Finite Group Databasebeta

← C13×#9985 #15696324

Subgroups — C13×#9985 #15696324

Order 3328.

502 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3095C212yesmaximal
2C13×#2817C211yesmaximal, characteristic
3C13×#1820C211yesmaximal, characteristic
4C13×#1511C212yesmaximal
5C13×#1306C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C2×C13×#117C2211yescharacteristic
8C13×#485—24no—
9C13×#484—22no—
10C13×#483—22no—
11C13×#428—22no—
12C13×#419—22no—
13C13×#407C2212yes—
14C13×#400—22no—
15C13×#397—22no—
16C13×#395—22no—
17C13×#381C2211yescharacteristic
18C13×#381C2211yescharacteristic
19C13×#342—22no—
20C13×#328—24no—
21C22×Q8×C13D412yes—
22C23×C4×C13C2311yescharacteristic
23C2×C13×M16—22no—
24C13×C22⋊Q8—22no—
25C13×C22⋊Q8—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C13×#117—22no—
29C13×#117—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C4⋊C4D412yes—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4D412yes—
38C2×C42×C13—21no—
39C13×#107—24no—
40C13×#106—24no—
41C13×#103—24no—
42C13×#103—24no—
43C13×C22⋊C8—22no—
44C13×C22⋊C8D414yes—
45C13×#95—24no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95—22no—
49#9985C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13C2×D411yescharacteristic
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13—44no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—42no—
59C22×C4×C13—41no—
60C22×C4×C13C2×D412yes—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×C4×C13#4111yescharacteristic
64C13×M16—44no—
65C2×C8×C13—24no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—82no—
73C13×C22⋊C4—41no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—42no—
79C42×C13—42no—
80#3095C2×C1312yes—
81#2817C2×C1311yescharacteristic
82#1820C2×C1311yescharacteristic
83#1511C2×C1312yes—
84#1306C2×C1311yescharacteristic
85C23×C13—22no—
86C23×C13—42no—
87C23×C13#12011yescharacteristic
88C23×C13#12111yescharacteristic
89C23×C13#12711yescharacteristic
90Q8×C13—44no—
91Q8×C13—82no—
92C2×C4×C13—24no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—44no—
97C2×C4×C13—44no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—44no—
103C2×C4×C13—82no—
104C2×C4×C13—81no—
105C2×C4×C13—82no—
106C2×C4×C13#12012yes—
107C2×C4×C13#12112yes—
108C8×C13—44no—
109C2×C22⋊Q8C22×C1312yes—
110C2×#117C22×C1311yescharacteristic
111#485—24no—
112#484—22no—
113#483—22no—
114#428—22no—
115#419—22no—
116#407C22×C1312yes—
117#400—22no—
118#397—22no—
119#395—22no—
120#381C22×C1311yescharacteristic
121#381C22×C1311yescharacteristic
122#342—22no—
123#328—24no—
124C22×C13—22no—
125C22×C13—22no—
126C22×C13—22no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—82no—
130C22×C13#39211yescharacteristic
131C22×C13#45812yes—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—82no—
135C4×C13—82no—
136C4×C13—82no—
137C4×C13—82no—
138C4×C13—161no—
139C22×Q8D4×C1312yes—
140C23×C4C23×C1311yescharacteristic
141C2×M16—22no—
142C22⋊Q8—22no—
143C22⋊Q8—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146#117—22no—
147#117—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4D4×C1312yes—
151C2×C4⋊C4D4×C1312yes—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—22no—
154C2×C22⋊C4—21no—
155C2×C22⋊C4D4×C1312yes—
156C2×C42—21no—
157#107—24no—
158#106—24no—
159#103—24no—
160#103—24no—
161C22⋊C8—22no—
162C22⋊C8D4×C1314yes—
163#95—24no—
164#95—22no—
165#95—22no—
166#95—22no—
167C2×C13—22no—
168C2×C13—41no—
169C2×C13—41no—
170C2×C13#200912yes—
171C2×C13#202211yescharacteristic
172C24C2×D4×C1311yescharacteristic
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—44no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—41no—
182C22×C4C2×D4×C1312yes—
183C22×C4C2×D4×C1311yescharacteristic
184C22×C4C2×D4×C1312yes—
185C22×C4C13×#4111yescharacteristic
186M16—44no—
187C2×C8—24no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—82no—
195C22⋊C4—41no—
196C22⋊C4—42no—
197C22⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C42—42no—
202C13#998511yescharacteristic, direct product factor, Sylow
203C23—22no—
204C23—42no—
205C23C13×#12011yescharacteristic
206C23C13×#12111yescharacteristic
207C23C13×#12711yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—82no—
222C2×C4—81no—
223C2×C4—82no—
224C2×C4C13×#12012yes—
225C2×C4C13×#12112yes—
226C8—44no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22C13×#39211yescharacteristic
234C22C13×#45812yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—82no—
241C4—161no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2C13×#200912yes—
246C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
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
49. #9985C13direct (N × H)
202. C13#9985direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30952
C13×#28172
C13×#18202
C13×#15112
C13×#13062
#998513