Subgroups — C₁₉×#23458 #18029417

Order 4864.

1250 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2026	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2025	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2024	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2023	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#544	—	2	4	no	—
16	C₁₉×#544	—	2	4	no	—
17	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#125	—	2	1	no	—
20	C₂×C₁₉×#125	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#417	—	2	4	no	—
27	C₁₉×#416	—	2	4	no	—
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	2	yes	—
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₂²	1	2	yes	—
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
34	C₁₉×#391	C₂²	1	2	yes	—
35	C₁₉×#390	C₂²	1	2	yes	—
36	C₁₉×#386	—	2	2	no	—
37	C₁₉×#380	—	2	1	no	—
38	C₁₉×#380	—	2	1	no	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#336	C₂²	1	2	yes	—
44	C₁₉×#336	C₂²	1	2	yes	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	Q₈	1	4	yes	complemented
51	C₂²×Q₈×C₁₉	—	2	2	no	—
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	—	2	1	no	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₂×M₁₆×C₁₉	—	2	2	no	—
61	C₂×M₁₆×C₁₉	—	2	2	no	—
62	C₂²×C₈×C₁₉	—	2	2	no	—
63	C₂²×C₈×C₁₉	—	2	2	no	—
64	C₂²×C₈×C₁₉	—	2	2	no	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
68	C₁₉×C₄⋊Q₈	—	2	8	no	—
69	C₁₉×C₄⋊Q₈	—	2	4	no	—
70	C₁₉×C₄⋊Q₈	—	2	4	no	—
71	C₁₉×#125	—	2	8	no	—
72	C₁₉×#125	—	2	4	no	—
73	C₁₉×#125	—	2	4	no	—
74	C₁₉×C₂²⋊Q₈	—	2	16	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
98	C₂×C₄²×C₁₉	—	2	1	no	—
99	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×#103	—	2	4	no	—
103	C₁₉×#102	—	2	2	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₁₉×#102	—	2	4	no	—
106	C₁₉×#95	—	2	2	no	—
107	C₁₉×#95	—	2	2	no	—
108	C₂⁴×C₁₉	—	2	1	no	—
109	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
110	#41×C₁₉	—	2	8	no	—
111	#41×C₁₉	—	2	8	no	—
112	#41×C₁₉	—	4	4	no	—
113	#41×C₁₉	—	4	4	no	—
114	C₂×Q₈×C₁₉	—	2	8	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	8	2	no	—
121	C₂×Q₈×C₁₉	—	8	2	no	—
122	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	4	2	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	4	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	—	8	1	no	—
143	C₂²×C₄×C₁₉	—	8	1	no	—
144	C₂²×C₄×C₁₉	—	8	1	no	—
145	C₂²×C₄×C₁₉	—	8	1	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
152	C₂²×C₄×C₁₉	#41	1	2	yes	—
153	C₂²×C₄×C₁₉	#41	1	2	yes	—
154	C₂²×C₄×C₁₉	#41	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₁₉	—	4	4	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	4	4	no	—
167	C₄⋊C₄×C₁₉	—	2	8	no	—
168	C₄⋊C₄×C₁₉	—	2	8	no	—
169	C₄⋊C₄×C₁₉	—	2	8	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	4	2	no	—
179	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
180	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
182	C₂²⋊C₄×C₁₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₉	—	2	4	no	—
184	C₂²⋊C₄×C₁₉	—	8	2	no	—
185	C₂²⋊C₄×C₁₉	—	8	2	no	—
186	C₄²×C₁₉	—	2	4	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	#23458	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂³×C₁₉	—	2	1	no	—
191	C₂³×C₁₉	—	2	1	no	—
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	2	1	no	—
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	4	1	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	#120	1	2	yes	—
202	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
203	C₂³×C₁₉	#124	1	2	yes	—
204	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₁₉	—	2	2	no	—
206	Q₈×C₁₉	—	2	2	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	8	8	no	—
210	D₄×C₁₉	—	2	2	no	—
211	D₄×C₁₉	—	2	2	no	—
212	D₄×C₁₉	—	4	8	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	8	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	8	4	no	—
