Subgroups — C₁₉×#22412 #18028371

Order 4864.

1462 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#550	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#413	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1965	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1900	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1785	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
11	C₁₉×#550	—	2	2	no	—
12	C₁₉×#550	—	2	4	no	—
13	C₁₉×#550	—	2	2	no	—
14	C₂×C₁₉×#127	C₄	1	2	yes	—
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₄	1	4	yes	—
17	C₂×C₁₉×#121	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#436	—	2	2	no	—
22	C₁₉×#435	—	2	4	no	—
23	C₈×D₄×C₁₉	—	2	2	no	—
24	C₁₉×#423	C₂²	1	2	yes	—
25	C₁₉×#413	—	2	8	no	—
26	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#101	C₂²	1	2	yes	—
28	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#100	C₂²	1	4	yes	—
30	C₂×C₁₉×#100	C₂²	1	4	yes	—
31	C₁₉×#407	C₂²	1	4	yes	—
32	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#343	C₂²	1	2	yes	—
34	C₁₉×#343	C₂²	1	2	yes	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	4	no	—
37	C₂×#41×C₁₉	—	2	4	no	—
38	C₂×#41×C₁₉	—	2	4	no	—
39	C₂×#41×C₁₉	—	4	4	no	—
40	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	—	2	8	no	—
51	C₂×M₁₆×C₁₉	—	4	4	no	—
52	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
53	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
54	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	4	no	—
56	C₁₉×#127	—	2	4	no	—
57	C₁₉×#127	—	2	4	no	—
58	C₁₉×#127	—	2	2	no	—
59	C₁₉×#127	—	2	2	no	—
60	C₁₉×#121	—	2	4	no	—
61	C₁₉×#121	—	2	4	no	—
62	C₁₉×#121	—	2	8	no	—
63	C₁₉×#121	—	2	8	no	—
64	C₄×Q₈×C₁₉	—	2	2	no	—
65	C₄×Q₈×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×C₁₉	—	2	2	no	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	D₄	1	2	yes	—
70	C₄×D₄×C₁₉	D₄	1	4	yes	—
71	C₄×D₄×C₁₉	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊C₈	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	2	no	—
81	C₁₉×#101	—	2	4	no	—
82	C₁₉×#101	—	2	2	no	—
83	C₁₉×#101	D₄	1	4	yes	complemented
84	C₁₉×#100	—	2	8	no	—
85	C₁₉×#100	—	4	4	no	—
86	C₁₉×C₂²⋊C₈	—	2	4	no	—
87	C₁₉×C₂²⋊C₈	—	2	4	no	—
88	C₁₉×#97	—	2	2	no	—
89	C₄×C₈×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
91	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
92	#41×C₁₉	—	4	8	no	—
93	#41×C₁₉	—	4	8	no	—
94	#41×C₁₉	—	4	8	no	—
95	#41×C₁₉	—	4	8	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₁₉	#41	1	2	yes	—
100	C₂×D₄×C₁₉	—	2	8	no	—
101	C₂×D₄×C₁₉	—	2	8	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	8	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	—	8	2	no	—
114	C₂×D₄×C₁₉	—	8	4	no	—
115	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	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	8	no	—
123	C₂²×C₄×C₁₉	—	4	4	no	—
124	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₁₉	—	2	2	no	—
133	M₁₆×C₁₉	—	2	4	no	—
134	M₁₆×C₁₉	—	2	2	no	—
135	M₁₆×C₁₉	—	2	4	no	—
136	M₁₆×C₁₉	—	2	2	no	—
137	M₁₆×C₁₉	—	4	8	no	—
138	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	4	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	4	8	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
151	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	C₂×D₄	1	2	yes	—
155	C₄²×C₁₉	C₂×D₄	1	2	yes	—
156	#22412	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	4	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	4	no	—
165	C₂³×C₁₉	—	4	4	no	—
166	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
168	Q₈×C₁₉	—	2	4	no	—
169	Q₈×C₁₉	—	2	4	no	—
170	D₄×C₁₉	—	2	4	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	16	no	—
173	D₄×C₁₉	—	4	4	no	—
174	D₄×C₁₉	—	4	4	no	—
175	D₄×C₁₉	—	4	4	no	—
176	D₄×C₁₉	—	4	4	no	—
177	D₄×C₁₉	—	8	4	no	—
178	D₄×C₁₉	—	8	8	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	8	no	—
191	C₂×C₄×C₁₉	—	4	8	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
203	C₈×C₁₉	—	2	4	no	—
204	C₈×C₁₉	—	4	4	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₂×#550	C₂×C₁₉	1	1	yes	characteristic
207	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
208	C₂×#413	C₂×C₁₉	1	2	yes	complemented
209	#1965	C₂×C₁₉	1	2	yes	complemented
210	#1900	C₂×C₁₉	1	4	yes	complemented
211	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1785	C₂×C₁₉	1	2	yes	complemented
213	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	2	4	no	—
218	C₂²×C₁₉	—	2	4	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	4	4	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	8	2	no	—
223	C₂²×C₁₉	—	8	2	no	—
224	C₂²×C₁₉	—	8	4	no	—
225	C₂²×C₁₉	—	8	4	no	—
226	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₁₉	#518	1	1	yes	characteristic
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	—	2	4	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	2	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	#413	1	2	yes	complemented
236	C₄×C₁₉	D₄²	1	2	yes	—
237	C₄×C₁₉	#546	1	2	yes	—
238	C₂²×#41	C₂²×C₁₉	1	2	yes	—
239	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
240	#550	—	2	2	no	—
241	#550	—	2	4	no	—
242	#550	—	2	2	no	—
243	C₂×#127	C₄×C₁₉	1	2	yes	—
