Finite Group Databasebeta

← C13×#10217 #15696556

Subgroups — C13×#10217 #15696556

Order 3328.

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3255C211yesmaximal, characteristic
2C13×#3237C212yesmaximal
3C13×#1995C211yesmaximal, characteristic
4C13×#1506C212yesmaximal
5C13×#1307C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C13×#533C2212yes—
8C13×#501—22no—
9C13×#491—22no—
10C13×#485—24no—
11C13×#477—22no—
12C13×#475—22no—
13C13×#475—22no—
14C13×#470—22no—
15C13×#462—22no—
16C13×#432C2212yes—
17C13×#423C2211yescharacteristic
18C13×#376C2211yescharacteristic
19C13×#339—22no—
20C13×#328—24no—
21C2×C13×Q16—22no—
22C2×C13×M16D412yes—
23C13×C4⋊Q8D412yes—
24C13×C4⋊Q8D412yes—
25C13×C4⋊Q8D412yes—
26C13×#125—22no—
27C13×#125—21no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C13×C22⋊Q8—22no—
31C4×Q8×C13—22no—
32C4×Q8×C13—22no—
33C4×Q8×C13—22no—
34C13×#117—21no—
35C13×#117—22no—
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38C13×#107—24no—
39C13×#106—22no—
40C13×#106—24no—
41C13×C4⋊C8—22no—
42C13×C4⋊C8—22no—
43C13×#103—24no—
44C13×#103—24no—
45C13×#103—24no—
46C13×C22⋊C8D414yes—
47C13×#97—22no—
48C13×#95—22no—
49#10217C1311yesmaximal, characteristic, direct product factor, Sylow
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C22×C4×C13—41no—
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D412yes—
56C13×Q16—82no—
57C13×M16—42no—
58C2×C8×C13—24no—
59C2×C8×C13—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C22⋊C4—41no—
70C13×C22⋊C4—42no—
71C42×C13—22no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13—42no—
75C42×C13C2×D411yescharacteristic
76C42×C13C2×D412yes—
77C42×C13#4111yescharacteristic
78#3255C2×C1311yescharacteristic
79#3237C2×C1312yes—
80#1995C2×C1311yescharacteristic
81#1506C2×C1312yes—
82#1307C2×C1311yescharacteristic
83C23×C13#12711yescharacteristic
84Q8×C13—44no—
85Q8×C13—42no—
86Q8×C13—42no—
87Q8×C13—82no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—82no—
96C2×C4×C13#12012yes—
97C2×C4×C13#12011yescharacteristic
98C2×C4×C13#12112yes—
99C2×C4×C13#12111yescharacteristic
100C8×C13—44no—
101C8×C13—42no—
102#533C22×C1311yescharacteristic
103#533C22×C1312yes—
104#501—22no—
105#491—22no—
106#485—24no—
107#477—22no—
108#475—22no—
109#475—22no—
110#470—22no—
111#462—22no—
112#432C22×C1312yes—
113#423C22×C1311yescharacteristic
114#376C22×C1311yescharacteristic
115#339—22no—
116#328—24no—
117C22×C13—21no—
118C22×C13—22no—
119C22×C13#39211yescharacteristic
120C4×C13—21no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—82no—
124C4×C13—82no—
125C4×C13—82no—
126C4×C13—82no—
127C4×C13#45511yescharacteristic
128C4×C13#45611yescharacteristic
129C2×Q16—22no—
130C2×M16D4×C1312yes—
131C4⋊Q8D4×C1312yes—
132C4⋊Q8D4×C1312yes—
133C4⋊Q8D4×C1312yes—
134#125—22no—
135#125—21no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142#117—21no—
143#117—22no—
144C2×C42—21no—
145C2×C42C23×C1311yescharacteristic
146#107—24no—
147#106—22no—
148#106—24no—
149C4⋊C8—22no—
150C4⋊C8—22no—
151#103—24no—
152#103—24no—
153#103—24no—
154C22⋊C8D4×C1314yes—
155#97—22no—
156#95—22no—
157C2×C13—41no—
158C2×C13#200711yescharacteristic
159C2×C13#200912yes—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C22×C4—41no—
164C22×C4C2×D4×C1311yescharacteristic
165C22×C4C2×D4×C1312yes—
166Q16—82no—
167M16—42no—
168C2×C8—24no—
169C2×C8—22no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C22⋊C4—41no—
180C22⋊C4—42no—
181C42—22no—
182C42—41no—
183C42—41no—
184C42—42no—
185C42C2×D4×C1311yescharacteristic
186C42C2×D4×C1312yes—
187C42C13×#4111yescharacteristic
188C13#1021711yescharacteristic, direct product factor, Sylow
189C23C13×#12711yescharacteristic
190Q8—44no—
191Q8—42no—
192Q8—42no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—82no—
202C2×C4C13×#12012yes—
203C2×C4C13×#12011yescharacteristic
204C2×C4C13×#12112yes—
205C2×C4C13×#12111yescharacteristic
206C8—44no—
207C8—42no—
208C22—21no—
209C22—22no—
210C22C13×#39211yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—82no—
217C4—82no—
218C4C13×#45511yescharacteristic
219C4C13×#45611yescharacteristic
220C2—41no—
221C2C13×#200711yescharacteristic
222C2C13×#200912yes—
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC23×C13#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
49. #10217C13direct (N × H)
188. C13#10217direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32552
C13×#32372
C13×#19952
C13×#15062
C13×#13072
#1021713