Finite Group Databasebeta

← C2×C13×#2198 #15719884

Subgroups — C2×C13×#2198 #15719884

Order 3328.

1244 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 222 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
1C2×C13×#559C211yesmaximal, characteristic, complemented
2C2×C13×#458C212yesmaximal, complemented
3C2×C13×#453C211yesmaximal, characteristic
4C13×#2198C218yesmaximal, direct product factor
5C2×C13×#353C211yesmaximal, characteristic, complemented
6C2×C13×#352C212yesmaximal, complemented
7C2×C13×H(5,𝔽2)C2211yescharacteristic
8C2×C13×AGL(1,ℤ/8)—21no—
9C13×#559—22no—
10C13×#559—24no—
11C13×#559C2214yescomplemented
12C2×C13×#127C2211yescharacteristic
13C2×C13×#124—22no—
14C2×C13×#123—21no—
15C2×C13×#123—22no—
16C2×C13×#123C2212yes—
17C2×C4×Q8×C13—21no—
18C2×C4×D4×C13—22no—
19C13×#458—24no—
20C13×#458C2218yescomplemented
21C13×#453—22no—
22C13×#453C2214yes—
23C2×C13×#104—21no—
24C2×C13×#100C2211yescharacteristic
25C2×C13×#99—22no—
26C2×C13×#99C2212yes—
27C13×#353C2214yescomplemented
28C13×#352C2218yescomplemented
29C13×H(5,𝔽2)—22no—
30C13×H(5,𝔽2)—21no—
31C13×H(5,𝔽2)—42no—
32C13×H(5,𝔽2)C2312yes—
33C2×C13×#41—21no—
34C2×C13×#41—41no—
35C22×Q8×C13—21no—
36C22×D4×C13—22no—
37C22×D4×C13—22no—
38C22×D4×C13—41no—
39C22×D4×C13D411yescharacteristic
40C22×D4×C13C2311yescharacteristic
41C23×C4×C13—21no—
42C23×C4×C13D412yes—
43C13×AGL(1,ℤ/8)—24no—
44C13×AGL(1,ℤ/8)—42no—
45C2×C13×SD16—41no—
46C2×C13×D8—41no—
47C2×C13×M16—21no—
48C13×#127—22no—
49C13×#127D412yes—
50C13×#127C2312yes—
51C13×#124—28no—
52C13×#124—28no—
53C13×#123—24no—
54C13×#123—24no—
55C13×#123—22no—
56C13×#123—22no—
57C13×#123—28no—
58C13×#123—44no—
59C13×#123D414yes—
60C13×#123C2314yes—
61C4×Q8×C13—24no—
62C4×Q8×C13—24no—
63C4×D4×C13—28no—
64C4×D4×C13—28no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—42no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—42no—
73C2×C13×C22⋊C4D412yes—
74C2×C42×C13—22no—
75C2×C42×C13D411yescharacteristic
76C13×#104—24no—
77C13×#100—21no—
78C13×#100C2312yes—
79C13×#99—22no—
80C13×#99—28no—
81C13×#99C2314yes—
82C2×#2198C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13—22no—
84C24×C13—21no—
85C24×C13C2×D412yes—
86C13×#41—22no—
87C13×#41—22no—
88C13×#41—42no—
89C13×#41—41no—
90C13×#41—44no—
91C13×#41—42no—
92C13×#41—41no—
93C2×Q8×C13—24no—
94C2×Q8×C13—21no—
95C2×Q8×C13—44no—
96C2×D4×C13—21no—
97C2×D4×C13—24no—
98C2×D4×C13—24no—
99C2×D4×C13—24no—
100C2×D4×C13—24no—
101C2×D4×C13—21no—
102C2×D4×C13—41no—
103C2×D4×C13—41no—
104C2×D4×C13—48no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—42no—
108C2×D4×C13—42no—
109C2×D4×C13—42no—
110C2×D4×C13—42no—
111C2×D4×C13—44no—
112C2×D4×C13—42no—
113C2×D4×C13—41no—
114C2×D4×C13C2×D412yes—
115C2×D4×C13C2×D412yes—
116C2×D4×C13C2×D411yescharacteristic
117C2×D4×C13C2411yescharacteristic
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—24no—
123C22×C4×C13—22no—
124C22×C4×C13—41no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13—81no—
129C22×C4×C13—81no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D414yes—
132C13×SD16—44no—
133C13×D8—44no—
134C13×M16—22no—
135C13×M16—41no—
136C2×C8×C13—41no—
137C13×C4⋊C4—24no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—24no—
140C13×C4⋊C4—48no—
141C13×C22⋊C4—28no—
