Subgroups — C₁₉×#60280 #18066239

Order 4864.

1852 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2994	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2986	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2979	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2977	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2965	C₂	1	4	yes	maximal, complemented
7	C₈×#41×C₁₉	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2922	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₉×#431	C₂	1	2	yes	maximal, complemented
10	C₁₉×#533	C₄	1	2	yes	—
11	C₁₉×#533	C₂²	1	1	yes	characteristic
12	C₁₉×#532	C₄	1	2	yes	—
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₁₉×#529	C₄	1	4	yes	—
15	C₁₉×#529	C₄	1	4	yes	—
16	C₁₉×#529	C₂²	1	4	yes	—
17	C₁₉×#525	C₄	1	4	yes	—
18	C₁₉×#525	C₂²	1	2	yes	—
19	C₄×#41×C₁₉	C₂²	1	4	yes	—
20	C₄×#41×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#446	C₂²	1	8	yes	complemented
23	C₈×Q₈×C₁₉	C₂²	1	8	yes	complemented
24	C₁₉×#436	C₂²	1	8	yes	complemented
25	C₁₉×#435	C₂²	1	16	yes	—
26	C₈×D₄×C₁₉	C₂²	1	16	yes	—
27	C₈×D₄×C₁₉	C₂²	1	8	yes	complemented
28	C₁₉×#433	C₂²	1	8	yes	—
29	C₁₉×#433	C₂²	1	8	yes	complemented
30	C₁₉×#431	C₂²	1	4	yes	—
31	C₁₉×#431	C₂²	1	2	yes	—
32	C₁₉×#431	C₂²	1	2	yes	—
33	C₁₉×#431	C₂²	1	4	yes	—
34	C₁₉×#431	C₂²	1	4	yes	—
35	C₁₉×#431	C₂²	1	8	yes	complemented
36	C₁₉×#424	C₂²	1	8	yes	complemented
37	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
38	C₁₉×#408	C₂²	1	8	yes	—
39	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
40	C₄×M₁₆×C₁₉	C₂²	1	4	yes	complemented
41	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	—
42	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	complemented
43	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
44	C₂×#41×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
50	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
51	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
53	C₁₉×#126	C₂×C₄	1	8	yes	—
54	C₁₉×#125	C₂×C₄	1	2	yes	—
55	C₁₉×#125	C₂×C₄	1	4	yes	—
56	C₁₉×#124	C₂×C₄	1	2	yes	—
57	C₁₉×#124	C₂×C₄	1	4	yes	—
58	C₁₉×#123	C₂×C₄	1	8	yes	—
59	C₁₉×#123	C₂×C₄	1	4	yes	—
60	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
61	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
62	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
63	C₁₉×#121	C₂×C₄	1	4	yes	—
64	C₁₉×#121	C₂×C₄	1	4	yes	—
65	C₁₉×#121	C₂×C₄	1	4	yes	—
66	C₁₉×#120	C₂×C₄	1	4	yes	—
67	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
68	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
69	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
70	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
71	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
72	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
73	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
74	C₄×D₄×C₁₉	C₂³	1	8	yes	—
75	C₄×D₄×C₁₉	C₂³	1	4	yes	—
76	C₁₉×#117	C₂×C₄	1	4	yes	—
77	C₁₉×#117	C₂×C₄	1	8	yes	—
78	C₁₉×#117	C₂³	1	4	yes	—
79	C₁₉×#117	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
90	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	16	yes	—
92	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
93	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
94	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
95	C₁₉×C₂²⋊C₈	C₂³	1	16	yes	—
96	C₁₉×#97	C₂³	1	8	yes	—
97	C₄×C₈×C₁₉	C₂³	1	8	yes	—
98	C₄×C₈×C₁₉	C₂³	1	8	yes	—
99	C₄×C₈×C₁₉	C₂³	1	4	yes	—
100	C₄×C₈×C₁₉	C₂³	1	4	yes	—
101	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	#41×C₁₉	—	2	16	no	—
103	#41×C₁₉	—	4	4	no	—
104	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
105	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
107	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
108	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
109	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	—	2	8	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
124	M₁₆×C₁₉	—	4	8	no	—
125	C₂×C₈×C₁₉	—	4	8	no	—
126	C₂×C₈×C₁₉	—	4	8	no	—
127	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
128	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
129	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
130	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
131	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
132	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
133	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
134	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
135	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
136	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
137	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
138	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
139	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
140	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
141	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
143	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
144	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
148	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₄²×C₁₉	C₂⁴	1	2	yes	—
