Subgroups — C₁₉×#10715 #18016674

Order 4864.

1534 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#336	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₉	—	2	2	no	—
7	C₂²×M₁₆×C₁₉	—	2	2	no	—
8	C₂²×M₁₆×C₁₉	—	2	8	no	—
9	C₂²×M₁₆×C₁₉	C₄	1	4	yes	complemented
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
13	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
15	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
16	C₂×C₁₉×C₂²⋊C₈	C₄	1	4	yes	complemented
17	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
18	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₁₉×#95	C₄	1	2	yes	—
20	C₁₉×#336	—	2	8	no	—
21	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	4	no	—
23	C₂³×C₄×C₁₉	—	2	4	no	—
24	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₉	D₄	1	2	yes	—
29	C₂³×C₄×C₁₉	D₄	1	2	yes	—
30	C₂³×C₄×C₁₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₉	—	2	16	no	—
34	C₂×M₁₆×C₁₉	—	2	16	no	—
35	C₂×M₁₆×C₁₉	—	2	8	no	—
36	C₂×M₁₆×C₁₉	—	2	16	no	—
37	C₂²×C₈×C₁₉	—	2	2	no	—
38	C₂²×C₈×C₁₉	—	2	2	no	—
39	C₂²×C₈×C₁₉	—	2	4	no	—
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	—	2	4	no	—
43	C₂²×C₈×C₁₉	—	2	4	no	—
44	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₁₉	D₄	1	8	yes	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
49	C₂×C₄²×C₁₉	—	2	2	no	—
50	C₂×C₄²×C₁₉	—	2	2	no	—
51	C₂×C₄²×C₁₉	—	2	4	no	—
52	C₂×C₄²×C₁₉	—	2	4	no	—
53	C₁₉×C₂²⋊C₈	—	2	8	no	—
54	C₁₉×#95	—	2	4	no	—
55	C₂⁴×C₁₉	—	2	4	no	—
56	C₂⁴×C₁₉	—	2	4	no	—
57	C₂⁴×C₁₉	—	2	4	no	—
58	C₂⁴×C₁₉	C₄²	1	2	yes	—
59	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
61	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	—	2	4	no	—
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	2	8	no	—
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	2	4	no	—
68	C₂²×C₄×C₁₉	—	2	8	no	—
69	C₂²×C₄×C₁₉	—	2	8	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	8	no	—
74	C₂²×C₄×C₁₉	—	2	4	no	—
75	C₂²×C₄×C₁₉	—	2	8	no	—
76	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
80	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₁₉	M₁₆	1	8	yes	complemented
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	4	yes	—
92	M₁₆×C₁₉	—	2	32	no	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₂×C₈×C₁₉	—	2	4	no	—
95	C₂×C₈×C₁₉	—	2	8	no	—
96	C₂×C₈×C₁₉	—	2	8	no	—
97	C₂×C₈×C₁₉	—	2	4	no	—
98	C₂×C₈×C₁₉	—	2	8	no	—
99	C₂×C₈×C₁₉	—	4	2	no	—
100	C₂×C₈×C₁₉	—	4	4	no	—
101	C₂×C₈×C₁₉	—	4	2	no	—
102	C₂×C₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
103	C₂²⋊C₄×C₁₉	—	2	16	no	—
104	C₄²×C₁₉	—	4	2	no	—
105	C₄²×C₁₉	—	4	4	no	—
106	C₄²×C₁₉	—	4	2	no	—
107	#10715	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₁₉	—	2	4	no	—
109	C₂³×C₁₉	—	2	4	no	—
110	C₂³×C₁₉	—	2	4	no	—
111	C₂³×C₁₉	—	2	4	no	—
112	C₂³×C₁₉	—	2	4	no	—
113	C₂³×C₁₉	—	2	4	no	—
114	C₂³×C₁₉	—	2	4	no	—
115	C₂³×C₁₉	—	2	4	no	—
116	C₂³×C₁₉	—	2	4	no	—
117	C₂³×C₁₉	—	4	8	no	—
118	C₂³×C₁₉	—	4	8	no	—
119	C₂³×C₁₉	#95	1	4	yes	—
120	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
121	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂³×C₁₉	C₄×D₄	1	4	yes	—
124	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
125	C₂³×C₁₉	#131	1	4	yes	—
126	C₂×C₄×C₁₉	—	2	4	no	—
127	C₂×C₄×C₁₉	—	2	4	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	8	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	8	no	—
133	C₂×C₄×C₁₉	—	2	8	no	—
134	C₂×C₄×C₁₉	—	2	8	no	—
