Finite Group Databasebeta

← C13×#13419 #15699758

Subgroups — C13×#13419 #15699758

Order 3328.

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

normal subgroups only

This group has 776 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×#2679C211yesmaximal, characteristic
2C2×C13×AΣL(1,𝔽16)C212yesmaximal, complemented
3C13×#1889C212yesmaximal, complemented
4C13×#1856C211yesmaximal, characteristic, complemented
5C13×#1393C211yesmaximal, characteristic, complemented
6C2×C13×#120—22no—
7C2×C13×#120C2212yes—
8C13×#518C2211yescharacteristic
9C13×#428—21no—
10C2×C13×#100C2211yescharacteristic
11C2×C13×#99C2212yes—
12C13×#394—21no—
13C13×#394—22no—
14C13×#390—21no—
15C13×#390C2211yescharacteristic
16C13×#379—22no—
17C13×AΣL(1,𝔽16)—24no—
18C13×#342—22no—
19C13×#339—21no—
20C25×C13D412yes—
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13—22no—
24C22×D4×C13C2311yescharacteristic
25C2×C13×M16—21no—
26C13×#120—22no—
27C13×#120—22no—
28C13×#120—22no—
29C13×#120—22no—
30C13×#120—48no—
31C4×D4×C13—41no—
32C4×D4×C13—41no—
33C13×#117—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—42no—
43C2×C13×C22⋊C4—42no—
44C2×C13×C22⋊C4D412yes—
45C2×C42×C13D411yescharacteristic
46C13×#107—41no—
47C13×#106—41no—
48C13×#100—21no—
49C13×#100D412yescomplemented
50C13×#99—22no—
51C13×#99—22no—
52C13×#95—21no—
53#13419C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—22no—
55C24×C13—22no—
56C24×C13—22no—
57C24×C13—42no—
58C24×C13—44no—
59C24×C13—42no—
60C24×C13—82no—
61C24×C13C2×D412yes—
62C2×D4×C13—24no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—44no—
66C2×D4×C13—44no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C2×D4×C13—81no—
70C2×D4×C13—81no—
71C2×D4×C13—82no—
72C2×D4×C13—81no—
73C2×D4×C13C2×D411yescharacteristic
74C2×D4×C13#4111yescharacteristic
75C2×D4×C13#4112yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—42no—
82C22×C4×C13C2×D411yescharacteristic
83C13×M16—22no—
84C13×M16—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—44no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—44no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—84no—
102C13×C22⋊C4—84no—
103C42×C13—41no—
104C42×C13—41no—
105#2679C2×C1311yescharacteristic
106C2×AΣL(1,𝔽16)C2×C1312yescomplemented
107#1889C2×C1312yescomplemented
108#1856C2×C1311yescharacteristic, complemented
109#1393C2×C1311yescharacteristic, complemented
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—24no—
113C23×C13—42no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—44no—
119C23×C13—44no—
120C23×C13—44no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—82no—
125C23×C13—84no—
126C23×C13—82no—
127C23×C13—88no—
128C23×C13—84no—
129C23×C13—82no—
130C23×C13#12011yescharacteristic
131C23×C13#12112yes—
132C23×C13#12312yes—
133D4×C13—41no—
134D4×C13—41no—
135D4×C13—42no—
136D4×C13—84no—
137D4×C13—84no—
138D4×C13—84no—
139D4×C13—84no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—82no—
153C2×C4×C13—82no—
154C2×C4×C13—82no—
155C2×C4×C13—82no—
156C2×C4×C13—82no—
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12411yescharacteristic
159C8×C13—42no—
160C2×#120—22no—
161C2×#120C22×C1312yes—
162#518C22×C1311yescharacteristic
163#428—21no—
164C2×#100C22×C1311yescharacteristic
165C2×#99C22×C1312yes—
166#394—21no—
167#394—22no—
168#390—21no—
169#390C22×C1311yescharacteristic
170#379—22no—
171AΣL(1,𝔽16)—24no—
172#342—22no—
173#339—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—42no—
179C22×C13—42no—
180C22×C13—44no—
181C22×C13—44no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13—48no—
