Subgroups — C₁₉×#60301 #18066260

Order 4864.

1760 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3480	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2994	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2993	C₂	1	3	yes	maximal, complemented
4	C₁₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2981	C₂	1	3	yes	maximal, complemented
9	C₁₉×#2979	C₂	1	3	yes	maximal, complemented
10	C₁₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2969	C₂	1	3	yes	maximal, complemented
12	C₁₉×#2966	C₂	1	3	yes	maximal, complemented
13	C₈×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2925	C₂	1	3	yes	maximal, complemented
15	C₁₉×#2922	C₂	1	3	yes	maximal, complemented
16	C₁₉×#559	C₄	1	3	yes	—
17	C₁₉×#557	C₄	1	1	yes	characteristic
18	C₁₉×#556	C₄	1	3	yes	—
19	C₁₉×#553	C₄	1	3	yes	—
20	C₁₉×#553	C₄	1	3	yes	—
21	C₁₉×#550	C₄	1	1	yes	characteristic
22	C₁₉×#548	C₄	1	1	yes	characteristic
23	C₁₉×#548	C₄	1	1	yes	characteristic
24	C₁₉×#532	C₂²	1	3	yes	—
25	C₁₉×#529	C₂²	1	3	yes	—
26	C₁₉×#529	C₂²	1	3	yes	—
27	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×#41×C₁₉	C₂²	1	3	yes	—
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#446	C₂²	1	3	yes	—
32	C₁₉×#446	C₂²	1	3	yes	—
33	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
35	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
36	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
37	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#436	C₂²	1	3	yes	—
40	C₁₉×#436	C₂²	1	6	yes	—
41	C₁₉×#436	C₂²	1	3	yes	—
42	C₁₉×#436	C₂²	1	3	yes	—
43	C₁₉×#436	C₂²	1	3	yes	—
44	C₁₉×#435	C₂²	1	6	yes	—
45	C₁₉×#435	C₂²	1	6	yes	—
46	C₈×D₄×C₁₉	C₂²	1	3	yes	—
47	C₈×D₄×C₁₉	C₂²	1	3	yes	—
48	C₈×D₄×C₁₉	C₂²	1	6	yes	—
49	C₈×D₄×C₁₉	C₂²	1	3	yes	—
50	C₈×D₄×C₁₉	C₂²	1	3	yes	—
51	C₁₉×#433	C₂²	1	1	yes	characteristic
52	C₁₉×#433	C₂²	1	3	yes	—
53	C₁₉×#433	C₂²	1	3	yes	—
54	C₁₉×#433	C₂²	1	3	yes	—
55	C₁₉×#433	C₂²	1	6	yes	—
56	C₁₉×#432	C₂²	1	3	yes	—
57	C₁₉×#432	C₂²	1	3	yes	—
58	C₁₉×#431	C₂²	1	3	yes	—
59	C₁₉×#431	C₂²	1	3	yes	—
60	C₁₉×#431	C₂²	1	3	yes	—
61	C₁₉×#431	C₂²	1	3	yes	—
62	C₁₉×#431	C₂²	1	3	yes	—
63	C₁₉×#431	C₂²	1	3	yes	—
64	C₁₉×#424	C₂²	1	3	yes	—
65	C₁₉×#424	C₂²	1	3	yes	—
66	C₁₉×#423	C₂²	1	3	yes	—
67	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
68	C₁₉×#408	C₂²	1	3	yes	—
69	C₁₉×#408	C₂²	1	3	yes	—
70	C₁₉×#408	C₂²	1	6	yes	—
71	C₁₉×#405	C₂²	1	6	yes	—
72	C₄×M₁₆×C₁₉	C₂²	1	3	yes	—
73	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
74	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×#41×C₁₉	C₂³	1	3	yes	—
77	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
79	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
80	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
81	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
82	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
83	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
84	C₁₉×C₄⋊Q₈	C₂×C₄	1	3	yes	—
85	C₁₉×#127	C₂×C₄	1	3	yes	—
86	C₁₉×#126	C₂×C₄	1	6	yes	—
87	C₁₉×#126	C₂×C₄	1	6	yes	—
88	C₁₉×#125	C₂×C₄	1	3	yes	—
89	C₁₉×#125	C₂×C₄	1	3	yes	—
90	C₁₉×#124	C₂×C₄	1	3	yes	—
91	C₁₉×#124	C₂×C₄	1	3	yes	—
92	C₁₉×#124	C₂×C₄	1	6	yes	—
93	C₁₉×#123	C₂×C₄	1	6	yes	—
94	C₁₉×#123	C₂×C₄	1	6	yes	—
95	C₁₉×C₂²⋊Q₈	C₂×C₄	1	3	yes	—
96	C₁₉×C₂²⋊Q₈	C₂×C₄	1	3	yes	—
97	C₁₉×#121	C₂×C₄	1	3	yes	—
98	C₁₉×#121	C₂×C₄	1	3	yes	—
99	C₁₉×#121	C₂×C₄	1	3	yes	—
100	C₁₉×#121	C₂×C₄	1	3	yes	—
101	C₁₉×#121	C₂×C₄	1	6	yes	—
102	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
104	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
105	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
106	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
107	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
108	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
110	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
111	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
112	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
113	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
114	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
115	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
116	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
117	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
118	C₄×D₄×C₁₉	C₂³	1	3	yes	—
119	C₄×D₄×C₁₉	C₂³	1	3	yes	—
120	C₄×D₄×C₁₉	C₂³	1	6	yes	—
121	C₁₉×#117	C₂×C₄	1	3	yes	—
122	C₁₉×#117	C₂×C₄	1	3	yes	—
123	C₁₉×#117	C₂³	1	3	yes	—
124	C₁₉×#117	C₂³	1	3	yes	—
125	C₁₉×#117	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
127	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
128	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
129	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
130	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
131	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
132	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
133	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
134	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
