Subgroups — C₁₉×#22485 #18028444

Order 4864.

1474 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1893	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1823	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#340	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	—	2	1	no	—
13	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#547	—	2	4	no	—
15	C₁₉×#547	C₄	1	8	yes	complemented
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#123	—	2	2	no	—
18	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×#121	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₈×D₄×C₁₉	—	2	4	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#389	—	2	1	no	—
33	C₁₉×#385	—	2	2	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#340	C₂²	1	1	yes	characteristic
44	C₂×#41×C₁₉	—	2	8	no	—
45	C₂×#41×C₁₉	—	4	4	no	—
46	C₂×#41×C₁₉	—	4	4	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	2	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	4	no	—
56	C₂²×C₈×C₁₉	—	2	4	no	—
57	C₂²×C₈×C₁₉	—	4	2	no	—
58	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
63	C₁₉×#123	—	2	16	no	—
64	C₁₉×C₂²⋊Q₈	—	2	8	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₁₉×#121	C₂×C₄	1	8	yes	complemented
67	C₄×D₄×C₁₉	—	2	2	no	—
68	C₄×D₄×C₁₉	—	4	4	no	—
69	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
70	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
71	C₄×D₄×C₁₉	D₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
80	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
81	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×C₄⋊C₈	—	2	2	no	—
94	C₁₉×#102	—	2	2	no	—
95	C₁₉×#102	—	2	2	no	—
96	C₁₉×#102	—	4	2	no	—
97	C₁₉×C₂²⋊C₈	—	2	4	no	—
98	C₄×C₈×C₁₉	—	2	2	no	—
99	C₁₉×#95	—	2	1	no	—
100	C₁₉×#95	—	2	2	no	—
101	C₂⁴×C₁₉	—	2	1	no	—
102	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
103	#41×C₁₉	—	4	32	no	—
104	C₂×Q₈×C₁₉	—	2	4	no	—
105	C₂×Q₈×C₁₉	—	4	2	no	—
106	C₂×Q₈×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	2	8	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	4	4	no	—
114	C₂×D₄×C₁₉	—	4	4	no	—
115	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
116	C₂×D₄×C₁₉	D₈	1	4	yes	—
117	C₂×D₄×C₁₉	SD₁₆	1	4	yes	—
118	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
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	8	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	4	4	no	—
132	C₂²×C₄×C₁₉	—	4	4	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	4	2	no	—
135	C₂²×C₄×C₁₉	—	4	4	no	—
136	C₂²×C₄×C₁₉	—	8	2	no	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	4	8	no	—
152	C₂×C₈×C₁₉	#41	1	2	yes	complemented
153	C₄⋊C₄×C₁₉	—	2	8	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	4	4	no	—
163	C₄⋊C₄×C₁₉	—	4	2	no	—
164	C₄⋊C₄×C₁₉	—	8	1	no	—
165	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
166	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
168	C₄⋊C₄×C₁₉	#41	1	2	yes	complemented
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	8	no	—
171	C₂²⋊C₄×C₁₉	—	4	4	no	—
172	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
173	C₄²×C₁₉	—	4	2	no	—
174	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
175	C₄²×C₁₉	C₂×D₄	1	2	yes	—
176	#22485	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	1	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	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂³×C₁₉	C₂×D₈	1	4	yes	—
190	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
191	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₁₉	—	4	8	no	—
193	D₄×C₁₉	—	2	2	no	—
194	D₄×C₁₉	—	2	2	no	—
195	D₄×C₁₉	—	4	16	no	—
196	D₄×C₁₉	—	4	1	no	—
197	D₄×C₁₉	—	4	1	no	—
198	D₄×C₁₉	#102	1	16	yes	complemented
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	16	no	—
217	C₂×C₄×C₁₉	—	4	8	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	8	8	no	—
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
227	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
229	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
230	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₁₉	—	2	2	no	—
237	C₈×C₁₉	—	4	2	no	—
238	C₈×C₁₉	—	4	1	no	—
239	C₂×#547	C₂×C₁₉	1	1	yes	characteristic
240	C₂×C₈×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
