Subgroups — C₁₉×#9963 #18015922

Order 4864.

1046 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2639	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1438	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×SD₁₆×C₁₉	—	2	1	no	—
10	C₂²×D₈×C₁₉	—	2	1	no	—
11	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
14	C₁₉×#450	—	2	2	no	—
15	C₁₉×#450	—	2	2	no	—
16	C₁₉×#447	—	2	2	no	—
17	C₁₉×#447	—	2	2	no	—
18	C₂×C₁₉×#102	—	2	1	no	—
19	C₂×C₁₉×#102	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₁₉×#400	—	2	1	no	—
23	C₁₉×#397	—	2	1	no	—
24	C₁₉×#394	—	2	1	no	—
25	C₁₉×#393	—	2	1	no	—
26	C₁₉×#386	—	2	2	no	—
27	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₁₉×#328	—	2	2	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₂⁵×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	4	4	no	—
40	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	D₄	1	2	yes	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	D₄	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₁₉	—	2	4	no	—
46	C₂×SD₁₆×C₁₉	—	4	4	no	—
47	C₂×D₈×C₁₉	—	2	4	no	—
48	C₂×D₈×C₁₉	—	4	4	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	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	—	2	1	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	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
69	C₁₉×#102	—	2	4	no	—
70	C₁₉×#102	—	2	4	no	—
71	C₁₉×C₂²⋊C₈	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
74	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	1	no	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	—	2	2	no	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	C₂⁴×C₁₉	—	4	2	no	—
85	C₂⁴×C₁₉	—	4	2	no	—
86	C₂⁴×C₁₉	—	4	2	no	—
87	C₂⁴×C₁₉	—	4	1	no	—
88	C₂⁴×C₁₉	—	4	1	no	—
89	C₂⁴×C₁₉	—	4	2	no	—
90	C₂⁴×C₁₉	—	4	2	no	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	1	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	4	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	2	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	—	4	1	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	—	4	2	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	2	no	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
134	SD₁₆×C₁₉	—	4	8	no	—
135	D₈×C₁₉	—	4	8	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	4	2	no	—
139	C₂×C₈×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₂²⋊C₄×C₁₉	—	4	16	no	—
147	C₂²⋊C₄×C₁₉	—	4	1	no	—
148	C₂²⋊C₄×C₁₉	—	4	1	no	—
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	4	1	no	—
151	C₂²⋊C₄×C₁₉	—	8	2	no	—
152	C₂²⋊C₄×C₁₉	—	8	2	no	—
153	#9963	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	1	no	—
155	C₂³×C₁₉	—	2	1	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	4	4	no	—
159	C₂³×C₁₉	—	4	4	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	4	no	—
164	C₂³×C₁₉	—	4	4	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	4	no	—
167	C₂³×C₁₉	—	4	4	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	8	2	no	—
174	C₂³×C₁₉	—	8	2	no	—
175	C₂³×C₁₉	—	8	2	no	—
176	C₂³×C₁₉	—	8	2	no	—
177	C₂³×C₁₉	—	8	2	no	—
178	C₂³×C₁₉	—	8	2	no	—
179	C₂³×C₁₉	—	8	1	no	—
180	C₂³×C₁₉	—	8	1	no	—
181	C₂³×C₁₉	—	8	1	no	—
182	C₂³×C₁₉	—	8	1	no	—
183	C₂³×C₁₉	#120	1	1	yes	characteristic
184	C₂³×C₁₉	#121	1	1	yes	characteristic
185	C₂³×C₁₉	#127	1	1	yes	characteristic
186	C₂³×C₁₉	#135	1	2	yes	—
187	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	8	1	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	4	no	—
195	D₄×C₁₉	—	4	4	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	8	1	no	—
198	D₄×C₁₉	—	8	2	no	—
199	D₄×C₁₉	—	8	1	no	—
200	D₄×C₁₉	—	8	1	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	4	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	8	1	no	—
222	C₂×C₄×C₁₉	—	8	1	no	—
223	C₂×C₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
228	C₈×C₁₉	—	4	2	no	—
229	C₈×C₁₉	—	4	2	no	—
230	C₂×#450	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
232	#2639	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
234	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1438	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1280	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	4	8	no	—
246	C₂²×C₁₉	—	4	4	no	—
247	C₂²×C₁₉	—	8	4	no	—
248	C₂²×C₁₉	—	8	4	no	—
249	C₂²×C₁₉	—	8	4	no	—
250	C₂²×C₁₉	—	8	4	no	—
251	C₂²×C₁₉	—	8	4	no	—
252	C₂²×C₁₉	—	8	2	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	—	8	2	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	1	no	—
258	C₂²×C₁₉	—	8	1	no	—
259	C₂²×C₁₉	#392	1	1	yes	characteristic
260	C₂²×C₁₉	#449	1	2	yes	—
261	C₂²×C₁₉	#453	1	1	yes	characteristic
262	C₂²×C₁₉	#454	1	1	yes	characteristic
263	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
264	C₂²×C₁₉	#463	1	2	yes	—
265	C₂²×C₁₉	#495	1	1	yes	characteristic
266	C₂²×C₁₉	#496	1	1	yes	characteristic
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	8	2	no	—
272	C₄×C₁₉	—	8	2	no	—
