Finite Group Databasebeta

← C13×#13388 #15699727

Subgroups — C13×#13388 #15699727

Order 3328.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3059C211yesmaximal, characteristic
2C13×#2159C211yesmaximal, characteristic, complemented
3C2×C13×#362C211yesmaximal, characteristic, complemented
4C2×C13×#358C211yesmaximal, characteristic, complemented
5C2×C13×#350C211yesmaximal, characteristic
6C13×#1816C211yesmaximal, characteristic
7C13×#1382C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C2×C13×#131C2211yescharacteristic
10C13×#536—21no—
11C2×C13×M32C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C13×#470—22no—
14C13×#467—21no—
15C13×#467—21no—
16C2×C13×#108C2211yescharacteristic
17C13×#427C2211yescharacteristic
18C2×C13×#107C2211yescharacteristic
19C13×#419—21no—
20C13×#417—21no—
21C13×#367—21no—
22C13×#366—21no—
23C13×#362—22no—
24C13×#358—22no—
25C13×#350—22no—
26C13×#343—21no—
27C2×C13×#41D411yescharacteristic
28C22×Q8×C13—21no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16—21no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16D412yes—
35C13×#131—21no—
36C13×#131—21no—
37C13×#131—21no—
38C13×#131—21no—
39C2×C13×M16—21no—
40C2×C13×M16—21no—
41C2×C13×M16D411yescharacteristic
42C22×C8×C13—21no—
43C22×C8×C13C2311yescharacteristic
44C13×C4⋊Q8—41no—
45C13×#124—41no—
46C13×#123—42no—
47C13×C22⋊Q8—22no—
48C13×C22⋊Q8—22no—
49C13×#117—21no—
50C2×C13×C4⋊C4—21no—
51C13×M32—21no—
52C13×M32D412yes—
53C2×C13×C16—21no—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C13×#108—21no—
58C13×#108—21no—
59C13×#107—21no—
60C13×#107—21no—
61C13×#107D411yescharacteristic
62C13×#107D411yescharacteristic
63C13×#106—21no—
64C13×#103—22no—
65C13×#103—22no—
66C13×#103—41no—
67C13×#102—41no—
68#13388C1311yesmaximal, characteristic, direct product factor, Sylow
69C13×#41—21no—
70C13×#41—21no—
71C13×#41—21no—
72C13×#41—21no—
73C2×Q8×C13—22no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13D811yescharacteristic
80C2×D4×C13—21no—
81C2×D4×C13D811yescharacteristic
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C13×Q16—22no—
87C13×Q16—22no—
88C13×Q16—41no—
89C13×Q16—41no—
90C13×M16—21no—
91C13×M16—21no—
92C13×M16—41no—
93C13×M16—41no—
94C13×M16—41no—
95C13×M16—41no—
96C2×C8×C13—21no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13#4111yescharacteristic
104C2×C8×C13#4111yescharacteristic
105C2×C8×C13#4111yescharacteristic
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—41no—
115C42×C13—41no—
116C13×C16—22no—
117C13×C16—41no—
118#3059C2×C1311yescharacteristic
119#2159C2×C1311yescharacteristic, complemented
120C2×#362C2×C1311yescharacteristic, complemented
121C2×#358C2×C1311yescharacteristic, complemented
122C2×#350C2×C1311yescharacteristic
123#1816C2×C1311yescharacteristic
124#1382C2×C1311yescharacteristic, complemented
125C23×C13—21no—
126C23×C13AGL(1,ℤ/8)11yescharacteristic
127Q8×C13—21no—
128Q8×C13—21no—
129Q8×C13—42no—
130Q8×C13—42no—
131Q8×C13—81no—
132Q8×C13—81no—
133D4×C13—21no—
134D4×C13—21no—
135D4×C13—41no—
136D4×C13—41no—
137C2×C4×C13—21no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—161no—
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13C2×D811yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C8×C13—41no—
154C8×C13—81no—
155C8×C13#12111yescharacteristic
156C8×C13#12111yescharacteristic
157C8×C13#12311yescharacteristic
158C8×C13#12411yescharacteristic
159C22×Q16C22×C1311yescharacteristic
160C2×#131C22×C1311yescharacteristic
161#536—21no—
162C2×M32C22×C1311yescharacteristic
163C22×C16C22×C1311yescharacteristic
164#470—22no—
165#467—21no—
166#467—21no—
167C2×#108C22×C1311yescharacteristic
168#427C22×C1311yescharacteristic
169C2×#107C22×C1311yescharacteristic