241	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1990	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#1988	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1893	C₂×C₁₉	1	2	yes	complemented
245	#1874	C₂×C₁₉	1	2	yes	complemented
246	#1823	C₂×C₁₉	1	2	yes	complemented
247	#1802	C₂×C₁₉	1	1	yes	characteristic, complemented
248	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
249	C₂×#340	C₂×C₁₉	1	2	yes	complemented
250	C₂²×C₁₉	—	2	4	no	—
251	C₂²×C₁₉	—	2	4	no	—
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	2	4	no	—
254	C₂²×C₁₉	—	2	4	no	—
255	C₂²×C₁₉	—	2	4	no	—
256	C₂²×C₁₉	—	4	2	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	8	1	no	—
260	C₂²×C₁₉	—	8	1	no	—
261	C₂²×C₁₉	—	8	1	no	—
262	C₂²×C₁₉	—	8	1	no	—
263	C₂²×C₁₉	C₂×#102	1	8	yes	—
264	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₁₉	#546	1	1	yes	characteristic
266	C₂²×C₁₉	#547	1	1	yes	characteristic
267	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
268	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
269	C₂²×C₁₉	#577	1	1	yes	characteristic
270	C₂²×C₁₉	#578	1	1	yes	characteristic
271	C₄×C₁₉	—	2	4	no	—
272	C₄×C₁₉	—	2	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	4	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	2	no	—
278	C₄×C₁₉	C₂×#102	1	4	yes	—
279	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
280	C₄×C₁₉	#520	1	1	yes	characteristic
281	C₄×C₁₉	#546	1	1	yes	characteristic
282	C₄×C₁₉	#547	1	1	yes	characteristic
283	C₂²×#41	—	2	1	no	—
284	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
285	#547	—	2	4	no	—
286	#547	C₄×C₁₉	1	8	yes	complemented
287	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#123	—	2	2	no	—
289	C₂×C₂²⋊Q₈	—	2	1	no	—
290	C₂×#121	C₂²×C₁₉	1	2	yes	—
291	C₂×C₄×D₄	—	2	1	no	—
292	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
295	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
296	C₈×D₄	—	2	4	no	—
297	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#102	C₂²×C₁₉	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
302	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
303	#389	—	2	1	no	—
304	#385	—	2	2	no	—
305	#384	C₂²×C₁₉	1	1	yes	characteristic
306	#380	C₂²×C₁₉	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
308	#340	C₂²×C₁₉	1	2	yes	—
309	#340	C₂²×C₁₉	1	1	yes	characteristic
310	#340	C₂²×C₁₉	1	2	yes	—
311	#340	C₂²×C₁₉	1	2	yes	—
312	#340	C₂²×C₁₉	1	2	yes	—
313	#340	C₂²×C₁₉	1	2	yes	—
314	#340	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₁₉	—	2	8	no	—
316	C₂×C₁₉	—	8	2	no	—
317	C₂×C₁₉	#2339	1	1	yes	characteristic
318	C₂×C₁₉	C₂²×#102	1	1	yes	characteristic
319	C₂×C₁₉	#2898	1	1	yes	characteristic
320	C₂×C₁₉	#3294	1	1	yes	characteristic
321	C₂×C₁₉	#3298	1	1	yes	characteristic
322	C₂×C₁₉	#3334	1	1	yes	characteristic
323	C₂×C₁₉	#3335	1	1	yes	characteristic
324	C₂×#41	—	2	8	no	—
325	C₂×#41	—	4	4	no	—
326	C₂×#41	—	4	4	no	—
327	C₂²×Q₈	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
330	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂³×C₄	—	2	2	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	2	no	—
334	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
335	C₂²×C₈	—	2	4	no	—
336	C₂²×C₈	—	2	4	no	—
337	C₂²×C₈	—	4	2	no	—
338	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
343	#123	—	2	16	no	—
344	C₂²⋊Q₈	—	2	8	no	—
345	#121	—	2	4	no	—
346	#121	C₂×C₄×C₁₉	1	8	yes	complemented
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	4	4	no	—
349	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
350	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
351	C₄×D₄	D₄×C₁₉	1	4	yes	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	4	2	no	—
360	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
361	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
373	C₄⋊C₈	—	2	2	no	—
374	#102	—	2	2	no	—
375	#102	—	2	2	no	—
376	#102	—	4	2	no	—
377	C₂²⋊C₈	—	2	4	no	—
378	C₄×C₈	—	2	2	no	—
379	#95	—	2	1	no	—
380	#95	—	2	2	no	—
381	C₁₉	#22485	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	—	2	1	no	—
383	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
384	#41	—	4	32	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	4	2	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
397	C₂×D₄	D₈×C₁₉	1	4	yes	—
398	C₂×D₄	SD₁₆×C₁₉	1	4	yes	—
399	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	8	2	no	—