142C13×C22⋊C4—24no—
143C13×C22⋊C4—24no—
144C13×C22⋊C4—22no—
145C13×C22⋊C4—24no—
146C13×C22⋊C4—24no—
147C13×C22⋊C4—42no—
148C13×C22⋊C4—48no—
149C13×C22⋊C4C2×D414yes—
150C42×C13—28no—
151C42×C13—21no—
152C42×C13C2×D412yes—
153C2×#559C2×C1311yescharacteristic, complemented
154C2×#458C2×C1312yescomplemented
155C2×#453C2×C1311yescharacteristic
156#2198C2×C1318yesdirect product factor
157C2×#353C2×C1311yescharacteristic, complemented
158C2×#352C2×C1312yescomplemented
159C23×C13—22no—
160C23×C13—22no—
161C23×C13—24no—
162C23×C13—22no—
163C23×C13—44no—
164C23×C13—44no—
165C23×C13—42no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—84no—
170C23×C13#12012yes—
171C23×C13#12011yescharacteristic
172C23×C13C22×D412yes—
173Q8×C13—22no—
174Q8×C13—48no—
175Q8×C13—41no—
176D4×C13—22no—
177D4×C13—41no—
178D4×C13—42no—
179D4×C13—41no—
180D4×C13—48no—
181D4×C13—48no—
182D4×C13—41no—
183D4×C13—42no—
184D4×C13—44no—
185D4×C13—44no—
186D4×C13—42no—
187D4×C13—42no—
188D4×C13—81no—
189C2×C4×C13—24no—
190C2×C4×C13—22no—
191C2×C4×C13—21no—
192C2×C4×C13—21no—
193C2×C4×C13—24no—
194C2×C4×C13—24no—
195C2×C4×C13—24no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—44no—
200C2×C4×C13—42no—
201C2×C4×C13—41no—
202C2×C4×C13—42no—
203C2×C4×C13—44no—
204C2×C4×C13—44no—
205C2×C4×C13—82no—
206C2×C4×C13—84no—
207C2×C4×C13—84no—
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C8×C13—42no—
211C2×H(5,𝔽2)C22×C1311yescharacteristic
212C2×AGL(1,ℤ/8)—21no—
213#559—22no—
214#559—24no—
215#559C22×C1314yescomplemented
216C2×#127C22×C1311yescharacteristic
217C2×#124—22no—
218C2×#123—21no—
219C2×#123—22no—
220C2×#123C22×C1312yes—
221C2×C4×Q8—21no—
222C2×C4×D4—22no—
223#458—24no—
224#458C22×C1318yescomplemented
225#453—22no—
226#453C22×C1314yes—
227C2×#104—21no—
228C2×#100C22×C1311yescharacteristic
229C2×#99—22no—
230C2×#99C22×C1312yes—
231#353C22×C1314yescomplemented
232#352C22×C1318yescomplemented
233C22×C13—22no—
234C22×C13—22no—
235C22×C13—22no—
236C22×C13—42no—
237C22×C13—42no—
238C22×C13—44no—
239C22×C13—44no—
240C22×C13—42no—
241C22×C13—42no—
242C22×C13—82no—
243C22×C13—82no—
244C22×C13—84no—
245C22×C13—82no—
246C22×C13—82no—
247C22×C13—162no—
248C22×C13B(4,𝔽2)11yescharacteristic
249C22×C13B(4,𝔽2)11yescharacteristic
250C22×C13C2×#12011yescharacteristic
251C4×C13—24no—
252C4×C13—21no—
253C4×C13—21no—
254C4×C13—44no—
255C4×C13—42no—
256C4×C13—44no—
257C4×C13—84no—
258H(5,𝔽2)—22no—
259H(5,𝔽2)—21no—
260H(5,𝔽2)—42no—
261H(5,𝔽2)C23×C1312yes—
262C2×#41—21no—
263C2×#41—41no—
264C22×Q8—21no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—41no—
268C22×D4D4×C1311yescharacteristic
269C22×D4C23×C1311yescharacteristic
270C23×C4—21no—
271C23×C4D4×C1312yes—
272AGL(1,ℤ/8)—24no—
273AGL(1,ℤ/8)—42no—
274C2×SD16—41no—
275C2×D8—41no—
276C2×M16—21no—
277#127—22no—
278#127D4×C1312yes—
279#127C23×C1312yes—
280#124—28no—
281#124—28no—
282#123—24no—
283#123—24no—
284#123—22no—
285#123—22no—
286#123—28no—
287#123—44no—
288#123D4×C1314yes—
289#123C23×C1314yes—
290C4×Q8—24no—
291C4×Q8—24no—
292C4×D4—28no—
293C4×D4—28no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—42no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4D4×C1312yes—
303C2×C42—22no—
304C2×C42D4×C1311yescharacteristic
305#104—24no—
306#100—21no—
