Subgroups — C₁₉×#14419 #18020378

Order 4864.

2982 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#386	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#386	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1438	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1438	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1434	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×#127	—	2	8	no	—
12	C₂×C₁₉×#127	C₄	1	8	yes	complemented
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#386	—	2	16	no	—
20	C₁₉×#386	—	2	8	no	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	4	yes	—
23	C₂×C₁₉×#95	C₂²	1	4	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂⁵×C₁₉	C₂³	1	2	yes	—
26	C₂⁵×C₁₉	C₂³	1	2	yes	—
27	C₂²×D₄×C₁₉	—	2	8	no	—
28	C₂²×D₄×C₁₉	—	2	8	no	—
29	C₂²×D₄×C₁₉	—	2	8	no	—
30	C₂²×D₄×C₁₉	—	2	4	no	—
31	C₂²×D₄×C₁₉	—	2	8	no	—
32	C₂²×D₄×C₁₉	—	4	1	no	—
33	C₂²×D₄×C₁₉	—	4	2	no	—
34	C₂²×D₄×C₁₉	—	4	1	no	—
35	C₂²×D₄×C₁₉	—	4	4	no	—
36	C₂²×D₄×C₁₉	—	4	4	no	—
37	C₂²×D₄×C₁₉	—	4	2	no	—
38	C₂²×D₄×C₁₉	—	4	1	no	—
39	C₂²×D₄×C₁₉	—	4	1	no	—
40	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
41	C₂²×D₄×C₁₉	C₂×C₄	1	16	yes	complemented
42	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
43	C₂²×D₄×C₁₉	D₄	1	8	yes	—
44	C₂³×C₄×C₁₉	—	2	4	no	—
45	C₂³×C₄×C₁₉	—	2	8	no	—
46	C₂³×C₄×C₁₉	—	4	2	no	—
47	C₂³×C₄×C₁₉	—	4	4	no	—
48	C₂³×C₄×C₁₉	—	4	2	no	—
49	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₁₉×#127	—	2	32	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
67	C₂×C₄²×C₁₉	—	2	4	no	—
68	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	complemented
69	C₁₉×#95	—	2	8	no	—
70	C₁₉×#95	—	2	8	no	—
71	C₁₉×#95	—	2	4	no	—
72	C₁₉×#95	D₄	1	8	yes	complemented
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	2	4	no	—
75	C₂⁴×C₁₉	—	2	2	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	—	2	4	no	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂⁴×C₁₉	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	4	no	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	—	2	4	no	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	2	4	no	—
88	C₂⁴×C₁₉	—	2	4	no	—
89	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
90	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
91	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
92	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
93	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
94	C₂×D₄×C₁₉	—	2	32	no	—
95	C₂×D₄×C₁₉	—	2	8	no	—
96	C₂×D₄×C₁₉	—	2	32	no	—
97	C₂×D₄×C₁₉	—	4	4	no	—
98	C₂×D₄×C₁₉	—	4	4	no	—
99	C₂×D₄×C₁₉	—	4	16	no	—
100	C₂×D₄×C₁₉	—	4	4	no	—
101	C₂×D₄×C₁₉	—	4	4	no	—
102	C₂×D₄×C₁₉	—	4	8	no	—
103	C₂×D₄×C₁₉	—	4	8	no	—
104	C₂×D₄×C₁₉	—	4	16	no	—
105	C₂×D₄×C₁₉	—	4	16	no	—
106	C₂×D₄×C₁₉	—	4	16	no	—
107	C₂×D₄×C₁₉	—	4	16	no	—
108	C₂×D₄×C₁₉	—	4	8	no	—
109	C₂×D₄×C₁₉	—	4	8	no	—
110	C₂×D₄×C₁₉	C₂²⋊C₄	1	16	yes	complemented
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	4	8	no	—
130	C₂²×C₄×C₁₉	—	4	16	no	—
131	C₂²×C₄×C₁₉	—	4	16	no	—
132	C₂²×C₄×C₁₉	—	4	8	no	—
133	C₂²×C₄×C₁₉	—	4	8	no	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₉	#41	1	4	yes	—
140	C₂²⋊C₄×C₁₉	—	4	8	no	—
141	C₂²⋊C₄×C₁₉	—	4	16	no	—
142	C₂²⋊C₄×C₁₉	—	4	16	no	—
143	C₂²⋊C₄×C₁₉	—	4	8	no	—
144	C₂²⋊C₄×C₁₉	—	4	8	no	—
145	C₄²×C₁₉	—	2	8	no	—
