Finite Group Databasebeta

← C13×#12700 #15699039

Subgroups — C13×#12700 #15699039

Order 3328.

1018 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C22×C13×C4⋊Q8C211yesmaximal, characteristic
2C2×C13×#356C214yesmaximal, complemented
3C13×#1784C212yesmaximal
4C23×Q8×C13C411yescharacteristic
5C23×Q8×C13C2211yescharacteristic
6C2×C13×C4⋊Q8—22no—
7C2×C13×C4⋊Q8—28no—
8C2×C13×C4⋊Q8C412yes—
9C2×C13×C4⋊Q8C2212yes—
10C22×C13×C4⋊C4—22no—
11C22×C42×C13C411yescharacteristic
12C2×C13×#101—22no—
13C2×C13×#101C2214yes—
14C13×#407—22no—
15C13×#356—28no—
16C22×Q8×C13—24no—
17C22×Q8×C13—24no—
18C22×Q8×C13—21no—
19C22×Q8×C13—42no—
20C22×Q8×C13—42no—
21C22×Q8×C13—42no—
22C22×Q8×C13—42no—
23C22×Q8×C13C2×C412yes—
24C22×Q8×C13C2×C411yescharacteristic
25C22×Q8×C13D412yes—
26C22×Q8×C13C2311yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13—21no—
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13D412yes—
31C2×C13×M16—24no—
32C13×C4⋊Q8—216no—
33C13×C4⋊Q8—24no—
34C13×C4⋊Q8—24no—
35C13×C4⋊Q8—24no—
36C13×C4⋊Q8D418yes—
37C2×C13×C4⋊C4—216no—
38C2×C13×C4⋊C4—24no—
39C2×C13×C4⋊C4—24no—
40C2×C42×C13—21no—
41C2×C42×C13—24no—
42C2×C42×C13C2×C412yes—
43C13×#101—28no—
44C13×#101—44no—
45C13×C22⋊C8—44no—
46#12700C1311yesmaximal, characteristic, direct product factor, Sylow
47C24×C13C22⋊C411yescharacteristic
48C2×Q8×C13—24no—
49C2×Q8×C13—24no—
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—24no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—42no—
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C2×Q8×C13—416no—
59C2×Q8×C13—416no—
60C2×Q8×C13—42no—
61C2×Q8×C13—42no—
62C2×Q8×C13—42no—
63C2×Q8×C13—42no—
64C2×Q8×C13C22⋊C414yes—
65C2×Q8×C13C2×D414yes—
66C22×C4×C13—24no—
67C22×C4×C13—28no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—24no—
73C22×C4×C13—24no—
74C22×C4×C13—22no—
75C22×C4×C13—24no—
76C22×C4×C13—42no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13C22⋊C412yes—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D412yes—
83C13×M16—44no—
84C13×M16—44no—
85C2×C8×C13—44no—
86C13×C4⋊C4—216no—
87C13×C4⋊C4—216no—
88C42×C13—24no—
89C42×C13—22no—
90C42×C13C22⋊C414yes—
91C22×C4⋊Q8C2×C1311yescharacteristic
92C2×#356C2×C1314yescomplemented
93#1784C2×C1312yes—
94C23×C13—24no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13#9912yes—
98C23×C13C2×C22⋊C411yescharacteristic
99Q8×C13—44no—
100Q8×C13—48no—
101Q8×C13—48no—
102Q8×C13—44no—
103Q8×C13—44no—
104Q8×C13—44no—
105C2×C4×C13—216no—
106C2×C4×C13—28no—
107C2×C4×C13—28no—
108C2×C4×C13—21no—
109C2×C4×C13—24no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—24no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—48no—
120C2×C4×C13—48no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13#9912yes—
124C2×C4×C13C2×C22⋊C412yes—
125C2×C4×C13#12014yes—
126C8×C13—84no—
127C23×Q8C4×C1311yescharacteristic
128C23×Q8C22×C1311yescharacteristic
129C2×C4⋊Q8—22no—
130C2×C4⋊Q8—28no—
131C2×C4⋊Q8C4×C1312yes—
132C2×C4⋊Q8C22×C1312yes—
133C22×C4⋊C4—22no—
134C22×C42C4×C1311yescharacteristic
135C2×#101—22no—
