Subgroups — C₁₉×#14040 #18019999

Order 4864.

1862 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1445	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1443	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1436	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1434	C₂	1	2	yes	maximal, complemented
8	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#385	C₄	1	8	yes	complemented
23	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₁₉×#95	—	2	4	no	—
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	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#95	C₂²	1	2	yes	—
31	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	C₂²	1	2	yes	—
36	C₂×C₁₉×#95	C₂²	1	2	yes	—
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	—	2	2	no	—
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	—	2	4	no	—
45	C₂³×C₄×C₁₉	—	2	4	no	—
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	—	4	2	no	—
49	C₂³×C₄×C₁₉	—	4	2	no	—
50	C₂³×C₄×C₁₉	—	4	2	no	—
51	C₂³×C₄×C₁₉	—	4	2	no	—
52	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
53	C₂³×C₄×C₁₉	D₄	1	4	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
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	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
78	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	—	2	4	no	—
82	C₂×C₄²×C₁₉	—	4	2	no	—
83	C₁₉×#95	—	2	4	no	—
84	C₁₉×#95	—	2	4	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	4	no	—
88	C₁₉×#95	—	2	4	no	—
89	C₁₉×#95	—	2	4	no	—
90	C₁₉×#95	—	4	2	no	—
91	C₁₉×#95	—	4	2	no	—
92	C₁₉×#95	—	4	2	no	—
93	C₁₉×#95	—	4	2	no	—
94	C₁₉×#95	—	4	2	no	—
95	C₁₉×#95	C₂×C₄	1	8	yes	complemented
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
102	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
103	C₂⁴×C₁₉	#41	1	2	yes	—
104	C₂⁴×C₁₉	#41	1	2	yes	—
105	C₂⁴×C₁₉	#41	1	2	yes	—
106	C₂⁴×C₁₉	#41	1	2	yes	—
107	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	8	no	—
112	C₂²×C₄×C₁₉	—	2	8	no	—
113	C₂²×C₄×C₁₉	—	2	8	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	2	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	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	8	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	4	8	no	—
161	C₂²×C₄×C₁₉	—	4	4	no	—
162	C₂²×C₄×C₁₉	—	4	8	no	—
163	C₂²×C₄×C₁₉	—	4	8	no	—
164	C₂²×C₄×C₁₉	—	4	8	no	—
165	C₂²×C₄×C₁₉	—	4	8	no	—
166	C₂²×C₄×C₁₉	—	4	4	no	—
167	C₂²×C₄×C₁₉	—	4	4	no	—
168	C₂²×C₄×C₁₉	—	4	4	no	—
169	C₂²×C₄×C₁₉	—	4	8	no	—
170	C₂²×C₄×C₁₉	—	4	4	no	—
171	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
178	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
179	C₂²×C₄×C₁₉	#41	1	4	yes	—
180	C₂²×C₄×C₁₉	#41	1	4	yes	—
181	C₄⋊C₄×C₁₉	—	4	8	no	—
182	C₂²⋊C₄×C₁₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₉	—	4	4	no	—
186	C₄²×C₁₉	—	4	4	no	—
187	C₄²×C₁₉	—	4	4	no	—
188	#14040	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	4	no	—
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	4	no	—
197	C₂³×C₁₉	—	2	4	no	—
198	C₂³×C₁₉	—	2	4	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	2	4	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	2	4	no	—
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	2	4	no	—
205	C₂³×C₁₉	#117	1	4	yes	—
206	C₂³×C₁₉	C₄×D₄	1	4	yes	—
207	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
208	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
209	C₂³×C₁₉	#123	1	4	yes	—
210	C₂³×C₁₉	#125	1	4	yes	—
