Subgroups — C₁₉×#11222 #18017181

Order 4864.

1190 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2315	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#342	C₂	1	2	yes	maximal
4	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#385	—	2	4	no	—
13	C₁₉×#385	—	2	2	no	—
14	C₁₉×#385	C₄	1	4	yes	complemented
15	C₁₉×#380	—	2	1	no	—
16	C₁₉×#380	—	2	1	no	—
17	C₂×C₁₉×#95	—	2	1	no	—
18	C₂×C₁₉×#95	—	2	4	no	—
19	C₁₉×#342	—	2	2	no	—
20	C₁₉×#342	—	2	4	no	—
21	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂³×C₄×C₁₉	—	2	1	no	—
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	4	4	no	—
29	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₉	D₄	1	4	yes	—
31	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
58	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
59	C₁₉×#95	—	2	2	no	—
60	C₁₉×#95	—	2	2	no	—
61	C₁₉×#95	—	2	4	no	—
62	C₁₉×#95	—	4	8	no	—
63	C₂⁴×C₁₉	—	4	2	no	—
64	C₂⁴×C₁₉	—	4	2	no	—
65	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
68	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
71	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
72	C₂⁴×C₁₉	#41	1	1	yes	characteristic
73	C₂⁴×C₁₉	#41	1	1	yes	characteristic
74	C₂⁴×C₁₉	#41	1	2	yes	—
75	C₂⁴×C₁₉	#41	1	2	yes	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	8	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	4	4	no	—
92	C₂²×C₄×C₁₉	—	4	4	no	—
93	C₂²×C₄×C₁₉	—	4	8	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	4	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	4	4	no	—
105	C₂²×C₄×C₁₉	—	4	4	no	—
106	C₂²×C₄×C₁₉	—	4	4	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
111	C₄⋊C₄×C₁₉	—	4	8	no	—
112	C₄⋊C₄×C₁₉	—	8	2	no	—
113	C₄⋊C₄×C₁₉	—	8	2	no	—
114	C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂²⋊C₄×C₁₉	—	2	4	no	—
116	C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₂²⋊C₄×C₁₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₉	—	4	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	2	no	—
125	C₂²⋊C₄×C₁₉	—	4	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	2	no	—
127	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	complemented
128	#11222	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	4	no	—
145	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₉	#117	1	1	yes	characteristic
148	C₂³×C₁₉	C₄×D₄	1	2	yes	—
149	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
150	C₂³×C₁₉	#120	1	1	yes	characteristic
151	C₂³×C₁₉	#121	1	1	yes	characteristic
152	C₂³×C₁₉	#121	1	2	yes	—
153	C₂³×C₁₉	#121	1	2	yes	—
154	C₂³×C₁₉	#121	1	1	yes	characteristic
155	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
157	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
159	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
160	C₂³×C₁₉	#123	1	1	yes	characteristic
161	C₂³×C₁₉	#123	1	2	yes	—
162	C₂³×C₁₉	#124	1	1	yes	characteristic
163	C₂³×C₁₉	#125	1	2	yes	—
164	C₂³×C₁₉	#125	1	2	yes	—
165	C₂³×C₁₉	#126	1	2	yes	—
166	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
167	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	8	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	8	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	8	no	—
188	C₂×C₄×C₁₉	—	4	8	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	8	1	no	—
195	C₂×C₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	—	8	4	no	—
198	C₂×C₄×C₁₉	—	8	4	no	—
199	#2315	C₂×C₁₉	1	1	yes	characteristic
200	C₂×#385	C₂×C₁₉	1	1	yes	characteristic
201	C₂×#342	C₂×C₁₉	1	2	yes	—
202	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
203	C₂²⋊#95	C₂×C₁₉	1	2	yes	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	4	no	—
206	C₂²×C₁₉	—	2	4	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	2	4	no	—
218	C₂²×C₁₉	—	2	4	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	4	1	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	1	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	#380	1	1	yes	characteristic
231	C₂²×C₁₉	#386	1	1	yes	characteristic
232	C₂²×C₁₉	#387	1	2	yes	—
233	C₂²×C₁₉	#389	1	2	yes	—
234	C₂²×C₁₉	#391	1	1	yes	characteristic
235	C₂²×C₁₉	#394	1	1	yes	characteristic
236	C₂²×C₁₉	#395	1	1	yes	characteristic
237	C₂²×C₁₉	#396	1	2	yes	—
238	C₂²×C₁₉	#398	1	1	yes	characteristic
239	C₂²×C₁₉	#398	1	2	yes	—
240	C₂²×C₁₉	#400	1	1	yes	characteristic
241	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
242	C₂²×C₁₉	#458	1	2	yes	—
243	C₄×C₁₉	—	4	4	no	—
244	C₄×C₁₉	—	4	4	no	—
245	C₄×C₁₉	—	4	2	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	8	4	no	—
248	C₄×C₁₉	—	8	4	no	—
249	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	—	2	1	no	—
