Subgroups — C₁₉×#13009 #18018968

Order 4864.

496 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#362	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#349	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1383	C₂	1	2	yes	maximal, complemented
6	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	—	2	1	no	—
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
10	C₂×C₁₉×M₃₂	C₂²	1	2	yes	—
11	C₁₉×#470	—	2	2	no	—
12	C₁₉×#470	C₄	1	4	yes	—
13	C₁₉×#430	—	2	4	no	—
14	C₂×C₁₉×#108	—	2	1	no	—
15	C₂×C₁₉×#108	C₂²	1	2	yes	—
16	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	—	2	1	no	—
18	C₁₉×#362	—	2	4	no	—
19	C₁₉×#349	—	2	2	no	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×Q₁₆×C₁₉	—	2	2	no	—
23	C₂×Q₁₆×C₁₉	—	2	1	no	—
24	C₂×Q₁₆×C₁₉	—	2	2	no	—
25	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×M₁₆×C₁₉	—	2	2	no	—
27	C₂×M₁₆×C₁₉	—	2	2	no	—
28	C₂×M₁₆×C₁₉	—	2	4	no	—
29	C₂×M₁₆×C₁₉	—	2	2	no	—
30	C₂×M₁₆×C₁₉	—	4	1	no	—
31	C₂×M₁₆×C₁₉	—	4	2	no	—
32	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
34	C₂²×C₈×C₁₉	—	4	1	no	—
35	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₁₉×C₂²⋊Q₈	—	2	4	no	—
38	C₁₉×C₂²⋊Q₈	—	4	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
42	C₁₉×M₃₂	—	2	2	no	—
43	C₁₉×M₃₂	—	2	2	no	—
44	C₂×C₁₆×C₁₉	—	2	2	no	—
45	C₁₉×#108	—	2	4	no	—
46	C₁₉×#108	—	2	2	no	—
47	C₁₉×#108	D₄	1	4	yes	—
48	C₁₉×#106	—	2	1	no	—
49	C₁₉×#106	C₂×C₄	1	2	yes	—
50	C₁₉×#103	—	2	4	no	—
51	C₂⁴×C₁₉	SD₁₆	1	1	yes	characteristic
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	4	1	no	—
54	C₂×Q₈×C₁₉	—	4	1	no	—
55	C₂×Q₈×C₁₉	—	4	1	no	—
56	C₂×Q₈×C₁₉	—	4	1	no	—
57	C₂×Q₈×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₉	D₈	1	2	yes	—
66	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	Q₁₆×C₁₉	—	2	4	no	—
69	Q₁₆×C₁₉	—	4	2	no	—
70	M₁₆×C₁₉	—	2	4	no	—
71	M₁₆×C₁₉	—	2	4	no	—
72	M₁₆×C₁₉	—	2	4	no	—
73	M₁₆×C₁₉	—	4	4	no	—
74	M₁₆×C₁₉	—	4	2	no	—
75	C₂×C₈×C₁₉	—	2	1	no	—
76	C₂×C₈×C₁₉	—	2	1	no	—
77	C₂×C₈×C₁₉	—	4	4	no	—
78	C₂×C₈×C₁₉	—	4	2	no	—
79	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
80	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
82	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₉	#41	1	2	yes	—
84	C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₄⋊C₄×C₁₉	—	4	4	no	—
86	C₄⋊C₄×C₁₉	—	4	1	no	—
87	C₂²⋊C₄×C₁₉	—	4	4	no	—
88	C₁₆×C₁₉	—	4	2	no	—
89	#13009	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂³×C₁₉	—	2	1	no	—
91	C₂³×C₁₉	—	2	1	no	—
92	C₂³×C₁₉	—	4	2	no	—
93	C₂³×C₁₉	#102	1	2	yes	—
94	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
95	Q₈×C₁₉	—	4	2	no	—
96	Q₈×C₁₉	—	4	2	no	—
97	Q₈×C₁₉	—	8	1	no	—
98	Q₈×C₁₉	—	8	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	8	2	no	—
108	C₂×C₄×C₁₉	—	8	1	no	—
109	C₂×C₄×C₁₉	—	8	1	no	—
110	C₂×C₄×C₁₉	#102	1	2	yes	—
111	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
115	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
117	C₈×C₁₉	—	2	2	no	—
118	C₈×C₁₉	—	4	4	no	—
119	C₈×C₁₉	C₄×D₄	1	2	yes	—
120	C₈×C₁₉	#121	1	2	yes	—
121	C₂×#470	C₂×C₁₉	1	1	yes	characteristic
122	C₂×#430	C₂×C₁₉	1	1	yes	characteristic
123	C₂×#362	C₂×C₁₉	1	2	yes	complemented
124	C₂×#349	C₂×C₁₉	1	1	yes	characteristic
125	#1383	C₂×C₁₉	1	2	yes	complemented
126	C₂²×C₁₉	—	2	2	no	—
127	C₂²×C₁₉	—	2	2	no	—
128	C₂²×C₁₉	—	4	2	no	—
129	C₂²×C₁₉	—	4	2	no	—
130	C₂²×C₁₉	—	8	1	no	—
131	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
132	C₂²×C₁₉	#448	1	1	yes	characteristic
133	C₂²×C₁₉	#481	1	1	yes	characteristic
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	8	2	no	—
136	C₄×C₁₉	—	8	2	no	—
137	C₄×C₁₉	#386	1	1	yes	characteristic
138	C₄×C₁₉	#417	1	1	yes	characteristic
139	C₄×C₁₉	#447	1	1	yes	characteristic
140	C₄×C₁₉	#480	1	1	yes	characteristic
141	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
142	C₂²×M₁₆	—	2	1	no	—
143	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
144	C₂×C₂²⋊Q₈	—	2	1	no	—
145	C₂×M₃₂	C₂²×C₁₉	1	2	yes	—
146	#470	—	2	2	no	—
147	#470	C₄×C₁₉	1	4	yes	—
148	#430	—	2	4	no	—
149	C₂×#108	—	2	1	no	—
150	C₂×#108	C₂²×C₁₉	1	2	yes	—
151	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
152	C₂×#103	—	2	1	no	—
