Finite Group Databasebeta

← C13×#7797 #15694136

Subgroups — C13×#7797 #15694136

Order 3328.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2683C211yesmaximal, characteristic
2C13×#2093C211yesmaximal, characteristic
3C13×#2083C212yesmaximal, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—22no—
7C2×C13×#107—22no—
8C2×C13×#107—21no—
9C2×C13×#102—21no—
10C13×#396—22no—
11C13×#395—21no—
12C13×#390C2211yescharacteristic
13C13×#389C2212yes—
14C13×#386—21no—
15C13×#384C2211yescharacteristic
16C13×#340—22no—
17C13×#336C2212yes—
18C13×#336C2211yescharacteristic
19C22×Q8×C13—21no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C22×C8×C13—22no—
23C22×C8×C13—21no—
24C13×C22⋊Q8—44no—
25C13×C22⋊Q8—44no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4D412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C13×#107—42no—
38C13×#107—44no—
39C13×#102—42no—
40C13×#95—21no—
41C13×#95—22no—
42#7797C1311yesmaximal, characteristic, direct product factor, Sylow
43C24×C13—21no—
44C2×Q8×C13—44no—
45C2×Q8×C13—81no—
46C2×D4×C13—21no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13Q1612yes—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—44no—
54C22×C4×C13—41no—
55C22×C4×C13—81no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C2×C8×C13—22no—
59C2×C8×C13—24no—
60C2×C8×C13—42no—
61C2×C8×C13—41no—
62C2×C8×C13—42no—
63C2×C8×C13—41no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—44no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4D814yes—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—81no—
79C42×C13—41no—
80#2683C2×C1311yescharacteristic
81#2093C2×C1311yescharacteristic
82#2083C2×C1312yescomplemented
83#1271C2×C1312yescomplemented
84#1270C2×C1311yescharacteristic
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—41no—
88C23×C13—42no—
89C23×C13—41no—
90C23×C13#12011yescharacteristic
91Q8×C13—84no—
92D4×C13—42no—
93D4×C13—81no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—24no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—84no—
107C2×C4×C13—82no—
108C2×C4×C13—81no—
109C2×C4×C13C2×D812yes—
110C2×C4×C13C2×Q1611yescharacteristic
111C2×C4×C13AGL(1,ℤ/8)12yes—
112C2×C4×C13#13711yescharacteristic
113C8×C13—44no—
114C8×C13—42no—
115C2×C22⋊Q8—22no—
116C2×#107—22no—
117C2×#107—21no—
118C2×#102—21no—
119#396—22no—
120#395—21no—
121#390C22×C1311yescharacteristic
122#389C22×C1312yes—
123#386—21no—
124#384C22×C1311yescharacteristic
125#340—22no—
126#336C22×C1312yes—
127#336C22×C1311yescharacteristic
128C22×C13—42no—
129C22×C13—44no—
130C22×C13—82no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13#44712yes—
134C22×C13#45111yescharacteristic
135C22×C13#45311yescharacteristic
136C22×C13#45612yes—
137C22×C13#45811yescharacteristic
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—44no—
143C4×C13—82no—
144C4×C13—81no—
145C4×C13—161no—
146C22×Q8—21no—
147C22×D4D4×C1311yescharacteristic
148C23×C4—21no—
149C22×C8—22no—
150C22×C8—21no—
151C22⋊Q8—44no—
152C22⋊Q8—44no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D4×C1312yes—
158C2×C4⋊C4D4×C1312yes—
159C2×C4⋊C4D4×C1311yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—21no—
163C2×C42C23×C1311yescharacteristic
164#107—42no—
165#107—44no—
166#102—42no—
167#95—21no—
168#95—22no—
169C2×C13—82no—
170C2×C13#161012yes—
171C2×C13#161411yescharacteristic
172C2×C13#161911yescharacteristic
173C2×C13#164912yes—
174C2×C13#166011yescharacteristic
175C24—21no—
176C2×Q8—44no—
177C2×Q8—81no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4C13×Q1612yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—21no—
185C22×C4—44no—
186C22×C4—41no—
187C22×C4—81no—
188C22×C4C2×D4×C1312yes—
189C22×C4C2×D4×C1311yescharacteristic
190C2×C8—22no—
191C2×C8—24no—
192C2×C8—42no—
193C2×C8—41no—
194C2×C8—42no—
195C2×C8—41no—
196C4⋊C4—22no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—44no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4C13×D814yes—
207C22⋊C4—44no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—81no—
211C42—41no—
212C13#779711yescharacteristic, direct product factor, Sylow
213C23—22no—
214C23—42no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23C13×#12011yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—82no—
236C2×C4—81no—
237C2×C4C2×C13×D812yes—
238C2×C4C2×C13×Q1611yescharacteristic
239C2×C4C13×AGL(1,ℤ/8)12yes—
240C2×C4C13×#13711yescharacteristic
241C8—44no—
242C8—42no—
243C22—42no—
244C22—44no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22C13×#44712yes—
249C22C13×#45111yescharacteristic
250C22C13×#45311yescharacteristic
251C22C13×#45612yes—
252C22C13×#45811yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—44no—
258C4—82no—
259C4—81no—
260C4—161no—
261C2—82no—
262C2C13×#161012yes—
263C2C13×#161411yescharacteristic
264C2C13×#161911yescharacteristic
265C2C13×#164912yes—
266C2C13×#166011yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
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
3. C13×#2083C2semidirect
4. C13×#1271C2semidirect
42. #7797C13direct (N × H)
82. #2083C2×C13semidirect
83. #1271C2×C13semidirect
212. C13#7797direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26832
C13×#20932
C13×#20832
C13×#12712
C13×#12702
#779713