Finite Group Databasebeta

← C13×#12257 #15698596

Subgroups — C13×#12257 #15698596

Order 3328.

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

normal subgroups only

This group has 342 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×#2571C211yesmaximal, characteristic
2C13×#2060C211yesmaximal, characteristic
3C13×#1617C212yesmaximal
4C13×#1353C212yesmaximal
5C13×#1325C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C13×#484—22no—
8C13×#428—21no—
9C13×#400—21no—
10C13×#400C2212yes—
11C13×#389—22no—
12C13×#384C2211yescharacteristic
13C13×#382—22no—
14C4×C13×C4⋊C4—21no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17C13×#328—22no—
18C13×#324C2212yes—
19C2×C13×M16—21no—
20C13×C4⋊Q8—41no—
21C13×#125—41no—
22C13×C22⋊Q8—22no—
23C13×#117—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13—22no—
32C2×C42×C13D411yescharacteristic
33C13×#107—41no—
34C13×#107—42no—
35C13×#106—41no—
36C13×#103—42no—
37C13×C22⋊C8—22no—
38C13×#95—21no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95D412yes—
43#12257C1311yesmaximal, characteristic, direct product factor, Sylow
44C2×Q8×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13C2×D411yescharacteristic
50C22×C4×C13C2×D412yes—
51C13×M16—22no—
52C13×M16—41no—
53C2×C8×C13—41no—
54C2×C8×C13—42no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—44no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—81no—
66C13×C22⋊C4—41no—
67C42×C13—21no—
68C42×C13—44no—
69C42×C13—41no—
70C42×C13Q1612yes—
71#2571C2×C1311yescharacteristic
72#2060C2×C1311yescharacteristic
73#1617C2×C1312yes—
74#1353C2×C1312yes—
75#1325C2×C1311yescharacteristic
76C23×C13#12011yescharacteristic
77Q8×C13—82no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13C2×Q1611yescharacteristic
96C2×C4×C13#13711yescharacteristic
97C8×C13—42no—
98C8×C13—82no—
99#544C22×C1311yescharacteristic
100#484—22no—
101#428—21no—
102#400—21no—
103#400C22×C1312yes—
104#389—22no—
105#384C22×C1311yescharacteristic
106#382—22no—
107C4×C4⋊C4—21no—
108#343C22×C1311yescharacteristic
109#339—21no—
110#328—22no—
111#324C22×C1312yes—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13#45111yescharacteristic
115C22×C13#45611yescharacteristic
116C22×C13B(4,𝔽2)11yescharacteristic
117C4×C13—24no—
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—82no—
122C4×C13—81no—
123C4×C13—81no—
124C4×C13—81no—
125C4×C13—82no—
126C2×M16—21no—
127C4⋊Q8—41no—
128#125—41no—
129C22⋊Q8—22no—
130#117—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4D4×C1311yescharacteristic
136C2×C4⋊C4D4×C1312yes—
137C2×C4⋊C4C23×C1311yescharacteristic
138C2×C42—22no—
139C2×C42D4×C1311yescharacteristic
140#107—41no—
141#107—42no—
142#106—41no—
143#103—42no—
144C22⋊C8—22no—
145#95—21no—
146#95—22no—
147#95—22no—
148#95—22no—
149#95D4×C1312yes—
150C2×C13—21no—
151C2×C13—21no—
152C2×C13#160511yescharacteristic
153C2×C13#219811yescharacteristic
154C2×C13#220411yescharacteristic
155C2×Q8—22no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—21no—
160C22×C4C2×D4×C1311yescharacteristic
161C22×C4C2×D4×C1312yes—
162M16—22no—
163M16—41no—
164C2×C8—41no—
165C2×C8—42no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—22no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—41no—
172C4⋊C4—42no—
173C4⋊C4—44no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—81no—
177C22⋊C4—41no—
178C42—21no—
179C42—44no—
180C42—41no—
181C42C13×Q1612yes—
182C13#1225711yescharacteristic, direct product factor, Sylow
183C23C13×#12011yescharacteristic
184Q8—82no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—42no—
202C2×C4C2×C13×Q1611yescharacteristic
203C2×C4C13×#13711yescharacteristic
204C8—42no—
205C8—82no—
206C22—21no—
207C22—21no—
208C22C13×#45111yescharacteristic
209C22C13×#45611yescharacteristic
210C22C13×B(4,𝔽2)11yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—82no—
216C4—81no—
217C4—81no—
218C4—81no—
219C4—82no—
220C2—21no—
221C2—21no—
222C2C13×#160511yescharacteristic
223C2C13×#219811yescharacteristic
224C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC23×C13#120
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
43. #12257C13direct (N × H)
182. C13#12257direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25712
C13×#20602
C13×#16172
C13×#13532
C13×#13252
#1225713