Subgroups — C₁₉×#10322 #18016281

Order 4864.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3187	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1520	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1289	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
10	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#121	—	2	1	no	—
12	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#120	—	2	1	no	—
14	C₁₉×#483	—	2	1	no	—
15	C₁₉×#481	—	2	1	no	—
16	C₁₉×#465	—	2	2	no	—
17	C₁₉×#450	—	2	1	no	—
18	C₁₉×#448	—	2	1	no	—
19	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₁₉×#386	—	2	2	no	—
23	C₁₉×#386	—	2	1	no	—
24	C₁₉×#385	—	2	2	no	—
25	C₁₉×#385	—	2	1	no	—
26	C₁₉×#380	—	2	1	no	—
27	C₁₉×#380	—	2	1	no	—
28	C₁₉×#380	C₂²	1	1	yes	characteristic
29	C₁₉×#380	C₂²	1	1	yes	characteristic
30	C₁₉×#379	—	2	1	no	—
31	C₁₉×#328	—	2	2	no	—
32	C₁₉×#327	—	2	2	no	—
33	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	—	2	1	no	—
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	—	4	4	no	—
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×SD₁₆×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	D₄	1	2	yes	complemented
50	C₁₉×C₂²⋊Q₈	—	2	1	no	—
51	C₁₉×C₂²⋊Q₈	—	2	1	no	—
52	C₁₉×C₂²⋊Q₈	—	2	1	no	—
53	C₁₉×C₂²⋊Q₈	—	2	1	no	—
54	C₁₉×C₂²⋊Q₈	—	4	4	no	—
55	C₁₉×#121	—	2	1	no	—
56	C₁₉×#121	—	2	1	no	—
57	C₁₉×#121	—	2	1	no	—
58	C₁₉×#121	—	2	1	no	—
59	C₁₉×#121	—	4	4	no	—
60	C₁₉×#120	—	4	2	no	—
61	C₁₉×#120	—	4	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₁₉×#106	—	2	2	no	—
77	C₁₉×#103	—	2	2	no	—
78	C₁₉×#102	—	2	2	no	—
79	C₁₉×C₂²⋊C₈	—	2	1	no	—
80	C₁₉×C₂²⋊C₈	—	2	1	no	—
81	C₁₉×C₂²⋊C₈	—	2	1	no	—
82	C₁₉×C₂²⋊C₈	—	2	1	no	—
83	C₁₉×C₂²⋊C₈	—	4	4	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	D₄	1	2	yes	—
87	C₁₉×#95	D₄	1	2	yes	complemented
88	C₂⁴×C₁₉	—	2	1	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	C₂⁴×C₁₉	—	2	1	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	—	4	2	no	—
96	C₂⁴×C₁₉	—	4	2	no	—
97	C₂⁴×C₁₉	SD₁₆	1	2	yes	complemented
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₉	—	2	1	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	4	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	4	1	no	—
109	C₂×D₄×C₁₉	—	4	1	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	—	4	1	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	4	2	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	—	4	2	no	—
128	C₂²×C₄×C₁₉	—	4	2	no	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	—	4	2	no	—
131	C₂²×C₄×C₁₉	—	4	2	no	—
132	C₂²×C₄×C₁₉	—	4	2	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	4	2	no	—
135	C₂²×C₄×C₁₉	—	4	2	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
146	SD₁₆×C₁₉	—	8	2	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	4	2	no	—
149	C₂×C₈×C₁₉	—	4	2	no	—
150	C₂×C₈×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	4	2	no	—
156	C₄⋊C₄×C₁₉	—	4	2	no	—
157	C₄⋊C₄×C₁₉	—	4	4	no	—
158	C₄⋊C₄×C₁₉	—	4	1	no	—
159	C₄⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₉	—	4	4	no	—
162	C₂²⋊C₄×C₁₉	—	4	4	no	—
163	C₂²⋊C₄×C₁₉	—	4	4	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₂²⋊C₄×C₁₉	—	4	1	no	—
166	C₂²⋊C₄×C₁₉	—	4	1	no	—
167	C₂²⋊C₄×C₁₉	—	4	1	no	—
168	C₂²⋊C₄×C₁₉	—	4	1	no	—
169	C₂²⋊C₄×C₁₉	—	4	1	no	—
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₂²⋊C₄×C₁₉	—	4	1	no	—
172	#10322	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	4	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	4	no	—
192	C₂³×C₁₉	—	4	4	no	—
193	C₂³×C₁₉	—	4	4	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	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	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	#120	1	1	yes	characteristic
