Subgroups — C₁₉×#32985 #18038944

Order 4864.

1430 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#485	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2848	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1873	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1825	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	—	2	1	no	—
17	C₂×C₁₉×#117	—	2	1	no	—
18	C₂×C₁₉×#117	—	2	8	no	—
19	C₂×C₁₉×#117	C₂²	1	2	yes	—
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄²×C₁₉	—	2	1	no	—
25	C₁₉×#485	—	2	8	no	—
26	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
28	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
29	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₁₉×#385	—	2	1	no	—
35	C₁₉×#385	—	2	1	no	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₁₉×#379	—	2	1	no	—
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#340	C₂²	1	2	yes	complemented
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	—	2	4	no	—
48	C₂³×C₄×C₁₉	—	2	4	no	—
49	C₂³×C₄×C₁₉	—	2	2	no	—
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
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	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×#117	—	2	8	no	—
66	C₁₉×#117	—	2	8	no	—
67	C₁₉×#117	—	2	4	no	—
68	C₁₉×#117	—	2	4	no	—
69	C₁₉×#117	—	2	4	no	—
70	C₁₉×#117	D₄	1	8	yes	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	—	2	8	no	—
93	C₂×C₄²×C₁₉	—	2	2	no	—
94	C₂×C₄²×C₁₉	—	2	2	no	—
95	C₁₉×#107	—	2	4	no	—
96	C₁₉×#106	—	2	4	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×C₂²⋊C₈	—	2	4	no	—
100	C₁₉×C₂²⋊C₈	—	2	2	no	—
101	C₁₉×C₂²⋊C₈	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	2	4	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	1	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₂⁴×C₁₉	—	2	2	no	—
107	C₂⁴×C₁₉	—	2	2	no	—
108	C₂⁴×C₁₉	—	2	2	no	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	—	4	1	no	—
112	C₂⁴×C₁₉	—	4	1	no	—
113	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	16	no	—
121	C₂²×C₄×C₁₉	—	2	16	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	—	4	2	no	—
150	C₂²×C₄×C₁₉	—	4	2	no	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	#41	1	4	yes	—
156	C₂²×C₄×C₁₉	#41	1	2	yes	—
157	C₂²×C₄×C₁₉	#41	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	4	no	—
166	C₄⋊C₄×C₁₉	—	2	4	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	4	2	no	—
174	C₄⋊C₄×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	4	2	no	—
176	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
177	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
178	C₂²⋊C₄×C₁₉	—	2	8	no	—
179	C₂²⋊C₄×C₁₉	—	2	8	no	—
180	C₂²⋊C₄×C₁₉	—	4	2	no	—
181	C₂²⋊C₄×C₁₉	—	4	2	no	—
182	C₂²⋊C₄×C₁₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₉	—	4	2	no	—
184	C₂²⋊C₄×C₁₉	—	4	2	no	—
185	C₂²⋊C₄×C₁₉	—	4	2	no	—
186	C₄²×C₁₉	—	2	8	no	—
187	C₄²×C₁₉	—	2	8	no	—
188	#32985	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	—	2	1	no	—
190	C₂³×C₁₉	—	2	1	no	—
191	C₂³×C₁₉	—	2	1	no	—
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	2	8	no	—
194	C₂³×C₁₉	—	2	1	no	—
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	2	1	no	—
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	4	4	no	—
207	C₂³×C₁₉	—	4	4	no	—
208	C₂³×C₁₉	—	4	4	no	—
209	C₂³×C₁₉	—	4	4	no	—
210	C₂³×C₁₉	—	4	4	no	—
211	C₂³×C₁₉	—	4	4	no	—
212	C₂³×C₁₉	#120	1	2	yes	—
213	C₂³×C₁₉	#123	1	2	yes	—
214	C₂³×C₁₉	#123	1	2	yes	—
215	C₂³×C₁₉	#135	1	2	yes	—
216	C₂³×C₁₉	#137	1	2	yes	—
217	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	2	8	no	—
221	C₂×C₄×C₁₉	—	2	8	no	—
222	C₂×C₄×C₁₉	—	2	8	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	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	4	no	—
237	C₂×C₄×C₁₉	—	4	8	no	—
238	C₂×C₄×C₁₉	—	4	8	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	#120	1	2	yes	—
256	C₂×C₄×C₁₉	#123	1	2	yes	—
