Finite Group Databasebeta

← C13×#7718 #15694057

Subgroups — C13×#7718 #15694057

Order 3328.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2854C211yesmaximal, characteristic
2C13×#1817C211yesmaximal, characteristic, complemented
3C13×#1817C211yesmaximal, characteristic, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C2×C13×C22⋊C8—21no—
10C2×C13×C22⋊C8—21no—
11C13×#390C411yescharacteristic
12C13×#390C2211yescharacteristic
13C13×#389C411yescharacteristic
14C13×#389C2211yescharacteristic
15C13×#388—21no—
16C13×#388—21no—
17C13×#386—21no—
18C13×#380C411yescharacteristic
19C13×#336—21no—
20C13×#336—21no—
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C22×C8×C13—22no—
29C22×C8×C13—22no—
30C13×#123—44no—
31C13×#121—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C42×C13—42no—
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×C42×C13C2311yescharacteristic
48C13×C22⋊C8—42no—
49C13×C22⋊C8—42no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53#7718C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—21no—
55C24×C13C22⋊C411yescharacteristic
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C2×C8×C13—42no—
81C2×C8×C13—42no—
82C2×C8×C13—42no—
83C2×C8×C13—42no—
84C2×C8×C13—42no—
85C2×C8×C13—42no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C42×C13—41no—
98C42×C13—41no—
99C42×C13—41no—
100C42×C13—41no—
101#2854C2×C1311yescharacteristic
102#1817C2×C1311yescharacteristic, complemented
103#1817C2×C1311yescharacteristic, complemented
104#1271C2×C1312yescomplemented
105#1270C2×C1312yescomplemented
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13#9912yes—
120C23×C13C2×C22⋊C411yescharacteristic
121D4×C13—82no—
122D4×C13—84no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—44no—
139C2×C4×C13—44no—
140C2×C4×C13—44no—
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#13112yes—
151C2×C4×C13#13512yes—
152C2×C4×C13AGL(1,ℤ/8)12yes—
153C8×C13—82no—
154C8×C13—82no—
155C2×#123—21no—
156C2×#121C4×C1311yescharacteristic
157C22×C42C22×C1311yescharacteristic
158C2×C22⋊C8—21no—
159C2×C22⋊C8—21no—
160#390C4×C1311yescharacteristic
161#390C22×C1311yescharacteristic
162#389C4×C1311yescharacteristic
163#389C22×C1311yescharacteristic
164#388—21no—
165#388—21no—
166#386—21no—
167#380C4×C1311yescharacteristic
168#336—21no—
169#336—21no—
170#336C22×C1312yes—
171#336C22×C1312yes—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#40811yescharacteristic
187C22×C13C2×#9911yescharacteristic
188C22×C13#41311yescharacteristic
189C22×C13#41611yescharacteristic
190C22×C13#41811yescharacteristic
191C22×C13#42111yescharacteristic
192C22×C13#42111yescharacteristic
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—22no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—81no—
200C4×C13—81no—
201C4×C13—81no—
202C22×D4—21no—
203C22×D4C2×C4×C1311yescharacteristic
204C23×C4C2×C4×C1311yescharacteristic
205C23×C4D4×C1311yescharacteristic
206C23×C4D4×C1311yescharacteristic
207C22×C8—22no—
208C22×C8—22no—
209#123—44no—
210#121—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C1311yescharacteristic
214C2×C4⋊C4C2×C4×C1311yescharacteristic
215C2×C4⋊C4C2×C4×C1311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—42no—
223C2×C42C2×C4×C1311yescharacteristic
224C2×C42D4×C1311yescharacteristic
225C2×C42D4×C1311yescharacteristic
226C2×C42C23×C1311yescharacteristic
227C22⋊C8—42no—
228C22⋊C8—42no—
229#95—21no—
230#95—21no—
231#95—21no—
232C2×C13—42no—
233C2×C13—161no—
234C2×C13#146811yescharacteristic
235C2×C13#148211yescharacteristic
236C2×C13#149611yescharacteristic
237C2×C13#151011yescharacteristic
238C2×C13#151611yescharacteristic
239C2×C13#153511yescharacteristic
240C2×C13#155311yescharacteristic
241C24—21no—
242C24C13×C22⋊C411yescharacteristic
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C13×C22⋊C411yescharacteristic
262C22×C4C13×C22⋊C411yescharacteristic
263C22×C4C13×C22⋊C411yescharacteristic
264C22×C4C22×C4×C1311yescharacteristic
265C22×C4C2×D4×C1311yescharacteristic
266C22×C4C2×D4×C1311yescharacteristic
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—41no—
288C13#771811yescharacteristic, direct product factor, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23C13×#9912yes—
303C23C2×C13×C22⋊C411yescharacteristic
304D4—82no—
305D4—84no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
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×C4C13×#13112yes—
334C2×C4C13×#13512yes—
335C2×C4C13×AGL(1,ℤ/8)12yes—
336C8—82no—
337C8—82no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22C13×#40811yescharacteristic
353C22C2×C13×#9911yescharacteristic
354C22C13×#41311yescharacteristic
355C22C13×#41611yescharacteristic
356C22C13×#41811yescharacteristic
357C22C13×#42111yescharacteristic
358C22C13×#42111yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—81no—
368C2—42no—
369C2—161no—
370C2C13×#146811yescharacteristic
371C2C13×#148211yescharacteristic
372C2C13×#149611yescharacteristic
373C2C13×#151011yescharacteristic
374C2C13×#151611yescharacteristic
375C2C13×#153511yescharacteristic
376C2C13×#155311yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1817C2semidirect
3. C13×#1817C2semidirect
4. C13×#1271C2semidirect
5. C13×#1270C2semidirect
53. #7718C13direct (N × H)
102. #1817C2×C13semidirect
103. #1817C2×C13semidirect
104. #1271C2×C13semidirect
105. #1270C2×C13semidirect
288. C13#7718direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28542
C13×#18172
C13×#12712
C13×#12702
#771813