Subgroups — C₁₉×#34254 #18040213

Order 4864.

2234 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2356	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2355	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2343	C₂	1	8	yes	maximal
5	C₁₉×#2320	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2295	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2274	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#519	C₄	1	16	yes	complemented
15	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
16	C₂×C₄×Q₈×C₁₉	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	C₂×C₁₉×#117	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#391	C₂²	1	2	yes	—
25	C₁₉×#391	C₂²	1	2	yes	—
26	C₁₉×#391	C₂²	1	4	yes	—
27	C₁₉×#391	C₂²	1	4	yes	—
28	C₁₉×#391	C₂²	1	2	yes	—
29	C₁₉×#391	C₂²	1	2	yes	—
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#389	C₂²	1	4	yes	—
32	C₁₉×#389	C₂²	1	2	yes	—
33	C₁₉×#387	C₂²	1	8	yes	—
34	C₁₉×#387	C₂²	1	8	yes	—
35	C₁₉×#387	C₂²	1	8	yes	—
36	C₁₉×#387	C₂²	1	8	yes	—
37	C₁₉×#385	C₂²	1	4	yes	—
38	C₁₉×#385	C₂²	1	4	yes	—
39	C₁₉×#384	C₂²	1	2	yes	—
40	C₁₉×#383	C₂²	1	8	yes	—
41	C₁₉×#382	C₂²	1	2	yes	—
42	C₁₉×#382	C₂²	1	8	yes	—
43	C₁₉×#381	C₂²	1	4	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	8	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
50	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
51	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
52	C₁₉×#376	C₂²	1	2	yes	—
53	C₁₉×#376	C₂²	1	8	yes	—
54	C₂×C₁₉×#95	C₂²	1	4	yes	—
55	C₄³×C₁₉	C₂²	1	2	yes	—
56	C₂²×Q₈×C₁₉	—	2	4	no	—
57	C₂²×Q₈×C₁₉	—	2	4	no	—
58	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	—
59	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₁₉	C₂×C₄	1	32	yes	complemented
66	C₄×Q₈×C₁₉	C₂×C₄	1	32	yes	complemented
67	C₁₉×#117	—	2	4	no	—
68	C₁₉×#117	—	2	4	no	—
69	C₁₉×#117	C₂×C₄	1	32	yes	—
70	C₁₉×#117	C₂×C₄	1	8	yes	—
71	C₁₉×#117	C₂×C₄	1	8	yes	—
72	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₉	—	2	4	no	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
98	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
99	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
100	C₁₉×#95	C₂³	1	8	yes	—
101	C₁₉×#95	C₂³	1	8	yes	—
102	C₁₉×#95	C₂³	1	4	yes	—
103	C₁₉×#95	C₂³	1	4	yes	—
104	C₁₉×#95	C₂³	1	4	yes	—
105	C₁₉×#95	C₂³	1	8	yes	—
106	C₁₉×#95	C₂³	1	8	yes	—
107	C₁₉×#95	C₂³	1	8	yes	—
108	C₁₉×#95	C₂³	1	8	yes	—
109	C₁₉×#95	C₂³	1	4	yes	—
110	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	—	2	32	no	—
112	C₂×Q₈×C₁₉	—	2	4	no	—
113	C₂×Q₈×C₁₉	—	2	4	no	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	—	2	4	no	—
116	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
117	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	—	4	4	no	—
125	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₁₉	#41	1	4	yes	—
128	C₂²×C₄×C₁₉	#41	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	8	no	—
146	C₄⋊C₄×C₁₉	—	4	4	no	—
147	C₄⋊C₄×C₁₉	—	4	8	no	—
148	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
149	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
150	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
151	C₂²⋊C₄×C₁₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
154	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	2	4	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	4	no	—
159	C₄²×C₁₉	—	2	4	no	—
160	C₄²×C₁₉	—	2	8	no	—
161	C₄²×C₁₉	—	4	4	no	—
162	C₄²×C₁₉	—	4	8	no	—
163	C₄²×C₁₉	C₂²×C₄	1	32	yes	—
164	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
165	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
166	#34254	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
170	C₂³×C₁₉	C₂×#41	1	2	yes	—
171	C₂³×C₁₉	C₂×#41	1	2	yes	—
172	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
173	Q₈×C₁₉	—	2	16	no	—
174	Q₈×C₁₉	—	2	16	no	—
175	C₂×C₄×C₁₉	—	2	16	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	8	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	4	8	no	—