150	C₄²×C₁₉	C₂⁴	1	4	yes	—
151	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
152	#60280	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
156	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
157	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
158	Q₈×C₁₉	—	2	8	no	—
159	Q₈×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	2	16	no	—
161	D₄×C₁₉	—	2	8	no	—
162	D₄×C₁₉	—	4	2	no	—
163	D₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	16	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	#131	1	8	yes	—
176	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
177	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
180	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
181	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
182	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
185	C₈×C₁₉	—	2	8	no	—
186	C₈×C₁₉	—	2	8	no	—
187	#3444	C₂×C₁₉	1	1	yes	characteristic
188	#2994	C₂×C₁₉	1	8	yes	complemented
189	#2986	C₂×C₁₉	1	2	yes	complemented
190	#2979	C₂×C₁₉	1	2	yes	complemented
191	#2977	C₂×C₁₉	1	4	yes	complemented
192	#2965	C₂×C₁₉	1	4	yes	complemented
193	C₈×#41	C₂×C₁₉	1	4	yes	complemented
194	#2922	C₂×C₁₉	1	4	yes	complemented
195	C₂×#431	C₂×C₁₉	1	2	yes	complemented
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	4	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	2	8	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	C₂×#131	1	4	yes	—
204	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	4	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	2	8	no	—
211	C₄×C₁₉	C₂×#131	1	4	yes	—
212	C₄×C₁₉	C₂×#131	1	4	yes	—
213	C₄×C₁₉	#585	1	2	yes	—
214	#533	C₄×C₁₉	1	2	yes	—
215	#533	C₂²×C₁₉	1	1	yes	characteristic
216	#532	C₄×C₁₉	1	2	yes	—
217	#532	C₂²×C₁₉	1	1	yes	characteristic
218	#529	C₄×C₁₉	1	4	yes	—
219	#529	C₄×C₁₉	1	4	yes	—
220	#529	C₂²×C₁₉	1	4	yes	—
221	#525	C₄×C₁₉	1	4	yes	—
222	#525	C₂²×C₁₉	1	2	yes	—
223	C₄×#41	C₂²×C₁₉	1	4	yes	—
224	C₄×#41	C₂²×C₁₉	1	2	yes	—
225	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
226	#446	C₂²×C₁₉	1	8	yes	complemented
227	C₈×Q₈	C₂²×C₁₉	1	8	yes	complemented
228	#436	C₂²×C₁₉	1	8	yes	complemented
229	#435	C₂²×C₁₉	1	16	yes	—
230	C₈×D₄	C₂²×C₁₉	1	16	yes	—
231	C₈×D₄	C₂²×C₁₉	1	8	yes	complemented
232	#433	C₂²×C₁₉	1	8	yes	—
233	#433	C₂²×C₁₉	1	8	yes	complemented
234	#431	C₂²×C₁₉	1	4	yes	—
235	#431	C₂²×C₁₉	1	2	yes	—
236	#431	C₂²×C₁₉	1	2	yes	—
237	#431	C₂²×C₁₉	1	4	yes	—
238	#431	C₂²×C₁₉	1	4	yes	—
239	#431	C₂²×C₁₉	1	8	yes	complemented
240	#424	C₂²×C₁₉	1	8	yes	complemented
241	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
242	#408	C₂²×C₁₉	1	8	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
244	C₄×M₁₆	C₂²×C₁₉	1	4	yes	complemented
245	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	—
246	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	complemented
247	C₂×C₁₉	—	2	4	no	—
248	C₂×C₁₉	—	4	4	no	—
249	C₂×C₁₉	—	4	1	no	—
250	C₂×C₁₉	#3428	1	1	yes	characteristic
251	C₂×C₁₉	C₂²×#131	1	2	yes	—
252	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
253	C₂×#41	C₂³×C₁₉	1	2	yes	—
254	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
257	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
258	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
259	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
260	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
261	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
262	#126	C₂×C₄×C₁₉	1	8	yes	—
263	#125	C₂×C₄×C₁₉	1	2	yes	—
264	#125	C₂×C₄×C₁₉	1	4	yes	—
265	#124	C₂×C₄×C₁₉	1	2	yes	—
266	#124	C₂×C₄×C₁₉	1	4	yes	—
267	#123	C₂×C₄×C₁₉	1	8	yes	—
268	#123	C₂×C₄×C₁₉	1	4	yes	—
269	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
270	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
271	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
272	#121	C₂×C₄×C₁₉	1	4	yes	—
273	#121	C₂×C₄×C₁₉	1	4	yes	—
274	#121	C₂×C₄×C₁₉	1	4	yes	—
275	#120	C₂×C₄×C₁₉	1	4	yes	—
276	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
277	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
278	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
279	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
280	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
281	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
282	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
283	C₄×D₄	C₂³×C₁₉	1	8	yes	—
284	C₄×D₄	C₂³×C₁₉	1	4	yes	—
285	#117	C₂×C₄×C₁₉	1	4	yes	—
286	#117	C₂×C₄×C₁₉	1	8	yes	—
287	#117	C₂³×C₁₉	1	2	yes	—
288	#117	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
290	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
291	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
292	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
293	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
294	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
298	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
299	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
300	C₄⋊C₈	C₂³×C₁₉	1	16	yes	—
301	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
