Finite Group Databasebeta

← C13×#10325 #15696664

Subgroups — C13×#10325 #15696664

Order 3328.

602 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3189C211yesmaximal, characteristic
2C13×#2855C212yesmaximal
3C13×#1817C211yesmaximal, characteristic
4C13×#1520C212yesmaximal
5C13×#1289C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C22×C42×C13C2211yescharacteristic
8C13×#484—22no—
9C13×#467—22no—
10C13×#451—22no—
11C2×C13×C22⋊C8C2211yescharacteristic
12C2×C13×C22⋊C8C2211yescharacteristic
13C13×#391—22no—
14C13×#389—22no—
15C13×#387—24no—
16C13×#385—22no—
17C13×#381—22no—
18C13×#380C2212yes—
19C13×#336—22no—
20C13×#328—24no—
21C22×Q8×C13D412yes—
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C2×C13×Q16—22no—
26C22×C8×C13—21no—
27C22×C8×C13D412yes—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—22no—
32C2×C13×C4⋊C4—24no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4D412yes—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C42×C13—22no—
39C2×C42×C13—22no—
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C13×#107—22no—
43C13×#103—24no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46C13×#95—24no—
47C13×#95—24no—
48C13×#95—24no—
49C13×#95D414yes—
50#10325C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C2×D411yescharacteristic
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—44no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—24no—
63C22×C4×C13—22no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13Q1612yescomplemented
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D412yes—
70C22×C4×C13#4111yescharacteristic
71C13×Q16—82no—
72C2×C8×C13—22no—
73C2×C8×C13—42no—
74C2×C8×C13—42no—
75C2×C8×C13—41no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—44no—
79C13×C4⋊C4—48no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—41no—
87C42×C13—42no—
88C42×C13—41no—
89#3189C2×C1311yescharacteristic
90#2855C2×C1312yes—
91#1817C2×C1311yescharacteristic
92#1520C2×C1312yes—
93#1289C2×C1311yescharacteristic
94C23×C13—41no—
95C23×C13—41no—
96C23×C13#12012yes—
97C23×C13#12111yescharacteristic
98C23×C13C2×Q1611yescharacteristic
99C23×C13#13511yescharacteristic
100C23×C13#13712yes—
101Q8×C13—44no—
102Q8×C13—82no—
103C2×C4×C13—24no—
104C2×C4×C13—22no—
105C2×C4×C13—24no—
106C2×C4×C13—22no—
107C2×C4×C13—24no—
108C2×C4×C13—22no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—44no—
118C2×C4×C13—44no—
119C2×C4×C13—44no—
120C2×C4×C13—44no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—44no—
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13#12112yes—
126C2×C4×C13#12711yescharacteristic
127C8×C13—42no—
128C8×C13—81no—
129C2×C22⋊Q8C22×C1312yes—
130C22×C42C22×C1311yescharacteristic
131#484—22no—
132#467—22no—
133#451—22no—
134C2×C22⋊C8C22×C1311yescharacteristic
135C2×C22⋊C8C22×C1311yescharacteristic
136#391—22no—
137#389—22no—
138#387—24no—
139#385—22no—
140#381—22no—
141#380C22×C1312yes—
142#336—22no—
143#328—24no—
144C22×C13—22no—
145C22×C13—21no—
146C22×C13—22no—
147C22×C13—21no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—42no—
151C22×C13#39211yescharacteristic
152C22×C13#45112yes—
153C22×C13#45212yes—
154C22×C13#46711yescharacteristic
155C22×C13#47011yescharacteristic
156C4×C13—21no—
157C4×C13—22no—
158C4×C13—42no—
159C4×C13—42no—
160C4×C13—84no—
161C4×C13—82no—
162C4×C13—82no—
163C4×C13#45812yes—
164C22×Q8D4×C1312yes—
165C23×C4D4×C1311yescharacteristic
166C23×C4D4×C1311yescharacteristic
167C23×C4C23×C1311yescharacteristic
168C2×Q16—22no—
169C22×C8—21no—
170C22×C8D4×C1312yes—
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C22⋊Q8—22no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4D4×C1312yes—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C42—21no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—21no—
185#107—22no—
186#103—24no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189#95—24no—
190#95—24no—
191#95—24no—
192#95D4×C1314yes—
193C2×C13—22no—
194C2×C13—22no—
195C2×C13—21no—
196C2×C13—21no—
197C2×C13#200111yescharacteristic
198C2×C13#201011yescharacteristic
199C2×C13#202211yescharacteristic
200C24C2×D4×C1311yescharacteristic
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—44no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4C13×Q1612yescomplemented
216C22×C4C2×D4×C1312yes—
217C22×C4C2×D4×C1311yescharacteristic
218C22×C4C2×D4×C1312yes—
219C22×C4C13×#4111yescharacteristic
220Q16—82no—
221C2×C8—22no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—41no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—44no—
228C4⋊C4—48no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C42—41no—
236C42—42no—
237C42—41no—
238C13#1032511yescharacteristic, direct product factor, Sylow
239C23—41no—
240C23—41no—
241C23C13×#12012yes—
242C23C13×#12111yescharacteristic
243C23C2×C13×Q1611yescharacteristic
244C23C13×#13511yescharacteristic
245C23C13×#13712yes—
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4C13×#12011yescharacteristic
270C2×C4C13×#12112yes—
271C2×C4C13×#12711yescharacteristic
272C8—42no—
273C8—81no—
274C22—22no—
275C22—21no—
276C22—22no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22C13×#39211yescharacteristic
282C22C13×#45112yes—
283C22C13×#45212yes—
284C22C13×#46711yescharacteristic
285C22C13×#47011yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—84no—
291C4—82no—
292C4—82no—
293C4C13×#45812yes—
294C2—22no—
295C2—22no—
296C2—21no—
297C2—21no—
298C2C13×#200111yescharacteristic
299C2C13×#201011yescharacteristic
300C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
50. #10325C13direct (N × H)
66. C22×C4×C13Q16semidirect
215. C22×C4C13×Q16semidirect
238. C13#10325direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31892
C13×#28552
C13×#18172
C13×#15202
C13×#12892
#1032513