Subgroups — C₁₉×#22411 #18028370

Order 4864.

1410 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#547	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×#1966	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1901	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1785	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₉×#100	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×#547	—	2	2	no	—
12	C₁₉×#547	—	2	4	no	—
13	C₁₉×#547	—	2	2	no	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#123	C₄	1	4	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×#121	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
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	4	yes	—
27	C₂×C₁₉×#101	C₂²	1	4	yes	—
28	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#100	C₂²	1	2	yes	—
30	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
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	2	yes	—
41	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂×M₁₆×C₁₉	—	2	4	no	—
48	C₂×M₁₆×C₁₉	—	2	8	no	—
49	C₂×M₁₆×C₁₉	—	4	4	no	—
50	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
51	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
52	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₉	—	2	4	no	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×#123	—	2	8	no	—
57	C₁₉×#123	—	2	8	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	4	no	—
60	C₁₉×#121	—	2	4	no	—
61	C₁₉×#121	—	2	4	no	—
62	C₄×D₄×C₁₉	—	2	2	no	—
63	C₄×D₄×C₁₉	—	2	2	no	—
64	C₄×D₄×C₁₉	D₄	1	2	yes	—
65	C₄×D₄×C₁₉	D₄	1	4	yes	—
66	C₄×D₄×C₁₉	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	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	2	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
77	C₂×C₂²⋊C₄×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	8	no	—
82	C₁₉×#101	—	4	4	no	—
83	C₁₉×#100	—	2	4	no	—
84	C₁₉×#100	—	2	2	no	—
85	C₁₉×#100	D₄	1	4	yes	complemented
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	2	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	4	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	4	no	—
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	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
107	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
108	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	8	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	4	4	no	—
119	C₂²×C₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	2	4	no	—
130	M₁₆×C₁₉	—	2	2	no	—
131	M₁₆×C₁₉	—	2	4	no	—
132	M₁₆×C₁₉	—	2	2	no	—
133	M₁₆×C₁₉	—	4	8	no	—
134	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	4	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	4	8	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	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	8	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	C₂×D₄	1	2	yes	—
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	#22411	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
164	C₂³×C₁₉	C₄×D₄	1	4	yes	—
165	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
166	Q₈×C₁₉	—	4	4	no	—
167	Q₈×C₁₉	—	4	4	no	—
168	D₄×C₁₉	—	2	4	no	—
169	D₄×C₁₉	—	2	4	no	—
170	D₄×C₁₉	—	2	4	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	16	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	8	no	—
186	C₂×C₄×C₁₉	—	4	8	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
199	C₈×C₁₉	—	2	4	no	—
200	C₈×C₁₉	—	4	4	no	—
201	C₈×C₁₉	—	4	2	no	—
202	C₂×#547	C₂×C₁₉	1	1	yes	characteristic
203	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
204	C₂×#413	C₂×C₁₉	1	2	yes	complemented
205	#1966	C₂×C₁₉	1	2	yes	complemented
206	#1901	C₂×C₁₉	1	4	yes	complemented
207	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1785	C₂×C₁₉	1	2	yes	complemented
209	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	2	4	no	—
215	C₂²×C₁₉	—	2	4	no	—
216	C₂²×C₁₉	—	4	4	no	—
217	C₂²×C₁₉	—	4	4	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	8	2	no	—
221	C₂²×C₁₉	—	8	2	no	—
222	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₁₉	#518	1	1	yes	characteristic
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	4	4	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	#413	1	2	yes	complemented
232	C₄×C₁₉	D₄²	1	2	yes	—
233	C₄×C₁₉	#546	1	2	yes	—
234	C₂²×#41	C₂²×C₁₉	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
236	#547	—	2	2	no	—
237	#547	—	2	4	no	—
238	#547	—	2	2	no	—
239	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×#123	C₄×C₁₉	1	4	yes	—
241	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
242	C₂×#121	C₄×C₁₉	1	2	yes	—
