Finite Group Databasebeta

← C13×#12269 #15698608

Subgroups — C13×#12269 #15698608

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×#2764C211yesmaximal, characteristic
2C13×#2030C211yesmaximal, characteristic
3C13×#1608C211yesmaximal, characteristic
4C13×#1602C211yesmaximal, characteristic
5C13×#1351C211yesmaximal, characteristic
6C13×#1344C211yesmaximal, characteristic
7C13×#1317C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C13×#483—21no—
10C13×#451—21no—
11C13×#400—21no—
12C13×#398—21no—
13C13×#397C2211yescharacteristic
14C13×#393C2211yescharacteristic
15C13×#391—21no—
16C13×#388—21no—
17C13×#385—21no—
18C13×#383—21no—
19C13×#381—21no—
20C13×#381C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C2×C13×Q16—41no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—41no—
33C13×C22⋊Q8—41no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13—21no—
45C13×#106—41no—
46C13×#103—41no—
47C13×#103—41no—
48C13×C22⋊C8—21no—
49C13×C22⋊C8—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—41no—
59C13×#95—41no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12269C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13C2×D411yescharacteristic
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C2×Q8×C13—42no—
67C2×Q8×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
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×C13—21no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×Q16—82no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C4⋊C4—81no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C42×C13—42no—
104#2764C2×C1311yescharacteristic
105#2030C2×C1311yescharacteristic
106#1608C2×C1311yescharacteristic
107#1602C2×C1311yescharacteristic
108#1351C2×C1311yescharacteristic
109#1344C2×C1311yescharacteristic
110#1317C2×C1311yescharacteristic
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13#12011yescharacteristic
116C23×C13#13511yescharacteristic
117C23×C13#13711yescharacteristic
118Q8×C13—42no—
119Q8×C13—81no—
120Q8×C13—81no—
121Q8×C13—81no—
122C2×C4×C13—22no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
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—42no—
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—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C8×C13—81no—
154C8×C13—81no—
155#543C22×C1311yescharacteristic
156#483—21no—
157#451—21no—
158#400—21no—
159#398—21no—
160#397C22×C1311yescharacteristic
161#393C22×C1311yescharacteristic
162#391—21no—
163#388—21no—
164#385—21no—
165#383—21no—
166#381—21no—
167#381C22×C1311yescharacteristic
168#342—21no—
169#342C22×C1311yescharacteristic
170#328—21no—
171#328—21no—
172#323C22×C1311yescharacteristic
173#323C22×C1311yescharacteristic
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—81no—
183C22×C13#45211yescharacteristic
184C22×C13#45511yescharacteristic
185C22×C13B(4,𝔽2)11yescharacteristic
186C4×C13—41no—
187C4×C13—42no—
188C4×C13—41no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—161no—
197C22×Q8D4×C1311yescharacteristic
198C23×C4D4×C1311yescharacteristic
199C2×Q16—41no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C22⋊Q8—41no—
203C22⋊Q8—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4D4×C1311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4D4×C1311yescharacteristic
213C2×C22⋊C4C23×C1311yescharacteristic
214C2×C42—21no—
215#106—41no—
216#103—41no—
217#103—41no—
218C22⋊C8—21no—
219C22⋊C8—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—41no—
229#95—41no—
230#95D4×C1311yescharacteristic
231#95D4×C1311yescharacteristic
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—41no—
235C2×C13—41no—
236C2×C13#160611yescharacteristic
237C2×C13#219711yescharacteristic
238C2×C13#220111yescharacteristic
239C24C2×D4×C1311yescharacteristic
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—42no—
243C2×Q8—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C2×D4×C1311yescharacteristic
258C22×C4C2×D4×C1311yescharacteristic
259Q16—82no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C42—42no—
280C13#1226911yescharacteristic, direct product factor, Sylow
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23C13×#12011yescharacteristic
286C23C13×#13511yescharacteristic
287C23C13×#13711yescharacteristic
288Q8—42no—
289Q8—81no—
290Q8—81no—
291Q8—81no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
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—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C8—81no—
324C8—81no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22C13×#45211yescharacteristic
335C22C13×#45511yescharacteristic
336C22C13×B(4,𝔽2)11yescharacteristic
337C4—41no—
338C4—42no—
339C4—41no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—161no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2C13×#160611yescharacteristic
353C2C13×#219711yescharacteristic
354C2C13×#220111yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
62. #12269C13direct (N × H)
280. C13#12269direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27642
C13×#20302
C13×#16082
C13×#16022
C13×#13512
C13×#13442
C13×#13172
#1226913