204	C₂³×C₁₉	#120	1	1	yes	characteristic
205	C₂³×C₁₉	#121	1	1	yes	characteristic
206	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
207	C₂³×C₁₉	#135	1	1	yes	characteristic
208	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₂³×C₁₉	#137	1	1	yes	characteristic
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	—	8	1	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	8	1	no	—
214	D₄×C₁₉	—	8	8	no	—
215	D₄×C₁₉	—	8	1	no	—
216	D₄×C₁₉	—	8	1	no	—
217	D₄×C₁₉	—	8	1	no	—
218	D₄×C₁₉	—	8	1	no	—
219	C₂×C₄×C₁₉	—	2	2	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	1	no	—
228	C₂×C₄×C₁₉	—	4	4	no	—
229	C₂×C₄×C₁₉	—	4	4	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	4	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	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	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
253	C₈×C₁₉	—	4	2	no	—
254	C₈×C₁₉	—	8	1	no	—
255	#3187	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2848	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2847	C₂×C₁₉	1	1	yes	characteristic
258	#1779	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1520	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1519	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1289	C₂×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	2	1	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	4	no	—
269	C₂²×C₁₉	—	2	4	no	—
270	C₂²×C₁₉	—	2	4	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	4	2	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	2	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	8	2	no	—
288	C₂²×C₁₉	—	8	2	no	—
289	C₂²×C₁₉	—	8	1	no	—
290	C₂²×C₁₉	—	8	1	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	#392	1	1	yes	characteristic
293	C₂²×C₁₉	#448	1	1	yes	characteristic
294	C₂²×C₁₉	#449	1	1	yes	characteristic
295	C₂²×C₁₉	#450	1	1	yes	characteristic
296	C₂²×C₁₉	#452	1	1	yes	characteristic
297	C₂²×C₁₉	#465	1	1	yes	characteristic
298	C₂²×C₁₉	#468	1	1	yes	characteristic
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	8	2	no	—
304	C₄×C₁₉	—	8	2	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	B(4,𝔽₂)	1	2	yes	—
309	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×C₂²⋊Q₈	—	2	1	no	—
311	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×#121	—	2	1	no	—
313	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#120	—	2	1	no	—
315	#483	—	2	1	no	—
316	#481	—	2	1	no	—
317	#465	—	2	2	no	—
318	#450	—	2	1	no	—
319	#448	—	2	1	no	—
320	C₂×C₂²⋊C₈	—	2	2	no	—
321	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
323	#386	—	2	1	no	—
324	#386	—	2	2	no	—
325	#385	—	2	1	no	—
326	#385	—	2	2	no	—
327	#380	—	2	1	no	—
328	#380	—	2	1	no	—
329	#380	C₂²×C₁₉	1	1	yes	characteristic
330	#380	C₂²×C₁₉	1	1	yes	characteristic
331	#379	—	2	1	no	—
332	#328	—	2	2	no	—
333	#327	—	2	2	no	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	1	no	—
337	C₂×C₁₉	—	2	1	no	—
338	C₂×C₁₉	—	2	1	no	—
339	C₂×C₁₉	—	2	1	no	—
340	C₂×C₁₉	—	4	4	no	—
341	C₂×C₁₉	—	16	1	no	—
342	C₂×C₁₉	#2000	1	1	yes	characteristic
343	C₂×C₁₉	#2010	1	1	yes	characteristic
344	C₂×C₁₉	#2021	1	1	yes	characteristic
345	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
346	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	—	4	4	no	—
357	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×SD₁₆	—	2	2	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	D₄×C₁₉	1	2	yes	complemented
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	—	4	4	no	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	4	4	no	—
372	#120	—	4	2	no	—
373	#120	—	4	2	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	#106	—	2	2	no	—
