Subgroups — C₁₉×#34948 #18040907

Order 4864.

1778 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2571	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2570	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2569	C₂	1	4	yes	maximal
4	C₁₉×#2552	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2442	C₂	1	4	yes	maximal
6	C₁₉×#2402	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₉×#125	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2296	C₂	1	2	yes	maximal
9	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2285	C₂	1	2	yes	maximal
11	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₉×#125	C₂²	1	4	yes	—
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#400	C₂²	1	8	yes	—
21	C₁₉×#400	C₂²	1	8	yes	—
22	C₁₉×#398	C₂²	1	8	yes	—
23	C₁₉×#398	C₂²	1	8	yes	—
24	C₁₉×#389	C₂²	1	4	yes	—
25	C₁₉×#389	C₂²	1	4	yes	—
26	C₁₉×#389	C₂²	1	4	yes	—
27	C₁₉×#389	C₂²	1	4	yes	—
28	C₁₉×#387	C₂²	1	8	yes	—
29	C₁₉×#387	C₂²	1	8	yes	—
30	C₁₉×#385	C₂²	1	8	yes	—
31	C₁₉×#384	C₂²	1	4	yes	—
32	C₁₉×#384	C₂²	1	2	yes	—
33	C₁₉×#382	C₂²	1	4	yes	—
34	C₁₉×#382	C₂²	1	2	yes	—
35	C₁₉×#382	C₂²	1	4	yes	—
36	C₁₉×#380	C₂²	1	2	yes	—
37	C₁₉×#380	C₂²	1	8	yes	—
38	C₁₉×#380	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
52	C₁₉×#376	C₂²	1	2	yes	—
53	C₂×C₁₉×#95	C₂²	1	2	yes	—
54	C₄³×C₁₉	C₂²	1	2	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×#125	—	2	16	no	—
60	C₁₉×#117	—	2	4	no	—
61	C₁₉×#117	—	2	4	no	—
62	C₁₉×#117	—	2	8	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	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	8	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₄²×C₁₉	—	2	8	no	—
80	C₂×C₄²×C₁₉	Q₈	1	8	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	2	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	4	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	4	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	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×#95	C₂³	1	4	yes	—
94	C₁₉×#95	C₂³	1	2	yes	—
95	C₁₉×#95	C₂³	1	2	yes	—
96	C₁₉×#95	C₂³	1	4	yes	—
97	C₁₉×#95	C₂³	1	4	yes	—
98	C₁₉×#95	C₂³	1	8	yes	—
99	C₁₉×#95	C₂³	1	4	yes	—
100	C₁₉×#95	C₂³	1	8	yes	—
101	C₁₉×#95	C₂³	1	4	yes	—
102	C₁₉×#95	C₂³	1	8	yes	—
103	C₁₉×#95	C₂³	1	8	yes	—
104	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	8	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	4	no	—
110	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
111	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₁₉	#41	1	4	yes	—
114	C₂²×C₄×C₁₉	#41	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	C₄⋊C₄×C₁₉	—	2	8	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	2	16	no	—
132	C₄⋊C₄×C₁₉	—	2	16	no	—
133	C₄⋊C₄×C₁₉	—	2	8	no	—
134	C₄⋊C₄×C₁₉	—	4	8	no	—
135	C₄⋊C₄×C₁₉	—	4	4	no	—
136	C₄⋊C₄×C₁₉	—	4	8	no	—
137	C₄⋊C₄×C₁₉	#41	1	8	yes	—
138	C₂²⋊C₄×C₁₉	—	2	4	no	—
139	C₂²⋊C₄×C₁₉	—	2	8	no	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₄²×C₁₉	—	2	4	no	—
142	C₄²×C₁₉	—	2	8	no	—
143	C₄²×C₁₉	—	2	4	no	—
144	C₄²×C₁₉	—	2	4	no	—
145	C₄²×C₁₉	—	2	4	no	—
146	C₄²×C₁₉	—	2	8	no	—
147	C₄²×C₁₉	—	2	8	no	—
148	C₄²×C₁₉	—	4	4	no	—
149	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
150	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
151	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
152	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
153	#34948	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	C₂²×Q₈	1	2	yes	—
157	C₂³×C₁₉	C₂×#41	1	2	yes	—
158	C₂³×C₁₉	C₂×#41	1	2	yes	—
159	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	8	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	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	4	no	—
176	C₂×C₄×C₁₉	—	2	8	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	16	no	—
180	C₂×C₄×C₁₉	#125	1	16	yes	complemented
181	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
182	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
183	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
184	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
186	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
188	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
193	#2571	C₂×C₁₉	1	2	yes	complemented
194	#2570	C₂×C₁₉	1	4	yes	complemented
195	#2569	C₂×C₁₉	1	4	yes	—
196	#2552	C₂×C₁₉	1	2	yes	complemented
197	#2442	C₂×C₁₉	1	4	yes	—
198	#2402	C₂×C₁₉	1	4	yes	complemented
199	C₄×#125	C₂×C₁₉	1	4	yes	complemented
200	#2296	C₂×C₁₉	1	2	yes	—
201	#2285	C₂×C₁₉	1	2	yes	—
202	#2285	C₂×C₁₉	1	1	yes	characteristic
203	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
204	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	C₂×#125	1	4	yes	—
210	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
211	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
212	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
213	C₂²×C₁₉	C₂²×#41	1	2	yes	—
214	C₂²×C₁₉	#585	1	2	yes	—
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	2	8	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	—	4	8	no	—
223	C₄×C₁₉	C₂×#125	1	4	yes	—
224	C₄×C₁₉	C₂×#125	1	4	yes	—
225	C₄×C₁₉	#533	1	4	yes	—
226	C₂×#125	C₂²×C₁₉	1	4	yes	—
227	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#117	C₂²×C₁₉	1	2	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
231	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
232	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
233	#400	C₂²×C₁₉	1	8	yes	—
234	#400	C₂²×C₁₉	1	8	yes	—
