Finite Group Databasebeta

← C13×#7817 #15694156

Subgroups — C13×#7817 #15694156

Order 3328.

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

normal subgroups only

This group has 410 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×#2734C211yesmaximal, characteristic
2C13×#2096C211yesmaximal, characteristic
3C13×#2084C212yesmaximal
4C13×#1272C211yesmaximal, characteristic
5C13×#1271C212yesmaximal
6C2×C13×C4⋊Q8—21no—
7C2×C13×#106—22no—
8C2×C13×#106—21no—
9C2×C13×#103—21no—
10C13×#398—21no—
11C13×#395—22no—
12C13×#391C2211yescharacteristic
13C13×#389C2212yes—
14C13×#387—22no—
15C13×#384C2211yescharacteristic
16C13×#340—22no—
17C13×#336C2211yescharacteristic
18C13×#336C2212yes—
19C22×Q8×C13—21no—
20C22×Q8×C13D411yescharacteristic
21C22×C8×C13—22no—
22C22×C8×C13—21no—
23C13×C4⋊Q8—42no—
24C13×C4⋊Q8—42no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4D412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C13×#106—42no—
36C13×#106—44no—
37C13×#103—42no—
38C13×#95—21no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95—22no—
42#7817C1311yesmaximal, characteristic, direct product factor, Sylow
43C2×Q8×C13—21no—
44C2×Q8×C13—42no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13—81no—
48C2×Q8×C13—81no—
49C2×Q8×C13SD1612yes—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—41no—
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D412yes—
57C2×C8×C13—22no—
58C2×C8×C13—24no—
59C2×C8×C13—42no—
60C2×C8×C13—41no—
61C2×C8×C13—42no—
62C2×C8×C13—41no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—44no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—81no—
74C13×C4⋊C4SD1614yes—
75C42×C13—41no—
76C42×C13—42no—
77#2734C2×C1311yescharacteristic
78#2096C2×C1311yescharacteristic
79#2084C2×C1312yes—
80#1272C2×C1311yescharacteristic
81#1271C2×C1312yes—
82C23×C13#12011yescharacteristic
83Q8×C13—42no—
84Q8×C13—81no—
85Q8×C13—84no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—24no—
91C2×C4×C13—22no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—82no—
102C2×C4×C13—81no—
103C2×C4×C13C2×SD1612yes—
104C2×C4×C13C2×SD1611yescharacteristic
105C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C13#13712yes—
107C8×C13—44no—
108C8×C13—42no—
109C2×C4⋊Q8—21no—
110C2×#106—22no—
111C2×#106—21no—
112C2×#103—21no—
113#398—21no—
114#395—22no—
115#391C22×C1311yescharacteristic
116#389C22×C1312yes—
117#387—22no—
118#384C22×C1311yescharacteristic
119#340—22no—
120#336C22×C1312yes—
121#336C22×C1311yescharacteristic
122C22×C13#44812yes—
123C22×C13#45011yescharacteristic
124C22×C13#45311yescharacteristic
125C22×C13#45612yes—
126C22×C13#45811yescharacteristic
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—42no—
132C4×C13—44no—
133C4×C13—82no—
134C4×C13—81no—
135C4×C13—161no—
136C22×Q8—21no—
137C22×Q8D4×C1311yescharacteristic
138C22×C8—22no—
139C22×C8—21no—
140C4⋊Q8—42no—
141C4⋊Q8—42no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4D4×C1312yes—
148C2×C4⋊C4D4×C1312yes—
149C2×C4⋊C4D4×C1311yescharacteristic
150C2×C42—21no—
151C2×C42C23×C1311yescharacteristic
152#106—42no—
153#106—44no—
154#103—42no—
155#95—21no—
156#95—22no—
157#95—22no—
158#95—22no—
159C2×C13#161112yes—
160C2×C13#161311yescharacteristic
161C2×C13#162311yescharacteristic
162C2×C13#165112yes—
163C2×C13#166011yescharacteristic
164C2×Q8—21no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—81no—
170C2×Q8C13×SD1612yes—
171C22×C4—22no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—41no—
176C22×C4C2×D4×C1311yescharacteristic
177C22×C4C2×D4×C1312yes—
178C2×C8—22no—
179C2×C8—24no—
180C2×C8—42no—
181C2×C8—41no—
182C2×C8—42no—
183C2×C8—41no—
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—44no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—81no—
195C4⋊C4C13×SD1614yes—
196C42—41no—
197C42—42no—
198C13#781711yescharacteristic, direct product factor, Sylow
199C23C13×#12011yescharacteristic
200Q8—42no—
201Q8—81no—
202Q8—84no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—82no—
219C2×C4—81no—
220C2×C4C2×C13×SD1612yes—
221C2×C4C2×C13×SD1611yescharacteristic
222C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
223C2×C4C13×#13712yes—
224C8—44no—
225C8—42no—
226C22C13×#44812yes—
227C22C13×#45011yescharacteristic
228C22C13×#45311yescharacteristic
229C22C13×#45612yes—
230C22C13×#45811yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—44no—
237C4—82no—
238C4—81no—
239C4—161no—
240C2C13×#161112yes—
241C2C13×#161311yescharacteristic
242C2C13×#162311yescharacteristic
243C2C13×#165112yes—
244C2C13×#166011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
42. #7817C13direct (N × H)
198. C13#7817direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27342
C13×#20962
C13×#20842
C13×#12722
C13×#12712
#781713