135	C₂×C₄×C₁₉	—	2	16	no	—
136	C₂×C₄×C₁₉	—	4	4	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	8	no	—
139	C₂×C₄×C₁₉	#95	1	4	yes	—
140	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#117	1	2	yes	—
146	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
147	C₂×C₄×C₁₉	#120	1	2	yes	—
148	C₂×C₄×C₁₉	#120	1	2	yes	—
149	C₂×C₄×C₁₉	#121	1	4	yes	—
150	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₁₉	#123	1	2	yes	—
152	C₂×C₄×C₁₉	#123	1	2	yes	—
153	C₈×C₁₉	—	2	8	no	—
154	C₈×C₁₉	—	4	4	no	—
155	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic
156	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
157	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
158	C₂×#336	C₂×C₁₉	1	4	yes	complemented
159	C₂²×C₁₉	—	2	4	no	—
160	C₂²×C₁₉	—	2	4	no	—
161	C₂²×C₁₉	—	2	4	no	—
162	C₂²×C₁₉	—	4	8	no	—
163	C₂²×C₁₉	—	4	8	no	—
164	C₂²×C₁₉	—	4	8	no	—
165	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
166	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
167	C₂²×C₁₉	#385	1	2	yes	—
168	C₂²×C₁₉	#386	1	2	yes	—
169	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
170	C₂²×C₁₉	#405	1	2	yes	—
171	C₂²×C₁₉	#407	1	2	yes	—
172	C₂²×C₁₉	#408	1	2	yes	—
173	C₂²×C₁₉	#423	1	2	yes	—
174	C₂²×C₁₉	#424	1	2	yes	—
175	C₂²×C₁₉	#435	1	8	yes	—
176	C₂²×C₁₉	#436	1	8	yes	—
177	C₄×C₁₉	—	2	4	no	—
178	C₄×C₁₉	—	4	8	no	—
179	C₄×C₁₉	#379	1	1	yes	characteristic
180	C₄×C₁₉	#380	1	2	yes	—
181	C₄×C₁₉	#381	1	1	yes	characteristic
182	C₄×C₁₉	#385	1	2	yes	—
183	C₄×C₁₉	#386	1	2	yes	—
184	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
185	C₂²×M₁₆	—	2	2	no	—
186	C₂²×M₁₆	—	2	2	no	—
187	C₂²×M₁₆	—	2	8	no	—
188	C₂²×M₁₆	C₄×C₁₉	1	4	yes	complemented
189	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
190	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
191	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
192	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
193	C₂×C₂²⋊C₈	—	2	2	no	—
194	C₂×C₂²⋊C₈	—	2	2	no	—
195	C₂×C₂²⋊C₈	C₄×C₁₉	1	4	yes	complemented
196	C₄×C₂²⋊C₄	—	2	2	no	—
197	C₄×C₂²⋊C₄	—	2	2	no	—
198	C₂×#95	C₄×C₁₉	1	2	yes	—
199	#336	—	2	8	no	—
200	C₂×C₁₉	—	4	4	no	—
201	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
202	C₂×C₁₉	#1728	1	1	yes	characteristic
203	C₂×C₁₉	#1729	1	1	yes	characteristic
204	C₂×C₁₉	#1753	1	4	yes	—
205	C₂×C₁₉	#1851	1	4	yes	—
206	C₂×C₁₉	#1870	1	4	yes	—
207	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
211	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
212	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
213	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
214	C₂³×C₄	D₄×C₁₉	1	2	yes	—
215	C₂³×C₄	D₄×C₁₉	1	2	yes	—
216	C₂³×C₄	D₄×C₁₉	1	2	yes	—
217	C₂³×C₄	Q₈×C₁₉	1	2	yes	—
218	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
219	C₂×M₁₆	—	2	16	no	—
220	C₂×M₁₆	—	2	16	no	—
221	C₂×M₁₆	—	2	8	no	—
222	C₂×M₁₆	—	2	16	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
231	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
232	C₂²×C₈	D₄×C₁₉	1	8	yes	—
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₂²⋊C₄	—	2	8	no	—
235	C₂×C₄²	—	2	4	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂²⋊C₈	—	2	8	no	—
240	#95	—	2	4	no	—
241	C₁₉	#10715	1	1	yes	characteristic, direct product factor, Sylow
242	C₂⁴	—	2	4	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	C₄²×C₁₉	1	2	yes	—
246	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