273	C₄×C₁₉	—	8	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₂²×SD₁₆	—	2	1	no	—
278	C₂²×D₈	—	2	1	no	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	—	2	2	no	—
282	#450	—	2	2	no	—
283	#450	—	2	2	no	—
284	#447	—	2	2	no	—
285	#447	—	2	2	no	—
286	C₂×#102	—	2	1	no	—
287	C₂×#102	—	2	1	no	—
288	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
290	#400	—	2	1	no	—
291	#397	—	2	1	no	—
292	#394	—	2	1	no	—
293	#393	—	2	1	no	—
294	#386	—	2	2	no	—
295	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
297	#328	—	2	2	no	—
298	#327	—	2	2	no	—
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	2	2	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	8	4	no	—
303	C₂×C₁₉	—	16	1	no	—
304	C₂×C₁₉	#1597	1	2	yes	—
305	C₂×C₁₉	#1600	1	2	yes	—
306	C₂×C₁₉	#2006	1	1	yes	characteristic
307	C₂×C₁₉	#2012	1	1	yes	characteristic
308	C₂×C₁₉	#2021	1	1	yes	characteristic
309	C₂⁵	—	2	1	no	—
310	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	4	4	no	—
318	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂²×D₄	D₄×C₁₉	1	2	yes	—
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	D₄×C₁₉	1	2	yes	—
322	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×SD₁₆	—	2	4	no	—
324	C₂×SD₁₆	—	4	4	no	—
325	C₂×D₈	—	2	4	no	—
326	C₂×D₈	—	4	4	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	2	1	no	—
333	#121	—	2	1	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	4	4	no	—
345	C₂×C₂²⋊C₄	—	4	4	no	—
346	C₂×C₂²⋊C₄	—	4	4	no	—
347	#102	—	2	4	no	—
348	#102	—	2	4	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
352	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	C₁₉	#9963	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	2	no	—
362	C₂⁴	—	2	1	no	—
363	C₂⁴	—	4	2	no	—
364	C₂⁴	—	4	2	no	—
365	C₂⁴	—	4	2	no	—
366	C₂⁴	—	4	1	no	—
367	C₂⁴	—	4	1	no	—
368	C₂⁴	—	4	2	no	—
369	C₂⁴	—	4	2	no	—
370	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	4	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	—	4	1	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
413	SD₁₆	—	4	8	no	—
414	D₈	—	4	8	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	4	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₂²⋊C₄	—	4	16	no	—
426	C₂²⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	4	1	no	—
430	C₂²⋊C₄	—	8	2	no	—
431	C₂²⋊C₄	—	8	2	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	4	4	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	8	2	no	—
452	C₂³	—	8	2	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	1	no	—
458	C₂³	—	8	1	no	—
459	C₂³	—	8	1	no	—
460	C₂³	—	8	1	no	—
461	C₂³	C₁₉×#120	1	1	yes	characteristic
462	C₂³	C₁₉×#121	1	1	yes	characteristic
463	C₂³	C₁₉×#127	1	1	yes	characteristic
464	C₂³	C₁₉×#135	1	2	yes	—
465	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
466	Q₈	—	4	2	no	—
467	Q₈	—	8	1	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	1	no	—
476	D₄	—	8	2	no	—
477	D₄	—	8	1	no	—
478	D₄	—	8	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	1	no	—
499	C₂×C₄	—	8	2	no	—
500	C₂×C₄	—	8	1	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
503	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
506	C₈	—	4	2	no	—
507	C₈	—	4	2	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	8	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	8	4	no	—
519	C₂²	—	8	4	no	—
520	C₂²	—	8	4	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	4	no	—
524	C₂²	—	8	4	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	C₁₉×#392	1	1	yes	characteristic
531	C₂²	C₁₉×#449	1	2	yes	—
532	C₂²	C₁₉×#453	1	1	yes	characteristic
533	C₂²	C₁₉×#454	1	1	yes	characteristic
534	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
535	C₂²	C₁₉×#463	1	2	yes	—
536	C₂²	C₁₉×#495	1	1	yes	characteristic
537	C₂²	C₁₉×#496	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	8	2	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	1	no	—
545	C₄	—	8	1	no	—
546	C₄	—	8	2	no	—
547	C₂	—	2	1	no	—
548	C₂	—	2	2	no	—
549	C₂	—	2	1	no	—
550	C₂	—	8	4	no	—
551	C₂	—	16	1	no	—
552	C₂	C₁₉×#1597	1	2	yes	—
553	C₂	C₁₉×#1600	1	2	yes	—
554	C₂	C₁₉×#2006	1	1	yes	characteristic
555	C₂	C₁₉×#2012	1	1	yes	characteristic
556	C₂	C₁₉×#2021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#447	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#450	C₂	semidirect
3. C₁₉×#2639	C₂	semidirect
4. C₂×C₁₉×#328	C₂	semidirect
5. C₂×C₁₉×#327	C₂	semidirect
6. C₁₉×#1438	C₂	semidirect
7. C₁₉×#1280	C₂	semidirect
153. #9963	C₁₉	direct (N × H)
230. C₂×#450	C₂×C₁₉	semidirect
232. #2639	C₂×C₁₉	semidirect
233. C₂×#328	C₂×C₁₉	semidirect
234. C₂×#327	C₂×C₁₉	semidirect
235. #1438	C₂×C₁₉	semidirect
236. #1280	C₂×C₁₉	semidirect
359. C₁₉	#9963	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×#450	2
C₂×C₁₉×#447	2
C₁₉×#2639	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₁₉×#1438	2
C₁₉×#1280	2
#9963	19

Subgroups — C19×#9963 #18015922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9963 #18015922