Finite Group Databasebeta

← C13×#9936 #15696275

Subgroups — C13×#9936 #15696275

Order 3328.

568 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3095C211yesmaximal, characteristic, complemented
3C13×#2624C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic, complemented
5C13×#1826C211yesmaximal, characteristic, complemented
6C13×#1507C211yesmaximal, characteristic
7C13×#1305C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#121C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C13×#485—22no—
12C13×#484—21no—
13C13×#484—21no—
14C13×#483—21no—
15C13×#480—21no—
16C13×#468—22no—
17C13×#450—21no—
18C13×#448—21no—
19C13×#428—21no—
20C13×#419—21no—
21C13×#407C2211yescharacteristic
22C13×#407C2211yescharacteristic
23C13×#399—21no—
24C13×#397—21no—
25C13×#394—22no—
26C13×#390—21no—
27C13×#389—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C13×#342—22no—
31C13×#339—22no—
32C13×#327—22no—
33C22×Q8×C13D411yescharacteristic
34C22×D4×C13—21no—
35C22×D4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C2×C13×SD16—22no—
38C2×C13×M16—21no—
39C2×C13×M16D412yes—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C13×#121—21no—
48C13×#117—21no—
49C13×#117—21no—
50C13×#117—21no—
51C13×#117—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4D412yes—
66C2×C42×C13—21no—
67C2×C42×C13—21no—
68C13×#107—22no—
69C13×#107—22no—
70C13×#106—22no—
71C13×#103—22no—
72C13×#103—22no—
73C13×#103—22no—
74C13×#102—22no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8D412yes—
79C13×#95—22no—
80C13×#95—21no—
81C13×#95—21no—
82#9936C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13—21no—
84C24×C13C2×D411yescharacteristic
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—42no—
88C2×D4×C13—21no—
89C2×D4×C13—21no—
90C2×D4×C13—42no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—82no—
94C22×C4×C13—21no—
95C22×C4×C13—22no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—42no—
101C22×C4×C13—41no—
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C13×SD16—82no—
109C13×M16—42no—
110C13×M16—42no—
111C2×C8×C13—22no—
112C2×C8×C13—22no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—42no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—82no—
125C13×C22⋊C4—22no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—42no—
134C13×C22⋊C4—82no—
135C13×C22⋊C4—82no—
136C42×C13—42no—
137C42×C13—41no—
138C42×C13—41no—
139#3193C2×C1311yescharacteristic
140#3095C2×C1311yescharacteristic, complemented
141#2624C2×C1311yescharacteristic
142#1996C2×C1311yescharacteristic, complemented
143#1826C2×C1311yescharacteristic, complemented
144#1507C2×C1311yescharacteristic
145#1305C2×C1311yescharacteristic, complemented
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—42no—
151C23×C13—42no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13#12011yescharacteristic
156C23×C13#12111yescharacteristic
157C23×C13#12711yescharacteristic
158Q8×C13—42no—
159Q8×C13—42no—
160D4×C13—42no—
161D4×C13—81no—
162D4×C13—82no—
163D4×C13—82no—
164C2×C4×C13—22no—
165C2×C4×C13—22no—
166C2×C4×C13—22no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—42no—
171C2×C4×C13—41no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—81no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13—81no—
188C2×C4×C13#12011yescharacteristic
189C2×C4×C13#12011yescharacteristic
190C2×C4×C13#12111yescharacteristic
191C2×C4×C13#12111yescharacteristic
192C8×C13—42no—
193C8×C13—42no—
194C2×C22⋊Q8C22×C1311yescharacteristic
195C2×#121C22×C1311yescharacteristic
196C2×#117C22×C1311yescharacteristic
197#485—22no—
198#484—21no—
199#484—21no—
200#483—21no—
201#480—21no—
202#468—22no—
203#450—21no—
204#448—21no—
205#428—21no—
206#419—21no—
207#407C22×C1311yescharacteristic
208#407C22×C1311yescharacteristic
209#399—21no—
210#397—21no—
211#394—22no—
212#390—21no—
213#389—21no—
214#380C22×C1311yescharacteristic
215C4×C22⋊C4C22×C1311yescharacteristic
216#342—22no—
217#339—22no—
218#327—22no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—82no—
230C22×C13—82no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13#39211yescharacteristic
235C22×C13#45511yescharacteristic
236C22×C13#45611yescharacteristic
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—82no—
241C4×C13—82no—
242C4×C13—81no—
243C4×C13—81no—
244C4×C13—81no—
245C4×C13—81no—
246C4×C13—81no—
247C4×C13#45812yes—
248C22×Q8D4×C1311yescharacteristic
249C22×D4—21no—
250C22×D4D4×C1311yescharacteristic
251C23×C4C23×C1311yescharacteristic
252C2×SD16—22no—
253C2×M16—21no—
254C2×M16D4×C1312yes—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#117—21no—
264#117—21no—
265#117—21no—
266#117—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4D4×C1311yescharacteristic
271C2×C4⋊C4D4×C1311yescharacteristic
272C2×C4⋊C4D4×C1311yescharacteristic
273C2×C4⋊C4D4×C1311yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4D4×C1312yes—
281C2×C42—21no—
282C2×C42—21no—
283#107—22no—
284#107—22no—
285#106—22no—
286#103—22no—
287#103—22no—
288#103—22no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8D4×C1312yes—
294#95—22no—
295#95—21no—
296#95—21no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13—41no—
300C2×C13—41no—
301C2×C13—161no—
302C2×C13#200711yescharacteristic
303C2×C13#200811yescharacteristic
304C2×C13#202211yescharacteristic
305C24—21no—
306C24C2×D4×C1311yescharacteristic
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—42no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—42no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—82no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4C2×D4×C1311yescharacteristic
325C22×C4C2×D4×C1311yescharacteristic
326C22×C4C2×D4×C1311yescharacteristic
327C22×C4C2×D4×C1311yescharacteristic
328C22×C4C2×D4×C1311yescharacteristic
329C22×C4C13×#4111yescharacteristic
330SD16—82no—
331M16—42no—
332M16—42no—
333C2×C8—22no—
334C2×C8—22no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—82no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—42no—
356C22⋊C4—82no—
357C22⋊C4—82no—
358C42—42no—
359C42—41no—
360C42—41no—
361C13#993611yescharacteristic, direct product factor, Sylow
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23C13×#12011yescharacteristic
372C23C13×#12111yescharacteristic
373C23C13×#12711yescharacteristic
374Q8—42no—
375Q8—42no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—82no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C13×#12011yescharacteristic
405C2×C4C13×#12011yescharacteristic
406C2×C4C13×#12111yescharacteristic
407C2×C4C13×#12111yescharacteristic
408C8—42no—
409C8—42no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—82no—
421C22—82no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22C13×#39211yescharacteristic
426C22C13×#45511yescharacteristic
427C22C13×#45611yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—82no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4C13×#45812yes—
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—161no—
444C2C13×#200711yescharacteristic
445C2C13×#200811yescharacteristic
446C2C13×#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
2. C13×#3095C2semidirect
4. C13×#1996C2semidirect
5. C13×#1826C2semidirect
7. C13×#1305C2semidirect
82. #9936C13direct (N × H)
140. #3095C2×C13semidirect
142. #1996C2×C13semidirect
143. #1826C2×C13semidirect
145. #1305C2×C13semidirect
361. C13#9936direct (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×#30952
C13×#26242
C13×#19962
C13×#18262
C13×#15072
C13×#13052
#993613