Subgroups — C₁₉×#8300 #18014259

Order 4864.

1158 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1817	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#324	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#323	C₂	1	2	yes	maximal
5	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
6	C₂×C₁₉×#117	—	2	4	no	—
7	C₂×C₁₉×#117	—	2	4	no	—
8	C₂×C₁₉×#117	—	2	4	no	—
9	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₁₉×#336	—	2	4	no	—
17	C₁₉×#324	—	2	4	no	—
18	C₁₉×#323	—	2	4	no	—
19	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	—	2	2	no	—
21	C₂³×C₄×C₁₉	—	2	2	no	—
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂³×C₄×C₁₉	—	2	2	no	—
24	C₂³×C₄×C₁₉	—	2	2	no	—
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂³×C₄×C₁₉	C₈	1	4	yes	complemented
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	—	2	4	no	—
34	C₁₉×#117	—	2	32	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
47	C₂×C₄²×C₁₉	—	2	2	no	—
48	C₂×C₄²×C₁₉	—	2	2	no	—
49	C₂×C₄²×C₁₉	—	2	2	no	—
50	C₂×C₄²×C₁₉	—	2	2	no	—
51	C₂×C₄²×C₁₉	—	2	2	no	—
52	C₂×C₄²×C₁₉	D₄	1	4	yes	—
53	C₁₉×C₂²⋊C₈	—	2	4	no	—
54	C₁₉×C₂²⋊C₈	—	2	4	no	—
55	C₂⁴×C₁₉	—	2	1	no	—
56	C₂⁴×C₁₉	—	2	1	no	—
57	C₂⁴×C₁₉	—	2	1	no	—
58	C₂⁴×C₁₉	—	2	1	no	—
59	C₂⁴×C₁₉	—	4	2	no	—
60	C₂⁴×C₁₉	—	4	2	no	—
61	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
63	C₂⁴×C₁₉	M₁₆	1	2	yes	—
64	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	—	2	8	no	—
66	C₂²×C₄×C₁₉	—	2	8	no	—
67	C₂²×C₄×C₁₉	—	2	8	no	—
68	C₂²×C₄×C₁₉	—	2	8	no	—
69	C₂²×C₄×C₁₉	—	2	8	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	2	8	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	—	4	2	no	—
88	C₂²×C₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
97	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
98	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₉	—	4	8	no	—
103	C₂×C₈×C₁₉	—	4	4	no	—
104	C₄⋊C₄×C₁₉	—	2	8	no	—
105	C₄⋊C₄×C₁₉	—	2	8	no	—
106	C₂²⋊C₄×C₁₉	—	2	8	no	—
107	C₂²⋊C₄×C₁₉	—	2	8	no	—
108	C₄²×C₁₉	—	2	8	no	—
109	C₄²×C₁₉	—	2	8	no	—
110	#8300	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	—	2	2	no	—
112	C₂³×C₁₉	—	2	2	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	2	no	—
115	C₂³×C₁₉	—	2	2	no	—
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	4	2	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	4	no	—
122	C₂³×C₁₉	—	4	4	no	—
123	C₂³×C₁₉	—	4	4	no	—
124	C₂³×C₁₉	—	4	4	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	C₂²⋊C₈	1	4	yes	—
130	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
134	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
135	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
136	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
137	C₂×C₄×C₁₉	—	2	32	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
166	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
167	C₂×C₄×C₁₉	#120	1	4	yes	—
168	C₈×C₁₉	—	8	4	no	—
169	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
170	#1817	C₂×C₁₉	1	2	yes	complemented
171	C₂×#324	C₂×C₁₉	1	2	yes	complemented
172	C₂×#323	C₂×C₁₉	1	2	yes	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	4	no	—
182	C₂²×C₁₉	—	4	4	no	—
183	C₂²×C₁₉	—	4	4	no	—
184	C₂²×C₁₉	—	4	4	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	#379	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
194	C₂²×C₁₉	#407	1	1	yes	characteristic
195	C₂²×C₁₉	#407	1	1	yes	characteristic
196	C₂²×C₁₉	#407	1	1	yes	characteristic
197	C₂²×C₁₉	#410	1	2	yes	—
198	C₂²×C₁₉	#413	1	2	yes	—
199	C₄×C₁₉	—	2	4	no	—
200	C₄×C₁₉	—	2	4	no	—
201	C₄×C₁₉	—	2	4	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₂⁴×C₄	C₄×C₁₉	1	1	yes	characteristic
206	C₂×#117	—	2	4	no	—
207	C₂×#117	—	2	4	no	—
