Finite Group Databasebeta

← C13×#13394 #15699733

Subgroups — C13×#13394 #15699733

Order 3328.

392 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#473C211yesmaximal, characteristic
2C2×C13×#368C211yesmaximal, characteristic, complemented
3C2×C13×#362C211yesmaximal, characteristic, complemented
4C2×C13×#358C211yesmaximal, characteristic, complemented
5C13×#2113C211yesmaximal, characteristic
6C13×#1816C211yesmaximal, characteristic
7C13×#1387C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C22×C13×Q16C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C2×C13×M32C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C13×#473—22no—
14C13×#473—22no—
15C2×C13×#108C2211yescharacteristic
16C2×C13×#108C2211yescharacteristic
17C2×C13×#107C2211yescharacteristic
18C13×#417—21no—
19C2×C13×#101—21no—
20C13×#368—22no—
21C13×#362—22no—
22C13×#358—22no—
23C13×C22⋊C16—22no—
24C13×#343—21no—
25C2×C13×#41D411yescharacteristic
26C22×Q8×C13—21no—
27C13×#137—24no—
28C13×#137—42no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16—21no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—41no—
35C2×C13×Q16D412yes—
36C2×C13×SD16—41no—
37C13×#131—21no—
38C13×#131—21no—
39C13×#131—21no—
40C13×#131—21no—
41C2×C13×M16—21no—
42C2×C13×M16—21no—
43C2×C13×M16—21no—
44C2×C13×M16D411yescharacteristic
45C22×C8×C13—21no—
46C22×C8×C13C2311yescharacteristic
47C2×C13×C4⋊C4—21no—
48C13×M32—21no—
49C13×M32—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C2×C13×C16—21no—
53C2×C13×C16D412yes—
54C13×#108—21no—
55C13×#108—21no—
56C13×#108—21no—
57C13×#108D412yes—
58C13×#107—21no—
59C13×#107—21no—
60C13×#103—41no—
61C13×#102—41no—
62C13×#101—24no—
63#13394C1311yesmaximal, characteristic, direct product factor, Sylow
64C13×#41—21no—
65C13×#41—21no—
66C13×#41—21no—
67C13×#41—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13D811yescharacteristic
75C2×D4×C13—21no—
76C2×D4×C13D811yescharacteristic
77C22×C4×C13—21no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13C2×D411yescharacteristic
81C13×Q16—22no—
82C13×Q16—22no—
83C13×Q16—44no—
84C13×Q16—41no—
85C13×Q16—41no—
86C13×SD16—44no—
87C13×M16—21no—
88C13×M16—22no—
89C13×M16—21no—
90C13×M16—41no—
91C13×M16—41no—
92C13×M16—41no—
93C13×M16—41no—
94C13×M16—41no—
95C2×C8×C13—21no—
96C2×C8×C13—41no—
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—41no—
107C13×C4⋊C4—41no—
108C13×C16—22no—
109C13×C16—41no—
110C2×#473C2×C1311yescharacteristic
111C2×#368C2×C1311yescharacteristic, complemented
112C2×#362C2×C1311yescharacteristic, complemented
113C2×#358C2×C1311yescharacteristic, complemented
114#2113C2×C1311yescharacteristic
115#1816C2×C1311yescharacteristic
116#1387C2×C1311yescharacteristic, complemented
117C23×C13—21no—
118C23×C13#13511yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121Q8×C13—42no—
122Q8×C13—42no—
123Q8×C13—81no—
124Q8×C13—81no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—41no—
128D4×C13—41no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—161no—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×D811yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C8×C13—41no—
144C8×C13—42no—
145C8×C13—81no—
146C8×C13#12111yescharacteristic
147C8×C13#12111yescharacteristic
148C8×C13#12311yescharacteristic
149C8×C13#12411yescharacteristic
150C2×#137—21no—
151C22×Q16C22×C1311yescharacteristic
152C2×#131C22×C1311yescharacteristic
153C2×M32C22×C1311yescharacteristic
154C22×C16C22×C1311yescharacteristic
155#473—22no—
156#473—22no—
157C2×#108C22×C1311yescharacteristic
158C2×#108C22×C1311yescharacteristic
159C2×#107C22×C1311yescharacteristic
160#417—21no—
161C2×#101—21no—
162#368—22no—
163#362—22no—