146	#14419	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	—	2	8	no	—
148	C₂³×C₁₉	—	2	4	no	—
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	2	8	no	—
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	2	4	no	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	2	4	no	—
155	C₂³×C₁₉	—	2	8	no	—
156	C₂³×C₁₉	—	2	8	no	—
157	C₂³×C₁₉	—	2	8	no	—
158	C₂³×C₁₉	—	2	8	no	—
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	8	no	—
161	C₂³×C₁₉	—	2	4	no	—
162	C₂³×C₁₉	—	2	4	no	—
163	C₂³×C₁₉	—	2	8	no	—
164	C₂³×C₁₉	—	4	4	no	—
165	C₂³×C₁₉	—	4	4	no	—
166	C₂³×C₁₉	—	4	4	no	—
167	C₂³×C₁₉	—	4	4	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	4	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	4	no	—
174	C₂³×C₁₉	—	4	4	no	—
175	C₂³×C₁₉	—	4	4	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	4	4	no	—
178	C₂³×C₁₉	—	4	4	no	—
179	C₂³×C₁₉	—	4	4	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	4	no	—
182	C₂³×C₁₉	—	4	4	no	—
183	C₂³×C₁₉	—	4	4	no	—
184	C₂³×C₁₉	—	4	4	no	—
185	C₂³×C₁₉	—	4	4	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	4	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
191	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
192	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
193	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
194	C₂³×C₁₉	C₂×#41	1	2	yes	—
195	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
196	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
199	D₄×C₁₉	—	4	16	no	—
200	D₄×C₁₉	—	4	64	no	—
201	D₄×C₁₉	—	4	16	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	8	no	—
209	C₂×C₄×C₁₉	—	2	8	no	—
210	C₂×C₄×C₁₉	—	2	8	no	—
211	C₂×C₄×C₁₉	—	2	8	no	—
212	C₂×C₄×C₁₉	—	2	8	no	—
213	C₂×C₄×C₁₉	—	4	32	no	—
214	C₂×C₄×C₁₉	—	4	4	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	4	4	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	4	no	—
220	C₂×C₄×C₁₉	—	4	4	no	—
221	C₂×C₄×C₁₉	—	4	4	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
226	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
227	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic
228	C₂×#386	C₂×C₁₉	1	4	yes	complemented
229	C₂×#386	C₂×C₁₉	1	2	yes	complemented
230	#1438	C₂×C₁₉	1	4	yes	complemented
231	#1438	C₂×C₁₉	1	2	yes	complemented
232	#1434	C₂×C₁₉	1	2	yes	complemented
233	C₂²×C₁₉	—	2	8	no	—
234	C₂²×C₁₉	—	2	16	no	—
235	C₂²×C₁₉	—	4	8	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	8	no	—
241	C₂²×C₁₉	—	4	8	no	—
242	C₂²×C₁₉	—	4	4	no	—
243	C₂²×C₁₉	—	4	4	no	—
244	C₂²×C₁₉	—	4	4	no	—
245	C₂²×C₁₉	—	4	8	no	—
246	C₂²×C₁₉	—	4	8	no	—
247	C₂²×C₁₉	—	4	4	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	8	4	no	—
250	C₂²×C₁₉	—	8	4	no	—
251	C₂²×C₁₉	—	8	4	no	—
252	C₂²×C₁₉	—	8	4	no	—
253	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
255	C₂²×C₁₉	#518	1	1	yes	characteristic
256	C₂²×C₁₉	#518	1	1	yes	characteristic
257	C₂²×C₁₉	#518	1	2	yes	—
258	C₂²×C₁₉	#534	1	2	yes	—
259	C₂²×C₁₉	#534	1	2	yes	—
260	C₂²×C₁₉	#535	1	4	yes	—
261	C₂²×C₁₉	#540	1	4	yes	—
262	C₂²×C₁₉	D₄²	1	4	yes	—
263	C₂²×C₁₉	D₄²	1	1	yes	characteristic
264	C₂²×C₁₉	#546	1	4	yes	—
265	C₂²×C₁₉	#550	1	2	yes	—
266	C₂²×C₁₉	#559	1	1	yes	characteristic
267	C₂²×C₁₉	#560	1	2	yes	—
268	C₂²×C₁₉	#560	1	2	yes	—
269	C₄×C₁₉	—	2	4	no	—
270	C₄×C₁₉	—	2	8	no	—
271	C₄×C₁₉	—	4	8	no	—
272	C₄×C₁₉	—	8	4	no	—
