Finite Group Databasebeta

← C13×#12153 #15698492

Subgroups — C13×#12153 #15698492

Order 3328.

424 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2582C211yesmaximal, characteristic, complemented
2C13×#2039C211yesmaximal, characteristic
3C13×#1610C212yesmaximal
4C13×#1346C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C13×#537C2211yescharacteristic
7C2×C4×Q8×C13—21no—
8C13×#480—22no—
9C2×C13×#104—21no—
10C13×#417—21no—
11C13×#398—21no—
12C13×#398C2212yes—
13C13×#391—22no—
14C13×#389—22no—
15C13×#384C2211yescharacteristic
16C13×#343C2211yescharacteristic
17C13×#327—22no—
18C13×#324C2212yes—
19C2×C13×#41—21no—
20C22×Q8×C13—21no—
21C2×C13×M16—21no—
22C13×C22⋊Q8—41no—
23C13×#121—22no—
24C13×#121—41no—
25C4×Q8×C13—42no—
26C4×Q8×C13—42no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D412yes—
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C42×C13—22no—
35C2×C42×C13D411yescharacteristic
36C13×#107—42no—
37C13×#104—42no—
38C13×#103—41no—
39C13×#102—41no—
40C13×#102—42no—
41C13×C22⋊C8—22no—
42C13×#95—22no—
43C13×#95—21no—
44C13×#95—22no—
45C13×#95D412yes—
46#12153C1311yesmaximal, characteristic, direct product factor, Sylow
47C13×#41—41no—
48C13×#41—41no—
49C13×#41—41no—
50C13×#41—41no—
51C2×Q8×C13—24no—
52C2×Q8×C13—21no—
53C2×Q8×C13—42no—
54C2×Q8×C13—42no—
55C2×D4×C13—21no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—41no—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D412yes—
65C13×M16—41no—
66C13×M16—41no—
67C2×C8×C13—42no—
68C2×C8×C13—41no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—44no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—81no—
78C13×C22⋊C4—42no—
79C42×C13—21no—
80C42×C13—44no—
81C42×C13D812yes—
82#2582C2×C1311yescharacteristic, complemented
83#2039C2×C1311yescharacteristic
84#1610C2×C1312yes—
85#1346C2×C1312yescomplemented
86#1325C2×C1311yescharacteristic, complemented
87C23×C13—41no—
88C23×C13#12011yescharacteristic
89Q8×C13—48no—
90Q8×C13—41no—
91Q8×C13—41no—
92D4×C13—41no—
93D4×C13—41no—
94D4×C13—82no—
95D4×C13—81no—
96D4×C13—81no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—24no—
103C2×C4×C13—22no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—81no—
114C2×C4×C13—81no—
115C2×C4×C13C2×D811yescharacteristic
116C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
117C8×C13—81no—
118C8×C13—82no—
119#537C22×C1311yescharacteristic
120C2×C4×Q8—21no—
121#480—22no—
122C2×#104—21no—
123#417—21no—
124#398—21no—
125#398C22×C1312yes—
126#391—22no—
127#389—22no—
128#384C22×C1311yescharacteristic
129#343C22×C1311yescharacteristic
130#327—22no—
131#324C22×C1312yes—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—81no—
135C22×C13—81no—
136C22×C13—81no—
137C22×C13#44711yescharacteristic
138C22×C13#45411yescharacteristic
139C22×C13B(4,𝔽2)11yescharacteristic
140C4×C13—24no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—44no—
144C4×C13—42no—
145C4×C13—82no—
146C4×C13—81no—
147C4×C13—81no—
148C2×#41—21no—
149C22×Q8—21no—
150C2×M16—21no—
151C22⋊Q8—41no—
152#121—22no—
153#121—41no—
154C4×Q8—42no—
155C4×Q8—42no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4D4×C1311yescharacteristic
161C2×C4⋊C4D4×C1312yes—
162C2×C4⋊C4C23×C1311yescharacteristic
163C2×C42—22no—
164C2×C42D4×C1311yescharacteristic
165#107—42no—
166#104—42no—
167#103—41no—
168#102—41no—
169#102—42no—
170C22⋊C8—22no—
171#95—22no—
172#95—21no—
173#95—22no—
174#95D4×C1312yes—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13—161no—
178C2×C13#159811yescharacteristic
179C2×C13#219811yescharacteristic
180C2×C13#220511yescharacteristic
181#41—41no—
182#41—41no—
183#41—41no—
184#41—41no—
185C2×Q8—24no—
186C2×Q8—21no—
187C2×Q8—42no—
188C2×Q8—42no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—41no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4C2×D4×C1311yescharacteristic
198C22×C4C2×D4×C1312yes—
199M16—41no—
200M16—41no—
201C2×C8—42no—
202C2×C8—41no—
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—44no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—81no—
212C22⋊C4—42no—
213C42—21no—
214C42—44no—
215C42C13×D812yes—
216C13#1215311yescharacteristic, direct product factor, Sylow
217C23—41no—
218C23C13×#12011yescharacteristic
219Q8—48no—
220Q8—41no—
221Q8—41no—
222D4—41no—
223D4—41no—
224D4—82no—
225D4—81no—
226D4—81no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4C2×C13×D811yescharacteristic
246C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
247C8—81no—
248C8—82no—
249C22—21no—
250C22—21no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22C13×#44711yescharacteristic
255C22C13×#45411yescharacteristic
256C22C13×B(4,𝔽2)11yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—42no—
262C4—82no—
263C4—81no—
264C4—81no—
265C2—21no—
266C2—21no—
267C2—161no—
268C2C13×#159811yescharacteristic
269C2C13×#219811yescharacteristic
270C2C13×#220511yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC13×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2582C2semidirect
4. C13×#1346C2semidirect
5. C13×#1325C2semidirect
46. #12153C13direct (N × H)
82. #2582C2×C13semidirect
85. #1346C2×C13semidirect
86. #1325C2×C13semidirect
216. C13#12153direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25822
C13×#20392
C13×#16102
C13×#13462
C13×#13252
#1215313