Finite Group Databasebeta

← C13×#12234 #15698573

Subgroups — C13×#12234 #15698573

Order 3328.

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

normal subgroups only

This group has 448 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×#2680C211yesmaximal, characteristic
2C13×#2060C211yesmaximal, characteristic, complemented
3C13×#1605C211yesmaximal, characteristic, complemented
4C13×#1599C211yesmaximal, characteristic
5C13×#1354C211yesmaximal, characteristic, complemented
6C13×#1345C211yesmaximal, characteristic
7C13×#1325C211yesmaximal, characteristic, complemented
8C13×#544C2211yescharacteristic
9C2×C13×#123—21no—
10C2×C13×C22⋊Q8—21no—
11C13×#451—21no—
12C13×#450—21no—
13C13×#428—21no—
14C13×#398—21no—
15C13×#397—21no—
16C13×#395C2211yescharacteristic
17C13×#394C2211yescharacteristic
18C13×#388—21no—
19C13×#385—21no—
20C13×#384C2211yescharacteristic
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C2×C13×Q16—41no—
31C2×C13×SD16—41no—
32C2×C13×M16—21no—
33C13×C4⋊Q8—41no—
34C13×#125—41no—
35C13×#123—44no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—44no—
39C13×#117—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C4⋊C4C2311yescharacteristic
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×#103—41no—
56C13×#102—41no—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95D411yescharacteristic
63C13×#95D411yescharacteristic
64#12234C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C2×Q8×C13—42no—
69C2×Q8×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—42no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13—81no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×Q16—82no—
84C13×SD16—82no—
85C13×M16—22no—
86C13×M16—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—42no—
99C13×C4⋊C4—42no—
100C13×C4⋊C4—42no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C22⋊C4—24no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C42×C13—21no—
111C42×C13—21no—
112C42×C13—41no—
113#2680C2×C1311yescharacteristic
114#2060C2×C1311yescharacteristic, complemented
115#1605C2×C1311yescharacteristic, complemented
116#1599C2×C1311yescharacteristic
117#1354C2×C1311yescharacteristic, complemented
118#1345C2×C1311yescharacteristic
119#1325C2×C1311yescharacteristic, complemented
120C23×C13—22no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13#12011yescharacteristic
128Q8×C13—42no—
129Q8×C13—81no—
130Q8×C13—81no—
131Q8×C13—81no—
132D4×C13—42no—
133D4×C13—81no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
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×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—84no—
158C2×C4×C13#13511yescharacteristic
159C2×C4×C13#13711yescharacteristic
160C8×C13—42no—
161C8×C13—81no—
162C8×C13—81no—
163#544C22×C1311yescharacteristic
164C2×#123—21no—
165C2×C22⋊Q8—21no—
166#451—21no—
167#450—21no—
168#428—21no—
169#398—21no—
170#397—21no—
171#395C22×C1311yescharacteristic
172#394C22×C1311yescharacteristic
173#388—21no—
174#385—21no—
175#384C22×C1311yescharacteristic
176#343C22×C1311yescharacteristic
177#339—21no—
178#328—21no—
179#328—21no—
180#324C22×C1311yescharacteristic
181#324C22×C1311yescharacteristic
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13#45211yescharacteristic
192C22×C13#45611yescharacteristic
193C22×C13B(4,𝔽2)11yescharacteristic
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—42no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—42no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205C22×Q8D4×C1311yescharacteristic
206C22×D4D4×C1311yescharacteristic
207C23×C4—21no—
208C2×Q16—41no—
209C2×SD16—41no—
210C2×M16—21no—
211C4⋊Q8—41no—
212#125—41no—
213#123—44no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—44no—
217#117—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C1311yescharacteristic
224C2×C4⋊C4C23×C1311yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C42D4×C1311yescharacteristic
231#107—41no—
232#106—41no—
233#103—41no—
234#102—41no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95D4×C1311yescharacteristic
241#95D4×C1311yescharacteristic
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—82no—
245C2×C13#160311yescharacteristic
246C2×C13#219611yescharacteristic
247C2×C13#220311yescharacteristic
248C24—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×D4—41no—
254C2×D4—42no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4C2×D4×C1311yescharacteristic
264C22×C4C2×D4×C1311yescharacteristic
265C22×C4C2×D4×C1311yescharacteristic
266Q16—82no—
267SD16—82no—
268M16—22no—
269M16—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—24no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C42—21no—
294C42—21no—
295C42—41no—
296C13#1223411yescharacteristic, direct product factor, Sylow
297C23—22no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23C13×#12011yescharacteristic
305Q8—42no—
306Q8—81no—
307Q8—81no—
308Q8—81no—
309D4—42no—
310D4—81no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
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×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—84no—
335C2×C4C13×#13511yescharacteristic
336C2×C4C13×#13711yescharacteristic
337C8—42no—
338C8—81no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22C13×#45211yescharacteristic
350C22C13×#45611yescharacteristic
351C22C13×B(4,𝔽2)11yescharacteristic
352C4—21no—
353C4—21no—
354C4—42no—
355C4—41no—
356C4—41no—
357C4—42no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—81no—
363C2—21no—
364C2—21no—
365C2—82no—
366C2C13×#160311yescharacteristic
367C2C13×#219611yescharacteristic
368C2C13×#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×#1605C2semidirect
5. C13×#1354C2semidirect
7. C13×#1325C2semidirect
64. #12234C13direct (N × H)
114. #2060C2×C13semidirect
115. #1605C2×C13semidirect
117. #1354C2×C13semidirect
119. #1325C2×C13semidirect
296. C13#12234direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26802
C13×#20602
C13×#16052
C13×#15992
C13×#13542
C13×#13452
C13×#13252
#1223413