Finite Group Databasebeta

← C13×#33564 #15719903

Subgroups — C13×#33564 #15719903

Order 3328.

1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 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×#3529C211yesmaximal, characteristic, complemented
2C13×#3018C213yesmaximal, complemented
3C13×#2203C216yesmaximal, complemented
4C13×#2202C212yesmaximal, complemented
5C13×#2132C213yesmaximal, complemented
6C13×#585C2211yescharacteristic, complemented
7C13×#575—23no—
8C13×#563C2213yescomplemented
9C13×#562—23no—
10C13×H(3,𝔽4)C2211yescharacteristic, complemented
11C13×#560—23no—
12C13×#532C2213yes—
13C13×#529—23no—
14C13×#525—23no—
15C13×#456C2216yescomplemented
16C13×#455—23no—
17C13×#454C2216yes—
18C13×#453—23no—
19C2×C13×#104—23no—
20C13×#413C2213yescomplemented
21C13×#356C2216yescomplemented
22C13×#355C2216yescomplemented
23C13×2−1+4—41no—
24C13×2−1+4C2312yes—
25C13×H(5,𝔽2)—23no—
26C13×H(5,𝔽2)—41no—
27C2×C13×#41—23no—
28C2×C13×#41—42no—
29C2×C13×#41D413yes—
30C2×C13×#41C2311yescharacteristic
31C23×C4×C13—21no—
32C13×#137—26no—
33C13×#137—43no—
34C13×AGL(1,ℤ/8)—26no—
35C13×AGL(1,ℤ/8)—43no—
36C13×#135—46no—
37C2×C13×M16—23no—
38C13×C4⋊Q8C2313yes—
39C13×#127D413yes—
40C13×#126—26no—
41C13×#125—23no—
42C13×#124—23no—
43C13×#124D413yes—
44C13×#124C2313yes—
45C13×#123—23no—
46C13×#123—26no—
47C13×#123—23no—
48C13×C22⋊Q8—23no—
49C13×C22⋊Q8—26no—
50C13×#121—26no—
51C13×#121—23no—
52C13×#121—26no—
53C13×#120—23no—
54C13×#120—23no—
55C4×Q8×C13—21no—
56C4×D4×C13—23no—
57C4×D4×C13—26no—
58C13×#117—23no—
59C2×C42×C13D413yes—
60C13×#104—26no—
61C13×#104—26no—
62C13×#101C2316yes—
63C13×#100—23no—
64#33564C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C13×#41—26no—
67C13×#41—26no—
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—43no—
71C13×#41—43no—
72C13×#41—43no—
73C13×#41—42no—
74C13×#41—46no—
75C13×#41—41no—
76C2×Q8×C13—21no—
77C2×Q8×C13—23no—
78C2×Q8×C13—42no—
79C2×Q8×C13C2×D413yes—
80C2×Q8×C13C2411yescharacteristic
81C2×D4×C13—23no—
82C2×D4×C13—23no—
83C2×D4×C13—26no—
84C2×D4×C13—23no—
85C2×D4×C13—46no—
86C2×D4×C13—43no—
87C2×D4×C13C2×D413yes—
88C2×D4×C13C2×D413yes—
89C22×C4×C13—23no—
90C22×C4×C13—23no—
91C22×C4×C13—23no—
92C22×C4×C13—43no—
93C22×C4×C13—81no—
94C22×C4×C13—81no—
95C22×C4×C13C2×D413yes—
96C13×Q16—46no—
97C13×SD16—46no—
98C13×SD16—46no—
99C13×D8—46no—
100C13×M16—26no—
101C13×M16—43no—
102C2×C8×C13—43no—
103C13×C4⋊C4—26no—
104C13×C4⋊C4—23no—
105C13×C4⋊C4—23no—
106C13×C4⋊C4—26no—
107C13×C22⋊C4—23no—
108C13×C22⋊C4—23no—
109C13×C22⋊C4—26no—
110C13×C22⋊C4—26no—
