Subgroups — C₂×C₁₉×#1390 #18018531

Order 4864.

1202 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#386	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1390	C₂	1	4	yes	maximal, direct product factor
5	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
7	C₂²×M₁₆×C₁₉	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
9	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
10	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₉×#100	—	2	2	no	—
12	C₂×C₁₉×#100	—	2	1	no	—
13	C₂×C₁₉×#100	C₄	1	4	yes	complemented
14	C₂×C₁₉×#100	C₂²	1	2	yes	—
15	C₂×C₁₉×#99	—	2	2	no	—
16	C₂×C₁₉×#99	—	2	1	no	—
17	C₂×C₁₉×#99	C₄	1	4	yes	complemented
18	C₂×C₁₉×#99	C₂²	1	2	yes	—
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#386	—	2	1	no	—
21	C₁₉×#386	C₄	1	2	yes	complemented
22	C₁₉×#386	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	—	2	1	no	—
24	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	—	4	2	no	—
27	C₂²×D₄×C₁₉	—	4	1	no	—
28	C₂²×D₄×C₁₉	—	4	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	2	yes	—
34	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
36	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	—	4	4	no	—
41	C₂³×C₄×C₁₉	—	4	1	no	—
42	C₂³×C₄×C₁₉	—	4	1	no	—
43	C₂³×C₄×C₁₉	—	4	1	no	—
44	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	complemented
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	4	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	4	2	no	—
49	C₂×M₁₆×C₁₉	—	4	1	no	—
50	C₂²×C₈×C₁₉	—	4	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
61	C₁₉×#100	—	2	4	no	—
62	C₁₉×#100	—	2	2	no	—
63	C₁₉×#100	C₂×C₄	1	4	yes	complemented
64	C₁₉×#99	—	2	4	no	—
65	C₁₉×#99	—	2	2	no	—
66	C₁₉×#99	C₂×C₄	1	4	yes	complemented
67	C₁₉×#95	—	2	2	no	—
68	C₁₉×#95	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	1	no	—
71	C₂⁴×C₁₉	—	2	1	no	—
72	C₂⁴×C₁₉	—	2	1	no	—
73	C₂⁴×C₁₉	—	2	2	no	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	C₂⁴×C₁₉	—	4	2	no	—
76	C₂⁴×C₁₉	—	4	2	no	—
77	C₂⁴×C₁₉	—	4	2	no	—
78	C₂⁴×C₁₉	—	4	2	no	—
79	C₂⁴×C₁₉	C₄²	1	2	yes	—
80	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
81	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
85	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
86	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂×D₄×C₁₉	—	4	2	no	—
89	C₂×D₄×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂×D₄×C₁₉	—	4	1	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	4	2	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	1	no	—
103	C₂×D₄×C₁₉	—	4	1	no	—
104	C₂×D₄×C₁₉	C₄²	1	2	yes	—
105	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
106	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
107	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
108	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
109	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
110	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂×D₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	4	4	no	—
121	C₂²×C₄×C₁₉	—	4	4	no	—
122	C₂²×C₄×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	—	4	8	no	—
125	C₂²×C₄×C₁₉	—	4	4	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	2	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	4	2	no	—
132	C₂²×C₄×C₁₉	—	4	2	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	4	2	no	—
135	C₂²×C₄×C₁₉	—	8	2	no	—
136	C₂²×C₄×C₁₉	—	8	2	no	—
137	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	M₁₆×C₁₉	—	2	4	no	—
142	M₁₆×C₁₉	—	4	4	no	—
143	M₁₆×C₁₉	—	4	2	no	—
144	C₂×C₈×C₁₉	—	4	4	no	—
145	C₂×C₈×C₁₉	—	4	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₉	—	4	4	no	—
149	C₂²⋊C₄×C₁₉	—	4	4	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₂²⋊C₄×C₁₉	—	4	2	no	—
152	C₂²⋊C₄×C₁₉	—	4	2	no	—
153	C₂×#1390	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	4	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	8	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	—	4	4	no	—
185	C₂³×C₁₉	—	4	4	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	8	1	no	—
192	C₂³×C₁₉	—	8	1	no	—
193	C₂³×C₁₉	—	8	4	no	—
194	C₂³×C₁₉	#95	1	2	yes	—
195	C₂³×C₁₉	#95	1	2	yes	—
196	C₂³×C₁₉	#95	1	2	yes	—
197	C₂³×C₁₉	#99	1	1	yes	characteristic
198	C₂³×C₁₉	#99	1	2	yes	—
199	C₂³×C₁₉	#99	1	1	yes	characteristic
200	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
