Finite Group Databasebeta

← C13×#10328 #15696667

Subgroups — C13×#10328 #15696667

Order 3328.

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3192C211yesmaximal, characteristic
2C13×#2504C211yesmaximal, characteristic, complemented
3C13×#2501C211yesmaximal, characteristic, complemented
4C13×#1821C211yesmaximal, characteristic, complemented
5C13×#1507C211yesmaximal, characteristic, complemented
6C13×#1507C211yesmaximal, characteristic, complemented
7C13×#1297C211yesmaximal, characteristic, complemented
8C2×C13×#123—22no—
9C2×C13×#121C2211yescharacteristic
10C2×C13×#121C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C13×#481—21no—
13C13×#481—21no—
14C13×#469—22no—
15C13×#447—21no—
16C13×#447—21no—
17C13×#407C2211yescharacteristic
18C13×#407C2211yescharacteristic
19C13×#399—22no—
20C13×#397—22no—
21C13×#390—21no—
22C13×#390—21no—
23C13×#386—22no—
24C13×#384—21no—
25C13×#382—21no—
26C4×C13×C22⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4C2211yescharacteristic
28C13×#343—22no—
29C13×#327—22no—
30C13×#327—22no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13D411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C23×C4×C13D412yes—
36C23×C4×C13C2311yescharacteristic
37C2×C13×D8—22no—
38C2×C13×M16—21no—
39C2×C13×M16D412yes—
40C13×#123—48no—
41C13×#121—21no—
42C13×#121—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C13×#121—21no—
48C13×#121—21no—
49C2×C13×C4⋊C4—24no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—24no—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C13×#106—22no—
67C13×#102—22no—
68C13×#102—22no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×#95—24no—
74C13×#95D412yes—
75C13×#95D412yes—
76#10328C1311yesmaximal, characteristic, direct product factor, Sylow
77C24×C13—21no—
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—42no—
85C2×D4×C13—42no—
86C2×D4×C13—44no—
87C2×D4×C13—44no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13—42no—
100C22×C4×C13—44no—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C13×D8—82no—
108C13×M16—42no—
109C13×M16—42no—
110C2×C8×C13—22no—
111C2×C8×C13—41no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—48no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C22⋊C4—24no—
122C13×C22⋊C4—48no—
123C13×C22⋊C4—42no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—84no—
129C42×C13—42no—
130C42×C13—42no—
131#3192C2×C1311yescharacteristic
132#2504C2×C1311yescharacteristic, complemented
133#2501C2×C1311yescharacteristic, complemented
134#1821C2×C1311yescharacteristic, complemented
135#1507C2×C1311yescharacteristic, complemented
136#1507C2×C1311yescharacteristic, complemented
137#1297C2×C1311yescharacteristic, complemented
138C23×C13—22no—
139C23×C13—22no—
140C23×C13—41no—
141C23×C13—42no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—42no—
148C23×C13—42no—
149C23×C13#12011yescharacteristic
150C23×C13#12011yescharacteristic
151C23×C13#12111yescharacteristic
152D4×C13—42no—
153D4×C13—42no—
154D4×C13—81no—
155D4×C13—81no—
156D4×C13—82no—
157D4×C13—82no—
158D4×C13—82no—
159D4×C13—82no—
160C2×C4×C13—22no—
161C2×C4×C13—22no—
162C2×C4×C13—22no—
163C2×C4×C13—24no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13—44no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—44no—
179C2×C4×C13—82no—
180C2×C4×C13#12011yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12711yescharacteristic
184C8×C13—42no—
185C8×C13—81no—
186C2×#123—22no—
187C2×#121C22×C1311yescharacteristic
188C2×#121C22×C1311yescharacteristic
189C22×C4⋊C4C22×C1311yescharacteristic
190#481—21no—
191#481—21no—
192#469—22no—
193#447—21no—
194#447—21no—
195#407C22×C1311yescharacteristic
196#407C22×C1311yescharacteristic
197#399—22no—
