Finite Group Databasebeta

← C13×#13465 #15699804

Subgroups — C13×#13465 #15699804

Order 3328.

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

normal subgroups only

This group has 384 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×#2809C211yesmaximal, characteristic
2C13×#1857C211yesmaximal, characteristic
3C13×#1857C212yesmaximal
4C13×#1394C211yesmaximal, characteristic
5C13×#1394C212yesmaximal
6C13×#519C2211yescharacteristic
7C13×#428—22no—
8C13×#428—21no—
9C2×C13×#101C2212yes—
10C2×C13×#101C2211yescharacteristic
11C13×#400—21no—
12C13×#398—22no—
13C13×#391C2211yescharacteristic
14C13×#391C2212yes—
15C13×#389—21no—
16C13×#387—22no—
17C13×#339—22no—
18C13×#339—21no—
19C22×Q8×C13C2311yescharacteristic
20C2×C13×M16—22no—
21C2×C13×M16—21no—
22C4×Q8×C13—41no—
23C4×Q8×C13—41no—
24C13×#117—22no—
25C13×#117—21no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13D412yes—
33C2×C42×C13D411yescharacteristic
34C13×#107—42no—
35C13×#107—41no—
36C13×#106—42no—
37C13×#106—41no—
38C13×#101—22no—
39C13×#101—21no—
40C13×#101Q814yes—
41C13×#101Q812yes—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—22no—
47#13465C1311yesmaximal, characteristic, direct product factor, Sylow
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13C2×Q812yes—
51C2×Q8×C13C2×Q811yescharacteristic
52C2×Q8×C13#4111yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13C2×D412yes—
58C22×C4×C13C2×D411yescharacteristic
59C13×M16—24no—
60C13×M16—22no—
61C13×M16—41no—
62C13×M16—42no—
63C2×C8×C13—42no—
64C2×C8×C13—41no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—44no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—81no—
74C13×C4⋊C4—81no—
75C13×C22⋊C4—41no—
76C42×C13—41no—
77C42×C13—42no—
78C42×C13—42no—
79C42×C13—41no—
80#2809C2×C1311yescharacteristic
81#1857C2×C1312yes—
82#1857C2×C1311yescharacteristic
83#1394C2×C1311yescharacteristic
84#1394C2×C1312yes—
85C23×C13#12011yescharacteristic
86Q8×C13—42no—
87Q8×C13—41no—
88Q8×C13—41no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13C22⋊Q812yes—
107C2×C4×C13C22⋊Q811yescharacteristic
108C2×C4×C13C4⋊Q812yes—
109C2×C4×C13C4⋊Q811yescharacteristic
110C8×C13—44no—
111C8×C13—42no—
112#519C22×C1311yescharacteristic
113#428—22no—
114#428—21no—
115C2×#101C22×C1312yes—
116C2×#101C22×C1311yescharacteristic
117#400—21no—
118#398—22no—
119#391C22×C1311yescharacteristic
120#391C22×C1312yes—
121#389—21no—
122#387—22no—
123#339—22no—
124#339—21no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#39511yescharacteristic
128C22×C13B(4,𝔽2)11yescharacteristic
129C22×C13#45811yescharacteristic
130C4×C13—22no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—42no—
135C4×C13—82no—
136C4×C13—81no—
137C4×C13—81no—
138C4×C13—81no—
139C4×C13—82no—
140C22×Q8C23×C1311yescharacteristic
141C2×M16—22no—
142C2×M16—21no—
143C4×Q8—41no—
144C4×Q8—41no—
145#117—22no—
146#117—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4D4×C1312yes—
152C2×C4⋊C4D4×C1311yescharacteristic
153C2×C42D4×C1312yes—
154C2×C42D4×C1311yescharacteristic
155#107—42no—
156#107—41no—
157#106—42no—
158#106—41no—
159#101—22no—
160#101—21no—
161#101Q8×C1314yes—
162#101Q8×C1312yes—
163#95—21no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#206211yescharacteristic
171C2×C13#220311yescharacteristic
172C2×C13#220411yescharacteristic
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8C2×Q8×C1312yes—
176C2×Q8C2×Q8×C1311yescharacteristic
177C2×Q8C13×#4111yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C2×D4×C1312yes—
183C22×C4C2×D4×C1311yescharacteristic
184M16—24no—
185M16—22no—
186M16—41no—
187M16—42no—
188C2×C8—42no—
189C2×C8—41no—
190C4⋊C4—22no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—44no—
197C4⋊C4—42no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C22⋊C4—41no—
201C42—41no—
202C42—42no—
203C42—42no—
204C42—41no—
205C13#1346511yescharacteristic, direct product factor, Sylow
206C23C13×#12011yescharacteristic
207Q8—42no—
208Q8—41no—
209Q8—41no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4C13×C22⋊Q812yes—
228C2×C4C13×C22⋊Q811yescharacteristic
229C2×C4C13×C4⋊Q812yes—
230C2×C4C13×C4⋊Q811yescharacteristic
231C8—44no—
232C8—42no—
233C22—21no—
234C22—21no—
235C22C13×#39511yescharacteristic
236C22C13×B(4,𝔽2)11yescharacteristic
237C22C13×#45811yescharacteristic
238C4—22no—
239C4—21no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—81no—
246C4—81no—
247C4—82no—
248C2—21no—
249C2—21no—
250C2C13×#206211yescharacteristic
251C2C13×#220311yescharacteristic
252C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C13
prime radicalC23×C13#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
47. #13465C13direct (N × H)
205. C13#13465direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28092
C13×#18572
C13×#13942
#1346513