Subgroups — C₂×C₁₉×#1729 #18026293

Order 4864.

2350 conjugacy classes of subgroups.

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

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

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1729	C₂	direct (N × H)
5. C₂×C₁₉×#336	C₂	semidirect
9. C₂²×M₁₆×C₁₉	C₄	semidirect
13. C₂³×C₈×C₁₉	C₄	semidirect
24. C₁₉×#336	C₂²	semidirect
40. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
50. C₂²×C₈×C₁₉	C₂×C₄	semidirect
113. C₂×#1729	C₁₉	direct (N × H)
157. #1729	C₂×C₁₉	direct (N × H)
158. C₂×#336	C₂×C₁₉	semidirect
182. C₂²×M₁₆	C₄×C₁₉	semidirect
186. C₂³×C₈	C₄×C₁₉	semidirect
197. #336	C₂²×C₁₉	semidirect
199. C₂×C₁₉	#1729	direct (N × H)
219. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
229. C₂²×C₈	C₂×C₄×C₁₉	semidirect
243. C₁₉	C₂×#1729	direct (N × H)
354. C₂	C₁₉×#1729	direct (N × H)

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
C₂⁴×C₈×C₁₉	2
C₂²×C₁₉×#117	2
C₁₉×#1729	2
C₂×C₁₉×#336	2
C₂×#1729	19

Subgroups — C2×C19×#1729 #18026293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1729 #18026293