Finite Group Databasebeta

← C13×#12241 #15698580

Subgroups — C13×#12241 #15698580

Order 3328.

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

normal subgroups only

This group has 324 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×#2769C211yesmaximal, characteristic
2C13×#2061C211yesmaximal, characteristic
3C13×#1617C211yesmaximal, characteristic
4C13×#1611C211yesmaximal, characteristic
5C13×#1353C211yesmaximal, characteristic
6C13×#1346C211yesmaximal, characteristic
7C13×#1324C211yesmaximal, characteristic
8C13×#544C2211yescharacteristic
9C13×#484—21no—
10C13×#483—21no—
11C13×#428—21no—
12C13×#400—21no—
13C13×#400C2211yescharacteristic
14C13×#398—21no—
15C13×#398C2211yescharacteristic
16C13×#389—21no—
17C13×#387—21no—
18C13×#387—21no—
19C13×#383—21no—
20C13×#382C2211yescharacteristic
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C2×C13×M16—21no—
28C13×C4⋊Q8—41no—
29C13×#125—41no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C13×#117—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4C2311yescharacteristic
41C2×C42×C13—21no—
42C2×C42×C13D411yescharacteristic
43C13×#107—41no—
44C13×#107—41no—
45C13×#106—41no—
46C13×#106—41no—
47C13×#103—41no—
48C13×#103—41no—
49C13×C22⋊C8—21no—
50C13×C22⋊C8—21no—
51C13×#95—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#12241C1311yesmaximal, characteristic, direct product factor, Sylow
63C2×Q8×C13—21no—
64C2×Q8×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C13×M16—22no—
75C13×M16—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—81no—
94C13×C22⋊C4—41no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—42no—
98C42×C13—41no—
99#2769C2×C1311yescharacteristic
100#2061C2×C1311yescharacteristic
101#1617C2×C1311yescharacteristic
102#1611C2×C1311yescharacteristic
103#1353C2×C1311yescharacteristic
104#1346C2×C1311yescharacteristic
105#1324C2×C1311yescharacteristic
106C23×C13#12011yescharacteristic
107Q8×C13—81no—
108Q8×C13—81no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
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#13511yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C8×C13—42no—
138C8×C13—81no—
139C8×C13—81no—
140#544C22×C1311yescharacteristic
141#484—21no—
142#483—21no—
143#428—21no—
144#400—21no—
145#400C22×C1311yescharacteristic
146#398—21no—
147#398C22×C1311yescharacteristic
148#389—21no—
149#387—21no—
150#387—21no—
151#383—21no—
152#382C22×C1311yescharacteristic
153#343C22×C1311yescharacteristic
154#339—21no—
155#328—21no—
156#328—21no—
157#324C22×C1311yescharacteristic
158#324C22×C1311yescharacteristic
159C22×C13—21no—
160C22×C13—21no—
161C22×C13#45211yescharacteristic
162C22×C13#45611yescharacteristic
163C22×C13B(4,𝔽2)11yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—42no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—81no—
170C4×C13—81no—
171C4×C13—81no—
172C4×C13—81no—
173C4×C13—81no—
174C4×C13—81no—
175C4×C13—81no—
176C2×M16—21no—
177C4⋊Q8—41no—
178#125—41no—
179C22⋊Q8—21no—
180C22⋊Q8—21no—
181#117—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4D4×C1311yescharacteristic
187C2×C4⋊C4D4×C1311yescharacteristic
188C2×C4⋊C4D4×C1311yescharacteristic
189C2×C4⋊C4C23×C1311yescharacteristic
190C2×C42—21no—
191C2×C42D4×C1311yescharacteristic
192#107—41no—
193#107—41no—
194#106—41no—
195#106—41no—
196#103—41no—
197#103—41no—
198C22⋊C8—21no—
199C22⋊C8—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95D4×C1311yescharacteristic
210#95D4×C1311yescharacteristic
211C2×C13—21no—
212C2×C13—21no—
213C2×C13#160311yescharacteristic
214C2×C13#220111yescharacteristic
215C2×C13#220411yescharacteristic
216C2×Q8—21no—
217C2×Q8—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4C2×D4×C1311yescharacteristic
225C22×C4C2×D4×C1311yescharacteristic
226C22×C4C2×D4×C1311yescharacteristic
227M16—22no—
228M16—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—81no—
247C22⋊C4—41no—
248C42—21no—
249C42—21no—
250C42—42no—
251C42—41no—
252C13#1224111yescharacteristic, direct product factor, Sylow
253C23C13×#12011yescharacteristic
254Q8—81no—
255Q8—81no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
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×C4C13×#13511yescharacteristic
283C2×C4C13×#13711yescharacteristic
284C8—42no—
285C8—81no—
286C8—81no—
287C22—21no—
288C22—21no—
289C22C13×#45211yescharacteristic
290C22C13×#45611yescharacteristic
291C22C13×B(4,𝔽2)11yescharacteristic
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2C13×#160311yescharacteristic
307C2C13×#220111yescharacteristic
308C2C13×#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. #12241C13direct (N × H)
252. C13#12241direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27692
C13×#20612
C13×#16172
C13×#16112
C13×#13532
C13×#13462
C13×#13242
#1224113