Subgroups — C₁₉×#21422 #18027381

Order 4864.

1318 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#538	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2312	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1996	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1964	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1898	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₉×#99	C₂	1	4	yes	maximal, complemented
8	C₁₉×#538	—	2	4	no	—
9	C₁₉×#538	—	2	4	no	—
10	C₂×C₁₉×#126	C₄	1	2	yes	complemented
11	C₂×C₁₉×#124	C₄	1	2	yes	complemented
12	C₂×C₁₉×#123	C₄	1	2	yes	complemented
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#121	C₄	1	2	yes	complemented
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#120	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#99	C₂²	1	8	yes	—
21	C₁₉×#388	—	2	4	no	—
22	C₁₉×#380	C₂²	1	2	yes	—
23	C₁₉×#379	C₂²	1	2	yes	—
24	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#342	C₂²	1	8	yes	—
29	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
31	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
34	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₉	—	2	2	no	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	complemented
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₁₉×#126	—	2	8	no	—
40	C₁₉×#124	—	2	8	no	—
41	C₁₉×#123	—	2	8	no	—
42	C₁₉×C₂²⋊Q₈	—	2	2	no	—
43	C₁₉×C₂²⋊Q₈	—	2	2	no	—
44	C₁₉×#121	—	2	2	no	—
45	C₁₉×#121	—	2	2	no	—
46	C₁₉×#121	—	2	8	no	—
47	C₁₉×#120	—	2	4	no	—
48	C₁₉×#120	—	2	4	no	—
49	C₄×D₄×C₁₉	—	2	4	no	—
50	C₄×D₄×C₁₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
65	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
66	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
68	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	—	2	2	no	—
73	C₂×C₄²×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	complemented
75	C₁₉×#99	—	2	16	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	4	no	—
81	C₂⁴×C₁₉	—	8	1	no	—
82	C₂⁴×C₁₉	—	8	1	no	—
83	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
84	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
86	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
87	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	8	1	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	8	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	—	8	2	no	—
97	C₂×D₄×C₁₉	—	8	2	no	—
98	C₂×D₄×C₁₉	—	8	1	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	8	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	8	1	no	—
104	C₂²×C₄×C₁₉	—	8	1	no	—
105	C₂²×C₄×C₁₉	—	8	2	no	—
106	C₂²×C₄×C₁₉	—	8	2	no	—
107	C₂²×C₄×C₁₉	—	8	2	no	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	8	2	no	—
123	C₂²⋊C₄×C₁₉	—	2	8	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	2	4	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₂²⋊C₄×C₁₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	2	8	no	—
132	C₂²⋊C₄×C₁₉	—	8	2	no	—
133	C₂²⋊C₄×C₁₉	—	8	2	no	—
134	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
135	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
136	C₂²⋊C₄×C₁₉	#41	1	8	yes	—
137	C₄²×C₁₉	—	2	4	no	—
138	C₄²×C₁₉	—	8	2	no	—
139	C₄²×C₁₉	—	8	2	no	—
140	C₄²×C₁₉	—	8	2	no	—
141	#21422	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	4	no	—
145	C₂³×C₁₉	—	2	4	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	4	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	8	8	no	—
159	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
161	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
162	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
163	C₂³×C₁₉	C₂×#41	1	4	yes	—
164	Q₈×C₁₉	—	8	2	no	—
165	D₄×C₁₉	—	4	4	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	8	2	no	—
168	D₄×C₁₉	—	8	4	no	—
169	D₄×C₁₉	—	8	4	no	—
170	C₂×C₄×C₁₉	—	2	2	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	—	2	8	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	8	4	no	—
190	C₂×C₄×C₁₉	—	8	8	no	—
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
192	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×#538	C₂×C₁₉	1	1	yes	characteristic
195	#2312	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#2273	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#1996	C₂×C₁₉	1	2	yes	complemented
198	#1964	C₂×C₁₉	1	2	yes	complemented
199	#1898	C₂×C₁₉	1	4	yes	complemented
200	C₄×#99	C₂×C₁₉	1	4	yes	complemented
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	4	4	no	—
211	C₂²×C₁₉	—	4	4	no	—
212	C₂²×C₁₉	—	4	4	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	8	4	no	—
217	C₂²×C₁₉	—	8	4	no	—
218	C₂²×C₁₉	—	8	4	no	—
219	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×C₁₉	C₄×#41	1	2	yes	—
221	C₂²×C₁₉	#525	1	2	yes	—
222	C₂²×C₁₉	#532	1	2	yes	—
223	C₄×C₁₉	—	2	4	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	4	8	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	8	4	no	—
231	#538	—	2	4	no	—
232	#538	—	2	4	no	—
233	C₂×#126	C₄×C₁₉	1	2	yes	complemented
234	C₂×#124	C₄×C₁₉	1	2	yes	complemented
235	C₂×#123	C₄×C₁₉	1	2	yes	complemented
236	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#121	C₄×C₁₉	1	2	yes	complemented
238	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#120	C₂²×C₁₉	1	2	yes	—
240	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×#99	C₂²×C₁₉	1	8	yes	—
244	#388	—	2	4	no	—
245	#380	C₂²×C₁₉	1	2	yes	—
246	#379	C₂²×C₁₉	1	2	yes	—
247	C₄×C₂²⋊C₄	—	2	4	no	—
248	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