211	C₂³×C₁₉	#126	1	4	yes	—
212	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
213	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
215	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
216	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
217	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
218	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
219	C₂³×C₁₉	C₂×#41	1	2	yes	—
220	C₂³×C₁₉	C₂×#41	1	2	yes	—
221	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
222	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	4	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	4	16	no	—
248	C₂×C₄×C₁₉	—	4	16	no	—
249	C₂×C₄×C₁₉	—	4	16	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	2	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	2	no	—
275	C₂×C₄×C₁₉	—	4	2	no	—
276	C₂×C₄×C₁₉	—	4	2	no	—
277	C₂×C₄×C₁₉	—	4	2	no	—
278	C₂×C₄×C₁₉	—	4	2	no	—
279	C₂×C₄×C₁₉	—	4	2	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	#123	1	4	yes	—
284	C₂×#385	C₂×C₁₉	1	1	yes	characteristic
285	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
286	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
287	#1445	C₂×C₁₉	1	2	yes	complemented
288	#1443	C₂×C₁₉	1	2	yes	complemented
289	#1436	C₂×C₁₉	1	2	yes	complemented
290	#1434	C₂×C₁₉	1	2	yes	complemented
291	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
292	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
293	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
294	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
295	C₂²×C₁₉	—	2	4	no	—
296	C₂²×C₁₉	—	2	4	no	—
297	C₂²×C₁₉	—	2	8	no	—
298	C₂²×C₁₉	—	2	8	no	—
299	C₂²×C₁₉	—	2	4	no	—
300	C₂²×C₁₉	—	2	4	no	—
301	C₂²×C₁₉	—	2	4	no	—
302	C₂²×C₁₉	—	2	8	no	—
303	C₂²×C₁₉	—	2	8	no	—
304	C₂²×C₁₉	—	2	4	no	—
305	C₂²×C₁₉	#387	1	8	yes	—
306	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
307	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
308	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
309	C₂²×C₁₉	C₄×#41	1	2	yes	—
310	C₂²×C₁₉	#518	1	2	yes	—
311	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
312	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
313	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
314	C₂²×C₁₉	#525	1	1	yes	characteristic
315	C₂²×C₁₉	C₂×#125	1	1	yes	characteristic
316	C₂²×C₁₉	C₂×#126	1	1	yes	characteristic
317	C₂²×C₁₉	#529	1	2	yes	—
318	C₂²×C₁₉	#534	1	1	yes	characteristic
319	C₂²×C₁₉	#535	1	1	yes	characteristic
320	C₂²×C₁₉	#538	1	2	yes	—
321	C₂²×C₁₉	#551	1	2	yes	—
322	C₂²×C₁₉	#551	1	2	yes	—
323	C₂²×C₁₉	#551	1	2	yes	—
324	C₂²×C₁₉	#551	1	2	yes	—
325	C₂²×C₁₉	#553	1	2	yes	—
326	C₂²×C₁₉	#553	1	2	yes	—
327	C₂²×C₁₉	#554	1	2	yes	—
328	C₂²×C₁₉	#554	1	2	yes	—
329	C₄×C₁₉	—	2	4	no	—
330	C₄×C₁₉	—	4	2	no	—
331	C₄×C₁₉	—	4	4	no	—
332	C₄×C₁₉	—	4	2	no	—
333	C₄×C₁₉	—	4	4	no	—
334	C₄×C₁₉	—	4	4	no	—
335	C₄×C₁₉	—	4	2	no	—
336	C₄×C₁₉	—	4	2	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	8	2	no	—
339	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
340	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
341	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
343	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
349	#385	C₄×C₁₉	1	8	yes	complemented
350	C₄×C₂²⋊C₄	—	2	4	no	—
351	C₂×#95	—	2	4	no	—
352	C₂×#95	C₂²×C₁₉	1	2	yes	—
353	C₂×#95	C₂²×C₁₉	1	2	yes	—
354	C₂×#95	C₂²×C₁₉	1	2	yes	—
355	C₂×#95	C₂²×C₁₉	1	2	yes	—
