Subgroups — C₁₉×#20581 #18026540

Order 4864.

3998 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#408	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1780	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1779	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₁₉	—	2	16	no	—
8	C₂²×#41×C₁₉	—	2	4	no	—
9	C₂²×#41×C₁₉	—	2	4	no	—
10	C₂²×#41×C₁₉	C₄	1	2	yes	—
11	C₂²×#41×C₁₉	C₄	1	2	yes	—
12	C₂²×#41×C₁₉	C₂²	1	2	yes	—
13	C₂²×#41×C₁₉	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
15	C₂³×D₄×C₁₉	C₄	1	2	yes	—
16	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₁₉	C₂²	1	2	yes	complemented
21	C₁₉×#408	—	2	16	no	—
22	C₁₉×#407	—	2	4	no	—
23	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	16	yes	complemented
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
29	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
30	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×#41×C₁₉	—	2	64	no	—
32	C₂×#41×C₁₉	—	2	64	no	—
33	C₂×#41×C₁₉	—	2	8	no	—
34	C₂×#41×C₁₉	—	2	8	no	—
35	C₂×#41×C₁₉	—	2	16	no	—
36	C₂×#41×C₁₉	—	2	8	no	—
37	C₂×#41×C₁₉	—	2	8	no	—
38	C₂×#41×C₁₉	—	2	16	no	—
39	C₂×#41×C₁₉	—	2	4	no	—
40	C₂×#41×C₁₉	—	2	4	no	—
41	C₂×#41×C₁₉	—	2	4	no	—
42	C₂×#41×C₁₉	—	2	8	no	—
43	C₂×#41×C₁₉	—	2	4	no	—
44	C₂×#41×C₁₉	D₄	1	16	yes	—
45	C₂²×Q₈×C₁₉	—	2	8	no	—
46	C₂²×Q₈×C₁₉	—	2	4	no	—
47	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
48	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₁₉	—	2	8	no	—
50	C₂²×D₄×C₁₉	—	2	16	no	—
51	C₂²×D₄×C₁₉	—	2	8	no	—
52	C₂²×D₄×C₁₉	—	2	4	no	—
53	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
54	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
56	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
57	C₂³×C₄×C₁₉	—	2	4	no	—
58	C₂³×C₄×C₁₉	—	2	4	no	—
59	C₂³×C₄×C₁₉	—	2	16	no	—
60	C₂³×C₄×C₁₉	—	2	8	no	—
61	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
63	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	D₄	1	4	yes	—
67	C₂³×C₄×C₁₉	D₄	1	4	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₁₉	—	2	4	no	—
73	C₂×M₁₆×C₁₉	—	2	8	no	—
74	C₂²×C₈×C₁₉	—	2	4	no	—
75	C₂²×C₈×C₁₉	—	2	8	no	—
76	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
77	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
78	C₁₉×C₂²⋊C₈	—	2	4	no	—
79	C₁₉×C₂²⋊C₈	—	2	4	no	—
80	C₁₉×C₂²⋊C₈	—	2	4	no	—
81	C₁₉×C₂²⋊C₈	—	2	4	no	—
82	C₁₉×C₂²⋊C₈	—	2	32	no	—
83	C₂⁴×C₁₉	—	2	8	no	—
84	C₂⁴×C₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	—	2	4	no	—
87	C₂⁴×C₁₉	—	2	8	no	—
88	C₂⁴×C₁₉	—	4	2	no	—
89	C₂⁴×C₁₉	—	4	4	no	—
90	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
91	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	#41×C₁₉	—	2	64	no	—
96	#41×C₁₉	—	2	64	no	—
97	#41×C₁₉	—	2	32	no	—
98	#41×C₁₉	—	2	32	no	—
99	#41×C₁₉	—	2	32	no	—
100	#41×C₁₉	—	2	32	no	—
101	C₂×Q₈×C₁₉	—	2	32	no	—
102	C₂×Q₈×C₁₉	—	2	8	no	—
103	C₂×Q₈×C₁₉	—	2	4	no	—
104	C₂×Q₈×C₁₉	—	2	4	no	—
105	C₂×Q₈×C₁₉	—	2	4	no	—
106	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	—
107	C₂×D₄×C₁₉	—	2	64	no	—
108	C₂×D₄×C₁₉	—	2	32	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	8	no	—
111	C₂×D₄×C₁₉	—	2	8	no	—
112	C₂×D₄×C₁₉	—	2	8	no	—
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	4	no	—
118	C₂×D₄×C₁₉	C₂²⋊C₄	1	16	yes	—
119	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
120	C₂²×C₄×C₁₉	—	2	32	no	—
121	C₂²×C₄×C₁₉	—	2	32	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	8	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	2	8	no	—
