Subgroups — C₁₉×#20637 #18026596

Order 4864.

1442 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×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#423	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#413	C₂	1	2	yes	maximal
4	C₁₉×#1801	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1800	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1742	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
9	C₄×#41×C₁₉	—	2	4	no	—
10	C₄×#41×C₁₉	—	2	2	no	—
11	C₄×#41×C₁₉	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₉	C₄	1	4	yes	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#117	C₄	1	2	yes	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#423	—	2	2	no	—
20	C₁₉×#423	—	2	2	no	—
21	C₁₉×#423	C₂²	1	8	yes	—
22	C₂×C₁₉×C₄⋊C₈	—	2	4	no	—
23	C₁₉×#413	—	2	8	no	—
24	C₂×C₁₉×#101	C₂²	1	4	yes	—
25	C₂×C₁₉×#100	C₂²	1	4	yes	—
26	C₁₉×#343	C₂²	1	8	yes	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	4	no	—
30	C₂×#41×C₁₉	D₄	1	4	yes	—
31	C₂×#41×C₁₉	Q₈	1	4	yes	—
32	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₉	—	2	4	no	—
40	C₂×M₁₆×C₁₉	—	2	8	no	—
41	C₂×M₁₆×C₁₉	—	2	8	no	—
42	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
43	C₂²×C₈×C₁₉	—	2	4	no	—
44	C₄×Q₈×C₁₉	—	2	4	no	—
45	C₄×Q₈×C₁₉	—	2	4	no	—
46	C₄×D₄×C₁₉	—	2	8	no	—
47	C₄×D₄×C₁₉	—	2	8	no	—
48	C₄×D₄×C₁₉	—	2	4	no	—
49	C₄×D₄×C₁₉	—	2	4	no	—
50	C₁₉×#117	—	2	2	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₁₉×#117	—	2	4	no	—
53	C₁₉×#117	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₉	—	2	2	no	—
59	C₂×C₄²×C₁₉	—	2	2	no	—
60	C₂×C₄²×C₁₉	—	2	4	no	—
61	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	D₄	1	4	yes	—
66	C₂×C₄²×C₁₉	D₄	1	2	yes	—
67	C₂×C₄²×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
69	C₁₉×C₄⋊C₈	—	2	8	no	—
70	C₁₉×C₄⋊C₈	—	2	8	no	—
71	C₁₉×#101	—	2	8	no	—
72	C₁₉×#100	—	2	8	no	—
73	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	#41×C₁₉	—	2	8	no	—
76	#41×C₁₉	—	2	8	no	—
77	#41×C₁₉	—	2	8	no	—
78	#41×C₁₉	—	2	8	no	—
79	C₂×Q₈×C₁₉	—	2	2	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
82	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	C₄⋊C₄	1	8	yes	—
88	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
89	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	4	4	no	—
96	C₂²×C₄×C₁₉	—	4	8	no	—
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₉	#41	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₉	—	2	8	no	—
112	M₁₆×C₁₉	—	2	8	no	—
113	M₁₆×C₁₉	—	4	8	no	—
114	C₂×C₈×C₁₉	—	2	8	no	—
115	C₂×C₈×C₁₉	—	4	8	no	—
116	C₄⋊C₄×C₁₉	—	2	8	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₉	—	2	8	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	4	no	—
122	C₄²×C₁₉	—	2	4	no	—
123	C₄²×C₁₉	—	2	2	no	—
124	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₁₉	C₂×D₄	1	4	yes	—
130	C₄²×C₁₉	C₂×D₄	1	4	yes	—
131	#20637	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
138	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
139	C₂³×C₁₉	#117	1	2	yes	—
140	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	2	4	no	—
142	Q₈×C₁₉	—	2	4	no	—
143	D₄×C₁₉	—	2	16	no	—
144	D₄×C₁₉	—	2	4	no	—
145	D₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	8	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	8	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	4	4	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	8	no	—
156	C₂×C₄×C₁₉	—	4	8	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₉	#117	1	2	yes	—
166	C₂×C₄×C₁₉	#121	1	4	yes	—
167	C₂×C₄×C₁₉	#121	1	4	yes	—
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
169	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
174	C₈×C₁₉	—	4	8	no	—
175	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
176	C₂×#423	C₂×C₁₉	1	2	yes	complemented
177	C₂×#413	C₂×C₁₉	1	2	yes	—
178	#1801	C₂×C₁₉	1	4	yes	complemented
179	#1800	C₂×C₁₉	1	4	yes	complemented
180	#1742	C₂×C₁₉	1	2	yes	complemented
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	4	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	4	2	no	—
185	C₂²×C₁₉	—	4	2	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	#380	1	4	yes	—
190	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	4	no	—
195	C₄×C₁₉	—	2	4	no	—
196	C₄×C₁₉	—	4	4	no	—
197	C₄×C₁₉	#380	1	2	yes	—
198	C₄×C₁₉	#380	1	2	yes	—
199	C₄×C₁₉	#413	1	4	yes	complemented
200	C₄×C₁₉	C₂×#121	1	2	yes	—
201	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
202	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
203	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
204	C₄×#41	—	2	4	no	—
205	C₄×#41	—	2	2	no	—
206	C₄×#41	—	2	2	no	—
207	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
208	C₂×C₄×D₄	C₄×C₁₉	1	4	yes	—
209	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
210	C₂×#117	C₄×C₁₉	1	2	yes	—
211	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
212	C₂²×C₄²	C₄×C₁₉	1	2	yes	—
213	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
