Finite Group Databasebeta

← C13×#9728 #15696067

Subgroups — C13×#9728 #15696067

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3167C211yesmaximal, characteristic
2C4×C13×#108C211yesmaximal, characteristic, complemented
3C13×#1526C211yesmaximal, characteristic, complemented
4C13×#1525C211yesmaximal, characteristic
5C13×#1485C211yesmaximal, characteristic, complemented
6C13×#1484C211yesmaximal, characteristic
7C13×#1451C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C13×#498C411yescharacteristic
11C13×#492C411yescharacteristic
12C13×#487C411yescharacteristic
13C13×#486C411yescharacteristic
14C13×#465—21no—
15C13×#465—21no—
16C4×C13×SD16—21no—
17C4×C13×SD16—21no—
18C13×#431C2211yescharacteristic
19C2×C13×#108—21no—
20C4×C13×M16C2211yescharacteristic
21C4×C13×M16C2211yescharacteristic
22C4×C13×M16C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C13×#341—21no—
25C13×#330—22no—
26C13×#329—22no—
27C13×Q8⋊C8—22no—
28C13×D4⋊C8—22no—
29C13×#322—21no—
30C13×#322—21no—
31C2×C13×#41—21no—
32C2×C13×SD16—21no—
33C2×C13×SD16—21no—
34C2×C13×M16—21no—
35C2×C13×M16—21no—
36C2×C13×M16—21no—
37C22×C8×C13D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C13×C4⋊Q8C2×C411yescharacteristic
40C13×C4⋊Q8C2×C411yescharacteristic
41C13×C4⋊Q8C2×C411yescharacteristic
42C13×#127C2×C411yescharacteristic
43C13×#125—21no—
44C13×#124—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×#121—21no—
48C13×#121—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C13×#117—21no—
54C2×C42×C13C2311yescharacteristic
55C13×#108—24no—
56C13×#106—21no—
57C13×#106—21no—
58C13×C4⋊C8D412yes—
59C13×#103—21no—
60C13×#103—21no—
61C13×#102—21no—
62C13×#102—21no—
63C13×C22⋊C8—21no—
64C13×#97—21no—
65C13×#97—21no—
66C13×#97D412yes—
67C4×C8×C13—21no—
68C4×C8×C13—21no—
69C4×C8×C13—21no—
70C4×C8×C13—21no—
71C4×C8×C13C2×C411yescharacteristic
72C4×C8×C13C2×C411yescharacteristic
73C4×C8×C13D411yescharacteristic
74C4×C8×C13D411yescharacteristic
75#9728C1311yesmaximal, characteristic, direct product factor, Sylow
76C13×#41—82no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13#4111yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C13×SD16—42no—
89C13×SD16—42no—
90C13×M16—22no—
91C13×M16—22no—
92C13×M16—42no—
93C13×M16—41no—
94C13×M16—41no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13C22⋊C411yescharacteristic
102C2×C8×C13C22⋊C411yescharacteristic
103C2×C8×C13C22⋊C411yescharacteristic
104C2×C8×C13C22⋊C411yescharacteristic
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C42×C13—41no—
117C42×C13C22×C411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13C2×D411yescharacteristic
121#3167C2×C1311yescharacteristic
122C4×#108C2×C1311yescharacteristic, complemented
123#1526C2×C1311yescharacteristic, complemented
124#1525C2×C1311yescharacteristic
125#1485C2×C1311yescharacteristic, complemented
126#1484C2×C1311yescharacteristic
127#1451C2×C1311yescharacteristic, complemented
128C23×C13—41no—
129C23×C13#12411yescharacteristic
130Q8×C13—41no—
131Q8×C13—41no—
132Q8×C13—42no—
133Q8×C13—81no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—42no—
137D4×C13—81no—
138D4×C13—82no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—82no—
147C2×C4×C13C2×C22⋊C411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12711yescharacteristic
153C8×C13—21no—
154C8×C13—21no—
155C8×C13—21no—
156C8×C13—42no—
157C8×C13—42no—
158C8×C13—42no—
159C8×C13—42no—
160C8×C13#10412yes—
161#533C22×C1311yescharacteristic
162#532C22×C1311yescharacteristic
163#498C4×C1311yescharacteristic
164#492C4×C1311yescharacteristic
165#487C4×C1311yescharacteristic
166#486C4×C1311yescharacteristic
167#465—21no—
168#465—21no—
169C4×SD16—21no—
170C4×SD16—21no—
171#431C22×C1311yescharacteristic
