Finite Group Databasebeta

← C13×#12273 #15698612

Subgroups — C13×#12273 #15698612

Order 3328.

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

normal subgroups only

This group has 364 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×#2586C211yesmaximal, characteristic
2C13×#2028C211yesmaximal, characteristic
3C13×#1611C211yesmaximal, characteristic
4C13×#1605C211yesmaximal, characteristic
5C13×#1354C211yesmaximal, characteristic
6C13×#1346C211yesmaximal, characteristic
7C13×#1319C211yesmaximal, characteristic
8C13×#544C2211yescharacteristic
9C13×#483—21no—
10C13×#451—21no—
11C13×#419—21no—
12C13×#398C2211yescharacteristic
13C13×#395—21no—
14C13×#395C2211yescharacteristic
15C13×#391—21no—
16C13×#391C2211yescharacteristic
17C13×#389—21no—
18C13×#387—21no—
19C13×#387—21no—
20C4×C13×C4⋊C4—21no—
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×Q8×C13D411yescharacteristic
29C2×C13×Q16—41no—
30C2×C13×M16—21no—
31C13×C4⋊Q8—41no—
32C13×#125—41no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×#117—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⋊C4D411yescharacteristic
42C2×C13×C4⋊C4C2311yescharacteristic
43C2×C42×C13—21no—
44C2×C42×C13—21no—
45C2×C42×C13D411yescharacteristic
46C13×#106—41no—
47C13×#103—41no—
48C13×#103—41no—
49C13×#103—41no—
50C13×#103—41no—
51C13×C22⋊C8—21no—
52C13×C22⋊C8—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#12273C1311yesmaximal, characteristic, direct product factor, Sylow
63C2×Q8×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—42no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C13×Q16—82no—
81C13×M16—41no—
82C13×M16—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—81no—
99C13×C4⋊C4—81no—
100C13×C22⋊C4—41no—
101C42×C13—41no—
102C42×C13—42no—
103C42×C13—41no—
104C42×C13—81no—
105#2586C2×C1311yescharacteristic
106#2028C2×C1311yescharacteristic
107#1611C2×C1311yescharacteristic
108#1605C2×C1311yescharacteristic
109#1354C2×C1311yescharacteristic
110#1346C2×C1311yescharacteristic
111#1319C2×C1311yescharacteristic
112C23×C13#12011yescharacteristic
113Q8×C13—42no—
114Q8×C13—42no—
115Q8×C13—81no—
116Q8×C13—81no—
117Q8×C13—81no—
118Q8×C13—81no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
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×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#13511yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C8×C13—81no—
148C8×C13—81no—
149C8×C13—81no—
150#544C22×C1311yescharacteristic
151#483—21no—
152#451—21no—
153#419—21no—
154#398C22×C1311yescharacteristic
155#395—21no—
156#395C22×C1311yescharacteristic
157#391—21no—
158#391C22×C1311yescharacteristic
159#389—21no—
160#387—21no—
161#387—21no—
162C4×C4⋊C4—21no—
163#343C22×C1311yescharacteristic
164#339—21no—
165#328—21no—
166#328—21no—
167#324C22×C1311yescharacteristic
168#324C22×C1311yescharacteristic
169C22×C13—21no—
170C22×C13—21no—
171C22×C13#45211yescharacteristic
172C22×C13#45511yescharacteristic
173C22×C13B(4,𝔽2)11yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—42no—
177C4×C13—42no—
178C4×C13—42no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—42no—
182C4×C13—81no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13—81no—
186C22×Q8D4×C1311yescharacteristic
187C22×Q8D4×C1311yescharacteristic
188C2×Q16—41no—
189C2×M16—21no—
190C4⋊Q8—41no—
191#125—41no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194#117—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4D4×C1311yescharacteristic
201C2×C4⋊C4C23×C1311yescharacteristic
202C2×C42—21no—
203C2×C42—21no—
204C2×C42D4×C1311yescharacteristic
205#106—41no—
206#103—41no—
207#103—41no—
208#103—41no—
209#103—41no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95D4×C1311yescharacteristic
220#95D4×C1311yescharacteristic
221C2×C13—21no—
222C2×C13—21no—
223C2×C13#160611yescharacteristic
224C2×C13#219711yescharacteristic
225C2×C13#220511yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C2×D4×C1311yescharacteristic
241C22×C4C2×D4×C1311yescharacteristic
242C22×C4C2×D4×C1311yescharacteristic
243Q16—82no—
244M16—41no—
245M16—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C4⋊C4—24no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C42—41no—
265C42—42no—
266C42—41no—
267C42—81no—
268C13#1227311yescharacteristic, direct product factor, Sylow
269C23C13×#12011yescharacteristic
270Q8—42no—
271Q8—42no—
272Q8—81no—
273Q8—81no—
274Q8—81no—
275Q8—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4C13×#13511yescharacteristic
303C2×C4C13×#13711yescharacteristic
304C8—81no—
305C8—81no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22C13×#45211yescharacteristic
310C22C13×#45511yescharacteristic
311C22C13×B(4,𝔽2)11yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—42no—
317C4—41no—
318C4—41no—
319C4—42no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—81no—
324C2—21no—
325C2—21no—
326C2C13×#160611yescharacteristic
327C2C13×#219711yescharacteristic
328C2C13×#220511yescharacteristic
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. #12273C13direct (N × H)
268. C13#12273direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25862
C13×#20282
C13×#16112
C13×#16052
C13×#13542
C13×#13462
C13×#13192
#1227313