136C2×#101C22×C1314yes—
137#407—22no—
138#356—28no—
139C22×C13—24no—
140C22×C13—24no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—22no—
144C22×C13#35614yescomplemented
145C22×C13#37911yescharacteristic
146C22×C13C2×#9911yescharacteristic
147C22×C13C2×#9911yescharacteristic
148C4×C13—28no—
149C4×C13—24no—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—42no—
153C4×C13—44no—
154C22×Q8—24no—
155C22×Q8—24no—
156C22×Q8—21no—
157C22×Q8—42no—
158C22×Q8—42no—
159C22×Q8—42no—
160C22×Q8—42no—
161C22×Q8C2×C4×C1312yes—
162C22×Q8C2×C4×C1311yescharacteristic
163C22×Q8D4×C1312yes—
164C22×Q8C23×C1311yescharacteristic
165C23×C4—21no—
166C23×C4—21no—
167C23×C4C2×C4×C1311yescharacteristic
168C23×C4D4×C1312yes—
169C2×M16—24no—
170C4⋊Q8—216no—
171C4⋊Q8—24no—
172C4⋊Q8—24no—
173C4⋊Q8—24no—
174C4⋊Q8D4×C1318yes—
175C2×C4⋊C4—216no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C42—21no—
179C2×C42—24no—
180C2×C42C2×C4×C1312yes—
181#101—28no—
182#101—44no—
183C22⋊C8—44no—
184C2×C13—21no—
185C2×C13—24no—
186C2×C13—21no—
187C2×C13#178111yescharacteristic
188C2×C13C2×#35612yes—
189C24C13×C22⋊C411yescharacteristic
190C2×Q8—24no—
191C2×Q8—24no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—24no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—416no—
201C2×Q8—416no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8C13×C22⋊C414yes—
207C2×Q8C2×D4×C1314yes—
208C22×C4—24no—
209C22×C4—28no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—24no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4C13×C22⋊C412yes—
222C22×C4C13×C22⋊C411yescharacteristic
223C22×C4C22×C4×C1311yescharacteristic
224C22×C4C2×D4×C1312yes—
225M16—44no—
226M16—44no—
227C2×C8—44no—
228C4⋊C4—216no—
229C4⋊C4—216no—
230C42—24no—
231C42—22no—
232C42C13×C22⋊C414yes—
233C13#1270011yescharacteristic, direct product factor, Sylow
234C23—21no—
235C23—21no—
236C23—24no—
237C23C13×#9912yes—
238C23C2×C13×C22⋊C411yescharacteristic
239Q8—44no—
240Q8—48no—
241Q8—44no—
242Q8—48no—
243Q8—44no—
244Q8—44no—
245C2×C4—216no—
246C2×C4—28no—
247C2×C4—28no—
248C2×C4—21no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—48no—
260C2×C4—48no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4C13×#9912yes—
264C2×C4C2×C13×C22⋊C412yes—
265C2×C4C13×#12014yes—
266C8—84no—
267C22—24no—
268C22—24no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22C13×#35614yescomplemented
273C22C13×#37911yescharacteristic
274C22C2×C13×#9911yescharacteristic
275C22C2×C13×#9911yescharacteristic
276C4—28no—
277C4—24no—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—44no—
282C2—21no—
283C2—21no—
284C2—24no—
285C2C13×#178111yescharacteristic
286C2C2×C13×#35612yes—
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C23×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#356C2semidirect
46. #12700C13direct (N × H)
92. C2×#356C2×C13semidirect
144. C22×C13#356semidirect
233. C13#12700direct (N × H)
272. C22C13×#356semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊Q82
C2×C13×#3562
C13×#17842
#1270013