172C2×#108—21no—
173C4×M16C22×C1311yescharacteristic
174C4×M16C22×C1311yescharacteristic
175C4×M16C22×C1311yescharacteristic
176C2×C4×C8C22×C1311yescharacteristic
177#341—21no—
178#330—22no—
179#329—22no—
180Q8⋊C8—22no—
181D4⋊C8—22no—
182#322—21no—
183#322—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13#39011yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13C2×#10411yescharacteristic
198C4×C13#42111yescharacteristic
199C4×C13#44412yes—
200C4×C13#47112yes—
201C2×#41—21no—
202C2×SD16—21no—
203C2×SD16—21no—
204C2×M16—21no—
205C2×M16—21no—
206C2×M16—21no—
207C22×C8D4×C1311yescharacteristic
208C22×C8D4×C1311yescharacteristic
209C4⋊Q8C2×C4×C1311yescharacteristic
210C4⋊Q8C2×C4×C1311yescharacteristic
211C4⋊Q8C2×C4×C1311yescharacteristic
212#127C2×C4×C1311yescharacteristic
213#125—21no—
214#124—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217#121—21no—
218#121—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×D4—21no—
222C4×D4—21no—
223#117—21no—
224C2×C42C23×C1311yescharacteristic
225#108—24no—
226#106—21no—
227#106—21no—
228C4⋊C8D4×C1312yes—
229#103—21no—
230#103—21no—
231#102—21no—
232#102—21no—
233C22⋊C8—21no—
234#97—21no—
235#97—21no—
236#97D4×C1312yes—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8—21no—
241C4×C8C2×C4×C1311yescharacteristic
242C4×C8C2×C4×C1311yescharacteristic
243C4×C8D4×C1311yescharacteristic
244C4×C8D4×C1311yescharacteristic
245C2×C13—41no—
246C2×C13—161no—
247C2×C13#197511yescharacteristic
248C2×C13#197711yescharacteristic
249C2×C13#198011yescharacteristic
250#41—82no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—41no—
259C22×C4C2×D4×C1311yescharacteristic
260C22×C4C13×#4111yescharacteristic
261C22×C4C13×#4111yescharacteristic
262SD16—42no—
263SD16—42no—
264M16—22no—
265M16—22no—
266M16—42no—
267M16—41no—
268M16—41no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8C13×C22⋊C411yescharacteristic
276C2×C8C13×C22⋊C411yescharacteristic
277C2×C8C13×C22⋊C411yescharacteristic
278C2×C8C13×C22⋊C411yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—41no—
291C42C22×C4×C1311yescharacteristic
292C42C2×D4×C1311yescharacteristic
293C42C2×D4×C1311yescharacteristic
294C42C2×D4×C1311yescharacteristic
295C13#972811yescharacteristic, direct product factor, Sylow
296C23—41no—
297C23C13×#12411yescharacteristic
298Q8—41no—
299Q8—41no—
300Q8—42no—
301Q8—81no—
302D4—41no—
303D4—41no—
304D4—42no—
305D4—81no—
306D4—82no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—82no—
315C2×C4C2×C13×C22⋊C411yescharacteristic
316C2×C4C4×D4×C1311yescharacteristic
317C2×C4C4×D4×C1311yescharacteristic
318C2×C4C13×#12111yescharacteristic
319C2×C4C13×#12111yescharacteristic
320C2×C4C13×#12711yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—42no—
325C8—42no—
326C8—42no—
327C8—42no—
328C8C13×#10412yes—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C13×#39011yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4C2×C13×#10411yescharacteristic
343C4C13×#42111yescharacteristic
344C4C13×#44412yes—
345C4C13×#47112yes—
346C2—41no—
347C2—161no—
348C2C13×#197511yescharacteristic
349C2C13×#197711yescharacteristic
350C2C13×#198011yescharacteristic
subgroupG/H
centerC2×C4×C13#121
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#390
prime radicalC13×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C13×#108C2semidirect
3. C13×#1526C2semidirect
5. C13×#1485C2semidirect
7. C13×#1451C2semidirect
75. #9728C13direct (N × H)
122. C4×#108C2×C13semidirect
123. #1526C2×C13semidirect
125. #1485C2×C13semidirect
127. #1451C2×C13semidirect
295. C13#9728direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31672
C4×C13×#1082
C13×#15262
C13×#15252
C13×#14852
C13×#14842
C13×#14512
#972813