Finite Group Databasebeta

← C13×#11867 #15698206

Subgroups — C13×#11867 #15698206

Order 3328.

376 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3060C211yesmaximal, characteristic
2C13×#2115C211yesmaximal, characteristic, complemented
3C13×#1812C211yesmaximal, characteristic, complemented
4C13×#1340C212yesmaximal, complemented
5C13×#1339C212yesmaximal, complemented
6C2×C13×#135C411yescharacteristic, complemented
7C2×C13×#131C2211yescharacteristic
8C13×#537—21no—
9C2×C13×M32—21no—
10C13×#470C411yescharacteristic, complemented
11C13×#470C2211yescharacteristic
12C13×#469C411yescharacteristic, complemented
13C13×#469C2211yescharacteristic
14C13×#465—21no—
15C13×#465—21no—
16C13×#427—21no—
17C2×C13×#106C411yescharacteristic, complemented
18C13×#417—21no—
19C13×#410—21no—
20C13×#349—21no—
21C13×#349C2212yes—
22C13×H(3,ℤ/4)C2212yes—
23C2×C13×#41—21no—
24C2×C13×#41D411yescharacteristic
25C13×#135—41no—
26C13×#135—41no—
27C2×C13×Q16C2×C411yescharacteristic
28C2×C13×SD16—21no—
29C2×C13×D8C2×C411yescharacteristic
30C13×#131—41no—
31C13×#131—41no—
32C2×C13×M16C2×C411yescharacteristic
33C2×C13×M16D411yescharacteristic
34C2×C13×M16C2311yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13D411yescharacteristic
37C22×C8×C13D411yescharacteristic
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—41no—
41C13×#121—21no—
42C13×#121—21no—
43C13×#121—41no—
44C13×#121—41no—
45C13×#121—41no—
46C13×#117—22no—
47C2×C13×C4⋊C4—21no—
48C13×M32—22no—
49C13×M32—41no—
50C2×C13×C16—41no—
51C13×#107—41no—
52C13×#106—21no—
53C13×#106—41no—
54C13×#106C2×C411yescharacteristic
55C13×#106C2×C411yescharacteristic
56C13×#103—21no—
57C13×#103—21no—
58C13×#102—21no—
59C13×#102—21no—
60C13×#99—41no—
61C13×#99—41no—
62#11867C1311yesmaximal, characteristic, direct product factor, Sylow
63C13×#41—41no—
64C13×#41—41no—
65C13×#41—42no—
66C13×#41—42no—
67C2×Q8×C13—21no—
68C2×Q8×C13SD1611yescharacteristic
69C2×D4×C13—21no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13D811yescharacteristic
74C2×D4×C13D811yescharacteristic
75C2×D4×C13SD1611yescharacteristic
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C13×Q16—41no—
82C13×SD16—41no—
83C13×SD16—41no—
84C13×D8—41no—
85C13×M16—41no—
86C13×M16—41no—
87C13×M16—41no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13C22⋊C411yescharacteristic
95C2×C8×C13C22⋊C411yescharacteristic
96C2×C8×C13C22×C411yescharacteristic
97C2×C8×C13C2×D411yescharacteristic
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—42no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—42no—
109C42×C13—42no—
110C13×C16—42no—
111#3060C2×C1311yescharacteristic
112#2115C2×C1311yescharacteristic, complemented
113#1812C2×C1311yescharacteristic, complemented
114#1340C2×C1312yescomplemented
115#1339C2×C1312yescomplemented
116C23×C13—41no—
117C23×C13#10211yescharacteristic
118C23×C13#10211yescharacteristic
119C23×C13C2×D811yescharacteristic
120Q8×C13—41no—
121Q8×C13—41no—
122Q8×C13—41no—
123D4×C13—41no—
124D4×C13—41no—
125D4×C13—41no—
126D4×C13—41no—
127D4×C13—41no—
128D4×C13—82no—
129D4×C13—161no—
130D4×C13—161no—
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—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—82no—
141C2×C4×C13—82no—
142C2×C4×C13—161no—
143C2×C4×C13#10211yescharacteristic
144C2×C4×C13#10211yescharacteristic
145C2×C4×C13C2×C22⋊C411yescharacteristic
146C2×C4×C13C2×SD1611yescharacteristic
147C8×C13—21no—
148C8×C13—21no—
149C8×C13—21no—
150C8×C13#9911yescharacteristic
151C8×C13#9911yescharacteristic
152C2×#135C4×C1311yescharacteristic, complemented
153C2×#131C22×C1311yescharacteristic
154#537—21no—
155C2×M32—21no—
156#470C4×C1311yescharacteristic, complemented
157#470C22×C1311yescharacteristic
158#469C4×C1311yescharacteristic, complemented
159#469C22×C1311yescharacteristic
