Finite Group Databasebeta

← C19×#13675 #18019634

Subgroups — C19×#13675 #18019634

Order 4864.

408 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 58 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×#3292C211yesmaximal, characteristic
2C19×#2198C212yesmaximal, complemented
3C19×#1620C211yesmaximal, characteristic, complemented
4C19×#1408C211yesmaximal, characteristic, complemented
5C19×#1402C212yesmaximal, complemented
6C19×#576—22no—
7C19×#559C2211yescharacteristic, complemented
8C19×#493C2211yescharacteristic
9C19×#472—22no—
10C19×#460—21no—
11C19×#458—22no—
12C19×#453—21no—
13C19×#453C2212yes—
14C19×#443—21no—
15C19×#353C2212yescomplemented
16C19×#352—22no—
17C19×#331C2211yescharacteristic, complemented
18C19×Q8⋊C8—21no—
19C19×H(5,𝔽2)—21no—
20C19×H(5,𝔽2)D412yes—
21C19×AGL(1,ℤ/8)—22no—
22C19×AGL(1,ℤ/8)—22no—
23C19×AGL(1,ℤ/8)—42no—
24C19×AGL(1,ℤ/8)—42no—
25C19×#135—21no—
26C19×#135—42no—
27C2×SD16×C19—41no—
28C2×D8×C19—22no—
29C2×D8×C19—42no—
30C19×#131—22no—
31C19×#127D411yescharacteristic
32C19×#127C2311yescharacteristic
33C19×#124—41no—
34C19×#123—22no—
35C19×#123—42no—
36C4×Q8×C19—21no—
37C4×D4×C19—41no—
38C19×#108—21no—
39C19×C4⋊C8—21no—
40C19×#104—22no—
41C19×#102—41no—
42C19×#100—21no—
43C19×#100D412yes—
44C19×#99—22no—
45C19×#99—42no—
46C4×C8×C19D411yescharacteristic
47#41×C19—22no—
48#41×C19—42no—
49#41×C19—42no—
50C2×Q8×C19—21no—
51C2×D4×C19—21no—
52C2×D4×C19—41no—
53C2×D4×C19—41no—
54C2×D4×C19—42no—
55C2×D4×C19—42no—
56C2×D4×C19—42no—
57C2×D4×C19—81no—
58C2×D4×C19C2×D412yes—
59C22×C4×C19—22no—
60Q16×C19—21no—
61SD16×C19—22no—
62SD16×C19—42no—
63SD16×C19—42no—
64SD16×C19—82no—
65D8×C19—21no—
66D8×C19—42no—
67D8×C19—42no—
68D8×C19—42no—
69D8×C19—42no—
70M16×C19—22no—
71M16×C19—42no—
72C2×C8×C19—21no—
73C2×C8×C19—42no—
74C2×C8×C19—41no—
75C4⋊C4×C19—21no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—82no—
78C22⋊C4×C19—22no—
79C22⋊C4×C19—42no—
80C22⋊C4×C19—42no—
81C22⋊C4×C19—82no—
82C42×C19—41no—
83C42×C19C2×D411yescharacteristic
84#13675C1911yesmaximal, characteristic, direct product factor, Sylow
85C23×C19—22no—
86C23×C19—42no—
87C23×C19—41no—
88C23×C19—81no—
89Q8×C19—22no—
90Q8×C19—41no—
91Q8×C19—41no—
92D4×C19—22no—
93D4×C19—42no—
94D4×C19—42no—
95D4×C19—42no—
96D4×C19—81no—
97D4×C19—81no—
98D4×C19—81no—
99D4×C19—81no—
100D4×C19—82no—
101D4×C19—82no—
102C2×C4×C19—21no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—81no—
108C2×C4×C19—82no—
109C2×C4×C19—82no—
110C2×C4×C19#12011yescharacteristic
111C8×C19—21no—
112C8×C19—21no—
113C8×C19—42no—
114C8×C19—81no—
115#3292C2×C1911yescharacteristic
116#2198C2×C1912yescomplemented
117#1620C2×C1911yescharacteristic, complemented
118#1408C2×C1911yescharacteristic, complemented
119#1402C2×C1912yescomplemented
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—82no—
123C22×C19—81no—
124C22×C19—161no—
125C22×C19—162no—
126C22×C19—321no—
127C22×C19B(4,𝔽2)11yescharacteristic
128C4×C19—21no—
129C4×C19—21no—
130C4×C19—21no—
131C4×C19—42no—
132C4×C19—81no—
133C4×C19—81no—
