Finite Group Databasebeta

← C13×#8505 #15694844

Subgroups — C13×#8505 #15694844

Order 3328.

648 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 142 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×#3531C211yesmaximal, characteristic
2C13×#1995C211yesmaximal, characteristic, complemented
3C13×#1544C211yesmaximal, characteristic, complemented
4C13×#1500C212yesmaximal, complemented
5C13×#1495C212yesmaximal, complemented
6C13×#564C411yescharacteristic, complemented
7C13×#563—22no—
8C13×#563—22no—
9C13×#563C412yescomplemented
10C13×#562—22no—
11C13×#562C411yescharacteristic, complemented
12C13×#533—22no—
13C13×#533C2211yescharacteristic
14C13×#529—22no—
15C13×#529—22no—
16C13×#529C2212yes—
17C13×#431C2212yes—
18C13×#423C2211yescharacteristic
19C13×#376C2211yescharacteristic
20C13×#339—22no—
21C13×#332—22no—
22C13×#328—22no—
23C13×#327—22no—
24C13×Q8⋊C8—22no—
25C13×D4⋊C8—22no—
26C2×C13×M16—21no—
27C13×C4⋊Q8—22no—
28C13×C4⋊Q8—22no—
29C13×C4⋊Q8D412yes—
30C13×#126—22no—
31C13×#126—22no—
32C13×#126—22no—
33C13×#126—22no—
34C13×#126—22no—
35C13×#125—22no—
36C13×#125—22no—
37C13×#125—22no—
38C13×#125—22no—
39C13×#125C2×C412yes—
40C13×#125C2×C411yescharacteristic
41C13×#125C2×C411yescharacteristic
42C13×#124—22no—
43C13×#124—22no—
44C13×#124C2×C412yes—
45C13×#123—22no—
46C13×#123—22no—
47C13×#123—22no—
48C13×#123—22no—
49C13×#123—22no—
50C13×C22⋊Q8—22no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8D412yes—
58C13×#121—22no—
59C13×#121—22no—
60C13×#121D412yes—
61C4×Q8×C13—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13D412yes—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C4×D4×C13D412yes—
67C13×#117—22no—
68C13×#117—22no—
69C13×#117D412yes—
70C2×C42×C13—22no—
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C13×C4⋊C8—22no—
74C13×C4⋊C8—22no—
75C13×C22⋊C8—22no—
76C4×C8×C13—22no—
77C13×#95—22no—
78#8505C1311yesmaximal, characteristic, direct product factor, Sylow
79C2×Q8×C13—22no—
80C2×Q8×C13—22no—
81C2×Q8×C13C22⋊C412yes—
82C2×D4×C13—22no—
83C2×D4×C13—22no—
84C2×D4×C13C22⋊C412yes—
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D412yes—
91C13×M16—42no—
92C2×C8×C13—42no—
93C2×C8×C13—41no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4C22⋊C412yes—
108C13×C4⋊C4C22⋊C412yes—
109C13×C4⋊C4C22⋊C412yes—
110C13×C4⋊C4C22⋊C412yes—
111C13×C22⋊C4—22no—
112C13×C22⋊C4—22no—
113C13×C22⋊C4—22no—
114C13×C22⋊C4—22no—
115C13×C22⋊C4—22no—
116C13×C22⋊C4—22no—
117C13×C22⋊C4—22no—
118C13×C22⋊C4—22no—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—22no—
121C42×C13—22no—
122C42×C13—22no—
123C42×C13—22no—
124C42×C13—22no—
125C42×C13—22no—
126C42×C13—41no—
127C42×C13C22×C411yescharacteristic
128C42×C13C2×D411yescharacteristic
129C42×C13C2×D412yes—
130#3531C2×C1311yescharacteristic
131#1995C2×C1311yescharacteristic, complemented
132#1544C2×C1311yescharacteristic, complemented
133#1500C2×C1312yescomplemented
134#1495C2×C1312yescomplemented
135C23×C13—22no—
136C23×C13#12011yescharacteristic
137Q8×C13—42no—
138Q8×C13—82no—
139Q8×C13—82no—
140D4×C13—42no—
141D4×C13—82no—
142D4×C13—82no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—82no—
155C2×C4×C13—82no—
156C2×C4×C13—82no—
157C2×C4×C13C2×C22⋊C411yescharacteristic
158C2×C4×C13C2×C22⋊C412yes—
159C2×C4×C13#12012yes—
160C2×C4×C13#12011yescharacteristic
161C8×C13—82no—
162C8×C13—81no—
163#564C4×C1311yescharacteristic, complemented
164#563—22no—
165#563—22no—
166#563C4×C1312yescomplemented
167#562—22no—
168#562C4×C1311yescharacteristic, complemented
169#533—22no—
170#533C22×C1311yescharacteristic
171#529—22no—
