Subgroups — C₁₉×#34815 #18040774

Order 4864.

1778 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2509	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2508	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2507	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2506	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2505	C₂	1	4	yes	maximal
6	C₁₉×#2473	C₂	1	4	yes	maximal
7	C₁₉×#2402	C₂	1	4	yes	maximal, complemented
8	C₄×C₁₉×#125	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#125	C₂²	1	4	yes	—
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#400	C₂²	1	4	yes	—
26	C₁₉×#400	C₂²	1	4	yes	—
27	C₁₉×#400	C₂²	1	4	yes	—
28	C₁₉×#400	C₂²	1	4	yes	—
29	C₁₉×#398	C₂²	1	4	yes	—
30	C₁₉×#398	C₂²	1	4	yes	—
31	C₁₉×#398	C₂²	1	4	yes	—
32	C₁₉×#398	C₂²	1	4	yes	—
33	C₁₉×#389	C₂²	1	4	yes	—
34	C₁₉×#389	C₂²	1	4	yes	—
35	C₁₉×#389	C₂²	1	2	yes	—
36	C₁₉×#389	C₂²	1	2	yes	—
37	C₁₉×#389	C₂²	1	2	yes	—
38	C₁₉×#389	C₂²	1	2	yes	—
39	C₁₉×#389	C₂²	1	2	yes	—
40	C₁₉×#389	C₂²	1	2	yes	—
41	C₁₉×#389	C₂²	1	2	yes	—
42	C₁₉×#389	C₂²	1	2	yes	—
43	C₁₉×#387	C₂²	1	4	yes	—
44	C₁₉×#387	C₂²	1	4	yes	—
45	C₁₉×#387	C₂²	1	4	yes	—
46	C₁₉×#387	C₂²	1	4	yes	—
47	C₁₉×#385	C₂²	1	2	yes	—
48	C₁₉×#385	C₂²	1	2	yes	—
49	C₁₉×#385	C₂²	1	4	yes	—
50	C₁₉×#385	C₂²	1	4	yes	—
51	C₁₉×#385	C₂²	1	2	yes	—
52	C₁₉×#385	C₂²	1	2	yes	—
53	C₁₉×#384	C₂²	1	1	yes	characteristic
54	C₁₉×#384	C₂²	1	1	yes	characteristic
55	C₁₉×#382	C₂²	1	4	yes	—
56	C₁₉×#382	C₂²	1	1	yes	characteristic
57	C₁₉×#382	C₂²	1	1	yes	characteristic
58	C₁₉×#380	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
64	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
72	C₁₉×#376	C₂²	1	2	yes	—
73	C₂×C₁₉×#95	C₂²	1	2	yes	—
74	C₄³×C₁₉	C₂²	1	2	yes	—
75	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#125	—	2	16	no	—
81	C₁₉×#117	—	2	4	no	—
82	C₁₉×#117	—	2	4	no	—
83	C₁₉×#117	—	2	4	no	—
84	C₁₉×#117	Q₈	1	8	yes	—
85	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₉	—	2	4	no	—
111	C₂×C₄²×C₁₉	—	2	4	no	—
112	C₂×C₄²×C₁₉	—	2	4	no	—
113	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
114	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
127	C₁₉×#95	C₂³	1	2	yes	—
128	C₁₉×#95	C₂³	1	2	yes	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₁₉×#95	C₂³	1	2	yes	—
131	C₁₉×#95	C₂³	1	4	yes	—
132	C₁₉×#95	C₂³	1	4	yes	—
133	C₁₉×#95	C₂³	1	4	yes	—
134	C₁₉×#95	C₂³	1	4	yes	—
135	C₁₉×#95	C₂³	1	4	yes	—
136	C₁₉×#95	C₂³	1	4	yes	—
137	C₁₉×#95	C₂³	1	4	yes	—
138	C₁₉×#95	C₂³	1	4	yes	—
139	C₁₉×#95	C₂³	1	4	yes	—
140	C₁₉×#95	C₂³	1	4	yes	—
141	C₁₉×#95	C₂³	1	4	yes	—
142	C₁₉×#95	C₂³	1	4	yes	—
143	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	4	no	—
147	C₂²×C₄×C₁₉	—	2	4	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	4	2	no	—
152	C₂²×C₄×C₁₉	—	4	2	no	—
153	C₂²×C₄×C₁₉	—	4	2	no	—
154	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₁₉	#41	1	4	yes	—
156	C₂²×C₄×C₁₉	#41	1	4	yes	—
157	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	—	2	4	no	—
