Finite Group Databasebeta

← C13×#13431 #15699770

Subgroups — C13×#13431 #15699770

Order 3328.

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3202C211yesmaximal, characteristic
2C13×#2135C212yesmaximal
3C13×#1915C212yesmaximal
4C13×#1858C211yesmaximal, characteristic
5C13×#1392C211yesmaximal, characteristic
6C13×#568C2211yescharacteristic
7C13×#536C2212yes—
8C13×#485—22no—
9C13×#470—21no—
10C13×#467—21no—
11C13×#451—22no—
12C13×#430—21no—
13C13×#413C2212yes—
14C13×#413C2211yescharacteristic
15C2×C13×#101—22no—
16C13×#408C2211yescharacteristic
17C13×#356—24no—
18C13×#344—22no—
19C13×#341—21no—
20C2×C13×#41C2311yescharacteristic
21C22×Q8×C13D412yes—
22C2×C13×Q16—21no—
23C2×C13×Q16—21no—
24C13×#131—42no—
25C2×C13×M16—22no—
26C2×C13×M16—21no—
27C2×C13×M16—21no—
28C2×C13×M16—22no—
29C2×C13×M16D411yescharacteristic
30C22×C8×C13D411yescharacteristic
31C13×C4⋊Q8—22no—
32C13×#124—22no—
33C13×#123—22no—
34C13×#123—22no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C13×#117D412yes—
38C13×#108—42no—
39C13×#107—21no—
40C13×#106—21no—
41C13×#103—22no—
42C13×#103—22no—
43C13×#101—22no—
44C13×#101—44no—
45C13×#101D412yes—
46C13×#100—21no—
47C13×#100—22no—
48C13×C22⋊C8—22no—
49#13431C1311yesmaximal, characteristic, direct product factor, Sylow
50C13×#41—41no—
51C13×#41—41no—
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—42no—
55C2×Q8×C13—42no—
56C2×Q8×C13C2×D411yescharacteristic
57C2×D4×C13#4111yescharacteristic
58C2×D4×C13#4112yes—
59C22×C4×C13—22no—
60C22×C4×C13C2×D412yes—
61C22×C4×C13C2×D411yescharacteristic
62C13×Q16—81no—
63C13×Q16—81no—
64C13×M16—24no—
65C13×M16—22no—
66C13×M16—22no—
67C13×M16—41no—
68C13×M16—41no—
69C13×M16—41no—
70C13×M16—42no—
71C13×M16—42no—
72C2×C8×C13—21no—
73C2×C8×C13—21no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—42no—
77C2×C8×C13—41no—
78C2×C8×C13—42no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C42×C13—22no—
86#3202C2×C1311yescharacteristic
87#2135C2×C1312yes—
88#1915C2×C1312yes—
89#1858C2×C1311yescharacteristic
90#1392C2×C1311yescharacteristic
91C23×C13#12312yes—
92C23×C13#12411yescharacteristic
93Q8×C13—41no—
94Q8×C13—42no—
95Q8×C13—42no—
96Q8×C13—82no—
97D4×C13—41no—
98D4×C13—42no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—44no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13#12011yescharacteristic
107C2×C4×C13#12112yes—
108C2×C4×C13#12111yescharacteristic
109C8×C13—42no—
110C8×C13—41no—
111C8×C13—42no—
112C8×C13—41no—
113C8×C13—82no—
114#568C22×C1311yescharacteristic
115#536C22×C1312yes—
116#485—22no—
117#470—21no—
118#467—21no—
119#451—22no—
120#430—21no—
121#413C22×C1312yes—
122#413C22×C1311yescharacteristic
123C2×#101—22no—
124#408C22×C1311yescharacteristic
125#356—24no—
126#344—22no—
127#341—21no—
128C22×C13—22no—
129C22×C13—21no—
130C22×C13—42no—
131C22×C13—41no—
132C22×C13#39411yescharacteristic
133C4×C13—21no—
134C4×C13—22no—
135C4×C13—82no—
136C4×C13—82no—
137C4×C13B(4,𝔽2)11yescharacteristic
138C4×C13#45811yescharacteristic
139C2×#41C23×C1311yescharacteristic
140C22×Q8D4×C1312yes—
141C2×Q16—21no—
142C2×Q16—21no—
143#131—42no—
144C2×M16—21no—
145C2×M16—22no—
146C2×M16—21no—
147C2×M16—22no—
148C2×M16D4×C1311yescharacteristic
149C22×C8D4×C1311yescharacteristic
150C4⋊Q8—22no—
151#124—22no—
152#123—22no—
153#123—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156#117D4×C1312yes—
157#108—42no—
158#107—21no—
159#106—21no—
160#103—22no—
161#103—22no—
162#101—22no—
163#101—44no—
164#101D4×C1312yes—
165#100—21no—
166#100—22no—
167C22⋊C8—22no—
168C2×C13—21no—
169C2×C13—42no—
170C2×C13—41no—
171C2×C13#204411yescharacteristic
172#41—41no—
173#41—41no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8C2×D4×C1311yescharacteristic
179C2×D4C13×#4111yescharacteristic
180C2×D4C13×#4112yes—
181C22×C4—22no—
182C22×C4C2×D4×C1312yes—
183C22×C4C2×D4×C1311yescharacteristic
184Q16—81no—
185Q16—81no—
186M16—24no—
187M16—22no—
188M16—22no—
189M16—41no—
190M16—41no—
191M16—41no—
192M16—42no—
193M16—42no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—42no—
199C2×C8—41no—
200C2×C8—42no—
201C4⋊C4—22no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C22⋊C4—22no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C42—22no—
208C13#1343111yescharacteristic, direct product factor, Sylow
209C23C13×#12312yes—
210C23C13×#12411yescharacteristic
211Q8—41no—
212Q8—42no—
213Q8—42no—
214Q8—82no—
215D4—41no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4C13×#12011yescharacteristic
225C2×C4C13×#12112yes—
226C2×C4C13×#12111yescharacteristic
227C8—42no—
228C8—41no—
229C8—42no—
230C8—41no—
231C8—82no—
232C22—22no—
233C22—21no—
234C22—42no—
235C22—41no—
236C22C13×#39411yescharacteristic
237C4—21no—
238C4—22no—
239C4—82no—
240C4—82no—
241C4C13×B(4,𝔽2)11yescharacteristic
242C4C13×#45811yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2C13×#204411yescharacteristic
subgroupG/H
center, socleC2×C13#2044
commutator, Frattini, cosocleC2×#41C23×C13
prime radicalC2×C13×#41C23
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
49. #13431C13direct (N × H)
208. C13#13431direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32022
C13×#21352
C13×#19152
C13×#18582
C13×#13922
#1343113