Subgroups — C₁₉×#26233 #18032192

Order 4864.

862 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#485	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2542	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2354	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1873	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	2	yes	—
17	C₁₉×#485	—	2	8	no	—
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#399	—	2	2	no	—
30	C₁₉×#390	—	2	1	no	—
31	C₁₉×#390	—	2	1	no	—
32	C₁₉×#388	—	2	2	no	—
33	C₁₉×#384	—	2	1	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₂²⋊Q₈	—	2	4	no	—
51	C₁₉×C₂²⋊Q₈	—	2	4	no	—
52	C₁₉×C₂²⋊Q₈	—	4	2	no	—
53	C₁₉×C₂²⋊Q₈	—	4	2	no	—
54	C₄×D₄×C₁₉	—	2	2	no	—
55	C₄×D₄×C₁₉	—	2	2	no	—
56	C₁₉×#117	—	2	4	no	—
57	C₁₉×#117	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	—	2	2	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	—	2	4	no	—
80	C₁₉×#106	—	2	2	no	—
81	C₁₉×#106	D₄	1	4	yes	complemented
82	C₁₉×C₄⋊C₈	—	2	2	no	—
83	C₁₉×#103	—	2	4	no	—
84	C₁₉×#103	—	2	4	no	—
85	C₁₉×#103	—	4	2	no	—
86	C₁₉×#103	—	4	2	no	—
87	C₁₉×C₂²⋊C₈	—	2	4	no	—
88	C₁₉×C₂²⋊C₈	—	4	2	no	—
89	C₄×C₈×C₁₉	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	4	4	no	—
137	C₄⋊C₄×C₁₉	—	4	4	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	4	2	no	—
141	C₄⋊C₄×C₁₉	—	8	1	no	—
142	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₁₉	#41	1	2	yes	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	—	4	4	no	—
147	C₂²⋊C₄×C₁₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₉	—	4	4	no	—
149	C₂²⋊C₄×C₁₉	—	8	2	no	—
150	C₄²×C₁₉	—	4	4	no	—
151	C₄²×C₁₉	—	4	2	no	—
152	C₄²×C₁₉	—	4	2	no	—
153	C₄²×C₁₉	#41	1	2	yes	—
154	C₄²×C₁₉	#41	1	2	yes	—
155	#26233	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	2	no	—
163	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	#123	1	2	yes	—
197	C₂×C₄×C₁₉	#123	1	2	yes	—
198	C₂×C₄×C₁₉	#135	1	2	yes	—
199	C₂×C₄×C₁₉	#137	1	2	yes	—
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
206	C₈×C₁₉	—	2	2	no	—
207	C₈×C₁₉	—	4	1	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₂×#485	C₂×C₁₉	1	2	yes	complemented
210	#2542	C₂×C₁₉	1	1	yes	characteristic
211	#2354	C₂×C₁₉	1	1	yes	characteristic
212	#2036	C₂×C₁₉	1	2	yes	complemented
213	#2035	C₂×C₁₉	1	2	yes	complemented
214	#1981	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1956	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1954	C₂×C₁₉	1	1	yes	characteristic
217	#1947	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1873	C₂×C₁₉	1	2	yes	complemented
219	C₄×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
228	C₂²×C₁₉	D₄²	1	1	yes	characteristic
229	C₂²×C₁₉	#546	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
231	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
232	C₂²×C₁₉	#577	1	1	yes	characteristic
233	C₂²×C₁₉	#578	1	1	yes	characteristic
234	C₄×C₁₉	—	2	2	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	—	8	2	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	#485	1	4	yes	complemented
243	C₄×C₁₉	#532	1	1	yes	characteristic
244	C₄×C₁₉	#540	1	1	yes	characteristic
245	C₄×C₁₉	#550	1	1	yes	characteristic
246	C₄×C₁₉	#559	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
249	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
250	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₉	1	2	yes	—
252	#485	—	2	8	no	—
253	C₂×#107	C₂²×C₁₉	1	2	yes	—
254	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×#103	C₂²×C₁₉	1	2	yes	—
258	C₂×#103	C₂²×C₁₉	1	2	yes	—
259	C₂×#103	C₂²×C₁₉	1	2	yes	—
260	C₂×#103	C₂²×C₁₉	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
264	#399	—	2	2	no	—
265	#390	—	2	1	no	—
266	#390	—	2	1	no	—
267	#388	—	2	2	no	—
268	#384	—	2	1	no	—
269	#384	C₂²×C₁₉	1	1	yes	characteristic
