Finite Group Databasebeta

← C13×#9972 #15696311

Subgroups — C13×#9972 #15696311

Order 3328.

632 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 138 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×#484C212yesmaximal
2C13×#2659C211yesmaximal, characteristic
3C2×C13×#328C212yesmaximal
4C13×#1445C211yesmaximal, characteristic
5C13×#1280C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#484—24no—
9C13×#484—24no—
10C2×C13×#107—22no—
11C2×C13×#103—22no—
12C2×C13×C22⋊C8C2212yes—
13C13×#398—22no—
14C13×#395—22no—
15C13×#380—22no—
16C2×C13×#95—22no—
17C2×C13×#95C2211yescharacteristic
18C2×C13×#95C2211yescharacteristic
19C13×#328—24no—
20C22×Q8×C13D412yes—
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13D412yes—
24C23×C4×C13C2311yescharacteristic
25C22×C8×C13—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4D412yes—
37C2×C13×C4⋊C4D412yes—
38C2×C13×C22⋊C4—22no—
39C13×#107—28no—
40C13×#103—28no—
41C13×C22⋊C8—22no—
42C13×C22⋊C8D414yes—
43C13×#95—24no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—44no—
47#9972C1311yesmaximal, characteristic, direct product factor, Sylow
48C24×C13C2×D411yescharacteristic
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—44no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—42no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—41no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—42no—
69C22×C4×C13Q1614yes—
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13#4111yescharacteristic
74C2×C8×C13—24no—
75C2×C8×C13—44no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—82no—
83C13×C4⋊C4—82no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C2×#484C2×C1312yes—
87#2659C2×C1311yescharacteristic
88C2×#328C2×C1312yes—
89#1445C2×C1311yescharacteristic
90#1280C2×C1311yescharacteristic
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—22no—
94C23×C13#12011yescharacteristic
95C23×C13#12111yescharacteristic
96C23×C13#12711yescharacteristic
97C23×C13C2×Q1612yes—
98C23×C13#13712yes—
99Q8×C13—44no—
100Q8×C13—82no—
101C2×C4×C13—24no—
102C2×C4×C13—24no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—44no—
109C2×C4×C13—44no—
110C2×C4×C13—42no—
111C2×C4×C13—44no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—44no—
118C2×C4×C13—82no—
119C2×C4×C13—82no—
120C2×C4×C13—81no—
121C2×C4×C13—82no—
122C2×C4×C13—81no—
123C2×C4×C13—81no—
124C2×C4×C13—81no—
125C2×C4×C13#12012yes—
126C2×C4×C13#12112yes—
127C8×C13—44no—
128C2×C22⋊Q8C22×C1312yes—
129C22×C4⋊C4C22×C1311yescharacteristic
130#484—24no—
131#484—24no—
132C2×#107—22no—
133C2×#103—22no—
134C2×C22⋊C8C22×C1312yes—
135#398—22no—
136#395—22no—
137#380—22no—
138C2×#95—22no—
139C2×#95C22×C1311yescharacteristic
140C2×#95C22×C1311yescharacteristic
141#328—24no—
142C22×C13—22no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13#39211yescharacteristic
151C22×C13#45112yes—
152C22×C13#45311yescharacteristic
153C22×C13#45411yescharacteristic
154C22×C13#45812yes—
155C22×C13#46212yes—
156C22×C13#49411yescharacteristic
157C22×C13#49711yescharacteristic
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—44no—
161C4×C13—82no—
162C4×C13—82no—
163C4×C13—82no—
164C4×C13—82no—
165C22×Q8D4×C1312yes—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4D4×C1312yes—
169C23×C4C23×C1311yescharacteristic
170C22×C8—22no—
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C22⋊Q8—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4D4×C1312yes—
182C2×C4⋊C4D4×C1312yes—
183C2×C22⋊C4—22no—
184#107—28no—
185#103—28no—
186C22⋊C8—22no—
187C22⋊C8D4×C1314yes—
188#95—24no—
189#95—22no—
190#95—22no—
191#95—44no—
192C2×C13—21no—
193C2×C13—22no—
194C2×C13—21no—
195C2×C13#161412yes—
196C2×C13#161712yes—
197C2×C13#200611yescharacteristic
198C2×C13#201611yescharacteristic
199C2×C13#202211yescharacteristic
200C24C2×D4×C1311yescharacteristic
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—44no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4C13×Q1614yes—
222C22×C4C2×D4×C1312yes—
223C22×C4C2×D4×C1311yescharacteristic
224C22×C4C2×D4×C1312yes—
225C22×C4C13×#4111yescharacteristic
226C2×C8—24no—
227C2×C8—44no—
228C4⋊C4—24no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—82no—
235C4⋊C4—82no—
236C22⋊C4—42no—
237C22⋊C4—42no—
238C13#997211yescharacteristic, direct product factor, Sylow
239C23—21no—
240C23—21no—
241C23—22no—
242C23C13×#12011yescharacteristic
243C23C13×#12111yescharacteristic
244C23C13×#12711yescharacteristic
245C23C2×C13×Q1612yes—
246C23C13×#13712yes—
247Q8—44no—
248Q8—82no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—82no—
267C2×C4—81no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4C13×#12012yes—
274C2×C4C13×#12112yes—
275C8—44no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22C13×#39211yescharacteristic
285C22C13×#45112yes—
286C22C13×#45311yescharacteristic
287C22C13×#45411yescharacteristic
288C22C13×#45812yes—
289C22C13×#46212yes—
290C22C13×#49411yescharacteristic
291C22C13×#49711yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—82no—
298C4—82no—
299C2—21no—
300C2—22no—
301C2—21no—
302C2C13×#161412yes—
303C2C13×#161712yes—
304C2C13×#200611yescharacteristic
305C2C13×#201611yescharacteristic
306C2C13×#202211yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
47. #9972C13direct (N × H)
238. C13#9972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4842
C13×#26592
C2×C13×#3282
C13×#14452
C13×#12802
#997213