Subgroups — C₁₉×#16229 #18022188

Order 4864.

1142 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#1446	C₂	1	2	yes	maximal
2	C₁₉×#1446	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1445	C₂	1	2	yes	maximal
4	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1441	C₂	1	2	yes	maximal
7	C₁₉×#1436	C₂	1	2	yes	maximal
8	C₁₉×#1436	C₂	1	2	yes	maximal
9	C₁₉×#1434	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#95	C₂²	1	2	yes	—
16	C₂×C₁₉×#95	C₂²	1	2	yes	—
17	C₂×C₁₉×#95	C₂²	1	2	yes	—
18	C₂×C₁₉×#95	C₂²	1	2	yes	—
19	C₂×C₁₉×#95	C₂²	1	2	yes	—
20	C₂×C₁₉×#95	C₂²	1	2	yes	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#95	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂²×Q₈×C₁₉	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	4	no	—
33	C₂²×Q₈×C₁₉	—	4	2	no	—
34	C₂²×Q₈×C₁₉	—	4	1	no	—
35	C₂²×Q₈×C₁₉	—	4	1	no	—
36	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
52	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	complemented
53	C₂×C₄²×C₁₉	—	2	4	no	—
54	C₂×C₄²×C₁₉	—	4	2	no	—
55	C₂×C₄²×C₁₉	—	4	2	no	—
56	C₁₉×#95	—	2	4	no	—
57	C₁₉×#95	—	2	4	no	—
58	C₁₉×#95	—	2	4	no	—
59	C₁₉×#95	—	2	4	no	—
60	C₁₉×#95	—	2	4	no	—
61	C₁₉×#95	—	4	2	no	—
62	C₁₉×#95	—	4	2	no	—
63	C₁₉×#95	—	4	2	no	—
64	C₁₉×#95	—	4	2	no	—
65	C₁₉×#95	—	4	1	no	—
66	C₁₉×#95	—	4	2	no	—
67	C₁₉×#95	—	4	1	no	—
68	C₁₉×#95	—	4	2	no	—
69	C₁₉×#95	—	4	1	no	—
70	C₁₉×#95	—	4	2	no	—
71	C₁₉×#95	Q₈	1	4	yes	complemented
72	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₁₉	—	4	8	no	—
74	C₂×Q₈×C₁₉	—	4	4	no	—
75	C₂×Q₈×C₁₉	—	4	4	no	—
76	C₂×Q₈×C₁₉	—	4	8	no	—
77	C₂×Q₈×C₁₉	—	4	4	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	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	—	2	2	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	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₁₉	#41	1	4	yes	—
132	C₂²×C₄×C₁₉	#41	1	4	yes	—
133	C₂²×C₄×C₁₉	#41	1	2	yes	—
134	C₂²×C₄×C₁₉	#41	1	4	yes	—
135	C₄⋊C₄×C₁₉	—	4	4	no	—
136	C₄⋊C₄×C₁₉	—	4	4	no	—
137	C₄⋊C₄×C₁₉	—	4	8	no	—
138	C₄²×C₁₉	—	4	8	no	—
139	#16229	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
141	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
143	C₂³×C₁₉	C₂×#41	1	2	yes	—
144	C₂³×C₁₉	C₂×#41	1	2	yes	—
145	C₂³×C₁₉	C₂×#41	1	2	yes	—
146	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
147	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
148	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
151	Q₈×C₁₉	—	4	16	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	#1446	C₂×C₁₉	1	2	yes	—
210	#1446	C₂×C₁₉	1	1	yes	characteristic
211	#1445	C₂×C₁₉	1	2	yes	—
212	#1445	C₂×C₁₉	1	1	yes	characteristic
213	#1442	C₂×C₁₉	1	1	yes	characteristic
214	#1441	C₂×C₁₉	1	2	yes	—
215	#1436	C₂×C₁₉	1	2	yes	—
216	#1436	C₂×C₁₉	1	2	yes	—
217	#1434	C₂×C₁₉	1	2	yes	—
218	C₂²×C₁₉	#529	1	2	yes	—
