Finite Group Databasebeta

← C13×#10216 #15696555

Subgroups — C13×#10216 #15696555

Order 3328.

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

normal subgroups only

This group has 468 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, complemented
2C13×#3235C212yesmaximal
3C13×#1963C211yesmaximal, characteristic
4C13×#1506C212yesmaximal, complemented
5C13×#1307C211yesmaximal, characteristic, complemented
6C13×#533C2212yes—
7C13×#532C2211yescharacteristic
8C13×#501—22no—
9C13×#490—22no—
10C13×#482—24no—
11C13×#476—22no—
12C13×#475—22no—
13C13×#474—22no—
14C13×#470—22no—
15C13×#462—22no—
16C13×#432C2212yes—
17C13×#423C2211yescharacteristic
18C2×C13×#104—22no—
19C13×#376C2211yescharacteristic
20C13×#328—24no—
21C2×C13×#41—21no—
22C2×C13×Q16—22no—
23C2×C13×M16D412yes—
24C13×C4⋊Q8D412yes—
25C13×C4⋊Q8D412yes—
26C13×C4⋊Q8D411yescharacteristic
27C13×#127D411yescharacteristic
28C13×#125—22no—
29C13×#124—21no—
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—22no—
32C13×#121—22no—
33C4×Q8×C13—22no—
34C4×Q8×C13—22no—
35C4×D4×C13—22no—
36C13×#117—22no—
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C13×#107—24no—
40C13×#106—22no—
41C13×#106—24no—
42C13×C4⋊C8—22no—
43C13×C4⋊C8—22no—
44C13×#104—44no—
45C13×#103—24no—
46C13×#102—24no—
47C13×#102—24no—
48C13×C22⋊C8D414yes—
49C13×#97—22no—
50C13×#95—22no—
51#10216C1311yesmaximal, characteristic, direct product factor, Sylow
52C13×#41—42no—
53C13×#41—42no—
54C2×Q8×C13—22no—
55C2×Q8×C13—21no—
56C2×Q8×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13—21no—
59C2×D4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D412yes—
64C13×Q16—82no—
65C13×M16—42no—
66C2×C8×C13—24no—
67C2×C8×C13—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C22⋊C4—42no—
76C13×C22⋊C4—42no—
77C42×C13—22no—
78C42×C13—41no—
79C42×C13—42no—
80C42×C13C2×D411yescharacteristic
81C42×C13C2×D412yes—
82C42×C13#4111yescharacteristic
83#3255C2×C1311yescharacteristic, complemented
84#3235C2×C1312yes—
85#1963C2×C1311yescharacteristic
86#1506C2×C1312yescomplemented
87#1307C2×C1311yescharacteristic, complemented
88C23×C13—41no—
89C23×C13#12711yescharacteristic
90Q8×C13—42no—
91Q8×C13—42no—
92Q8×C13—42no—
93Q8×C13—82no—
94D4×C13—44no—
95D4×C13—42no—
96D4×C13—82no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—82no—
105C2×C4×C13—81no—
106C2×C4×C13—81no—
107C2×C4×C13#12012yes—
108C2×C4×C13#12011yescharacteristic
109C2×C4×C13#12112yes—
110C2×C4×C13#12111yescharacteristic
111C8×C13—44no—
112C8×C13—42no—
113#533C22×C1312yes—
114#532C22×C1311yescharacteristic
115#501—22no—
116#490—22no—
117#482—24no—
118#476—22no—
119#475—22no—
120#474—22no—
121#470—22no—
122#462—22no—
123#432C22×C1312yes—
124#423C22×C1311yescharacteristic
125C2×#104—22no—
126#376C22×C1311yescharacteristic
127#328—24no—
128C22×C13—21no—
129C22×C13—22no—
130C22×C13—81no—
131C22×C13—82no—
132C22×C13#39211yescharacteristic
133C4×C13—21no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—82no—
137C4×C13—81no—
138C4×C13—82no—
139C4×C13—82no—
140C4×C13#45311yescharacteristic
141C4×C13#45411yescharacteristic
142C2×#41—21no—
143C2×Q16—22no—
144C2×M16D4×C1312yes—
145C4⋊Q8D4×C1311yescharacteristic
146C4⋊Q8D4×C1312yes—
147C4⋊Q8D4×C1312yes—
148#127D4×C1311yescharacteristic
149#125—22no—
150#124—21no—
151C22⋊Q8—22no—
152C22⋊Q8—22no—
153#121—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×D4—22no—
157#117—22no—
158C2×C42—21no—
159C2×C42C23×C1311yescharacteristic
160#107—24no—
161#106—22no—
162#106—24no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165#104—44no—
166#103—24no—
167#102—24no—
168#102—24no—
169C22⋊C8D4×C1314yes—
170#97—22no—
171#95—22no—
172C2×C13—41no—
173C2×C13—161no—
174C2×C13#200611yescharacteristic
175C2×C13#200912yes—
176#41—42no—
177#41—42no—
178C2×Q8—22no—
179C2×Q8—21no—
180C2×Q8—22no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4C2×D4×C1311yescharacteristic
187C22×C4C2×D4×C1312yes—
188Q16—82no—
189M16—42no—
190C2×C8—24no—
191C2×C8—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C42—22no—
202C42—41no—
203C42—42no—
204C42C2×D4×C1311yescharacteristic
205C42C2×D4×C1312yes—
206C42C13×#4111yescharacteristic
207C13#1021611yescharacteristic, direct product factor, Sylow
208C23—41no—
209C23C13×#12711yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—42no—
213Q8—82no—
214D4—44no—
215D4—42no—
216D4—82no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—82no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4C13×#12012yes—
228C2×C4C13×#12011yescharacteristic
229C2×C4C13×#12112yes—
230C2×C4C13×#12111yescharacteristic
231C8—44no—
232C8—42no—
233C22—21no—
234C22—22no—
235C22—81no—
236C22—82no—
237C22C13×#39211yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—82no—
242C4—81no—
243C4—82no—
244C4—82no—
245C4C13×#45311yescharacteristic
246C4C13×#45411yescharacteristic
247C2—41no—
248C2—161no—
249C2C13×#200611yescharacteristic
250C2C13×#200912yes—
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#532C22
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
1. C13×#3255C2semidirect
4. C13×#1506C2semidirect
5. C13×#1307C2semidirect
51. #10216C13direct (N × H)
83. #3255C2×C13semidirect
86. #1506C2×C13semidirect
87. #1307C2×C13semidirect
207. C13#10216direct (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×#32352
C13×#19632
C13×#15062
C13×#13072
#1021613