Finite Group Databasebeta

← C13×#10389 #15696728

Subgroups — C13×#10389 #15696728

Order 3328.

406 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2608C211yesmaximal, characteristic
2C13×#1826C212yesmaximal
3C13×#1820C211yesmaximal, characteristic
4C13×#1306C211yesmaximal, characteristic
5C13×#1284C212yesmaximal
6C2×C13×#117C2211yescharacteristic
7C13×#407C2212yes—
8C13×#396—22no—
9C13×#389—22no—
10C13×#387—22no—
11C13×#381C2211yescharacteristic
12C13×#381C2211yescharacteristic
13C4×C13×C22⋊C4C2212yes—
14C13×#342—22no—
15C13×#339—22no—
16C13×#339—22no—
17C23×C4×C13C2311yescharacteristic
18C2×C13×M16—22no—
19C13×#117—22no—
20C13×#117—22no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4Q812yes—
25C2×C13×C22⋊C4—22no—
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4—21no—
28C2×C13×C22⋊C4D412yes—
29C2×C42×C13—21no—
30C2×C42×C13D412yes—
31C2×C42×C13D412yes—
32C13×C22⋊C8—22no—
33C13×C22⋊C8—22no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95—22no—
38#10389C1311yesmaximal, characteristic, direct product factor, Sylow
39C24×C13C2×D411yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—42no—
45C22×C4×C13—41no—
46C22×C4×C13C2×D412yes—
47C22×C4×C13C2×Q811yescharacteristic
48C22×C4×C13#4112yes—
49C22×C4×C13#4111yescharacteristic
50C13×M16—42no—
51C13×M16—42no—
52C2×C8×C13—42no—
53C13×C4⋊C4—24no—
54C13×C4⋊C4—44no—
55C13×C4⋊C4—44no—
56C13×C4⋊C4—82no—
57C13×C22⋊C4—44no—
58C13×C22⋊C4—41no—
59C13×C22⋊C4—41no—
60C13×C22⋊C4—42no—
61C13×C22⋊C4—42no—
62C42×C13—42no—
63C42×C13—42no—
64C42×C13—42no—
65#2608C2×C1311yescharacteristic
66#1826C2×C1312yes—
67#1820C2×C1311yescharacteristic
68#1306C2×C1311yescharacteristic
69#1284C2×C1312yes—
70C23×C13—22no—
71C23×C13—42no—
72C23×C13#12011yescharacteristic
73C23×C13C22⋊Q811yescharacteristic
74C23×C13#12411yescharacteristic
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—24no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—82no—
91C2×C4×C13—81no—
92C2×C4×C13—82no—
93C2×C4×C13C22⋊Q812yes—
94C2×C4×C13#12412yes—
95C8×C13—82no—
96C2×#117C22×C1311yescharacteristic
97#407C22×C1312yes—
98#396—22no—
99#389—22no—
100#387—22no—
101#381C22×C1311yescharacteristic
102#381C22×C1311yescharacteristic
103C4×C22⋊C4C22×C1312yes—
104#342—22no—
105#339—22no—
106#339—22no—
107C22×C13—22no—
108C22×C13—21no—
109C22×C13—21no—
110C22×C13—22no—
111C22×C13—22no—
112C22×C13—82no—
113C22×C13#39311yescharacteristic
114C22×C13#45812yes—
115C4×C13—22no—
116C4×C13—22no—
117C4×C13—44no—
118C4×C13—82no—
119C4×C13—82no—
120C4×C13—82no—
121C4×C13—161no—
122C23×C4C23×C1311yescharacteristic
123C2×M16—22no—
124#117—22no—
125#117—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4Q8×C1312yes—
130C2×C22⋊C4—21no—
131C2×C22⋊C4—22no—
132C2×C22⋊C4—21no—
133C2×C22⋊C4D4×C1312yes—
134C2×C42—21no—
135C2×C42D4×C1312yes—
136C2×C42D4×C1312yes—
137C22⋊C8—22no—
138C22⋊C8—22no—
139#95—22no—
140#95—22no—
141#95—22no—
142#95—22no—
143C2×C13—22no—
144C2×C13—41no—
145C2×C13—41no—
146C2×C13#203011yescharacteristic
147C2×C13#203112yes—
148C24C2×D4×C1311yescharacteristic
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—42no—
154C22×C4—41no—
155C22×C4C2×D4×C1312yes—
156C22×C4C2×Q8×C1311yescharacteristic
157C22×C4C13×#4112yes—
158C22×C4C13×#4111yescharacteristic
159M16—42no—
160M16—42no—
161C2×C8—42no—
162C4⋊C4—24no—
163C4⋊C4—44no—
164C4⋊C4—44no—
165C4⋊C4—82no—
166C22⋊C4—44no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—42no—
172C42—42no—
173C42—42no—
174C13#1038911yescharacteristic, direct product factor, Sylow
175C23—22no—
176C23—42no—
177C23C13×#12011yescharacteristic
178C23C13×C22⋊Q811yescharacteristic
179C23C13×#12411yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4C13×C22⋊Q812yes—
199C2×C4C13×#12412yes—
200C8—82no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22C13×#39311yescharacteristic
208C22C13×#45812yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—82no—
215C4—161no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2C13×#203011yescharacteristic
220C2C13×#203112yes—
subgroupG/H
center, socleC22×C13#393
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
38. #10389C13direct (N × H)
174. C13#10389direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26082
C13×#18262
C13×#18202
C13×#13062
C13×#12842
#1038913