Finite Group Databasebeta

← C13×#12240 #15698579

Subgroups — C13×#12240 #15698579

Order 3328.

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

normal subgroups only

This group has 350 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×#2792C211yesmaximal, characteristic
2C13×#2060C211yesmaximal, characteristic
3C13×#1611C211yesmaximal, characteristic
4C13×#1605C211yesmaximal, characteristic
5C13×#1354C211yesmaximal, characteristic
6C13×#1346C211yesmaximal, characteristic
7C13×#1325C211yesmaximal, characteristic
8C13×#544C2211yescharacteristic
9C13×#483—21no—
10C13×#451—21no—
11C13×#428—21no—
12C13×#398—21no—
13C13×#398C2211yescharacteristic
14C13×#395—21no—
15C13×#395C2211yescharacteristic
16C13×#389—21no—
17C13×#389—21no—
18C13×#387—21no—
19C13×#387—21no—
20C13×#384C2211yescharacteristic
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C2×C13×Q16—41no—
29C2×C13×M16—21no—
30C13×C4⋊Q8—41no—
31C13×#125—41no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×#117—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—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⋊C4D411yescharacteristic
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4C2311yescharacteristic
45C2×C42×C13—21no—
46C2×C42×C13D411yescharacteristic
47C13×#107—41no—
48C13×#106—41no—
49C13×#106—41no—
50C13×#103—41no—
51C13×#103—41no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12240C1311yesmaximal, characteristic, direct product factor, Sylow
63C2×Q8×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—41no—
66C2×Q8×C13—81no—
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×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×Q16—82no—
77C13×M16—22no—
78C13×M16—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—24no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—81no—
96C13×C4⋊C4—81no—
97C13×C4⋊C4—81no—
98C13×C4⋊C4—81no—
99C13×C22⋊C4—41no—
100C42×C13—21no—
101C42×C13—21no—
102C42×C13—41no—
103C42×C13—81no—
104#2792C2×C1311yescharacteristic
105#2060C2×C1311yescharacteristic
106#1611C2×C1311yescharacteristic
107#1605C2×C1311yescharacteristic
108#1354C2×C1311yescharacteristic
109#1346C2×C1311yescharacteristic
110#1325C2×C1311yescharacteristic
111C23×C13#12011yescharacteristic
112Q8×C13—42no—
113Q8×C13—81no—
114Q8×C13—81no—
115Q8×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
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—41no—
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#13511yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C8×C13—42no—
145C8×C13—81no—
146C8×C13—81no—
147#544C22×C1311yescharacteristic
148#483—21no—
149#451—21no—
150#428—21no—
151#398—21no—
152#398C22×C1311yescharacteristic
153#395—21no—
154#395C22×C1311yescharacteristic
155#389—21no—
156#389—21no—
157#387—21no—
158#387—21no—
159#384C22×C1311yescharacteristic
160#343C22×C1311yescharacteristic
161#339—21no—
162#328—21no—
163#328—21no—
164#324C22×C1311yescharacteristic
165#324C22×C1311yescharacteristic
166C22×C13—21no—
167C22×C13—21no—
168C22×C13#45211yescharacteristic
169C22×C13#45611yescharacteristic
170C22×C13B(4,𝔽2)11yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—42no—
174C4×C13—42no—
175C4×C13—42no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—81no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183C22×Q8D4×C1311yescharacteristic
184C2×Q16—41no—
185C2×M16—21no—
186C4⋊Q8—41no—
187#125—41no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190#117—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4D4×C1311yescharacteristic
199C2×C4⋊C4D4×C1311yescharacteristic
200C2×C4⋊C4C23×C1311yescharacteristic
201C2×C42—21no—
202C2×C42D4×C1311yescharacteristic
203#107—41no—
204#106—41no—
205#106—41no—
206#103—41no—
207#103—41no—
208C22⋊C8—21no—
209C22⋊C8—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95D4×C1311yescharacteristic
217#95D4×C1311yescharacteristic
218C2×C13—21no—
219C2×C13—21no—
220C2×C13#160311yescharacteristic
221C2×C13#220011yescharacteristic
222C2×C13#220511yescharacteristic
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—81no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C2×D4×C1311yescharacteristic
234C22×C4C2×D4×C1311yescharacteristic
235C22×C4C2×D4×C1311yescharacteristic
236Q16—82no—
237M16—22no—
238M16—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C4⋊C4—24no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C22⋊C4—41no—
260C42—21no—
261C42—21no—
262C42—41no—
263C42—81no—
264C13#1224011yescharacteristic, direct product factor, Sylow
265C23C13×#12011yescharacteristic
266Q8—42no—
267Q8—81no—
268Q8—81no—
269Q8—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4C13×#13511yescharacteristic
297C2×C4C13×#13711yescharacteristic
298C8—42no—
299C8—81no—
300C8—81no—
301C22—21no—
302C22—21no—
303C22C13×#45211yescharacteristic
304C22C13×#45611yescharacteristic
305C22C13×B(4,𝔽2)11yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—42no—
310C4—42no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4—81no—
316C4—81no—
317C4—81no—
318C2—21no—
319C2—21no—
320C2C13×#160311yescharacteristic
321C2C13×#220011yescharacteristic
322C2C13×#220511yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC23×C13#120
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
62. #12240C13direct (N × H)
264. C13#12240direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27922
C13×#20602
C13×#16112
C13×#16052
C13×#13542
C13×#13462
C13×#13252
#1224013