Subgroups — C₁₉×#22483 #18028442

Order 4864.

1126 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#555	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1997	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1900	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1822	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₉×#100	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×#555	—	2	2	no	—
11	C₁₉×#555	—	2	4	no	—
12	C₁₉×#555	—	2	2	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	C₄	1	4	yes	—
15	C₂×C₁₉×#121	C₄	1	2	yes	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₄	1	2	yes	—
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×#100	C₂²	1	2	yes	—
26	C₂×C₁₉×#100	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×D₄×C₁₉	C₂×C₄	1	4	yes	—
36	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂×M₁₆×C₁₉	—	2	4	no	—
41	C₂×M₁₆×C₁₉	—	2	8	no	—
42	C₂×M₁₆×C₁₉	—	4	4	no	—
43	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
44	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
45	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	—	2	4	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×#124	—	2	8	no	—
50	C₁₉×#124	—	2	8	no	—
51	C₁₉×#121	—	2	4	no	—
52	C₁₉×#121	—	2	4	no	—
53	C₁₉×#121	—	2	4	no	—
54	C₁₉×#121	—	2	4	no	—
55	C₄×D₄×C₁₉	—	2	2	no	—
56	C₄×D₄×C₁₉	—	2	2	no	—
57	C₄×D₄×C₁₉	D₄	1	2	yes	—
58	C₄×D₄×C₁₉	D₄	1	4	yes	—
59	C₄×D₄×C₁₉	D₄	1	2	yes	—
60	C₁₉×#117	—	2	4	no	—
61	C₁₉×#117	—	2	4	no	—
62	C₁₉×#117	—	2	4	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	—	2	2	no	—
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×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₉	C₂×C₄	1	4	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×#100	—	2	4	no	—
78	C₁₉×#100	—	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	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂×Q₈×C₁₉	—	2	4	no	—
86	C₂×Q₈×C₁₉	—	8	2	no	—
87	C₂×D₄×C₁₉	—	2	8	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	8	4	no	—
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	2	4	no	—
112	M₁₆×C₁₉	—	2	2	no	—
113	M₁₆×C₁₉	—	2	4	no	—
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	4	8	no	—
116	M₁₆×C₁₉	#41	1	4	yes	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	4	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	4	8	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
126	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₁₉	—	2	8	no	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
133	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
134	C₄²×C₁₉	—	2	4	no	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	C₂×D₄	1	2	yes	—
137	C₄²×C₁₉	C₂×D₄	1	2	yes	—
138	#22483	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
150	Q₈×C₁₉	—	8	4	no	—
151	D₄×C₁₉	—	2	4	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	8	8	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	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
177	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
179	C₈×C₁₉	—	2	4	no	—
180	C₈×C₁₉	—	4	4	no	—
181	C₈×C₁₉	—	4	2	no	—
182	C₂×#555	C₂×C₁₉	1	1	yes	characteristic
183	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
184	#1997	C₂×C₁₉	1	2	yes	complemented
185	#1900	C₂×C₁₉	1	4	yes	complemented
186	#1822	C₂×C₁₉	1	2	yes	complemented
187	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1742	C₂×C₁₉	1	2	yes	complemented
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	4	no	—
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	4	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	8	2	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
204	C₂²×C₁₉	#520	1	1	yes	characteristic
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	4	no	—
211	C₄×C₁₉	#413	1	2	yes	—
212	C₄×C₁₉	#546	1	2	yes	—
213	C₄×C₁₉	#547	1	2	yes	—
214	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
215	#555	—	2	2	no	—
216	#555	—	2	4	no	—
217	#555	—	2	2	no	—
218	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×#124	C₄×C₁₉	1	4	yes	—
220	C₂×#121	C₄×C₁₉	1	2	yes	—
221	C₂×#121	C₂²×C₁₉	1	2	yes	—
222	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#117	C₄×C₁₉	1	2	yes	—
225	C₂×#117	C₂²×C₁₉	1	2	yes	—
226	#436	—	2	2	no	—
227	#435	—	2	4	no	—
228	C₈×D₄	—	2	2	no	—
