22C13×#39411yescharacteristic
220C22C13×#46711yescharacteristic
221C22C13×#47011yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—82no—
227C4—82no—
228C4C13×#45411yescharacteristic
229C4C13×#45511yescharacteristic
230C4C13×#46212yes—
231C4C13×#46412yes—
232C2—21no—
233C2—21no—
234C2C13×#204011yescharacteristic
235C2C13×#205011yescharacteristic
236C2C13×#205611yescharacteristic
subgroupG/H
center, socleC22×C13#394
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC23×C13#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
42. #10523C13direct (N × H)
71. C42×C13Q16semidirect
188. C42C13×Q16semidirect
191. C13#10523direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32492
C13×#19942
C13×#18312
C13×#15502
C13×#12922
#1052313