172	C₄⋊C₄×C₁₉	—	2	4	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	4	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	8	no	—
180	C₄⋊C₄×C₁₉	—	2	8	no	—
181	C₄⋊C₄×C₁₉	—	2	8	no	—
182	C₄⋊C₄×C₁₉	—	2	8	no	—
183	C₄⋊C₄×C₁₉	—	2	8	no	—
184	C₄⋊C₄×C₁₉	—	4	4	no	—
185	C₄⋊C₄×C₁₉	—	4	4	no	—
186	C₄⋊C₄×C₁₉	—	4	4	no	—
187	C₄⋊C₄×C₁₉	—	4	4	no	—
188	C₄⋊C₄×C₁₉	—	4	4	no	—
189	C₄⋊C₄×C₁₉	C₂×Q₈	1	8	yes	—
190	C₄⋊C₄×C₁₉	#41	1	8	yes	—
191	C₂²⋊C₄×C₁₉	—	2	4	no	—
192	C₂²⋊C₄×C₁₉	—	2	4	no	—
193	C₂²⋊C₄×C₁₉	—	2	4	no	—
194	C₂²⋊C₄×C₁₉	C₂×Q₈	1	8	yes	—
195	C₄²×C₁₉	—	2	2	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	4	no	—
198	C₄²×C₁₉	—	2	4	no	—
199	C₄²×C₁₉	—	2	4	no	—
200	C₄²×C₁₉	—	2	4	no	—
201	C₄²×C₁₉	—	2	2	no	—
202	C₄²×C₁₉	—	2	2	no	—
203	C₄²×C₁₉	—	2	4	no	—
204	C₄²×C₁₉	—	2	4	no	—
205	C₄²×C₁₉	—	2	4	no	—
206	C₄²×C₁₉	—	2	8	no	—
207	C₄²×C₁₉	—	4	4	no	—
208	C₄²×C₁₉	C₂×Q₈	1	8	yes	—
209	#34815	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	2	2	no	—
212	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
213	C₂³×C₁₉	C₂×#41	1	2	yes	—
214	C₂³×C₁₉	C₂×#41	1	2	yes	—
215	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
216	C₂×C₄×C₁₉	—	2	8	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	4	8	no	—
246	C₂×C₄×C₁₉	—	4	8	no	—
247	C₂×C₄×C₁₉	—	4	4	no	—
248	C₂×C₄×C₁₉	#125	1	16	yes	complemented
249	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
250	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
251	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
252	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
253	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
254	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
255	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
256	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
257	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
258	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
259	#2509	C₂×C₁₉	1	2	yes	complemented
260	#2508	C₂×C₁₉	1	2	yes	complemented
261	#2507	C₂×C₁₉	1	2	yes	complemented
262	#2506	C₂×C₁₉	1	2	yes	complemented
263	#2505	C₂×C₁₉	1	4	yes	—
264	#2473	C₂×C₁₉	1	4	yes	—
265	#2402	C₂×C₁₉	1	4	yes	complemented
266	C₄×#125	C₂×C₁₉	1	4	yes	complemented
267	#2296	C₂×C₁₉	1	1	yes	characteristic
268	#2296	C₂×C₁₉	1	1	yes	characteristic
269	#2296	C₂×C₁₉	1	1	yes	characteristic
270	#2296	C₂×C₁₉	1	1	yes	characteristic
271	#2285	C₂×C₁₉	1	1	yes	characteristic
272	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
273	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	4	no	—
277	C₂²×C₁₉	—	2	4	no	—
278	C₂²×C₁₉	C₂×#125	1	4	yes	—
279	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
280	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
281	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
282	C₂²×C₁₉	C₂²×#41	1	2	yes	—
283	C₂²×C₁₉	#585	1	2	yes	—
284	C₄×C₁₉	—	2	4	no	—
285	C₄×C₁₉	—	2	4	no	—
286	C₄×C₁₉	—	2	4	no	—
287	C₄×C₁₉	—	2	8	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	4	4	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	C₂×#125	1	4	yes	—