307#100C23×C1312yes—
308#99—22no—
309#99—28no—
310#99C23×C1314yes—
311C2×C13—21no—
312C2×C13—21no—
313C2×C13—42no—
314C2×C13—42no—
315C2×C13—82no—
316C2×C13—82no—
317C2×C13#219812yesdirect product factor
318C2×C13C2×B(4,𝔽2)11yescharacteristic
319C24—22no—
320C24—21no—
321C24C2×D4×C1312yes—
322#41—22no—
323#41—22no—
324#41—42no—
325#41—41no—
326#41—44no—
327#41—42no—
328#41—41no—
329C2×Q8—24no—
330C2×Q8—21no—
331C2×Q8—44no—
332C2×D4—21no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—48no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—44no—
348C2×D4—41no—
349C2×D4—42no—
350C2×D4C2×D4×C1312yes—
351C2×D4C2×D4×C1312yes—
352C2×D4C2×D4×C1311yescharacteristic
353C2×D4C24×C1311yescharacteristic
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—81no—
365C22×C4—81no—
366C22×C4C2×D4×C1311yescharacteristic
367C22×C4C2×D4×C1314yes—
368SD16—44no—
369D8—44no—
370M16—22no—
371M16—41no—
372C2×C8—41no—
373C4⋊C4—24no—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—48no—
377C22⋊C4—28no—
378C22⋊C4—24no—
379C22⋊C4—24no—
380C22⋊C4—22no—
381C22⋊C4—24no—
382C22⋊C4—24no—
383C22⋊C4—42no—
384C22⋊C4—48no—
385C22⋊C4C2×D4×C1314yes—
386C42—28no—
387C42—21no—
388C42C2×D4×C1312yes—
389C13C2×#219811yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23—22no—
392C23—24no—
393C23—22no—
394C23—44no—
395C23—44no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—84no—
401C23C13×#12011yescharacteristic
402C23C13×#12012yes—
403C23C22×D4×C1312yes—
404Q8—22no—
405Q8—48no—
406Q8—41no—
407D4—22no—
408D4—41no—
409D4—42no—
410D4—41no—
411D4—42no—
412D4—41no—
413D4—48no—
414D4—48no—
415D4—44no—
416D4—44no—
417D4—42no—
418D4—42no—
419D4—81no—
420C2×C4—24no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—82no—
437C2×C4—84no—
438C2×C4—84no—
439C2×C4C13×#12011yescharacteristic
440C2×C4C22×D4×C1311yescharacteristic
441C8—42no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—42no—
446C22—42no—
447C22—44no—
448C22—44no—
449C22—42no—
450C22—42no—
451C22—82no—
452C22—82no—
453C22—84no—
454C22—82no—
455C22—82no—
456C22—162no—
457C22C13×B(4,𝔽2)11yescharacteristic
458C22C13×B(4,𝔽2)11yescharacteristic
459C22C2×C13×#12011yescharacteristic
460C4—24no—
461C4—21no—
462C4—21no—
463C4—44no—
464C4—42no—
465C4—44no—
466C4—84no—
467C2—21no—
468C2—21no—
469C2—42no—
470C2—42no—
471C2—82no—
472C2—82no—
473C2C13×#219812yesdirect product factor
474C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C13
prime radicalC2×C13×#453C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C13×#559C2semidirect
2. C2×C13×#458C2semidirect
4. C13×#2198C2direct (N × H)
5. C2×C13×#353C2semidirect
6. C2×C13×#352C2semidirect
11. C13×#559C22semidirect
20. C13×#458C22semidirect
27. C13×#353C22semidirect
28. C13×#352C22semidirect
82. C2×#2198C13direct (N × H)
153. C2×#559C2×C13semidirect
154. C2×#458C2×C13semidirect
156. #2198C2×C13direct (N × H)
157. C2×#353C2×C13semidirect
158. C2×#352C2×C13semidirect
215. #559C22×C13semidirect
224. #458C22×C13semidirect
231. #353C22×C13semidirect
232. #352C22×C13semidirect
317. C2×C13#2198direct (N × H)
389. C13C2×#2198direct (N × H)
473. C2C13×#2198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5592
C2×C13×#4582
C2×C13×#4532
C13×#21982
C2×C13×#3532
C2×C13×#3522
C2×#219813