128	C₂²×C₄×C₁₉	—	2	8	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	16	no	—
131	C₂²×C₄×C₁₉	—	2	16	no	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	8	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
139	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	16	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	M₁₆×C₁₉	—	4	8	no	—
154	C₂×C₈×C₁₉	—	2	4	no	—
155	C₂×C₈×C₁₉	—	2	8	no	—
156	C₂×C₈×C₁₉	—	2	4	no	—
157	C₂×C₈×C₁₉	—	2	8	no	—
158	C₂×C₈×C₁₉	—	4	8	no	—
159	#20581	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	16	no	—
165	C₂³×C₁₉	—	2	4	no	—
166	C₂³×C₁₉	—	2	4	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	8	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	8	no	—
172	C₂³×C₁₉	—	2	8	no	—
173	C₂³×C₁₉	—	2	8	no	—
174	C₂³×C₁₉	—	4	4	no	—
175	C₂³×C₁₉	—	4	16	no	—
176	C₂³×C₁₉	—	4	32	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	8	no	—
179	C₂³×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
180	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂³×C₁₉	#131	1	4	yes	—
185	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
186	Q₈×C₁₉	—	2	16	no	—
187	Q₈×C₁₉	—	2	16	no	—
188	D₄×C₁₉	—	2	32	no	—
189	D₄×C₁₉	—	2	16	no	—
190	D₄×C₁₉	—	2	32	no	—
191	D₄×C₁₉	—	2	16	no	—
192	C₂×C₄×C₁₉	—	2	16	no	—
193	C₂×C₄×C₁₉	—	2	32	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	8	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	16	no	—
202	C₂×C₄×C₁₉	—	2	16	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	8	no	—
206	C₂×C₄×C₁₉	—	2	8	no	—
207	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
209	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
211	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₁₉	#120	1	8	yes	—
213	C₂×C₄×C₁₉	#120	1	8	yes	—
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
217	C₈×C₁₉	—	4	4	no	—
218	C₈×C₁₉	—	4	4	no	—
219	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic
220	C₂×#408	C₂×C₁₉	1	4	yes	complemented
221	C₂×#407	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1780	C₂×C₁₉	1	4	yes	complemented
224	#1779	C₂×C₁₉	1	4	yes	complemented
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	8	no	—
229	C₂²×C₁₉	—	2	8	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	16	no	—
234	C₂²×C₁₉	—	2	8	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	4	16	no	—
237	C₂²×C₁₉	—	4	32	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	4	no	—
241	C₂²×C₁₉	—	4	8	no	—
242	C₂²×C₁₉	#379	1	4	yes	—
243	C₂²×C₁₉	#408	1	4	yes	complemented
244	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
246	C₂²×C₁₉	C₂×#131	1	2	yes	—
247	C₂²×C₁₉	#568	1	2	yes	—
248	C₄×C₁₉	—	2	2	no	—
249	C₄×C₁₉	—	2	8	no	—
250	C₄×C₁₉	—	2	2	no	—
251	C₄×C₁₉	#379	1	4	yes	—
252	C₄×C₁₉	C₂×#120	1	2	yes	—
253	C₄×C₁₉	C₂×#120	1	2	yes	—
254	C₂²×#41	—	2	16	no	—
255	C₂²×#41	—	2	4	no	—
256	C₂²×#41	—	2	4	no	—
257	C₂²×#41	C₄×C₁₉	1	2	yes	—
258	C₂²×#41	C₄×C₁₉	1	2	yes	—
259	C₂²×#41	C₂²×C₁₉	1	2	yes	—
260	C₂²×#41	C₂²×C₁₉	1	2	yes	—
261	C₂³×Q₈	C₄×C₁₉	1	1	yes	characteristic
262	C₂³×D₄	C₄×C₁₉	1	2	yes	—
263	C₂³×D₄	C₄×C₁₉	1	1	yes	characteristic
264	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
265	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
266	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
267	C₂³×C₈	C₂²×C₁₉	1	2	yes	complemented
268	#408	—	2	16	no	—
269	#407	—	2	4	no	—
270	C₂×C₂²⋊C₈	—	2	4	no	—
271	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
272	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
273	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