201	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	4	2	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	2	no	—
211	D₄×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	4	1	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	4	no	—
226	C₂×C₄×C₁₉	—	4	8	no	—
227	C₂×C₄×C₁₉	—	4	4	no	—
228	C₂×C₄×C₁₉	—	4	4	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	8	4	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	2	no	—
238	C₂×C₄×C₁₉	—	8	8	no	—
239	C₂×C₄×C₁₉	#95	1	2	yes	—
240	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₈×C₁₉	—	4	4	no	—
243	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic
244	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic
245	C₂×#386	C₂×C₁₉	1	1	yes	characteristic
246	#1390	C₂×C₁₉	1	4	yes	direct product factor
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	4	no	—
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	2	2	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	1	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	4	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	4	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	4	no	—
280	C₂²×C₁₉	—	4	4	no	—
281	C₂²×C₁₉	—	8	1	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	—	8	2	no	—
284	C₂²×C₁₉	—	8	2	no	—
285	C₂²×C₁₉	#342	1	2	yes	—
286	C₂²×C₁₉	#342	1	2	yes	—
287	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	2	yes	—
288	C₂²×C₁₉	#352	1	2	yes	—
289	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
291	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	2	2	no	—
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	4	4	no	—
296	C₄×C₁₉	—	8	2	no	—
297	C₄×C₁₉	—	8	4	no	—
298	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
299	C₂⁴×C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
300	C₂²×M₁₆	—	2	1	no	—
301	C₂²×C₂²⋊C₄	—	2	1	no	—
302	C₂²×C₂²⋊C₄	—	2	1	no	—
303	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
304	C₂×#100	—	2	1	no	—
305	C₂×#100	—	2	2	no	—
306	C₂×#100	C₄×C₁₉	1	4	yes	complemented
307	C₂×#100	C₂²×C₁₉	1	2	yes	—
308	C₂×#99	—	2	1	no	—
309	C₂×#99	—	2	2	no	—
310	C₂×#99	C₄×C₁₉	1	4	yes	complemented
311	C₂×#99	C₂²×C₁₉	1	2	yes	—
312	#386	—	2	1	no	—
313	#386	—	2	1	no	—
314	#386	C₄×C₁₉	1	2	yes	complemented
315	#386	C₂²×C₁₉	1	2	yes	—
316	C₂×#95	—	2	1	no	—
317	C₂×C₁₉	—	2	1	no	—
318	C₂×C₁₉	—	2	1	no	—
319	C₂×C₁₉	—	2	2	no	—
320	C₂×C₁₉	—	4	1	no	—
321	C₂×C₁₉	—	4	2	no	—
322	C₂×C₁₉	—	4	1	no	—
323	C₂×C₁₉	—	4	1	no	—
324	C₂×C₁₉	—	4	2	no	—
325	C₂×C₁₉	—	4	1	no	—
326	C₂×C₁₉	#1390	1	4	yes	direct product factor
327	C₂×C₁₉	C₂×#342	1	1	yes	characteristic
328	C₂×C₁₉	C₂×AΣL(1,𝔽₁₆)	1	1	yes	characteristic
329	C₂×C₁₉	C₂×#352	1	1	yes	characteristic
330	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
331	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
332	C₂²×D₄	—	4	1	no	—
333	C₂²×D₄	—	4	2	no	—
334	C₂²×D₄	—	4	1	no	—
335	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
336	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
337	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
338	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
339	C₂²×D₄	D₄×C₁₉	1	2	yes	—
340	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
341	C₂²×D₄	Q₈×C₁₉	1	2	yes	—
342	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	—	4	4	no	—
347	C₂³×C₄	—	4	1	no	—
348	C₂³×C₄	—	4	1	no	—
349	C₂³×C₄	—	4	1	no	—
350	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	complemented
351	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
352	C₂×M₁₆	—	2	4	no	—
353	C₂×M₁₆	—	2	2	no	—
354	C₂×M₁₆	—	4	2	no	—
355	C₂×M₁₆	—	4	1	no	—
356	C₂²×C₈	—	4	1	no	—
357	C₂×C₂²⋊C₄	—	2	4	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	4	4	no	—
363	C₂×C₂²⋊C₄	—	4	1	no	—
364	C₂×C₂²⋊C₄	—	4	2	no	—
365	C₂×C₂²⋊C₄	—	4	2	no	—
366	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
367	#100	—	2	4	no	—
368	#100	—	2	2	no	—
369	#100	C₂×C₄×C₁₉	1	4	yes	complemented
370	#99	—	2	4	no	—
371	#99	—	2	2	no	—
372	#99	C₂×C₄×C₁₉	1	4	yes	complemented
373	#95	—	2	2	no	—
374	#95	—	2	2	no	—
375	C₁₉	C₂×#1390	1	1	yes	characteristic, direct product factor, Sylow
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	1	no	—
378	C₂⁴	—	2	1	no	—
379	C₂⁴	—	2	1	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	—	4	2	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	—	4	2	no	—