356	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#95	C₂²×C₁₉	1	2	yes	—
358	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#95	C₂²×C₁₉	1	2	yes	—
360	C₂×#95	C₂²×C₁₉	1	2	yes	—
361	C₂×#95	C₂²×C₁₉	1	2	yes	—
362	C₂×#95	C₂²×C₁₉	1	2	yes	—
363	C₂×#95	C₂²×C₁₉	1	2	yes	—
364	C₂×#95	C₂²×C₁₉	1	2	yes	—
365	C₂×C₁₉	—	2	8	no	—
366	C₂×C₁₉	C₂×#387	1	1	yes	characteristic
367	C₂×C₁₉	C₄×#123	1	1	yes	characteristic
368	C₂×C₁₉	#2321	1	1	yes	characteristic
369	C₂×C₁₉	#2353	1	2	yes	—
370	C₂×C₁₉	#2368	1	2	yes	—
371	C₂×C₁₉	#2482	1	1	yes	characteristic
372	C₂×C₁₉	#2483	1	1	yes	characteristic
373	C₂×C₁₉	#2487	1	1	yes	characteristic
374	C₂×C₁₉	#2505	1	2	yes	—
375	C₂×C₁₉	#2510	1	2	yes	—
376	C₂×C₁₉	#2579	1	1	yes	characteristic
377	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
378	C₂³×C₄	—	2	2	no	—
379	C₂³×C₄	—	2	2	no	—
380	C₂³×C₄	—	2	2	no	—
381	C₂³×C₄	—	2	2	no	—
382	C₂³×C₄	—	2	2	no	—
383	C₂³×C₄	—	2	4	no	—
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	—	2	2	no	—
386	C₂³×C₄	—	2	2	no	—
387	C₂³×C₄	—	4	2	no	—
388	C₂³×C₄	—	4	2	no	—
389	C₂³×C₄	—	4	2	no	—
390	C₂³×C₄	—	4	2	no	—
391	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
392	C₂³×C₄	D₄×C₁₉	1	4	yes	—
393	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
394	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
402	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	—	4	2	no	—
404	C₂×C₄⋊C₄	—	4	2	no	—
405	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₂²⋊C₄	—	2	2	no	—
410	C₂×C₂²⋊C₄	—	2	2	no	—
411	C₂×C₂²⋊C₄	—	2	2	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	2	no	—
414	C₂×C₂²⋊C₄	—	2	2	no	—
415	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
417	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
418	C₂×C₄²	—	2	2	no	—
419	C₂×C₄²	—	2	2	no	—
420	C₂×C₄²	—	2	4	no	—
421	C₂×C₄²	—	4	2	no	—
422	#95	—	2	4	no	—
423	#95	—	2	4	no	—
424	#95	—	2	2	no	—
425	#95	—	2	2	no	—
426	#95	—	2	4	no	—
427	#95	—	2	4	no	—
428	#95	—	2	4	no	—
429	#95	—	4	2	no	—
430	#95	—	4	2	no	—
431	#95	—	4	2	no	—
432	#95	—	4	2	no	—
433	#95	—	4	2	no	—
434	#95	C₂×C₄×C₁₉	1	8	yes	complemented
435	C₁₉	#14040	1	1	yes	characteristic, direct product factor, Sylow
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
441	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
442	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
443	C₂⁴	#41×C₁₉	1	2	yes	—
444	C₂⁴	#41×C₁₉	1	2	yes	—
445	C₂⁴	#41×C₁₉	1	2	yes	—
446	C₂⁴	#41×C₁₉	1	2	yes	—
447	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	8	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	4	8	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	—	4	8	no	—
503	C₂²×C₄	—	4	8	no	—
504	C₂²×C₄	—	4	8	no	—
505	C₂²×C₄	—	4	8	no	—
506	C₂²×C₄	—	4	4	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	—	4	4	no	—
509	C₂²×C₄	—	4	8	no	—
510	C₂²×C₄	—	4	4	no	—
511	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
512	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
513	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
514	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
515	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
517	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
518	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
519	C₂²×C₄	#41×C₁₉	1	4	yes	—
520	C₂²×C₄	#41×C₁₉	1	4	yes	—
521	C₄⋊C₄	—	4	8	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	2	8	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₄²	—	4	4	no	—
