Finite Group Databasebeta

← C19×#13562 #18019521

Subgroups — C19×#13562 #18019521

Order 4864.

490 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C19×#3018C211yesmaximal, characteristic
2C19×#2126C211yesmaximal, characteristic, complemented
3C19×#1560C211yesmaximal, characteristic, complemented
4C19×#1402C214yesmaximal, complemented
5C19×#585C411yescharacteristic, complemented
6C19×#575—21no—
7C19×#532C2211yescharacteristic
8C19×#456—21no—
9C19×#455C412yescomplemented
10C19×#454—21no—
11C19×#453C2212yes—
12C19×#423—21no—
13C2×C19×#104—21no—
14C19×#413C411yescharacteristic, complemented
15C19×#410—21no—
16C19×#354—21no—
17C19×#353C2212yescomplemented
18C19×#333—21no—
19C19×#331C2212yescomplemented
20C19×2−1+4—21no—
21C19×2−1+4—41no—
22C19×H(5,𝔽2)—41no—
23C19×H(5,𝔽2)—41no—
24C19×H(5,𝔽2)C2×C412yes—
25C2×#41×C19—21no—
26C2×#41×C19—41no—
27C2×#41×C19—42no—
28C2×#41×C19C2×C411yescharacteristic
29C2×#41×C19D411yescharacteristic
30C19×#137—22no—
31C19×#137—41no—
32C19×AGL(1,ℤ/8)—22no—
33C19×AGL(1,ℤ/8)—41no—
34C19×#135—42no—
35C2×M16×C19—21no—
36C2×M16×C19—41no—
37C19×C4⋊Q8D411yescharacteristic
38C19×#127C2311yescharacteristic
39C19×#124C2×C411yescharacteristic
40C19×#124D411yescharacteristic
41C19×#121—41no—
42C4×D4×C19—41no—
43C19×#117—41no—
44C2×C42×C19D411yescharacteristic
45C19×C4⋊C8—22no—
46C19×C4⋊C8—41no—
47C19×#104—22no—
48C19×#104—22no—
49C19×#101—21no—
50C19×#100C2×C412yes—
51C19×#99—22no—
52C19×#99—41no—
53#41×C19—22no—
54#41×C19—22no—
55#41×C19—41no—
56#41×C19—42no—
57#41×C19—41no—
58#41×C19—41no—
59#41×C19—41no—
60#41×C19—41no—
61#41×C19—42no—
62#41×C19—42no—
63#41×C19—44no—
64#41×C19—42no—
65#41×C19—41no—
66#41×C19—42no—
67C2×Q8×C19—21no—
68C2×Q8×C19—42no—
69C2×Q8×C19—41no—
70C2×Q8×C19C22⋊C411yescharacteristic
71C2×Q8×C19C22⋊C411yescharacteristic
72C2×D4×C19—21no—
73C2×D4×C19—21no—
74C2×D4×C19—21no—
75C2×D4×C19—41no—
76C2×D4×C19—42no—
77C2×D4×C19—44no—
78C2×D4×C19—41no—
79C2×D4×C19—42no—
80C2×D4×C19—41no—
81C2×D4×C19C22×C411yescharacteristic
82C2×D4×C19C2×D411yescharacteristic
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—41no—
87C22×C4×C19—42no—
88C22×C4×C19C22⋊C411yescharacteristic
89Q16×C19—42no—
90SD16×C19—42no—
91SD16×C19—42no—
92D8×C19—42no—
93M16×C19—22no—
94M16×C19—41no—
95M16×C19—82no—
96C2×C8×C19—41no—
97C2×C8×C19—42no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—81no—
100C22⋊C4×C19—41no—
101C22⋊C4×C19—41no—
102C22⋊C4×C19—42no—
103C42×C19—21no—
104C42×C19—81no—
105C42×C19C22⋊C411yescharacteristic
106C42×C19C2×D411yescharacteristic
107#13562C1911yesmaximal, characteristic, direct product factor, Sylow
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—41no—
111C23×C19—42no—
112C23×C19#9911yescharacteristic
113Q8×C19—22no—
114Q8×C19—41no—
115Q8×C19—41no—
116Q8×C19—42no—
117Q8×C19—41no—
118D4×C19—22no—
119D4×C19—41no—
120D4×C19—41no—
121D4×C19—42no—
122D4×C19—42no—
123D4×C19—42no—
124D4×C19—44no—
125D4×C19—42no—
126D4×C19—41no—
127D4×C19—81no—
128D4×C19—81no—
129D4×C19—81no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—42no—
139C2×C4×C19—41no—
140C2×C4×C19—44no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—82no—
148C2×C4×C19#9911yescharacteristic
149C2×C4×C19C2×C22⋊C411yescharacteristic
150C8×C19—42no—
151C8×C19—82no—
152#3018C2×C1911yescharacteristic
153#2126C2×C1911yescharacteristic, complemented
154#1560C2×C1911yescharacteristic, complemented
155#1402C2×C1914yescomplemented
156C22×C19—21no—
157C22×C19—41no—
158C22×C19—42no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—81no—
162C22×C19—81no—
163C22×C19—161no—
164C22×C19—162no—
165C22×C19C2×#9911yescharacteristic
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—41no—
170C4×C19—41no—
171C4×C19—41no—
172C4×C19—42no—
173C4×C19—162no—
174C4×C19AΣL(1,𝔽16)11yescharacteristic
