Finite Group Databasebeta

← C13×#10224 #15696563

Subgroups — C13×#10224 #15696563

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3230C211yesmaximal, characteristic
2C13×#3209C211yesmaximal, characteristic
3C13×#3162C211yesmaximal, characteristic
4C13×#1993C211yesmaximal, characteristic
5C13×#1518C211yesmaximal, characteristic
6C13×#1518C211yesmaximal, characteristic
7C13×#1281C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#533C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C13×#501—21no—
12C13×#501—21no—
13C13×#501—21no—
14C13×#501—21no—
15C13×#500—21no—
16C13×#494—21no—
17C13×#487—21no—
18C13×#487—21no—
19C13×#484—22no—
20C13×#477—22no—
21C13×#462—22no—
22C13×#451—22no—
23C13×#431C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C13×#427—22no—
26C2×C13×#97C2211yescharacteristic
27C13×#382C2211yescharacteristic
28C13×#340—22no—
29C13×#328—22no—
30C13×#328—22no—
31C22×Q8×C13—21no—
32C2×C13×Q16—24no—
33C22×C8×C13D412yes—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8D412yes—
38C13×C4⋊Q8D411yescharacteristic
39C13×C4⋊Q8D411yescharacteristic
40C13×C4⋊Q8D411yescharacteristic
41C13×C4⋊Q8D411yescharacteristic
42C13×#125—21no—
43C13×#125—21no—
44C13×C22⋊Q8—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C13×#117—21no—
53C13×#117—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C42×C13C2311yescharacteristic
58C13×#107—22no—
59C13×#107—22no—
60C13×#107—24no—
61C13×#106—22no—
62C13×#106—22no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#103—24no—
66C13×#103—24no—
67C13×C22⋊C8D412yes—
68C13×C22⋊C8D412yes—
69C13×#97—21no—
70C13×#97—21no—
71C4×C8×C13—21no—
72C4×C8×C13—21no—
73C13×#95—21no—
74C13×#95—21no—
75#10224C1311yesmaximal, characteristic, direct product factor, Sylow
76C2×Q8×C13—21no—
77C2×Q8×C13—22no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—41no—
82C2×Q8×C13—82no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C13×Q16—84no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13Q1614yescomplemented
94C13×C4⋊C4—21no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—42no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C42×C13—41no—
114C42×C13—41no—
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119#3230C2×C1311yescharacteristic
120#3209C2×C1311yescharacteristic
121#3162C2×C1311yescharacteristic
122#1993C2×C1311yescharacteristic
123#1518C2×C1311yescharacteristic
124#1518C2×C1311yescharacteristic
125#1281C2×C1311yescharacteristic
126C23×C13#12711yescharacteristic
127Q8×C13—42no—
128Q8×C13—44no—
129Q8×C13—42no—
130Q8×C13—82no—
131Q8×C13—81no—
132Q8×C13—81no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—82no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13#12011yescharacteristic
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13C2×Q1612yes—
151C2×C4×C13#13712yes—
152C8×C13—24no—
153C8×C13—42no—
154C8×C13—42no—
155#533C22×C1311yescharacteristic
156#533C22×C1311yescharacteristic
157C2×C4⋊Q8C22×C1311yescharacteristic
158#501—21no—
159#501—21no—
160#501—21no—
161#501—21no—
162#500—21no—
163#494—21no—
164#487—21no—
165#487—21no—
166#484—22no—
167#477—22no—
168#462—22no—
169#451—22no—
170#431C22×C1311yescharacteristic
171#431C22×C1311yescharacteristic
172#427—22no—
173C2×#97C22×C1311yescharacteristic
174#382C22×C1311yescharacteristic
175#340—22no—
176#328—22no—
177#328—22no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#39211yescharacteristic
181C22×C13#49411yescharacteristic
182C22×C13#49711yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—82no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13—161no—
193C4×C13#45112yes—
194C4×C13#46212yes—
195C22×Q8—21no—
196C2×Q16—24no—
197C22×C8D4×C1312yes—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8D4×C1312yes—
202C4⋊Q8D4×C1311yescharacteristic
203C4⋊Q8D4×C1311yescharacteristic
204C4⋊Q8D4×C1311yescharacteristic
205C4⋊Q8D4×C1311yescharacteristic
206#125—21no—
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216#117—21no—
217#117—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C42C23×C1311yescharacteristic
222#107—22no—
223#107—22no—
224#107—24no—
225#106—22no—
226#106—22no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229#103—24no—
230#103—24no—
231C22⋊C8D4×C1312yes—
232C22⋊C8D4×C1312yes—
233#97—21no—
234#97—21no—
235C4×C8—21no—
236C4×C8—21no—
237#95—21no—
238#95—21no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13#200811yescharacteristic
242C2×C13#200911yescharacteristic
243C2×C13#201611yescharacteristic
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—82no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4C2×D4×C1311yescharacteristic
254C22×C4C2×D4×C1311yescharacteristic
255C22×C4C2×D4×C1311yescharacteristic
256Q16—84no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8C13×Q1614yescomplemented
262C4⋊C4—21no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C42—41no—
282C42—41no—
283C42C2×D4×C1311yescharacteristic
284C42C2×D4×C1311yescharacteristic
285C42C2×D4×C1311yescharacteristic
286C42C13×#4111yescharacteristic
287C13#1022411yescharacteristic, direct product factor, Sylow
288C23C13×#12711yescharacteristic
289Q8—42no—
290Q8—44no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—82no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4C13×#12011yescharacteristic
307C2×C4C13×#12011yescharacteristic
308C2×C4C13×#12011yescharacteristic
309C2×C4C13×#12111yescharacteristic
310C2×C4C13×#12111yescharacteristic
311C2×C4C13×#12111yescharacteristic
312C2×C4C2×C13×Q1612yes—
313C2×C4C13×#13712yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22—21no—
318C22—21no—
319C22C13×#39211yescharacteristic
320C22C13×#49411yescharacteristic
321C22C13×#49711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4C13×#45112yes—
333C4C13×#46212yes—
334C2—21no—
335C2—21no—
336C2C13×#200811yescharacteristic
337C2C13×#200911yescharacteristic
338C2C13×#201611yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC23×C13#127
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
75. #10224C13direct (N × H)
93. C2×C8×C13Q16semidirect
261. C2×C8C13×Q16semidirect
287. C13#10224direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32302
C13×#32092
C13×#31622
C13×#19932
C13×#15182
C13×#12812
#1022413