208	C₂×#117	—	2	4	no	—
209	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
211	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic
212	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
213	C₂²×C₄²	C₄×C₁₉	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
216	#336	—	2	4	no	—
217	#324	—	2	4	no	—
218	#323	—	2	4	no	—
219	C₂×C₁₉	—	2	1	no	—
220	C₂×C₁₉	—	2	1	no	—
221	C₂×C₁₉	—	2	1	no	—
222	C₂×C₁₉	—	2	1	no	—
223	C₂×C₁₉	—	4	4	no	—
224	C₂×C₁₉	#1458	1	2	yes	—
225	C₂×C₁₉	#1464	1	2	yes	—
226	C₂×C₁₉	#1779	1	1	yes	characteristic
227	C₂×C₁₉	#1782	1	1	yes	characteristic
228	C₂×C₁₉	#1785	1	1	yes	characteristic
229	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	C₈×C₁₉	1	4	yes	complemented
237	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
238	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
239	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂²×C₈	—	2	4	no	—
244	#117	—	2	32	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	D₄×C₁₉	1	4	yes	—
263	C₂²⋊C₈	—	2	4	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	C₁₉	#8300	1	1	yes	characteristic, direct product factor, Sylow
266	C₂⁴	—	2	1	no	—
267	C₂⁴	—	2	1	no	—
268	C₂⁴	—	2	1	no	—
269	C₂⁴	—	2	1	no	—
270	C₂⁴	—	4	2	no	—
271	C₂⁴	—	4	2	no	—
272	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
273	C₂⁴	C₂×C₈×C₁₉	1	2	yes	—
274	C₂⁴	M₁₆×C₁₉	1	2	yes	—
275	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
302	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
303	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
307	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
308	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
309	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂×C₈	—	4	8	no	—
314	C₂×C₈	—	4	4	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₂²⋊C₄	—	2	8	no	—
318	C₂²⋊C₄	—	2	8	no	—
319	C₄²	—	2	8	no	—
320	C₄²	—	2	8	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	C₁₉×C₂²⋊C₈	1	4	yes	—
340	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
341	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
342	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
343	C₂³	C₂²×C₈×C₁₉	1	1	yes	characteristic
344	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
345	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
346	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
347	C₂×C₄	—	2	32	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	C₁₉×C₂²⋊C₈	1	4	yes	—
376	C₂×C₄	C₁₉×C₂²⋊C₈	1	4	yes	—
377	C₂×C₄	C₁₉×#120	1	4	yes	—
378	C₈	—	8	4	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	C₁₉×#379	1	1	yes	characteristic
397	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
398	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
399	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
400	C₂²	C₁₉×#407	1	1	yes	characteristic
401	C₂²	C₁₉×#407	1	1	yes	characteristic
402	C₂²	C₁₉×#407	1	1	yes	characteristic
403	C₂²	C₁₉×#410	1	2	yes	—
404	C₂²	C₁₉×#413	1	2	yes	—
405	C₄	—	2	4	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	4	4	no	—
416	C₂	C₁₉×#1458	1	2	yes	—
417	C₂	C₁₉×#1464	1	2	yes	—
418	C₂	C₁₉×#1779	1	1	yes	characteristic
419	C₂	C₁₉×#1782	1	1	yes	characteristic
420	C₂	C₁₉×#1785	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1817	C₂	semidirect
3. C₂×C₁₉×#324	C₂	semidirect
26. C₂³×C₄×C₁₉	C₈	semidirect
110. #8300	C₁₉	direct (N × H)
170. #1817	C₂×C₁₉	semidirect
171. C₂×#324	C₂×C₁₉	semidirect
236. C₂³×C₄	C₈×C₁₉	semidirect
265. C₁₉	#8300	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#117	2
C₁₉×#1817	2
C₂×C₁₉×#324	2
C₂×C₁₉×#323	2
#8300	19

Subgroups — C19×#8300 #18014259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8300 #18014259