273	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
274	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
275	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
276	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
277	C₂×#127	—	2	8	no	—
278	C₂×#127	C₄×C₁₉	1	8	yes	complemented
279	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
280	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
281	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
282	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
284	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
285	#386	—	2	8	no	—
286	#386	—	2	16	no	—
287	C₂×#95	C₂²×C₁₉	1	2	yes	—
288	C₂×#95	C₂²×C₁₉	1	4	yes	—
289	C₂×#95	C₂²×C₁₉	1	4	yes	—
290	C₂×#95	C₂²×C₁₉	1	2	yes	—
291	C₂×C₁₉	—	4	8	no	—
292	C₂×C₁₉	—	8	4	no	—
293	C₂×C₁₉	#2308	1	1	yes	characteristic
294	C₂×C₁₉	#2328	1	2	yes	—
295	C₂×C₁₉	D₄×C₂²⋊C₄	1	2	yes	—
296	C₂×C₁₉	#2366	1	1	yes	characteristic
297	C₂×C₁₉	#2380	1	1	yes	characteristic
298	C₂×C₁₉	#2669	1	2	yes	—
299	C₂×C₁₉	#2673	1	4	yes	—
300	C₂×C₁₉	#2709	1	2	yes	—
301	C₂⁵	C₂³×C₁₉	1	2	yes	—
302	C₂⁵	C₂³×C₁₉	1	2	yes	—
303	C₂²×D₄	—	2	8	no	—
304	C₂²×D₄	—	2	8	no	—
305	C₂²×D₄	—	2	4	no	—
306	C₂²×D₄	—	2	8	no	—
307	C₂²×D₄	—	2	8	no	—
308	C₂²×D₄	—	4	1	no	—
309	C₂²×D₄	—	4	2	no	—
310	C₂²×D₄	—	4	1	no	—
311	C₂²×D₄	—	4	4	no	—
312	C₂²×D₄	—	4	4	no	—
313	C₂²×D₄	—	4	2	no	—
314	C₂²×D₄	—	4	1	no	—
315	C₂²×D₄	—	4	1	no	—
316	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
317	C₂²×D₄	C₂×C₄×C₁₉	1	16	yes	complemented
318	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
319	C₂²×D₄	D₄×C₁₉	1	8	yes	—
320	C₂³×C₄	—	2	4	no	—
321	C₂³×C₄	—	2	8	no	—
322	C₂³×C₄	—	4	2	no	—
323	C₂³×C₄	—	4	4	no	—
324	C₂³×C₄	—	4	2	no	—
325	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
326	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
327	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
329	#127	—	2	32	no	—
330	C₂×C₂²⋊C₄	—	2	8	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	2	8	no	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	4	2	no	—
336	C₂×C₂²⋊C₄	—	4	4	no	—
337	C₂×C₂²⋊C₄	—	4	4	no	—
338	C₂×C₂²⋊C₄	—	4	4	no	—
339	C₂×C₂²⋊C₄	—	4	2	no	—
340	C₂×C₂²⋊C₄	—	4	2	no	—
341	C₂×C₂²⋊C₄	—	4	2	no	—
342	C₂×C₂²⋊C₄	—	4	4	no	—
343	C₂×C₄²	—	2	4	no	—
344	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	complemented
345	#95	—	2	8	no	—
346	#95	—	2	8	no	—
347	#95	—	2	4	no	—
348	#95	D₄×C₁₉	1	8	yes	complemented
349	C₁₉	#14419	1	1	yes	characteristic, direct product factor, Sylow
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	2	4	no	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
367	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
368	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
369	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
370	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
371	C₂×D₄	—	2	32	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	32	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	16	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	8	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	—	4	16	no	—
382	C₂×D₄	—	4	16	no	—
383	C₂×D₄	—	4	16	no	—
384	C₂×D₄	—	4	16	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	C₂²⋊C₄×C₁₉	1	16	yes	complemented
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	4	8	no	—
