Finite Group Databasebeta

← C13×#12157 #15698496

Subgroups — C13×#12157 #15698496

Order 3328.

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

normal subgroups only

This group has 372 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×#2822C211yesmaximal, characteristic, complemented
2C13×#2040C211yesmaximal, characteristic
3C13×#1610C212yesmaximal
4C13×#1346C212yesmaximal, complemented
5C13×#1324C211yesmaximal, characteristic, complemented
6C13×#537C2211yescharacteristic
7C2×C13×#125—21no—
8C13×#480—22no—
9C2×C13×#104—21no—
10C13×#417—21no—
11C13×#400—22no—
12C13×#398—21no—
13C13×#398—22no—
14C13×#398C2212yes—
15C13×#382C2211yescharacteristic
16C13×#343C2211yescharacteristic
17C13×#327—22no—
18C13×#324C2212yes—
19C2×C13×#41—21no—
20C2×C13×M16—21no—
21C13×#125—42no—
22C13×#125—42no—
23C13×C22⋊Q8—41no—
24C13×#121—22no—
25C13×#121—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D412yes—
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C42×C13D411yescharacteristic
35C13×#107—42no—
36C13×#104—42no—
37C13×#103—41no—
38C13×#102—41no—
39C13×#102—42no—
40C13×C22⋊C8—22no—
41C13×#95—22no—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95D412yes—
46#12157C1311yesmaximal, characteristic, direct product factor, Sylow
47C13×#41—41no—
48C13×#41—41no—
49C13×#41—41no—
50C13×#41—41no—
51C2×Q8×C13—21no—
52C2×D4×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—41no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C13×M16—41no—
63C13×M16—41no—
64C2×C8×C13—42no—
65C2×C8×C13—41no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—44no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—81no—
76C13×C22⋊C4—42no—
77C42×C13—21no—
78C42×C13D812yes—
79#2822C2×C1311yescharacteristic, complemented
80#2040C2×C1311yescharacteristic
81#1610C2×C1312yes—
82#1346C2×C1312yescomplemented
83#1324C2×C1311yescharacteristic, complemented
84C23×C13—41no—
85C23×C13#12011yescharacteristic
86Q8×C13—41no—
87Q8×C13—41no—
88D4×C13—41no—
89D4×C13—41no—
90D4×C13—82no—
91D4×C13—81no—
92D4×C13—81no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—81no—
110C2×C4×C13—81no—
111C2×C4×C13C2×D811yescharacteristic
112C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
113C8×C13—81no—
114C8×C13—82no—
115#537C22×C1311yescharacteristic
116C2×#125—21no—
117#480—22no—
118C2×#104—21no—
119#417—21no—
120#400—22no—
121#398—21no—
122#398—22no—
123#398C22×C1312yes—
124#382C22×C1311yescharacteristic
125#343C22×C1311yescharacteristic
126#327—22no—
127#324C22×C1312yes—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—81no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13#44711yescharacteristic
134C22×C13#45411yescharacteristic
135C22×C13B(4,𝔽2)11yescharacteristic
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—82no—
141C4×C13—82no—
142C4×C13—81no—
143C4×C13—81no—
144C2×#41—21no—
145C2×M16—21no—
146#125—42no—
147#125—42no—
148C22⋊Q8—41no—
149#121—22no—
150#121—41no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4D4×C1311yescharacteristic
157C2×C4⋊C4D4×C1312yes—
158C2×C4⋊C4C23×C1311yescharacteristic
159C2×C42D4×C1311yescharacteristic
160#107—42no—
161#104—42no—
162#103—41no—
163#102—41no—
164#102—42no—
165C22⋊C8—22no—
166#95—22no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95D4×C1312yes—
171C2×C13—21no—
172C2×C13—21no—
173C2×C13—161no—
174C2×C13#159811yescharacteristic
175C2×C13#220111yescharacteristic
176C2×C13#220311yescharacteristic
177#41—41no—
178#41—41no—
179#41—41no—
180#41—41no—
181C2×Q8—21no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—41no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—41no—
190C22×C4C2×D4×C1311yescharacteristic
191C22×C4C2×D4×C1312yes—
192M16—41no—
193M16—41no—
194C2×C8—42no—
195C2×C8—41no—
196C4⋊C4—22no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—81no—
206C22⋊C4—42no—
207C42—21no—
208C42C13×D812yes—
209C13#1215711yescharacteristic, direct product factor, Sylow
210C23—41no—
211C23C13×#12011yescharacteristic
212Q8—41no—
213Q8—41no—
214D4—41no—
215D4—41no—
216D4—82no—
217D4—81no—
218D4—81no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4C2×C13×D811yescharacteristic
238C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
239C8—81no—
240C8—82no—
241C22—21no—
242C22—21no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22C13×#44711yescharacteristic
247C22C13×#45411yescharacteristic
248C22C13×B(4,𝔽2)11yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—161no—
260C2C13×#159811yescharacteristic
261C2C13×#220111yescharacteristic
262C2C13×#220311yescharacteristic
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×#2822C2semidirect
4. C13×#1346C2semidirect
5. C13×#1324C2semidirect
46. #12157C13direct (N × H)
79. #2822C2×C13semidirect
82. #1346C2×C13semidirect
83. #1324C2×C13semidirect
209. C13#12157direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28222
C13×#20402
C13×#16102
C13×#13462
C13×#13242
#1215713