135	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
136	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
137	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
138	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
139	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
140	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
141	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
142	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
143	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
144	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
145	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
146	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
147	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
148	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
149	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
150	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
151	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
152	C₁₉×#97	C₂³	1	1	yes	characteristic
153	C₁₉×#97	C₂³	1	3	yes	—
154	C₁₉×#97	C₂³	1	6	yes	—
155	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
156	C₄×C₈×C₁₉	C₂³	1	3	yes	—
157	C₄×C₈×C₁₉	C₂³	1	3	yes	—
158	C₄×C₈×C₁₉	C₂³	1	3	yes	—
159	C₄×C₈×C₁₉	C₂³	1	3	yes	—
160	C₄×C₈×C₁₉	C₂³	1	3	yes	—
161	C₄×C₈×C₁₉	C₂³	1	6	yes	—
162	#41×C₁₉	—	2	4	no	—
163	#41×C₁₉	—	2	4	no	—
164	#41×C₁₉	—	4	3	no	—
165	#41×C₁₉	—	4	3	no	—
166	C₂×Q₈×C₁₉	—	2	4	no	—
167	C₂×Q₈×C₁₉	C₂²×C₄	1	3	yes	—
168	C₂×Q₈×C₁₉	C₂²×C₄	1	3	yes	—
169	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
171	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
172	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
173	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
174	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
175	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
176	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
177	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
178	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
179	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
180	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
181	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
182	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
184	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
185	M₁₆×C₁₉	—	4	3	no	—
186	M₁₆×C₁₉	—	4	6	no	—
187	M₁₆×C₁₉	—	4	3	no	—
188	C₂×C₈×C₁₉	—	4	3	no	—
189	C₂×C₈×C₁₉	—	4	6	no	—
190	C₂×C₈×C₁₉	—	4	3	no	—
191	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
193	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
195	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
196	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
197	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
199	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
200	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
201	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
202	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
203	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
204	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
207	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
208	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
209	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
210	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
211	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
212	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
213	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
214	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
215	C₂²⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
216	C₂²⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
217	C₂²⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
218	C₂²⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
219	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
220	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
221	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
222	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
223	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
224	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
225	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
226	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
227	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
228	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₄²×C₁₉	C₂⁴	1	3	yes	—
230	C₄²×C₁₉	C₂⁴	1	3	yes	—
231	#60301	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
233	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
234	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
235	Q₈×C₁₉	—	2	6	no	—
236	Q₈×C₁₉	—	4	3	no	—
237	Q₈×C₁₉	#131	1	4	yes	—
238	D₄×C₁₉	—	2	6	no	—
239	D₄×C₁₉	—	2	6	no	—
240	D₄×C₁₉	—	4	6	no	—
241	D₄×C₁₉	—	4	3	no	—
242	D₄×C₁₉	—	4	3	no	—
243	D₄×C₁₉	—	4	3	no	—
244	C₂×C₄×C₁₉	—	2	6	no	—
245	C₂×C₄×C₁₉	—	2	6	no	—
246	C₂×C₄×C₁₉	—	2	6	no	—