214	#423	—	2	2	no	—
215	#423	—	2	2	no	—
216	#423	C₂²×C₁₉	1	8	yes	—
217	C₂×C₄⋊C₈	—	2	4	no	—
218	#413	—	2	8	no	—
219	C₂×#101	C₂²×C₁₉	1	4	yes	—
220	C₂×#100	C₂²×C₁₉	1	4	yes	—
221	#343	C₂²×C₁₉	1	8	yes	—
222	C₂×C₁₉	—	2	1	no	—
223	C₂×C₁₉	—	2	1	no	—
224	C₂×C₁₉	—	2	4	no	—
225	C₂×C₁₉	—	4	4	no	—
226	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
227	C₂×C₁₉	C₂×#413	1	2	yes	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	D₄×C₁₉	1	4	yes	—
232	C₂×#41	Q₈×C₁₉	1	4	yes	—
233	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
234	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
235	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
237	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
238	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	—	2	8	no	—
242	C₂×M₁₆	—	2	8	no	—
243	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
244	C₂²×C₈	—	2	4	no	—
245	C₄×Q₈	—	2	4	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×D₄	—	2	8	no	—
248	C₄×D₄	—	2	8	no	—
249	C₄×D₄	—	2	4	no	—
250	C₄×D₄	—	2	4	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	4	no	—
254	#117	—	2	4	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
258	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	4	no	—
262	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
263	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
264	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₁₉	1	4	yes	—
267	C₂×C₄²	D₄×C₁₉	1	2	yes	—
268	C₂×C₄²	D₄×C₁₉	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
270	C₄⋊C₈	—	2	8	no	—
271	C₄⋊C₈	—	2	8	no	—
272	#101	—	2	8	no	—
273	#100	—	2	8	no	—
274	C₁₉	#20637	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
276	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
277	#41	—	2	8	no	—
278	#41	—	2	8	no	—
279	#41	—	2	8	no	—
280	#41	—	2	8	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
284	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₄⋊C₄×C₁₉	1	8	yes	—
290	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
291	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
301	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	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	4	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
311	C₂²×C₄	#41×C₁₉	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
313	M₁₆	—	2	8	no	—
314	M₁₆	—	2	8	no	—
315	M₁₆	—	4	8	no	—
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	—	4	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	8	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
327	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
328	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
329	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
330	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
331	C₄²	C₂×D₄×C₁₉	1	4	yes	—
332	C₄²	C₂×D₄×C₁₉	1	4	yes	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
338	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
339	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
340	C₂³	C₁₉×#117	1	2	yes	—
341	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	2	4	no	—
344	D₄	—	2	16	no	—
345	D₄	—	2	4	no	—
346	D₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
364	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
365	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
366	C₂×C₄	C₁₉×#117	1	2	yes	—
367	C₂×C₄	C₁₉×#121	1	4	yes	—
368	C₂×C₄	C₁₉×#121	1	4	yes	—
369	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
370	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
371	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
373	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
375	C₈	—	4	8	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	C₁₉×#380	1	4	yes	—
385	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
386	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
387	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
388	C₄	—	2	4	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	4	no	—
392	C₄	C₁₉×#380	1	2	yes	—
393	C₄	C₁₉×#380	1	2	yes	—
394	C₄	C₁₉×#413	1	4	yes	complemented
395	C₄	C₂×C₁₉×#121	1	2	yes	—
396	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	2	4	no	—
400	C₂	—	4	4	no	—
401	C₂	C₂×C₁₉×#380	1	1	yes	characteristic
402	C₂	C₂×C₁₉×#413	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#423	C₂	semidirect
4. C₁₉×#1801	C₂	semidirect
5. C₁₉×#1800	C₂	semidirect
6. C₁₉×#1742	C₂	semidirect
131. #20637	C₁₉	direct (N × H)
176. C₂×#423	C₂×C₁₉	semidirect
178. #1801	C₂×C₁₉	semidirect
179. #1800	C₂×C₁₉	semidirect
180. #1742	C₂×C₁₉	semidirect
199. C₄×C₁₉	#413	semidirect
274. C₁₉	#20637	direct (N × H)
394. C₄	C₁₉×#413	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₂×C₁₉×#423	2
C₂×C₁₉×#413	2
C₁₉×#1801	2
C₁₉×#1800	2
C₁₉×#1742	2
#20637	19

Subgroups — C19×#20637 #18026596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20637 #18026596