257	C₂×C₄×C₁₉	#123	1	2	yes	—
258	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
262	C₈×C₁₉	—	4	2	no	—
263	C₈×C₁₉	—	4	2	no	—
264	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
265	C₂×#485	C₂×C₁₉	1	2	yes	complemented
266	#2848	C₂×C₁₉	1	1	yes	characteristic
267	#1873	C₂×C₁₉	1	2	yes	complemented
268	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1854	C₂×C₁₉	1	2	yes	complemented
271	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1825	C₂×C₁₉	1	2	yes	complemented
274	#1779	C₂×C₁₉	1	1	yes	characteristic
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	2	no	—
279	C₂²×C₁₉	—	2	2	no	—
280	C₂²×C₁₉	—	2	2	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	2	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	4	16	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	#485	1	4	yes	complemented
297	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
298	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
299	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
300	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
301	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
302	C₂²×C₁₉	#575	1	1	yes	characteristic
303	C₂²×C₁₉	#575	1	1	yes	characteristic
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	2	no	—
307	C₄×C₁₉	—	4	4	no	—
308	C₄×C₁₉	—	4	4	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	—	8	1	no	—
312	C₄×C₁₉	—	8	1	no	—
313	C₄×C₁₉	#525	1	2	yes	—
314	C₄×C₁₉	#525	1	2	yes	—
315	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#117	—	2	1	no	—
320	C₂×#117	—	2	1	no	—
321	C₂×#117	—	2	8	no	—
322	C₂×#117	C₂²×C₁₉	1	2	yes	—
323	C₂×#117	C₂²×C₁₉	1	2	yes	—
324	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	—	2	1	no	—
327	C₂²×C₄²	—	2	1	no	—
328	#485	—	2	8	no	—
329	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
330	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
331	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
332	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
333	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
334	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
337	#385	—	2	1	no	—
338	#385	—	2	1	no	—
339	#385	—	2	1	no	—
340	#380	C₂²×C₁₉	1	1	yes	characteristic
341	#380	C₂²×C₁₉	1	1	yes	characteristic
342	#380	C₂²×C₁₉	1	1	yes	characteristic
343	#379	—	2	1	no	—
344	#340	C₂²×C₁₉	1	2	yes	complemented
345	#340	C₂²×C₁₉	1	2	yes	complemented
346	#340	C₂²×C₁₉	1	2	yes	complemented
347	#340	C₂²×C₁₉	1	2	yes	complemented
348	C₂×C₁₉	—	2	4	no	—
349	C₂×C₁₉	—	4	2	no	—
350	C₂×C₁₉	—	4	2	no	—
351	C₂×C₁₉	#2849	1	1	yes	characteristic
352	C₂×C₁₉	#3002	1	1	yes	characteristic
353	C₂×C₁₉	#3007	1	1	yes	characteristic
354	C₂×C₁₉	C₂×#485	1	1	yes	characteristic
355	C₂×C₁₉	#3091	1	1	yes	characteristic
356	C₂×C₁₉	#3093	1	1	yes	characteristic
357	C₂×C₁₉	#3095	1	1	yes	characteristic
358	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	C₂³×C₄	—	2	4	no	—
361	C₂³×C₄	—	2	4	no	—
362	C₂³×C₄	—	2	2	no	—
363	C₂³×C₄	—	2	2	no	—
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
367	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
373	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
374	C₂²⋊Q₈	—	2	4	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	#117	—	2	8	no	—
379	#117	—	2	8	no	—
380	#117	—	2	4	no	—
381	#117	—	2	4	no	—
382	#117	—	2	4	no	—
383	#117	D₄×C₁₉	1	8	yes	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	4	no	—
387	C₂×C₄⋊C₄	—	2	4	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
396	C₂×C₂²⋊C₄	—	2	8	no	—
397	C₂×C₂²⋊C₄	—	2	2	no	—
398	C₂×C₂²⋊C₄	—	2	2	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₄²	—	2	8	no	—
406	C₂×C₄²	—	2	2	no	—
407	C₂×C₄²	—	2	2	no	—
408	#107	—	2	4	no	—
409	#106	—	2	4	no	—
410	#103	—	2	4	no	—
411	#103	—	2	4	no	—
412	C₂²⋊C₈	—	2	4	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	—	2	2	no	—
