Finite Group Databasebeta

← C13×#12258 #15698597

Subgroups — C13×#12258 #15698597

Order 3328.

352 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2612C211yesmaximal, characteristic
2C13×#2061C211yesmaximal, characteristic
3C13×#1617C211yesmaximal, characteristic
4C13×#1605C211yesmaximal, characteristic
5C13×#1354C211yesmaximal, characteristic
6C13×#1353C211yesmaximal, characteristic
7C13×#1324C211yesmaximal, characteristic
8C13×#544C2211yescharacteristic
9C13×#484—21no—
10C13×#451—21no—
11C13×#428—21no—
12C13×#400C2211yescharacteristic
13C13×#398—21no—
14C13×#395C2211yescharacteristic
15C13×#391—21no—
16C13×#389—21no—
17C13×#387—21no—
18C13×#387—21no—
19C13×#382C2211yescharacteristic
20C13×#376—21no—
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C2×C13×Q16—41no—
29C2×C13×M16—21no—
30C13×C4⋊Q8—41no—
31C13×#125—41no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×#117—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4C2311yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13—21no—
44C2×C42×C13D411yescharacteristic
45C13×#107—41no—
46C13×#107—41no—
47C13×#106—41no—
48C13×#103—41no—
49C13×#103—41no—
50C13×C22⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12258C1311yesmaximal, characteristic, direct product factor, Sylow
63C2×Q8×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—42no—
66C2×Q8×C13—41no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×Q16—82no—
77C13×M16—22no—
78C13×M16—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C22⋊C4—41no—
96C42×C13—21no—
97C42×C13—42no—
98C42×C13—42no—
99C42×C13—41no—
100C42×C13Q1612yescomplemented
101#2612C2×C1311yescharacteristic
102#2061C2×C1311yescharacteristic
103#1617C2×C1311yescharacteristic
104#1605C2×C1311yescharacteristic
105#1354C2×C1311yescharacteristic
106#1353C2×C1311yescharacteristic
107#1324C2×C1311yescharacteristic
108C23×C13#12011yescharacteristic
109Q8×C13—42no—
110Q8×C13—81no—
111Q8×C13—81no—
112Q8×C13—81no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13C2×Q1611yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C8×C13—42no—
142C8×C13—81no—
143C8×C13—81no—
144#544C22×C1311yescharacteristic
145#484—21no—
146#451—21no—
147#428—21no—
148#400C22×C1311yescharacteristic
149#398—21no—
150#395C22×C1311yescharacteristic
151#391—21no—
152#389—21no—
153#387—21no—
154#387—21no—
155#382C22×C1311yescharacteristic
156#376—21no—
157#343C22×C1311yescharacteristic
158#339—21no—
159#328—21no—
160#328—21no—
161#324C22×C1311yescharacteristic
162#324C22×C1311yescharacteristic
163C22×C13—21no—
164C22×C13—21no—
165C22×C13#45111yescharacteristic
166C22×C13#45611yescharacteristic
167C22×C13B(4,𝔽2)11yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—42no—
171C4×C13—42no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—42no—
175C4×C13—81no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—81no—
180C22×Q8D4×C1311yescharacteristic
181C2×Q16—41no—
182C2×M16—21no—
183C4⋊Q8—41no—
184#125—41no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187#117—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4D4×C1311yescharacteristic
193C2×C4⋊C4D4×C1311yescharacteristic
194C2×C4⋊C4C23×C1311yescharacteristic
195C2×C42—21no—
196C2×C42—21no—
197C2×C42D4×C1311yescharacteristic
198#107—41no—
199#107—41no—
200#106—41no—
201#103—41no—
202#103—41no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95D4×C1311yescharacteristic
214#95D4×C1311yescharacteristic
215C2×C13—21no—
216C2×C13—21no—
217C2×C13#160511yescharacteristic
218C2×C13#219711yescharacteristic
219C2×C13#220411yescharacteristic
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—42no—
223C2×Q8—41no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4C2×D4×C1311yescharacteristic
231C22×C4C2×D4×C1311yescharacteristic
232C22×C4C2×D4×C1311yescharacteristic
233Q16—82no—
234M16—22no—
235M16—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—81no—
252C22⋊C4—41no—
253C42—21no—
254C42—42no—
255C42—42no—
256C42—41no—
257C42C13×Q1612yescomplemented
258C13#1225811yescharacteristic, direct product factor, Sylow
259C23C13×#12011yescharacteristic
260Q8—42no—
261Q8—81no—
262Q8—81no—
263Q8—81no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4C2×C13×Q1611yescharacteristic
291C2×C4C13×#13711yescharacteristic
292C8—42no—
293C8—81no—
294C8—81no—
295C22—21no—
296C22—21no—
297C22C13×#45111yescharacteristic
298C22C13×#45611yescharacteristic
299C22C13×B(4,𝔽2)11yescharacteristic
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—42no—
307C4—81no—
308C4—81no—
309C4—81no—
310C4—81no—
311C4—81no—
312C2—21no—
313C2—21no—
314C2C13×#160511yescharacteristic
315C2C13×#219711yescharacteristic
316C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC23×C13#120
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
62. #12258C13direct (N × H)
100. C42×C13Q16semidirect
257. C42C13×Q16semidirect
258. C13#12258direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26122
C13×#20612
C13×#16172
C13×#16052
C13×#13542
C13×#13532
C13×#13242
#1225813