527	C₄²	—	4	4	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	C₁₉×#117	1	4	yes	—
545	C₂³	C₄×D₄×C₁₉	1	4	yes	—
546	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
547	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
548	C₂³	C₁₉×#123	1	4	yes	—
549	C₂³	C₁₉×#125	1	4	yes	—
550	C₂³	C₁₉×#126	1	4	yes	—
551	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
552	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
554	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
555	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
556	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
557	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
558	C₂³	C₂×#41×C₁₉	1	2	yes	—
559	C₂³	C₂×#41×C₁₉	1	2	yes	—
560	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
561	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	4	16	no	—
587	C₂×C₄	—	4	16	no	—
588	C₂×C₄	—	4	16	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	C₁₉×#123	1	4	yes	—
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	2	8	no	—
627	C₂²	—	2	8	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	8	no	—
632	C₂²	—	2	8	no	—
633	C₂²	C₁₉×#387	1	8	yes	—
634	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
635	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
636	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
637	C₂²	C₄×#41×C₁₉	1	2	yes	—
638	C₂²	C₁₉×#518	1	2	yes	—
639	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
640	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
641	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
642	C₂²	C₁₉×#525	1	1	yes	characteristic
643	C₂²	C₂×C₁₉×#125	1	1	yes	characteristic
644	C₂²	C₂×C₁₉×#126	1	1	yes	characteristic
645	C₂²	C₁₉×#529	1	2	yes	—
646	C₂²	C₁₉×#534	1	1	yes	characteristic
647	C₂²	C₁₉×#535	1	1	yes	characteristic
648	C₂²	C₁₉×#538	1	2	yes	—
649	C₂²	C₁₉×#551	1	2	yes	—
650	C₂²	C₁₉×#551	1	2	yes	—
651	C₂²	C₁₉×#551	1	2	yes	—
652	C₂²	C₁₉×#551	1	2	yes	—
653	C₂²	C₁₉×#553	1	2	yes	—
654	C₂²	C₁₉×#553	1	2	yes	—
655	C₂²	C₁₉×#554	1	2	yes	—
656	C₂²	C₁₉×#554	1	2	yes	—
657	C₄	—	2	4	no	—
658	C₄	—	4	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	4	no	—
666	C₄	—	8	2	no	—
667	C₂	—	2	8	no	—
668	C₂	C₂×C₁₉×#387	1	1	yes	characteristic
669	C₂	C₄×C₁₉×#123	1	1	yes	characteristic
670	C₂	C₁₉×#2321	1	1	yes	characteristic
671	C₂	C₁₉×#2353	1	2	yes	—
672	C₂	C₁₉×#2368	1	2	yes	—
673	C₂	C₁₉×#2482	1	1	yes	characteristic
674	C₂	C₁₉×#2483	1	1	yes	characteristic
675	C₂	C₁₉×#2487	1	1	yes	characteristic
676	C₂	C₁₉×#2505	1	2	yes	—
677	C₂	C₁₉×#2510	1	2	yes	—
678	C₂	C₁₉×#2579	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1445	C₂	semidirect
5. C₁₉×#1443	C₂	semidirect
6. C₁₉×#1436	C₂	semidirect
7. C₁₉×#1434	C₂	semidirect
22. C₁₉×#385	C₄	semidirect
66. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
95. C₁₉×#95	C₂×C₄	semidirect
188. #14040	C₁₉	direct (N × H)
287. #1445	C₂×C₁₉	semidirect
288. #1443	C₂×C₁₉	semidirect
289. #1436	C₂×C₁₉	semidirect
290. #1434	C₂×C₁₉	semidirect
349. #385	C₄×C₁₉	semidirect
405. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
434. #95	C₂×C₄×C₁₉	semidirect
435. C₁₉	#14040	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×#385	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₂²×C₁₉×#95	2
C₁₉×#1445	2
C₁₉×#1443	2
C₁₉×#1436	2
C₁₉×#1434	2
C₁₉×C₂²⋊#95	2
#14040	19

Subgroups — C19×#14040 #18019999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14040 #18019999