238	C₂×C₄×C₁₉	—	8	4	no	—
239	C₂×C₄×C₁₉	#120	1	2	yes	—
240	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
241	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
242	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
243	C₂×C₄×C₁₉	#124	1	4	yes	—
244	C₂×C₄×C₁₉	#124	1	4	yes	—
245	C₂×C₄×C₁₉	#124	1	2	yes	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₈×C₁₉	—	4	2	no	—
255	C₂×#544	C₂×C₁₉	1	1	yes	characteristic, complemented
256	C₂×#417	C₂×C₁₉	1	1	yes	characteristic
257	C₂×#416	C₂×C₁₉	1	1	yes	characteristic
258	#2311	C₂×C₁₉	1	1	yes	characteristic
259	#2026	C₂×C₁₉	1	2	yes	complemented
260	#2025	C₂×C₁₉	1	2	yes	complemented
261	#2024	C₂×C₁₉	1	2	yes	complemented
262	#2023	C₂×C₁₉	1	2	yes	complemented
263	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1729	C₂×C₁₉	1	1	yes	characteristic, complemented
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	2	2	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	—	8	1	no	—
279	C₂²×C₁₉	#393	1	4	yes	—
280	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
281	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
282	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
283	C₂²×C₁₉	#576	1	1	yes	characteristic
284	C₂²×C₁₉	#577	1	1	yes	characteristic
285	C₂²×C₁₉	#577	1	1	yes	characteristic
286	C₂²×C₁₉	#578	1	1	yes	characteristic
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	4	4	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	8	2	no	—
294	C₄×C₁₉	#393	1	4	yes	—
295	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
296	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
297	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
298	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
299	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
300	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
301	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
302	#544	—	2	4	no	—
303	#544	—	2	4	no	—
304	C₂×C₄⋊Q₈	—	2	1	no	—
305	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
306	C₂×#125	—	2	1	no	—
307	C₂×#125	C₂²×C₁₉	1	2	yes	—
308	C₂×C₂²⋊Q₈	—	2	2	no	—
309	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
313	#417	—	2	4	no	—
314	#416	—	2	4	no	—
315	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×#103	C₂²×C₁₉	1	2	yes	—
318	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#102	C₂²×C₁₉	1	2	yes	—
321	#391	C₂²×C₁₉	1	2	yes	—
322	#390	C₂²×C₁₉	1	2	yes	—
323	#386	—	2	2	no	—
324	#380	—	2	1	no	—
325	#380	—	2	1	no	—
326	#340	C₂²×C₁₉	1	2	yes	—
327	#340	C₂²×C₁₉	1	2	yes	—
328	#340	C₂²×C₁₉	1	2	yes	—
329	#340	C₂²×C₁₉	1	2	yes	—
330	#336	C₂²×C₁₉	1	2	yes	—
331	#336	C₂²×C₁₉	1	2	yes	—
332	C₂×C₁₉	—	2	4	no	—
333	C₂×C₁₉	—	8	2	no	—
334	C₂×C₁₉	C₂×#393	1	1	yes	characteristic
335	C₂×C₁₉	#3012	1	1	yes	characteristic
336	C₂×C₁₉	#3013	1	1	yes	characteristic
337	C₂×C₁₉	#3083	1	1	yes	characteristic
338	C₂×C₁₉	#3084	1	1	yes	characteristic
339	C₂×C₁₉	#3136	1	1	yes	characteristic
340	C₂×C₁₉	#3137	1	1	yes	characteristic
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	2	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	Q₈×C₁₉	1	4	yes	complemented
347	C₂²×Q₈	—	2	2	no	—
348	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	—	2	2	no	—
361	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
364	C₄⋊Q₈	—	2	8	no	—
365	C₄⋊Q₈	—	2	4	no	—
366	C₄⋊Q₈	—	2	4	no	—
367	#125	—	2	8	no	—
368	#125	—	2	4	no	—
369	#125	—	2	4	no	—
370	C₂²⋊Q₈	—	2	16	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	—	2	2	no	—
374	#117	D₄×C₁₉	1	4	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
396	#103	—	2	2	no	—
397	#103	—	2	2	no	—
398	#103	—	2	4	no	—
399	#102	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	4	no	—