247	C₂×C₄×C₁₉	—	2	3	no	—
248	C₂×C₄×C₁₉	—	2	3	no	—
249	C₂×C₄×C₁₉	—	2	3	no	—
250	C₂×C₄×C₁₉	—	2	3	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	4	3	no	—
254	C₂×C₄×C₁₉	—	4	3	no	—
255	C₂×C₄×C₁₉	—	4	3	no	—
256	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
260	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
263	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
264	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
265	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
266	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
267	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	3	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	2	3	no	—
272	C₈×C₁₉	—	2	3	no	—
273	C₈×C₁₉	—	2	1	no	—
274	C₈×C₁₉	—	2	1	no	—
275	C₈×C₁₉	—	2	3	no	—
276	#3480	C₂×C₁₉	1	1	yes	characteristic
277	#2994	C₂×C₁₉	1	3	yes	complemented
278	#2993	C₂×C₁₉	1	3	yes	complemented
279	#2991	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#2988	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#2984	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#2982	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#2981	C₂×C₁₉	1	3	yes	complemented
284	#2979	C₂×C₁₉	1	3	yes	complemented
285	#2971	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#2969	C₂×C₁₉	1	3	yes	complemented
287	#2966	C₂×C₁₉	1	3	yes	complemented
288	C₈×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#2925	C₂×C₁₉	1	3	yes	complemented
290	#2922	C₂×C₁₉	1	3	yes	complemented
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	3	no	—
293	C₂²×C₁₉	—	2	3	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	3	no	—
296	C₂²×C₁₉	—	2	3	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	3	no	—
299	C₂²×C₁₉	—	2	3	no	—
300	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	3	no	—
303	C₄×C₁₉	—	2	3	no	—
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	2	3	no	—
307	C₄×C₁₉	—	2	1	no	—
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	2	3	no	—
310	C₄×C₁₉	—	2	3	no	—
311	C₄×C₁₉	C₂×#131	1	6	yes	—
312	C₄×C₁₉	#585	1	1	yes	characteristic
313	C₄×C₁₉	#585	1	1	yes	characteristic
314	#559	C₄×C₁₉	1	3	yes	—
315	#557	C₄×C₁₉	1	1	yes	characteristic
316	#556	C₄×C₁₉	1	3	yes	—
317	#553	C₄×C₁₉	1	3	yes	—
318	#553	C₄×C₁₉	1	3	yes	—
319	#550	C₄×C₁₉	1	1	yes	characteristic
320	#548	C₄×C₁₉	1	1	yes	characteristic
321	#548	C₄×C₁₉	1	1	yes	characteristic
322	#532	C₂²×C₁₉	1	3	yes	—
323	#529	C₂²×C₁₉	1	3	yes	—
324	#529	C₂²×C₁₉	1	3	yes	—
325	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
326	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
327	C₄×#41	C₂²×C₁₉	1	3	yes	—
328	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
329	#446	C₂²×C₁₉	1	3	yes	—
330	#446	C₂²×C₁₉	1	3	yes	—
331	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
332	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
333	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
334	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
335	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
337	#436	C₂²×C₁₉	1	3	yes	—
338	#436	C₂²×C₁₉	1	6	yes	—
339	#436	C₂²×C₁₉	1	3	yes	—
340	#436	C₂²×C₁₉	1	3	yes	—
341	#436	C₂²×C₁₉	1	3	yes	—
342	#435	C₂²×C₁₉	1	6	yes	—
343	#435	C₂²×C₁₉	1	6	yes	—
344	C₈×D₄	C₂²×C₁₉	1	3	yes	—
345	C₈×D₄	C₂²×C₁₉	1	3	yes	—
346	C₈×D₄	C₂²×C₁₉	1	6	yes	—
347	C₈×D₄	C₂²×C₁₉	1	3	yes	—
348	C₈×D₄	C₂²×C₁₉	1	3	yes	—
349	#433	C₂²×C₁₉	1	1	yes	characteristic
350	#433	C₂²×C₁₉	1	3	yes	—
351	#433	C₂²×C₁₉	1	3	yes	—
352	#433	C₂²×C₁₉	1	3	yes	—
353	#433	C₂²×C₁₉	1	6	yes	—
354	#432	C₂²×C₁₉	1	3	yes	—
355	#432	C₂²×C₁₉	1	3	yes	—
356	#431	C₂²×C₁₉	1	3	yes	—
357	#431	C₂²×C₁₉	1	3	yes	—
358	#431	C₂²×C₁₉	1	3	yes	—
359	#431	C₂²×C₁₉	1	3	yes	—
360	#431	C₂²×C₁₉	1	3	yes	—
361	#431	C₂²×C₁₉	1	3	yes	—
362	#424	C₂²×C₁₉	1	3	yes	—
363	#424	C₂²×C₁₉	1	3	yes	—
364	#423	C₂²×C₁₉	1	3	yes	—
365	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
366	#408	C₂²×C₁₉	1	3	yes	—
367	#408	C₂²×C₁₉	1	3	yes	—
368	#408	C₂²×C₁₉	1	6	yes	—
369	#405	C₂²×C₁₉	1	6	yes	—
370	C₄×M₁₆	C₂²×C₁₉	1	3	yes	—
371	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
372	C₂×C₁₉	—	4	1	no	—
373	C₂×C₁₉	—	4	3	no	—
374	C₂×C₁₉	—	4	3	no	—
375	C₂×C₁₉	#3428	1	1	yes	characteristic
376	C₂×C₁₉	C₂²×#131	1	1	yes	characteristic
377	C₂×C₁₉	#3573	1	1	yes	characteristic
378	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
379	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
380	C₂×#41	C₂³×C₁₉	1	3	yes	—
381	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
382	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
383	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
384	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
385	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
386	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
387	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
388	C₄⋊Q₈	C₂×C₄×C₁₉	1	3	yes	—
389	#127	C₂×C₄×C₁₉	1	3	yes	—
390	#126	C₂×C₄×C₁₉	1	6	yes	—
391	#126	C₂×C₄×C₁₉	1	6	yes	—
392	#125	C₂×C₄×C₁₉	1	3	yes	—
393	#125	C₂×C₄×C₁₉	1	3	yes	—
