Finite Group Databasebeta

← C13×#10207 #15696546

Subgroups — C13×#10207 #15696546

Order 3328.

474 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3249C211yesmaximal, characteristic
2C13×#3229C211yesmaximal, characteristic
3C13×#3139C211yesmaximal, characteristic
4C13×#1988C211yesmaximal, characteristic
5C13×#1986C211yesmaximal, characteristic
6C13×#1503C211yesmaximal, characteristic
7C13×#1283C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#533C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C13×#498—21no—
12C13×#491—22no—
13C13×#487—21no—
14C13×#487—21no—
15C13×#487—21no—
16C13×#483—22no—
17C13×#477—21no—
18C13×#477—21no—
19C13×#475—22no—
20C13×#467—22no—
21C13×#462—21no—
22C13×#462—21no—
23C13×#431C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C13×#419—22no—
26C4×C13×M16C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#340—22no—
29C13×#339—22no—
30C13×#328—22no—
31C22×Q8×C13—21no—
32C2×C13×Q16—22no—
33C2×C13×M16D412yes—
34C22×C8×C13D412yes—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8D411yescharacteristic
39C13×C4⋊Q8D411yescharacteristic
40C13×C4⋊Q8D412yes—
41C13×C4⋊Q8D411yescharacteristic
42C13×C4⋊Q8D411yescharacteristic
43C13×#125—21no—
44C13×#125—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C13×C22⋊Q8—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×Q8×C13—21no—
53C13×#117—21no—
54C13×#117—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C42×C13—21no—
59C2×C42×C13C2311yescharacteristic
60C13×#107—22no—
61C13×#106—24no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#103—24no—
66C13×#103—24no—
67C13×#103—22no—
68C13×#103—22no—
69C13×#103—24no—
70C13×C22⋊C8D412yes—
71C13×#97—21no—
72C4×C8×C13—21no—
73C4×C8×C13—21no—
74C13×#95—21no—
75#10207C1311yesmaximal, characteristic, direct product factor, Sylow
76C2×Q8×C13—21no—
77C2×Q8×C13—22no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—41no—
82C2×Q8×C13—42no—
83C2×Q8×C13—42no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C13×Q16—82no—
90C13×M16—22no—
91C13×M16—22no—
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—42no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C42×C13—41no—
117C42×C13—41no—
118C42×C13—42no—
119C42×C13C2×D411yescharacteristic
120C42×C13C2×D411yescharacteristic
121C42×C13C2×D411yescharacteristic
122C42×C13#4111yescharacteristic
123#3249C2×C1311yescharacteristic
124#3229C2×C1311yescharacteristic
125#3139C2×C1311yescharacteristic
126#1988C2×C1311yescharacteristic
127#1986C2×C1311yescharacteristic
128#1503C2×C1311yescharacteristic
129#1283C2×C1311yescharacteristic
130C23×C13#12711yescharacteristic
131Q8×C13—42no—
132Q8×C13—44no—
133Q8×C13—41no—
134Q8×C13—41no—
135Q8×C13—41no—
136Q8×C13—41no—
137Q8×C13—81no—
138Q8×C13—82no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—42no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#13512yes—
159C2×C4×C13#13712yes—
160C8×C13—42no—
161C8×C13—42no—
162C8×C13—42no—
163#533C22×C1311yescharacteristic
164#533C22×C1311yescharacteristic
165C2×C4⋊Q8C22×C1311yescharacteristic
166#498—21no—
167#491—22no—
168#487—21no—
169#487—21no—
170#487—21no—
171#483—22no—
172#477—21no—
173#477—21no—
174#475—22no—
175#467—22no—
176#462—21no—
177#462—21no—
178#431C22×C1311yescharacteristic
179C2×C4⋊C8C22×C1311yescharacteristic
180#419—22no—
181C4×M16C22×C1311yescharacteristic
182C4×C4⋊C4C22×C1311yescharacteristic
183#340—22no—
184#339—22no—
185#328—22no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13#39211yescharacteristic
189C22×C13#49511yescharacteristic
190C22×C13#49711yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—82no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—81no—
199C4×C13—82no—
200C4×C13#45212yes—
201C4×C13#45511yescharacteristic
202C4×C13#45611yescharacteristic
203C4×C13#46412yes—
204C22×Q8—21no—
205C2×Q16—22no—
206C2×M16D4×C1312yes—
207C22×C8D4×C1312yes—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8D4×C1312yes—
212C4⋊Q8D4×C1311yescharacteristic
213C4⋊Q8D4×C1311yescharacteristic
214C4⋊Q8D4×C1311yescharacteristic
215C4⋊Q8D4×C1311yescharacteristic
216#125—21no—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226#117—21no—
227#117—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42—21no—
232C2×C42C23×C1311yescharacteristic
233#107—22no—
234#106—24no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238#103—24no—
239#103—24no—
240#103—22no—
241#103—22no—
242#103—24no—
243C22⋊C8D4×C1312yes—
244#97—21no—
245C4×C8—21no—
246C4×C8—21no—
247#95—21no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13#200711yescharacteristic
251C2×C13#200911yescharacteristic
252C2×C13#201511yescharacteristic
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—41no—
259C2×Q8—42no—
260C2×Q8—42no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4C2×D4×C1311yescharacteristic
264C22×C4C2×D4×C1311yescharacteristic
265C22×C4C2×D4×C1311yescharacteristic
266Q16—82no—
267M16—22no—
268M16—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—42no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C42—41no—
294C42—41no—
295C42—42no—
296C42C2×D4×C1311yescharacteristic
297C42C2×D4×C1311yescharacteristic
298C42C2×D4×C1311yescharacteristic
299C42C13×#4111yescharacteristic
300C13#1020711yescharacteristic, direct product factor, Sylow
301C23C13×#12711yescharacteristic
302Q8—42no—
303Q8—44no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308Q8—81no—
309Q8—82no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C13×#12011yescharacteristic
324C2×C4C13×#12011yescharacteristic
325C2×C4C13×#12011yescharacteristic
326C2×C4C13×#12111yescharacteristic
327C2×C4C13×#12111yescharacteristic
328C2×C4C13×#12111yescharacteristic
329C2×C4C13×#13512yes—
330C2×C4C13×#13712yes—
331C8—42no—
332C8—42no—
333C8—42no—
334C22—21no—
335C22—21no—
336C22C13×#39211yescharacteristic
337C22C13×#49511yescharacteristic
338C22C13×#49711yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—82no—
348C4C13×#45212yes—
349C4C13×#45511yescharacteristic
350C4C13×#45611yescharacteristic
351C4C13×#46412yes—
352C2—21no—
353C2—21no—
354C2C13×#200711yescharacteristic
355C2C13×#200911yescharacteristic
356C2C13×#201511yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC23×C13#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
75. #10207C13direct (N × H)
300. C13#10207direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32492
C13×#32292
C13×#31392
C13×#19882
C13×#19862
C13×#15032
C13×#12832
#1020713