251	#342	C₂²×C₁₉	1	8	yes	—
252	C₂×C₁₉	—	2	2	no	—
253	C₂×C₁₉	—	2	2	no	—
254	C₂×C₁₉	—	2	2	no	—
255	C₂×C₁₉	—	4	4	no	—
256	C₂×C₁₉	—	8	2	no	—
257	C₂×C₁₉	#2297	1	1	yes	characteristic
258	C₂×C₁₉	#2883	1	1	yes	characteristic
259	C₂×C₁₉	#2883	1	1	yes	characteristic
260	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
261	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
263	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
264	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
265	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	complemented
268	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
270	#126	—	2	8	no	—
271	#124	—	2	8	no	—
272	#123	—	2	8	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	#121	—	2	2	no	—
276	#121	—	2	2	no	—
277	#121	—	2	8	no	—
278	#120	—	2	4	no	—
279	#120	—	2	4	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
284	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
285	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
286	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
292	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
296	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
297	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
298	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	complemented
306	#99	—	2	16	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	C₁₉	#21422	1	1	yes	characteristic, direct product factor, Sylow
312	C₂⁴	—	2	4	no	—
313	C₂⁴	—	8	1	no	—
314	C₂⁴	—	8	1	no	—
315	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
316	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
317	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
318	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
319	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	8	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	8	2	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂×D₄	—	8	1	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	8	1	no	—
336	C₂²×C₄	—	8	1	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	8	2	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
367	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
368	C₂²⋊C₄	#41×C₁₉	1	8	yes	—
369	C₄²	—	2	4	no	—
370	C₄²	—	8	2	no	—
371	C₄²	—	8	2	no	—
372	C₄²	—	8	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	8	8	no	—
390	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
391	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
392	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
393	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
394	C₂³	C₂×#41×C₁₉	1	4	yes	—
395	Q₈	—	8	2	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	4	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	4	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	8	4	no	—
421	C₂×C₄	—	8	8	no	—
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
424	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	8	4	no	—
441	C₂²	—	8	4	no	—
442	C₂²	—	8	4	no	—
443	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
444	C₂²	C₄×#41×C₁₉	1	2	yes	—
445	C₂²	C₁₉×#525	1	2	yes	—
446	C₂²	C₁₉×#532	1	2	yes	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	8	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	4	no	—
455	C₂	—	2	2	no	—
456	C₂	—	2	2	no	—
457	C₂	—	2	2	no	—
458	C₂	—	4	4	no	—
459	C₂	—	8	2	no	—
460	C₂	C₁₉×#2297	1	1	yes	characteristic
461	C₂	C₁₉×#2883	1	1	yes	characteristic
462	C₂	C₁₉×#2883	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#538	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2312	C₂	semidirect
3. C₁₉×#2273	C₂	semidirect
4. C₁₉×#1996	C₂	semidirect
5. C₁₉×#1964	C₂	semidirect
6. C₁₉×#1898	C₂	semidirect
7. C₄×C₁₉×#99	C₂	semidirect
10. C₂×C₁₉×#126	C₄	semidirect
11. C₂×C₁₉×#124	C₄	semidirect
12. C₂×C₁₉×#123	C₄	semidirect
14. C₂×C₁₉×#121	C₄	semidirect
30. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
33. C₂²×D₄×C₁₉	C₂×C₄	semidirect
36. C₂³×C₄×C₁₉	C₂×C₄	semidirect
52. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
53. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
54. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
55. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
64. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
65. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
74. C₂×C₄²×C₁₉	C₂×C₄	semidirect
141. #21422	C₁₉	direct (N × H)
195. #2312	C₂×C₁₉	semidirect
196. #2273	C₂×C₁₉	semidirect
197. #1996	C₂×C₁₉	semidirect
198. #1964	C₂×C₁₉	semidirect
199. #1898	C₂×C₁₉	semidirect
200. C₄×#99	C₂×C₁₉	semidirect
233. C₂×#126	C₄×C₁₉	semidirect
234. C₂×#124	C₄×C₁₉	semidirect
235. C₂×#123	C₄×C₁₉	semidirect
237. C₂×#121	C₄×C₁₉	semidirect
261. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
264. C₂²×D₄	C₂×C₄×C₁₉	semidirect
267. C₂³×C₄	C₂×C₄×C₁₉	semidirect
283. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
284. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
285. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
286. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
295. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
296. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
305. C₂×C₄²	C₂×C₄×C₁₉	semidirect
311. C₁₉	#21422	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#538	2
C₁₉×#2312	2
C₁₉×#2273	2
C₁₉×#1996	2
C₁₉×#1964	2
C₁₉×#1898	2
C₄×C₁₉×#99	2
#21422	19

Subgroups — C19×#21422 #18027381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21422 #18027381