Finite Group Databasebeta

← C13×#12176 #15698515

Subgroups — C13×#12176 #15698515

Order 3328.

486 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2677C211yesmaximal, characteristic, complemented
2C13×#2044C211yesmaximal, characteristic
3C13×#1613C211yesmaximal, characteristic
4C13×#1601C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1351C211yesmaximal, characteristic, complemented
7C13×#1326C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C2×C13×C4⋊Q8—21no—
10C2×C13×C22⋊Q8—21no—
11C13×#481—21no—
12C13×#448—21no—
13C2×C13×#99—21no—
14C13×#399C2211yescharacteristic
15C13×#398—21no—
16C13×#395—21no—
17C13×#393C2211yescharacteristic
18C13×#388—21no—
19C13×#387—21no—
20C13×#386—21no—
21C13×#385C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13—21no—
28C22×Q8×C13D411yescharacteristic
29C22×D4×C13—21no—
30C23×C4×C13D411yescharacteristic
31C2×C13×SD16—41no—
32C13×C4⋊Q8—44no—
33C13×#123—41no—
34C13×C22⋊Q8—44no—
35C13×#121—21no—
36C13×#121—21no—
37C13×#120—41no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—41no—
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C13×C22⋊C4C2311yescharacteristic
51C2×C42×C13—21no—
52C13×#106—41no—
53C13×#103—41no—
54C13×#102—41no—
55C13×#99—42no—
56C13×C22⋊C8—21no—
57C13×C22⋊C8—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—41no—
63C13×#95D411yescharacteristic
64C13×#95D411yescharacteristic
65#12176C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—21no—
67C24×C13C2×D411yescharacteristic
68C2×Q8×C13—42no—
69C2×Q8×C13—42no—
70C2×Q8×C13—42no—
71C2×Q8×C13—41no—
72C2×Q8×C13—81no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—42no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C13×SD16—82no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—42no—
101C13×C4⋊C4—42no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—42no—
104C13×C4⋊C4—42no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—82no—
114C13×C22⋊C4SD1612yescomplemented
115C42×C13—42no—
116#2677C2×C1311yescharacteristic, complemented
117#2044C2×C1311yescharacteristic
118#1613C2×C1311yescharacteristic
119#1601C2×C1311yescharacteristic
120#1352C2×C1311yescharacteristic, complemented
121#1351C2×C1311yescharacteristic, complemented
122#1326C2×C1311yescharacteristic, complemented
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—81no—
131C23×C13—81no—
132C23×C13#12011yescharacteristic
133C23×C13C2×SD1611yescharacteristic
134C23×C13#13711yescharacteristic
135Q8×C13—42no—
136Q8×C13—81no—
137Q8×C13—84no—
138D4×C13—81no—
139D4×C13—81no—
140D4×C13—81no—
141D4×C13—81no—
142D4×C13—81no—
143D4×C13—81no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
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—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C8×C13—81no—
175C8×C13—81no—
176#534C22×C1311yescharacteristic
177C2×C4⋊Q8—21no—
178C2×C22⋊Q8—21no—
179#481—21no—
180#448—21no—
181C2×#99—21no—
182#399C22×C1311yescharacteristic
183#398—21no—
184#395—21no—
185#393C22×C1311yescharacteristic
186#388—21no—
187#387—21no—
188#386—21no—
189#385C22×C1311yescharacteristic
190#342C22×C1311yescharacteristic
191#327—21no—
192#327—21no—
193#323C22×C1311yescharacteristic
194#323C22×C1311yescharacteristic
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—81no—
204C22×C13—82no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—161no—
209C22×C13#44811yescharacteristic
210C22×C13#45411yescharacteristic
211C22×C13B(4,𝔽2)11yescharacteristic
212C4×C13—42no—
213C4×C13—42no—
214C4×C13—41no—
215C4×C13—42no—
216C4×C13—42no—
217C4×C13—41no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13—81no—
221C4×C13—161no—
222C22×Q8—21no—
223C22×Q8D4×C1311yescharacteristic
224C22×D4—21no—
225C23×C4D4×C1311yescharacteristic
226C2×SD16—41no—
227C4⋊Q8—44no—
228#123—41no—
229C22⋊Q8—44no—
230#121—21no—
231#121—21no—
232#120—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C1311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—41no—
244C2×C22⋊C4D4×C1311yescharacteristic
245C2×C22⋊C4C23×C1311yescharacteristic
246C2×C42—21no—
247#106—41no—
248#103—41no—
249#102—41no—
250#99—42no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—41no—
258#95D4×C1311yescharacteristic
259#95D4×C1311yescharacteristic
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—41no—
263C2×C13—41no—
264C2×C13—161no—
265C2×C13#159911yescharacteristic
266C2×C13#219611yescharacteristic
267C2×C13#220111yescharacteristic
268C24—21no—
269C24C2×D4×C1311yescharacteristic
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8—81no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C2×D4×C1311yescharacteristic
294C22×C4C2×D4×C1311yescharacteristic
295SD16—82no—
296C2×C8—41no—
297C2×C8—41no—
298C4⋊C4—24no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C22⋊C4—21no—
308C22⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—82no—
316C22⋊C4C13×SD1612yescomplemented
317C42—42no—
318C13#1217611yescharacteristic, direct product factor, Sylow
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—81no—
327C23—81no—
328C23C13×#12011yescharacteristic
329C23C2×C13×SD1611yescharacteristic
330C23C13×#13711yescharacteristic
331Q8—42no—
332Q8—81no—
333Q8—84no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339D4—81no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C8—81no—
371C8—81no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—82no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—161no—
386C22C13×#44811yescharacteristic
387C22C13×#45411yescharacteristic
388C22C13×B(4,𝔽2)11yescharacteristic
389C4—42no—
390C4—42no—
391C4—41no—
392C4—42no—
393C4—42no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—161no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—161no—
404C2C13×#159911yescharacteristic
405C2C13×#219611yescharacteristic
406C2C13×#220111yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2677C2semidirect
5. C13×#1352C2semidirect
6. C13×#1351C2semidirect
7. C13×#1326C2semidirect
65. #12176C13direct (N × H)
114. C13×C22⋊C4SD16semidirect
116. #2677C2×C13semidirect
120. #1352C2×C13semidirect
121. #1351C2×C13semidirect
122. #1326C2×C13semidirect
316. C22⋊C4C13×SD16semidirect
318. C13#12176direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26772
C13×#20442
C13×#16132
C13×#16012
C13×#13522
C13×#13512
C13×#13262
#1217613