Finite Group Databasebeta

← C13×#12146 #15698485

Subgroups — C13×#12146 #15698485

Order 3328.

380 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2792C211yesmaximal, characteristic, complemented
2C13×#2039C211yesmaximal, characteristic
3C13×#1610C211yesmaximal, characteristic
4C13×#1604C211yesmaximal, characteristic
5C13×#1354C211yesmaximal, characteristic, complemented
6C13×#1346C211yesmaximal, characteristic, complemented
7C13×#1325C211yesmaximal, characteristic, complemented
8C13×#537C2211yescharacteristic
9C13×#480—21no—
10C13×#448—21no—
11C2×C13×#104—21no—
12C13×#417—21no—
13C13×#398—21no—
14C13×#398C2211yescharacteristic
15C13×#395—21no—
16C13×#395C2211yescharacteristic
17C13×#389—21no—
18C13×#389—21no—
19C13×#387—21no—
20C13×#387—21no—
21C13×#384C2211yescharacteristic
22C13×#343C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C2×C13×#41—21no—
28C22×Q8×C13D411yescharacteristic
29C2×C13×SD16—41no—
30C2×C13×M16—21no—
31C13×C22⋊Q8—41no—
32C13×#121—21no—
33C13×#121—21no—
34C13×#121—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4C2311yescharacteristic
45C2×C42×C13—21no—
46C2×C42×C13D411yescharacteristic
47C13×#107—41no—
48C13×#104—42no—
49C13×#103—41no—
50C13×#103—41no—
51C13×#102—41no—
52C13×#102—41no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95D411yescharacteristic
62C13×#95D411yescharacteristic
63#12146C1311yesmaximal, characteristic, direct product factor, Sylow
64C13×#41—41no—
65C13×#41—41no—
66C13×#41—41no—
67C13×#41—41no—
68C2×Q8×C13—21no—
69C2×Q8×C13—41no—
70C2×Q8×C13—81no—
71C2×D4×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13—41no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—41no—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C13×SD16—82no—
86C13×M16—41no—
87C13×M16—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C13×C4⋊C4—24no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—81no—
100C13×C4⋊C4—81no—
101C13×C4⋊C4—81no—
102C13×C4⋊C4—81no—
103C13×C4⋊C4—81no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C42×C13—21no—
107C42×C13—21no—
108C42×C13—81no—
109#2792C2×C1311yescharacteristic, complemented
110#2039C2×C1311yescharacteristic
111#1610C2×C1311yescharacteristic
112#1604C2×C1311yescharacteristic
113#1354C2×C1311yescharacteristic, complemented
114#1346C2×C1311yescharacteristic, complemented
115#1325C2×C1311yescharacteristic, complemented
116C23×C13—41no—
117C23×C13#12011yescharacteristic
118Q8×C13—41no—
119Q8×C13—41no—
120Q8×C13—42no—
121Q8×C13—81no—
122D4×C13—41no—
123D4×C13—41no—
124D4×C13—81no—
125D4×C13—81no—
126D4×C13—81no—
127D4×C13—81no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C2×C4×C13#13511yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C8×C13—81no—
158C8×C13—81no—
159C8×C13—81no—
160#537C22×C1311yescharacteristic
161#480—21no—
162#448—21no—
163C2×#104—21no—
164#417—21no—
165#398—21no—
166#398C22×C1311yescharacteristic
167#395—21no—
168#395C22×C1311yescharacteristic
169#389—21no—
170#389—21no—
171#387—21no—
172#387—21no—
173#384C22×C1311yescharacteristic
174#343C22×C1311yescharacteristic
175#327—21no—
176#327—21no—
177#324C22×C1311yescharacteristic
178#324C22×C1311yescharacteristic
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13#44911yescharacteristic
185C22×C13#45411yescharacteristic
186C22×C13B(4,𝔽2)11yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13—42no—
191C4×C13—42no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C2×#41—21no—
199C22×Q8D4×C1311yescharacteristic
200C2×SD16—41no—
201C2×M16—21no—
202C22⋊Q8—41no—
203#121—21no—
204#121—21no—
205#121—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4D4×C1311yescharacteristic
214C2×C4⋊C4D4×C1311yescharacteristic
215C2×C4⋊C4C23×C1311yescharacteristic
216C2×C42—21no—
217C2×C42D4×C1311yescharacteristic
218#107—41no—
219#104—42no—
220#103—41no—
221#103—41no—
222#102—41no—
223#102—41no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95D4×C1311yescharacteristic
233#95D4×C1311yescharacteristic
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—161no—
237C2×C13#159711yescharacteristic
238C2×C13#220011yescharacteristic
239C2×C13#220511yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—81no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4C2×D4×C1311yescharacteristic
259C22×C4C2×D4×C1311yescharacteristic
260C22×C4C2×D4×C1311yescharacteristic
261SD16—82no—
262M16—41no—
263M16—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C4⋊C4—24no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—21no—
283C42—21no—
284C42—81no—
285C13#1214611yescharacteristic, direct product factor, Sylow
286C23—41no—
287C23C13×#12011yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—42no—
291Q8—81no—
292D4—41no—
293D4—41no—
294D4—81no—
295D4—81no—
296D4—81no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4C13×#13511yescharacteristic
326C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
327C8—81no—
328C8—81no—
329C8—81no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C13×#44911yescharacteristic
336C22C13×#45411yescharacteristic
337C22C13×B(4,𝔽2)11yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2C13×#159711yescharacteristic
353C2C13×#220011yescharacteristic
354C2C13×#220511yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC13×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2792C2semidirect
5. C13×#1354C2semidirect
6. C13×#1346C2semidirect
7. C13×#1325C2semidirect
63. #12146C13direct (N × H)
109. #2792C2×C13semidirect
113. #1354C2×C13semidirect
114. #1346C2×C13semidirect
115. #1325C2×C13semidirect
285. C13#12146direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27922
C13×#20392
C13×#16102
C13×#16042
C13×#13542
C13×#13462
C13×#13252
#1214613