Finite Group Databasebeta

← C13×#12185 #15698524

Subgroups — C13×#12185 #15698524

Order 3328.

360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2844C211yesmaximal, characteristic, complemented
2C13×#2040C211yesmaximal, characteristic
3C13×#1616C212yesmaximal
4C13×#1353C212yesmaximal, complemented
5C13×#1324C211yesmaximal, characteristic, complemented
6C13×#537C2211yescharacteristic
7C13×#481—22no—
8C2×C13×#104—21no—
9C13×#417—21no—
10C13×#400—22no—
11C13×#400C2212yes—
12C13×#395—22no—
13C13×#395—21no—
14C13×#382—21no—
15C13×#382C2211yescharacteristic
16C13×#343C2211yescharacteristic
17C13×#327—22no—
18C13×#324C2212yes—
19C2×C13×#41—21no—
20C22×Q8×C13—21no—
21C2×C13×M16—21no—
22C13×C22⋊Q8—41no—
23C13×#121—22no—
24C13×#121—41no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13D411yescharacteristic
32C13×#106—42no—
33C13×#104—42no—
34C13×#103—41no—
35C13×#102—41no—
36C13×#102—42no—
37C13×C22⋊C8—22no—
38C13×#95—22no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95D412yes—
44#12185C1311yesmaximal, characteristic, direct product factor, Sylow
45C13×#41—41no—
46C13×#41—41no—
47C13×#41—41no—
48C13×#41—41no—
49C2×Q8×C13—21no—
50C2×Q8×C13—82no—
51C2×Q8×C13—81no—
52C2×D4×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C13×M16—41no—
63C13×M16—41no—
64C2×C8×C13—42no—
65C2×C8×C13—41no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—81no—
71C13×C4⋊C4—81no—
72C13×C4⋊C4—82no—
73C13×C22⋊C4—42no—
74C42×C13—21no—
75C42×C13SD1612yes—
76#2844C2×C1311yescharacteristic, complemented
77#2040C2×C1311yescharacteristic
78#1616C2×C1312yes—
79#1353C2×C1312yescomplemented
80#1324C2×C1311yescharacteristic, complemented
81C23×C13—41no—
82C23×C13#12011yescharacteristic
83Q8×C13—41no—
84Q8×C13—41no—
85Q8×C13—84no—
86D4×C13—41no—
87D4×C13—41no—
88D4×C13—82no—
89D4×C13—81no—
90D4×C13—81no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—81no—
108C2×C4×C13—81no—
109C2×C4×C13C2×SD1611yescharacteristic
110C2×C4×C13#13711yescharacteristic
111C8×C13—81no—
112C8×C13—82no—
113#537C22×C1311yescharacteristic
114#481—22no—
115C2×#104—21no—
116#417—21no—
117#400—22no—
118#400C22×C1312yes—
119#395—22no—
120#395—21no—
121#382—21no—
122#382C22×C1311yescharacteristic
123#343C22×C1311yescharacteristic
124#327—22no—
125#324C22×C1312yes—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—81no—
129C22×C13—81no—
130C22×C13—81no—
131C22×C13#44811yescharacteristic
132C22×C13#45411yescharacteristic
133C22×C13B(4,𝔽2)11yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—42no—
138C4×C13—82no—
139C4×C13—81no—
140C4×C13—81no—
141C4×C13—82no—
142C2×#41—21no—
143C22×Q8—21no—
144C2×M16—21no—
145C22⋊Q8—41no—
146#121—22no—
147#121—41no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4D4×C1311yescharacteristic
152C2×C4⋊C4D4×C1312yes—
153C2×C4⋊C4C23×C1311yescharacteristic
154C2×C42D4×C1311yescharacteristic
155#106—42no—
156#104—42no—
157#103—41no—
158#102—41no—
159#102—42no—
160C22⋊C8—22no—
161#95—22no—
162#95—21no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95D4×C1312yes—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13—161no—
170C2×C13#159911yescharacteristic
171C2×C13#220111yescharacteristic
172C2×C13#220211yescharacteristic
173#41—41no—
174#41—41no—
175#41—41no—
176#41—41no—
177C2×Q8—21no—
178C2×Q8—82no—
179C2×Q8—81no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—41no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4C2×D4×C1311yescharacteristic
189C22×C4C2×D4×C1312yes—
190M16—41no—
191M16—41no—
192C2×C8—42no—
193C2×C8—41no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C22⋊C4—42no—
202C42—21no—
203C42C13×SD1612yes—
204C13#1218511yescharacteristic, direct product factor, Sylow
205C23—41no—
206C23C13×#12011yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—84no—
210D4—41no—
211D4—41no—
212D4—82no—
213D4—81no—
214D4—81no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4C2×C13×SD1611yescharacteristic
234C2×C4C13×#13711yescharacteristic
235C8—81no—
236C8—82no—
237C22—21no—
238C22—21no—
239C22—81no—
240C22—81no—
241C22—81no—
242C22C13×#44811yescharacteristic
243C22C13×#45411yescharacteristic
244C22C13×B(4,𝔽2)11yescharacteristic
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—82no—
250C4—81no—
251C4—81no—
252C4—82no—
253C2—21no—
254C2—21no—
255C2—161no—
256C2C13×#159911yescharacteristic
257C2C13×#220111yescharacteristic
258C2C13×#220211yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC13×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2844C2semidirect
4. C13×#1353C2semidirect
5. C13×#1324C2semidirect
44. #12185C13direct (N × H)
76. #2844C2×C13semidirect
79. #1353C2×C13semidirect
80. #1324C2×C13semidirect
204. C13#12185direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28442
C13×#20402
C13×#16162
C13×#13532
C13×#13242
#1218513