Finite Group Databasebeta

← C13×#7810 #15694149

Subgroups — C13×#7810 #15694149

Order 3328.

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

normal subgroups only

This group has 478 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×#2733C211yesmaximal, characteristic
2C13×#2096C211yesmaximal, characteristic, complemented
3C13×#2071C212yesmaximal, complemented
4C13×#1272C211yesmaximal, characteristic, complemented
5C13×#1270C212yesmaximal, complemented
6C2×C13×#124—21no—
7C2×C13×#106—21no—
8C2×C13×#103—21no—
9C2×C13×#102—22no—
10C13×#394—21no—
11C13×#392—22no—
12C13×#391C2211yescharacteristic
13C13×#390C2212yes—
14C13×#388—22no—
15C13×#384C2211yescharacteristic
16C13×#340—22no—
17C13×#336C2211yescharacteristic
18C13×#336C2212yes—
19C22×Q8×C13D411yescharacteristic
20C22×D4×C13—21no—
21C22×D4×C13—21no—
22C22×D4×C13D412yes—
23C22×C8×C13—21no—
24C22×C8×C13—22no—
25C13×#124—42no—
26C13×#124—42no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C13×#106—42no—
38C13×#103—42no—
39C13×#102—44no—
40C13×#95—21no—
41C13×#95—22no—
42#7810C1311yesmaximal, characteristic, direct product factor, Sylow
43C24×C13—22no—
44C2×Q8×C13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13SD1612yes—
48C2×D4×C13—22no—
49C2×D4×C13—22no—
50C2×D4×C13—42no—
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—81no—
54C2×D4×C13—81no—
55C2×D4×C13—81no—
56C2×D4×C13—82no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—41no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D412yes—
63C2×C8×C13—22no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C2×C8×C13—42no—
67C2×C8×C13—42no—
68C2×C8×C13—42no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—82no—
81C42×C13—41no—
82C42×C13—42no—
83#2733C2×C1311yescharacteristic
84#2096C2×C1311yescharacteristic, complemented
85#2071C2×C1312yescomplemented
86#1272C2×C1311yescharacteristic, complemented
87#1270C2×C1312yescomplemented
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13#12011yescharacteristic
96Q8×C13—42no—
97Q8×C13—81no—
98D4×C13—44no—
99D4×C13—82no—
100D4×C13—84no—
101D4×C13—84no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—82no—
115C2×C4×C13—81no—
116C2×C4×C13C2×SD1611yescharacteristic
117C2×C4×C13#13512yes—
118C2×C4×C13AGL(1,ℤ/8)12yes—
119C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
120C8×C13—42no—
121C8×C13—82no—
122C2×#124—21no—
123C2×#106—21no—
124C2×#103—21no—
125C2×#102—22no—
126#394—21no—
127#392—22no—
128#391C22×C1311yescharacteristic
129#390C22×C1312yes—
130#388—22no—
131#384C22×C1311yescharacteristic
132#340—22no—
133#336C22×C1312yes—
134#336C22×C1311yescharacteristic
135C22×C13—82no—
136C22×C13—82no—
137C22×C13—82no—
138C22×C13—82no—
139C22×C13—82no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13#44912yes—
143C22×C13#45011yescharacteristic
144C22×C13#45311yescharacteristic
145C22×C13#45512yes—
146C22×C13#45811yescharacteristic
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—42no—
152C4×C13—82no—
153C4×C13—81no—
154C4×C13—161no—
155C22×Q8D4×C1311yescharacteristic
156C22×D4—21no—
157C22×D4—21no—
158C22×D4D4×C1312yes—
159C22×C8—21no—
160C22×C8—22no—
161#124—42no—
162#124—42no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4D4×C1312yes—
166C2×C4⋊C4D4×C1311yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C42—21no—
172C2×C42C23×C1311yescharacteristic
173#106—42no—
174#103—42no—
175#102—44no—
176#95—21no—
177#95—22no—
178C2×C13—162no—
179C2×C13#161212yes—
180C2×C13#161311yescharacteristic
181C2×C13#162411yescharacteristic
182C2×C13#164212yes—
183C2×C13#165911yescharacteristic
184C24—22no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8C13×SD1612yes—
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—81no—
195C2×D4—81no—
196C2×D4—81no—
197C2×D4—82no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—41no—
202C22×C4C2×D4×C1311yescharacteristic
203C22×C4C2×D4×C1312yes—
204C2×C8—22no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C22⋊C4—44no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—82no—
222C42—41no—
223C42—42no—
224C13#781011yescharacteristic, direct product factor, Sylow
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23C13×#12011yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—44no—
236D4—82no—
237D4—84no—
238D4—84no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4C2×C13×SD1611yescharacteristic
254C2×C4C13×#13512yes—
255C2×C4C13×AGL(1,ℤ/8)12yes—
256C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
257C8—42no—
258C8—82no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22C13×#44912yes—
267C22C13×#45011yescharacteristic
268C22C13×#45311yescharacteristic
269C22C13×#45512yes—
270C22C13×#45811yescharacteristic
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—82no—
277C4—81no—
278C4—161no—
279C2—162no—
280C2C13×#161212yes—
281C2C13×#161311yescharacteristic
282C2C13×#162411yescharacteristic
283C2C13×#164212yes—
284C2C13×#165911yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#2733C2
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
2. C13×#2096C2semidirect
3. C13×#2071C2semidirect
4. C13×#1272C2semidirect
5. C13×#1270C2semidirect
42. #7810C13direct (N × H)
84. #2096C2×C13semidirect
85. #2071C2×C13semidirect
86. #1272C2×C13semidirect
87. #1270C2×C13semidirect
224. C13#7810direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27332
C13×#20962
C13×#20712
C13×#12722
C13×#12702
#781013