251	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
252	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
255	#385	—	2	4	no	—
256	#385	—	2	2	no	—
257	#385	C₄×C₁₉	1	4	yes	complemented
258	#380	—	2	1	no	—
259	#380	—	2	1	no	—
260	C₂×#95	—	2	1	no	—
261	C₂×#95	—	2	4	no	—
262	#342	—	2	2	no	—
263	#342	—	2	4	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	2	no	—
266	C₂×C₁₉	—	2	2	no	—
267	C₂×C₁₉	—	2	2	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	2	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	#1441	1	1	yes	characteristic
273	C₂×C₁₉	#1889	1	1	yes	characteristic
274	C₂×C₁₉	#1890	1	1	yes	characteristic
275	C₂×C₁₉	#2044	1	2	yes	—
276	C₂×C₁₉	#2062	1	2	yes	—
277	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	—	2	2	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	—	4	4	no	—
285	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
286	C₂³×C₄	D₄×C₁₉	1	4	yes	—
287	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	2	4	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	4	4	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
311	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
312	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
313	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
314	C₂×C₂²⋊C₄	Q₈×C₁₉	1	2	yes	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	4	no	—
318	#95	—	4	8	no	—
319	C₁₉	#11222	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁴	—	4	2	no	—
321	C₂⁴	—	4	2	no	—
322	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
323	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
325	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
327	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
328	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
329	C₂⁴	#41×C₁₉	1	1	yes	characteristic
330	C₂⁴	#41×C₁₉	1	1	yes	characteristic
331	C₂⁴	#41×C₁₉	1	2	yes	—
332	C₂⁴	#41×C₁₉	1	2	yes	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	8	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
367	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
368	C₄⋊C₄	—	4	8	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	4	yes	complemented
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
402	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
403	C₂³	C₁₉×#117	1	1	yes	characteristic
404	C₂³	C₄×D₄×C₁₉	1	2	yes	—
405	C₂³	C₄×Q₈×C₁₉	1	2	yes	—
406	C₂³	C₁₉×#120	1	1	yes	characteristic
407	C₂³	C₁₉×#121	1	1	yes	characteristic
408	C₂³	C₁₉×#121	1	2	yes	—
409	C₂³	C₁₉×#121	1	2	yes	—
410	C₂³	C₁₉×#121	1	1	yes	characteristic
411	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
412	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
413	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
414	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
415	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
416	C₂³	C₁₉×#123	1	1	yes	characteristic
417	C₂³	C₁₉×#123	1	2	yes	—
418	C₂³	C₁₉×#124	1	1	yes	characteristic
419	C₂³	C₁₉×#125	1	2	yes	—
420	C₂³	C₁₉×#125	1	2	yes	—
421	C₂³	C₁₉×#126	1	2	yes	—
422	C₂³	C₁₉×C₄⋊Q₈	1	2	yes	—
423	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	8	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	—	8	1	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	—	8	4	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	C₁₉×#380	1	1	yes	characteristic
482	C₂²	C₁₉×#386	1	1	yes	characteristic
483	C₂²	C₁₉×#387	1	2	yes	—
484	C₂²	C₁₉×#389	1	2	yes	—
485	C₂²	C₁₉×#391	1	1	yes	characteristic
486	C₂²	C₁₉×#394	1	1	yes	characteristic
487	C₂²	C₁₉×#395	1	1	yes	characteristic
488	C₂²	C₁₉×#396	1	2	yes	—
489	C₂²	C₁₉×#398	1	1	yes	characteristic
490	C₂²	C₁₉×#398	1	2	yes	—
491	C₂²	C₁₉×#400	1	1	yes	characteristic
492	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
493	C₂²	C₁₉×#458	1	2	yes	—
494	C₄	—	4	4	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	4	no	—
499	C₄	—	8	4	no	—
500	C₂	—	2	1	no	—
501	C₂	—	2	2	no	—
502	C₂	—	2	2	no	—
503	C₂	—	2	2	no	—
504	C₂	—	2	1	no	—
505	C₂	—	2	2	no	—
506	C₂	—	2	1	no	—
507	C₂	—	2	1	no	—
508	C₂	C₁₉×#1441	1	1	yes	characteristic
509	C₂	C₁₉×#1889	1	1	yes	characteristic
510	C₂	C₁₉×#1890	1	1	yes	characteristic
511	C₂	C₁₉×#2044	1	2	yes	—
512	C₂	C₁₉×#2062	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₁₉×#385	C₄	semidirect
127. C₂²⋊C₄×C₁₉	C₄⋊C₄	semidirect
128. #11222	C₁₉	direct (N × H)
257. #385	C₄×C₁₉	semidirect
319. C₁₉	#11222	direct (N × H)
384. C₂²⋊C₄	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2315	2
C₂×C₁₉×#385	2
C₂×C₁₉×#342	2
C₁₉×C₂²⋊#95	2
#11222	19

Subgroups — C19×#11222 #18017181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11222 #18017181