Finite Group Databasebeta

← C13×#12264 #15698603

Subgroups — C13×#12264 #15698603

Order 3328.

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

normal subgroups only

This group has 468 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×#2736C211yesmaximal, characteristic
2C13×#2029C211yesmaximal, characteristic
3C13×#1608C211yesmaximal, characteristic, complemented
4C13×#1602C211yesmaximal, characteristic, complemented
5C13×#1351C211yesmaximal, characteristic, complemented
6C13×#1344C211yesmaximal, characteristic, complemented
7C13×#1316C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C13×#483—21no—
10C13×#451—21no—
11C13×#397—21no—
12C13×#397C2211yescharacteristic
13C13×#393—21no—
14C13×#393C2211yescharacteristic
15C13×#388—21no—
16C13×#388—21no—
17C13×#388—21no—
18C13×#379—21no—
19C13×#379—21no—
20C13×#379C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C25×C13D411yescharacteristic
28C22×Q8×C13D411yescharacteristic
29C2×C13×Q16—41no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—41no—
33C13×C22⋊Q8—41no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—41no—
47C2×C13×C22⋊C4—41no—
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4C2311yescharacteristic
50C2×C42×C13—21no—
51C13×#106—41no—
52C13×#103—41no—
53C13×#103—41no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12264C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C24×C13—21no—
65C24×C13—21no—
66C24×C13—41no—
67C24×C13—41no—
68C24×C13—42no—
69C24×C13—81no—
70C24×C13C2×D411yescharacteristic
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—41no—
74C2×Q8×C13—81no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C13×Q16—82no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—81no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—81no—
105C13×C22⋊C4—81no—
106C13×C22⋊C4—81no—
107C13×C22⋊C4—81no—
108C13×C22⋊C4—81no—
109C13×C22⋊C4—82no—
110C13×C22⋊C4—82no—
111C42×C13—81no—
112#2736C2×C1311yescharacteristic
113#2029C2×C1311yescharacteristic
114#1608C2×C1311yescharacteristic, complemented
115#1602C2×C1311yescharacteristic, complemented
116#1351C2×C1311yescharacteristic, complemented
117#1344C2×C1311yescharacteristic, complemented
118#1316C2×C1311yescharacteristic
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—22no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—81no—
134C23×C13—82no—
135C23×C13—81no—
136C23×C13—84no—
137C23×C13—82no—
138C23×C13—81no—
139C23×C13#12011yescharacteristic
140C23×C13#13511yescharacteristic
141C23×C13#13711yescharacteristic
142Q8×C13—42no—
143Q8×C13—81no—
144Q8×C13—81no—
145Q8×C13—81no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
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—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C8×C13—81no—
173C8×C13—81no—
174#543C22×C1311yescharacteristic
175#483—21no—
176#451—21no—
177#397—21no—
178#397C22×C1311yescharacteristic
179#393—21no—
180#393C22×C1311yescharacteristic
181#388—21no—
182#388—21no—
183#388—21no—
184#379—21no—
185#379—21no—
186#379C22×C1311yescharacteristic
187#342—21no—
188#342C22×C1311yescharacteristic
189#328—21no—
190#328—21no—
191#323C22×C1311yescharacteristic
192#323C22×C1311yescharacteristic
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—44no—
204C22×C13—42no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—82no—
209C22×C13—82no—
210C22×C13—82no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13#45211yescharacteristic
214C22×C13#45511yescharacteristic
215C22×C13B(4,𝔽2)11yescharacteristic
216C4×C13—41no—
217C4×C13—41no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13—81no—
223C4×C13—81no—
224C4×C13—81no—
225C4×C13—161no—
226C25D4×C1311yescharacteristic
227C22×Q8D4×C1311yescharacteristic
228C2×Q16—41no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C22⋊Q8—41no—
232C22⋊Q8—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C1311yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—41no—
247C2×C22⋊C4D4×C1311yescharacteristic
248C2×C22⋊C4C23×C1311yescharacteristic
249C2×C42—21no—
250#106—41no—
251#103—41no—
252#103—41no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95D4×C1311yescharacteristic
260#95D4×C1311yescharacteristic
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—41no—
264C2×C13—41no—
265C2×C13—82no—
266C2×C13#160611yescharacteristic
267C2×C13#219711yescharacteristic
268C2×C13#219911yescharacteristic
269C24—21no—
270C24—21no—
271C24—21no—
272C24—41no—
273C24—41no—
274C24—42no—
275C24—81no—
276C24C2×D4×C1311yescharacteristic
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—41no—
280C2×Q8—81no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4C2×D4×C1311yescharacteristic
290C22×C4C2×D4×C1311yescharacteristic
291Q16—82no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—81no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—81no—
313C22⋊C4—81no—
314C22⋊C4—81no—
315C22⋊C4—82no—
316C22⋊C4—82no—
317C42—81no—
318C13#1226411yescharacteristic, direct product factor, Sylow
319C23—21no—
320C23—21no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—81no—
334C23—82no—
335C23—81no—
336C23—82no—
337C23—84no—
338C23—81no—
339C23C13×#12011yescharacteristic
340C23C13×#13511yescharacteristic
341C23C13×#13711yescharacteristic
342Q8—42no—
343Q8—81no—
344Q8—81no—
345Q8—81no—
346C2×C4—21no—
347C2×C4—21no—
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—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C8—81no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—44no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—81no—
394C22C13×#45211yescharacteristic
395C22C13×#45511yescharacteristic
396C22C13×B(4,𝔽2)11yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C4—161no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—82no—
412C2C13×#160611yescharacteristic
413C2C13×#219711yescharacteristic
414C2C13×#219911yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC25×C13D4
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
3. C13×#1608C2semidirect
4. C13×#1602C2semidirect
5. C13×#1351C2semidirect
6. C13×#1344C2semidirect
62. #12264C13direct (N × H)
114. #1608C2×C13semidirect
115. #1602C2×C13semidirect
116. #1351C2×C13semidirect
117. #1344C2×C13semidirect
318. C13#12264direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27362
C13×#20292
C13×#16082
C13×#16022
C13×#13512
C13×#13442
C13×#13162
#1226413