Subgroups — C₁₉×#17372 #18023331

Order 4864.

1174 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2983	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1466	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1464	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1460	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1458	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₄	1	1	yes	characteristic
8	C₁₉×#520	—	2	8	no	—
9	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
12	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
19	C₁₉×#446	—	2	8	no	—
20	C₁₉×#432	C₂²	1	8	yes	—
21	C₁₉×#431	C₂²	1	4	yes	—
22	C₁₉×#324	C₂²	1	4	yes	—
23	C₁₉×#323	C₂²	1	4	yes	—
24	C₁₉×#323	C₂²	1	8	yes	—
25	C₂×#41×C₁₉	—	2	4	no	—
26	C₂×#41×C₁₉	—	2	4	no	—
27	C₂×#41×C₁₉	—	2	4	no	—
28	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₄×Q₈×C₁₉	—	2	4	no	—
37	C₄×Q₈×C₁₉	D₄	1	8	yes	—
38	C₄×D₄×C₁₉	—	2	8	no	—
39	C₄×D₄×C₁₉	—	2	4	no	—
40	C₄×D₄×C₁₉	—	2	4	no	—
41	C₄×D₄×C₁₉	—	2	8	no	—
42	C₁₉×#117	—	2	4	no	—
43	C₁₉×#117	—	2	8	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
61	C₁₉×C₄⋊C₈	—	2	4	no	—
62	C₁₉×C₄⋊C₈	—	2	8	no	—
63	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
64	C₁₉×#97	—	2	8	no	—
65	C₄×C₈×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
67	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	#41×C₁₉	—	2	32	no	—
69	C₂×Q₈×C₁₉	—	2	2	no	—
70	C₂×Q₈×C₁₉	—	2	2	no	—
71	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	2	4	no	—
74	C₂×D₄×C₁₉	—	2	4	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	M₁₆	1	4	yes	—
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	8	2	no	—
87	C₂²×C₄×C₁₉	—	8	2	no	—
88	C₂²×C₄×C₁₉	—	8	2	no	—
89	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₉	—	2	8	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
106	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
107	C₂²⋊C₄×C₁₉	—	2	2	no	—
108	C₂²⋊C₄×C₁₉	—	2	4	no	—
109	C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂²⋊C₄×C₁₉	—	2	4	no	—
111	C₄²×C₁₉	—	2	4	no	—
112	C₄²×C₁₉	—	2	2	no	—
113	C₄²×C₁₉	C₂×D₄	1	4	yes	—
114	C₄²×C₁₉	C₂×D₄	1	8	yes	—
115	#17372	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	1	no	—
122	C₂³×C₁₉	—	4	2	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
125	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
126	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
127	Q₈×C₁₉	—	2	8	no	—
128	D₄×C₁₉	—	2	16	no	—
129	D₄×C₁₉	—	2	8	no	—
130	C₂×C₄×C₁₉	—	2	16	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	8	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	8	4	no	—
146	C₂×C₄×C₁₉	—	8	4	no	—
147	C₂×C₄×C₁₉	—	8	4	no	—
148	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
151	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
153	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
154	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
156	C₈×C₁₉	—	4	8	no	—
157	C₂×#520	C₂×C₁₉	1	1	yes	characteristic
158	#2983	C₂×C₁₉	1	2	yes	complemented
159	#1466	C₂×C₁₉	1	4	yes	complemented
160	#1464	C₂×C₁₉	1	4	yes	complemented
161	#1460	C₂×C₁₉	1	2	yes	complemented
162	#1458	C₂×C₁₉	1	2	yes	complemented
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	4	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	4	4	no	—
168	C₂²×C₁₉	—	4	2	no	—
169	C₂²×C₁₉	—	4	2	no	—
170	C₂²×C₁₉	—	4	4	no	—
171	C₂²×C₁₉	—	4	2	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
177	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
178	C₄×C₁₉	—	2	2	no	—
179	C₄×C₁₉	—	2	4	no	—
180	C₄×C₁₉	—	2	2	no	—
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	4	no	—
183	C₄×C₁₉	—	4	1	no	—
184	C₄×C₁₉	—	4	2	no	—
185	C₄×C₁₉	—	4	1	no	—
186	C₄×C₁₉	#407	1	4	yes	—
187	C₂²×#41	C₄×C₁₉	1	1	yes	characteristic
188	#520	—	2	8	no	—
189	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
191	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
192	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
193	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