219	C₂²×C₁₉	#533	1	2	yes	—
220	C₂²×C₁₉	#533	1	2	yes	—
221	C₂²×C₁₉	#538	1	1	yes	characteristic
222	C₂²×C₁₉	#538	1	2	yes	—
223	C₂²×C₁₉	#538	1	2	yes	—
224	C₂²×C₁₉	#542	1	2	yes	—
225	C₂²×C₁₉	#543	1	1	yes	characteristic
226	C₂²×C₁₉	#544	1	1	yes	characteristic
227	C₂²×C₁₉	#551	1	2	yes	—
228	C₂²×C₁₉	#551	1	1	yes	characteristic
229	C₂²×C₁₉	#551	1	2	yes	—
230	C₂²×C₁₉	#551	1	1	yes	characteristic
231	C₂²×C₁₉	#552	1	2	yes	—
232	C₂²×C₁₉	#554	1	2	yes	—
233	C₂²×C₁₉	#554	1	2	yes	—
234	C₂²×C₁₉	#554	1	1	yes	characteristic
235	C₂²×C₁₉	#555	1	1	yes	characteristic
236	C₂²×C₁₉	#557	1	1	yes	characteristic
237	C₂²×C₁₉	Q₈²	1	1	yes	characteristic
238	C₂²×C₁₉	#559	1	2	yes	—
239	C₂²×C₁₉	#560	1	1	yes	characteristic
240	C₂²×C₁₉	#562	1	1	yes	characteristic
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	—	4	4	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	4	no	—
249	C₄×C₁₉	—	8	2	no	—
250	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
252	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
255	C₂×#95	C₂²×C₁₉	1	2	yes	—
256	C₂×#95	C₂²×C₁₉	1	2	yes	—
257	C₂×#95	C₂²×C₁₉	1	2	yes	—
258	C₂×#95	C₂²×C₁₉	1	2	yes	—
259	C₂×#95	C₂²×C₁₉	1	2	yes	—
260	C₂×#95	C₂²×C₁₉	1	2	yes	—
261	C₂×#95	C₂²×C₁₉	1	2	yes	—
262	C₂×#95	C₂²×C₁₉	1	2	yes	—
263	C₂×#95	C₂²×C₁₉	1	2	yes	—
264	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#95	C₂²×C₁₉	1	2	yes	—
266	C₂×#95	C₂²×C₁₉	1	2	yes	—
267	C₂×#95	C₂²×C₁₉	1	2	yes	—
268	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×C₁₉	#2520	1	2	yes	—
272	C₂×C₁₉	#2572	1	1	yes	characteristic
273	C₂×C₁₉	#2586	1	2	yes	—
274	C₂×C₁₉	#2589	1	2	yes	—
275	C₂×C₁₉	#2607	1	1	yes	characteristic
276	C₂×C₁₉	#2612	1	1	yes	characteristic
277	C₂×C₁₉	#2735	1	1	yes	characteristic
278	C₂×C₁₉	#2742	1	1	yes	characteristic
279	C₂×C₁₉	#2751	1	2	yes	—
280	C₂×C₁₉	#2784	1	1	yes	characteristic
281	C₂×C₁₉	#2806	1	1	yes	characteristic
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×Q₈	—	2	4	no	—
284	C₂²×Q₈	—	4	2	no	—
285	C₂²×Q₈	—	4	1	no	—
286	C₂²×Q₈	—	4	1	no	—
287	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
291	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
292	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
293	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
294	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
295	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	4	1	no	—
300	C₂×C₄⋊C₄	—	4	1	no	—
301	C₂×C₄⋊C₄	—	4	1	no	—
302	C₂×C₄⋊C₄	—	4	2	no	—
303	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	complemented
304	C₂×C₄²	—	2	4	no	—
305	C₂×C₄²	—	4	2	no	—
306	C₂×C₄²	—	4	2	no	—
307	#95	—	2	4	no	—
308	#95	—	2	4	no	—
309	#95	—	2	4	no	—
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	4	2	no	—
313	#95	—	4	2	no	—
314	#95	—	4	2	no	—
315	#95	—	4	2	no	—
316	#95	—	4	2	no	—
317	#95	—	4	1	no	—
