Subgroups — C₁₉×#22479 #18028438

Order 4864.

1322 conjugacy classes of subgroups.

The subgroup lattice has 452 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	C₁₉×#1997	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1900	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1821	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#343	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₁₉	C₄	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	C₄	1	2	yes	—
17	C₂×C₁₉×#121	C₂²	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	C₂²	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	C₂×C₁₉×#100	C₂²	1	2	yes	—
26	C₂×C₁₉×#100	C₂²	1	2	yes	—
27	C₁₉×#407	C₂²	1	4	yes	—
28	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#343	C₂²	1	4	yes	—
30	C₁₉×#343	C₂²	1	4	yes	—
31	C₁₉×#343	C₂²	1	1	yes	characteristic
32	C₁₉×#343	C₂²	1	2	yes	—
33	C₁₉×#343	C₂²	1	1	yes	characteristic
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	4	8	no	—
38	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
41	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	—	2	8	no	—
47	C₂×M₁₆×C₁₉	—	4	4	no	—
48	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
50	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	—	2	4	no	—
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×#123	—	2	8	no	—
55	C₁₉×#123	—	2	8	no	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×#121	—	2	4	no	—
59	C₁₉×#121	—	2	4	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	—	2	2	no	—
62	C₄×D₄×C₁₉	D₄	1	2	yes	—
63	C₄×D₄×C₁₉	D₄	1	4	yes	—
64	C₄×D₄×C₁₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
74	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×C₄⋊C₈	—	2	2	no	—
77	C₁₉×C₄⋊C₈	—	2	2	no	—
78	C₁₉×#100	—	2	4	no	—
79	C₁₉×#100	—	4	2	no	—
80	C₁₉×C₂²⋊C₈	—	2	4	no	—
81	C₁₉×C₂²⋊C₈	—	2	4	no	—
82	C₁₉×#97	—	2	2	no	—
83	C₄×C₈×C₁₉	—	2	2	no	—
84	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
86	#41×C₁₉	—	4	16	no	—
87	#41×C₁₉	—	4	8	no	—
88	#41×C₁₉	—	4	8	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	4	4	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	4	8	no	—
100	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
101	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	4	4	no	—
111	C₂²×C₄×C₁₉	—	4	8	no	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₁₉	—	2	2	no	—
121	M₁₆×C₁₉	—	2	4	no	—
122	M₁₆×C₁₉	—	2	2	no	—
123	M₁₆×C₁₉	—	2	4	no	—
124	M₁₆×C₁₉	—	2	2	no	—
125	M₁₆×C₁₉	—	4	8	no	—
126	M₁₆×C₁₉	#41	1	4	yes	complemented
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	4	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	4	8	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₁₉	—	2	4	no	—
138	C₂²⋊C₄×C₁₉	—	2	8	no	—
139	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
140	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
141	C₄²×C₁₉	C₂×D₄	1	2	yes	—
142	C₄²×C₁₉	C₂×D₄	1	2	yes	—
143	#22479	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
156	Q₈×C₁₉	—	4	4	no	—
157	Q₈×C₁₉	—	4	4	no	—
158	D₄×C₁₉	—	2	4	no	—
159	D₄×C₁₉	—	2	2	no	—
160	D₄×C₁₉	—	4	8	no	—
161	D₄×C₁₉	—	4	8	no	—
162	D₄×C₁₉	—	4	2	no	—
163	D₄×C₁₉	—	4	2	no	—
164	D₄×C₁₉	#100	1	4	yes	complemented
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	8	no	—
177	C₂×C₄×C₁₉	—	4	8	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
187	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₁₉	—	2	4	no	—
190	C₈×C₁₉	—	4	4	no	—
191	C₈×C₁₉	—	4	2	no	—
192	C₂×#547	C₂×C₁₉	1	1	yes	characteristic
193	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
194	#1997	C₂×C₁₉	1	2	yes	complemented
195	#1900	C₂×C₁₉	1	4	yes	complemented
196	#1821	C₂×C₁₉	1	2	yes	complemented
197	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
198	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
199	C₂×#343	C₂×C₁₉	1	2	yes	complemented
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	2	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	4	4	no	—
208	C₂²×C₁₉	—	4	4	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	8	2	no	—
213	C₂²×C₁₉	—	8	2	no	—
214	C₂²×C₁₉	C₂×#100	1	4	yes	—
215	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
217	C₂²×C₁₉	#520	1	1	yes	characteristic
218	C₄×C₁₉	—	2	4	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	4	no	—
223	C₄×C₁₉	C₂×#100	1	2	yes	—
224	C₄×C₁₉	#546	1	2	yes	—
225	C₄×C₁₉	#547	1	2	yes	—
226	C₂²×#41	C₄×C₁₉	1	2	yes	—
227	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
228	#547	—	2	2	no	—
229	#547	—	2	4	no	—
230	#547	—	2	2	no	—
231	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#123	C₄×C₁₉	1	4	yes	—
