Finite Group Databasebeta

← C13×#12249 #15698588

Subgroups — C13×#12249 #15698588

Order 3328.

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

normal subgroups only

This group has 386 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×#2823C211yesmaximal, characteristic
2C13×#2060C211yesmaximal, characteristic, complemented
3C13×#1611C211yesmaximal, characteristic, complemented
4C13×#1599C211yesmaximal, characteristic
5C13×#1346C211yesmaximal, characteristic, complemented
6C13×#1345C211yesmaximal, characteristic
7C13×#1325C211yesmaximal, characteristic, complemented
8C13×#544C2211yescharacteristic
9C2×C13×#126—21no—
10C13×#483—21no—
11C13×#450—21no—
12C13×#428—21no—
13C13×#398—21no—
14C13×#398C2211yescharacteristic
15C13×#396—21no—
16C13×#396—21no—
17C13×#396—21no—
18C13×#394—21no—
19C13×#394C2211yescharacteristic
20C13×#384C2211yescharacteristic
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C2×C13×SD16—41no—
29C2×C13×M16—21no—
30C13×C4⋊Q8—41no—
31C13×#126—42no—
32C13×#126—42no—
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⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C13×C4⋊C4C2311yescharacteristic
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C42×C13D411yescharacteristic
53C13×#107—41no—
54C13×#106—41no—
55C13×#106—41no—
56C13×#103—41no—
57C13×#102—41no—
58C13×C22⋊C8—21no—
59C13×C22⋊C8—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95D411yescharacteristic
63C13×#95D411yescharacteristic
64#12249C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
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×SD16—82no—
79C13×M16—22no—
80C13×M16—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—81no—
98C13×C4⋊C4—81no—
99C13×C4⋊C4—81no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—81no—
106C13×C22⋊C4—81no—
107C13×C22⋊C4—81no—
108C42×C13—21no—
109C42×C13—41no—
110C42×C13SD1612yescomplemented
111#2823C2×C1311yescharacteristic
112#2060C2×C1311yescharacteristic, complemented
113#1611C2×C1311yescharacteristic, complemented
114#1599C2×C1311yescharacteristic
115#1346C2×C1311yescharacteristic, complemented
116#1345C2×C1311yescharacteristic
117#1325C2×C1311yescharacteristic, complemented
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13#12011yescharacteristic
126Q8×C13—81no—
127Q8×C13—81no—
128D4×C13—42no—
129D4×C13—81no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
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—41no—
152C2×C4×C13—41no—
153C2×C4×C13C2×SD1611yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C8×C13—42no—
156C8×C13—81no—
157C8×C13—81no—
158#544C22×C1311yescharacteristic
159C2×#126—21no—
160#483—21no—
161#450—21no—
162#428—21no—
163#398—21no—
164#398C22×C1311yescharacteristic
165#396—21no—
166#396—21no—
167#396—21no—
168#394—21no—
169#394C22×C1311yescharacteristic
170#384C22×C1311yescharacteristic
171#343C22×C1311yescharacteristic
172#339—21no—
173#328—21no—
174#328—21no—
175#324C22×C1311yescharacteristic
176#324C22×C1311yescharacteristic
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#45011yescharacteristic
187C22×C13#45611yescharacteristic
188C22×C13B(4,𝔽2)11yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—81no—
199C4×C13—81no—
200C22×D4D4×C1311yescharacteristic
201C2×SD16—41no—
202C2×M16—21no—
203C4⋊Q8—41no—
204#126—42no—
205#126—42no—
206#125—41no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209#117—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4D4×C1311yescharacteristic
217C2×C4⋊C4D4×C1311yescharacteristic
218C2×C4⋊C4C23×C1311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42D4×C1311yescharacteristic
226#107—41no—
227#106—41no—
228#106—41no—
229#103—41no—
230#102—41no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233#95—21no—
234#95—21no—
235#95D4×C1311yescharacteristic
236#95D4×C1311yescharacteristic
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—161no—
240C2×C13#160411yescharacteristic
241C2×C13#220011yescharacteristic
242C2×C13#220311yescharacteristic
243C24—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×D4—41no—
247C2×D4—81no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×D4×C1311yescharacteristic
254C22×C4C2×D4×C1311yescharacteristic
255C22×C4C2×D4×C1311yescharacteristic
256SD16—82no—
257M16—22no—
258M16—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C22⋊C4—81no—
286C42—21no—
287C42—41no—
288C42C13×SD1612yescomplemented
289C13#1224911yescharacteristic, direct product factor, Sylow
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C13×#12011yescharacteristic
298Q8—81no—
299Q8—81no—
300D4—42no—
301D4—81no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
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×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4C2×C13×SD1611yescharacteristic
326C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
327C8—42no—
328C8—81no—
329C8—81no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22C13×#45011yescharacteristic
340C22C13×#45611yescharacteristic
341C22C13×B(4,𝔽2)11yescharacteristic
342C4—21no—
343C4—21no—
344C4—42no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C2—21no—
354C2—21no—
355C2—161no—
356C2C13×#160411yescharacteristic
357C2C13×#220011yescharacteristic
358C2C13×#220311yescharacteristic
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×#2060C2semidirect
3. C13×#1611C2semidirect
5. C13×#1346C2semidirect
7. C13×#1325C2semidirect
64. #12249C13direct (N × H)
110. C42×C13SD16semidirect
112. #2060C2×C13semidirect
113. #1611C2×C13semidirect
115. #1346C2×C13semidirect
117. #1325C2×C13semidirect
288. C42C13×SD16semidirect
289. C13#12249direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28232
C13×#20602
C13×#16112
C13×#15992
C13×#13462
C13×#13452
C13×#13252
#1224913