Finite Group Databasebeta

← C13×#12180 #15698519

Subgroups — C13×#12180 #15698519

Order 3328.

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

normal subgroups only

This group has 472 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×#2551C211yesmaximal, characteristic, complemented
2C13×#2039C211yesmaximal, characteristic
3C13×#1604C212yesmaximal
4C13×#1354C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C13×#537C2211yescharacteristic
7C2×C13×C4⋊Q8—22no—
8C13×#448—22no—
9C2×C13×#104—21no—
10C13×#417—21no—
11C13×#395—21no—
12C13×#395C2212yes—
13C13×#389—22no—
14C13×#384C2211yescharacteristic
15C4×C13×C4⋊C4—21no—
16C13×#343C2211yescharacteristic
17C13×#327—22no—
18C13×#324C2212yes—
19C2×C13×#41—21no—
20C22×Q8×C13—21no—
21C22×Q8×C13D412yes—
22C2×C13×SD16—42no—
23C2×C13×M16—21no—
24C13×C4⋊Q8—48no—
25C13×C22⋊Q8—41no—
26C13×#121—22no—
27C13×#121—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C42×C13—22no—
36C2×C42×C13D411yescharacteristic
37C13×#104—42no—
38C13×#103—42no—
39C13×#103—41no—
40C13×#102—41no—
41C13×C22⋊C8—22no—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95D412yes—
45#12180C1311yesmaximal, characteristic, direct product factor, Sylow
46C13×#41—41no—
47C13×#41—41no—
48C13×#41—41no—
49C13×#41—41no—
50C2×Q8×C13—21no—
51C2×Q8×C13—44no—
52C2×Q8×C13—44no—
53C2×Q8×C13—42no—
54C2×Q8×C13—81no—
55C2×D4×C13—21no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D412yes—
65C13×SD16—84no—
66C13×M16—41no—
67C13×M16—41no—
68C2×C8×C13—42no—
69C2×C8×C13—41no—
70C13×C4⋊C4—24no—
71C13×C4⋊C4—24no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—44no—
77C13×C4⋊C4—44no—
78C13×C22⋊C4—42no—
79C42×C13—21no—
80C42×C13—44no—
81C42×C13SD1612yescomplemented
82#2551C2×C1311yescharacteristic, complemented
83#2039C2×C1311yescharacteristic
84#1604C2×C1312yes—
85#1354C2×C1312yescomplemented
86#1325C2×C1311yescharacteristic, complemented
87C23×C13—41no—
88C23×C13#12011yescharacteristic
89Q8×C13—41no—
90Q8×C13—41no—
91Q8×C13—44no—
92Q8×C13—82no—
93Q8×C13—84no—
94D4×C13—41no—
95D4×C13—41no—
96D4×C13—82no—
97D4×C13—81no—
98D4×C13—81no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—24no—
105C2×C4×C13—24no—
106C2×C4×C13—22no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13C2×SD1611yescharacteristic
118C2×C4×C13#13711yescharacteristic
119C8×C13—81no—
120C8×C13—82no—
121#537C22×C1311yescharacteristic
122C2×C4⋊Q8—22no—
123#448—22no—
124C2×#104—21no—
125#417—21no—
126#395—21no—
127#395C22×C1312yes—
128#389—22no—
129#384C22×C1311yescharacteristic
130C4×C4⋊C4—21no—
131#343C22×C1311yescharacteristic
132#327—22no—
133#324C22×C1312yes—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—81no—
137C22×C13—81no—
138C22×C13—81no—
139C22×C13#44811yescharacteristic
140C22×C13#45411yescharacteristic
141C22×C13B(4,𝔽2)11yescharacteristic
142C4×C13—24no—
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—44no—
146C4×C13—42no—
147C4×C13—44no—
148C4×C13—81no—
149C4×C13—81no—
150C2×#41—21no—
151C22×Q8—21no—
152C22×Q8D4×C1312yes—
153C2×SD16—42no—
154C2×M16—21no—
155C4⋊Q8—48no—
156C22⋊Q8—41no—
157#121—22no—
158#121—41no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4D4×C1311yescharacteristic
165C2×C4⋊C4C23×C1311yescharacteristic
166C2×C42—22no—
167C2×C42D4×C1311yescharacteristic
168#104—42no—
169#103—42no—
170#103—41no—
171#102—41no—
172C22⋊C8—22no—
173#95—21no—
174#95—22no—
175#95D4×C1312yes—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13—161no—
179C2×C13#159911yescharacteristic
180C2×C13#219611yescharacteristic
181C2×C13#220511yescharacteristic
182#41—41no—
183#41—41no—
184#41—41no—
185#41—41no—
186C2×Q8—21no—
187C2×Q8—44no—
188C2×Q8—44no—
189C2×Q8—42no—
190C2×Q8—81no—
191C2×D4—21no—
192C2×D4—22no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—41no—
199C22×C4C2×D4×C1311yescharacteristic
200C22×C4C2×D4×C1312yes—
201SD16—84no—
202M16—41no—
203M16—41no—
204C2×C8—42no—
205C2×C8—41no—
206C4⋊C4—24no—
207C4⋊C4—24no—
208C4⋊C4—22no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—44no—
212C4⋊C4—44no—
213C4⋊C4—44no—
214C22⋊C4—42no—
215C42—21no—
216C42—44no—
217C42C13×SD1612yescomplemented
218C13#1218011yescharacteristic, direct product factor, Sylow
219C23—41no—
220C23C13×#12011yescharacteristic
221Q8—41no—
222Q8—41no—
223Q8—44no—
224Q8—82no—
225Q8—84no—
226D4—41no—
227D4—41no—
228D4—82no—
229D4—81no—
230D4—81no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—24no—
237C2×C4—24no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4C2×C13×SD1611yescharacteristic
250C2×C4C13×#13711yescharacteristic
251C8—81no—
252C8—82no—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22C13×#44811yescharacteristic
259C22C13×#45411yescharacteristic
260C22C13×B(4,𝔽2)11yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—44no—
265C4—42no—
266C4—44no—
267C4—81no—
268C4—81no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2C13×#159911yescharacteristic
273C2C13×#219611yescharacteristic
274C2C13×#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×#2551C2semidirect
4. C13×#1354C2semidirect
5. C13×#1325C2semidirect
45. #12180C13direct (N × H)
81. C42×C13SD16semidirect
82. #2551C2×C13semidirect
85. #1354C2×C13semidirect
86. #1325C2×C13semidirect
217. C42C13×SD16semidirect
218. C13#12180direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25512
C13×#20392
C13×#16042
C13×#13542
C13×#13252
#1218013