233	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
234	C₂×#121	C₂²×C₁₉	1	2	yes	—
235	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
238	#436	—	2	2	no	—
239	#435	—	2	4	no	—
240	C₈×D₄	—	2	2	no	—
241	#423	C₂²×C₁₉	1	2	yes	—
242	C₂×#100	C₂²×C₁₉	1	2	yes	—
243	C₂×#100	C₂²×C₁₉	1	2	yes	—
244	#407	C₂²×C₁₉	1	4	yes	—
245	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
246	#343	C₂²×C₁₉	1	2	yes	—
247	#343	C₂²×C₁₉	1	1	yes	characteristic
248	#343	C₂²×C₁₉	1	4	yes	—
249	#343	C₂²×C₁₉	1	4	yes	—
250	#343	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	4	no	—
254	C₂×C₁₉	—	4	2	no	—
255	C₂×C₁₉	—	8	2	no	—
256	C₂×C₁₉	#2339	1	1	yes	characteristic
257	C₂×C₁₉	C₂²×#100	1	1	yes	characteristic
258	C₂×C₁₉	#2889	1	1	yes	characteristic
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	4	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	4	8	no	—
263	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
264	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
266	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
268	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	—	2	8	no	—
272	C₂×M₁₆	—	4	4	no	—
273	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
274	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
275	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
276	C₂²×C₈	—	2	4	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	#123	—	2	8	no	—
280	#123	—	2	8	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	#121	—	2	4	no	—
284	#121	—	2	4	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	D₄×C₁₉	1	2	yes	—
288	C₄×D₄	D₄×C₁₉	1	4	yes	—
289	C₄×D₄	D₄×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
300	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	#100	—	2	4	no	—
304	#100	—	4	2	no	—
305	C₂²⋊C₈	—	2	4	no	—
306	C₂²⋊C₈	—	2	4	no	—
307	#97	—	2	2	no	—
308	C₄×C₈	—	2	2	no	—
309	C₁₉	#22479	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
312	#41	—	4	16	no	—
313	#41	—	4	8	no	—
314	#41	—	4	8	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	4	8	no	—
326	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
327	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
328	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	8	no	—
338	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	4	8	no	—
352	M₁₆	#41×C₁₉	1	4	yes	complemented
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	4	8	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
362	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
366	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
367	C₄²	C₂×D₄×C₁₉	1	2	yes	—
368	C₄²	C₂×D₄×C₁₉	1	2	yes	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
380	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
381	Q₈	—	4	4	no	—
382	Q₈	—	4	4	no	—
383	D₄	—	2	4	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	8	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	C₁₉×#100	1	4	yes	complemented
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
411	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
412	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	4	4	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	C₂×C₁₉×#100	1	4	yes	—
432	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
433	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
434	C₂²	C₁₉×#520	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	C₂×C₁₉×#100	1	2	yes	—
441	C₄	C₁₉×#546	1	2	yes	—
442	C₄	C₁₉×#547	1	2	yes	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	4	no	—
446	C₂	—	4	2	no	—
447	C₂	—	8	2	no	—
448	C₂	C₁₉×#2339	1	1	yes	characteristic
449	C₂	C₂²×C₁₉×#100	1	1	yes	characteristic
450	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. C₁₉×#1997	C₂	semidirect
4. C₁₉×#1900	C₂	semidirect
5. C₁₉×#1821	C₂	semidirect
6. C₁₉×#1800	C₂	semidirect
7. C₄×C₁₉×#100	C₂	semidirect
8. C₂×C₁₉×#343	C₂	semidirect
126. M₁₆×C₁₉	#41	semidirect
143. #22479	C₁₉	direct (N × H)
164. D₄×C₁₉	#100	semidirect
193. D₄×M₁₆	C₂×C₁₉	semidirect
194. #1997	C₂×C₁₉	semidirect
195. #1900	C₂×C₁₉	semidirect
196. #1821	C₂×C₁₉	semidirect
197. #1800	C₂×C₁₉	semidirect
198. C₄×#100	C₂×C₁₉	semidirect
199. C₂×#343	C₂×C₁₉	semidirect
309. C₁₉	#22479	direct (N × H)
352. M₁₆	#41×C₁₉	semidirect
389. D₄	C₁₉×#100	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
C₁₉×#1997	2
C₁₉×#1900	2
C₁₉×#1821	2
C₁₉×#1800	2
C₄×C₁₉×#100	2
C₂×C₁₉×#343	2
#22479	19

Subgroups — C19×#22479 #18028438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22479 #18028438