Finite Group Databasebeta

← C13×#12265 #15698604

Subgroups — C13×#12265 #15698604

Order 3328.

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

normal subgroups only

This group has 362 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×#2771C211yesmaximal, characteristic
2C13×#2030C211yesmaximal, characteristic
3C13×#1614C211yesmaximal, characteristic
4C13×#1608C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic
6C13×#1344C211yesmaximal, characteristic
7C13×#1317C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C13×#484—21no—
10C13×#483—21no—
11C13×#400—21no—
12C13×#400—21no—
13C13×#399C2211yescharacteristic
14C13×#397C2211yescharacteristic
15C13×#389—21no—
16C13×#388—21no—
17C13×#387—21no—
18C13×#385—21no—
19C13×#381—21no—
20C13×#381C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×C22⋊Q8—21no—
29C13×C22⋊Q8—21no—
30C13×C22⋊Q8—41no—
31C13×C22⋊Q8—41no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
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×#107—41no—
46C13×#106—41no—
47C13×#103—41no—
48C13×#103—41no—
49C13×C22⋊C8—21no—
50C13×C22⋊C8—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#12265C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13C2×D411yescharacteristic
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
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—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C42×C13—81no—
103#2771C2×C1311yescharacteristic
104#2030C2×C1311yescharacteristic
105#1614C2×C1311yescharacteristic
106#1608C2×C1311yescharacteristic
107#1352C2×C1311yescharacteristic
108#1344C2×C1311yescharacteristic
109#1317C2×C1311yescharacteristic
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13#12011yescharacteristic
115C23×C13#13511yescharacteristic
116C23×C13#13711yescharacteristic
117Q8×C13—81no—
118Q8×C13—81no—
119C2×C4×C13—22no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
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—42no—
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—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C8×C13—81no—
151C8×C13—81no—
152#543C22×C1311yescharacteristic
153#484—21no—
154#483—21no—
155#400—21no—
156#400—21no—
157#399C22×C1311yescharacteristic
158#397C22×C1311yescharacteristic
159#389—21no—
160#388—21no—
161#387—21no—
162#385—21no—
163#381—21no—
164#381C22×C1311yescharacteristic
165#342—21no—
166#342C22×C1311yescharacteristic
167#328—21no—
168#328—21no—
169#323C22×C1311yescharacteristic
170#323C22×C1311yescharacteristic
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—81no—
180C22×C13#45211yescharacteristic
181C22×C13#45511yescharacteristic
182C22×C13B(4,𝔽2)11yescharacteristic
183C4×C13—42no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—161no—
194C23×C4D4×C1311yescharacteristic
195C22⋊Q8—21no—
196C22⋊Q8—21no—
197C22⋊Q8—41no—
198C22⋊Q8—41no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4D4×C1311yescharacteristic
204C2×C4⋊C4D4×C1311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4D4×C1311yescharacteristic
210C2×C22⋊C4C23×C1311yescharacteristic
211C2×C42—21no—
212#107—41no—
213#106—41no—
214#103—41no—
215#103—41no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—41no—
226#95—41no—
227#95D4×C1311yescharacteristic
228#95D4×C1311yescharacteristic
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—41no—
232C2×C13—41no—
233C2×C13#160611yescharacteristic
234C2×C13#219811yescharacteristic
235C2×C13#220111yescharacteristic
236C24C2×D4×C1311yescharacteristic
237C2×Q8—21no—
238C2×Q8—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C1311yescharacteristic
253C22×C4C2×D4×C1311yescharacteristic
254C2×C8—41no—
255C2×C8—41no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C22⋊C4—41no—
267C22⋊C4—42no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42—81no—
276C13#1226511yescharacteristic, direct product factor, Sylow
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23C13×#12011yescharacteristic
282C23C13×#13511yescharacteristic
283C23C13×#13711yescharacteristic
284Q8—81no—
285Q8—81no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
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—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C8—81no—
318C8—81no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22C13×#45211yescharacteristic
329C22C13×#45511yescharacteristic
330C22C13×B(4,𝔽2)11yescharacteristic
331C4—42no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—161no—
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2C13×#160611yescharacteristic
347C2C13×#219811yescharacteristic
348C2C13×#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. #12265C13direct (N × H)
276. C13#12265direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27712
C13×#20302
C13×#16142
C13×#16082
C13×#13522
C13×#13442
C13×#13172
#1226513