274	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
275	C₂×C₂²⋊C₈	C₂²×C₁₉	1	16	yes	complemented
276	C₂×C₁₉	—	2	4	no	—
277	C₂×C₁₉	—	2	4	no	—
278	C₂×C₁₉	—	4	2	no	—
279	C₂×C₁₉	—	4	8	no	—
280	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#408	1	1	yes	characteristic
282	C₂×C₁₉	#2879	1	1	yes	characteristic
283	C₂×C₁₉	#2880	1	4	yes	—
284	C₂⁵	C₂×C₄×C₁₉	1	2	yes	—
285	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₂×#41	—	2	64	no	—
287	C₂×#41	—	2	64	no	—
288	C₂×#41	—	2	8	no	—
289	C₂×#41	—	2	8	no	—
290	C₂×#41	—	2	16	no	—
291	C₂×#41	—	2	8	no	—
292	C₂×#41	—	2	8	no	—
293	C₂×#41	—	2	16	no	—
294	C₂×#41	—	2	4	no	—
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	8	no	—
298	C₂×#41	—	2	4	no	—
299	C₂×#41	D₄×C₁₉	1	16	yes	—
300	C₂²×Q₈	—	2	8	no	—
301	C₂²×Q₈	—	2	4	no	—
302	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
303	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
304	C₂²×D₄	—	2	8	no	—
305	C₂²×D₄	—	2	16	no	—
306	C₂²×D₄	—	2	8	no	—
307	C₂²×D₄	—	2	4	no	—
308	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
309	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
310	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
311	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
312	C₂³×C₄	—	2	4	no	—
313	C₂³×C₄	—	2	4	no	—
314	C₂³×C₄	—	2	16	no	—
315	C₂³×C₄	—	2	8	no	—
316	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
317	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
318	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
319	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
321	C₂³×C₄	D₄×C₁₉	1	4	yes	—
322	C₂³×C₄	D₄×C₁₉	1	4	yes	—
323	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
325	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×M₁₆	—	2	4	no	—
328	C₂×M₁₆	—	2	8	no	—
329	C₂²×C₈	—	2	4	no	—
330	C₂²×C₈	—	2	8	no	—
331	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
332	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
333	C₂²⋊C₈	—	2	4	no	—
334	C₂²⋊C₈	—	2	4	no	—
335	C₂²⋊C₈	—	2	4	no	—
336	C₂²⋊C₈	—	2	4	no	—
337	C₂²⋊C₈	—	2	32	no	—
338	C₁₉	#20581	1	1	yes	characteristic, direct product factor, Sylow
339	C₂⁴	—	2	8	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	4	no	—
342	C₂⁴	—	2	4	no	—
343	C₂⁴	—	2	8	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	4	4	no	—
346	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
347	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
349	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
350	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
351	#41	—	2	64	no	—
352	#41	—	2	64	no	—
353	#41	—	2	32	no	—
354	#41	—	2	32	no	—
355	#41	—	2	32	no	—
356	#41	—	2	32	no	—
357	C₂×Q₈	—	2	32	no	—
358	C₂×Q₈	—	2	8	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	—
363	C₂×D₄	—	2	64	no	—
364	C₂×D₄	—	2	32	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	C₂²⋊C₄×C₁₉	1	16	yes	—
375	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
376	C₂²×C₄	—	2	32	no	—
377	C₂²×C₄	—	2	32	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	16	no	—
387	C₂²×C₄	—	2	16	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
394	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
395	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
396	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
398	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	16	yes	—
403	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
409	M₁₆	—	4	8	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	2	8	no	—
