Finite Group Databasebeta

← C13×#10584 #15696923

Subgroups — C13×#10584 #15696923

Order 3328.

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

normal subgroups only

This group has 374 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×#2844C211yesmaximal, characteristic
2C13×#1847C211yesmaximal, characteristic
3C13×#1836C212yesmaximal
4C13×#1295C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×C13×#107—21no—
7C2×C13×#106—21no—
8C2×C13×#97C2212yes—
9C2×C13×#97C2211yescharacteristic
10C13×#400—22no—
11C13×#400—21no—
12C13×#395—22no—
13C13×#395—21no—
14C13×#384C2211yescharacteristic
15C13×#382C2212yes—
16C13×#382C2211yescharacteristic
17C13×#340—22no—
18C13×#340—22no—
19C22×Q8×C13—21no—
20C22×C8×C13—21no—
21C22×C8×C13—22no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13C2311yescharacteristic
31C13×#107—42no—
32C13×#106—42no—
33C13×#97—21no—
34C13×#97—22no—
35C13×#97Q812yescomplemented
36C13×#97Q814yescomplemented
37C13×#95—22no—
38C13×#95—21no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95—22no—
43#10584C1311yesmaximal, characteristic, direct product factor, Sylow
44C2×Q8×C13—81no—
45C2×Q8×C13—82no—
46C22×C4×C13—21no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—41no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D412yes—
53C2×C8×C13—22no—
54C2×C8×C13—22no—
55C2×C8×C13—22no—
56C2×C8×C13—24no—
57C2×C8×C13—42no—
58C2×C8×C13—42no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—44no—
66C13×C4⋊C4—81no—
67C13×C4⋊C4—82no—
68C42×C13C2×Q811yescharacteristic
69C42×C13C2×Q812yes—
70C42×C13#4111yescharacteristic
71#2844C2×C1311yescharacteristic
72#1847C2×C1311yescharacteristic
73#1836C2×C1312yes—
74#1295C2×C1312yes—
75#1295C2×C1311yescharacteristic
76C23×C13#12011yescharacteristic
77Q8×C13—84no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—81no—
93C2×C4×C13—82no—
94C2×C4×C13C22⋊Q811yescharacteristic
95C2×C4×C13C22⋊Q812yes—
96C2×C4×C13C4⋊Q811yescharacteristic
97C2×C4×C13C4⋊Q812yes—
98C8×C13—24no—
99C8×C13—44no—
100C2×#107—21no—
101C2×#106—21no—
102C2×#97C22×C1312yes—
103C2×#97C22×C1311yescharacteristic
104#400—22no—
105#400—21no—
106#395—22no—
107#395—21no—
108#384C22×C1311yescharacteristic
109#382C22×C1312yes—
110#382C22×C1311yescharacteristic
111#340—22no—
112#340—22no—
113C22×C13#39511yescharacteristic
114C22×C13#45311yescharacteristic
115C22×C13#45412yes—
116C22×C13#45512yes—
117C22×C13#45611yescharacteristic
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—81no—
123C4×C13—81no—
124C4×C13—82no—
125C4×C13—82no—
126C4×C13—161no—
127C22×Q8—21no—
128C22×C8—21no—
129C22×C8—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4D4×C1312yes—
135C2×C4⋊C4D4×C1312yes—
136C2×C4⋊C4D4×C1311yescharacteristic
137C2×C4⋊C4D4×C1311yescharacteristic
138C2×C42C23×C1311yescharacteristic
139#107—42no—
140#106—42no—
141#97—21no—
142#97—22no—
143#97Q8×C1312yescomplemented
144#97Q8×C1314yescomplemented
145#95—22no—
146#95—21no—
147#95—21no—
148#95—22no—
149#95—22no—
150#95—22no—
151C2×C13#165711yescharacteristic
152C2×C13#165911yescharacteristic
153C2×C13#166412yes—
154C2×C13#206011yescharacteristic
155C2×C13#206112yes—
156C2×Q8—81no—
157C2×Q8—82no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4—41no—
163C22×C4C2×D4×C1311yescharacteristic
164C22×C4C2×D4×C1312yes—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—24no—
169C2×C8—42no—
170C2×C8—42no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—44no—
178C4⋊C4—81no—
179C4⋊C4—82no—
180C42C2×Q8×C1311yescharacteristic
181C42C2×Q8×C1312yes—
182C42C13×#4111yescharacteristic
183C13#1058411yescharacteristic, direct product factor, Sylow
184C23C13×#12011yescharacteristic
185Q8—84no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—81no—
201C2×C4—82no—
202C2×C4C13×C22⋊Q811yescharacteristic
203C2×C4C13×C22⋊Q812yes—
204C2×C4C13×C4⋊Q811yescharacteristic
205C2×C4C13×C4⋊Q812yes—
206C8—24no—
207C8—44no—
208C22C13×#39511yescharacteristic
209C22C13×#45311yescharacteristic
210C22C13×#45412yes—
211C22C13×#45512yes—
212C22C13×#45611yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—82no—
220C4—82no—
221C4—161no—
222C2C13×#165711yescharacteristic
223C2C13×#165911yescharacteristic
224C2C13×#166412yes—
225C2C13×#206011yescharacteristic
226C2C13×#206112yes—
subgroupG/H
center, socle, prime radicalC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
35. C13×#97Q8semidirect
36. C13×#97Q8semidirect
43. #10584C13direct (N × H)
143. #97Q8×C13semidirect
144. #97Q8×C13semidirect
183. C13#10584direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28442
C13×#18472
C13×#18362
C13×#12952
#1058413