Subgroups — C₂×C₁₉×#1462 #18023313

Order 4864.

2790 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#407	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1462	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₉×#323	C₂	1	4	yes	maximal, complemented
5	C₂⁶×C₁₉	C₄	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₉	—	2	2	no	—
9	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
10	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	C₂²×C₂²⋊C₄×C₁₉	—	2	4	no	—
12	C₂²×C₂²⋊C₄×C₁₉	C₄	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
16	C₁₉×#407	—	2	4	no	—
17	C₁₉×#407	C₂²	1	8	yes	complemented
18	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
20	C₁₉×#323	C₂²	1	16	yes	complemented
21	C₂⁵×C₁₉	—	2	2	no	—
22	C₂⁵×C₁₉	—	2	1	no	—
23	C₂⁵×C₁₉	—	2	1	no	—
24	C₂⁵×C₁₉	—	2	8	no	—
25	C₂⁵×C₁₉	—	4	4	no	—
26	C₂⁵×C₁₉	—	4	4	no	—
27	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂⁵×C₁₉	C₂×C₄	1	4	yes	—
29	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₉	—	2	2	no	—
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	—	4	4	no	—
34	C₂³×C₄×C₁₉	—	4	4	no	—
35	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	2	yes	—
40	C₂³×C₄×C₁₉	D₄	1	2	yes	—
41	C₂³×C₄×C₁₉	D₄	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂×M₁₆×C₁₉	—	2	8	no	—
45	C₂×M₁₆×C₁₉	—	4	8	no	—
46	C₂²×C₈×C₁₉	—	2	4	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
57	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
58	C₁₉×C₂²⋊C₈	—	2	8	no	—
59	C₁₉×C₂²⋊C₈	—	2	4	no	—
60	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	complemented
61	C₂⁴×C₁₉	—	2	4	no	—
62	C₂⁴×C₁₉	—	2	4	no	—
63	C₂⁴×C₁₉	—	2	4	no	—
64	C₂⁴×C₁₉	—	2	16	no	—
65	C₂⁴×C₁₉	—	2	8	no	—
66	C₂⁴×C₁₉	—	2	8	no	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	2	4	no	—
72	C₂⁴×C₁₉	—	2	16	no	—
73	C₂⁴×C₁₉	—	4	4	no	—
74	C₂⁴×C₁₉	—	4	8	no	—
75	C₂⁴×C₁₉	—	4	4	no	—
76	C₂⁴×C₁₉	—	4	8	no	—
77	C₂⁴×C₁₉	—	4	64	no	—
78	C₂⁴×C₁₉	—	4	8	no	—
79	C₂⁴×C₁₉	—	4	4	no	—
80	C₂⁴×C₁₉	—	4	8	no	—
81	C₂⁴×C₁₉	—	4	4	no	—
82	C₂⁴×C₁₉	—	4	4	no	—
83	C₂⁴×C₁₉	—	4	4	no	—
84	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
85	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂⁴×C₁₉	M₁₆	1	8	yes	complemented
88	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
89	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₉	—	2	8	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	4	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	4	no	—
99	C₂²×C₄×C₁₉	—	4	8	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
102	C₂²×C₄×C₁₉	—	4	8	no	—
103	C₂²×C₄×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	4	4	no	—
105	C₂²×C₄×C₁₉	—	4	8	no	—
106	C₂²×C₄×C₁₉	—	4	4	no	—
107	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	M₁₆×C₁₉	—	4	16	no	—
120	C₂×C₈×C₁₉	—	2	8	no	—
121	C₂×C₈×C₁₉	—	4	8	no	—
122	C₂²⋊C₄×C₁₉	—	2	8	no	—
123	C₂²⋊C₄×C₁₉	—	2	16	no	—
124	C₂²⋊C₄×C₁₉	—	2	8	no	—
125	C₂×#1462	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	2	32	no	—
127	C₂³×C₁₉	—	2	4	no	—
128	C₂³×C₁₉	—	2	4	no	—
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	4	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	16	no	—
140	C₂³×C₁₉	—	2	16	no	—
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	—	2	4	no	—
143	C₂³×C₁₉	—	2	8	no	—
144	C₂³×C₁₉	—	2	8	no	—
145	C₂³×C₁₉	—	4	16	no	—
146	C₂³×C₁₉	—	4	4	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	—	4	64	no	—
149	C₂³×C₁₉	—	4	64	no	—
150	C₂³×C₁₉	—	4	4	no	—
151	C₂³×C₁₉	—	4	8	no	—
152	C₂³×C₁₉	—	4	4	no	—
153	C₂³×C₁₉	—	4	8	no	—
154	C₂³×C₁₉	—	4	32	no	—
155	C₂³×C₁₉	—	4	32	no	—
156	C₂³×C₁₉	—	4	16	no	—
157	C₂³×C₁₉	—	4	8	no	—
158	C₂³×C₁₉	—	4	4	no	—
159	C₂³×C₁₉	—	4	8	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	#99	1	4	yes	—
162	C₂³×C₁₉	#100	1	4	yes	—
