Finite Group Databasebeta

← C13×#13421 #15699760

Subgroups — C13×#13421 #15699760

Order 3328.

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

normal subgroups only

This group has 496 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×#2724C211yesmaximal, characteristic
2C2×C13×#352C212yesmaximal
3C13×#1890C212yesmaximal
4C13×#1856C211yesmaximal, characteristic
5C13×#1393C211yesmaximal, characteristic
6C2×C13×#123C2212yes—
7C13×#518C2211yescharacteristic
8C13×#428—21no—
9C2×C13×#100C2211yescharacteristic
10C2×C13×#99C2212yes—
11C13×#398—21no—
12C13×#397—22no—
13C13×#390C2211yescharacteristic
14C13×#389—21no—
15C13×#385—22no—
16C13×#381—22no—
17C13×#352—24no—
18C13×#342—22no—
19C13×#339—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13D412yes—
22C2×C13×M16—21no—
23C13×#123—22no—
24C13×#123—22no—
25C13×#123—22no—
26C13×#123—22no—
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C13×#117—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4D412yes—
40C2×C42×C13D411yescharacteristic
41C13×#107—41no—
42C13×#106—41no—
43C13×#100—21no—
44C13×#100D412yes—
45C13×#99—22no—
46C13×#99—22no—
47C13×#95—22no—
48C13×#95—22no—
49C13×#95—21no—
50C13×#95—42no—
51C13×#95—42no—
52#13421C1311yesmaximal, characteristic, direct product factor, Sylow
53C24×C13C2×D412yes—
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C2×D4×C13C2×D411yescharacteristic
57C2×D4×C13#4111yescharacteristic
58C2×D4×C13#4112yes—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13C2×D411yescharacteristic
71C13×M16—22no—
72C13×M16—41no—
73C2×C8×C13—41no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—81no—
81C13×C4⋊C4—81no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C42×C13—41no—
92C42×C13—41no—
93#2724C2×C1311yescharacteristic
94C2×#352C2×C1312yes—
95#1890C2×C1312yes—
96#1856C2×C1311yescharacteristic
97#1393C2×C1311yescharacteristic
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13#12011yescharacteristic
103C23×C13#12112yes—
104C23×C13#12312yes—
105D4×C13—41no—
106D4×C13—41no—
107D4×C13—42no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—44no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—82no—
125C2×C4×C13—82no—
126C2×C4×C13—82no—
127C2×C4×C13—82no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12411yescharacteristic
132C8×C13—42no—
133C2×#123C22×C1312yes—
134#518C22×C1311yescharacteristic
135#428—21no—
136C2×#100C22×C1311yescharacteristic
137C2×#99C22×C1312yes—
138#398—21no—
139#397—22no—
140#390C22×C1311yescharacteristic
141#389—21no—
142#385—22no—
143#381—22no—
144#352—24no—
145#342—22no—
146#339—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—22no—
150C22×C13—22no—
151C22×C13—42no—
152C22×C13—42no—
153C22×C13—42no—
154C22×C13—42no—
155C22×C13—82no—
156C22×C13#39411yescharacteristic
157C22×C13B(4,𝔽2)11yescharacteristic
158C22×C13#45811yescharacteristic
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—42no—
162C4×C13—82no—
163C4×C13—81no—
164C4×C13—81no—
165C4×C13—81no—
166C4×C13—82no—
167C4×C13—162no—
168C22×D4C23×C1311yescharacteristic
169C23×C4D4×C1312yes—
170C2×M16—21no—
171#123—22no—
172#123—22no—
173#123—22no—
174#123—22no—
175C4×D4—41no—
176C4×D4—41no—
177#117—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4D4×C1311yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4D4×C1312yes—
188C2×C42D4×C1311yescharacteristic
189#107—41no—
190#106—41no—
191#100—21no—
192#100D4×C1312yes—
193#99—22no—
194#99—22no—
195#95—22no—
196#95—22no—
197#95—21no—
198#95—42no—
199#95—42no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—42no—
203C2×C13—42no—
204C2×C13#204411yescharacteristic
205C2×C13#219811yescharacteristic
206C2×C13#220111yescharacteristic
207C24C2×D4×C1312yes—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4C2×D4×C1311yescharacteristic
211C2×D4C13×#4111yescharacteristic
212C2×D4C13×#4112yes—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4C2×D4×C1311yescharacteristic
225M16—22no—
226M16—41no—
227C2×C8—41no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C22⋊C4—41no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C42—41no—
246C42—41no—
247C13#1342111yescharacteristic, direct product factor, Sylow
248C23—22no—
249C23—22no—
250C23—42no—
251C23—42no—
252C23C13×#12011yescharacteristic
253C23C13×#12112yes—
254C23C13×#12312yes—
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4C13×#12111yescharacteristic
281C2×C4C13×#12411yescharacteristic
282C8—42no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—82no—
292C22C13×#39411yescharacteristic
293C22C13×B(4,𝔽2)11yescharacteristic
294C22C13×#45811yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—82no—
299C4—82no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—162no—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2C13×#204411yescharacteristic
309C2C13×#219811yescharacteristic
310C2C13×#220111yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
52. #13421C13direct (N × H)
247. C13#13421direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27242
C2×C13×#3522
C13×#18902
C13×#18562
C13×#13932
#1342113