Subgroups — C₁₉×#22484 #18028443

Order 4864.

1062 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#556	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal
3	C₁₉×#1997	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1901	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1822	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1742	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
10	C₁₉×#556	—	2	2	no	—
11	C₁₉×#556	—	2	4	no	—
12	C₁₉×#556	—	2	2	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#126	C₄	1	4	yes	—
15	C₂×C₁₉×#124	C₄	1	2	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₁₉×#436	—	2	2	no	—
22	C₁₉×#435	—	2	4	no	—
23	C₈×D₄×C₁₉	—	2	2	no	—
24	C₁₉×#423	C₂²	1	2	yes	—
25	C₂×C₁₉×#101	C₂²	1	2	yes	—
26	C₂×C₁₉×#101	C₂²	1	2	yes	—
27	C₁₉×#407	C₂²	1	4	yes	—
28	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#343	C₂²	1	4	yes	—
30	C₁₉×#343	C₂²	1	4	yes	—
31	C₁₉×#343	C₂²	1	1	yes	characteristic
32	C₁₉×#343	C₂²	1	2	yes	—
33	C₁₉×#343	C₂²	1	1	yes	characteristic
34	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂×M₁₆×C₁₉	—	2	4	no	—
39	C₂×M₁₆×C₁₉	—	2	8	no	—
40	C₂×M₁₆×C₁₉	—	4	4	no	—
41	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
42	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
43	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₉	—	2	4	no	—
45	C₁₉×C₄⋊Q₈	—	2	2	no	—
46	C₁₉×C₄⋊Q₈	—	2	2	no	—
47	C₁₉×#126	—	2	8	no	—
48	C₁₉×#126	—	2	8	no	—
49	C₁₉×#124	—	2	4	no	—
50	C₁₉×#124	—	2	4	no	—
51	C₁₉×C₂²⋊Q₈	—	2	4	no	—
52	C₁₉×C₂²⋊Q₈	—	2	4	no	—
53	C₄×Q₈×C₁₉	—	2	4	no	—
54	C₄×Q₈×C₁₉	—	2	2	no	—
55	C₄×Q₈×C₁₉	—	2	2	no	—
56	C₄×Q₈×C₁₉	—	2	2	no	—
57	C₄×Q₈×C₁₉	—	2	2	no	—
58	C₄×D₄×C₁₉	D₄	1	2	yes	—
59	C₄×D₄×C₁₉	D₄	1	4	yes	—
60	C₄×D₄×C₁₉	D₄	1	2	yes	—
61	C₁₉×#117	—	2	4	no	—
62	C₁₉×#117	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
70	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
73	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊C₈	—	2	2	no	—
76	C₁₉×C₄⋊C₈	—	2	2	no	—
77	C₁₉×#101	—	2	4	no	—
78	C₁₉×#101	—	4	2	no	—
79	C₁₉×C₂²⋊C₈	—	2	4	no	—
80	C₁₉×C₂²⋊C₈	—	2	4	no	—
81	C₁₉×#97	—	2	2	no	—
82	C₄×C₈×C₁₉	—	2	2	no	—
83	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	4	4	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₁₉	—	2	2	no	—
107	M₁₆×C₁₉	—	2	4	no	—
108	M₁₆×C₁₉	—	2	2	no	—
109	M₁₆×C₁₉	—	2	4	no	—
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	4	8	no	—
112	M₁₆×C₁₉	#41	1	4	yes	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	4	8	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²⋊C₄×C₁₉	—	2	8	no	—
127	C₂²⋊C₄×C₁₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
129	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
130	C₄²×C₁₉	—	2	4	no	—
131	C₄²×C₁₉	—	2	4	no	—
132	C₄²×C₁₉	—	2	2	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	C₂×D₄	1	2	yes	—
135	C₄²×C₁₉	C₂×D₄	1	2	yes	—
136	#22484	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
143	Q₈×C₁₉	—	4	4	no	—
144	Q₈×C₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	4	2	no	—
146	Q₈×C₁₉	—	4	4	no	—
147	D₄×C₁₉	—	2	4	no	—
148	D₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₁₉	—	2	4	no	—
174	C₈×C₁₉	—	4	4	no	—
175	C₈×C₁₉	—	4	2	no	—
176	C₂×#556	C₂×C₁₉	1	1	yes	characteristic
177	D₄×M₁₆	C₂×C₁₉	1	2	yes	—
178	#1997	C₂×C₁₉	1	2	yes	complemented
179	#1901	C₂×C₁₉	1	4	yes	complemented
180	#1822	C₂×C₁₉	1	2	yes	complemented
181	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1742	C₂×C₁₉	1	2	yes	complemented
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	4	no	—
187	C₂²×C₁₉	—	2	4	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	8	2	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
193	C₂²×C₁₉	#520	1	1	yes	characteristic
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	4	4	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	#413	1	2	yes	—
202	C₄×C₁₉	#546	1	2	yes	—
203	C₄×C₁₉	#547	1	2	yes	—
204	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
205	#556	—	2	2	no	—
206	#556	—	2	4	no	—
207	#556	—	2	2	no	—
208	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×#126	C₄×C₁₉	1	4	yes	—
210	C₂×#124	C₄×C₁₉	1	2	yes	—