163	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
168	C₂³×C₁₉	C₂×M₁₆	1	8	yes	complemented
169	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	8	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	8	no	—
184	C₂×C₄×C₁₉	—	4	8	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
190	C₈×C₁₉	—	4	8	no	—
191	C₂³×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
192	C₂×#407	C₂×C₁₉	1	2	yes	complemented
193	#1462	C₂×C₁₉	1	8	yes	direct product factor
194	C₂×#323	C₂×C₁₉	1	4	yes	complemented
195	C₂²×C₁₉	—	2	16	no	—
196	C₂²×C₁₉	—	2	16	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	8	no	—
206	C₂²×C₁₉	—	2	8	no	—
207	C₂²×C₁₉	—	2	8	no	—
208	C₂²×C₁₉	—	2	8	no	—
209	C₂²×C₁₉	—	4	8	no	—
210	C₂²×C₁₉	—	4	8	no	—
211	C₂²×C₁₉	—	4	16	no	—
212	C₂²×C₁₉	—	4	32	no	—
213	C₂²×C₁₉	—	4	32	no	—
214	C₂²×C₁₉	—	4	4	no	—
215	C₂²×C₁₉	—	4	4	no	—
216	C₂²×C₁₉	—	4	16	no	—
217	C₂²×C₁₉	#407	1	2	yes	—
218	C₂²×C₁₉	#407	1	2	yes	—
219	C₂²×C₁₉	C₂×#99	1	4	yes	—
220	C₂²×C₁₉	C₂×#99	1	2	yes	—
221	C₂²×C₁₉	C₂×#100	1	4	yes	—
222	C₂²×C₁₉	C₂×#100	1	2	yes	—
223	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×C₁₉	C₂²×M₁₆	1	2	yes	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	2	4	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₂⁶	C₄×C₁₉	1	1	yes	characteristic
230	C₂⁴×C₄	C₄×C₁₉	1	1	yes	characteristic
231	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
232	C₂²×M₁₆	—	2	2	no	—
233	C₂²×C₂²⋊C₄	—	2	2	no	—
234	C₂²×C₂²⋊C₄	—	2	2	no	—
235	C₂²×C₂²⋊C₄	—	2	4	no	—
236	C₂²×C₂²⋊C₄	C₄×C₁₉	1	4	yes	—
237	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
239	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
240	#407	—	2	4	no	—
241	#407	C₂²×C₁₉	1	8	yes	complemented
242	C₂×C₂²⋊C₈	—	2	2	no	—
243	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	complemented
244	#323	C₂²×C₁₉	1	16	yes	complemented
245	C₂×C₁₉	—	2	2	no	—
246	C₂×C₁₉	—	2	2	no	—
247	C₂×C₁₉	—	2	4	no	—
248	C₂×C₁₉	—	2	4	no	—
249	C₂×C₁₉	—	4	8	no	—
250	C₂×C₁₉	#1462	1	4	yes	direct product factor
251	C₂×C₁₉	C₂×#407	1	1	yes	characteristic
252	C₂×C₁₉	C₂²×#99	1	1	yes	characteristic
253	C₂×C₁₉	C₂²×#100	1	1	yes	characteristic
254	C₂⁵	—	2	2	no	—
255	C₂⁵	—	2	1	no	—
256	C₂⁵	—	2	1	no	—
257	C₂⁵	—	2	8	no	—
258	C₂⁵	—	4	4	no	—
259	C₂⁵	—	4	4	no	—
260	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
261	C₂⁵	C₂×C₄×C₁₉	1	4	yes	—
262	C₂⁵	C₂×C₄×C₁₉	1	2	yes	—
263	C₂³×C₄	—	2	2	no	—
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	—	4	4	no	—
267	C₂³×C₄	—	4	4	no	—
268	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
269	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
270	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
271	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
272	C₂³×C₄	D₄×C₁₉	1	2	yes	—
273	C₂³×C₄	D₄×C₁₉	1	2	yes	—
274	C₂³×C₄	D₄×C₁₉	1	4	yes	—
275	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
277	C₂×M₁₆	—	2	8	no	—
278	C₂×M₁₆	—	4	8	no	—
279	C₂²×C₈	—	2	4	no	—
280	C₂×C₂²⋊C₄	—	2	8	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₂²⋊C₄	—	2	8	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	8	no	—
288	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
291	C₂²⋊C₈	—	2	8	no	—
292	C₂²⋊C₈	—	2	4	no	—
293	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	complemented
294	C₁₉	C₂×#1462	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁴	—	2	4	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	2	16	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	8	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	—	2	16	no	—
307	C₂⁴	—	4	4	no	—
308	C₂⁴	—	4	8	no	—
309	C₂⁴	—	4	4	no	—
310	C₂⁴	—	4	8	no	—
311	C₂⁴	—	4	64	no	—
312	C₂⁴	—	4	8	no	—
313	C₂⁴	—	4	4	no	—
314	C₂⁴	—	4	8	no	—
315	C₂⁴	—	4	4	no	—
316	C₂⁴	—	4	4	no	—
317	C₂⁴	—	4	4	no	—
