Finite Group Databasebeta

← C13×#13368 #15699707

Subgroups — C13×#13368 #15699707

Order 3328.

370 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3162C211yesmaximal, characteristic
2C13×#2141C212yesmaximal
3C13×#1971C211yesmaximal, characteristic
4C13×#1386C212yesmaximal
5C13×#1377C211yesmaximal, characteristic
6C22×C13×Q16C2211yescharacteristic
7C13×#533—21no—
8C2×C13×M32C2212yes—
9C13×#501—24no—
10C13×#427—21no—
11C13×#427C2212yes—
12C2×C13×#106C2211yescharacteristic
13C2×C13×#103—21no—
14C2×C13×#97C2211yescharacteristic
15C13×#391—21no—
16C13×#358—24no—
17C22×Q8×C13—21no—
18C2×C13×Q16—22no—
19C2×C13×Q16—22no—
20C2×C13×Q16—21no—
21C2×C13×Q16Q812yescomplemented
22C22×C8×C13D411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C13×C4⋊Q8—22no—
25C13×#125—22no—
26C13×C22⋊Q8—42no—
27C4×Q8×C13—42no—
28C13×#117—22no—
29C2×C13×C4⋊C4—21no—
30C2×C42×C13D411yescharacteristic
31C13×M32—22no—
32C13×M32—22no—
33C2×C13×C16—22no—
34C13×#107—22no—
35C13×#107D414yes—
36C13×#106—22no—
37C13×#106—22no—
38C13×#106—22no—
39C13×#103—42no—
40C13×#97—22no—
41C13×#95—42no—
42#13368C1311yesmaximal, characteristic, direct product factor, Sylow
43C2×Q8×C13—22no—
44C2×Q8×C13—42no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13—41no—
52C22×C4×C13D812yes—
53C22×C4×C13C2×D411yescharacteristic
54C13×Q16—24no—
55C13×Q16—42no—
56C2×C8×C13—21no—
57C2×C8×C13—21no—
58C2×C8×C13SD1612yes—
59C2×C8×C13C2×D412yes—
60C2×C8×C13C2×Q811yescharacteristic
61C2×C8×C13#4112yes—
62C2×C8×C13#4111yescharacteristic
63C13×C4⋊C4—24no—
64C13×C4⋊C4—44no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C22⋊C4—42no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—42no—
72C13×C16—42no—
73#3162C2×C1311yescharacteristic
74#2141C2×C1312yes—
75#1971C2×C1311yescharacteristic
76#1386C2×C1312yes—
77#1377C2×C1311yescharacteristic
78C23×C13C2×D811yescharacteristic
79Q8×C13—42no—
80Q8×C13—42no—
81Q8×C13—84no—
82Q8×C13—81no—
83Q8×C13—81no—
84C2×C4×C13—22no—
85C2×C4×C13—42no—
86C2×C4×C13—44no—
87C2×C4×C13—42no—
88C2×C4×C13—81no—
89C2×C4×C13—81no—
90C2×C4×C13—82no—
91C2×C4×C13—81no—
92C2×C4×C13#12011yescharacteristic
93C2×C4×C13C22⋊Q811yescharacteristic
94C2×C4×C13#12411yescharacteristic
95C2×C4×C13C2×SD1611yescharacteristic
96C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C13#13711yescharacteristic
98C8×C13—22no—
99C8×C13C22⋊Q812yes—
100C8×C13#12412yes—
101C22×Q16C22×C1311yescharacteristic
102#533—21no—
103C2×M32C22×C1312yes—
104#501—24no—
105#427—21no—
106#427C22×C1312yes—
107C2×#106C22×C1311yescharacteristic
108C2×#103—21no—
109C2×#97C22×C1311yescharacteristic
110#391—21no—
111#358—24no—
112C22×C13—22no—
113C22×C13#44711yescharacteristic
114C22×C13#47411yescharacteristic
115C22×C13#48611yescharacteristic
116C4×C13—42no—
117C4×C13—84no—
118C4×C13—82no—
119C4×C13—161no—
120C4×C13#39311yescharacteristic
121C4×C13#44811yescharacteristic
122C4×C13#47611yescharacteristic
123C4×C13#48911yescharacteristic
124C22×Q8—21no—
125C2×Q16—22no—
126C2×Q16—22no—
127C2×Q16—21no—
128C2×Q16Q8×C1312yescomplemented
129C22×C8D4×C1311yescharacteristic
130C22×C8C23×C1311yescharacteristic
131C4⋊Q8—22no—
132#125—22no—
133C22⋊Q8—42no—
134C4×Q8—42no—
135#117—22no—
136C2×C4⋊C4—21no—
137C2×C42D4×C1311yescharacteristic
138M32—22no—
139M32—22no—
140C2×C16—22no—
141#107—22no—
142#107D4×C1314yes—
143#106—22no—
144#106—22no—
145#106—22no—
146#103—42no—
147#97—22no—
148#95—42no—
149C2×C13—21no—
150C2×C13—21no—
151C2×C13#202311yescharacteristic
152C2×C13#219112yes—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4C13×D812yes—
163C22×C4C2×D4×C1311yescharacteristic
164Q16—24no—
165Q16—42no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8C13×SD1612yes—
169C2×C8C2×D4×C1312yes—
170C2×C8C2×Q8×C1311yescharacteristic
171C2×C8C13×#4112yes—
172C2×C8C13×#4111yescharacteristic
173C4⋊C4—24no—
174C4⋊C4—44no—
175C4⋊C4—42no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C22⋊C4—42no—
179C42—21no—
180C42—21no—
181C42—42no—
182C16—42no—
183C13#1336811yescharacteristic, direct product factor, Sylow
184C23C2×C13×D811yescharacteristic
185Q8—42no—
186Q8—42no—
187Q8—84no—
188Q8—81no—
189Q8—81no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—44no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4—81no—
198C2×C4C13×#12011yescharacteristic
199C2×C4C13×C22⋊Q811yescharacteristic
200C2×C4C13×#12411yescharacteristic
201C2×C4C2×C13×SD1611yescharacteristic
202C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
203C2×C4C13×#13711yescharacteristic
204C8—22no—
205C8C13×C22⋊Q812yes—
206C8C13×#12412yes—
207C22—22no—
208C22C13×#44711yescharacteristic
209C22C13×#47411yescharacteristic
210C22C13×#48611yescharacteristic
211C4—42no—
212C4—82no—
213C4—84no—
214C4—161no—
215C4C13×#39311yescharacteristic
216C4C13×#44811yescharacteristic
217C4C13×#47611yescharacteristic
218C4C13×#48911yescharacteristic
219C2—21no—
220C2—21no—
221C2C13×#202311yescharacteristic
222C2C13×#219112yes—
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC23×C13C2×D8
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G

Complements

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

NH ≅ G/Ntype
21. C2×C13×Q16Q8semidirect
42. #13368C13direct (N × H)
128. C2×Q16Q8×C13semidirect
183. C13#13368direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31622
C13×#21412
C13×#19712
C13×#13862
C13×#13772
#1336813