229	#423	C₂²×C₁₉	1	2	yes	—
230	C₂×#100	C₂²×C₁₉	1	2	yes	—
231	C₂×#100	C₂²×C₁₉	1	2	yes	—
232	#407	C₂²×C₁₉	1	4	yes	—
233	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
234	#343	C₂²×C₁₉	1	2	yes	—
235	#343	C₂²×C₁₉	1	1	yes	characteristic
236	#343	C₂²×C₁₉	1	4	yes	—
237	#343	C₂²×C₁₉	1	4	yes	—
238	#343	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	4	4	no	—
242	C₂×C₁₉	—	8	2	no	—
243	C₂×C₁₉	#2339	1	1	yes	characteristic
244	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
245	C₂×C₁₉	#2888	1	1	yes	characteristic
246	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
247	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
248	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
251	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	8	no	—
254	C₂×M₁₆	—	4	4	no	—
255	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
256	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
257	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
258	C₂²×C₈	—	2	4	no	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	#124	—	2	8	no	—
262	#124	—	2	8	no	—
263	#121	—	2	4	no	—
264	#121	—	2	4	no	—
265	#121	—	2	4	no	—
266	#121	—	2	4	no	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	D₄×C₁₉	1	2	yes	—
270	C₄×D₄	D₄×C₁₉	1	4	yes	—
271	C₄×D₄	D₄×C₁₉	1	2	yes	—
272	#117	—	2	4	no	—
273	#117	—	2	4	no	—
274	#117	—	2	4	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
282	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
285	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
286	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	#100	—	2	4	no	—
290	#100	—	4	2	no	—
291	C₂²⋊C₈	—	2	4	no	—
292	C₂²⋊C₈	—	2	4	no	—
293	#97	—	2	2	no	—
294	C₄×C₈	—	2	2	no	—
295	C₁₉	#22483	1	1	yes	characteristic, direct product factor, Sylow
296	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
297	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	8	2	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	8	4	no	—
307	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
308	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
319	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	8	no	—
329	M₁₆	#41×C₁₉	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	4	8	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
339	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
340	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
346	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	4	no	—
349	C₄²	C₂×D₄×C₁₉	1	2	yes	—
350	C₄²	C₂×D₄×C₁₉	1	2	yes	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
361	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
362	Q₈	—	8	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	8	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
388	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
389	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	4	4	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
407	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
408	C₂²	C₁₉×#520	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	4	no	—
415	C₄	C₁₉×#413	1	2	yes	—
416	C₄	C₁₉×#546	1	2	yes	—
417	C₄	C₁₉×#547	1	2	yes	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	4	4	no	—
421	C₂	—	8	2	no	—
422	C₂	C₁₉×#2339	1	1	yes	characteristic
423	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
424	C₂	C₁₉×#2888	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	C₂×C₁₉×#555	C₂
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
2. D₄×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#1997	C₂	semidirect
4. C₁₉×#1900	C₂	semidirect
5. C₁₉×#1822	C₂	semidirect
6. C₁₉×#1800	C₂	semidirect
7. C₄×C₁₉×#100	C₂	semidirect
8. C₁₉×#1742	C₂	semidirect
138. #22483	C₁₉	direct (N × H)
183. D₄×M₁₆	C₂×C₁₉	semidirect
184. #1997	C₂×C₁₉	semidirect
185. #1900	C₂×C₁₉	semidirect
186. #1822	C₂×C₁₉	semidirect
187. #1800	C₂×C₁₉	semidirect
188. C₄×#100	C₂×C₁₉	semidirect
189. #1742	C₂×C₁₉	semidirect
295. C₁₉	#22483	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×#555	2
D₄×M₁₆×C₁₉	2
C₁₉×#1997	2
C₁₉×#1900	2
C₁₉×#1822	2
C₁₉×#1800	2
C₄×C₁₉×#100	2
C₁₉×#1742	2
#22483	19

Subgroups — C19×#22483 #18028442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22483 #18028442