Finite Group Databasebeta

← C13×#12255 #15698594

Subgroups — C13×#12255 #15698594

Order 3328.

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

normal subgroups only

This group has 378 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×#2807C211yesmaximal, characteristic
2C13×#2062C211yesmaximal, characteristic
3C13×#1614C211yesmaximal, characteristic
4C13×#1614C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic
6C13×#1352C211yesmaximal, characteristic
7C13×#1326C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C13×#484—21no—
10C13×#484—21no—
11C13×#400—21no—
12C13×#399C2211yescharacteristic
13C13×#399C2211yescharacteristic
14C13×#398—21no—
15C13×#389—21no—
16C13×#389—21no—
17C13×#388—21no—
18C13×#385—21no—
19C13×#385—21no—
20C13×#385C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×C22⋊Q8—21no—
29C13×C22⋊Q8—21no—
30C13×C22⋊Q8—41no—
31C13×C22⋊Q8—41no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—41no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C42×C13—21no—
48C13×#107—41no—
49C13×#107—41no—
50C13×#103—41no—
51C13×#103—41no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—41no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12255C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13C2×D411yescharacteristic
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—81no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C4⋊C4—81no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C4⋊C4—82no—
94C13×C22⋊C4—21no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—81no—
102C13×C22⋊C4Q1612yes—
103C42×C13—81no—
104#2807C2×C1311yescharacteristic
105#2062C2×C1311yescharacteristic
106#1614C2×C1311yescharacteristic
107#1614C2×C1311yescharacteristic
108#1352C2×C1311yescharacteristic
109#1352C2×C1311yescharacteristic
110#1326C2×C1311yescharacteristic
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13#12011yescharacteristic
116C23×C13C2×Q1611yescharacteristic
117C23×C13#13711yescharacteristic
118Q8×C13—81no—
119Q8×C13—81no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—41no—
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—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C8×C13—81no—
152C8×C13—81no—
153#543C22×C1311yescharacteristic
154#484—21no—
155#484—21no—
156#400—21no—
157#399C22×C1311yescharacteristic
158#399C22×C1311yescharacteristic
159#398—21no—
160#389—21no—
161#389—21no—
162#388—21no—
163#385—21no—
164#385—21no—
165#385C22×C1311yescharacteristic
166#342—21no—
167#342C22×C1311yescharacteristic
168#328—21no—
169#328—21no—
170#323C22×C1311yescharacteristic
171#323C22×C1311yescharacteristic
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—81no—
181C22×C13#45111yescharacteristic
182C22×C13#45611yescharacteristic
183C22×C13B(4,𝔽2)11yescharacteristic
184C4×C13—42no—
185C4×C13—42no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—81no—
189C4×C13—82no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195C23×C4D4×C1311yescharacteristic
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C22⋊Q8—41no—
199C22⋊Q8—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4D4×C1311yescharacteristic
208C2×C4⋊C4D4×C1311yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4D4×C1311yescharacteristic
214C2×C22⋊C4C23×C1311yescharacteristic
215C2×C42—21no—
216#107—41no—
217#107—41no—
218#103—41no—
219#103—41no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—41no—
228#95D4×C1311yescharacteristic
229#95D4×C1311yescharacteristic
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—41no—
233C2×C13—41no—
234C2×C13#160511yescharacteristic
235C2×C13#219811yescharacteristic
236C2×C13#220011yescharacteristic
237C24C2×D4×C1311yescharacteristic
238C2×Q8—21no—
239C2×Q8—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—81no—
251C22×C4C2×D4×C1311yescharacteristic
252C22×C4C2×D4×C1311yescharacteristic
253C2×C8—41no—
254C2×C8—41no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—82no—
268C22⋊C4—21no—
269C22⋊C4—22no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—81no—
276C22⋊C4C13×Q1612yes—
277C42—81no—
278C13#1225511yescharacteristic, direct product factor, Sylow
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23C13×#12011yescharacteristic
284C23C2×C13×Q1611yescharacteristic
285C23C13×#13711yescharacteristic
286Q8—81no—
287Q8—81no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C8—81no—
320C8—81no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22C13×#45111yescharacteristic
331C22C13×#45611yescharacteristic
332C22C13×B(4,𝔽2)11yescharacteristic
333C4—42no—
334C4—42no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—82no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C2—21no—
345C2—21no—
346C2—41no—
347C2—41no—
348C2C13×#160511yescharacteristic
349C2C13×#219811yescharacteristic
350C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
62. #12255C13direct (N × H)
278. C13#12255direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28072
C13×#20622
C13×#16142
C13×#13522
C13×#13262
#1225513