Finite Group Databasebeta

← C13×#7819 #15694158

Subgroups — C13×#7819 #15694158

Order 3328.

434 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2724C211yesmaximal, characteristic
2C13×#2093C211yesmaximal, characteristic
3C13×#2084C212yesmaximal, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#107—21no—
8C2×C13×#106—22no—
9C2×C13×#102—21no—
10C13×#398—21no—
11C13×#397—22no—
12C13×#390C2211yescharacteristic
13C13×#389C2212yes—
14C13×#385—22no—
15C13×#384C2211yescharacteristic
16C13×#340—22no—
17C13×#336C2212yes—
18C13×#336C2211yescharacteristic
19C22×D4×C13D411yescharacteristic
20C23×C4×C13—21no—
21C22×C8×C13—22no—
22C22×C8×C13—21no—
23C13×#123—42no—
24C13×#123—42no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13C2311yescharacteristic
36C13×#107—42no—
37C13×#106—44no—
38C13×#102—42no—
39C13×#95—22no—
40C13×#95—21no—
41C13×#95—22no—
42#7819C1311yesmaximal, characteristic, direct product factor, Sylow
43C24×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13SD1612yes—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—42no—
52C22×C4×C13—41no—
53C22×C4×C13—81no—
54C22×C4×C13—81no—
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D412yes—
57C2×C8×C13—22no—
58C2×C8×C13—24no—
59C2×C8×C13—42no—
60C2×C8×C13—41no—
61C2×C8×C13—42no—
62C2×C8×C13—41no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—81no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C42×C13—41no—
79#2724C2×C1311yescharacteristic
80#2093C2×C1311yescharacteristic
81#2084C2×C1312yescomplemented
82#1271C2×C1312yescomplemented
83#1270C2×C1311yescharacteristic
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—41no—
87C23×C13—42no—
88C23×C13—41no—
89C23×C13#12011yescharacteristic
90D4×C13—42no—
91D4×C13—81no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—84no—
105C2×C4×C13—82no—
106C2×C4×C13—81no—
107C2×C4×C13C2×SD1611yescharacteristic
108C2×C4×C13#13512yes—
109C2×C4×C13AGL(1,ℤ/8)12yes—
110C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
111C8×C13—44no—
112C8×C13—42no—
113C2×#123—21no—
114C2×#107—21no—
115C2×#106—22no—
116C2×#102—21no—
117#398—21no—
118#397—22no—
119#390C22×C1311yescharacteristic
120#389C22×C1312yes—
121#385—22no—
122#384C22×C1311yescharacteristic
123#340—22no—
124#336C22×C1312yes—
125#336C22×C1311yescharacteristic
126C22×C13—42no—
127C22×C13—44no—
128C22×C13—82no—
129C22×C13—81no—
130C22×C13—81no—
131C22×C13#44912yes—
132C22×C13#45011yescharacteristic
133C22×C13#45311yescharacteristic
134C22×C13#45612yes—
135C22×C13#45811yescharacteristic
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—82no—
141C4×C13—81no—
142C4×C13—82no—
143C4×C13—161no—
144C22×D4D4×C1311yescharacteristic
145C23×C4—21no—
146C22×C8—22no—
147C22×C8—21no—
148#123—42no—
149#123—42no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4D4×C1312yes—
155C2×C4⋊C4D4×C1312yes—
156C2×C4⋊C4D4×C1311yescharacteristic
157C2×C22⋊C4—22no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—22no—
160C2×C42C23×C1311yescharacteristic
161#107—42no—
162#106—44no—
163#102—42no—
164#95—22no—
165#95—21no—
166#95—22no—
167C2×C13—82no—
168C2×C13#160912yes—
169C2×C13#161311yescharacteristic
170C2×C13#162011yescharacteristic
171C2×C13#165412yes—
172C2×C13#166011yescharacteristic
173C24—21no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4C13×SD1612yes—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—42no—
182C22×C4—41no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4C2×D4×C1311yescharacteristic
186C22×C4C2×D4×C1312yes—
187C2×C8—22no—
188C2×C8—24no—
189C2×C8—42no—
190C2×C8—41no—
191C2×C8—42no—
192C2×C8—41no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—81no—
204C22⋊C4—42no—
205C22⋊C4—44no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—41no—
209C13#781911yescharacteristic, direct product factor, Sylow
210C23—22no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23—41no—
215C23C13×#12011yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—82no—
232C2×C4—81no—
233C2×C4C2×C13×SD1611yescharacteristic
234C2×C4C13×#13512yes—
235C2×C4C13×AGL(1,ℤ/8)12yes—
236C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
237C8—44no—
238C8—42no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22C13×#44912yes—
245C22C13×#45011yescharacteristic
246C22C13×#45311yescharacteristic
247C22C13×#45612yes—
248C22C13×#45811yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—82no—
254C4—81no—
255C4—82no—
256C4—161no—
257C2—82no—
258C2C13×#160912yes—
259C2C13×#161311yescharacteristic
260C2C13×#162011yescharacteristic
261C2C13×#165412yes—
262C2C13×#166011yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2084C2semidirect
4. C13×#1271C2semidirect
42. #7819C13direct (N × H)
81. #2084C2×C13semidirect
82. #1271C2×C13semidirect
209. C13#7819direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27242
C13×#20932
C13×#20842
C13×#12712
C13×#12702
#781913