Finite Group Databasebeta

← C13×#12272 #15698611

Subgroups — C13×#12272 #15698611

Order 3328.

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

normal subgroups only

This group has 372 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×#2593C211yesmaximal, characteristic
2C13×#2027C211yesmaximal, characteristic
3C13×#1617C211yesmaximal, characteristic, complemented
4C13×#1611C211yesmaximal, characteristic, complemented
5C13×#1353C211yesmaximal, characteristic, complemented
6C13×#1346C211yesmaximal, characteristic, complemented
7C13×#1318C211yesmaximal, characteristic
8C13×#544C2211yescharacteristic
9C13×#484—21no—
10C13×#483—21no—
11C13×#418—21no—
12C13×#400C2211yescharacteristic
13C13×#398C2211yescharacteristic
14C13×#394—21no—
15C13×#390C2211yescharacteristic
16C13×#388—21no—
17C13×#388—21no—
18C13×#388—21no—
19C13×#388—21no—
20C4×C13×C4⋊C4—21no—
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C2×C13×M16—21no—
29C13×C4⋊Q8—41no—
30C13×#125—41no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—21no—
33C13×#117—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4C2311yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C42×C13—21no—
46C2×C42×C13—21no—
47C2×C42×C13D411yescharacteristic
48C13×#107—41no—
49C13×#106—41no—
50C13×#103—41no—
51C13×#103—41no—
52C13×#102—41no—
53C13×#102—41no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12272C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×M16—41no—
79C13×M16—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—81no—
101C13×C22⋊C4—81no—
102C42×C13—41no—
103C42×C13—42no—
104C42×C13—41no—
105C42×C13—81no—
106#2593C2×C1311yescharacteristic
107#2027C2×C1311yescharacteristic
108#1617C2×C1311yescharacteristic, complemented
109#1611C2×C1311yescharacteristic, complemented
110#1353C2×C1311yescharacteristic, complemented
111#1346C2×C1311yescharacteristic, complemented
112#1318C2×C1311yescharacteristic
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#12011yescharacteristic
121Q8×C13—81no—
122Q8×C13—81no—
123D4×C13—42no—
124D4×C13—81no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
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—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13#13711yescharacteristic
150C8×C13—81no—
151C8×C13—81no—
152C8×C13—81no—
153#544C22×C1311yescharacteristic
154#484—21no—
155#483—21no—
156#418—21no—
157#400C22×C1311yescharacteristic
158#398C22×C1311yescharacteristic
159#394—21no—
160#390C22×C1311yescharacteristic
161#388—21no—
162#388—21no—
163#388—21no—
164#388—21no—
165C4×C4⋊C4—21no—
166#343C22×C1311yescharacteristic
167#339—21no—
168#328—21no—
169#328—21no—
170#324C22×C1311yescharacteristic
171#324C22×C1311yescharacteristic
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13#45211yescharacteristic
182C22×C13#45511yescharacteristic
183C22×C13B(4,𝔽2)11yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—42no—
187C4×C13—42no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195C22×D4D4×C1311yescharacteristic
196C2×M16—21no—
197C4⋊Q8—41no—
198#125—41no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4D4×C1311yescharacteristic
205C2×C4⋊C4D4×C1311yescharacteristic
206C2×C4⋊C4C23×C1311yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42D4×C1311yescharacteristic
216#107—41no—
217#106—41no—
218#103—41no—
219#103—41no—
220#102—41no—
221#102—41no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95D4×C1311yescharacteristic
229#95D4×C1311yescharacteristic
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—161no—
233C2×C13#160611yescharacteristic
234C2×C13#219811yescharacteristic
235C2×C13#220411yescharacteristic
236C24—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4C2×D4×C1311yescharacteristic
249C22×C4C2×D4×C1311yescharacteristic
250C22×C4C2×D4×C1311yescharacteristic
251M16—41no—
252M16—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—81no—
274C22⋊C4—81no—
275C42—41no—
276C42—42no—
277C42—41no—
278C42—81no—
279C13#1227211yescharacteristic, direct product factor, Sylow
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C13×#12011yescharacteristic
288Q8—81no—
289Q8—81no—
290D4—42no—
291D4—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
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×C4C13×#13511yescharacteristic
316C2×C4C13×#13711yescharacteristic
317C8—81no—
318C8—81no—
319C8—81no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22C13×#45211yescharacteristic
330C22C13×#45511yescharacteristic
331C22C13×B(4,𝔽2)11yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—81no—
343C2—21no—
344C2—21no—
345C2—161no—
346C2C13×#160611yescharacteristic
347C2C13×#219811yescharacteristic
348C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC22×D4×C13D4
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
3. C13×#1617C2semidirect
4. C13×#1611C2semidirect
5. C13×#1353C2semidirect
6. C13×#1346C2semidirect
62. #12272C13direct (N × H)
108. #1617C2×C13semidirect
109. #1611C2×C13semidirect
110. #1353C2×C13semidirect
111. #1346C2×C13semidirect
279. C13#12272direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25932
C13×#20272
C13×#16172
C13×#16112
C13×#13532
C13×#13462
C13×#13182
#1227213