160#465—21no—
161#465—21no—
162#427—21no—
163C2×#106C4×C1311yescharacteristic, complemented
164#417—21no—
165#410—21no—
166#349—21no—
167#349C22×C1312yes—
168H(3,ℤ/4)C22×C1312yes—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13C2×#10211yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—81no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13—162no—
186C4×C13C2×#9911yescharacteristic
187C4×C13#42111yescharacteristic
188C2×#41—21no—
189C2×#41D4×C1311yescharacteristic
190#135—41no—
191#135—41no—
192C2×Q16C2×C4×C1311yescharacteristic
193C2×SD16—21no—
194C2×D8C2×C4×C1311yescharacteristic
195#131—41no—
196#131—41no—
197C2×M16C2×C4×C1311yescharacteristic
198C2×M16D4×C1311yescharacteristic
199C2×M16C23×C1311yescharacteristic
200C22×C8C2×C4×C1311yescharacteristic
201C22×C8D4×C1311yescharacteristic
202C22×C8D4×C1311yescharacteristic
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C22⋊Q8—41no—
206#121—21no—
207#121—21no—
208#121—41no—
209#121—41no—
210#121—41no—
211#117—22no—
212C2×C4⋊C4—21no—
213M32—22no—
214M32—41no—
215C2×C16—41no—
216#107—41no—
217#106—21no—
218#106—41no—
219#106C2×C4×C1311yescharacteristic
220#106C2×C4×C1311yescharacteristic
221#103—21no—
222#103—21no—
223#102—21no—
224#102—21no—
225#99—41no—
226#99—41no—
227C2×C13—21no—
228C2×C13—41no—
229C2×C13—41no—
230C2×C13—41no—
231C2×C13—161no—
232C2×C13#151911yescharacteristic
233#41—41no—
234#41—41no—
235#41—42no—
236#41—42no—
237C2×Q8—21no—
238C2×Q8C13×SD1611yescharacteristic
239C2×D4—21no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4C13×D811yescharacteristic
244C2×D4C13×D811yescharacteristic
245C2×D4C13×SD1611yescharacteristic
246C22×C4—41no—
247C22×C4—41no—
248C22×C4C13×C22⋊C411yescharacteristic
249C22×C4C13×C22⋊C411yescharacteristic
250C22×C4C2×D4×C1311yescharacteristic
251Q16—41no—
252SD16—41no—
253SD16—41no—
254D8—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8C13×C22⋊C411yescharacteristic
265C2×C8C13×C22⋊C411yescharacteristic
266C2×C8C22×C4×C1311yescharacteristic
267C2×C8C2×D4×C1311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—42no—
279C42—42no—
280C16—42no—
281C13#1186711yescharacteristic, direct product factor, Sylow
282C23—41no—
283C23C13×#10211yescharacteristic
284C23C13×#10211yescharacteristic
285C23C2×C13×D811yescharacteristic
286Q8—41no—
287Q8—41no—
288Q8—41no—
289D4—41no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—41no—
294D4—82no—
295D4—161no—
296D4—161no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—161no—
309C2×C4C13×#10211yescharacteristic
310C2×C4C13×#10211yescharacteristic
311C2×C4C2×C13×C22⋊C411yescharacteristic
312C2×C4C2×C13×SD1611yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8C13×#9911yescharacteristic
317C8C13×#9911yescharacteristic
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×C13×#10211yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—162no—
335C4C2×C13×#9911yescharacteristic
336C4C13×#42111yescharacteristic
337C2—21no—
338C2—41no—
339C2—41no—
340C2—41no—
341C2—161no—
342C2C13×#151911yescharacteristic
subgroupG/H
center, socleC2×C13#1519
commutatorC2×C8C22×C4×C13
Frattini, cosocleC2×M16C23×C13
prime radicalC13×#3060C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2115C2semidirect
3. C13×#1812C2semidirect
4. C13×#1340C2semidirect
5. C13×#1339C2semidirect
6. C2×C13×#135C4semidirect
10. C13×#470C4semidirect
12. C13×#469C4semidirect
17. C2×C13×#106C4semidirect
62. #11867C13direct (N × H)
112. #2115C2×C13semidirect
113. #1812C2×C13semidirect
114. #1340C2×C13semidirect
115. #1339C2×C13semidirect
152. C2×#135C4×C13semidirect
156. #470C4×C13semidirect
158. #469C4×C13semidirect
163. C2×#106C4×C13semidirect
281. C13#11867direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30602
C13×#21152
C13×#18122
C13×#13402
C13×#13392
#1186713