175C4×C19AΣL(1,𝔽16)11yescharacteristic
176#585C4×C1911yescharacteristic, complemented
177#575—21no—
178#532C22×C1911yescharacteristic
179#456—21no—
180#455C4×C1912yescomplemented
181#454—21no—
182#453C22×C1912yes—
183#423—21no—
184C2×#104—21no—
185#413C4×C1911yescharacteristic, complemented
186#410—21no—
187#354—21no—
188#353C22×C1912yescomplemented
189#333—21no—
190#331C22×C1912yescomplemented
191C2×C19—21no—
192C2×C19—41no—
193C2×C19—81no—
194C2×C19—81no—
195C2×C19—82no—
196C2×C19C2×AΣL(1,𝔽16)11yescharacteristic
1972−1+4—21no—
1982−1+4—41no—
199H(5,𝔽2)—41no—
200H(5,𝔽2)—41no—
201H(5,𝔽2)C2×C4×C1912yes—
202C2×#41—21no—
203C2×#41—41no—
204C2×#41—42no—
205C2×#41C2×C4×C1911yescharacteristic
206C2×#41D4×C1911yescharacteristic
207#137—22no—
208#137—41no—
209AGL(1,ℤ/8)—22no—
210AGL(1,ℤ/8)—41no—
211#135—42no—
212C2×M16—21no—
213C2×M16—41no—
214C4⋊Q8D4×C1911yescharacteristic
215#127C23×C1911yescharacteristic
216#124C2×C4×C1911yescharacteristic
217#124D4×C1911yescharacteristic
218#121—41no—
219C4×D4—41no—
220#117—41no—
221C2×C42D4×C1911yescharacteristic
222C4⋊C8—22no—
223C4⋊C8—41no—
224#104—22no—
225#104—22no—
226#101—21no—
227#100C2×C4×C1912yes—
228#99—22no—
229#99—41no—
230C19#1356211yescharacteristic, direct product factor, Sylow
231#41—22no—
232#41—22no—
233#41—41no—
234#41—42no—
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239#41—42no—
240#41—42no—
241#41—44no—
242#41—42no—
243#41—41no—
244#41—42no—
245C2×Q8—21no—
246C2×Q8—42no—
247C2×Q8—41no—
248C2×Q8C22⋊C4×C1911yescharacteristic
249C2×Q8C22⋊C4×C1911yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—42no—
255C2×D4—44no—
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—41no—
259C2×D4C22×C4×C1911yescharacteristic
260C2×D4C2×D4×C1911yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4C22⋊C4×C1911yescharacteristic
267Q16—42no—
268SD16—42no—
269SD16—42no—
270D8—42no—
271M16—22no—
272M16—41no—
273M16—82no—
274C2×C8—41no—
275C2×C8—42no—
276C4⋊C4—41no—
277C4⋊C4—81no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C42—21no—
282C42—81no—
283C42C22⋊C4×C1911yescharacteristic
284C42C2×D4×C1911yescharacteristic
285C23—21no—
286C23—21no—
287C23—41no—
288C23—42no—
289C23C19×#9911yescharacteristic
290Q8—22no—
291Q8—41no—
292Q8—41no—
293Q8—42no—
294Q8—41no—
295D4—22no—
296D4—41no—
297D4—41no—
298D4—42no—
299D4—42no—
300D4—42no—
301D4—44no—
302D4—42no—
303D4—41no—
304D4—81no—
305D4—81no—
306D4—81no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—44no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4C19×#9911yescharacteristic
326C2×C4C2×C22⋊C4×C1911yescharacteristic
327C8—42no—
328C8—82no—
329C22—21no—
330C22—41no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22—161no—
337C22—162no—
338C22C2×C19×#9911yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—42no—
346C4—162no—
347C4C19×AΣL(1,𝔽16)11yescharacteristic
348C4C19×AΣL(1,𝔽16)11yescharacteristic
349C2—21no—
350C2—41no—
351C2—81no—
352C2—81no—
353C2—82no—
354C2C2×C19×AΣL(1,𝔽16)11yescharacteristic
subgroupG/H
center, socleC2×C19C2×AΣL(1,𝔽16)
commutatorC2×D4C22×C4×C19
Frattini, cosocle#127C23×C19
prime radicalC19×#3018C2
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C22×C4×C19 ◁ C19×#532 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2126C2semidirect
3. C19×#1560C2semidirect
4. C19×#1402C2semidirect
5. C19×#585C4semidirect
9. C19×#455C4semidirect
14. C19×#413C4semidirect
17. C19×#353C22semidirect
19. C19×#331C22semidirect
107. #13562C19direct (N × H)
153. #2126C2×C19semidirect
154. #1560C2×C19semidirect
155. #1402C2×C19semidirect
176. #585C4×C19semidirect
180. #455C4×C19semidirect
185. #413C4×C19semidirect
188. #353C22×C19semidirect
190. #331C22×C19semidirect
230. C19#13562direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#30182
C19×#21262
C19×#15602
C19×#14022
#1356219