385	C₂⁴	—	4	2	no	—
386	C₂⁴	C₄²×C₁₉	1	2	yes	—
387	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
388	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
389	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
391	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	—
392	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	—
393	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
394	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	C₄²×C₁₉	1	2	yes	—
412	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
413	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
414	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
415	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
416	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
417	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
418	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
419	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂×D₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	8	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	8	2	no	—
443	C₂²×C₄	—	8	2	no	—
444	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
445	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	M₁₆	—	2	4	no	—
449	M₁₆	—	4	4	no	—
450	M₁₆	—	4	2	no	—
451	C₂×C₈	—	4	4	no	—
452	C₂×C₈	—	4	2	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	4	4	no	—
456	C₂²⋊C₄	—	4	4	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	—	4	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	8	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	8	4	no	—
498	C₂³	—	8	1	no	—
499	C₂³	—	8	1	no	—
500	C₂³	C₁₉×#95	1	2	yes	—
501	C₂³	C₁₉×#95	1	2	yes	—
502	C₂³	C₁₉×#95	1	2	yes	—
503	C₂³	C₁₉×#99	1	2	yes	—
504	C₂³	C₁₉×#99	1	1	yes	characteristic
505	C₂³	C₁₉×#99	1	1	yes	characteristic
506	C₂³	C₂×C₄²×C₁₉	1	1	yes	characteristic
507	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
508	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
509	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
510	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	4	no	—
542	C₂×C₄	—	8	8	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₁₉×#95	1	2	yes	—
546	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
548	C₈	—	4	4	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	2	no	—
587	C₂²	C₁₉×#342	1	2	yes	—
588	C₂²	C₁₉×#342	1	2	yes	—
589	C₂²	C₁₉×AΣL(1,𝔽₁₆)	1	2	yes	—
590	C₂²	C₁₉×#352	1	2	yes	—
591	C₂²	C₂×C₁₉×#95	1	1	yes	characteristic
592	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
593	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	4	no	—
598	C₄	—	8	2	no	—
599	C₄	—	8	4	no	—
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	2	2	no	—
603	C₂	—	4	1	no	—
604	C₂	—	4	1	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	4	1	no	—
608	C₂	—	4	2	no	—
609	C₂	C₁₉×#1390	1	4	yes	direct product factor
610	C₂	C₂×C₁₉×#342	1	1	yes	characteristic
611	C₂	C₂×C₁₉×AΣL(1,𝔽₁₆)	1	1	yes	characteristic
612	C₂	C₂×C₁₉×#352	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#99
commutator	C₂³	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂³×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1390	C₂	direct (N × H)
6. C₂⁴×C₄×C₁₉	C₄	semidirect
10. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
13. C₂×C₁₉×#100	C₄	semidirect
17. C₂×C₁₉×#99	C₄	semidirect
21. C₁₉×#386	C₄	semidirect
44. C₂³×C₄×C₁₉	C₂×C₄	semidirect
60. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
63. C₁₉×#100	C₂×C₄	semidirect
66. C₁₉×#99	C₂×C₄	semidirect
153. C₂×#1390	C₁₉	direct (N × H)
246. #1390	C₂×C₁₉	direct (N × H)
299. C₂⁴×C₄	C₄×C₁₉	semidirect
303. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
306. C₂×#100	C₄×C₁₉	semidirect
310. C₂×#99	C₄×C₁₉	semidirect
314. #386	C₄×C₁₉	semidirect
326. C₂×C₁₉	#1390	direct (N × H)
350. C₂³×C₄	C₂×C₄×C₁₉	semidirect
366. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
369. #100	C₂×C₄×C₁₉	semidirect
372. #99	C₂×C₄×C₁₉	semidirect
375. C₁₉	C₂×#1390	direct (N × H)
609. C₂	C₁₉×#1390	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#100	2
C₂²×C₁₉×#99	2
C₂×C₁₉×#386	2
C₁₉×#1390	2
C₂×#1390	19

Subgroups — C2×C19×#1390 #18018531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1390 #18018531