243	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₄×C₁₉	1	2	yes	—
246	#436	—	2	2	no	—
247	#435	—	2	4	no	—
248	C₈×D₄	—	2	2	no	—
249	#423	C₂²×C₁₉	1	2	yes	—
250	#413	—	2	8	no	—
251	C₂×#101	C₂²×C₁₉	1	4	yes	—
252	C₂×#101	C₂²×C₁₉	1	4	yes	—
253	C₂×#100	C₂²×C₁₉	1	2	yes	—
254	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
256	#407	C₂²×C₁₉	1	4	yes	—
257	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
258	#343	C₂²×C₁₉	1	2	yes	—
259	#343	C₂²×C₁₉	1	2	yes	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	4	4	no	—
263	C₂×C₁₉	—	4	4	no	—
264	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
266	C₂×C₁₉	#2889	1	1	yes	characteristic
267	C₂×#41	—	2	4	no	—
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	2	4	no	—
270	C₂×#41	—	2	4	no	—
271	C₂×#41	—	4	4	no	—
272	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
273	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
274	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
275	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
277	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
278	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	—	2	8	no	—
281	C₂×M₁₆	—	4	4	no	—
282	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
283	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
284	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
285	C₂²×C₈	—	2	4	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	#123	—	2	8	no	—
289	#123	—	2	8	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	#121	—	2	4	no	—
293	#121	—	2	4	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	D₄×C₁₉	1	2	yes	—
297	C₄×D₄	D₄×C₁₉	1	4	yes	—
298	C₄×D₄	D₄×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
304	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
310	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	#101	—	2	8	no	—
314	#101	—	4	4	no	—
315	#100	—	2	4	no	—
316	#100	—	2	2	no	—
317	#100	D₄×C₁₉	1	4	yes	complemented
318	C₂²⋊C₈	—	2	4	no	—
319	C₂²⋊C₈	—	2	4	no	—
320	#97	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₁₉	#22411	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
324	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
325	#41	—	4	8	no	—
326	#41	—	4	8	no	—
327	#41	—	4	8	no	—
328	#41	—	4	8	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
340	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
341	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
342	C₂×D₄	#41×C₁₉	1	2	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	4	8	no	—
367	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	4	8	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
384	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
385	C₄²	C₂×D₄×C₁₉	1	2	yes	—
386	C₄²	C₂×D₄×C₁₉	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
396	C₂³	C₄×D₄×C₁₉	1	4	yes	—
397	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
398	Q₈	—	4	4	no	—
399	Q₈	—	4	4	no	—
400	D₄	—	2	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	16	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
425	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
426	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
429	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
431	C₈	—	2	4	no	—
432	C₈	—	4	4	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
447	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
448	C₂²	C₁₉×#518	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	2	no	—
455	C₄	C₁₉×#413	1	2	yes	complemented
456	C₄	D₄²×C₁₉	1	2	yes	—
457	C₄	C₁₉×#546	1	2	yes	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	4	no	—
461	C₂	—	4	4	no	—
462	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
463	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
464	C₂	C₁₉×#2889	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×#547	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×#1966	C₂	semidirect
5. C₁₉×#1901	C₂	semidirect
6. C₁₉×#1800	C₂	semidirect
7. C₁₉×#1785	C₂	semidirect
8. C₄×C₁₉×#100	C₂	semidirect
85. C₁₉×#100	D₄	semidirect
154. #22411	C₁₉	direct (N × H)
203. D₄×M₁₆	C₂×C₁₉	semidirect
204. C₂×#413	C₂×C₁₉	semidirect
205. #1966	C₂×C₁₉	semidirect
206. #1901	C₂×C₁₉	semidirect
207. #1800	C₂×C₁₉	semidirect
208. #1785	C₂×C₁₉	semidirect
209. C₄×#100	C₂×C₁₉	semidirect
231. C₄×C₁₉	#413	semidirect
317. #100	D₄×C₁₉	semidirect
322. C₁₉	#22411	direct (N × H)
455. 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×#547	2
D₄×M₁₆×C₁₉	2
C₂×C₁₉×#413	2
C₁₉×#1966	2
C₁₉×#1901	2
C₁₉×#1800	2
C₁₉×#1785	2
C₄×C₁₉×#100	2
#22411	19

Subgroups — C19×#22411 #18028370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22411 #18028370