Finite Group Databasebeta

← C13×#12239 #15698578

Subgroups — C13×#12239 #15698578

Order 3328.

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

normal subgroups only

This group has 378 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×#2785C211yesmaximal, characteristic
2C13×#2061C211yesmaximal, characteristic, complemented
3C13×#1605C211yesmaximal, characteristic, complemented
4C13×#1599C211yesmaximal, characteristic
5C13×#1354C211yesmaximal, characteristic, complemented
6C13×#1345C211yesmaximal, characteristic
7C13×#1324C211yesmaximal, characteristic, complemented
8C13×#544C2211yescharacteristic
9C13×#451—21no—
10C13×#450—21no—
11C13×#428—21no—
12C13×#395C2211yescharacteristic
13C13×#394—21no—
14C13×#394C2211yescharacteristic
15C13×#393—21no—
16C13×#388—21no—
17C13×#388—21no—
18C13×#388—21no—
19C13×#382—21no—
20C13×#382C2211yescharacteristic
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C2×C13×Q16—41no—
30C2×C13×SD16—41no—
31C2×C13×M16—21no—
32C13×C4⋊Q8—41no—
33C13×#125—41no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C13×#117—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4C2311yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C42×C13—21no—
48C2×C42×C13D411yescharacteristic
49C13×#107—41no—
50C13×#106—41no—
51C13×#103—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×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12239C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C2×Q8×C13—41no—
67C2×Q8×C13—81no—
68C2×D4×C13—41no—
69C2×D4×C13—81no—
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×Q16—82no—
79C13×SD16—82no—
80C13×M16—22no—
81C13×M16—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—81no—
94C13×C4⋊C4—81no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—81no—
101C13×C22⋊C4—81no—
102C13×C22⋊C4—81no—
103C42×C13—21no—
104C42×C13—21no—
105C42×C13—42no—
106C42×C13—41no—
107#2785C2×C1311yescharacteristic
108#2061C2×C1311yescharacteristic, complemented
109#1605C2×C1311yescharacteristic, complemented
110#1599C2×C1311yescharacteristic
111#1354C2×C1311yescharacteristic, complemented
112#1345C2×C1311yescharacteristic
113#1324C2×C1311yescharacteristic, complemented
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13#12011yescharacteristic
122Q8×C13—42no—
123Q8×C13—81no—
124Q8×C13—81no—
125Q8×C13—81no—
126D4×C13—42no—
127D4×C13—81no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—22no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
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—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C8×C13—42no—
154C8×C13—81no—
155C8×C13—81no—
156#544C22×C1311yescharacteristic
157#451—21no—
158#450—21no—
159#428—21no—
160#395C22×C1311yescharacteristic
161#394—21no—
162#394C22×C1311yescharacteristic
163#393—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#382—21no—
168#382C22×C1311yescharacteristic
169#343C22×C1311yescharacteristic
170#339—21no—
171#328—21no—
172#328—21no—
173#324C22×C1311yescharacteristic
174#324C22×C1311yescharacteristic
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13#45211yescharacteristic
185C22×C13#45611yescharacteristic
186C22×C13B(4,𝔽2)11yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C22×Q8D4×C1311yescharacteristic
199C22×D4D4×C1311yescharacteristic
200C2×Q16—41no—
201C2×SD16—41no—
202C2×M16—21no—
203C4⋊Q8—41no—
204#125—41no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207#117—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4D4×C1311yescharacteristic
211C2×C4⋊C4C23×C1311yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C42—21no—
219C2×C42D4×C1311yescharacteristic
220#107—41no—
221#106—41no—
222#103—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#95D4×C1311yescharacteristic
232#95D4×C1311yescharacteristic
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—161no—
236C2×C13#160311yescharacteristic
237C2×C13#219911yescharacteristic
238C2×C13#220411yescharacteristic
239C24—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—81no—
244C2×D4—41no—
245C2×D4—81no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4C2×D4×C1311yescharacteristic
252C22×C4C2×D4×C1311yescharacteristic
253C22×C4C2×D4×C1311yescharacteristic
254Q16—82no—
255SD16—82no—
256M16—22no—
257M16—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—81no—
277C22⋊C4—81no—
278C22⋊C4—81no—
279C42—21no—
280C42—21no—
281C42—42no—
282C42—41no—
283C13#1223911yescharacteristic, direct product factor, Sylow
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C13×#12011yescharacteristic
292Q8—42no—
293Q8—81no—
294Q8—81no—
295Q8—81no—
296D4—42no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
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×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4C13×#13511yescharacteristic
322C2×C4C13×#13711yescharacteristic
323C8—42no—
324C8—81no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C13×#45211yescharacteristic
336C22C13×#45611yescharacteristic
337C22C13×B(4,𝔽2)11yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2C13×#160311yescharacteristic
353C2C13×#219911yescharacteristic
354C2C13×#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
2. C13×#2061C2semidirect
3. C13×#1605C2semidirect
5. C13×#1354C2semidirect
7. C13×#1324C2semidirect
62. #12239C13direct (N × H)
108. #2061C2×C13semidirect
109. #1605C2×C13semidirect
111. #1354C2×C13semidirect
113. #1324C2×C13semidirect
283. C13#12239direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27852
C13×#20612
C13×#16052
C13×#15992
C13×#13542
C13×#13452
C13×#13242
#1223913