247	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	—
248	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	C₄²×C₁₉	1	2	yes	—
264	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
265	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
266	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
267	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
268	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
269	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
270	C₂²×C₄	M₁₆×C₁₉	1	8	yes	complemented
271	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
277	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
278	C₂²×C₄	#41×C₁₉	1	4	yes	—
279	M₁₆	—	2	32	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	8	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
290	C₂²⋊C₄	—	2	16	no	—
291	C₄²	—	4	2	no	—
292	C₄²	—	4	4	no	—
293	C₄²	—	4	2	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	8	no	—
305	C₂³	C₁₉×#95	1	4	yes	—
306	C₂³	C₂×C₄²×C₁₉	1	1	yes	characteristic
307	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
309	C₂³	C₄×D₄×C₁₉	1	4	yes	—
310	C₂³	C₂×M₁₆×C₁₉	1	4	yes	—
311	C₂³	C₁₉×#131	1	4	yes	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	C₁₉×#95	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
328	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
331	C₂×C₄	C₁₉×#117	1	2	yes	—
332	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
333	C₂×C₄	C₁₉×#120	1	2	yes	—
334	C₂×C₄	C₁₉×#120	1	2	yes	—
335	C₂×C₄	C₁₉×#121	1	4	yes	—
336	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
337	C₂×C₄	C₁₉×#123	1	2	yes	—
338	C₂×C₄	C₁₉×#123	1	2	yes	—
339	C₈	—	2	8	no	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	4	8	no	—
345	C₂²	—	4	8	no	—
346	C₂²	—	4	8	no	—
347	C₂²	C₂×C₁₉×#95	1	1	yes	characteristic
348	C₂²	C₄×C₂²⋊C₄×C₁₉	1	2	yes	—
349	C₂²	C₁₉×#385	1	2	yes	—
350	C₂²	C₁₉×#386	1	2	yes	—
351	C₂²	C₄×M₁₆×C₁₉	1	2	yes	—
352	C₂²	C₁₉×#405	1	2	yes	—
353	C₂²	C₁₉×#407	1	2	yes	—
354	C₂²	C₁₉×#408	1	2	yes	—
355	C₂²	C₁₉×#423	1	2	yes	—
356	C₂²	C₁₉×#424	1	2	yes	—
357	C₂²	C₁₉×#435	1	8	yes	—
358	C₂²	C₁₉×#436	1	8	yes	—
359	C₄	—	2	4	no	—
360	C₄	—	4	8	no	—
361	C₄	C₁₉×#379	1	1	yes	characteristic
362	C₄	C₁₉×#380	1	2	yes	—
363	C₄	C₁₉×#381	1	1	yes	characteristic
364	C₄	C₁₉×#385	1	2	yes	—
365	C₄	C₁₉×#386	1	2	yes	—
366	C₂	—	4	4	no	—
367	C₂	C₁₉×C₂²⋊#95	1	1	yes	characteristic
368	C₂	C₁₉×#1728	1	1	yes	characteristic
369	C₂	C₁₉×#1729	1	1	yes	characteristic
370	C₂	C₁₉×#1753	1	4	yes	—
371	C₂	C₁₉×#1851	1	4	yes	—
372	C₂	C₁₉×#1870	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₉	C₂³
commutator	C₂³	C₂×C₄²×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂⁴×C₁₉	C₂²×C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#336	C₂	semidirect
9. C₂²×M₁₆×C₁₉	C₄	semidirect
16. C₂×C₁₉×C₂²⋊C₈	C₄	semidirect
83. C₂²×C₄×C₁₉	M₁₆	semidirect
102. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
107. #10715	C₁₉	direct (N × H)
158. C₂×#336	C₂×C₁₉	semidirect
188. C₂²×M₁₆	C₄×C₁₉	semidirect
195. C₂×C₂²⋊C₈	C₄×C₁₉	semidirect
241. C₁₉	#10715	direct (N × H)
270. C₂²×C₄	M₁₆×C₁₉	semidirect
289. C₂×C₈	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₉	2
C₂²×C₁₉×C₂²⋊C₈	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#336	2
#10715	19

Subgroups — C19×#10715 #18016674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10715 #18016674