Finite Group Databasebeta

← C13×#13228 #15699567

Subgroups — C13×#13228 #15699567

Order 3328.

490 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×#2545C211yesmaximal, characteristic
2C2×C13×#356C212yesmaximal, complemented
3C2×C13×#355C212yesmaximal
4C13×#1801C211yesmaximal, characteristic, complemented
5C4×C13×#101C211yesmaximal, characteristic, complemented
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#124C411yescharacteristic
8C2×C13×#124C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C13×#423—21no—
11C2×C13×#101C2212yes—
12C2×C13×#101C2212yes—
13C4×C13×M16—21no—
14C13×#396—21no—
15C13×#396—21no—
16C13×#391C411yescharacteristic
17C13×#390C411yescharacteristic
18C13×#388—21no—
19C13×#388—21no—
20C4×C13×C4⋊C4C411yescharacteristic
21C13×#356—24no—
22C13×#355—24no—
23C13×#343—21no—
24C13×#343—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×Q8×C13C2311yescharacteristic
27C22×D4×C13C2×C411yescharacteristic
28C2×C13×M16—22no—
29C2×C13×M16—22no—
30C13×C4⋊Q8—22no—
31C13×C4⋊Q8—22no—
32C13×#124—22no—
33C13×#124—22no—
34C13×#124—41no—
35C13×#124—41no—
36C4×Q8×C13—41no—
37C4×Q8×C13—41no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C42×C13C2×C411yescharacteristic
51C2×C42×C13C2×C411yescharacteristic
52C2×C42×C13C2×C411yescharacteristic
53C2×C42×C13D411yescharacteristic
54C2×C42×C13D411yescharacteristic
55C13×C4⋊C8—41no—
56C13×C4⋊C8—41no—
57C13×#101—22no—
58C13×#101—22no—
59C13×#101—22no—
60C13×#101D414yes—
61C13×#97—41no—
62C4×C8×C13—41no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95—21no—
66#13228C1311yesmaximal, characteristic, direct product factor, Sylow
67C24×C13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13C2×D412yes—
74C2×Q8×C13#4112yes—
75C2×D4×C13—22no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22×C411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C13×M16—24no—
89C13×M16—42no—
90C13×M16—42no—
91C13×M16—42no—
92C2×C8×C13—42no—
93C2×C8×C13—42no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—42no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C42×C13—21no—
110C42×C13—21no—
111C42×C13—21no—
112C42×C13—21no—
113C42×C13—21no—
114C42×C13—21no—
115C42×C13—22no—
116C42×C13—22no—
117#2545C2×C1311yescharacteristic
118C2×#356C2×C1312yescomplemented
119C2×#355C2×C1312yes—
120#1801C2×C1311yescharacteristic, complemented
121C4×#101C2×C1311yescharacteristic, complemented
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13C2×C22⋊C411yescharacteristic
130Q8×C13—42no—
131Q8×C13—42no—
132Q8×C13—82no—
133D4×C13—82no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
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—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13#9911yescharacteristic
157C2×C4×C13#9911yescharacteristic
158C2×C4×C13C4×D412yes—
159C2×C4×C13#12112yes—
160C2×C4×C13#12411yescharacteristic
161C2×C4×C13#12711yescharacteristic
162C8×C13—44no—
163C8×C13—82no—
164C2×C4⋊Q8C22×C1311yescharacteristic
165C2×#124C4×C1311yescharacteristic
166C2×#124C22×C1311yescharacteristic
167C2×C4×Q8C22×C1311yescharacteristic
168#423—21no—
169C2×#101C22×C1312yes—
170C2×#101C22×C1312yes—
171C4×M16—21no—
172#396—21no—
173#396—21no—
174#391C4×C1311yescharacteristic
175#390C4×C1311yescharacteristic
176#388—21no—
177#388—21no—
178C4×C4⋊C4C4×C1311yescharacteristic
179#356—24no—
180#355—24no—
181#343—21no—
182#343—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13#39011yescharacteristic
193C22×C13C2×#9911yescharacteristic
194C22×C13#41011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—21no—
199C4×C13—22no—
200C4×C13—21no—
201C4×C13—42no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—81no—
206C4×C13—81no—
207C22×Q8C2×C4×C1311yescharacteristic
208C22×Q8C23×C1311yescharacteristic
209C22×D4C2×C4×C1311yescharacteristic
210C2×M16—22no—
211C2×M16—22no—
212C4⋊Q8—22no—
213C4⋊Q8—22no—
214#124—22no—
215#124—22no—
216#124—41no—
217#124—41no—
218C4×Q8—41no—
219C4×Q8—41no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×C4×C1311yescharacteristic
224C2×C4⋊C4D4×C1311yescharacteristic
225C2×C4⋊C4D4×C1311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C42C2×C4×C1311yescharacteristic
233C2×C42C2×C4×C1311yescharacteristic
234C2×C42C2×C4×C1311yescharacteristic
235C2×C42D4×C1311yescharacteristic
236C2×C42D4×C1311yescharacteristic
237C4⋊C8—41no—
238C4⋊C8—41no—
239#101—22no—
240#101—22no—
241#101—22no—
242#101D4×C1314yes—
243#97—41no—
244C4×C8—41no—
245#95—21no—
246#95—21no—
247#95—21no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—161no—
251C2×C13#196411yescharacteristic
252C2×C13#213211yescharacteristic
253C2×C13#213311yescharacteristic
254C24—21no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8C2×D4×C1312yes—
261C2×Q8C13×#4112yes—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4C13×C22⋊C411yescharacteristic
269C22×C4C13×C22⋊C411yescharacteristic
270C22×C4C13×C22⋊C411yescharacteristic
271C22×C4C13×C22⋊C411yescharacteristic
272C22×C4C22×C4×C1311yescharacteristic
273C22×C4C2×D4×C1311yescharacteristic
274C22×C4C2×D4×C1311yescharacteristic
275M16—24no—
276M16—42no—
277M16—42no—
278M16—42no—
279C2×C8—42no—
280C2×C8—42no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—22no—
303C42—22no—
304C13#1322811yescharacteristic, direct product factor, Sylow
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23C2×C13×C22⋊C411yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—82no—
316D4—82no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4C13×#9911yescharacteristic
340C2×C4C13×#9911yescharacteristic
341C2×C4C4×D4×C1312yes—
342C2×C4C13×#12112yes—
343C2×C4C13×#12411yescharacteristic
344C2×C4C13×#12711yescharacteristic
345C8—44no—
346C8—82no—
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C13×#39011yescharacteristic
357C22C2×C13×#9911yescharacteristic
358C22C13×#41011yescharacteristic
359C4—21no—
360C4—21no—
361C4—22no—
362C4—21no—
363C4—22no—
364C4—21no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C2—21no—
372C2—21no—
373C2—161no—
374C2C13×#196411yescharacteristic
375C2C13×#213211yescharacteristic
376C2C13×#213311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#356C2semidirect
4. C13×#1801C2semidirect
5. C4×C13×#101C2semidirect
66. #13228C13direct (N × H)
118. C2×#356C2×C13semidirect
120. #1801C2×C13semidirect
121. C4×#101C2×C13semidirect
304. C13#13228direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25452
C2×C13×#3562
C2×C13×#3552
C13×#18012
C4×C13×#1012
#1322813