318	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
319	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
320	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
321	C₂⁴	M₁₆×C₁₉	1	8	yes	complemented
322	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
323	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
324	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	8	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
342	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
343	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
346	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
353	M₁₆	—	4	16	no	—
354	C₂×C₈	—	2	8	no	—
355	C₂×C₈	—	4	8	no	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	16	no	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂³	—	2	32	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	16	no	—
373	C₂³	—	2	16	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	8	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	16	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	64	no	—
382	C₂³	—	4	64	no	—
383	C₂³	—	4	16	no	—
384	C₂³	—	4	32	no	—
385	C₂³	—	4	32	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	8	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	8	no	—
393	C₂³	—	4	4	no	—
394	C₂³	C₁₉×#99	1	4	yes	—
395	C₂³	C₁₉×#100	1	4	yes	—
396	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
397	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
398	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
399	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
400	C₂³	C₂×M₁₆×C₁₉	1	4	yes	—
401	C₂³	C₂×M₁₆×C₁₉	1	8	yes	complemented
402	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
421	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
422	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
423	C₈	—	4	8	no	—
424	C₂²	—	2	16	no	—
425	C₂²	—	2	16	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	32	no	—
441	C₂²	—	4	32	no	—
442	C₂²	—	4	8	no	—
443	C₂²	—	4	16	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	C₁₉×#407	1	2	yes	—
447	C₂²	C₁₉×#407	1	2	yes	—
448	C₂²	C₂×C₁₉×#99	1	4	yes	—
449	C₂²	C₂×C₁₉×#99	1	2	yes	—
450	C₂²	C₂×C₁₉×#100	1	4	yes	—
451	C₂²	C₂×C₁₉×#100	1	2	yes	—
452	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
453	C₂²	C₂²×M₁₆×C₁₉	1	2	yes	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	4	no	—
457	C₄	—	4	4	no	—
458	C₂	—	2	2	no	—
459	C₂	—	2	4	no	—
460	C₂	—	2	4	no	—
461	C₂	—	2	2	no	—
462	C₂	—	4	8	no	—
463	C₂	C₁₉×#1462	1	4	yes	direct product factor
464	C₂	C₂×C₁₉×#407	1	1	yes	characteristic
465	C₂	C₂²×C₁₉×#99	1	1	yes	characteristic
466	C₂	C₂²×C₁₉×#100	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁶×C₁₉	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#407	C₂	semidirect
3. C₁₉×#1462	C₂	direct (N × H)
4. C₂×C₁₉×#323	C₂	semidirect
17. C₁₉×#407	C₂²	semidirect
19. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
20. C₁₉×#323	C₂²	semidirect
60. C₁₉×C₂²⋊C₈	C₂³	semidirect
87. C₂⁴×C₁₉	M₁₆	semidirect
125. C₂×#1462	C₁₉	direct (N × H)
168. C₂³×C₁₉	C₂×M₁₆	semidirect
192. C₂×#407	C₂×C₁₉	semidirect
193. #1462	C₂×C₁₉	direct (N × H)
194. C₂×#323	C₂×C₁₉	semidirect
241. #407	C₂²×C₁₉	semidirect
243. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
244. #323	C₂²×C₁₉	semidirect
250. C₂×C₁₉	#1462	direct (N × H)
293. C₂²⋊C₈	C₂³×C₁₉	semidirect
294. C₁₉	C₂×#1462	direct (N × H)
321. C₂⁴	M₁₆×C₁₉	semidirect
401. C₂³	C₂×M₁₆×C₁₉	semidirect
463. C₂	C₁₉×#1462	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×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#407	2
C₁₉×#1462	2
C₂×C₁₉×#323	2
C₂×#1462	19

Subgroups — C2×C19×#1462 #18023313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1462 #18023313