111C13×C22⋊C4—26no—
112C42×C13—23no—
113C42×C13C2×D413yes—
114C42×C13C2×D413yes—
115#3529C2×C1311yescharacteristic, complemented
116#3018C2×C1313yescomplemented
117#2203C2×C1316yescomplemented
118#2202C2×C1312yescomplemented
119#2132C2×C1313yescomplemented
120C23×C13—23no—
121C23×C13—43no—
122C23×C13—81no—
123C23×C13—82no—
124C23×C13#12013yes—
125Q8×C13—26no—
126Q8×C13—41no—
127Q8×C13—43no—
128Q8×C13—41no—
129Q8×C13—81no—
130D4×C13—26no—
131D4×C13—43no—
132D4×C13—43no—
133D4×C13—46no—
134D4×C13—42no—
135D4×C13—41no—
136D4×C13—83no—
137D4×C13—86no—
138D4×C13—83no—
139C2×C4×C13—23no—
140C2×C4×C13—23no—
141C2×C4×C13—23no—
142C2×C4×C13—23no—
143C2×C4×C13—23no—
144C2×C4×C13—46no—
145C2×C4×C13—43no—
146C2×C4×C13—43no—
147C2×C4×C13—43no—
148C2×C4×C13—42no—
149C2×C4×C13—83no—
150C2×C4×C13—83no—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13C22×D413yes—
153C8×C13—46no—
154#585C22×C1311yescharacteristic, complemented
155#575—23no—
156#563C22×C1313yescomplemented
157#562—23no—
158H(3,𝔽4)C22×C1311yescharacteristic, complemented
159#560—23no—
160#532C22×C1313yes—
161#529—23no—
162#525—23no—
163#456C22×C1316yescomplemented
164#455—23no—
165#454C22×C1316yes—
166#453—23no—
167C2×#104—23no—
168#413C22×C1313yescomplemented
169#356C22×C1316yescomplemented
170#355C22×C1316yescomplemented
171C22×C13—23no—
172C22×C13—43no—
173C22×C13—46no—
174C22×C13—42no—
175C22×C13—43no—
176C22×C13—84no—
177C22×C13—163no—
178C22×C13C2×#12011yescharacteristic
179C4×C13—23no—
180C4×C13—43no—
181C4×C13—43no—
182C4×C13—43no—
183C4×C13—42no—
184C4×C13B(4,𝔽2)11yescharacteristic
185C4×C13B(4,𝔽2)11yescharacteristic
1862−1+4—41no—
1872−1+4C23×C1312yes—
188H(5,𝔽2)—23no—
189H(5,𝔽2)—41no—
190C2×#41—23no—
191C2×#41—42no—
192C2×#41D4×C1313yes—
193C2×#41C23×C1311yescharacteristic
194C23×C4—21no—
195#137—26no—
196#137—43no—
197AGL(1,ℤ/8)—26no—
198AGL(1,ℤ/8)—43no—
199#135—46no—
200C2×M16—23no—
201C4⋊Q8C23×C1313yes—
202#127D4×C1313yes—
203#126—26no—
204#125—23no—
205#124—23no—
206#124D4×C1313yes—
207#124C23×C1313yes—
208#123—23no—
209#123—26no—
210#123—23no—
211C22⋊Q8—23no—
212C22⋊Q8—26no—
213#121—26no—
214#121—23no—
215#121—26no—
216#120—23no—
217#120—23no—
218C4×Q8—21no—
219C4×D4—23no—
220C4×D4—26no—
221#117—23no—
222C2×C42D4×C1313yes—
223#104—26no—
224#104—26no—
225#101C23×C1316yes—
226#100—23no—
227C2×C13—21no—
228C2×C13—43no—
229C2×C13—83no—
230C2×C13—82no—
231C2×C13C2×B(4,𝔽2)11yescharacteristic
232C24—21no—
233#41—26no—
234#41—26no—
235#41—41no—
236#41—41no—
237#41—43no—
238#41—43no—
239#41—43no—
240#41—42no—
241#41—46no—