394	#124	C₂×C₄×C₁₉	1	3	yes	—
395	#124	C₂×C₄×C₁₉	1	3	yes	—
396	#124	C₂×C₄×C₁₉	1	6	yes	—
397	#123	C₂×C₄×C₁₉	1	6	yes	—
398	#123	C₂×C₄×C₁₉	1	6	yes	—
399	C₂²⋊Q₈	C₂×C₄×C₁₉	1	3	yes	—
400	C₂²⋊Q₈	C₂×C₄×C₁₉	1	3	yes	—
401	#121	C₂×C₄×C₁₉	1	3	yes	—
402	#121	C₂×C₄×C₁₉	1	3	yes	—
403	#121	C₂×C₄×C₁₉	1	3	yes	—
404	#121	C₂×C₄×C₁₉	1	3	yes	—
405	#121	C₂×C₄×C₁₉	1	6	yes	—
406	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
407	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
408	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
409	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
410	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
411	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
412	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
414	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
415	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
416	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
417	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
418	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
419	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
420	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
421	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
422	C₄×D₄	C₂³×C₁₉	1	3	yes	—
423	C₄×D₄	C₂³×C₁₉	1	3	yes	—
424	C₄×D₄	C₂³×C₁₉	1	6	yes	—
425	#117	C₂×C₄×C₁₉	1	3	yes	—
426	#117	C₂×C₄×C₁₉	1	3	yes	—
427	#117	C₂³×C₁₉	1	1	yes	characteristic
428	#117	C₂³×C₁₉	1	3	yes	—
429	#117	C₂³×C₁₉	1	3	yes	—
430	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
431	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
432	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
433	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
434	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
435	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
436	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
437	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
438	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
439	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
440	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
443	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
444	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
445	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
446	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
448	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
449	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
450	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
451	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
452	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
453	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
454	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
455	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
456	#97	C₂³×C₁₉	1	1	yes	characteristic
457	#97	C₂³×C₁₉	1	3	yes	—
458	#97	C₂³×C₁₉	1	6	yes	—
459	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
460	C₄×C₈	C₂³×C₁₉	1	3	yes	—
461	C₄×C₈	C₂³×C₁₉	1	3	yes	—
462	C₄×C₈	C₂³×C₁₉	1	3	yes	—
463	C₄×C₈	C₂³×C₁₉	1	3	yes	—
464	C₄×C₈	C₂³×C₁₉	1	3	yes	—
465	C₄×C₈	C₂³×C₁₉	1	6	yes	—
466	C₁₉	#60301	1	1	yes	characteristic, direct product factor, Sylow
467	#41	—	2	4	no	—
468	#41	—	2	4	no	—
469	#41	—	4	3	no	—
470	#41	—	4	3	no	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	C₂²×C₄×C₁₉	1	3	yes	—
473	C₂×Q₈	C₂²×C₄×C₁₉	1	3	yes	—
474	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
475	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
476	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
477	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
478	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
479	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
480	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
481	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
482	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
483	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
484	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
485	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
486	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
487	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
489	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
490	M₁₆	—	4	3	no	—
491	M₁₆	—	4	6	no	—
492	M₁₆	—	4	3	no	—
493	C₂×C₈	—	4	3	no	—
494	C₂×C₈	—	4	6	no	—
495	C₂×C₈	—	4	3	no	—
496	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
497	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
498	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
499	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
500	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
501	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
502	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
503	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
504	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
