Finite Group Databasebeta

← C13×#12179 #15698518

Subgroups — C13×#12179 #15698518

Order 3328.

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

normal subgroups only

This group has 412 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, complemented
2C13×#2044C211yesmaximal, characteristic
3C13×#1613C211yesmaximal, characteristic
4C13×#1613C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1352C211yesmaximal, characteristic, complemented
7C13×#1326C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C13×#481—21no—
10C13×#481—21no—
11C2×C13×#99—21no—
12C13×#400—21no—
13C13×#399C2211yescharacteristic
14C13×#399C2211yescharacteristic
15C13×#398—21no—
16C13×#389—21no—
17C13×#389—21no—
18C13×#388—21no—
19C13×#386—21no—
20C13×#385—21no—
21C13×#385C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×D4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C13×#123—41no—
30C13×#121—21no—
31C13×#121—21no—
32C13×#120—41no—
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—21no—
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—41no—
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C42×C13—21no—
48C13×#106—41no—
49C13×#106—41no—
50C13×#102—41no—
51C13×#102—41no—
52C13×#99—42no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—41no—
61C13×#95D411yescharacteristic
62C13×#95D411yescharacteristic
63#12179C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—21no—
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—81no—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—81no—
96C13×C4⋊C4—81no—
97C13×C4⋊C4—81no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—81no—
106C13×C22⋊C4—82no—
107C13×C22⋊C4SD1612yes—
108C42×C13—81no—
109#2807C2×C1311yescharacteristic, complemented
110#2044C2×C1311yescharacteristic
111#1613C2×C1311yescharacteristic
112#1613C2×C1311yescharacteristic
113#1352C2×C1311yescharacteristic, complemented
114#1352C2×C1311yescharacteristic, complemented
115#1326C2×C1311yescharacteristic, complemented
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—81no—
124C23×C13—81no—
125C23×C13#12011yescharacteristic
126C23×C13C2×SD1611yescharacteristic
127C23×C13#13711yescharacteristic
128D4×C13—81no—
129D4×C13—81no—
130D4×C13—81no—
131D4×C13—81no—
132D4×C13—81no—
133D4×C13—81no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
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—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—81no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C8×C13—81no—
165C8×C13—81no—
166#534C22×C1311yescharacteristic
167#481—21no—
168#481—21no—
169C2×#99—21no—
170#400—21no—
171#399C22×C1311yescharacteristic
172#399C22×C1311yescharacteristic
173#398—21no—
174#389—21no—
175#389—21no—
176#388—21no—
177#386—21no—
178#385—21no—
179#385C22×C1311yescharacteristic
180#342C22×C1311yescharacteristic
181#327—21no—
182#327—21no—
183#323C22×C1311yescharacteristic
184#323C22×C1311yescharacteristic
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—81no—
194C22×C13—82no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—161no—
199C22×C13#44811yescharacteristic
200C22×C13#45411yescharacteristic
201C22×C13B(4,𝔽2)11yescharacteristic
202C4×C13—42no—
203C4×C13—42no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13—161no—
212C22×D4—21no—
213C23×C4D4×C1311yescharacteristic
214#123—41no—
215#121—21no—
216#121—21no—
217#120—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C1311yescharacteristic
225C2×C4⋊C4D4×C1311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4D4×C1311yescharacteristic
231C2×C22⋊C4C23×C1311yescharacteristic
232C2×C42—21no—
233#106—41no—
234#106—41no—
235#102—41no—
236#102—41no—
237#99—42no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—41no—
246#95D4×C1311yescharacteristic
247#95D4×C1311yescharacteristic
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—41no—
251C2×C13—41no—
252C2×C13—161no—
253C2×C13#159911yescharacteristic
254C2×C13#219811yescharacteristic
255C2×C13#220011yescharacteristic
256C24—21no—
257C24C2×D4×C1311yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—81no—
276C22×C4C2×D4×C1311yescharacteristic
277C22×C4C2×D4×C1311yescharacteristic
278C2×C8—41no—
279C2×C8—41no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C22⋊C4—21no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C22⋊C4—82no—
299C22⋊C4C13×SD1612yes—
300C42—81no—
301C13#1217911yescharacteristic, direct product factor, Sylow
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—81no—
310C23—81no—
311C23C13×#12011yescharacteristic
312C23C2×C13×SD1611yescharacteristic
313C23C13×#13711yescharacteristic
314D4—81no—
315D4—81no—
316D4—81no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C8—81no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—82no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—161no—
366C22C13×#44811yescharacteristic
367C22C13×#45411yescharacteristic
368C22C13×B(4,𝔽2)11yescharacteristic
369C4—42no—
370C4—42no—
371C4—41no—
372C4—41no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—161no—
379C2—21no—
380C2—21no—
381C2—41no—
382C2—41no—
383C2—161no—
384C2C13×#159911yescharacteristic
385C2C13×#219811yescharacteristic
386C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#534C22
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
1. C13×#2807C2semidirect
5. C13×#1352C2semidirect
6. C13×#1352C2semidirect
7. C13×#1326C2semidirect
63. #12179C13direct (N × H)
109. #2807C2×C13semidirect
113. #1352C2×C13semidirect
114. #1352C2×C13semidirect
115. #1326C2×C13semidirect
301. C13#12179direct (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×#20442
C13×#16132
C13×#13522
C13×#13262
#1217913