Finite Group Databasebeta

← C13×#12215 #15698554

Subgroups — C13×#12215 #15698554

Order 3328.

400 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2607C211yesmaximal, characteristic
2C13×#2030C211yesmaximal, characteristic
3C13×#1602C212yesmaximal
4C13×#1351C212yesmaximal
5C13×#1317C211yesmaximal, characteristic
6C13×#543C2211yescharacteristic
7C13×#451—22no—
8C13×#399—21no—
9C13×#393C2212yes—
10C13×#391—22no—
11C13×#387—22no—
12C13×#381—21no—
13C13×#381C2211yescharacteristic
14C4×C13×C22⋊C4—21no—
15C13×#342—21no—
16C13×#342C2211yescharacteristic
17C13×#328—22no—
18C13×#323C2212yes—
19C22×Q8×C13D412yes—
20C23×C4×C13D411yescharacteristic
21C2×C13×Q16—42no—
22C13×C22⋊Q8—22no—
23C13×C22⋊Q8—42no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C22⋊C4—22no—
27C2×C13×C22⋊C4—21no—
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2311yescharacteristic
31C2×C42×C13—21no—
32C2×C42×C13—21no—
33C13×#103—42no—
34C13×C22⋊C8—22no—
35C13×#95—22no—
36C13×#95—21no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—42no—
40C13×#95D412yes—
41#12215C1311yesmaximal, characteristic, direct product factor, Sylow
42C24×C13C2×D411yescharacteristic
43C2×Q8×C13—22no—
44C2×Q8×C13—44no—
45C2×Q8×C13—42no—
46C22×C4×C13—21no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13Q1612yescomplemented
56C22×C4×C13C2×D412yes—
57C13×Q16—84no—
58C2×C8×C13—42no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—44no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—81no—
63C13×C22⋊C4—41no—
64C13×C22⋊C4—44no—
65C13×C22⋊C4—41no—
66C13×C22⋊C4—41no—
67C13×C22⋊C4—41no—
68C13×C22⋊C4—41no—
69C13×C22⋊C4—41no—
70C42×C13—81no—
71C42×C13—81no—
72#2607C2×C1311yescharacteristic
73#2030C2×C1311yescharacteristic
74#1602C2×C1312yes—
75#1351C2×C1312yes—
76#1317C2×C1311yescharacteristic
77C23×C13—21no—
78C23×C13—21no—
79C23×C13—42no—
80C23×C13#12011yescharacteristic
81C23×C13C2×Q1611yescharacteristic
82C23×C13#13711yescharacteristic
83Q8×C13—44no—
84Q8×C13—82no—
85Q8×C13—82no—
86C2×C4×C13—24no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—42no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—81no—
102C2×C4×C13—82no—
103C2×C4×C13—81no—
104C2×C4×C13—82no—
105C8×C13—82no—
106#543C22×C1311yescharacteristic
107#451—22no—
108#399—21no—
109#393C22×C1312yes—
110#391—22no—
111#387—22no—
112#381—21no—
113#381C22×C1311yescharacteristic
114C4×C22⋊C4—21no—
115#342—21no—
116#342C22×C1311yescharacteristic
117#328—22no—
118#323C22×C1312yes—
119C22×C13—22no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—42no—
125C22×C13—81no—
126C22×C13#45111yescharacteristic
127C22×C13#45511yescharacteristic
128C22×C13B(4,𝔽2)11yescharacteristic
129C4×C13—42no—
130C4×C13—42no—
131C4×C13—44no—
132C4×C13—82no—
133C4×C13—81no—
134C4×C13—82no—
135C4×C13—161no—
136C22×Q8D4×C1312yes—
137C23×C4D4×C1311yescharacteristic
138C2×Q16—42no—
139C22⋊Q8—22no—
140C22⋊Q8—42no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C22⋊C4—21no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4D4×C1311yescharacteristic
147C2×C22⋊C4C23×C1311yescharacteristic
148C2×C42—21no—
149C2×C42—21no—
150#103—42no—
151C22⋊C8—22no—
152#95—22no—
153#95—21no—
154#95—22no—
155#95—22no—
156#95—42no—
157#95D4×C1312yes—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—41no—
161C2×C13—41no—
162C2×C13#160211yescharacteristic
163C2×C13#219712yes—
164C24C2×D4×C1311yescharacteristic
165C2×Q8—22no—
166C2×Q8—44no—
167C2×Q8—42no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4C13×Q1612yescomplemented
178C22×C4C2×D4×C1312yes—
179Q16—84no—
180C2×C8—42no—
181C4⋊C4—22no—
182C4⋊C4—44no—
183C4⋊C4—42no—
184C4⋊C4—81no—
185C22⋊C4—41no—
186C22⋊C4—44no—
187C22⋊C4—41no—
188C22⋊C4—41no—
189C22⋊C4—41no—
190C22⋊C4—41no—
191C22⋊C4—41no—
192C42—81no—
193C42—81no—
194C13#1221511yescharacteristic, direct product factor, Sylow
195C23—21no—
196C23—21no—
197C23—42no—
198C23C13×#12011yescharacteristic
199C23C2×C13×Q1611yescharacteristic
200C23C13×#13711yescharacteristic
201Q8—44no—
202Q8—82no—
203Q8—82no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—81no—
220C2×C4—82no—
221C2×C4—81no—
222C2×C4—82no—
223C8—82no—
224C22—22no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—81no—
231C22C13×#45111yescharacteristic
232C22C13×#45511yescharacteristic
233C22C13×B(4,𝔽2)11yescharacteristic
234C4—42no—
235C4—42no—
236C4—44no—
237C4—82no—
238C4—81no—
239C4—82no—
240C4—161no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2C13×#160211yescharacteristic
246C2C13×#219712yes—
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
41. #12215C13direct (N × H)
55. C22×C4×C13Q16semidirect
177. C22×C4C13×Q16semidirect
194. C13#12215direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26072
C13×#20302
C13×#16022
C13×#13512
C13×#13172
#1221513