197	C₂×C₄×C₁₉	—	8	4	no	—
198	C₂×C₄×C₁₉	#117	1	16	yes	—
199	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
200	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
201	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
202	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
204	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
205	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
206	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
209	C₂×#519	C₂×C₁₉	1	1	yes	characteristic
210	#2356	C₂×C₁₉	1	4	yes	complemented
211	#2355	C₂×C₁₉	1	4	yes	complemented
212	#2343	C₂×C₁₉	1	8	yes	—
213	#2320	C₂×C₁₉	1	4	yes	complemented
214	#2317	C₂×C₁₉	1	1	yes	characteristic
215	#2310	C₂×C₁₉	1	1	yes	characteristic
216	#2296	C₂×C₁₉	1	1	yes	characteristic
217	#2295	C₂×C₁₉	1	4	yes	complemented
218	C₂×#391	C₂×C₁₉	1	1	yes	characteristic
219	#2274	C₂×C₁₉	1	1	yes	characteristic
220	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
221	C₂²×C₁₉	—	2	4	no	—
222	C₂²×C₁₉	—	2	4	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	C₂×#117	1	4	yes	—
226	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
227	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
228	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
229	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
230	C₂²×C₁₉	#585	1	2	yes	—
231	C₄×C₁₉	—	2	8	no	—
232	C₄×C₁₉	—	2	8	no	—
233	C₄×C₁₉	—	2	8	no	—
234	C₄×C₁₉	—	2	4	no	—
235	C₄×C₁₉	—	4	4	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	C₂×#117	1	4	yes	—
241	C₄×C₁₉	C₂×#117	1	4	yes	—
242	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
243	#519	C₄×C₁₉	1	16	yes	complemented
244	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
245	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
246	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×#117	C₂²×C₁₉	1	4	yes	—
250	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
252	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
253	#391	C₂²×C₁₉	1	4	yes	—
254	#391	C₂²×C₁₉	1	2	yes	—
255	#391	C₂²×C₁₉	1	2	yes	—
256	#391	C₂²×C₁₉	1	2	yes	—
257	#391	C₂²×C₁₉	1	4	yes	—
258	#391	C₂²×C₁₉	1	2	yes	—
259	#389	C₂²×C₁₉	1	4	yes	—
260	#389	C₂²×C₁₉	1	2	yes	—
261	#389	C₂²×C₁₉	1	2	yes	—
262	#387	C₂²×C₁₉	1	8	yes	—
263	#387	C₂²×C₁₉	1	8	yes	—
264	#387	C₂²×C₁₉	1	8	yes	—
265	#387	C₂²×C₁₉	1	8	yes	—
266	#385	C₂²×C₁₉	1	4	yes	—
267	#385	C₂²×C₁₉	1	4	yes	—
268	#384	C₂²×C₁₉	1	2	yes	—
269	#383	C₂²×C₁₉	1	8	yes	—
270	#382	C₂²×C₁₉	1	2	yes	—
271	#382	C₂²×C₁₉	1	8	yes	—
272	#381	C₂²×C₁₉	1	4	yes	—
273	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
274	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
275	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
276	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
277	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
278	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
279	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
280	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
281	#376	C₂²×C₁₉	1	2	yes	—
282	#376	C₂²×C₁₉	1	8	yes	—
283	C₂×#95	C₂²×C₁₉	1	4	yes	—
284	C₄³	C₂²×C₁₉	1	2	yes	—
285	C₂×C₁₉	—	2	4	no	—
286	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
287	C₂×C₁₉	C₄×2₋¹⁺⁴	1	2	yes	—
288	C₂×C₁₉	#3495	1	2	yes	—
289	C₂×C₁₉	#3509	1	1	yes	characteristic
290	C₂×C₁₉	#3510	1	1	yes	characteristic
291	C₂²×Q₈	—	2	4	no	—
292	C₂²×Q₈	—	2	4	no	—
293	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	—
294	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
295	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
299	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
300	C₄×Q₈	C₂×C₄×C₁₉	1	32	yes	complemented
301	C₄×Q₈	C₂×C₄×C₁₉	1	32	yes	complemented
302	#117	—	2	4	no	—
303	#117	—	2	4	no	—
304	#117	C₂×C₄×C₁₉	1	32	yes	—
305	#117	C₂×C₄×C₁₉	1	8	yes	—
306	#117	C₂×C₄×C₁₉	1	8	yes	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