412	C₂×C₈	—	2	4	no	—
413	C₂×C₈	—	2	8	no	—
414	C₂×C₈	—	4	8	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	16	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	8	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	16	no	—
431	C₂³	—	4	32	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	8	no	—
434	C₂³	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
435	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
436	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
437	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
438	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
439	C₂³	C₁₉×#131	1	4	yes	—
440	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
441	Q₈	—	2	16	no	—
442	Q₈	—	2	16	no	—
443	D₄	—	2	32	no	—
444	D₄	—	2	16	no	—
445	D₄	—	2	32	no	—
446	D₄	—	2	16	no	—
447	C₂×C₄	—	2	16	no	—
448	C₂×C₄	—	2	32	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	16	no	—
459	C₂×C₄	—	2	16	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
463	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
464	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
466	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
467	C₂×C₄	C₁₉×#120	1	8	yes	—
468	C₂×C₄	C₁₉×#120	1	8	yes	—
469	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
472	C₈	—	4	4	no	—
473	C₈	—	4	4	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	2	8	no	—
480	C₂²	—	2	8	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	16	no	—
485	C₂²	—	4	16	no	—
486	C₂²	—	4	32	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	8	no	—
491	C₂²	C₁₉×#379	1	4	yes	—
492	C₂²	C₁₉×#408	1	4	yes	complemented
493	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
494	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
495	C₂²	C₂×C₁₉×#131	1	2	yes	—
496	C₂²	C₁₉×#568	1	2	yes	—
497	C₄	—	2	2	no	—
498	C₄	—	2	8	no	—
499	C₄	—	2	2	no	—
500	C₄	C₁₉×#379	1	4	yes	—
501	C₄	C₂×C₁₉×#120	1	2	yes	—
502	C₄	C₂×C₁₉×#120	1	2	yes	—
503	C₂	—	2	4	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	2	no	—
506	C₂	—	4	8	no	—
507	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
508	C₂	C₂×C₁₉×#408	1	1	yes	characteristic
509	C₂	C₁₉×#2879	1	1	yes	characteristic
510	C₂	C₁₉×#2880	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂³×#41×C₁₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#408	C₂	semidirect
3. C₂×C₁₉×#407	C₂	semidirect
4. C₂²×C₁₉×C₂²⋊C₈	C₂	semidirect
5. C₁₉×#1780	C₂	semidirect
6. C₁₉×#1779	C₂	semidirect
19. C₂²×M₁₆×C₁₉	C₂²	semidirect
20. C₂³×C₈×C₁₉	C₂²	semidirect
26. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
27. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
28. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
159. #20581	C₁₉	direct (N × H)
220. C₂×#408	C₂×C₁₉	semidirect
221. C₂×#407	C₂×C₁₉	semidirect
222. C₂²×C₂²⋊C₈	C₂×C₁₉	semidirect
223. #1780	C₂×C₁₉	semidirect
224. #1779	C₂×C₁₉	semidirect
243. C₂²×C₁₉	#408	semidirect
266. C₂²×M₁₆	C₂²×C₁₉	semidirect
267. C₂³×C₈	C₂²×C₁₉	semidirect
273. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
274. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
275. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
338. C₁₉	#20581	direct (N × H)
492. C₂²	C₁₉×#408	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₉	2
C₂×C₁₉×#408	2
C₂×C₁₉×#407	2
C₂²×C₁₉×C₂²⋊C₈	2
C₁₉×#1780	2
C₁₉×#1779	2
#20581	19

Subgroups — C19×#20581 #18026540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20581 #18026540