170#419—21no—
171#417—21no—
172#367—21no—
173#366—21no—
174#362—22no—
175#358—22no—
176#350—22no—
177#343—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13#44711yescharacteristic
184C22×C13#46811yescharacteristic
185C22×C13#48211yescharacteristic
186C4×C13—41no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13—82no—
190C4×C13—161no—
191C4×C13#39411yescharacteristic
192C4×C13#45211yescharacteristic
193C4×C13#46611yescharacteristic
194C4×C13#48011yescharacteristic
195C2×#41D4×C1311yescharacteristic
196C22×Q8—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16D4×C1312yes—
203#131—21no—
204#131—21no—
205#131—21no—
206#131—21no—
207C2×M16—21no—
208C2×M16—21no—
209C2×M16D4×C1311yescharacteristic
210C22×C8—21no—
211C22×C8C23×C1311yescharacteristic
212C4⋊Q8—41no—
213#124—41no—
214#123—42no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217#117—21no—
218C2×C4⋊C4—21no—
219M32—21no—
220M32D4×C1312yes—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—21no—
224C2×C16—21no—
225#108—21no—
226#108—21no—
227#107—21no—
228#107—21no—
229#107D4×C1311yescharacteristic
230#107D4×C1311yescharacteristic
231#106—21no—
232#103—22no—
233#103—22no—
234#103—41no—
235#102—41no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—81no—
239C2×C13#203311yescharacteristic
240C2×C13#219311yescharacteristic
241C2×C13#219511yescharacteristic
242#41—21no—
243#41—21no—
244#41—21no—
245#41—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8C13×D811yescharacteristic
253C2×D4—21no—
254C2×D4C13×D811yescharacteristic
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4C2×D4×C1311yescharacteristic
259Q16—22no—
260Q16—22no—
261Q16—41no—
262Q16—41no—
263M16—21no—
264M16—21no—
265M16—41no—
266M16—41no—
267M16—41no—
268M16—41no—
269C2×C8—21no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8C2×D4×C1311yescharacteristic
274C2×C8C2×D4×C1311yescharacteristic
275C2×C8C2×D4×C1311yescharacteristic
276C2×C8C13×#4111yescharacteristic
277C2×C8C13×#4111yescharacteristic
278C2×C8C13×#4111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C42—41no—
289C16—22no—
290C16—41no—
291C13#1338811yescharacteristic, direct product factor, Sylow
292C23—21no—
293C23C13×AGL(1,ℤ/8)11yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—41no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—161no—
314C2×C4C13×#12011yescharacteristic
315C2×C4C13×#12111yescharacteristic
316C2×C4C13×#12311yescharacteristic
317C2×C4C2×C13×D811yescharacteristic
318C2×C4C13×#13511yescharacteristic
319C2×C4C13×#13711yescharacteristic
320C8—41no—
321C8—81no—
322C8C13×#12111yescharacteristic
323C8C13×#12111yescharacteristic
324C8C13×#12311yescharacteristic
325C8C13×#12411yescharacteristic
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22C13×#44711yescharacteristic
332C22C13×#46811yescharacteristic
333C22C13×#48211yescharacteristic
334C4—41no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—161no—
339C4C13×#39411yescharacteristic
340C4C13×#45211yescharacteristic
341C4C13×#46611yescharacteristic
342C4C13×#48011yescharacteristic
343C2—21no—
344C2—21no—
345C2—81no—
346C2C13×#203311yescharacteristic
347C2C13×#219311yescharacteristic
348C2C13×#219511yescharacteristic
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#41D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2159C2semidirect
3. C2×C13×#362C2semidirect
4. C2×C13×#358C2semidirect
7. C13×#1382C2semidirect
68. #13388C13direct (N × H)
119. #2159C2×C13semidirect
120. C2×#362C2×C13semidirect
121. C2×#358C2×C13semidirect
124. #1382C2×C13semidirect
291. C13#13388direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30592
C13×#21592
C2×C13×#3622
C2×C13×#3582
C2×C13×#3502
C13×#18162
C13×#13822
#1338813