Finite Group Databasebeta

← C13×#12191 #15698530

Subgroups — C13×#12191 #15698530

Order 3328.

484 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2752C211yesmaximal, characteristic, complemented
2C13×#2022C211yesmaximal, characteristic, complemented
3C13×#1613C211yesmaximal, characteristic, complemented
4C13×#1595C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic, complemented
7C13×#1317C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C2×C13×#123—21no—
10C13×#481—21no—
11C13×#447—21no—
12C2×C13×#99—21no—
13C13×#399C2211yescharacteristic
14C13×#397—21no—
15C13×#394—21no—
16C13×#392C2211yescharacteristic
17C13×#390—21no—
18C13×#388—21no—
19C13×#387—21no—
20C13×#386—21no—
21C13×#381C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13D411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C2×C13×D8—41no—
32C13×#123—42no—
33C13×#123—41no—
34C13×#123—42no—
35C13×#121—21no—
36C13×#121—21no—
37C13×#120—41no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—41no—
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
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—41no—
50C2×C13×C22⋊C4D411yescharacteristic
51C2×C13×C22⋊C4C2311yescharacteristic
52C2×C42×C13—21no—
53C13×#106—41no—
54C13×#102—41no—
55C13×#102—41no—
56C13×#99—42no—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95D411yescharacteristic
64C13×#95D411yescharacteristic
65#12191C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—21no—
67C24×C13—21no—
68C24×C13C2×D411yescharacteristic
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—41no—
72C2×D4×C13—42no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—81no—
82C2×D4×C13—81no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C13×D8—82no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—44no—
104C13×C4⋊C4—81no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—44no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—81no—
114C13×C22⋊C4—81no—
115C13×C22⋊C4—81no—
116C13×C22⋊C4—81no—
117C13×C22⋊C4—81no—
118C42×C13—81no—
119#2752C2×C1311yescharacteristic, complemented
120#2022C2×C1311yescharacteristic, complemented
121#1613C2×C1311yescharacteristic, complemented
122#1595C2×C1311yescharacteristic
123#1352C2×C1311yescharacteristic, complemented
124#1343C2×C1311yescharacteristic, complemented
125#1317C2×C1311yescharacteristic, complemented
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—81no—
141C23×C13—81no—
142C23×C13#12011yescharacteristic
143C23×C13#13511yescharacteristic
144C23×C13AGL(1,ℤ/8)11yescharacteristic
145D4×C13—42no—
146D4×C13—82no—
147D4×C13—82no—
148D4×C13—81no—
149D4×C13—81no—
150D4×C13—81no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154D4×C13—81no—
155C2×C4×C13—22no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13—81no—
182C8×C13—81no—
183C8×C13—81no—
184#534C22×C1311yescharacteristic
185C2×#123—21no—
186#481—21no—
187#447—21no—
188C2×#99—21no—
189#399C22×C1311yescharacteristic
190#397—21no—
191#394—21no—
192#392C22×C1311yescharacteristic
193#390—21no—
194#388—21no—
195#387—21no—
196#386—21no—
197#381C22×C1311yescharacteristic
198#342C22×C1311yescharacteristic
199#327—21no—
200#327—21no—
201#323C22×C1311yescharacteristic
202#323C22×C1311yescharacteristic
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—82no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—161no—
224C22×C13#44911yescharacteristic
225C22×C13#45311yescharacteristic
226C22×C13B(4,𝔽2)11yescharacteristic
227C4×C13—42no—
228C4×C13—41no—
229C4×C13—41no—
230C4×C13—81no—
231C4×C13—81no—
232C4×C13—82no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13—81no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4D4×C1311yescharacteristic
239C23×C4D4×C1311yescharacteristic
240C2×D8—41no—
241#123—42no—
242#123—41no—
243#123—42no—
244#121—21no—
245#121—21no—
246#120—41no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4D4×C1311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—41no—
259C2×C22⋊C4D4×C1311yescharacteristic
260C2×C22⋊C4C23×C1311yescharacteristic
261C2×C42—21no—
262#106—41no—
263#102—41no—
264#102—41no—
265#99—42no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95D4×C1311yescharacteristic
273#95D4×C1311yescharacteristic
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—41no—
277C2×C13—41no—
278C2×C13—161no—
279C2×C13—161no—
280C2×C13#160011yescharacteristic
281C2×C13#219811yescharacteristic
282C2×C13#220011yescharacteristic
283C24—21no—
284C24—21no—
285C24C2×D4×C1311yescharacteristic
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—81no—
299C2×D4—81no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C1311yescharacteristic
312C22×C4C2×D4×C1311yescharacteristic
313D8—82no—
314C2×C8—41no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—44no—
321C4⋊C4—81no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—44no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C42—81no—
336C13#1219111yescharacteristic, direct product factor, Sylow
337C23—21no—
338C23—21no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—81no—
352C23—81no—
353C23C13×#12011yescharacteristic
354C23C13×#13511yescharacteristic
355C23C13×AGL(1,ℤ/8)11yescharacteristic
356D4—42no—
357D4—82no—
358D4—82no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C8—81no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—161no—
416C22C13×#44911yescharacteristic
417C22C13×#45311yescharacteristic
418C22C13×B(4,𝔽2)11yescharacteristic
419C4—42no—
420C4—41no—
421C4—41no—
422C4—81no—
423C4—81no—
424C4—82no—
425C4—81no—
426C4—81no—
427C4—81no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—161no—
433C2—161no—
434C2C13×#160011yescharacteristic
435C2C13×#219811yescharacteristic
436C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#1595C2
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×#2752C2semidirect
2. C13×#2022C2semidirect
3. C13×#1613C2semidirect
5. C13×#1352C2semidirect
6. C13×#1343C2semidirect
7. C13×#1317C2semidirect
65. #12191C13direct (N × H)
119. #2752C2×C13semidirect
120. #2022C2×C13semidirect
121. #1613C2×C13semidirect
123. #1352C2×C13semidirect
124. #1343C2×C13semidirect
125. #1317C2×C13semidirect
336. C13#12191direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27522
C13×#20222
C13×#16132
C13×#15952
C13×#13522
C13×#13432
C13×#13172
#1219113