407	C₂²×C₄	—	4	16	no	—
408	C₂²×C₄	—	4	16	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
414	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
415	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
416	C₂²×C₄	#41×C₁₉	1	4	yes	—
417	C₂²⋊C₄	—	4	8	no	—
418	C₂²⋊C₄	—	4	16	no	—
419	C₂²⋊C₄	—	4	16	no	—
420	C₂²⋊C₄	—	4	8	no	—
421	C₂²⋊C₄	—	4	8	no	—
422	C₄²	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	4	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	2	no	—
466	C₂³	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
467	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
468	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
469	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
470	C₂³	C₂×#41×C₁₉	1	2	yes	—
471	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
472	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
475	D₄	—	4	16	no	—
476	D₄	—	4	64	no	—
477	D₄	—	4	16	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	4	32	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
502	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	16	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	8	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	4	8	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	8	4	no	—
520	C₂²	—	8	4	no	—
521	C₂²	—	8	4	no	—
522	C₂²	—	8	4	no	—
523	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
524	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
525	C₂²	C₁₉×#518	1	1	yes	characteristic
526	C₂²	C₁₉×#518	1	1	yes	characteristic
527	C₂²	C₁₉×#518	1	2	yes	—
528	C₂²	C₁₉×#534	1	2	yes	—
529	C₂²	C₁₉×#534	1	2	yes	—
530	C₂²	C₁₉×#535	1	4	yes	—
531	C₂²	C₁₉×#540	1	4	yes	—
532	C₂²	D₄²×C₁₉	1	1	yes	characteristic
533	C₂²	D₄²×C₁₉	1	4	yes	—
534	C₂²	C₁₉×#546	1	4	yes	—
535	C₂²	C₁₉×#550	1	2	yes	—
536	C₂²	C₁₉×#559	1	1	yes	characteristic
537	C₂²	C₁₉×#560	1	2	yes	—
538	C₂²	C₁₉×#560	1	2	yes	—
539	C₄	—	2	4	no	—
540	C₄	—	2	8	no	—
541	C₄	—	4	8	no	—
542	C₄	—	8	4	no	—
543	C₂	—	4	8	no	—
544	C₂	—	8	4	no	—
545	C₂	C₁₉×#2308	1	1	yes	characteristic
546	C₂	C₁₉×#2328	1	2	yes	—
547	C₂	D₄×C₂²⋊C₄×C₁₉	1	2	yes	—
548	C₂	C₁₉×#2366	1	1	yes	characteristic
549	C₂	C₁₉×#2380	1	1	yes	characteristic
550	C₂	C₁₉×#2669	1	2	yes	—
551	C₂	C₁₉×#2673	1	4	yes	—
552	C₂	C₁₉×#2709	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#386	C₂	semidirect
3. C₂×C₁₉×#386	C₂	semidirect
4. C₁₉×#1438	C₂	semidirect
5. C₁₉×#1438	C₂	semidirect
6. C₁₉×#1434	C₂	semidirect
12. C₂×C₁₉×#127	C₄	semidirect
41. C₂²×D₄×C₁₉	C₂×C₄	semidirect
42. C₂²×D₄×C₁₉	C₂×C₄	semidirect
68. C₂×C₄²×C₁₉	C₂×C₄	semidirect
72. C₁₉×#95	D₄	semidirect
110. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
146. #14419	C₁₉	direct (N × H)
228. C₂×#386	C₂×C₁₉	semidirect
229. C₂×#386	C₂×C₁₉	semidirect
230. #1438	C₂×C₁₉	semidirect
231. #1438	C₂×C₁₉	semidirect
232. #1434	C₂×C₁₉	semidirect
278. C₂×#127	C₄×C₁₉	semidirect
317. C₂²×D₄	C₂×C₄×C₁₉	semidirect
318. C₂²×D₄	C₂×C₄×C₁₉	semidirect
344. C₂×C₄²	C₂×C₄×C₁₉	semidirect
348. #95	D₄×C₁₉	semidirect
349. C₁₉	#14419	direct (N × H)
387. C₂×D₄	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
C₂²×C₁₉×#127	2
C₂×C₁₉×#386	2
C₁₉×#1438	2
C₁₉×#1434	2
#14419	19

Subgroups — C19×#14419 #18020378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14419 #18020378