Finite Group Databasebeta

← C13×#10258 #15696597

Subgroups — C13×#10258 #15696597

Order 3328.

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

normal subgroups only

This group has 526 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×#3249C211yesmaximal, characteristic, complemented
2C13×#3077C212yesmaximal
3C13×#1954C211yesmaximal, characteristic
4C13×#1493C212yesmaximal, complemented
5C13×#1292C211yesmaximal, characteristic, complemented
6C13×#533C2212yes—
7C2×C4×D4×C13C2211yescharacteristic
8C13×#478—24no—
9C13×#477—22no—
10C13×#476—22no—
11C13×#474—22no—
12C13×#467—22no—
13C13×#462—22no—
14C13×#428—22no—
15C13×#423C2212yes—
16C2×C13×C4⋊C8C2211yescharacteristic
17C13×#418—22no—
18C2×C13×C22⋊C8—22no—
19C2×C4×C8×C13C2211yescharacteristic
20C13×Q8⋊C8—24no—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13—21no—
23C2×C13×Q16—22no—
24C2×C13×M16—22no—
25C22×C8×C13—21no—
26C22×C8×C13D412yes—
27C13×C4⋊Q8D412yes—
28C13×C4⋊Q8D412yes—
29C13×#125—22no—
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—22no—
32C4×Q8×C13—22no—
33C4×Q8×C13—22no—
34C4×D4×C13—22no—
35C4×D4×C13—22no—
36C13×#117—22no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C42×C13C2311yescharacteristic
40C13×#107—24no—
41C13×#107—22no—
42C13×#106—24no—
43C13×C4⋊C8—22no—
44C13×C4⋊C8—22no—
45C13×C4⋊C8D414yes—
46C13×#103—24no—
47C13×#102—24no—
48C13×#102—24no—
49C13×C22⋊C8—44no—
50C4×C8×C13—22no—
51#10258C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—21no—
57C2×D4×C13—22no—
58C2×D4×C13Q1612yescomplemented
59C22×C4×C13—21no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C13×Q16—82no—
68C13×M16—42no—
69C13×M16—42no—
70C2×C8×C13—22no—
71C2×C8×C13—24no—
72C2×C8×C13—22no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—42no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C42×C13—42no—
86C42×C13C2×D412yes—
87C42×C13C2×D412yes—
88#3249C2×C1311yescharacteristic, complemented
89#3077C2×C1312yes—
90#1954C2×C1311yescharacteristic
91#1493C2×C1312yescomplemented
92#1292C2×C1311yescharacteristic, complemented
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13#12111yescharacteristic
99Q8×C13—44no—
100Q8×C13—42no—
101Q8×C13—42no—
102D4×C13—24no—
103D4×C13—42no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—82no—
112C2×C4×C13—81no—
113C2×C4×C13—81no—
114C2×C4×C13#12012yes—
115C2×C4×C13#12011yescharacteristic
116C2×C4×C13#12112yes—
117C2×C4×C13#12711yescharacteristic
118C2×C4×C13C2×Q1611yescharacteristic
119C2×C4×C13#13511yescharacteristic
120C2×C4×C13#13712yes—
121C8×C13—42no—
122C8×C13—44no—
123C8×C13—42no—
124#533C22×C1312yes—
125C2×C4×D4C22×C1311yescharacteristic
126#478—24no—
127#477—22no—
128#476—22no—
129#474—22no—
130#467—22no—
131#462—22no—
132#428—22no—
133#423C22×C1312yes—
134C2×C4⋊C8C22×C1311yescharacteristic
135#418—22no—
136C2×C22⋊C8—22no—
137C2×C4×C8C22×C1311yescharacteristic
138Q8⋊C8—24no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—44no—
142C22×C13—42no—
143C22×C13—82no—
144C22×C13—81no—
145C22×C13—81no—
146C22×C13#39211yescharacteristic
147C22×C13#46711yescharacteristic
148C22×C13#47011yescharacteristic
149C4×C13—21no—
150C4×C13—22no—
151C4×C13—81no—
152C4×C13—82no—
153C4×C13—82no—
154C4×C13#45112yes—
155C4×C13#45212yes—
156C4×C13#45311yescharacteristic
157C4×C13#45411yescharacteristic
158C22×D4D4×C1311yescharacteristic
159C23×C4—21no—
160C2×Q16—22no—
161C2×M16—22no—
162C22×C8—21no—
163C22×C8D4×C1312yes—
164C4⋊Q8D4×C1312yes—
165C4⋊Q8D4×C1312yes—
166#125—22no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×D4—22no—
172C4×D4—22no—
173#117—22no—
174C2×C4⋊C4D4×C1311yescharacteristic
175C2×C22⋊C4—21no—
176C2×C42C23×C1311yescharacteristic
177#107—24no—
178#107—22no—
179#106—24no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8D4×C1314yes—
183#103—24no—
184#102—24no—
185#102—24no—
186C22⋊C8—44no—
187C4×C8—22no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—82no—
191C2×C13#200111yescharacteristic
192C2×C13#200611yescharacteristic
193C2×C13#201711yescharacteristic
194C24—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—22no—
200C2×D4C13×Q1612yescomplemented
201C22×C4—21no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C2×D4×C1311yescharacteristic
207C22×C4C2×D4×C1311yescharacteristic
208C22×C4C13×#4111yescharacteristic
209Q16—82no—
210M16—42no—
211M16—42no—
212C2×C8—22no—
213C2×C8—24no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—42no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C42—42no—
228C42C2×D4×C1312yes—
229C42C2×D4×C1312yes—
230C13#1025811yescharacteristic, direct product factor, Sylow
231C23—22no—
232C23—42no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23C13×#12111yescharacteristic
237Q8—44no—
238Q8—42no—
239Q8—42no—
240D4—24no—
241D4—42no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4C13×#12012yes—
253C2×C4C13×#12011yescharacteristic
254C2×C4C13×#12112yes—
255C2×C4C13×#12711yescharacteristic
256C2×C4C2×C13×Q1611yescharacteristic
257C2×C4C13×#13511yescharacteristic
258C2×C4C13×#13712yes—
259C8—42no—
260C8—44no—
261C8—42no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22C13×#39211yescharacteristic
270C22C13×#46711yescharacteristic
271C22C13×#47011yescharacteristic
272C4—21no—
273C4—22no—
274C4—81no—
275C4—82no—
276C4—82no—
277C4C13×#45112yes—
278C4C13×#45212yes—
279C4C13×#45311yescharacteristic
280C4C13×#45411yescharacteristic
281C2—21no—
282C2—21no—
283C2—82no—
284C2C13×#200111yescharacteristic
285C2C13×#200611yescharacteristic
286C2C13×#201711yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3249C2semidirect
4. C13×#1493C2semidirect
5. C13×#1292C2semidirect
51. #10258C13direct (N × H)
58. C2×D4×C13Q16semidirect
88. #3249C2×C13semidirect
91. #1493C2×C13semidirect
92. #1292C2×C13semidirect
200. C2×D4C13×Q16semidirect
230. C13#10258direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32492
C13×#30772
C13×#19542
C13×#14932
C13×#12922
#1025813