185C22×C13—44no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13—82no—
189C22×C13—84no—
190C22×C13—84no—
191C22×C13—84no—
192C22×C13—82no—
193C22×C13—82no—
194C22×C13#39411yescharacteristic
195C22×C13B(4,𝔽2)11yescharacteristic
196C22×C13#45811yescharacteristic
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—42no—
200C4×C13—82no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—162no—
205C25D4×C1312yes—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—22no—
209C22×D4C23×C1311yescharacteristic
210C2×M16—21no—
211#120—22no—
212#120—22no—
213#120—22no—
214#120—22no—
215#120—48no—
216C4×D4—41no—
217C4×D4—41no—
218#117—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4D4×C1311yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—42no—
228C2×C22⋊C4—42no—
229C2×C22⋊C4D4×C1312yes—
230C2×C42D4×C1311yescharacteristic
231#107—41no—
232#106—41no—
233#100—21no—
234#100D4×C1312yescomplemented
235#99—22no—
236#99—22no—
237#95—21no—
238C2×C13—21no—
239C2×C13—21no—
240C2×C13—42no—
241C2×C13—42no—
242C2×C13—84no—
243C2×C13#204411yescharacteristic
244C2×C13#219611yescharacteristic
245C2×C13#219911yescharacteristic
246C24—22no—
247C24—22no—
248C24—22no—
249C24—42no—
250C24—44no—
251C24—42no—
252C24—82no—
253C24C2×D4×C1312yes—
254C2×D4—24no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—44no—
258C2×D4—44no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—81no—
262C2×D4—81no—
263C2×D4—82no—
264C2×D4—81no—
265C2×D4C2×D4×C1311yescharacteristic
266C2×D4C13×#4111yescharacteristic
267C2×D4C13×#4112yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—42no—
274C22×C4C2×D4×C1311yescharacteristic
275M16—22no—
276M16—41no—
277C2×C8—41no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—44no—
285C22⋊C4—44no—
286C22⋊C4—42no—
287C22⋊C4—44no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—84no—
294C22⋊C4—84no—
295C42—41no—
296C42—41no—
297C13#1341911yescharacteristic, direct product factor, Sylow
298C23—22no—
299C23—22no—
300C23—24no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—44no—
307C23—44no—
308C23—44no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—82no—
313C23—84no—
314C23—82no—
315C23—84no—
316C23—88no—
317C23—82no—
318C23C13×#12011yescharacteristic
319C23C13×#12112yes—
320C23C13×#12312yes—
321D4—41no—
322D4—41no—
323D4—42no—
324D4—84no—
325D4—84no—
326D4—84no—
327D4—84no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4C13×#12111yescharacteristic
346C2×C4C13×#12411yescharacteristic
347C8—42no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—22no—
352C22—42no—
353C22—42no—
354C22—44no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—48no—
359C22—44no—
360C22—82no—
361C22—82no—
362C22—82no—
363C22—84no—
364C22—84no—
365C22—84no—
366C22—82no—
367C22—82no—
368C22C13×#39411yescharacteristic
369C22C13×B(4,𝔽2)11yescharacteristic
370C22C13×#45811yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—162no—
379C2—21no—
380C2—21no—
381C2—42no—
382C2—42no—
383C2—84no—
384C2C13×#204411yescharacteristic
385C2C13×#219611yescharacteristic
386C2C13×#219911yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC13×#2679C2
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
2. C2×C13×AΣL(1,𝔽16)C2semidirect
3. C13×#1889C2semidirect
4. C13×#1856C2semidirect
5. C13×#1393C2semidirect
49. C13×#100D4semidirect
53. #13419C13direct (N × H)
106. C2×AΣL(1,𝔽16)C2×C13semidirect
107. #1889C2×C13semidirect
108. #1856C2×C13semidirect
109. #1393C2×C13semidirect
234. #100D4×C13semidirect
297. C13#13419direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26792
C2×C13×AΣL(1,𝔽16)2
C13×#18892
C13×#18562
C13×#13932
#1341913