Finite Group Databasebeta

← C13×#12365 #15698704

Subgroups — C13×#12365 #15698704

Order 3328.

346 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3291C211yesmaximal, characteristic
2C13×#2230C212yesmaximal, complemented
3C13×#1708C211yesmaximal, characteristic, complemented
4C13×#1359C211yesmaximal, characteristic, complemented
5C13×#1335C212yesmaximal, complemented
6C13×#577—22no—
7C13×#498C2211yescharacteristic, complemented
8C13×#492C2211yescharacteristic
9C13×#487—21no—
10C13×#486—21no—
11C13×#471—22no—
12C13×#456—21no—
13C13×#453—21no—
14C13×#443C2212yes—
15C13×#365—22no—
16C13×#364C2212yescomplemented
17C13×#360—22no—
18C82×C13C2211yescharacteristic, complemented
19C13×2−1+4—21no—
20C13×H(5,𝔽2)—21no—
21C13×#137—22no—
22C13×#137—42no—
23C13×AGL(1,ℤ/8)—22no—
24C13×AGL(1,ℤ/8)—42no—
25C13×#135—42no—
26C13×#135D412yes—
27C2×C13×SD16—22no—
28C2×C13×SD16—42no—
29C13×#131—22no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8D411yescharacteristic
32C13×#127D411yescharacteristic
33C13×M32—22no—
34C13×#108D412yes—
35C13×#106—22no—
36C13×#104—22no—
37C13×#103—42no—
38C13×#102—42no—
39C13×#101—21no—
40C13×#100—21no—
41C4×C8×C13—21no—
42C4×C8×C13C2311yescharacteristic
43#12365C1311yesmaximal, characteristic, direct product factor, Sylow
44C13×#41—22no—
45C13×#41—42no—
46C13×#41—42no—
47C13×#41—81no—
48C2×Q8×C13—21no—
49C2×Q8×C13—41no—
50C2×Q8×C13—42no—
51C2×D4×C13—21no—
52C2×D4×C13—41no—
53C2×D4×C13—42no—
54C2×D4×C13—81no—
55C13×Q16—42no—
56C13×Q16SD1612yes—
57C13×SD16—22no—
58C13×SD16—42no—
59C13×SD16—42no—
60C13×SD16—42no—
61C13×SD16—42no—
62C13×D8—42no—
63C13×D8SD1612yes—
64C13×M16—22no—
65C13×M16—42no—
66C2×C8×C13—22no—
67C2×C8×C13—42no—
68C2×C8×C13C2×D412yes—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C42×C13C2×D411yescharacteristic
73C13×C16—42no—
74#3291C2×C1311yescharacteristic
75#2230C2×C1312yescomplemented
76#1708C2×C1311yescharacteristic, complemented
77#1359C2×C1311yescharacteristic, complemented
78#1335C2×C1312yescomplemented
79C23×C13—41no—
80C23×C13—81no—
81Q8×C13—22no—
82Q8×C13—42no—
83Q8×C13—82no—
84Q8×C13—81no—
85D4×C13—22no—
86D4×C13—42no—
87D4×C13—42no—
88D4×C13—82no—
89D4×C13—82no—
90D4×C13—81no—
91C2×C4×C13—21no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—81no—
95C2×C4×C13—82no—
96C2×C4×C13—81no—
97C2×C4×C13#12011yescharacteristic
98C8×C13—42no—
99C8×C13—42no—
100C8×C13C2×SD1612yes—
101C8×C13AGL(1,ℤ/8)12yes—
102#577—22no—
103#498C22×C1311yescharacteristic, complemented
104#492C22×C1311yescharacteristic
105#487—21no—
106#486—21no—
107#471—22no—
108#456—21no—
109#453—21no—
110#443C22×C1312yes—
111#365—22no—
112#364C22×C1312yescomplemented
113#360—22no—
114C82C22×C1311yescharacteristic, complemented
115C22×C13—42no—
116C22×C13—81no—
117C22×C13—161no—
118C22×C13—321no—
119C22×C13#45311yescharacteristic
120C4×C13—22no—
121C4×C13—42no—
122C4×C13—81no—
123C4×C13—161no—
124C4×C13#45012yes—
1252−1+4—21no—
126H(5,𝔽2)—21no—
127#137—22no—
128#137—42no—
129AGL(1,ℤ/8)—22no—
130AGL(1,ℤ/8)—42no—
131#135—42no—
132#135D4×C1312yes—
133C2×SD16—22no—
134C2×SD16—42no—
135#131—22no—
136C4⋊Q8—21no—
137C4⋊Q8D4×C1311yescharacteristic
138#127D4×C1311yescharacteristic
139M32—22no—
140#108D4×C1312yes—
141#106—22no—
142#104—22no—
143#103—42no—
144#102—42no—
145#101—21no—
146#100—21no—
147C4×C8—21no—
148C4×C8C23×C1311yescharacteristic
149C2×C13—21no—
150C2×C13—82no—
151C2×C13—161no—
152C2×C13#162911yescharacteristic
153#41—22no—
154#41—42no—
155#41—42no—
156#41—81no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—42no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—42no—
163C2×D4—81no—
164Q16—42no—
165Q16C13×SD1612yes—
166SD16—22no—
167SD16—42no—
168SD16—42no—
169SD16—42no—
170SD16—42no—
171D8—42no—
172D8C13×SD1612yes—
173M16—22no—
174M16—42no—
175C2×C8—22no—
176C2×C8—42no—
177C2×C8C2×D4×C1312yes—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C42C2×D4×C1311yescharacteristic
182C16—42no—
183C13#1236511yescharacteristic, direct product factor, Sylow
184C23—41no—
185C23—81no—
186Q8—22no—
187Q8—42no—
188Q8—82no—
189Q8—81no—
190D4—22no—
191D4—42no—
192D4—42no—
193D4—82no—
194D4—82no—
195D4—81no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—81no—
200C2×C4—82no—
201C2×C4—81no—
202C2×C4C13×#12011yescharacteristic
203C8—42no—
204C8—42no—
205C8C2×C13×SD1612yes—
206C8C13×AGL(1,ℤ/8)12yes—
207C22—42no—
208C22—81no—
209C22—161no—
210C22—321no—
211C22C13×#45311yescharacteristic
212C4—22no—
213C4—42no—
214C4—81no—
215C4—161no—
216C4C13×#45012yes—
217C2—21no—
218C2—82no—
219C2—161no—
220C2C13×#162911yescharacteristic
subgroupG/H
center, socleC2×C13#1629
commutator, Frattini, cosocleC4×C8C23×C13
prime radicalC13×#3291C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2230C2semidirect
3. C13×#1708C2semidirect
4. C13×#1359C2semidirect
5. C13×#1335C2semidirect
7. C13×#498C22semidirect
16. C13×#364C22semidirect
18. C82×C13C22semidirect
43. #12365C13direct (N × H)
75. #2230C2×C13semidirect
76. #1708C2×C13semidirect
77. #1359C2×C13semidirect
78. #1335C2×C13semidirect
103. #498C22×C13semidirect
112. #364C22×C13semidirect
114. C82C22×C13semidirect
183. C13#12365direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32912
C13×#22302
C13×#17082
C13×#13592
C13×#13352
#1236513