244	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×#121	C₄×C₁₉	1	4	yes	—
246	C₂×#121	C₂²×C₁₉	1	2	yes	—
247	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
250	#436	—	2	2	no	—
251	#435	—	2	4	no	—
252	C₈×D₄	—	2	2	no	—
253	#423	C₂²×C₁₉	1	2	yes	—
254	#413	—	2	8	no	—
255	C₂×#101	C₂²×C₁₉	1	2	yes	—
256	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#100	C₂²×C₁₉	1	4	yes	—
259	C₂×#100	C₂²×C₁₉	1	4	yes	—
260	#407	C₂²×C₁₉	1	4	yes	—
261	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
262	#343	C₂²×C₁₉	1	2	yes	—
263	#343	C₂²×C₁₉	1	2	yes	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	4	4	no	—
267	C₂×C₁₉	—	8	4	no	—
268	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
270	C₂×C₁₉	#2888	1	1	yes	characteristic
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	4	4	no	—
276	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
277	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
278	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
279	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
280	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
281	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
282	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
283	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
284	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
285	C₂×M₁₆	—	2	4	no	—
286	C₂×M₁₆	—	2	8	no	—
287	C₂×M₁₆	—	4	4	no	—
288	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
289	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
290	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
291	C₂²×C₈	—	2	4	no	—
292	#127	—	2	4	no	—
293	#127	—	2	4	no	—
294	#127	—	2	2	no	—
295	#127	—	2	2	no	—
296	#121	—	2	4	no	—
297	#121	—	2	4	no	—
298	#121	—	2	8	no	—
299	#121	—	2	8	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	D₄×C₁₉	1	2	yes	—
306	C₄×D₄	D₄×C₁₉	1	4	yes	—
307	C₄×D₄	D₄×C₁₉	1	2	yes	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
312	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
313	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
314	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	2	no	—
317	#101	—	2	4	no	—
318	#101	—	2	2	no	—
319	#101	D₄×C₁₉	1	4	yes	complemented
320	#100	—	2	8	no	—
321	#100	—	4	4	no	—
322	C₂²⋊C₈	—	2	4	no	—
323	C₂²⋊C₈	—	2	4	no	—
324	#97	—	2	2	no	—
325	C₄×C₈	—	2	2	no	—
326	C₁₉	#22412	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
328	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
329	#41	—	4	8	no	—
330	#41	—	4	8	no	—
331	#41	—	4	8	no	—
332	#41	—	4	8	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
336	C₂×Q₈	#41×C₁₉	1	2	yes	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂×D₄	—	8	4	no	—
352	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
353	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	4	no	—
374	M₁₆	—	4	8	no	—
375	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	4	8	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
384	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
388	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	C₂×D₄×C₁₉	1	2	yes	—
392	C₄²	C₂×D₄×C₁₉	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
403	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	16	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	8	4	no	—
414	D₄	—	8	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
435	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
437	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
438	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
439	C₈	—	2	4	no	—
440	C₈	—	4	4	no	—
441	C₈	—	4	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	4	no	—
453	C₂²	—	8	4	no	—
454	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
455	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
456	C₂²	C₁₉×#518	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	C₁₉×#413	1	2	yes	complemented
464	C₄	D₄²×C₁₉	1	2	yes	—
465	C₄	C₁₉×#546	1	2	yes	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	4	4	no	—
469	C₂	—	8	4	no	—
470	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
471	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
472	C₂	C₁₉×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#550	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₁₉	C₂	semidirect
3. C₂×C₁₉×#413	C₂	semidirect
4. C₁₉×#1965	C₂	semidirect
5. C₁₉×#1900	C₂	semidirect
6. C₁₉×#1801	C₂	semidirect
7. C₁₉×#1785	C₂	semidirect
8. C₄×C₁₉×#101	C₂	semidirect
83. C₁₉×#101	D₄	semidirect
156. #22412	C₁₉	direct (N × H)
207. D₄×M₁₆	C₂×C₁₉	semidirect
208. C₂×#413	C₂×C₁₉	semidirect
209. #1965	C₂×C₁₉	semidirect
210. #1900	C₂×C₁₉	semidirect
211. #1801	C₂×C₁₉	semidirect
212. #1785	C₂×C₁₉	semidirect
213. C₄×#101	C₂×C₁₉	semidirect
235. C₄×C₁₉	#413	semidirect
319. #101	D₄×C₁₉	semidirect
326. C₁₉	#22412	direct (N × H)
463. C₄	C₁₉×#413	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#550	2
D₄×M₁₆×C₁₉	2
C₂×C₁₉×#413	2
C₁₉×#1965	2
C₁₉×#1900	2
C₁₉×#1801	2
C₁₉×#1785	2
C₄×C₁₉×#101	2
#22412	19

Subgroups — C19×#22412 #18028371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22412 #18028371