415	C₂²⋊C₈	—	2	4	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	C₁₉	#32985	1	1	yes	characteristic, direct product factor, Sylow
420	C₂⁴	—	2	2	no	—
421	C₂⁴	—	2	2	no	—
422	C₂⁴	—	2	2	no	—
423	C₂⁴	—	2	2	no	—
424	C₂⁴	—	2	2	no	—
425	C₂⁴	—	4	1	no	—
426	C₂⁴	—	4	1	no	—
427	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂²×C₄	—	2	16	no	—
435	C₂²×C₄	—	2	16	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
467	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	#41×C₁₉	1	4	yes	—
470	C₂²×C₄	#41×C₁₉	1	2	yes	—
471	C₂²×C₄	#41×C₁₉	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
491	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₄²	—	2	8	no	—
501	C₄²	—	2	8	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	8	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	4	no	—
521	C₂³	—	4	4	no	—
522	C₂³	—	4	4	no	—
523	C₂³	—	4	4	no	—
524	C₂³	—	4	4	no	—
525	C₂³	C₁₉×#120	1	2	yes	—
526	C₂³	C₁₉×#123	1	2	yes	—
527	C₂³	C₁₉×#123	1	2	yes	—
528	C₂³	C₁₉×#135	1	2	yes	—
529	C₂³	C₁₉×#137	1	2	yes	—
530	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
531	Q₈	—	4	2	no	—
532	Q₈	—	4	2	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	2	8	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	C₁₉×#120	1	2	yes	—
569	C₂×C₄	C₁₉×#123	1	2	yes	—
570	C₂×C₄	C₁₉×#123	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
572	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
575	C₈	—	4	2	no	—
576	C₈	—	4	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	4	16	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	C₁₉×#485	1	4	yes	complemented
599	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
600	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
601	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
602	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
603	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
604	C₂²	C₁₉×#575	1	1	yes	characteristic
605	C₂²	C₁₉×#575	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	4	no	—
610	C₄	—	4	4	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	C₁₉×#525	1	2	yes	—
616	C₄	C₁₉×#525	1	2	yes	—
617	C₂	—	2	4	no	—
618	C₂	—	4	2	no	—
619	C₂	—	4	2	no	—
620	C₂	C₁₉×#2849	1	1	yes	characteristic
621	C₂	C₁₉×#3002	1	1	yes	characteristic
622	C₂	C₁₉×#3007	1	1	yes	characteristic
623	C₂	C₂×C₁₉×#485	1	1	yes	characteristic
624	C₂	C₁₉×#3091	1	1	yes	characteristic
625	C₂	C₁₉×#3093	1	1	yes	characteristic
626	C₂	C₁₉×#3095	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#485	C₂	semidirect
4. C₁₉×#1873	C₂	semidirect
5. C₁₉×#1872	C₂	semidirect
6. C₁₉×#1872	C₂	semidirect
7. C₁₉×#1854	C₂	semidirect
8. C₁₉×#1853	C₂	semidirect
9. C₁₉×#1852	C₂	semidirect
10. C₁₉×#1825	C₂	semidirect
26. C₂×C₁₉×#107	C₂²	semidirect
27. C₂×C₁₉×#106	C₂²	semidirect
28. C₂×C₁₉×#103	C₂²	semidirect
29. C₂×C₁₉×#103	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#340	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
188. #32985	C₁₉	direct (N × H)
265. C₂×#485	C₂×C₁₉	semidirect
267. #1873	C₂×C₁₉	semidirect
268. #1872	C₂×C₁₉	semidirect
269. #1872	C₂×C₁₉	semidirect
270. #1854	C₂×C₁₉	semidirect
271. #1853	C₂×C₁₉	semidirect
272. #1852	C₂×C₁₉	semidirect
273. #1825	C₂×C₁₉	semidirect
296. C₂²×C₁₉	#485	semidirect
329. C₂×#107	C₂²×C₁₉	semidirect
330. C₂×#106	C₂²×C₁₉	semidirect
331. C₂×#103	C₂²×C₁₉	semidirect
332. C₂×#103	C₂²×C₁₉	semidirect
344. #340	C₂²×C₁₉	semidirect
345. #340	C₂²×C₁₉	semidirect
346. #340	C₂²×C₁₉	semidirect
347. #340	C₂²×C₁₉	semidirect
419. C₁₉	#32985	direct (N × H)
598. C₂²	C₁₉×#485	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#117	2
C₂×C₁₉×#485	2
C₁₉×#2848	2
C₁₉×#1873	2
C₁₉×#1872	2
C₁₉×#1854	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1825	2
C₁₉×#1779	2
#32985	19

Subgroups — C19×#32985 #18038944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32985 #18038944