Finite Group Databasebeta

← C13×#12178 #15698517

Subgroups — C13×#12178 #15698517

Order 3328.

422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2742C211yesmaximal, characteristic, complemented
2C13×#2044C211yesmaximal, characteristic
3C13×#1613C211yesmaximal, characteristic
4C13×#1601C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1351C211yesmaximal, characteristic, complemented
7C13×#1326C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C13×#481—21no—
10C13×#448—21no—
11C2×C13×#99—21no—
12C13×#400—21no—
13C13×#399C2211yescharacteristic
14C13×#395—21no—
15C13×#393C2211yescharacteristic
16C13×#389—21no—
17C13×#388—21no—
18C13×#387—21no—
19C13×#386—21no—
20C13×#385C2211yescharacteristic
21C13×#380—21no—
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—41no—
32C13×#121—21no—
33C13×#121—21no—
34C13×#120—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—41no—
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C42×C13—21no—
48C13×#106—41no—
49C13×#103—41no—
50C13×#102—41no—
51C13×#99—42no—
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—21no—
60C13×#95—41no—
61C13×#95D411yescharacteristic
62C13×#95D411yescharacteristic
63#12178C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—21no—
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—41no—
67C2×Q8×C13—81no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
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—21no—
83C22×C4×C13—42no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
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—42no—
95C13×C4⋊C4—42no—
96C13×C4⋊C4—81no—
97C13×C4⋊C4—81no—
98C13×C4⋊C4—81no—
99C13×C22⋊C4—21no—
100C13×C22⋊C4—41no—
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—82no—
108C13×C22⋊C4SD1612yescomplemented
109C42×C13—81no—
110#2742C2×C1311yescharacteristic, complemented
111#2044C2×C1311yescharacteristic
112#1613C2×C1311yescharacteristic
113#1601C2×C1311yescharacteristic
114#1352C2×C1311yescharacteristic, complemented
115#1351C2×C1311yescharacteristic, complemented
116#1326C2×C1311yescharacteristic, complemented
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—81no—
125C23×C13—81no—
126C23×C13#12011yescharacteristic
127C23×C13C2×SD1611yescharacteristic
128C23×C13#13711yescharacteristic
129Q8×C13—42no—
130Q8×C13—81no—
131D4×C13—81no—
132D4×C13—81no—
133D4×C13—81no—
134D4×C13—81no—
135D4×C13—81no—
136D4×C13—81no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—42no—
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—81no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C8×C13—81no—
168C8×C13—81no—
169#534C22×C1311yescharacteristic
170#481—21no—
171#448—21no—
172C2×#99—21no—
173#400—21no—
174#399C22×C1311yescharacteristic
175#395—21no—
176#393C22×C1311yescharacteristic
177#389—21no—
178#388—21no—
179#387—21no—
180#386—21no—
181#385C22×C1311yescharacteristic
182#380—21no—
183#342C22×C1311yescharacteristic
184#327—21no—
185#327—21no—
186#323C22×C1311yescharacteristic
187#323C22×C1311yescharacteristic
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—81no—
197C22×C13—82no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—161no—
202C22×C13#44811yescharacteristic
203C22×C13#45411yescharacteristic
204C22×C13B(4,𝔽2)11yescharacteristic
205C4×C13—42no—
206C4×C13—41no—
207C4×C13—42no—
208C4×C13—41no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13—81no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13—161no—
215C22×Q8D4×C1311yescharacteristic
216C22×D4—21no—
217C23×C4D4×C1311yescharacteristic
218C2×SD16—41no—
219#123—41no—
220#121—21no—
221#121—21no—
222#120—41no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4D4×C1311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—41no—
233C2×C22⋊C4D4×C1311yescharacteristic
234C2×C22⋊C4C23×C1311yescharacteristic
235C2×C42—21no—
236#106—41no—
237#103—41no—
238#102—41no—
239#99—42no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—41no—
249#95D4×C1311yescharacteristic
250#95D4×C1311yescharacteristic
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—41no—
254C2×C13—41no—
255C2×C13—161no—
256C2×C13#159911yescharacteristic
257C2×C13#219711yescharacteristic
258C2×C13#220011yescharacteristic
259C24—21no—
260C24C2×D4×C1311yescharacteristic
261C2×Q8—41no—
262C2×Q8—81no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4C2×D4×C1311yescharacteristic
282C22×C4C2×D4×C1311yescharacteristic
283SD16—82no—
284C2×C8—41no—
285C2×C8—41no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—81no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C22⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—82no—
303C22⋊C4C13×SD1612yescomplemented
304C42—81no—
305C13#1217811yescharacteristic, direct product factor, Sylow
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—81no—
314C23—81no—
315C23C13×#12011yescharacteristic
316C23C2×C13×SD1611yescharacteristic
317C23C13×#13711yescharacteristic
318Q8—42no—
319Q8—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
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—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C8—81no—
357C8—81no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—82no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—161no—
372C22C13×#44811yescharacteristic
373C22C13×#45411yescharacteristic
374C22C13×B(4,𝔽2)11yescharacteristic
375C4—42no—
376C4—41no—
377C4—42no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—161no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—161no—
390C2C13×#159911yescharacteristic
391C2C13×#219711yescharacteristic
392C2C13×#220011yescharacteristic
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×#2742C2semidirect
5. C13×#1352C2semidirect
6. C13×#1351C2semidirect
7. C13×#1326C2semidirect
63. #12178C13direct (N × H)
108. C13×C22⋊C4SD16semidirect
110. #2742C2×C13semidirect
114. #1352C2×C13semidirect
115. #1351C2×C13semidirect
116. #1326C2×C13semidirect
303. C22⋊C4C13×SD16semidirect
305. C13#12178direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27422
C13×#20442
C13×#16132
C13×#16012
C13×#13522
C13×#13512
C13×#13262
#1217813