153	#362	—	2	4	no	—
154	#349	—	2	2	no	—
155	C₂×C₁₉	—	2	1	no	—
156	C₂×C₁₉	—	2	1	no	—
157	C₂×C₁₉	—	4	2	no	—
158	C₂×C₁₉	#1874	1	1	yes	characteristic
159	C₂×C₁₉	#2239	1	2	yes	—
160	C₂²×Q₈	—	2	1	no	—
161	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
162	C₂×Q₁₆	—	2	2	no	—
163	C₂×Q₁₆	—	2	1	no	—
164	C₂×Q₁₆	—	2	2	no	—
165	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
166	C₂×M₁₆	—	2	2	no	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂×M₁₆	—	2	4	no	—
169	C₂×M₁₆	—	2	2	no	—
170	C₂×M₁₆	—	4	1	no	—
171	C₂×M₁₆	—	4	2	no	—
172	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
173	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
174	C₂²×C₈	—	4	1	no	—
175	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
176	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
177	C₂²⋊Q₈	—	2	4	no	—
178	C₂²⋊Q₈	—	4	2	no	—
179	C₂×C₄⋊C₄	—	2	1	no	—
180	C₂×C₄⋊C₄	—	4	1	no	—
181	C₂×C₂²⋊C₄	—	4	1	no	—
182	M₃₂	—	2	2	no	—
183	M₃₂	—	2	2	no	—
184	C₂×C₁₆	—	2	2	no	—
185	#108	—	2	4	no	—
186	#108	—	2	2	no	—
187	#108	D₄×C₁₉	1	4	yes	—
188	#106	—	2	1	no	—
189	#106	C₂×C₄×C₁₉	1	2	yes	—
190	#103	—	2	4	no	—
191	C₁₉	#13009	1	1	yes	characteristic, direct product factor, Sylow
192	C₂⁴	SD₁₆×C₁₉	1	1	yes	characteristic
193	C₂×Q₈	—	2	2	no	—
194	C₂×Q₈	—	4	1	no	—
195	C₂×Q₈	—	4	1	no	—
196	C₂×Q₈	—	4	1	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂×Q₈	—	4	1	no	—
199	C₂²×C₄	—	2	1	no	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	4	1	no	—
204	C₂²×C₄	—	4	1	no	—
205	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
206	C₂²×C₄	D₈×C₁₉	1	2	yes	—
207	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
208	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
209	Q₁₆	—	2	4	no	—
210	Q₁₆	—	4	2	no	—
211	M₁₆	—	2	4	no	—
212	M₁₆	—	2	4	no	—
213	M₁₆	—	2	4	no	—
214	M₁₆	—	4	4	no	—
215	M₁₆	—	4	2	no	—
216	C₂×C₈	—	2	1	no	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	4	4	no	—
219	C₂×C₈	—	4	2	no	—
220	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
221	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
222	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
223	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
224	C₂×C₈	#41×C₁₉	1	2	yes	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	4	1	no	—
227	C₄⋊C₄	—	4	4	no	—
228	C₂²⋊C₄	—	4	4	no	—
229	C₁₆	—	4	2	no	—
230	C₂³	—	2	1	no	—
231	C₂³	—	2	1	no	—
232	C₂³	—	4	2	no	—
233	C₂³	C₁₉×#102	1	2	yes	—
234	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
235	Q₈	—	4	2	no	—
236	Q₈	—	4	2	no	—
237	Q₈	—	8	1	no	—
238	Q₈	—	8	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	8	2	no	—
248	C₂×C₄	—	8	1	no	—
249	C₂×C₄	—	8	1	no	—
250	C₂×C₄	C₁₉×#102	1	2	yes	—
251	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
252	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
253	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
254	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
255	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
257	C₈	—	2	2	no	—
258	C₈	—	4	4	no	—
259	C₈	C₄×D₄×C₁₉	1	2	yes	—
260	C₈	C₁₉×#121	1	2	yes	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	4	2	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	8	1	no	—
266	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
267	C₂²	C₁₉×#448	1	1	yes	characteristic
268	C₂²	C₁₉×#481	1	1	yes	characteristic
269	C₄	—	2	2	no	—
270	C₄	—	8	2	no	—
271	C₄	—	8	2	no	—
272	C₄	C₁₉×#386	1	1	yes	characteristic
273	C₄	C₁₉×#417	1	1	yes	characteristic
274	C₄	C₁₉×#447	1	1	yes	characteristic
275	C₄	C₁₉×#480	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	4	2	no	—
279	C₂	C₁₉×#1874	1	1	yes	characteristic
280	C₂	C₁₉×#2239	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#481
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#362	C₂	semidirect
5. C₁₉×#1383	C₂	semidirect
89. #13009	C₁₉	direct (N × H)
123. C₂×#362	C₂×C₁₉	semidirect
125. #1383	C₂×C₁₉	semidirect
191. C₁₉	#13009	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#470	2
C₂×C₁₉×#430	2
C₂×C₁₉×#362	2
C₂×C₁₉×#349	2
C₁₉×#1383	2
#13009	19

Subgroups — C19×#13009 #18018968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13009 #18018968