505	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
506	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
507	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
508	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
509	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
512	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
513	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
514	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
515	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
516	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
517	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
518	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
519	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
521	C₂²⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
522	C₂²⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
523	C₂²⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
524	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
525	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
526	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
527	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
528	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
529	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
530	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
531	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
532	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
533	C₄²	C₂⁴×C₁₉	1	3	yes	—
534	C₄²	C₂⁴×C₁₉	1	3	yes	—
535	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
536	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
537	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
538	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
539	Q₈	—	2	6	no	—
540	Q₈	—	4	3	no	—
541	Q₈	C₁₉×#131	1	4	yes	—
542	D₄	—	2	6	no	—
543	D₄	—	2	6	no	—
544	D₄	—	4	3	no	—
545	D₄	—	4	3	no	—
546	D₄	—	4	3	no	—
547	D₄	—	4	6	no	—
548	C₂×C₄	—	2	6	no	—
549	C₂×C₄	—	2	6	no	—
550	C₂×C₄	—	2	6	no	—
551	C₂×C₄	—	2	3	no	—
552	C₂×C₄	—	2	3	no	—
553	C₂×C₄	—	2	3	no	—
554	C₂×C₄	—	2	3	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	3	no	—
558	C₂×C₄	—	4	3	no	—
559	C₂×C₄	—	4	3	no	—
560	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
561	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
562	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
563	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
564	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
567	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
568	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
569	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
570	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
571	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
572	C₈	—	2	1	no	—
573	C₈	—	2	3	no	—
574	C₈	—	2	1	no	—
575	C₈	—	2	3	no	—
576	C₈	—	2	3	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	3	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	3	no	—
582	C₂²	—	2	3	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	3	no	—
585	C₂²	—	2	3	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	3	no	—
588	C₂²	—	2	3	no	—
589	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
590	C₄	—	2	1	no	—
591	C₄	—	2	3	no	—
592	C₄	—	2	3	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	3	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	3	no	—
599	C₄	—	2	3	no	—
600	C₄	C₂×C₁₉×#131	1	6	yes	—
601	C₄	C₁₉×#585	1	1	yes	characteristic
602	C₄	C₁₉×#585	1	1	yes	characteristic
603	C₂	—	4	1	no	—
604	C₂	—	4	3	no	—
605	C₂	—	4	3	no	—
606	C₂	C₁₉×#3428	1	1	yes	characteristic
607	C₂	C₂²×C₁₉×#131	1	1	yes	characteristic
608	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3480	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2994	C₂	semidirect
3. C₁₉×#2993	C₂	semidirect
4. C₁₉×#2991	C₂	semidirect
5. C₁₉×#2988	C₂	semidirect
6. C₁₉×#2984	C₂	semidirect
7. C₁₉×#2982	C₂	semidirect
8. C₁₉×#2981	C₂	semidirect
9. C₁₉×#2979	C₂	semidirect
10. C₁₉×#2971	C₂	semidirect
11. C₁₉×#2969	C₂	semidirect
12. C₁₉×#2966	C₂	semidirect
13. C₈×#41×C₁₉	C₂	semidirect
14. C₁₉×#2925	C₂	semidirect
15. C₁₉×#2922	C₂	semidirect
231. #60301	C₁₉	direct (N × H)
277. #2994	C₂×C₁₉	semidirect
278. #2993	C₂×C₁₉	semidirect
279. #2991	C₂×C₁₉	semidirect
280. #2988	C₂×C₁₉	semidirect
281. #2984	C₂×C₁₉	semidirect
282. #2982	C₂×C₁₉	semidirect
283. #2981	C₂×C₁₉	semidirect
284. #2979	C₂×C₁₉	semidirect
285. #2971	C₂×C₁₉	semidirect
286. #2969	C₂×C₁₉	semidirect
287. #2966	C₂×C₁₉	semidirect
288. C₈×#41	C₂×C₁₉	semidirect
289. #2925	C₂×C₁₉	semidirect
290. #2922	C₂×C₁₉	semidirect
466. C₁₉	#60301	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×#3480	2
C₁₉×#2994	2
C₁₉×#2993	2
C₁₉×#2991	2
C₁₉×#2988	2
C₁₉×#2984	2
C₁₉×#2982	2
C₁₉×#2981	2
C₁₉×#2979	2
C₁₉×#2971	2
C₁₉×#2969	2
C₁₉×#2966	2
C₈×#41×C₁₉	2
C₁₉×#2925	2
C₁₉×#2922	2
#60301	19

Subgroups — C19×#60301 #18066260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60301 #18066260