195	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#117	C₂²×C₁₉	1	2	yes	—
197	C₂²×C₄⋊C₄	C₄×C₁₉	1	2	yes	—
198	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
199	#446	—	2	8	no	—
200	#432	C₂²×C₁₉	1	8	yes	—
201	#431	C₂²×C₁₉	1	4	yes	—
202	#324	C₂²×C₁₉	1	4	yes	—
203	#323	C₂²×C₁₉	1	4	yes	—
204	#323	C₂²×C₁₉	1	8	yes	—
205	C₂×C₁₉	—	2	1	no	—
206	C₂×C₁₉	—	2	1	no	—
207	C₂×C₁₉	—	4	4	no	—
208	C₂×C₁₉	—	4	2	no	—
209	C₂×C₁₉	C₂×#407	1	1	yes	characteristic
210	C₂×C₁₉	#2884	1	1	yes	characteristic
211	C₂×C₁₉	#2888	1	1	yes	characteristic
212	C₂×#41	—	2	4	no	—
213	C₂×#41	—	2	4	no	—
214	C₂×#41	—	2	4	no	—
215	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
216	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
217	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
219	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
220	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
221	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
222	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
223	C₄×Q₈	—	2	4	no	—
224	C₄×Q₈	D₄×C₁₉	1	8	yes	—
225	C₄×D₄	—	2	8	no	—
226	C₄×D₄	—	2	4	no	—
227	C₄×D₄	—	2	4	no	—
228	C₄×D₄	—	2	8	no	—
229	#117	—	2	4	no	—
230	#117	—	2	8	no	—
231	C₂×C₄⋊C₄	—	2	8	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
244	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
245	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
248	C₄⋊C₈	—	2	4	no	—
249	C₄⋊C₈	—	2	8	no	—
250	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
251	#97	—	2	8	no	—
252	C₄×C₈	—	2	4	no	—
253	C₁₉	#17372	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
255	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
256	#41	—	2	32	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	M₁₆×C₁₉	1	4	yes	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	8	2	no	—
275	C₂²×C₄	—	8	2	no	—
276	C₂²×C₄	—	8	2	no	—
277	C₂²×C₄	M₁₆×C₁₉	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
287	C₂×C₈	—	2	8	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
294	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	2	no	—
301	C₄²	C₂×D₄×C₁₉	1	4	yes	—
302	C₄²	C₂×D₄×C₁₉	1	8	yes	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₂×M₁₆×C₁₉	1	4	yes	—
312	C₂³	C₂×M₁₆×C₁₉	1	2	yes	—
313	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
314	Q₈	—	2	8	no	—
315	D₄	—	2	16	no	—
316	D₄	—	2	8	no	—
317	C₂×C₄	—	2	16	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	8	4	no	—
333	C₂×C₄	—	8	4	no	—
334	C₂×C₄	—	8	4	no	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
339	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
340	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
341	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
342	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
343	C₈	—	4	8	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
357	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
358	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	4	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	4	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	1	no	—
367	C₄	C₁₉×#407	1	4	yes	—
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	4	4	no	—
371	C₂	—	4	2	no	—
372	C₂	C₂×C₁₉×#407	1	1	yes	characteristic
373	C₂	C₁₉×#2884	1	1	yes	characteristic
374	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	C₂²×#41×C₁₉	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2983	C₂	semidirect
3. C₁₉×#1466	C₂	semidirect
4. C₁₉×#1464	C₂	semidirect
5. C₁₉×#1460	C₂	semidirect
6. C₁₉×#1458	C₂	semidirect
115. #17372	C₁₉	direct (N × H)
158. #2983	C₂×C₁₉	semidirect
159. #1466	C₂×C₁₉	semidirect
160. #1464	C₂×C₁₉	semidirect
161. #1460	C₂×C₁₉	semidirect
162. #1458	C₂×C₁₉	semidirect
253. C₁₉	#17372	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×#520	2
C₁₉×#2983	2
C₁₉×#1466	2
C₁₉×#1464	2
C₁₉×#1460	2
C₁₉×#1458	2
#17372	19

Subgroups — C19×#17372 #18023331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17372 #18023331