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	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
323	C₂×C₄²	—	2	4	no	—
324	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
328	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
330	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
331	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
332	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
334	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
335	#95	C₂³×C₁₉	1	8	yes	—
336	#95	C₂³×C₁₉	1	8	yes	—
337	#95	C₂³×C₁₉	1	4	yes	—
338	#95	C₂³×C₁₉	1	4	yes	—
339	#95	C₂³×C₁₉	1	4	yes	—
340	#95	C₂³×C₁₉	1	8	yes	—
341	#95	C₂³×C₁₉	1	8	yes	—
342	#95	C₂³×C₁₉	1	8	yes	—
343	#95	C₂³×C₁₉	1	8	yes	—
344	#95	C₂³×C₁₉	1	4	yes	—
345	C₁₉	#34254	1	1	yes	characteristic, direct product factor, Sylow
346	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
347	C₂×Q₈	—	2	32	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
353	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
363	C₂²×C₄	#41×C₁₉	1	4	yes	—
364	C₂²×C₄	#41×C₁₉	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	8	no	—
384	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
385	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
386	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
390	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	8	no	—
397	C₄²	—	4	4	no	—
398	C₄²	—	4	8	no	—
399	C₄²	C₂²×C₄×C₁₉	1	32	yes	—
400	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
401	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
405	C₂³	C₂×#41×C₁₉	1	2	yes	—
406	C₂³	C₂×#41×C₁₉	1	2	yes	—
407	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
408	Q₈	—	2	16	no	—
409	Q₈	—	2	16	no	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	8	4	no	—
433	C₂×C₄	C₁₉×#117	1	16	yes	—
434	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
435	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
436	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
437	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
438	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
439	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
440	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
441	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
442	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
443	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	C₂×C₁₉×#117	1	4	yes	—
449	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
450	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
451	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
452	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
453	C₂²	C₁₉×#585	1	2	yes	—
454	C₄	—	2	8	no	—
455	C₄	—	2	8	no	—
456	C₄	—	2	4	no	—
457	C₄	—	2	8	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	2	no	—
463	C₄	C₂×C₁₉×#117	1	4	yes	—
464	C₄	C₂×C₁₉×#117	1	4	yes	—
465	C₂	—	2	4	no	—
466	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
467	C₂	C₄×C₁₉×2₋¹⁺⁴	1	2	yes	—
468	C₂	C₁₉×#3495	1	2	yes	—
469	C₂	C₁₉×#3509	1	1	yes	characteristic
470	C₂	C₁₉×#3510	1	1	yes	characteristic

	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
2. C₁₉×#2356	C₂	semidirect
3. C₁₉×#2355	C₂	semidirect
5. C₁₉×#2320	C₂	semidirect
9. C₁₉×#2295	C₂	semidirect
14. C₁₉×#519	C₄	semidirect
65. C₄×Q₈×C₁₉	C₂×C₄	semidirect
66. C₄×Q₈×C₁₉	C₂×C₄	semidirect
166. #34254	C₁₉	direct (N × H)
210. #2356	C₂×C₁₉	semidirect
211. #2355	C₂×C₁₉	semidirect
213. #2320	C₂×C₁₉	semidirect
217. #2295	C₂×C₁₉	semidirect
243. #519	C₄×C₁₉	semidirect
300. C₄×Q₈	C₂×C₄×C₁₉	semidirect
301. C₄×Q₈	C₂×C₄×C₁₉	semidirect
345. C₁₉	#34254	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×#519	2
C₁₉×#2356	2
C₁₉×#2355	2
C₁₉×#2343	2
C₁₉×#2320	2
C₁₉×#2317	2
C₁₉×#2310	2
C₁₉×#2296	2
C₁₉×#2295	2
C₂×C₁₉×#391	2
C₁₉×#2274	2
C₄×C₁₉×#117	2
#34254	19

Subgroups — C19×#34254 #18040213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34254 #18040213