Subgroups — C₁₉×#34403 #18040362

Order 4864.

1898 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2378	C₂	1	4	yes	maximal
3	C₁₉×#2370	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2356	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2347	C₂	1	2	yes	maximal
6	C₁₉×#2346	C₂	1	2	yes	maximal
7	C₁₉×#2332	C₂	1	4	yes	maximal
8	C₁₉×#2331	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2331	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2320	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#533	C₄	1	16	yes	complemented
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#125	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₂×C₁₉×#117	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#391	C₂²	1	8	yes	—
24	C₁₉×#391	C₂²	1	8	yes	—
25	C₁₉×#389	C₂²	1	8	yes	—
26	C₁₉×#389	C₂²	1	4	yes	—
27	C₁₉×#389	C₂²	1	4	yes	—
28	C₁₉×#388	C₂²	1	8	yes	—
29	C₁₉×#388	C₂²	1	8	yes	—
30	C₁₉×#387	C₂²	1	8	yes	—
31	C₁₉×#387	C₂²	1	8	yes	—
32	C₁₉×#387	C₂²	1	8	yes	—
33	C₁₉×#387	C₂²	1	8	yes	—
34	C₁₉×#383	C₂²	1	2	yes	—
35	C₁₉×#383	C₂²	1	2	yes	—
36	C₁₉×#383	C₂²	1	4	yes	—
37	C₁₉×#382	C₂²	1	2	yes	—
38	C₁₉×#382	C₂²	1	2	yes	—
39	C₁₉×#382	C₂²	1	4	yes	—
40	C₁₉×#381	C₂²	1	2	yes	—
41	C₁₉×#381	C₂²	1	2	yes	—
42	C₁₉×#380	C₂²	1	2	yes	—
43	C₁₉×#380	C₂²	1	2	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
50	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₁₉×#376	C₂²	1	2	yes	—
54	C₁₉×#376	C₂²	1	2	yes	—
55	C₁₉×#376	C₂²	1	4	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	—
62	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	—
63	C₁₉×#125	C₂×C₄	1	16	yes	—
64	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
65	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
66	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
67	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
68	C₁₉×#117	C₂×C₄	1	16	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#95	C₂³	1	2	yes	—
95	C₁₉×#95	C₂³	1	4	yes	—
96	C₁₉×#95	C₂³	1	4	yes	—
97	C₁₉×#95	C₂³	1	4	yes	—
98	C₁₉×#95	C₂³	1	4	yes	—
99	C₁₉×#95	C₂³	1	8	yes	—
100	C₁₉×#95	C₂³	1	2	yes	—
101	C₁₉×#95	C₂³	1	4	yes	—
102	C₁₉×#95	C₂³	1	4	yes	—
103	C₁₉×#95	C₂³	1	4	yes	—
104	C₁₉×#95	C₂³	1	8	yes	—
105	C₁₉×#95	C₂³	1	8	yes	—
106	C₁₉×#95	C₂³	1	8	yes	—
107	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂×Q₈×C₁₉	—	4	4	no	—
109	C₂×Q₈×C₁₉	—	4	4	no	—
110	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
111	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	C₄⋊C₄×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	4	8	no	—
131	C₄⋊C₄×C₁₉	—	4	4	no	—
132	C₄⋊C₄×C₁₉	—	4	8	no	—
133	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
134	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
135	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
136	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
137	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
138	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
139	C₂²⋊C₄×C₁₉	—	4	2	no	—
140	C₂²⋊C₄×C₁₉	—	4	4	no	—
141	C₂²⋊C₄×C₁₉	—	4	2	no	—
142	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
143	C₄²×C₁₉	—	2	4	no	—
144	C₄²×C₁₉	—	2	4	no	—
145	C₄²×C₁₉	—	4	4	no	—
146	C₄²×C₁₉	—	4	8	no	—
147	C₄²×C₁₉	—	4	8	no	—
148	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
149	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
150	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
151	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
152	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
153	#34403	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
158	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
159	Q₈×C₁₉	—	4	8	no	—
160	Q₈×C₁₉	—	4	8	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	8	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	8	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	8	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	8	no	—
176	C₂×C₄×C₁₉	—	2	8	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
186	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
187	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
188	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
189	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
190	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
191	#2378	C₂×C₁₉	1	4	yes	—
192	#2370	C₂×C₁₉	1	4	yes	complemented
193	#2356	C₂×C₁₉	1	4	yes	complemented
194	#2347	C₂×C₁₉	1	2	yes	—
195	#2346	C₂×C₁₉	1	2	yes	—
196	#2332	C₂×C₁₉	1	4	yes	—
197	#2331	C₂×C₁₉	1	2	yes	complemented
198	#2331	C₂×C₁₉	1	2	yes	complemented
199	#2320	C₂×C₁₉	1	4	yes	complemented
200	#2283	C₂×C₁₉	1	1	yes	characteristic
201	#2283	C₂×C₁₉	1	1	yes	characteristic
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
208	C₂²×C₁₉	#585	1	2	yes	—
209	C₂²×C₁₉	#585	1	2	yes	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	8	no	—
216	C₄×C₁₉	—	2	8	no	—
217	C₄×C₁₉	—	4	4	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	8	no	—
220	C₄×C₁₉	#519	1	4	yes	—
221	#533	C₄×C₁₉	1	16	yes	complemented
222	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#125	C₂²×C₁₉	1	2	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
227	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
229	C₂×#117	C₂²×C₁₉	1	2	yes	—
230	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