318	#95	—	4	2	no	—
319	#95	—	4	1	no	—
320	#95	—	4	2	no	—
321	#95	—	4	1	no	—
322	#95	Q₈×C₁₉	1	4	yes	complemented
323	C₁₉	#16229	1	1	yes	characteristic, direct product factor, Sylow
324	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
325	C₂×Q₈	—	4	8	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	8	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
383	C₂²×C₄	#41×C₁₉	1	2	yes	—
384	C₂²×C₄	#41×C₁₉	1	4	yes	—
385	C₂²×C₄	#41×C₁₉	1	4	yes	—
386	C₂²×C₄	#41×C₁₉	1	4	yes	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	8	no	—
390	C₄²	—	4	8	no	—
391	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
392	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
393	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
394	C₂³	C₂×#41×C₁₉	1	2	yes	—
395	C₂³	C₂×#41×C₁₉	1	2	yes	—
396	C₂³	C₂×#41×C₁₉	1	2	yes	—
397	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
399	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
402	Q₈	—	4	16	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	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	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂²	C₁₉×#529	1	2	yes	—
461	C₂²	C₁₉×#533	1	2	yes	—
462	C₂²	C₁₉×#533	1	2	yes	—
463	C₂²	C₁₉×#538	1	2	yes	—
464	C₂²	C₁₉×#538	1	1	yes	characteristic
465	C₂²	C₁₉×#538	1	2	yes	—
466	C₂²	C₁₉×#542	1	2	yes	—
467	C₂²	C₁₉×#543	1	1	yes	characteristic
468	C₂²	C₁₉×#544	1	1	yes	characteristic
469	C₂²	C₁₉×#551	1	2	yes	—
470	C₂²	C₁₉×#551	1	1	yes	characteristic
471	C₂²	C₁₉×#551	1	1	yes	characteristic
472	C₂²	C₁₉×#551	1	2	yes	—
473	C₂²	C₁₉×#552	1	2	yes	—
474	C₂²	C₁₉×#554	1	2	yes	—
475	C₂²	C₁₉×#554	1	2	yes	—
476	C₂²	C₁₉×#554	1	1	yes	characteristic
477	C₂²	C₁₉×#555	1	1	yes	characteristic
478	C₂²	C₁₉×#557	1	1	yes	characteristic
479	C₂²	Q₈²×C₁₉	1	1	yes	characteristic
480	C₂²	C₁₉×#559	1	2	yes	—
481	C₂²	C₁₉×#560	1	1	yes	characteristic
482	C₂²	C₁₉×#562	1	1	yes	characteristic
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₂	C₁₉×#2520	1	2	yes	—
493	C₂	C₁₉×#2572	1	1	yes	characteristic
494	C₂	C₁₉×#2586	1	2	yes	—
495	C₂	C₁₉×#2589	1	2	yes	—
496	C₂	C₁₉×#2607	1	1	yes	characteristic
497	C₂	C₁₉×#2612	1	1	yes	characteristic
498	C₂	C₁₉×#2735	1	1	yes	characteristic
499	C₂	C₁₉×#2742	1	1	yes	characteristic
500	C₂	C₁₉×#2751	1	2	yes	—
501	C₂	C₁₉×#2784	1	1	yes	characteristic
502	C₂	C₁₉×#2806	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
52. C₂×C₄⋊C₄×C₁₉	Q₈	semidirect
71. C₁₉×#95	Q₈	semidirect
139. #16229	C₁₉	direct (N × H)
303. C₂×C₄⋊C₄	Q₈×C₁₉	semidirect
322. #95	Q₈×C₁₉	semidirect
323. C₁₉	#16229	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#1446	2
C₁₉×#1445	2
C₁₉×#1442	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×#1434	2
#16229	19

Subgroups — C19×#16229 #18022188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16229 #18022188