Finite Group Databasebeta

← C13×#10574 #15696913

Subgroups — C13×#10574 #15696913

Order 3328.

494 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 162 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×#2551C211yesmaximal, characteristic
2C13×#1948C212yesmaximal
3C13×#1844C211yesmaximal, characteristic
4C13×#1296C211yesmaximal, characteristic
5C13×#1279C212yesmaximal
6C2×C13×C4⋊Q8—22no—
7C2×C13×#106—22no—
8C2×C13×#106—22no—
9C2×C13×C4⋊C8C2212yes—
10C2×C4×C8×C13C2211yescharacteristic
11C13×#395—22no—
12C13×#389—22no—
13C13×#384C2211yescharacteristic
14C13×#384C2211yescharacteristic
15C4×C13×C4⋊C4C2212yes—
16C13×#340—22no—
17C22×Q8×C13—22no—
18C22×C8×C13—21no—
19C22×C8×C13—22no—
20C13×C4⋊Q8—44no—
21C13×C4⋊Q8—44no—
22C2×C13×C4⋊C4—24no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4D412yes—
29C2×C42×C13—22no—
30C2×C42×C13C2311yescharacteristic
31C13×#106—44no—
32C13×#106—44no—
33C13×C4⋊C8—22no—
34C13×C4⋊C8Q814yescomplemented
35C4×C8×C13—21no—
36C4×C8×C13Q812yescomplemented
37C13×#95—22no—
38C13×#95—22no—
39#10574C1311yesmaximal, characteristic, direct product factor, Sylow
40C2×Q8×C13—48no—
41C2×Q8×C13—82no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—41no—
46C22×C4×C13C2×D411yescharacteristic
47C22×C4×C13C2×D412yes—
48C2×C8×C13—22no—
49C2×C8×C13—22no—
50C2×C8×C13—22no—
51C2×C8×C13—24no—
52C2×C8×C13—42no—
53C2×C8×C13—42no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—48no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4SD1614yes—
64C13×C4⋊C4SD1614yes—
65C42×C13—42no—
66C42×C13—42no—
67C42×C13C2×Q811yescharacteristic
68C42×C13C2×Q812yes—
69C42×C13#4111yescharacteristic
70#2551C2×C1311yescharacteristic
71#1948C2×C1312yes—
72#1844C2×C1311yescharacteristic
73#1296C2×C1311yescharacteristic
74#1279C2×C1312yes—
75C23×C13#12011yescharacteristic
76Q8×C13—88no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—24no—
80C2×C4×C13—24no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—44no—
86C2×C4×C13—42no—
87C2×C4×C13—82no—
88C2×C4×C13—81no—
89C2×C4×C13C22⋊Q811yescharacteristic
90C2×C4×C13C22⋊Q812yes—
91C2×C4×C13C4⋊Q811yescharacteristic
92C2×C4×C13C4⋊Q812yes—
93C2×C4×C13C2×SD1612yes—
94C2×C4×C13C2×SD1612yes—
95C2×C4×C13AGL(1,ℤ/8)12yes—
96C2×C4×C13#13712yes—
97C8×C13—24no—
98C8×C13—44no—
99C2×C4⋊Q8—22no—
100C2×#106—22no—
101C2×#106—22no—
102C2×C4⋊C8C22×C1312yes—
103C2×C4×C8C22×C1311yescharacteristic
104#395—22no—
105#389—22no—
106#384C22×C1311yescharacteristic
107#384C22×C1311yescharacteristic
108C4×C4⋊C4C22×C1312yes—
109#340—22no—
110C22×C13#39511yescharacteristic
111C22×C13#44812yes—
112C22×C13#45012yes—
113C22×C13#45311yescharacteristic
114C22×C13#45611yescharacteristic
115C4×C13—21no—
116C4×C13—21no—
117C4×C13—44no—
118C4×C13—44no—
119C4×C13—82no—
120C4×C13—161no—
121C4×C13#47512yes—
122C4×C13#47612yes—
123C4×C13#49812yes—
124C4×C13#50112yes—
125C22×Q8—22no—
126C22×C8—21no—
127C22×C8—22no—
128C4⋊Q8—44no—
129C4⋊Q8—44no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4D4×C1312yes—
135C2×C4⋊C4D4×C1312yes—
136C2×C4⋊C4D4×C1312yes—
137C2×C42—22no—
138C2×C42C23×C1311yescharacteristic
139#106—44no—
140#106—44no—
141C4⋊C8—22no—
142C4⋊C8Q8×C1314yescomplemented
143C4×C8—21no—
144C4×C8Q8×C1312yescomplemented
145#95—22no—
146#95—22no—
147C2×C13#162311yescharacteristic
148C2×C13#162911yescharacteristic
149C2×C13#165112yes—
150C2×C13#205812yes—
151C2×C13#206011yescharacteristic
152C2×Q8—48no—
153C2×Q8—82no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—41no—
158C22×C4C2×D4×C1311yescharacteristic
159C22×C4C2×D4×C1312yes—
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—24no—
164C2×C8—42no—
165C2×C8—42no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—42no—
169C4⋊C4—48no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4C13×SD1614yes—
176C4⋊C4C13×SD1614yes—
177C42—42no—
178C42—42no—
179C42C2×Q8×C1311yescharacteristic
180C42C2×Q8×C1312yes—
181C42C13×#4111yescharacteristic
182C13#1057411yescharacteristic, direct product factor, Sylow
183C23C13×#12011yescharacteristic
184Q8—88no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—42no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4C13×C22⋊Q811yescharacteristic
198C2×C4C13×C22⋊Q812yes—
199C2×C4C13×C4⋊Q811yescharacteristic
200C2×C4C13×C4⋊Q812yes—
201C2×C4C2×C13×SD1612yes—
202C2×C4C2×C13×SD1612yes—
203C2×C4C13×AGL(1,ℤ/8)12yes—
204C2×C4C13×#13712yes—
205C8—24no—
206C8—44no—
207C22C13×#39511yescharacteristic
208C22C13×#44812yes—
209C22C13×#45012yes—
210C22C13×#45311yescharacteristic
211C22C13×#45611yescharacteristic
212C4—21no—
213C4—21no—
214C4—44no—
215C4—44no—
216C4—82no—
217C4—161no—
218C4C13×#47512yes—
219C4C13×#47612yes—
220C4C13×#49812yes—
221C4C13×#50112yes—
222C2C13×#162311yescharacteristic
223C2C13×#162911yescharacteristic
224C2C13×#165112yes—
225C2C13×#205812yes—
226C2C13×#206011yescharacteristic
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
34. C13×C4⋊C8Q8semidirect
36. C4×C8×C13Q8semidirect
39. #10574C13direct (N × H)
142. C4⋊C8Q8×C13semidirect
144. C4×C8Q8×C13semidirect
182. C13#10574direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25512
C13×#19482
C13×#18442
C13×#12962
C13×#12792
#1057413