134C4×C19—162no—
135#576—22no—
136#559C22×C1911yescharacteristic, complemented
137#493C22×C1911yescharacteristic
138#472—22no—
139#460—21no—
140#458—22no—
141#453—21no—
142#453C22×C1912yes—
143#443—21no—
144#353C22×C1912yescomplemented
145#352—22no—
146#331C22×C1911yescharacteristic, complemented
147Q8⋊C8—21no—
148C2×C19—21no—
149C2×C19—82no—
150C2×C19—82no—
151C2×C19—161no—
152C2×C19#219611yescharacteristic
153H(5,𝔽2)—21no—
154H(5,𝔽2)D4×C1912yes—
155AGL(1,ℤ/8)—22no—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—42no—
158AGL(1,ℤ/8)—42no—
159#135—21no—
160#135—42no—
161C2×SD16—41no—
162C2×D8—22no—
163C2×D8—42no—
164#131—22no—
165#127D4×C1911yescharacteristic
166#127C23×C1911yescharacteristic
167#124—41no—
168#123—22no—
169#123—42no—
170C4×Q8—21no—
171C4×D4—41no—
172#108—21no—
173C4⋊C8—21no—
174#104—22no—
175#102—41no—
176#100—21no—
177#100D4×C1912yes—
178#99—22no—
179#99—42no—
180C4×C8D4×C1911yescharacteristic
181C19#1367511yescharacteristic, direct product factor, Sylow
182#41—22no—
183#41—42no—
184#41—42no—
185C2×Q8—21no—
186C2×D4—21no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—42no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—81no—
193C2×D4C2×D4×C1912yes—
194C22×C4—22no—
195Q16—21no—
196SD16—22no—
197SD16—42no—
198SD16—42no—
199SD16—82no—
200D8—21no—
201D8—42no—
202D8—42no—
203D8—42no—
204D8—42no—
205M16—22no—
206M16—42no—
207C2×C8—21no—
208C2×C8—42no—
209C2×C8—41no—
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—82no—
213C22⋊C4—22no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—41no—
218C42C2×D4×C1911yescharacteristic
219C23—22no—
220C23—42no—
221C23—41no—
222C23—81no—
223Q8—22no—
224Q8—41no—
225Q8—41no—
226D4—22no—
227D4—42no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—81no—
234D4—82no—
235D4—82no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4C19×#12011yescharacteristic
245C8—21no—
246C8—21no—
247C8—42no—
248C8—81no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22—81no—
253C22—161no—
254C22—162no—
255C22—321no—
256C22C19×B(4,𝔽2)11yescharacteristic
257C4—21no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—81no—
262C4—81no—
263C4—162no—
264C2—21no—
265C2—82no—
266C2—82no—
267C2—161no—
268C2C19×#219611yescharacteristic
subgroupG/H
center, socleC2×C19#2196
commutator, Frattini, cosocle#127C23×C19
prime radicalC19×#3292C2
LCSG ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ C22×C19 ◁ C2×C4×C19 ◁ C19×#127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2198C2semidirect
3. C19×#1620C2semidirect
4. C19×#1408C2semidirect
5. C19×#1402C2semidirect
7. C19×#559C22semidirect
15. C19×#353C22semidirect
17. C19×#331C22semidirect
84. #13675C19direct (N × H)
116. #2198C2×C19semidirect
117. #1620C2×C19semidirect
118. #1408C2×C19semidirect
119. #1402C2×C19semidirect
136. #559C22×C19semidirect
144. #353C22×C19semidirect
146. #331C22×C19semidirect
181. C19#13675direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#32922
C19×#21982
C19×#16202
C19×#14082
C19×#14022
#1367519