235	#398	C₂²×C₁₉	1	8	yes	—
236	#398	C₂²×C₁₉	1	8	yes	—
237	#389	C₂²×C₁₉	1	4	yes	—
238	#389	C₂²×C₁₉	1	4	yes	—
239	#389	C₂²×C₁₉	1	4	yes	—
240	#389	C₂²×C₁₉	1	4	yes	—
241	#387	C₂²×C₁₉	1	8	yes	—
242	#387	C₂²×C₁₉	1	8	yes	—
243	#385	C₂²×C₁₉	1	8	yes	—
244	#384	C₂²×C₁₉	1	4	yes	—
245	#384	C₂²×C₁₉	1	2	yes	—
246	#382	C₂²×C₁₉	1	4	yes	—
247	#382	C₂²×C₁₉	1	2	yes	—
248	#382	C₂²×C₁₉	1	4	yes	—
249	#380	C₂²×C₁₉	1	2	yes	—
250	#380	C₂²×C₁₉	1	8	yes	—
251	#380	C₂²×C₁₉	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
254	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	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×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
260	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
261	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
262	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
264	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
265	#376	C₂²×C₁₉	1	2	yes	—
266	C₂×#95	C₂²×C₁₉	1	2	yes	—
267	C₄³	C₂²×C₁₉	1	2	yes	—
268	C₂×C₁₉	—	2	4	no	—
269	C₂×C₁₉	C₂²×#125	1	1	yes	characteristic
270	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
271	C₂×C₁₉	#3458	1	1	yes	characteristic
272	C₂×C₁₉	#3475	1	2	yes	—
273	C₂×C₁₉	#3480	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
275	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	#125	—	2	16	no	—
279	#117	—	2	4	no	—
280	#117	—	2	4	no	—
281	#117	—	2	8	no	—
282	C₂×C₄⋊C₄	—	2	8	no	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
298	C₂×C₄²	—	2	8	no	—
299	C₂×C₄²	Q₈×C₁₉	1	8	yes	—
300	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
301	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
304	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
305	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
307	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
308	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
312	#95	C₂³×C₁₉	1	4	yes	—
313	#95	C₂³×C₁₉	1	2	yes	—
314	#95	C₂³×C₁₉	1	2	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	4	yes	—
319	#95	C₂³×C₁₉	1	8	yes	—
320	#95	C₂³×C₁₉	1	4	yes	—
321	#95	C₂³×C₁₉	1	8	yes	—
322	#95	C₂³×C₁₉	1	8	yes	—
323	C₁₉	#34948	1	1	yes	characteristic, direct product factor, Sylow
324	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
331	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
332	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
333	C₂²×C₄	#41×C₁₉	1	4	yes	—
334	C₂²×C₄	#41×C₁₉	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	16	no	—
352	C₄⋊C₄	—	2	16	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	4	8	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	8	no	—
357	C₄⋊C₄	#41×C₁₉	1	8	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	8	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	8	no	—
367	C₄²	—	2	8	no	—
368	C₄²	—	4	4	no	—
369	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
370	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
371	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
372	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
376	C₂³	C₂×#41×C₁₉	1	2	yes	—
377	C₂³	C₂×#41×C₁₉	1	2	yes	—
378	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	C₁₉×#125	1	16	yes	complemented
400	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
401	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
402	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
403	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
404	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
405	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
406	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
407	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
408	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
409	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
410	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
411	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	C₂×C₁₉×#125	1	4	yes	—
417	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
418	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
419	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
420	C₂²	C₂²×#41×C₁₉	1	2	yes	—
421	C₂²	C₁₉×#585	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	8	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	8	no	—
430	C₄	C₂×C₁₉×#125	1	4	yes	—
431	C₄	C₂×C₁₉×#125	1	4	yes	—
432	C₄	C₁₉×#533	1	4	yes	—
433	C₂	—	2	4	no	—
434	C₂	C₂²×C₁₉×#125	1	1	yes	characteristic
435	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
436	C₂	C₁₉×#3458	1	1	yes	characteristic
437	C₂	C₁₉×#3475	1	2	yes	—
438	C₂	C₁₉×#3480	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2571	C₂	semidirect
2. C₁₉×#2570	C₂	semidirect
4. C₁₉×#2552	C₂	semidirect
6. C₁₉×#2402	C₂	semidirect
7. C₄×C₁₉×#125	C₂	semidirect
153. #34948	C₁₉	direct (N × H)
180. C₂×C₄×C₁₉	#125	semidirect
193. #2571	C₂×C₁₉	semidirect
194. #2570	C₂×C₁₉	semidirect
196. #2552	C₂×C₁₉	semidirect
198. #2402	C₂×C₁₉	semidirect
199. C₄×#125	C₂×C₁₉	semidirect
323. C₁₉	#34948	direct (N × H)
399. C₂×C₄	C₁₉×#125	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2571	2
C₁₉×#2570	2
C₁₉×#2569	2
C₁₉×#2552	2
C₁₉×#2442	2
C₁₉×#2402	2
C₄×C₁₉×#125	2
C₁₉×#2296	2
C₁₉×#2285	2
C₄×C₁₉×#117	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#34948	19

Subgroups — C19×#34948 #18040907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34948 #18040907