418	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
422	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	4	8	no	—
433	C₂×C₈	#41×C₁₉	1	2	yes	complemented
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	4	4	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	8	1	no	—
446	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
447	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
448	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
449	C₄⋊C₄	#41×C₁₉	1	2	yes	complemented
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	4	4	no	—
453	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
454	C₄²	—	4	2	no	—
455	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
456	C₄²	C₂×D₄×C₁₉	1	2	yes	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
469	C₂³	C₂×D₈×C₁₉	1	4	yes	—
470	C₂³	C₂×SD₁₆×C₁₉	1	4	yes	—
471	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
472	Q₈	—	4	8	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	16	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	C₁₉×#102	1	16	yes	complemented
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	16	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	8	8	no	—
505	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
506	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
507	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
508	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
509	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
510	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
516	C₈	—	2	2	no	—
517	C₈	—	4	2	no	—
518	C₈	—	4	1	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	C₂×C₁₉×#102	1	8	yes	—
533	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
534	C₂²	C₁₉×#546	1	1	yes	characteristic
535	C₂²	C₁₉×#547	1	1	yes	characteristic
536	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
537	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
538	C₂²	C₁₉×#577	1	1	yes	characteristic
539	C₂²	C₁₉×#578	1	1	yes	characteristic
540	C₄	—	2	4	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	8	2	no	—
546	C₄	—	8	1	no	—
547	C₄	C₂×C₁₉×#102	1	4	yes	—
548	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
549	C₄	C₁₉×#520	1	1	yes	characteristic
550	C₄	C₁₉×#546	1	1	yes	characteristic
551	C₄	C₁₉×#547	1	1	yes	characteristic
552	C₂	—	2	8	no	—
553	C₂	—	8	2	no	—
554	C₂	C₁₉×#2339	1	1	yes	characteristic
555	C₂	C₂²×C₁₉×#102	1	1	yes	characteristic
556	C₂	C₁₉×#2898	1	1	yes	characteristic
557	C₂	C₁₉×#3294	1	1	yes	characteristic
558	C₂	C₁₉×#3298	1	1	yes	characteristic
559	C₂	C₁₉×#3334	1	1	yes	characteristic
560	C₂	C₁₉×#3335	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₄×C₁₉	C₂	semidirect
3. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#1990	C₂	semidirect
5. C₁₉×#1988	C₂	semidirect
6. C₁₉×#1893	C₂	semidirect
7. C₁₉×#1874	C₂	semidirect
8. C₁₉×#1823	C₂	semidirect
9. C₁₉×#1802	C₂	semidirect
10. C₄×C₁₉×#102	C₂	semidirect
11. C₂×C₁₉×#340	C₂	semidirect
15. C₁₉×#547	C₄	semidirect
62. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
66. C₁₉×#121	C₂×C₄	semidirect
70. C₄×D₄×C₁₉	C₂×C₄	semidirect
80. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
152. C₂×C₈×C₁₉	#41	semidirect
168. C₄⋊C₄×C₁₉	#41	semidirect
176. #22485	C₁₉	direct (N × H)
198. D₄×C₁₉	#102	semidirect
240. C₂×C₈×D₄	C₂×C₁₉	semidirect
241. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
242. #1990	C₂×C₁₉	semidirect
243. #1988	C₂×C₁₉	semidirect
244. #1893	C₂×C₁₉	semidirect
245. #1874	C₂×C₁₉	semidirect
246. #1823	C₂×C₁₉	semidirect
247. #1802	C₂×C₁₉	semidirect
248. C₄×#102	C₂×C₁₉	semidirect
249. C₂×#340	C₂×C₁₉	semidirect
286. #547	C₄×C₁₉	semidirect
342. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
346. #121	C₂×C₄×C₁₉	semidirect
350. C₄×D₄	C₂×C₄×C₁₉	semidirect
360. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
381. C₁₉	#22485	direct (N × H)
433. C₂×C₈	#41×C₁₉	semidirect
449. C₄⋊C₄	#41×C₁₉	semidirect
478. D₄	C₁₉×#102	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#547	2
C₂×C₈×D₄×C₁₉	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#1990	2
C₁₉×#1988	2
C₁₉×#1893	2
C₁₉×#1874	2
C₁₉×#1823	2
C₁₉×#1802	2
C₄×C₁₉×#102	2
C₂×C₁₉×#340	2
#22485	19

Subgroups — C19×#22485 #18028444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22485 #18028444