402	#95	—	2	2	no	—
403	#95	—	2	2	no	—
404	C₁₉	#23458	1	1	yes	characteristic, direct product factor, Sylow
405	C₂⁴	—	2	1	no	—
406	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
407	#41	—	2	8	no	—
408	#41	—	2	8	no	—
409	#41	—	4	4	no	—
410	#41	—	4	4	no	—
411	C₂×Q₈	—	2	8	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	8	2	no	—
418	C₂×Q₈	—	8	2	no	—
419	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	4	2	no	—
428	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	8	1	no	—
440	C₂²×C₄	—	8	1	no	—
441	C₂²×C₄	—	8	1	no	—
442	C₂²×C₄	—	8	1	no	—
443	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
449	C₂²×C₄	#41×C₁₉	1	2	yes	—
450	C₂²×C₄	#41×C₁₉	1	2	yes	—
451	C₂²×C₄	#41×C₁₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
453	M₁₆	—	4	4	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	4	4	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
477	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
478	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	8	2	no	—
482	C₂²⋊C₄	—	8	2	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	C₁₉×#120	1	2	yes	—
498	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
499	C₂³	C₁₉×#124	1	2	yes	—
500	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	8	8	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	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	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	—	8	4	no	—
535	C₂×C₄	C₁₉×#120	1	2	yes	—
536	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
537	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
538	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
539	C₂×C₄	C₁₉×#124	1	2	yes	—
540	C₂×C₄	C₁₉×#124	1	4	yes	—
541	C₂×C₄	C₁₉×#124	1	4	yes	—
542	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
546	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	C₁₉×#393	1	4	yes	—
565	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
566	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
567	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
568	C₂²	C₁₉×#576	1	1	yes	characteristic
569	C₂²	C₁₉×#577	1	1	yes	characteristic
570	C₂²	C₁₉×#577	1	1	yes	characteristic
571	C₂²	C₁₉×#578	1	1	yes	characteristic
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	2	no	—
579	C₄	C₁₉×#393	1	4	yes	—
580	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
581	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
582	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
583	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
584	C₂	—	2	4	no	—
585	C₂	—	8	2	no	—
586	C₂	C₂×C₁₉×#393	1	1	yes	characteristic
587	C₂	C₁₉×#3012	1	1	yes	characteristic
588	C₂	C₁₉×#3013	1	1	yes	characteristic
589	C₂	C₁₉×#3083	1	1	yes	characteristic
590	C₂	C₁₉×#3084	1	1	yes	characteristic
591	C₂	C₁₉×#3136	1	1	yes	characteristic
592	C₂	C₁₉×#3137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#544	C₂	semidirect
5. C₁₉×#2026	C₂	semidirect
6. C₁₉×#2025	C₂	semidirect
7. C₁₉×#2024	C₂	semidirect
8. C₁₉×#2023	C₂	semidirect
9. C₁₉×#1736	C₂	semidirect
10. C₂×C₁₉×#340	C₂	semidirect
11. C₁₉×#1729	C₂	semidirect
50. C₂×#41×C₁₉	Q₈	semidirect
189. #23458	C₁₉	direct (N × H)
255. C₂×#544	C₂×C₁₉	semidirect
259. #2026	C₂×C₁₉	semidirect
260. #2025	C₂×C₁₉	semidirect
261. #2024	C₂×C₁₉	semidirect
262. #2023	C₂×C₁₉	semidirect
263. #1736	C₂×C₁₉	semidirect
264. C₂×#340	C₂×C₁₉	semidirect
265. #1729	C₂×C₁₉	semidirect
346. C₂×#41	Q₈×C₁₉	semidirect
404. C₁₉	#23458	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×#544	2
C₂×C₁₉×#417	2
C₂×C₁₉×#416	2
C₁₉×#2311	2
C₁₉×#2026	2
C₁₉×#2025	2
C₁₉×#2024	2
C₁₉×#2023	2
C₁₉×#1736	2
C₂×C₁₉×#340	2
C₁₉×#1729	2
#23458	19

Subgroups — C19×#23458 #18029417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23458 #18029417