Finite Group Databasebeta

← C13×#11854 #15698193

Subgroups — C13×#11854 #15698193

Order 3328.

412 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2583C211yesmaximal, characteristic
2C13×#1821C211yesmaximal, characteristic
3C2×C13×#324C211yesmaximal, characteristic
4C13×#1354C212yesmaximal, complemented
5C13×#1346C212yesmaximal, complemented
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#407—21no—
9C2×C13×C22⋊C8—21no—
10C13×#398C411yescharacteristic
11C13×#398C2211yescharacteristic
12C13×#395C411yescharacteristic
13C13×#395C2211yescharacteristic
14C13×#389—21no—
15C13×#389—21no—
16C13×#385—21no—
17C13×#385—21no—
18C4×C13×C22⋊C4C411yescharacteristic
19C13×#343—21no—
20C13×#343C2212yes—
21C13×#324—21no—
22C13×#324C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C2×C13×M16—22no—
28C22×C8×C13—41no—
29C13×C22⋊Q8—41no—
30C13×C22⋊Q8—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4—41no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C4⋊C4C2311yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C42×C13—21no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—41no—
48C13×C22⋊C8—41no—
49C13×C22⋊C8—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56#11854C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13C22⋊C411yescharacteristic
58C2×Q8×C13—41no—
59C2×Q8×C13—81no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—41no—
72C22×C4×C13—81no—
73C22×C4×C13—81no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C13×M16—42no—
81C13×M16—42no—
82C2×C8×C13—42no—
83C2×C8×C13—42no—
84C2×C8×C13—82no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—81no—
94C13×C4⋊C4—81no—
95C13×C22⋊C4—24no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C42×C13—81no—
99#2583C2×C1311yescharacteristic
100#1821C2×C1311yescharacteristic
101C2×#324C2×C1311yescharacteristic
102#1354C2×C1312yescomplemented
103#1346C2×C1312yescomplemented
104C23×C13—22no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13#9911yescharacteristic
109C23×C13#9911yescharacteristic
110C23×C13C2×C22⋊C411yescharacteristic
111Q8×C13—82no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
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—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13#13512yes—
144C8×C13—82no—
145C8×C13—82no—
146C2×C22⋊Q8C4×C1311yescharacteristic
147C22×C4⋊C4C22×C1311yescharacteristic
148#407—21no—
149C2×C22⋊C8—21no—
150#398C4×C1311yescharacteristic
151#398C22×C1311yescharacteristic
152#395C4×C1311yescharacteristic
153#395C22×C1311yescharacteristic
154#389—21no—
155#389—21no—
156#385—21no—
157#385—21no—
158C4×C22⋊C4C4×C1311yescharacteristic
159#343—21no—
160#343C22×C1312yes—
161#324—21no—
162#324C22×C1312yes—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13#35612yes—
173C22×C13C2×#9911yescharacteristic
174C22×C13#41611yescharacteristic
175C22×C13#42111yescharacteristic
176C4×C13—22no—
177C4×C13—42no—
178C4×C13—42no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—81no—
185C4×C13—81no—
186C22×Q8C2×C4×C1311yescharacteristic
187C23×C4C2×C4×C1311yescharacteristic
188C23×C4D4×C1311yescharacteristic
189C23×C4D4×C1311yescharacteristic
190C2×M16—22no—
191C22×C8—41no—
192C22⋊Q8—41no—
193C22⋊Q8—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4C2×C4×C1311yescharacteristic
202C2×C4⋊C4C2×C4×C1311yescharacteristic
203C2×C4⋊C4D4×C1311yescharacteristic
204C2×C4⋊C4D4×C1311yescharacteristic
205C2×C4⋊C4C23×C1311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42—21no—
209C22⋊C8—22no—
210C22⋊C8—41no—
211C22⋊C8—41no—
212C22⋊C8—41no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95C2×C4×C1311yescharacteristic
218#95C2×C4×C1311yescharacteristic
219C2×C13—21no—
220C2×C13—21no—
221C2×C13—22no—
222C2×C13—41no—
223C2×C13#151611yescharacteristic
224C2×C13#212111yescharacteristic
225C2×C13C2×#35611yescharacteristic
226C24C13×C22⋊C411yescharacteristic
227C2×Q8—41no—
228C2×Q8—81no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4C13×C22⋊C411yescharacteristic
244C22×C4C13×C22⋊C411yescharacteristic
245C22×C4C13×C22⋊C411yescharacteristic
246C22×C4C22×C4×C1311yescharacteristic
247C22×C4C2×D4×C1311yescharacteristic
248C22×C4C2×D4×C1311yescharacteristic
249M16—42no—
250M16—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—82no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C22⋊C4—24no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C42—81no—
268C13#1185411yescharacteristic, direct product factor, Sylow
269C23—21no—
270C23—21no—
271C23—22no—
272C23—41no—
273C23C13×#9911yescharacteristic
274C23C13×#9911yescharacteristic
275C23C2×C13×C22⋊C411yescharacteristic
276Q8—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4C13×#13512yes—
309C8—82no—
310C8—82no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22C13×#35612yes—
321C22C2×C13×#9911yescharacteristic
322C22C13×#41611yescharacteristic
323C22C13×#42111yescharacteristic
324C4—22no—
325C4—42no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—41no—
338C2C13×#151611yescharacteristic
339C2C13×#212111yescharacteristic
340C2C2×C13×#35611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1354C2semidirect
5. C13×#1346C2semidirect
56. #11854C13direct (N × H)
102. #1354C2×C13semidirect
103. #1346C2×C13semidirect
268. C13#11854direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25832
C13×#18212
C2×C13×#3242
C13×#13542
C13×#13462
#1185413