297	C₄×C₁₉	C₂×#125	1	4	yes	—
298	C₂×#125	C₂²×C₁₉	1	4	yes	—
299	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
304	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
305	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
307	#400	C₂²×C₁₉	1	4	yes	—
308	#400	C₂²×C₁₉	1	4	yes	—
309	#400	C₂²×C₁₉	1	4	yes	—
310	#400	C₂²×C₁₉	1	4	yes	—
311	#398	C₂²×C₁₉	1	4	yes	—
312	#398	C₂²×C₁₉	1	4	yes	—
313	#398	C₂²×C₁₉	1	4	yes	—
314	#398	C₂²×C₁₉	1	4	yes	—
315	#389	C₂²×C₁₉	1	4	yes	—
316	#389	C₂²×C₁₉	1	4	yes	—
317	#389	C₂²×C₁₉	1	2	yes	—
318	#389	C₂²×C₁₉	1	2	yes	—
319	#389	C₂²×C₁₉	1	2	yes	—
320	#389	C₂²×C₁₉	1	2	yes	—
321	#389	C₂²×C₁₉	1	2	yes	—
322	#389	C₂²×C₁₉	1	2	yes	—
323	#389	C₂²×C₁₉	1	2	yes	—
324	#389	C₂²×C₁₉	1	2	yes	—
325	#387	C₂²×C₁₉	1	4	yes	—
326	#387	C₂²×C₁₉	1	4	yes	—
327	#387	C₂²×C₁₉	1	4	yes	—
328	#387	C₂²×C₁₉	1	4	yes	—
329	#385	C₂²×C₁₉	1	2	yes	—
330	#385	C₂²×C₁₉	1	2	yes	—
331	#385	C₂²×C₁₉	1	4	yes	—
332	#385	C₂²×C₁₉	1	4	yes	—
333	#385	C₂²×C₁₉	1	2	yes	—
334	#385	C₂²×C₁₉	1	2	yes	—
335	#384	C₂²×C₁₉	1	1	yes	characteristic
336	#384	C₂²×C₁₉	1	1	yes	characteristic
337	#382	C₂²×C₁₉	1	4	yes	—
338	#382	C₂²×C₁₉	1	1	yes	characteristic
339	#382	C₂²×C₁₉	1	1	yes	characteristic
340	#380	C₂²×C₁₉	1	4	yes	—
341	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
343	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
344	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
345	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
346	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
347	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
348	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
349	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
352	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
354	#376	C₂²×C₁₉	1	2	yes	—
355	C₂×#95	C₂²×C₁₉	1	2	yes	—
356	C₄³	C₂²×C₁₉	1	2	yes	—
357	C₂×C₁₉	—	2	4	no	—
358	C₂×C₁₉	C₂²×#125	1	1	yes	characteristic
359	C₂×C₁₉	#3444	1	1	yes	characteristic
360	C₂×C₁₉	#3455	1	1	yes	characteristic
361	C₂×C₁₉	#3475	1	2	yes	—
362	C₂×C₁₉	Q₈×#41	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
365	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
368	#125	—	2	16	no	—
369	#117	—	2	4	no	—
370	#117	—	2	4	no	—
371	#117	—	2	4	no	—
372	#117	Q₈×C₁₉	1	8	yes	—
373	C₂×C₄⋊C₄	—	2	8	no	—
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
398	C₂×C₄²	—	2	4	no	—
399	C₂×C₄²	—	2	4	no	—
400	C₂×C₄²	—	2	4	no	—
401	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
403	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
410	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
414	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
415	#95	C₂³×C₁₉	1	2	yes	—
416	#95	C₂³×C₁₉	1	2	yes	—
417	#95	C₂³×C₁₉	1	2	yes	—
418	#95	C₂³×C₁₉	1	2	yes	—
419	#95	C₂³×C₁₉	1	4	yes	—
420	#95	C₂³×C₁₉	1	4	yes	—
421	#95	C₂³×C₁₉	1	4	yes	—
422	#95	C₂³×C₁₉	1	4	yes	—
423	#95	C₂³×C₁₉	1	4	yes	—
424	#95	C₂³×C₁₉	1	4	yes	—