198#397—22no—
199#390—21no—
200#390—21no—
201#386—22no—
202#384—21no—
203#382—21no—
204C4×C22⋊C4C22×C1311yescharacteristic
205C4×C22⋊C4C22×C1311yescharacteristic
206#343—22no—
207#327—22no—
208#327—22no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—44no—
217C22×C13—84no—
218C22×C13—84no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13#39211yescharacteristic
226C22×C13#45312yes—
227C22×C13#45412yes—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—44no—
232C4×C13—82no—
233C4×C13—82no—
234C4×C13—81no—
235C4×C13—81no—
236C4×C13#45812yes—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4D4×C1311yescharacteristic
240C22×D4D4×C1311yescharacteristic
241C23×C4D4×C1312yes—
242C23×C4C23×C1311yescharacteristic
243C2×D8—22no—
244C2×M16—21no—
245C2×M16D4×C1312yes—
246#123—48no—
247#121—21no—
248#121—21no—
249#121—21no—
250#121—21no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4D4×C1311yescharacteristic
263C2×C4⋊C4D4×C1311yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—24no—
270C2×C42—21no—
271C2×C42—21no—
272#106—22no—
273#102—22no—
274#102—22no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—24no—
280#95D4×C1312yes—
281#95D4×C1312yes—
282C2×C13—22no—
283C2×C13—22no—
284C2×C13—41no—
285C2×C13—161no—
286C2×C13—161no—
287C2×C13#200211yescharacteristic
288C2×C13#200311yescharacteristic
289C2×C13#202211yescharacteristic
290C24—21no—
291C24—21no—
292C24C2×D4×C1311yescharacteristic
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—44no—
300C2×D4—44no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4C2×D4×C1311yescharacteristic
315C22×C4C2×D4×C1311yescharacteristic
316C22×C4C2×D4×C1311yescharacteristic
317C22×C4C2×D4×C1311yescharacteristic
318C22×C4C2×D4×C1311yescharacteristic
319C22×C4C13×#4111yescharacteristic
320D8—82no—
321M16—42no—
322M16—42no—
323C2×C8—22no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—48no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C22⋊C4—24no—
335C22⋊C4—48no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—84no—
342C42—42no—
343C42—42no—
344C13#1032811yescharacteristic, direct product factor, Sylow
345C23—22no—
346C23—22no—
347C23—41no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—42no—
355C23—42no—
356C23C13×#12011yescharacteristic
357C23C13×#12011yescharacteristic
358C23C13×#12111yescharacteristic
359D4—42no—
360D4—42no—
361D4—81no—
362D4—81no—
363D4—82no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—82no—
387C2×C4C13×#12011yescharacteristic
388C2×C4C13×#12111yescharacteristic
389C2×C4C13×#12111yescharacteristic
390C2×C4C13×#12711yescharacteristic
391C8—42no—
392C8—81no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—44no—
401C22—84no—
402C22—84no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22C13×#39211yescharacteristic
410C22C13×#45312yes—
411C22C13×#45412yes—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—44no—
416C4—82no—
417C4—82no—
418C4—81no—
419C4—81no—
420C4C13×#45812yes—
421C2—22no—
422C2—22no—
423C2—41no—
424C2—161no—
425C2—161no—
426C2C13×#200211yescharacteristic
427C2C13×#200311yescharacteristic
428C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#3192C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2504C2semidirect
3. C13×#2501C2semidirect
4. C13×#1821C2semidirect
5. C13×#1507C2semidirect
6. C13×#1507C2semidirect
7. C13×#1297C2semidirect
76. #10328C13direct (N × H)
132. #2504C2×C13semidirect
133. #2501C2×C13semidirect
134. #1821C2×C13semidirect
135. #1507C2×C13semidirect
136. #1507C2×C13semidirect
137. #1297C2×C13semidirect
344. C13#10328direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31922
C13×#25042
C13×#25012
C13×#18212
C13×#15072
C13×#12972
#1032813