Finite Group Databasebeta

← C13×#12230 #15698569

Subgroups — C13×#12230 #15698569

Order 3328.

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

normal subgroups only

This group has 422 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×#2824C211yesmaximal, characteristic
2C13×#2062C211yesmaximal, characteristic, complemented
3C13×#1602C211yesmaximal, characteristic, complemented
4C13×#1596C211yesmaximal, characteristic
5C13×#1351C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic
7C13×#1326C211yesmaximal, characteristic, complemented
8C13×#543C2211yescharacteristic
9C13×#451—21no—
10C13×#450—21no—
11C13×#400—21no—
12C13×#397—21no—
13C13×#394—21no—
14C13×#394—21no—
15C13×#393—21no—
16C13×#393C2211yescharacteristic
17C13×#392C2211yescharacteristic
18C13×#386—21no—
19C13×#385—21no—
20C13×#385C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13—21no—
29C22×D4×C13D411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C2×C13×Q16—41no—
32C2×C13×SD16—41no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—41no—
36C13×C22⋊Q8—41no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—41no—
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—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4C2311yescharacteristic
50C13×#103—41no—
51C13×#102—41no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—41no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12230C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C24×C13C2×D411yescharacteristic
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—41no—
68C2×Q8×C13—81no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—81no—
73C2×D4×C13—81no—
74C2×D4×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×C13—41no—
84C22×C4×C13—81no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C13×Q16—82no—
88C13×SD16—82no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—81no—
96C13×C4⋊C4—81no—
97C13×C4⋊C4—82no—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—21no—
100C13×C22⋊C4—21no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—81no—
106C13×C22⋊C4—81no—
107C13×C22⋊C4—81no—
108C13×C22⋊C4—81no—
109C13×C22⋊C4—81no—
110C13×C22⋊C4—81no—
111#2824C2×C1311yescharacteristic
112#2062C2×C1311yescharacteristic, complemented
113#1602C2×C1311yescharacteristic, complemented
114#1596C2×C1311yescharacteristic
115#1351C2×C1311yescharacteristic, complemented
116#1343C2×C1311yescharacteristic
117#1326C2×C1311yescharacteristic, complemented
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13#12011yescharacteristic
130C23×C13#13511yescharacteristic
131C23×C13#13711yescharacteristic
132Q8×C13—42no—
133Q8×C13—81no—
134Q8×C13—81no—
135Q8×C13—81no—
136D4×C13—42no—
137D4×C13—81no—
138D4×C13—82no—
139D4×C13—82no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
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—42no—
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—81no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C8×C13—81no—
169C8×C13—81no—
170#543C22×C1311yescharacteristic
171#451—21no—
172#450—21no—
173#400—21no—
174#397—21no—
175#394—21no—
176#394—21no—
177#393—21no—
178#393C22×C1311yescharacteristic
179#392C22×C1311yescharacteristic
180#386—21no—
181#385—21no—
182#385C22×C1311yescharacteristic
183#342—21no—
184#342C22×C1311yescharacteristic
185#328—21no—
186#328—21no—
187#323C22×C1311yescharacteristic
188#323C22×C1311yescharacteristic
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13#45211yescharacteristic
206C22×C13#45611yescharacteristic
207C22×C13B(4,𝔽2)11yescharacteristic
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—81no—
211C4×C13—81no—
212C4×C13—81no—
213C4×C13—82no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C22×Q8D4×C1311yescharacteristic
219C22×D4—21no—
220C22×D4D4×C1311yescharacteristic
221C23×C4D4×C1311yescharacteristic
222C2×Q16—41no—
223C2×SD16—41no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—41no—
227C22⋊Q8—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—41no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4D4×C1311yescharacteristic
240C2×C22⋊C4C23×C1311yescharacteristic
241#103—41no—
242#102—41no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—41no—
251#95D4×C1311yescharacteristic
252#95D4×C1311yescharacteristic
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—41no—
256C2×C13—41no—
257C2×C13—161no—
258C2×C13#160311yescharacteristic
259C2×C13#219911yescharacteristic
260C2×C13#220011yescharacteristic
261C24—21no—
262C24C2×D4×C1311yescharacteristic
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—81no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—81no—
271C2×D4—81no—
272C2×D4—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—81no—
283C22×C4C2×D4×C1311yescharacteristic
284C22×C4C2×D4×C1311yescharacteristic
285Q16—82no—
286SD16—82no—
287C2×C8—41no—
288C2×C8—41no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—81no—
294C4⋊C4—81no—
295C4⋊C4—82no—
296C22⋊C4—22no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C13#1223011yescharacteristic, direct product factor, Sylow
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C13×#12011yescharacteristic
322C23C13×#13511yescharacteristic
323C23C13×#13711yescharacteristic
324Q8—42no—
325Q8—81no—
326Q8—81no—
327Q8—81no—
328D4—42no—
329D4—81no—
330D4—82no—
331D4—82no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C8—81no—
361C8—81no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22C13×#45211yescharacteristic
379C22C13×#45611yescharacteristic
380C22C13×B(4,𝔽2)11yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—82no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2C13×#160311yescharacteristic
397C2C13×#219911yescharacteristic
398C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#392C22
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
2. C13×#2062C2semidirect
3. C13×#1602C2semidirect
5. C13×#1351C2semidirect
7. C13×#1326C2semidirect
62. #12230C13direct (N × H)
112. #2062C2×C13semidirect
113. #1602C2×C13semidirect
115. #1351C2×C13semidirect
117. #1326C2×C13semidirect
309. C13#12230direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28242
C13×#20622
C13×#16022
C13×#15962
C13×#13512
C13×#13432
C13×#13262
#1223013