425	#95	C₂³×C₁₉	1	4	yes	—
426	#95	C₂³×C₁₉	1	4	yes	—
427	#95	C₂³×C₁₉	1	4	yes	—
428	#95	C₂³×C₁₉	1	4	yes	—
429	#95	C₂³×C₁₉	1	4	yes	—
430	#95	C₂³×C₁₉	1	4	yes	—
431	C₁₉	#34815	1	1	yes	characteristic, direct product factor, Sylow
432	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
444	C₂²×C₄	#41×C₁₉	1	4	yes	—
445	C₂²×C₄	#41×C₁₉	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	C₂×Q₈×C₁₉	1	8	yes	—
479	C₄⋊C₄	#41×C₁₉	1	8	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	C₂×Q₈×C₁₉	1	8	yes	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	4	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	8	no	—
496	C₄²	—	4	4	no	—
497	C₄²	C₂×Q₈×C₁₉	1	8	yes	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
501	C₂³	C₂×#41×C₁₉	1	2	yes	—
502	C₂³	C₂×#41×C₁₉	1	2	yes	—
503	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	C₁₉×#125	1	16	yes	complemented
537	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
538	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
539	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
540	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
541	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
542	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
543	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
544	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
545	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
546	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	C₂×C₁₉×#125	1	4	yes	—
552	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
553	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
554	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
555	C₂²	C₂²×#41×C₁₉	1	2	yes	—
556	C₂²	C₁₉×#585	1	2	yes	—
557	C₄	—	2	4	no	—
558	C₄	—	2	4	no	—
559	C₄	—	2	4	no	—
560	C₄	—	2	8	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	4	no	—
569	C₄	C₂×C₁₉×#125	1	4	yes	—
570	C₄	C₂×C₁₉×#125	1	4	yes	—
571	C₂	—	2	4	no	—
572	C₂	C₂²×C₁₉×#125	1	1	yes	characteristic
573	C₂	C₁₉×#3444	1	1	yes	characteristic
574	C₂	C₁₉×#3455	1	1	yes	characteristic
575	C₂	C₁₉×#3475	1	2	yes	—
576	C₂	Q₈×#41×C₁₉	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×#2509	C₂	semidirect
2. C₁₉×#2508	C₂	semidirect
3. C₁₉×#2507	C₂	semidirect
4. C₁₉×#2506	C₂	semidirect
7. C₁₉×#2402	C₂	semidirect
8. C₄×C₁₉×#125	C₂	semidirect
209. #34815	C₁₉	direct (N × H)
248. C₂×C₄×C₁₉	#125	semidirect
259. #2509	C₂×C₁₉	semidirect
260. #2508	C₂×C₁₉	semidirect
261. #2507	C₂×C₁₉	semidirect
262. #2506	C₂×C₁₉	semidirect
265. #2402	C₂×C₁₉	semidirect
266. C₄×#125	C₂×C₁₉	semidirect
431. C₁₉	#34815	direct (N × H)
536. 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×#2509	2
C₁₉×#2508	2
C₁₉×#2507	2
C₁₉×#2506	2
C₁₉×#2505	2
C₁₉×#2473	2
C₁₉×#2402	2
C₄×C₁₉×#125	2
C₁₉×#2296	2
C₁₉×#2285	2
C₄×C₁₉×#117	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#34815	19

Subgroups — C19×#34815 #18040774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34815 #18040774