Finite Group Databasebeta

← C13×#10429 #15696768

Subgroups — C13×#10429 #15696768

Order 3328.

402 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2822C211yesmaximal, characteristic
2C13×#1992C212yesmaximal
3C13×#1847C211yesmaximal, characteristic
4C2×C13×#330C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×C13×#125C2212yes—
7C2×C13×#107—21no—
8C2×C13×#106—21no—
9C2×C13×#97C2212yes—
10C2×C13×#97C2211yescharacteristic
11C13×#400—22no—
12C13×#398—21no—
13C13×#398—21no—
14C13×#398—22no—
15C13×#384C2211yescharacteristic
16C13×#382C2211yescharacteristic
17C13×#340—22no—
18C13×#340—22no—
19C13×#330—24no—
20C22×C8×C13—21no—
21C22×C8×C13—22no—
22C13×#125—22no—
23C13×#125—22no—
24C13×#125—22no—
25C13×#125—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C4⋊C4D412yes—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C42×C13C2311yescharacteristic
37C13×#107—42no—
38C13×#106—42no—
39C13×#97—22no—
40C13×#97—21no—
41C13×#97—22no—
42C13×#97D412yes—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—22no—
48#10429C1311yesmaximal, characteristic, direct product factor, Sylow
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—41no—
54C22×C4×C13C2×D412yes—
55C22×C4×C13C2×D411yescharacteristic
56C2×C8×C13—22no—
57C2×C8×C13—22no—
58C2×C8×C13—22no—
59C2×C8×C13—24no—
60C2×C8×C13—42no—
61C2×C8×C13—42no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—44no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—81no—
76C13×C4⋊C4—81no—
77C42×C13C2×D411yescharacteristic
78C42×C13#4111yescharacteristic
79C42×C13#4112yes—
80#2822C2×C1311yescharacteristic
81#1992C2×C1312yes—
82#1847C2×C1311yescharacteristic
83C2×#330C2×C1312yes—
84#1295C2×C1311yescharacteristic
85C23×C13#12011yescharacteristic
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—81no—
101C2×C4×C13—82no—
102C2×C4×C13#12112yes—
103C2×C4×C13#12111yescharacteristic
104C2×C4×C13#12312yes—
105C2×C4×C13#12411yescharacteristic
106C8×C13—24no—
107C8×C13—44no—
108C2×#125C22×C1312yes—
109C2×#107—21no—
110C2×#106—21no—
111C2×#97C22×C1312yes—
112C2×#97C22×C1311yescharacteristic
113#400—22no—
114#398—21no—
115#398—21no—
116#398—22no—
117#384C22×C1311yescharacteristic
118#382C22×C1311yescharacteristic
119#340—22no—
120#340—22no—
121#330—24no—
122C22×C13#39411yescharacteristic
123C22×C13#45311yescharacteristic
124C22×C13#45412yes—
125C22×C13#45612yes—
126C22×C13#45611yescharacteristic
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—81no—
132C4×C13—81no—
133C4×C13—82no—
134C4×C13—82no—
135C4×C13—161no—
136C22×C8—21no—
137C22×C8—22no—
138#125—22no—
139#125—22no—
140#125—22no—
141#125—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4D4×C1312yes—
149C2×C4⋊C4D4×C1312yes—
150C2×C4⋊C4D4×C1311yescharacteristic
151C2×C4⋊C4D4×C1311yescharacteristic
152C2×C42C23×C1311yescharacteristic
153#107—42no—
154#106—42no—
155#97—22no—
156#97—21no—
157#97—22no—
158#97D4×C1312yes—
159#95—22no—
160#95—22no—
161#95—21no—
162#95—21no—
163#95—22no—
164C2×C13#165711yescharacteristic
165C2×C13#166011yescharacteristic
166C2×C13#166312yes—
167C2×C13#203812yes—
168C2×C13#203911yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C2×D4×C1312yes—
175C22×C4C2×D4×C1311yescharacteristic
176C2×C8—22no—
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—24no—
180C2×C8—42no—
181C2×C8—42no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—44no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C42C2×D4×C1311yescharacteristic
198C42C13×#4111yescharacteristic
199C42C13×#4112yes—
200C13#1042911yescharacteristic, direct product factor, Sylow
201C23C13×#12011yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
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—81no—
217C2×C4—82no—
218C2×C4C13×#12112yes—
219C2×C4C13×#12111yescharacteristic
220C2×C4C13×#12312yes—
221C2×C4C13×#12411yescharacteristic
222C8—24no—
223C8—44no—
224C22C13×#39411yescharacteristic
225C22C13×#45311yescharacteristic
226C22C13×#45412yes—
227C22C13×#45612yes—
228C22C13×#45611yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—82no—
234C4—82no—
235C4—81no—
236C4—81no—
237C4—161no—
238C2C13×#165711yescharacteristic
239C2C13×#166011yescharacteristic
240C2C13×#166312yes—
241C2C13×#203812yes—
242C2C13×#203911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
48. #10429C13direct (N × H)
200. C13#10429direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28222
C13×#19922
C13×#18472
C2×C13×#3302
C13×#12952
#1042913