Finite Group Databasebeta

← C13×#10332 #15696671

Subgroups — C13×#10332 #15696671

Order 3328.

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

normal subgroups only

This group has 600 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×#3193C211yesmaximal, characteristic
2C13×#2504C211yesmaximal, characteristic
3C13×#2503C211yesmaximal, characteristic, complemented
4C13×#1821C211yesmaximal, characteristic, complemented
5C13×#1508C211yesmaximal, characteristic, complemented
6C13×#1507C211yesmaximal, characteristic
7C13×#1297C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C13×#484—21no—
12C13×#480—21no—
13C13×#468—22no—
14C13×#450—21no—
15C13×#448—21no—
16C13×#407C2211yescharacteristic
17C13×#407C2211yescharacteristic
18C13×#400—22no—
19C13×#397—22no—
20C13×#391—21no—
21C13×#390—21no—
22C13×#386—22no—
23C13×#382—21no—
24C13×#382—21no—
25C13×#381—22no—
26C4×C13×C22⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4C2211yescharacteristic
28C13×#343—22no—
29C13×#328—22no—
30C13×#327—22no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13D411yescharacteristic
34C23×C4×C13D412yes—
35C23×C4×C13C2311yescharacteristic
36C2×C13×SD16—22no—
37C2×C13×M16—21no—
38C2×C13×M16D412yes—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—24no—
61C2×C42×C13—21no—
62C2×C42×C13—21no—
63C13×#107—22no—
64C13×#103—22no—
65C13×#102—22no—
66C13×C22⋊C8—21no—
67C13×C22⋊C8—21no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—21no—
70C13×#95—24no—
71C13×#95—24no—
72C13×#95—24no—
73C13×#95D412yes—
74C13×#95D412yes—
75#10332C1311yesmaximal, characteristic, direct product factor, Sylow
76C24×C13—21no—
77C24×C13C2×D411yescharacteristic
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—42no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—42no—
84C2×D4×C13—44no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C22×C4×C13—22no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—42no—
96C22×C4×C13—44no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C13×SD16—82no—
104C13×M16—42no—
105C13×M16—42no—
106C2×C8×C13—22no—
107C2×C8×C13—41no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C22⋊C4—42no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—84no—
125C42×C13—42no—
126C42×C13—42no—
127#3193C2×C1311yescharacteristic
128#2504C2×C1311yescharacteristic
129#2503C2×C1311yescharacteristic, complemented
130#1821C2×C1311yescharacteristic, complemented
131#1508C2×C1311yescharacteristic, complemented
132#1507C2×C1311yescharacteristic
133#1297C2×C1311yescharacteristic, complemented
134C23×C13—22no—
135C23×C13—22no—
136C23×C13—41no—
137C23×C13—42no—
138C23×C13—42no—
139C23×C13—41no—
140C23×C13—42no—
141C23×C13#12011yescharacteristic
142C23×C13#12011yescharacteristic
143C23×C13#12111yescharacteristic
144Q8×C13—42no—
145Q8×C13—81no—
146D4×C13—42no—
147D4×C13—81no—
148D4×C13—82no—
149D4×C13—82no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13—44no—
171C2×C4×C13—82no—
172C2×C4×C13#12011yescharacteristic
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12711yescharacteristic
176C8×C13—42no—
177C8×C13—81no—
178C2×C22⋊Q8C22×C1311yescharacteristic
179C2×#121C22×C1311yescharacteristic
180C22×C4⋊C4C22×C1311yescharacteristic
181#484—21no—
182#480—21no—
183#468—22no—
184#450—21no—
185#448—21no—
186#407C22×C1311yescharacteristic
187#407C22×C1311yescharacteristic
188#400—22no—
189#397—22no—
190#391—21no—
191#390—21no—
192#386—22no—
193#382—21no—
194#382—21no—
195#381—22no—
196C4×C22⋊C4C22×C1311yescharacteristic
197C4×C22⋊C4C22×C1311yescharacteristic
198#343—22no—
199#328—22no—
200#327—22no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—44no—
209C22×C13—84no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13#39211yescharacteristic
214C22×C13#45412yes—
215C22×C13#45512yes—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—82no—
220C4×C13—82no—
221C4×C13—81no—
222C4×C13—81no—
223C4×C13—82no—
224C4×C13—81no—
225C4×C13#45812yes—
226C22×Q8D4×C1311yescharacteristic
227C22×D4—21no—
228C22×D4D4×C1311yescharacteristic
229C23×C4D4×C1312yes—
230C23×C4C23×C1311yescharacteristic
231C2×SD16—22no—
232C2×M16—21no—
233C2×M16D4×C1312yes—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238#121—21no—
239#121—21no—
240#121—21no—
241#121—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1311yescharacteristic
250C2×C4⋊C4D4×C1311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—24no—
256C2×C42—21no—
257C2×C42—21no—
258#107—22no—
259#103—22no—
260#102—22no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265#95—24no—
266#95—24no—
267#95—24no—
268#95D4×C1312yes—
269#95D4×C1312yes—
270C2×C13—22no—
271C2×C13—22no—
272C2×C13—41no—
273C2×C13—161no—
274C2×C13#200311yescharacteristic
275C2×C13#200411yescharacteristic
276C2×C13#202211yescharacteristic
277C24—21no—
278C24C2×D4×C1311yescharacteristic
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—42no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—42no—
285C2×D4—44no—
286C2×D4—41no—
287C2×D4—41no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—42no—
297C22×C4—44no—
298C22×C4C2×D4×C1311yescharacteristic
299C22×C4C2×D4×C1311yescharacteristic
300C22×C4C2×D4×C1311yescharacteristic
301C22×C4C2×D4×C1311yescharacteristic
302C22×C4C2×D4×C1311yescharacteristic
303C22×C4C13×#4111yescharacteristic
304SD16—82no—
305M16—42no—
306M16—42no—
307C2×C8—22no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—84no—
326C42—42no—
327C42—42no—
328C13#1033211yescharacteristic, direct product factor, Sylow
329C23—22no—
330C23—22no—
331C23—41no—
332C23—42no—
333C23—42no—
334C23—41no—
335C23—42no—
336C23C13×#12011yescharacteristic
337C23C13×#12011yescharacteristic
338C23C13×#12111yescharacteristic
339Q8—42no—
340Q8—81no—
341D4—42no—
342D4—81no—
343D4—82no—
344D4—82no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—44no—
366C2×C4—82no—
367C2×C4C13×#12011yescharacteristic
368C2×C4C13×#12111yescharacteristic
369C2×C4C13×#12111yescharacteristic
370C2×C4C13×#12711yescharacteristic
371C8—42no—
372C8—81no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22—84no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C13×#39211yescharacteristic
386C22C13×#45412yes—
387C22C13×#45512yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—82no—
392C4—82no—
393C4—81no—
394C4—81no—
395C4—82no—
396C4—81no—
397C4C13×#45812yes—
398C2—22no—
399C2—22no—
400C2—41no—
401C2—161no—
402C2C13×#200311yescharacteristic
403C2C13×#200411yescharacteristic
404C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
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
3. C13×#2503C2semidirect
4. C13×#1821C2semidirect
5. C13×#1508C2semidirect
7. C13×#1297C2semidirect
75. #10332C13direct (N × H)
129. #2503C2×C13semidirect
130. #1821C2×C13semidirect
131. #1508C2×C13semidirect
133. #1297C2×C13semidirect
328. C13#10332direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31932
C13×#25042
C13×#25032
C13×#18212
C13×#15082
C13×#15072
C13×#12972
#1033213