211	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
212	C₂×C₄×Q₈	C₄×C₁₉	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×#117	C₂²×C₁₉	1	2	yes	—
216	#436	—	2	2	no	—
217	#435	—	2	4	no	—
218	C₈×D₄	—	2	2	no	—
219	#423	C₂²×C₁₉	1	2	yes	—
220	C₂×#101	C₂²×C₁₉	1	2	yes	—
221	C₂×#101	C₂²×C₁₉	1	2	yes	—
222	#407	C₂²×C₁₉	1	4	yes	—
223	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
224	#343	C₂²×C₁₉	1	2	yes	—
225	#343	C₂²×C₁₉	1	1	yes	characteristic
226	#343	C₂²×C₁₉	1	4	yes	—
227	#343	C₂²×C₁₉	1	4	yes	—
228	#343	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₁₉	—	2	1	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	—	4	4	no	—
232	C₂×C₁₉	#2339	1	1	yes	characteristic
233	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
234	C₂×C₁₉	#2889	1	1	yes	characteristic
235	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
236	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
237	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	—	4	4	no	—
242	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
243	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
244	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
245	C₂²×C₈	—	2	4	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	2	2	no	—
248	#126	—	2	8	no	—
249	#126	—	2	8	no	—
250	#124	—	2	4	no	—
251	#124	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×D₄	D₄×C₁₉	1	2	yes	—
260	C₄×D₄	D₄×C₁₉	1	4	yes	—
261	C₄×D₄	D₄×C₁₉	1	2	yes	—
262	#117	—	2	4	no	—
263	#117	—	2	4	no	—
264	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
271	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
272	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
273	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
274	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
275	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	#101	—	2	4	no	—
279	#101	—	4	2	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₁₉	#22484	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
295	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
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	4	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
306	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	4	8	no	—
314	M₁₆	#41×C₁₉	1	4	yes	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	4	8	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
326	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
327	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
328	C₂²⋊C₄	—	2	8	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
331	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	C₂×D₄×C₁₉	1	2	yes	—
337	C₄²	C₂×D₄×C₁₉	1	2	yes	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
343	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
344	Q₈	—	4	4	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
371	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
372	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	4	4	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
386	C₂²	C₁₉×#520	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	4	2	no	—
394	C₄	C₁₉×#413	1	2	yes	—
395	C₄	C₁₉×#546	1	2	yes	—
396	C₄	C₁₉×#547	1	2	yes	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	4	4	no	—
400	C₂	C₁₉×#2339	1	1	yes	characteristic
401	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
402	C₂	C₁₉×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1997	C₂	semidirect
4. C₁₉×#1901	C₂	semidirect
5. C₁₉×#1822	C₂	semidirect
6. C₁₉×#1801	C₂	semidirect
7. C₄×C₁₉×#101	C₂	semidirect
8. C₁₉×#1742	C₂	semidirect
136. #22484	C₁₉	direct (N × H)
178. #1997	C₂×C₁₉	semidirect
179. #1901	C₂×C₁₉	semidirect
180. #1822	C₂×C₁₉	semidirect
181. #1801	C₂×C₁₉	semidirect
182. C₄×#101	C₂×C₁₉	semidirect
183. #1742	C₂×C₁₉	semidirect
284. C₁₉	#22484	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#556	2
D₄×M₁₆×C₁₉	2
C₁₉×#1997	2
C₁₉×#1901	2
C₁₉×#1822	2
C₁₉×#1801	2
C₄×C₁₉×#101	2
C₁₉×#1742	2
#22484	19

Subgroups — C19×#22484 #18028443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22484 #18028443