270	#380	C₂²×C₁₉	1	2	yes	—
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
274	#340	C₂²×C₁₉	1	1	yes	characteristic
275	#340	C₂²×C₁₉	1	2	yes	—
276	#340	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×C₁₉	—	8	2	no	—
278	C₂×C₁₉	#2445	1	1	yes	characteristic
279	C₂×C₁₉	C₂×#485	1	1	yes	characteristic
280	C₂×C₁₉	#3097	1	1	yes	characteristic
281	C₂×C₁₉	#3276	1	1	yes	characteristic
282	C₂×C₁₉	#3284	1	1	yes	characteristic
283	C₂×C₁₉	#3302	1	1	yes	characteristic
284	C₂×C₁₉	#3329	1	1	yes	characteristic
285	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
286	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	4	2	no	—
296	C₂²⋊Q₈	—	4	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	#117	—	2	4	no	—
300	#117	—	4	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
322	#107	—	2	4	no	—
323	#106	—	2	2	no	—
324	#106	D₄×C₁₉	1	4	yes	complemented
325	C₄⋊C₈	—	2	2	no	—
326	#103	—	2	4	no	—
327	#103	—	2	4	no	—
328	#103	—	4	2	no	—
329	#103	—	4	2	no	—
330	C₂²⋊C₈	—	2	4	no	—
331	C₂²⋊C₈	—	4	2	no	—
332	C₄×C₈	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	1	no	—
335	#95	—	2	1	no	—
336	C₁₉	#26233	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	8	1	no	—
386	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
387	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
388	C₄⋊C₄	#41×C₁₉	1	2	yes	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₄²	—	4	4	no	—
395	C₄²	—	4	2	no	—
396	C₄²	—	4	2	no	—
397	C₄²	#41×C₁₉	1	2	yes	—
398	C₄²	#41×C₁₉	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	4	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	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	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	C₁₉×#123	1	2	yes	—
440	C₂×C₄	C₁₉×#123	1	2	yes	—
441	C₂×C₄	C₁₉×#135	1	2	yes	—
442	C₂×C₄	C₁₉×#137	1	2	yes	—
443	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
447	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
460	C₂²	D₄²×C₁₉	1	1	yes	characteristic
461	C₂²	C₁₉×#546	1	1	yes	characteristic
462	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
463	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
464	C₂²	C₁₉×#577	1	1	yes	characteristic
465	C₂²	C₁₉×#578	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₁₉×#485	1	4	yes	complemented
475	C₄	C₁₉×#532	1	1	yes	characteristic
476	C₄	C₁₉×#540	1	1	yes	characteristic
477	C₄	C₁₉×#550	1	1	yes	characteristic
478	C₄	C₁₉×#559	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	C₁₉×#2445	1	1	yes	characteristic
481	C₂	C₂×C₁₉×#485	1	1	yes	characteristic
482	C₂	C₁₉×#3097	1	1	yes	characteristic
483	C₂	C₁₉×#3276	1	1	yes	characteristic
484	C₂	C₁₉×#3284	1	1	yes	characteristic
485	C₂	C₁₉×#3302	1	1	yes	characteristic
486	C₂	C₁₉×#3329	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#485	C₂	semidirect
4. C₁₉×#2036	C₂	semidirect
5. C₁₉×#2035	C₂	semidirect
6. C₁₉×#1981	C₂	semidirect
7. C₁₉×#1956	C₂	semidirect
9. C₁₉×#1947	C₂	semidirect
10. C₁₉×#1873	C₂	semidirect
11. C₄×C₁₉×#106	C₂	semidirect
81. C₁₉×#106	D₄	semidirect
155. #26233	C₁₉	direct (N × H)
209. C₂×#485	C₂×C₁₉	semidirect
212. #2036	C₂×C₁₉	semidirect
213. #2035	C₂×C₁₉	semidirect
214. #1981	C₂×C₁₉	semidirect
215. #1956	C₂×C₁₉	semidirect
217. #1947	C₂×C₁₉	semidirect
218. #1873	C₂×C₁₉	semidirect
219. C₄×#106	C₂×C₁₉	semidirect
242. C₄×C₁₉	#485	semidirect
324. #106	D₄×C₁₉	semidirect
336. C₁₉	#26233	direct (N × H)
474. C₄	C₁₉×#485	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#485	2
C₁₉×#2542	2
C₁₉×#2354	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#1981	2
C₁₉×#1956	2
C₁₉×#1954	2
C₁₉×#1947	2
C₁₉×#1873	2
C₄×C₁₉×#106	2
#26233	19

Subgroups — C19×#26233 #18032192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26233 #18032192