Finite Group Databasebeta

← C13×#10346 #15696685

Subgroups — C13×#10346 #15696685

Order 3328.

500 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2646C211yesmaximal, characteristic
2C13×#1823C212yesmaximal
3C13×#1445C211yesmaximal, characteristic
4C13×#1294C212yesmaximal
5C13×#1280C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×C13×C22⋊C8C2212yes—
8C13×#400—22no—
9C13×#398—22no—
10C13×#385—22no—
11C13×#380C2212yes—
12C2×C13×#95—22no—
13C2×C13×#95C2211yescharacteristic
14C2×C13×#95C2211yescharacteristic
15C13×#340—22no—
16C13×#340—22no—
17C23×C4×C13—21no—
18C23×C4×C13—21no—
19C23×C4×C13D412yes—
20C23×C4×C13C2311yescharacteristic
21C22×C8×C13—22no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4Q812yes—
30C2×C13×C22⋊C4—22no—
31C13×C22⋊C8—22no—
32C13×C22⋊C8—22no—
33C13×#95—22no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95—44no—
39#10346C1311yesmaximal, characteristic, direct product factor, Sylow
40C24×C13C2×D411yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—42no—
49C22×C4×C13—42no—
50C22×C4×C13—42no—
51C22×C4×C13—41no—
52C22×C4×C13—42no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13C2×D412yes—
60C22×C4×C13C2×Q811yescharacteristic
61C22×C4×C13#4112yes—
62C22×C4×C13#4111yescharacteristic
63C2×C8×C13—42no—
64C2×C8×C13—42no—
65C2×C8×C13—42no—
66C13×C4⋊C4—24no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—82no—
71C13×C4⋊C4—82no—
72C13×C22⋊C4—42no—
73C13×C22⋊C4—42no—
74#2646C2×C1311yescharacteristic
75#1823C2×C1312yes—
76#1445C2×C1311yescharacteristic
77#1294C2×C1312yes—
78#1280C2×C1311yescharacteristic
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—22no—
82C23×C13#12011yescharacteristic
83C23×C13C22⋊Q811yescharacteristic
84C23×C13#12411yescharacteristic
85C23×C13#13512yes—
86C23×C13AGL(1,ℤ/8)12yes—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—44no—
93C2×C4×C13—42no—
94C2×C4×C13—44no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—44no—
106C2×C4×C13—82no—
107C2×C4×C13—81no—
108C2×C4×C13—82no—
109C2×C4×C13—81no—
110C2×C4×C13—81no—
111C2×C4×C13—81no—
112C2×C4×C13—82no—
113C2×C4×C13C22⋊Q812yes—
114C2×C4×C13#12412yes—
115C8×C13—82no—
116C22×C4⋊C4C22×C1311yescharacteristic
117C2×C22⋊C8C22×C1312yes—
118#400—22no—
119#398—22no—
120#385—22no—
121#380C22×C1312yes—
122C2×#95—22no—
123C2×#95C22×C1311yescharacteristic
124C2×#95C22×C1311yescharacteristic
125#340—22no—
126#340—22no—
127C22×C13—22no—
128C22×C13—22no—
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13#39311yescharacteristic
136C22×C13#44912yes—
137C22×C13#45511yescharacteristic
138C22×C13#45611yescharacteristic
139C22×C13#45812yes—
140C22×C13#47812yes—
141C22×C13#48811yescharacteristic
142C22×C13#49011yescharacteristic
143C4×C13—22no—
144C4×C13—22no—
145C4×C13—82no—
146C4×C13—82no—
147C4×C13—82no—
148C4×C13—82no—
149C4×C13—82no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4D4×C1312yes—
153C23×C4C23×C1311yescharacteristic
154C22×C8—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4D4×C1312yes—
161C2×C4⋊C4D4×C1312yes—
162C2×C4⋊C4Q8×C1312yes—
163C2×C22⋊C4—22no—
164C22⋊C8—22no—
165C22⋊C8—22no—
166#95—22no—
167#95—22no—
168#95—22no—
169#95—22no—
170#95—22no—
171#95—44no—
172C2×C13—21no—
173C2×C13—22no—
174C2×C13—21no—
175C2×C13#160912yes—
176C2×C13#161212yes—
177C2×C13#202511yescharacteristic
178C2×C13#202811yescharacteristic
179C2×C13#203011yescharacteristic
180C24C2×D4×C1311yescharacteristic
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—41no—
192C22×C4—42no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4C2×D4×C1312yes—
200C22×C4C2×Q8×C1311yescharacteristic
201C22×C4C13×#4112yes—
202C22×C4C13×#4111yescharacteristic
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C4⋊C4—24no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C13#1034611yescharacteristic, direct product factor, Sylow
215C23—21no—
216C23—21no—
217C23—22no—
218C23C13×#12011yescharacteristic
219C23C13×C22⋊Q811yescharacteristic
220C23C13×#12411yescharacteristic
221C23C13×#13512yes—
222C23C13×AGL(1,ℤ/8)12yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4C13×C22⋊Q812yes—
250C2×C4C13×#12412yes—
251C8—82no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—22no—
260C22C13×#39311yescharacteristic
261C22C13×#44912yes—
262C22C13×#45511yescharacteristic
263C22C13×#45611yescharacteristic
264C22C13×#45812yes—
265C22C13×#47812yes—
266C22C13×#48811yescharacteristic
267C22C13×#49011yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—82no—
274C4—82no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2C13×#160912yes—
279C2C13×#161212yes—
280C2C13×#202511yescharacteristic
281C2C13×#202811yescharacteristic
282C2C13×#203011yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
39. #10346C13direct (N × H)
214. C13#10346direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26462
C13×#18232
C13×#14452
C13×#12942
C13×#12802
#1034613