389	#103	—	2	2	no	—
390	#102	—	2	2	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	2	1	no	—
395	C₂²⋊C₈	—	4	4	no	—
396	#95	—	2	2	no	—
397	#95	—	2	2	no	—
398	#95	D₄×C₁₉	1	2	yes	—
399	#95	D₄×C₁₉	1	2	yes	complemented
400	C₁₉	#10322	1	1	yes	characteristic, direct product factor, Sylow
401	C₂⁴	—	2	1	no	—
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	—	2	1	no	—
405	C₂⁴	—	2	1	no	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	—	4	2	no	—
409	C₂⁴	—	4	2	no	—
410	C₂⁴	SD₁₆×C₁₉	1	2	yes	complemented
411	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	4	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
459	SD₁₆	—	8	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	4	2	no	—
463	C₂×C₈	—	4	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₄⋊C₄	—	4	4	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	4	no	—
474	C₂²⋊C₄	—	4	4	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	4	4	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	4	no	—
504	C₂³	—	4	4	no	—
505	C₂³	—	4	4	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	C₁₉×#120	1	1	yes	characteristic
516	C₂³	C₁₉×#120	1	1	yes	characteristic
517	C₂³	C₁₉×#121	1	1	yes	characteristic
518	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
519	C₂³	C₁₉×#135	1	1	yes	characteristic
520	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
521	C₂³	C₁₉×#137	1	1	yes	characteristic
522	Q₈	—	4	2	no	—
523	Q₈	—	8	1	no	—
524	D₄	—	4	2	no	—
525	D₄	—	8	1	no	—
526	D₄	—	8	8	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	8	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
562	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
563	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
564	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
565	C₈	—	4	2	no	—
566	C₈	—	8	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	8	2	no	—
593	C₂²	—	8	2	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	C₁₉×#392	1	1	yes	characteristic
598	C₂²	C₁₉×#448	1	1	yes	characteristic
599	C₂²	C₁₉×#449	1	1	yes	characteristic
600	C₂²	C₁₉×#450	1	1	yes	characteristic
601	C₂²	C₁₉×#452	1	1	yes	characteristic
602	C₂²	C₁₉×#465	1	1	yes	characteristic
603	C₂²	C₁₉×#468	1	1	yes	characteristic
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	4	2	no	—
608	C₄	—	8	2	no	—
609	C₄	—	8	2	no	—
610	C₄	—	8	1	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	C₁₉×B(4,𝔽₂)	1	2	yes	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	4	4	no	—
621	C₂	—	16	1	no	—
622	C₂	C₁₉×#2000	1	1	yes	characteristic
623	C₂	C₁₉×#2010	1	1	yes	characteristic
624	C₂	C₁₉×#2021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3187	C₂	semidirect
2. C₁₉×#2848	C₂	semidirect
4. C₁₉×#1779	C₂	semidirect
5. C₁₉×#1520	C₂	semidirect
6. C₁₉×#1519	C₂	semidirect
7. C₁₉×#1289	C₂	semidirect
34. C₂²×Q₈×C₁₉	D₄	semidirect
49. C₂²×C₈×C₁₉	D₄	semidirect
67. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
87. C₁₉×#95	D₄	semidirect
97. C₂⁴×C₁₉	SD₁₆	semidirect
172. #10322	C₁₉	direct (N × H)
255. #3187	C₂×C₁₉	semidirect
256. #2848	C₂×C₁₉	semidirect
258. #1779	C₂×C₁₉	semidirect
259. #1520	C₂×C₁₉	semidirect
260. #1519	C₂×C₁₉	semidirect
261. #1289	C₂×C₁₉	semidirect
346. C₂²×Q₈	D₄×C₁₉	semidirect
361. C₂²×C₈	D₄×C₁₉	semidirect
379. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
399. #95	D₄×C₁₉	semidirect
400. C₁₉	#10322	direct (N × H)
410. C₂⁴	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3187	2
C₁₉×#2848	2
C₁₉×#2847	2
C₁₉×#1779	2
C₁₉×#1520	2
C₁₉×#1519	2
C₁₉×#1289	2
#10322	19

Subgroups — C19×#10322 #18016281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10322 #18016281