Finite Group Databasebeta

← C13×#12250 #15698589

Subgroups — C13×#12250 #15698589

Order 3328.

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

normal subgroups only

This group has 454 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×#2819C211yesmaximal, characteristic
2C13×#2061C211yesmaximal, characteristic, complemented
3C13×#1599C212yesmaximal, complemented
4C13×#1345C212yesmaximal, complemented
5C13×#1324C211yesmaximal, characteristic, complemented
6C13×#544C2211yescharacteristic
7C2×C13×#124—21no—
8C13×#450—22no—
9C13×#428—21no—
10C13×#394—21no—
11C13×#394C2212yes—
12C13×#393—22no—
13C13×#392—22no—
14C13×#382C2211yescharacteristic
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17C13×#328—22no—
18C13×#324C2212yes—
19C22×Q8×C13—21no—
20C22×D4×C13—21no—
21C22×D4×C13—21no—
22C22×D4×C13D412yes—
23C2×C13×SD16—42no—
24C2×C13×M16—21no—
25C13×C4⋊Q8—41no—
26C13×#125—41no—
27C13×#124—42no—
28C13×#124—42no—
29C13×C22⋊Q8—22no—
30C13×#117—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C42×C13D411yescharacteristic
38C13×#107—41no—
39C13×#106—41no—
40C13×#102—42no—
41C13×C22⋊C8—22no—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95D412yes—
45#12250C1311yesmaximal, characteristic, direct product factor, Sylow
46C24×C13—22no—
47C2×Q8×C13—22no—
48C2×Q8×C13—42no—
49C2×Q8×C13—81no—
50C2×Q8×C13—81no—
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—82no—
54C2×D4×C13—81no—
55C2×D4×C13—81no—
56C2×D4×C13—82no—
57C2×D4×C13—81no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D412yes—
63C13×SD16—84no—
64C13×M16—22no—
65C13×M16—41no—
66C2×C8×C13—41no—
67C2×C8×C13—42no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—42no—
74C13×C22⋊C4—44no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—82no—
79C13×C22⋊C4—82no—
80C42×C13—21no—
81C42×C13—41no—
82C42×C13SD1612yescomplemented
83#2819C2×C1311yescharacteristic
84#2061C2×C1311yescharacteristic, complemented
85#1599C2×C1312yescomplemented
86#1345C2×C1312yescomplemented
87#1324C2×C1311yescharacteristic, complemented
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—84no—
97Q8×C13—82no—
98D4×C13—44no—
99D4×C13—84no—
100D4×C13—82no—
101D4×C13—84no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
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—41no—
116C2×C4×C13C2×SD1611yescharacteristic
117C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
118C8×C13—42no—
119C8×C13—82no—
120#544C22×C1311yescharacteristic
121C2×#124—21no—
122#450—22no—
123#428—21no—
124#394—21no—
125#394C22×C1312yes—
126#393—22no—
127#392—22no—
128#382C22×C1311yescharacteristic
129#343C22×C1311yescharacteristic
130#339—21no—
131#328—22no—
132#324C22×C1312yes—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—82no—
136C22×C13—82no—
137C22×C13—82no—
138C22×C13—82no—
139C22×C13—82no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13#45011yescharacteristic
143C22×C13#45611yescharacteristic
144C22×C13B(4,𝔽2)11yescharacteristic
145C4×C13—21no—
146C4×C13—21no—
147C4×C13—42no—
148C4×C13—42no—
149C4×C13—82no—
150C4×C13—81no—
151C4×C13—81no—
152C4×C13—81no—
153C22×Q8—21no—
154C22×D4—21no—
155C22×D4—21no—
156C22×D4D4×C1312yes—
157C2×SD16—42no—
158C2×M16—21no—
159C4⋊Q8—41no—
160#125—41no—
161#124—42no—
162#124—42no—
163C22⋊Q8—22no—
164#117—21no—
165C2×C4⋊C4D4×C1311yescharacteristic
166C2×C4⋊C4C23×C1311yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C42D4×C1311yescharacteristic
172#107—41no—
173#106—41no—
174#102—42no—
175C22⋊C8—22no—
176#95—21no—
177#95—22no—
178#95D4×C1312yes—
179C2×C13—21no—
180C2×C13—21no—
181C2×C13—162no—
182C2×C13#160411yescharacteristic
183C2×C13#219911yescharacteristic
184C2×C13#220211yescharacteristic
185C24—22no—
186C2×Q8—22no—
187C2×Q8—42no—
188C2×Q8—81no—
189C2×Q8—81no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—82no—
193C2×D4—81no—
194C2×D4—81no—
195C2×D4—82no—
196C2×D4—81no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4C2×D4×C1311yescharacteristic
201C22×C4C2×D4×C1312yes—
202SD16—84no—
203M16—22no—
204M16—41no—
205C2×C8—41no—
206C2×C8—42no—
207C4⋊C4—22no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C22⋊C4—44no—
214C22⋊C4—41no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—82no—
218C22⋊C4—82no—
219C42—21no—
220C42—41no—
221C42C13×SD1612yescomplemented
222C13#1225011yescharacteristic, direct product factor, Sylow
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23C13×#12011yescharacteristic
231Q8—82no—
232Q8—84no—
233D4—44no—
234D4—82no—
235D4—84no—
236D4—84no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4C2×C13×SD1611yescharacteristic
252C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
253C8—42no—
254C8—82no—
255C22—21no—
256C22—21no—
257C22—82no—
258C22—82no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22C13×#45011yescharacteristic
265C22C13×#45611yescharacteristic
266C22C13×B(4,𝔽2)11yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—82no—
272C4—81no—
273C4—81no—
274C4—81no—
275C2—21no—
276C2—21no—
277C2—162no—
278C2C13×#160411yescharacteristic
279C2C13×#219911yescharacteristic
280C2C13×#220211yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC13×#2819C2
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
2. C13×#2061C2semidirect
3. C13×#1599C2semidirect
4. C13×#1345C2semidirect
5. C13×#1324C2semidirect
45. #12250C13direct (N × H)
82. C42×C13SD16semidirect
84. #2061C2×C13semidirect
85. #1599C2×C13semidirect
86. #1345C2×C13semidirect
87. #1324C2×C13semidirect
221. C42C13×SD16semidirect
222. C13#12250direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28192
C13×#20612
C13×#15992
C13×#13452
C13×#13242
#1225013