242#41—41no—
243C2×Q8—21no—
244C2×Q8—23no—
245C2×Q8—42no—
246C2×Q8C2×D4×C1313yes—
247C2×Q8C24×C1311yescharacteristic
248C2×D4—23no—
249C2×D4—23no—
250C2×D4—26no—
251C2×D4—23no—
252C2×D4—46no—
253C2×D4—43no—
254C2×D4C2×D4×C1313yes—
255C2×D4C2×D4×C1313yes—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—43no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4C2×D4×C1313yes—
263Q16—46no—
264SD16—46no—
265SD16—46no—
266D8—46no—
267M16—26no—
268M16—43no—
269C2×C8—43no—
270C4⋊C4—26no—
271C4⋊C4—23no—
272C4⋊C4—23no—
273C4⋊C4—26no—
274C22⋊C4—23no—
275C22⋊C4—23no—
276C22⋊C4—26no—
277C22⋊C4—26no—
278C22⋊C4—26no—
279C42—23no—
280C42C2×D4×C1313yes—
281C42C2×D4×C1313yes—
282C13#3356411yescharacteristic, direct product factor, Sylow
283C23—23no—
284C23—43no—
285C23—81no—
286C23—82no—
287C23C13×#12013yes—
288Q8—26no—
289Q8—41no—
290Q8—43no—
291Q8—41no—
292Q8—81no—
293D4—26no—
294D4—43no—
295D4—43no—
296D4—46no—
297D4—42no—
298D4—41no—
299D4—83no—
300D4—86no—
301D4—83no—
302C2×C4—23no—
303C2×C4—23no—
304C2×C4—23no—
305C2×C4—23no—
306C2×C4—23no—
307C2×C4—46no—
308C2×C4—43no—
309C2×C4—43no—
310C2×C4—43no—
311C2×C4—42no—
312C2×C4—83no—
313C2×C4—83no—
314C2×C4C13×#12011yescharacteristic
315C2×C4C22×D4×C1313yes—
316C8—46no—
317C22—23no—
318C22—43no—
319C22—46no—
320C22—42no—
321C22—43no—
322C22—84no—
323C22—163no—
324C22C2×C13×#12011yescharacteristic
325C4—23no—
326C4—43no—
327C4—43no—
328C4—43no—
329C4—42no—
330C4C13×B(4,𝔽2)11yescharacteristic
331C4C13×B(4,𝔽2)11yescharacteristic
332C2—21no—
333C2—43no—
334C2—83no—
335C2—82no—
336C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
centerC4×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C13
socleC2×C13C2×B(4,𝔽2)
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3529C2semidirect
2. C13×#3018C2semidirect
3. C13×#2203C2semidirect
4. C13×#2202C2semidirect
5. C13×#2132C2semidirect
6. C13×#585C22semidirect
8. C13×#563C22semidirect
10. C13×H(3,𝔽4)C22semidirect
15. C13×#456C22semidirect
20. C13×#413C22semidirect
21. C13×#356C22semidirect
22. C13×#355C22semidirect
64. #33564C13direct (N × H)
115. #3529C2×C13semidirect
116. #3018C2×C13semidirect
117. #2203C2×C13semidirect
118. #2202C2×C13semidirect
119. #2132C2×C13semidirect
154. #585C22×C13semidirect
156. #563C22×C13semidirect
158. H(3,𝔽4)C22×C13semidirect
163. #456C22×C13semidirect
168. #413C22×C13semidirect
169. #356C22×C13semidirect
170. #355C22×C13semidirect
282. C13#33564direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35292
C13×#30182
C13×#22032
C13×#22022
C13×#21322
#3356413