Subgroups — C₁₉×#9907 #18015866

Order 4864.

418 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2859	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1296	C₂	1	2	yes	maximal
5	C₁₉×#1296	C₂	1	2	yes	maximal
6	C₂×C₁₉×#125	—	2	1	no	—
7	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₉×#97	—	2	1	no	—
10	C₁₉×#389	—	2	1	no	—
11	C₁₉×#389	—	2	1	no	—
12	C₁₉×#389	C₄	1	2	yes	—
13	C₁₉×#389	C₄	1	2	yes	—
14	C₁₉×#384	C₂²	1	1	yes	characteristic
15	C₁₉×#384	C₂²	1	1	yes	characteristic
16	C₁₉×#382	—	2	1	no	—
17	C₄³×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#336	—	2	1	no	—
19	C₁₉×#336	—	2	1	no	—
20	C₁₉×#336	—	2	1	no	—
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₁₉×#125	—	4	4	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	4	no	—
41	C₁₉×C₄⋊C₈	Q₈	1	4	yes	—
42	C₁₉×#97	—	4	2	no	—
43	C₁₉×#95	—	2	2	no	—
44	C₁₉×#95	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₁₉	—	2	4	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₄⋊C₄×C₁₉	—	4	4	no	—
63	C₄⋊C₄×C₁₉	—	4	4	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	1	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄²×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	1	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	4	1	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
77	C₄²×C₁₉	#41	1	2	yes	—
78	#9907	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
101	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
102	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#135	1	2	yes	—
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
107	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#137	1	2	yes	—
109	C₈×C₁₉	—	4	4	no	—
110	C₈×C₁₉	—	8	2	no	—
111	#2859	C₂×C₁₉	1	1	yes	characteristic
112	#1831	C₂×C₁₉	1	1	yes	characteristic
113	#1767	C₂×C₁₉	1	1	yes	characteristic
114	#1296	C₂×C₁₉	1	2	yes	—
115	#1296	C₂×C₁₉	1	2	yes	—
116	C₂²×C₁₉	#391	1	1	yes	characteristic
117	C₂²×C₁₉	#413	1	1	yes	characteristic
118	C₂²×C₁₉	#413	1	1	yes	characteristic
119	C₂²×C₁₉	#416	1	1	yes	characteristic
120	C₂²×C₁₉	#417	1	1	yes	characteristic
121	C₂²×C₁₉	#418	1	1	yes	characteristic
122	C₂²×C₁₉	#419	1	1	yes	characteristic
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	—	4	1	no	—
125	C₄×C₁₉	—	4	1	no	—
126	C₄×C₁₉	—	4	1	no	—
127	C₄×C₁₉	—	4	1	no	—
128	C₄×C₁₉	—	8	2	no	—
129	C₄×C₁₉	—	8	2	no	—
130	C₄×C₁₉	#478	1	2	yes	—
131	C₄×C₁₉	#479	1	2	yes	—
132	C₄×C₁₉	#489	1	2	yes	—
133	C₄×C₁₉	#501	1	2	yes	—
134	C₂×#125	—	2	1	no	—
135	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
136	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
137	C₂×#97	—	2	1	no	—
138	#389	—	2	1	no	—
139	#389	—	2	1	no	—
140	#389	C₄×C₁₉	1	2	yes	—
141	#389	C₄×C₁₉	1	2	yes	—
142	#384	C₂²×C₁₉	1	1	yes	characteristic
143	#384	C₂²×C₁₉	1	1	yes	characteristic
144	#382	—	2	1	no	—
145	C₄³	C₂²×C₁₉	1	1	yes	characteristic
146	#336	—	2	1	no	—
147	#336	—	2	1	no	—
148	#336	—	2	1	no	—
149	C₂×C₁₉	#1553	1	1	yes	characteristic
150	C₂×C₁₉	#1554	1	1	yes	characteristic
151	C₂×C₁₉	#1557	1	1	yes	characteristic
152	C₂×C₁₉	#1559	1	1	yes	characteristic
153	C₂×C₁₉	#1989	1	1	yes	characteristic
154	C₂×C₁₉	#1993	1	1	yes	characteristic
155	C₂×C₁₉	#1998	1	1	yes	characteristic
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	2	2	no	—
158	#125	—	4	4	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	—	2	1	no	—
165	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
166	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
167	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
168	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
169	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
170	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
171	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
172	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
173	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	2	4	no	—
176	C₄⋊C₈	Q₈×C₁₉	1	4	yes	—
177	#97	—	4	2	no	—
178	#95	—	2	2	no	—
179	#95	—	2	2	no	—
180	C₁₉	#9907	1	1	yes	characteristic, direct product factor, Sylow
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
184	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
185	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
187	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄⋊C₄	—	4	4	no	—
199	C₄⋊C₄	—	4	4	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	4	1	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	1	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	2	2	no	—
208	C₄²	—	2	1	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	4	1	no	—
211	C₄²	—	4	1	no	—
212	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
213	C₄²	#41×C₁₉	1	2	yes	—
214	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
236	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
237	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
238	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
239	C₂×C₄	C₁₉×#135	1	2	yes	—
240	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
243	C₂×C₄	C₁₉×#137	1	2	yes	—
244	C₈	—	4	4	no	—
245	C₈	—	8	2	no	—
246	C₂²	C₁₉×#391	1	1	yes	characteristic
247	C₂²	C₁₉×#413	1	1	yes	characteristic
248	C₂²	C₁₉×#413	1	1	yes	characteristic
249	C₂²	C₁₉×#416	1	1	yes	characteristic
250	C₂²	C₁₉×#417	1	1	yes	characteristic
251	C₂²	C₁₉×#418	1	1	yes	characteristic
252	C₂²	C₁₉×#419	1	1	yes	characteristic
253	C₄	—	2	2	no	—
254	C₄	—	4	1	no	—
255	C₄	—	4	1	no	—
256	C₄	—	4	1	no	—
257	C₄	—	4	1	no	—
258	C₄	—	8	2	no	—
259	C₄	—	8	2	no	—
260	C₄	C₁₉×#478	1	2	yes	—
261	C₄	C₁₉×#479	1	2	yes	—
262	C₄	C₁₉×#489	1	2	yes	—
263	C₄	C₁₉×#501	1	2	yes	—
264	C₂	C₁₉×#1553	1	1	yes	characteristic
265	C₂	C₁₉×#1554	1	1	yes	characteristic
266	C₂	C₁₉×#1557	1	1	yes	characteristic
267	C₂	C₁₉×#1559	1	1	yes	characteristic
268	C₂	C₁₉×#1989	1	1	yes	characteristic
269	C₂	C₁₉×#1993	1	1	yes	characteristic
270	C₂	C₁₉×#1998	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
78. #9907	C₁₉	direct (N × H)
180. C₁₉	#9907	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2859	2
C₁₉×#1831	2
C₁₉×#1767	2
C₁₉×#1296	2
#9907	19

Subgroups — C19×#9907 #18015866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9907 #18015866