302	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
303	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
304	C₂²⋊C₈	C₂³×C₁₉	1	16	yes	—
305	#97	C₂³×C₁₉	1	8	yes	—
306	C₄×C₈	C₂³×C₁₉	1	4	yes	—
307	C₄×C₈	C₂³×C₁₉	1	4	yes	—
308	C₄×C₈	C₂³×C₁₉	1	8	yes	—
309	C₄×C₈	C₂³×C₁₉	1	8	yes	—
310	C₁₉	#60280	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
312	#41	—	2	16	no	—
313	#41	—	4	4	no	—
314	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
315	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
316	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
317	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
318	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
319	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
327	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
334	M₁₆	—	4	8	no	—
335	C₂×C₈	—	4	8	no	—
336	C₂×C₈	—	4	8	no	—
337	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
338	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
339	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
340	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
341	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
342	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
343	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
344	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
345	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
346	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
347	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
348	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
349	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
350	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
351	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
352	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
353	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
354	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
355	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
356	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
357	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
358	C₄²	C₂⁴×C₁₉	1	2	yes	—
359	C₄²	C₂⁴×C₁₉	1	4	yes	—
360	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
361	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
362	C₂³	—	2	4	no	—
363	C₂³	—	4	1	no	—
364	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
365	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
366	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
367	Q₈	—	2	8	no	—
368	Q₈	—	4	2	no	—
369	D₄	—	2	16	no	—
370	D₄	—	2	8	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	C₁₉×#131	1	8	yes	—
385	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
386	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
388	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
389	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
390	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
391	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
392	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
393	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
394	C₈	—	2	8	no	—
395	C₈	—	2	8	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	8	no	—
402	C₂²	—	4	4	no	—
403	C₂²	C₂×C₁₉×#131	1	4	yes	—
404	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	4	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	8	no	—
411	C₄	C₂×C₁₉×#131	1	4	yes	—
412	C₄	C₂×C₁₉×#131	1	4	yes	—
413	C₄	C₁₉×#585	1	2	yes	—
414	C₂	—	2	4	no	—
415	C₂	—	4	1	no	—
416	C₂	—	4	4	no	—
417	C₂	C₁₉×#3428	1	1	yes	characteristic
418	C₂	C₂²×C₁₉×#131	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3444	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×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×#2986	C₂	semidirect
4. C₁₉×#2979	C₂	semidirect
5. C₁₉×#2977	C₂	semidirect
6. C₁₉×#2965	C₂	semidirect
7. C₈×#41×C₁₉	C₂	semidirect
8. C₁₉×#2922	C₂	semidirect
9. C₂×C₁₉×#431	C₂	semidirect
22. C₁₉×#446	C₂²	semidirect
23. C₈×Q₈×C₁₉	C₂²	semidirect
24. C₁₉×#436	C₂²	semidirect
27. C₈×D₄×C₁₉	C₂²	semidirect
29. C₁₉×#433	C₂²	semidirect
35. C₁₉×#431	C₂²	semidirect
36. C₁₉×#424	C₂²	semidirect
40. C₄×M₁₆×C₁₉	C₂²	semidirect
42. C₂×C₄×C₈×C₁₉	C₂²	semidirect
152. #60280	C₁₉	direct (N × H)
188. #2994	C₂×C₁₉	semidirect
189. #2986	C₂×C₁₉	semidirect
190. #2979	C₂×C₁₉	semidirect
191. #2977	C₂×C₁₉	semidirect
192. #2965	C₂×C₁₉	semidirect
193. C₈×#41	C₂×C₁₉	semidirect
194. #2922	C₂×C₁₉	semidirect
195. C₂×#431	C₂×C₁₉	semidirect
226. #446	C₂²×C₁₉	semidirect
227. C₈×Q₈	C₂²×C₁₉	semidirect
228. #436	C₂²×C₁₉	semidirect
231. C₈×D₄	C₂²×C₁₉	semidirect
233. #433	C₂²×C₁₉	semidirect
239. #431	C₂²×C₁₉	semidirect
240. #424	C₂²×C₁₉	semidirect
244. C₄×M₁₆	C₂²×C₁₉	semidirect
246. C₂×C₄×C₈	C₂²×C₁₉	semidirect
310. C₁₉	#60280	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×#3444	2
C₁₉×#2994	2
C₁₉×#2986	2
C₁₉×#2979	2
C₁₉×#2977	2
C₁₉×#2965	2
C₈×#41×C₁₉	2
C₁₉×#2922	2
C₂×C₁₉×#431	2
#60280	19

Subgroups — C19×#60280 #18066239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60280 #18066239