Finite Group Databasebeta

← C13×#12193 #15698532

Subgroups — C13×#12193 #15698532

Order 3328.

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

normal subgroups only

This group has 442 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×#2764C211yesmaximal, characteristic, complemented
2C13×#2022C211yesmaximal, characteristic
3C13×#1607C211yesmaximal, characteristic
4C13×#1601C211yesmaximal, characteristic
5C13×#1351C211yesmaximal, characteristic, complemented
6C13×#1344C211yesmaximal, characteristic, complemented
7C13×#1317C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C2×C13×#123—21no—
10C13×#480—21no—
11C13×#448—21no—
12C2×C13×#99—21no—
13C13×#400—21no—
14C13×#398—21no—
15C13×#397C2211yescharacteristic
16C13×#393C2211yescharacteristic
17C13×#391—21no—
18C13×#388—21no—
19C13×#385—21no—
20C13×#383—21no—
21C13×#381C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13—21no—
29C23×C4×C13D411yescharacteristic
30C2×C13×SD16—41no—
31C13×#123—42no—
32C13×#123—41no—
33C13×#123—42no—
34C13×#121—21no—
35C13×#121—21no—
36C13×#120—41no—
37C2×C13×C4⋊C4—21no—
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—41no—
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4C2311yescharacteristic
48C2×C42×C13—21no—
49C13×#107—41no—
50C13×#103—41no—
51C13×#102—41no—
52C13×#99—42no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95D411yescharacteristic
64C13×#95D411yescharacteristic
65#12193C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—21no—
67C24×C13C2×D411yescharacteristic
68C2×Q8×C13—42no—
69C2×Q8×C13—41no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
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—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C13×SD16—82no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—44no—
99C13×C4⋊C4—81no—
100C13×C4⋊C4—81no—
101C13×C4⋊C4—81no—
102C13×C22⋊C4—22no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—44no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C42×C13—42no—
113#2764C2×C1311yescharacteristic, complemented
114#2022C2×C1311yescharacteristic
115#1607C2×C1311yescharacteristic
116#1601C2×C1311yescharacteristic
117#1351C2×C1311yescharacteristic, complemented
118#1344C2×C1311yescharacteristic, complemented
119#1317C2×C1311yescharacteristic, complemented
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13#12011yescharacteristic
130C23×C13#13511yescharacteristic
131C23×C13AGL(1,ℤ/8)11yescharacteristic
132Q8×C13—42no—
133Q8×C13—81no—
134D4×C13—81no—
135D4×C13—81no—
136D4×C13—81no—
137D4×C13—81no—
138D4×C13—81no—
139D4×C13—81no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
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—41no—
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—81no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C8×C13—81no—
171C8×C13—81no—
172#534C22×C1311yescharacteristic
173C2×#123—21no—
174#480—21no—
175#448—21no—
176C2×#99—21no—
177#400—21no—
178#398—21no—
179#397C22×C1311yescharacteristic
180#393C22×C1311yescharacteristic
181#391—21no—
182#388—21no—
183#385—21no—
184#383—21no—
185#381C22×C1311yescharacteristic
186#342C22×C1311yescharacteristic
187#327—21no—
188#327—21no—
189#323C22×C1311yescharacteristic
190#323C22×C1311yescharacteristic
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—81no—
200C22×C13—82no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—161no—
205C22×C13#44911yescharacteristic
206C22×C13#45311yescharacteristic
207C22×C13B(4,𝔽2)11yescharacteristic
208C4×C13—41no—
209C4×C13—42no—
210C4×C13—41no—
211C4×C13—81no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13—82no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C22×Q8D4×C1311yescharacteristic
219C22×D4—21no—
220C23×C4D4×C1311yescharacteristic
221C2×SD16—41no—
222#123—42no—
223#123—41no—
224#123—42no—
225#121—21no—
226#121—21no—
227#120—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4D4×C1311yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—41no—
237C2×C22⋊C4D4×C1311yescharacteristic
238C2×C22⋊C4C23×C1311yescharacteristic
239C2×C42—21no—
240#107—41no—
241#103—41no—
242#102—41no—
243#99—42no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95D4×C1311yescharacteristic
255#95D4×C1311yescharacteristic
256C2×C13—21no—
257C2×C13—21no—
258C2×C13—41no—
259C2×C13—41no—
260C2×C13—161no—
261C2×C13#160011yescharacteristic
262C2×C13#219711yescharacteristic
263C2×C13#220111yescharacteristic
264C24—21no—
265C24C2×D4×C1311yescharacteristic
266C2×Q8—42no—
267C2×Q8—41no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×D4×C1311yescharacteristic
289C22×C4C2×D4×C1311yescharacteristic
290SD16—82no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—44no—
297C4⋊C4—81no—
298C4⋊C4—81no—
299C4⋊C4—81no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—44no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—42no—
311C13#1219311yescharacteristic, direct product factor, Sylow
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—81no—
320C23—81no—
321C23C13×#12011yescharacteristic
322C23C13×#13511yescharacteristic
323C23C13×AGL(1,ℤ/8)11yescharacteristic
324Q8—42no—
325Q8—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
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—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C8—81no—
363C8—81no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—161no—
378C22C13×#44911yescharacteristic
379C22C13×#45311yescharacteristic
380C22C13×B(4,𝔽2)11yescharacteristic
381C4—41no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2C13×#160011yescharacteristic
397C2C13×#219711yescharacteristic
398C2C13×#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×#2764C2semidirect
5. C13×#1351C2semidirect
6. C13×#1344C2semidirect
7. C13×#1317C2semidirect
65. #12193C13direct (N × H)
113. #2764C2×C13semidirect
117. #1351C2×C13semidirect
118. #1344C2×C13semidirect
119. #1317C2×C13semidirect
311. C13#12193direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27642
C13×#20222
C13×#16072
C13×#16012
C13×#13512
C13×#13442
C13×#13172
#1219313