231	#391	C₂²×C₁₉	1	8	yes	—
232	#391	C₂²×C₁₉	1	8	yes	—
233	#389	C₂²×C₁₉	1	8	yes	—
234	#389	C₂²×C₁₉	1	4	yes	—
235	#389	C₂²×C₁₉	1	4	yes	—
236	#388	C₂²×C₁₉	1	8	yes	—
237	#388	C₂²×C₁₉	1	8	yes	—
238	#387	C₂²×C₁₉	1	8	yes	—
239	#387	C₂²×C₁₉	1	8	yes	—
240	#387	C₂²×C₁₉	1	8	yes	—
241	#387	C₂²×C₁₉	1	8	yes	—
242	#383	C₂²×C₁₉	1	2	yes	—
243	#383	C₂²×C₁₉	1	4	yes	—
244	#383	C₂²×C₁₉	1	2	yes	—
245	#382	C₂²×C₁₉	1	2	yes	—
246	#382	C₂²×C₁₉	1	4	yes	—
247	#382	C₂²×C₁₉	1	2	yes	—
248	#381	C₂²×C₁₉	1	2	yes	—
249	#381	C₂²×C₁₉	1	2	yes	—
250	#380	C₂²×C₁₉	1	2	yes	—
251	#380	C₂²×C₁₉	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
254	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
255	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
256	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
257	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
258	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
260	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
261	#376	C₂²×C₁₉	1	4	yes	—
262	#376	C₂²×C₁₉	1	2	yes	—
263	#376	C₂²×C₁₉	1	2	yes	—
264	C₂×C₁₉	—	4	2	no	—
265	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
266	C₂×C₁₉	#3428	1	1	yes	characteristic
267	C₂×C₁₉	#3428	1	1	yes	characteristic
268	C₂×C₁₉	#3565	1	4	yes	—
269	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
270	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
275	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
276	#125	C₂×C₄×C₁₉	1	16	yes	—
277	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
278	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
279	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
280	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
281	#117	C₂×C₄×C₁₉	1	16	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
296	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
297	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
298	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
299	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
300	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
301	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
307	#95	C₂³×C₁₉	1	2	yes	—
308	#95	C₂³×C₁₉	1	4	yes	—
309	#95	C₂³×C₁₉	1	4	yes	—
310	#95	C₂³×C₁₉	1	4	yes	—
311	#95	C₂³×C₁₉	1	4	yes	—
312	#95	C₂³×C₁₉	1	8	yes	—
313	#95	C₂³×C₁₉	1	2	yes	—
314	#95	C₂³×C₁₉	1	4	yes	—
315	#95	C₂³×C₁₉	1	4	yes	—
316	#95	C₂³×C₁₉	1	4	yes	—
317	#95	C₂³×C₁₉	1	8	yes	—
318	#95	C₂³×C₁₉	1	8	yes	—
319	#95	C₂³×C₁₉	1	8	yes	—
320	C₁₉	#34403	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
325	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
331	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
335	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	4	8	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	8	no	—
347	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
348	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
349	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
350	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
351	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
352	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	4	4	no	—
360	C₄²	—	4	8	no	—
361	C₄²	—	4	8	no	—
362	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
363	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
364	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
365	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
366	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
371	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
372	Q₈	—	4	8	no	—
373	Q₈	—	4	8	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
395	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
397	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
398	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
399	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
400	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
401	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
402	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
408	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
409	C₂²	C₁₉×#585	1	2	yes	—
410	C₂²	C₁₉×#585	1	2	yes	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	8	no	—
417	C₄	—	2	8	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	8	no	—
421	C₄	C₁₉×#519	1	4	yes	—
422	C₂	—	4	2	no	—
423	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
424	C₂	C₁₉×#3428	1	1	yes	characteristic
425	C₂	C₁₉×#3428	1	1	yes	characteristic
426	C₂	C₁₉×#3565	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2370	C₂	semidirect
4. C₁₉×#2356	C₂	semidirect
8. C₁₉×#2331	C₂	semidirect
9. C₁₉×#2331	C₂	semidirect
10. C₁₉×#2320	C₂	semidirect
13. C₁₉×#533	C₄	semidirect
153. #34403	C₁₉	direct (N × H)
192. #2370	C₂×C₁₉	semidirect
193. #2356	C₂×C₁₉	semidirect
197. #2331	C₂×C₁₉	semidirect
198. #2331	C₂×C₁₉	semidirect
199. #2320	C₂×C₁₉	semidirect
221. #533	C₄×C₁₉	semidirect
320. C₁₉	#34403	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×#533	2
C₁₉×#2378	2
C₁₉×#2370	2
C₁₉×#2356	2
C₁₉×#2347	2
C₁₉×#2346	2
C₁₉×#2332	2
C₁₉×#2331	2
C₁₉×#2320	2
C₁₉×#2283	2
#34403	19

Subgroups — C19×#34403 #18040362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34403 #18040362