164#358—22no—
165C22⋊C16—22no—
166#343—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13#45211yescharacteristic
173C22×C13#46611yescharacteristic
174C22×C13#48211yescharacteristic
175C4×C13—41no—
176C4×C13—82no—
177C4×C13—161no—
178C4×C13#39411yescharacteristic
179C4×C13#44711yescharacteristic
180C4×C13#46811yescharacteristic
181C4×C13#48011yescharacteristic
182C2×#41D4×C1311yescharacteristic
183C22×Q8—21no—
184#137—24no—
185#137—42no—
186C2×Q16—21no—
187C2×Q16—21no—
188C2×Q16—21no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—41no—
192C2×Q16D4×C1312yes—
193C2×SD16—41no—
194#131—21no—
195#131—21no—
196#131—21no—
197#131—21no—
198C2×M16—21no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16D4×C1311yescharacteristic
202C22×C8—21no—
203C22×C8C23×C1311yescharacteristic
204C2×C4⋊C4—21no—
205M32—21no—
206M32—21no—
207C2×C16—21no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16D4×C1312yes—
211#108—21no—
212#108—21no—
213#108—21no—
214#108D4×C1312yes—
215#107—21no—
216#107—21no—
217#103—41no—
218#102—41no—
219#101—24no—
220C2×C13—21no—
221C2×C13—21no—
222C2×C13—81no—
223C2×C13#203311yescharacteristic
224C2×C13#222211yescharacteristic
225C2×C13#222311yescharacteristic
226#41—21no—
227#41—21no—
228#41—21no—
229#41—21no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8C13×D811yescharacteristic
237C2×D4—21no—
238C2×D4C13×D811yescharacteristic
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×D4×C1311yescharacteristic
243Q16—22no—
244Q16—22no—
245Q16—44no—
246Q16—41no—
247Q16—41no—
248SD16—44no—
249M16—21no—
250M16—22no—
251M16—21no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257C2×C8—21no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8C2×D4×C1311yescharacteristic
263C2×C8C2×D4×C1311yescharacteristic
264C2×C8C2×D4×C1311yescharacteristic
265C2×C8C13×#4111yescharacteristic
266C2×C8C13×#4111yescharacteristic
267C2×C8C13×#4111yescharacteristic
268C4⋊C4—41no—
269C4⋊C4—41no—
270C16—22no—
271C16—41no—
272C13#1339411yescharacteristic, direct product factor, Sylow
273C23—21no—
274C23C13×#13511yescharacteristic
275Q8—21no—
276Q8—21no—
277Q8—42no—
278Q8—42no—
279Q8—81no—
280Q8—81no—
281D4—21no—
282D4—21no—
283D4—41no—
284D4—41no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—161no—
293C2×C4C13×#12011yescharacteristic
294C2×C4C13×#12111yescharacteristic
295C2×C4C13×#12311yescharacteristic
296C2×C4C2×C13×D811yescharacteristic
297C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
298C2×C4C13×#13711yescharacteristic
299C8—41no—
300C8—42no—
301C8—81no—
302C8C13×#12111yescharacteristic
303C8C13×#12111yescharacteristic
304C8C13×#12311yescharacteristic
305C8C13×#12411yescharacteristic
306C22—21no—
307C22—21no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C13×#45211yescharacteristic
312C22C13×#46611yescharacteristic
313C22C13×#48211yescharacteristic
314C4—41no—
315C4—82no—
316C4—161no—
317C4C13×#39411yescharacteristic
318C4C13×#44711yescharacteristic
319C4C13×#46811yescharacteristic
320C4C13×#48011yescharacteristic
321C2—21no—
322C2—21no—
323C2—81no—
324C2C13×#203311yescharacteristic
325C2C13×#222211yescharacteristic
326C2C13×#222311yescharacteristic
subgroupG/H
center, socleC22×C13#466
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. C2×C13×#368C2semidirect
3. C2×C13×#362C2semidirect
4. C2×C13×#358C2semidirect
7. C13×#1387C2semidirect
63. #13394C13direct (N × H)
111. C2×#368C2×C13semidirect
112. C2×#362C2×C13semidirect
113. C2×#358C2×C13semidirect
116. #1387C2×C13semidirect
272. C13#13394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4732
C2×C13×#3682
C2×C13×#3622
C2×C13×#3582
C13×#21132
C13×#18162
C13×#13872
#1339413