Finite Group Databasebeta

← C13×#7812 #15694151

Subgroups — C13×#7812 #15694151

Order 3328.

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

normal subgroups only

This group has 398 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×#2811C211yesmaximal, characteristic
2C13×#2096C211yesmaximal, characteristic
3C13×#2072C212yesmaximal
4C13×#1272C212yesmaximal
5C13×#1272C211yesmaximal, characteristic
6C2×C13×#106—21no—
7C2×C13×#103—22no—
8C2×C13×#103—21no—
9C13×#395—22no—
10C13×#395—21no—
11C13×#391—22no—
12C13×#391—21no—
13C13×#391C2212yes—
14C13×#391C2211yescharacteristic
15C13×#384C2211yescharacteristic
16C13×#340—22no—
17C13×#336C2212yes—
18C13×#336C2211yescharacteristic
19C22×Q8×C13—21no—
20C22×Q8×C13D412yes—
21C22×Q8×C13D411yescharacteristic
22C22×C8×C13—21no—
23C22×C8×C13—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13C2311yescharacteristic
32C13×#106—42no—
33C13×#103—42no—
34C13×#103—44no—
35C13×#95—21no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40#7812C1311yesmaximal, characteristic, direct product factor, Sylow
41C2×Q8×C13—22no—
42C2×Q8×C13—21no—
43C2×Q8×C13—41no—
44C2×Q8×C13—42no—
45C2×Q8×C13—42no—
46C2×Q8×C13—41no—
47C2×Q8×C13—81no—
48C2×Q8×C13—82no—
49C2×Q8×C13SD1614yes—
50C2×Q8×C13Q1612yes—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13—41no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C2×C8×C13—22no—
59C2×C8×C13—41no—
60C2×C8×C13—41no—
61C2×C8×C13—42no—
62C2×C8×C13—42no—
63C2×C8×C13—42no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—81no—
71C13×C4⋊C4—82no—
72C42×C13—41no—
73C42×C13—81no—
74#2811C2×C1311yescharacteristic
75#2096C2×C1311yescharacteristic
76#2072C2×C1312yes—
77#1272C2×C1311yescharacteristic
78#1272C2×C1312yes—
79C23×C13#12011yescharacteristic
80Q8×C13—44no—
81Q8×C13—42no—
82Q8×C13—82no—
83Q8×C13—81no—
84Q8×C13—84no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—24no—
90C2×C4×C13—22no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
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—82no—
101C2×C4×C13—81no—
102C2×C4×C13C2×SD1612yes—
103C2×C4×C13C2×Q1611yescharacteristic
104C2×C4×C13#13712yes—
105C2×C4×C13#13711yescharacteristic
106C8×C13—42no—
107C8×C13—82no—
108C2×#106—21no—
109C2×#103—22no—
110C2×#103—21no—
111#395—22no—
112#395—21no—
113#391—22no—
114#391—21no—
115#391C22×C1312yes—
116#391C22×C1311yescharacteristic
117#384C22×C1311yescharacteristic
118#340—22no—
119#336C22×C1312yes—
120#336C22×C1311yescharacteristic
121C22×C13#44812yes—
122C22×C13#45111yescharacteristic
123C22×C13#45311yescharacteristic
124C22×C13#45512yes—
125C22×C13#45811yescharacteristic
126C4×C13—22no—
127C4×C13—22no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—44no—
131C4×C13—42no—
132C4×C13—81no—
133C4×C13—82no—
134C4×C13—161no—
135C22×Q8—21no—
136C22×Q8D4×C1312yes—
137C22×Q8D4×C1311yescharacteristic
138C22×C8—21no—
139C22×C8—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4D4×C1312yes—
145C2×C4⋊C4D4×C1311yescharacteristic
146C2×C42—21no—
147C2×C42C23×C1311yescharacteristic
148#106—42no—
149#103—42no—
150#103—44no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95—22no—
155#95—22no—
156C2×C13#160812yes—
157C2×C13#161411yescharacteristic
158C2×C13#162311yescharacteristic
159C2×C13#164512yes—
160C2×C13#165911yescharacteristic
161C2×Q8—22no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—81no—
168C2×Q8—82no—
169C2×Q8C13×SD1614yes—
170C2×Q8C13×Q1612yes—
171C22×C4—22no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—41no—
176C22×C4C2×D4×C1312yes—
177C22×C4C2×D4×C1311yescharacteristic
178C2×C8—22no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—81no—
191C4⋊C4—82no—
192C42—41no—
193C42—81no—
194C13#781211yescharacteristic, direct product factor, Sylow
195C23C13×#12011yescharacteristic
196Q8—44no—
197Q8—42no—
198Q8—82no—
199Q8—81no—
200Q8—84no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—82no—
217C2×C4—81no—
218C2×C4C2×C13×SD1612yes—
219C2×C4C2×C13×Q1611yescharacteristic
220C2×C4C13×#13712yes—
221C2×C4C13×#13711yescharacteristic
222C8—42no—
223C8—82no—
224C22C13×#44812yes—
225C22C13×#45111yescharacteristic
226C22C13×#45311yescharacteristic
227C22C13×#45512yes—
228C22C13×#45811yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—44no—
234C4—42no—
235C4—81no—
236C4—82no—
237C4—161no—
238C2C13×#160812yes—
239C2C13×#161411yescharacteristic
240C2C13×#162311yescharacteristic
241C2C13×#164512yes—
242C2C13×#165911yescharacteristic
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
40. #7812C13direct (N × H)
194. C13#7812direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28112
C13×#20962
C13×#20722
C13×#12722
#781213