172#529—22no—
173#529C22×C1312yes—
174#431C22×C1312yes—
175#423C22×C1311yescharacteristic
176#376C22×C1311yescharacteristic
177#339—22no—
178#332—22no—
179#328—22no—
180#327—22no—
181Q8⋊C8—22no—
182D4⋊C8—22no—
183C22×C13—21no—
184C22×C13—22no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—42no—
188C22×C13#37911yescharacteristic
189C4×C13—21no—
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—42no—
193C4×C13—42no—
194C4×C13—42no—
195C4×C13—42no—
196C4×C13—42no—
197C4×C13—82no—
198C4×C13#45411yescharacteristic
199C4×C13#45611yescharacteristic
200C2×M16—21no—
201C4⋊Q8—22no—
202C4⋊Q8—22no—
203C4⋊Q8D4×C1312yes—
204#126—22no—
205#126—22no—
206#126—22no—
207#126—22no—
208#126—22no—
209#125—22no—
210#125—22no—
211#125—22no—
212#125—22no—
213#125C2×C4×C1312yes—
214#125C2×C4×C1311yescharacteristic
215#125C2×C4×C1311yescharacteristic
216#124—22no—
217#124—22no—
218#124C2×C4×C1312yes—
219#123—22no—
220#123—22no—
221#123—22no—
222#123—22no—
223#123—22no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8D4×C1312yes—
232#121—22no—
233#121—22no—
234#121D4×C1312yes—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×Q8D4×C1312yes—
238C4×D4—22no—
239C4×D4—22no—
240C4×D4D4×C1312yes—
241#117—22no—
242#117—22no—
243#117D4×C1312yes—
244C2×C42—22no—
245C2×C42—21no—
246C2×C42C23×C1311yescharacteristic
247C4⋊C8—22no—
248C4⋊C8—22no—
249C22⋊C8—22no—
250C4×C8—22no—
251#95—22no—
252C2×C13—41no—
253C2×C13—82no—
254C2×C13#179311yescharacteristic
255C2×C13#179412yes—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8C13×C22⋊C412yes—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4C13×C22⋊C412yes—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4C2×D4×C1311yescharacteristic
267C22×C4C2×D4×C1312yes—
268M16—42no—
269C2×C8—42no—
270C2×C8—41no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4C13×C22⋊C412yes—
285C4⋊C4C13×C22⋊C412yes—
286C4⋊C4C13×C22⋊C412yes—
287C4⋊C4C13×C22⋊C412yes—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C42—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42C22×C4×C1311yescharacteristic
305C42C2×D4×C1312yes—
306C42C2×D4×C1311yescharacteristic
307C13#850511yescharacteristic, direct product factor, Sylow
308C23—22no—
309C23C13×#12011yescharacteristic
310Q8—42no—
311Q8—82no—
312Q8—82no—
313D4—42no—
314D4—82no—
315D4—82no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4C2×C13×C22⋊C411yescharacteristic
331C2×C4C2×C13×C22⋊C412yes—
332C2×C4C13×#12012yes—
333C2×C4C13×#12011yescharacteristic
334C8—82no—
335C8—81no—
336C22—21no—
337C22—22no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22C13×#37911yescharacteristic
342C4—21no—
343C4—22no—
344C4—22no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—42no—
349C4—42no—
350C4—82no—
351C4C13×#45411yescharacteristic
352C4C13×#45611yescharacteristic
353C2—41no—
354C2—82no—
355C2C13×#179311yescharacteristic
356C2C13×#179412yes—
subgroupG/H
centerC2×C4×C13#120
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#379
prime radicalC13×#3531C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1995C2semidirect
3. C13×#1544C2semidirect
4. C13×#1500C2semidirect
5. C13×#1495C2semidirect
6. C13×#564C4semidirect
9. C13×#563C4semidirect
11. C13×#562C4semidirect
78. #8505C13direct (N × H)
131. #1995C2×C13semidirect
132. #1544C2×C13semidirect
133. #1500C2×C13semidirect
134. #1495C2×C13semidirect
163. #564C4×C13semidirect
166. #563C4×C13semidirect
168. #562C4×C13semidirect
307. C13#8505direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35312
C13×#19952
C13×#15442
C13×#15002
C13×#14952
#850513