Subgroups — C₁₉×#20605 #18026564

Order 4864.

3966 conjugacy classes of subgroups.

The subgroup lattice has 602 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×#421	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1789	C₂	1	8	yes	maximal, complemented
6	C₂²×#41×C₁₉	—	2	16	no	—
7	C₂²×#41×C₁₉	—	2	2	no	—
8	C₂²×#41×C₁₉	—	2	1	no	—
9	C₂²×#41×C₁₉	—	2	2	no	—
10	C₂²×#41×C₁₉	—	2	1	no	—
11	C₂²×#41×C₁₉	C₄	1	4	yes	complemented
12	C₂²×#41×C₁₉	C₄	1	2	yes	complemented
13	C₂²×#41×C₁₉	C₂²	1	4	yes	—
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₁₉	—	2	1	no	—
17	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
18	C₂⁴×C₄×C₁₉	—	2	1	no	—
19	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
21	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
22	C₁₉×#421	—	2	16	no	—
23	C₂×C₁₉×#104	C₂²	1	16	yes	complemented
24	C₁₉×#407	—	2	1	no	—
25	C₁₉×#407	—	2	1	no	—
26	C₁₉×#407	C₂²	1	4	yes	complemented
27	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
28	C₁₉×#381	—	2	1	no	—
29	C₁₉×#380	—	2	2	no	—
30	C₁₉×#379	—	2	1	no	—
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
32	C₂⁵×C₁₉	—	2	1	no	—
33	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
34	C₂×#41×C₁₉	—	2	16	no	—
35	C₂×#41×C₁₉	—	2	32	no	—
36	C₂×#41×C₁₉	—	2	32	no	—
37	C₂×#41×C₁₉	—	2	16	no	—
38	C₂×#41×C₁₉	—	2	32	no	—
39	C₂×#41×C₁₉	—	2	32	no	—
40	C₂×#41×C₁₉	—	2	8	no	—
41	C₂×#41×C₁₉	—	2	8	no	—
42	C₂×#41×C₁₉	—	2	4	no	—
43	C₂×#41×C₁₉	—	2	4	no	—
44	C₂×#41×C₁₉	—	2	4	no	—
45	C₂×#41×C₁₉	—	2	4	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	8	no	—
48	C₂×#41×C₁₉	—	2	4	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
51	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
52	C₂×#41×C₁₉	D₄	1	16	yes	—
53	C₂×#41×C₁₉	C₂³	1	4	yes	—
54	C₂²×Q₈×C₁₉	—	2	8	no	—
55	C₂²×Q₈×C₁₉	—	2	2	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
58	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
59	C₂²×D₄×C₁₉	—	2	16	no	—
60	C₂²×D₄×C₁₉	—	2	4	no	—
61	C₂²×D₄×C₁₉	—	2	2	no	—
62	C₂²×D₄×C₁₉	—	2	4	no	—
63	C₂²×D₄×C₁₉	—	2	2	no	—
64	C₂²×D₄×C₁₉	—	2	8	no	—
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	—	2	2	no	—
67	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
68	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
69	C₂³×C₄×C₁₉	—	2	16	no	—
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₂³×C₄×C₁₉	—	2	4	no	—
72	C₂³×C₄×C₁₉	—	2	2	no	—
73	C₂³×C₄×C₁₉	—	2	4	no	—
74	C₂³×C₄×C₁₉	—	2	2	no	—
75	C₂³×C₄×C₁₉	—	2	8	no	—
76	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₁₉	D₄	1	2	yes	—
80	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₉	D₄	1	2	yes	—
82	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₁₉	—	2	2	no	—
87	C₂×M₁₆×C₁₉	—	2	8	no	—
88	C₂×M₁₆×C₁₉	C₂³	1	4	yes	complemented
89	C₂²×C₈×C₁₉	—	2	2	no	—
90	C₁₉×#117	—	2	8	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₄²×C₁₉	C₂³	1	4	yes	complemented
95	C₁₉×#104	—	2	32	no	—
96	C₁₉×C₂²⋊C₈	—	2	4	no	—
97	C₁₉×C₂²⋊C₈	—	2	4	no	—
98	C₁₉×#95	—	2	4	no	—
99	C₂⁴×C₁₉	—	2	8	no	—
100	C₂⁴×C₁₉	—	2	4	no	—
101	C₂⁴×C₁₉	—	2	2	no	—
102	C₂⁴×C₁₉	—	2	4	no	—
103	C₂⁴×C₁₉	—	4	4	no	—
104	C₂⁴×C₁₉	—	4	8	no	—
105	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
107	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
109	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
110	#41×C₁₉	—	2	32	no	—
111	#41×C₁₉	—	2	32	no	—
112	#41×C₁₉	—	2	32	no	—
113	#41×C₁₉	—	2	32	no	—
114	#41×C₁₉	—	2	32	no	—
115	#41×C₁₉	—	2	16	no	—
116	#41×C₁₉	—	2	16	no	—
117	#41×C₁₉	—	2	8	no	—
118	#41×C₁₉	—	2	16	no	—
119	#41×C₁₉	—	2	16	no	—
120	#41×C₁₉	—	2	8	no	—
121	#41×C₁₉	C₂²⋊C₄	1	16	yes	complemented
122	#41×C₁₉	C₂×D₄	1	16	yes	—
123	C₂×Q₈×C₁₉	—	2	16	no	—
124	C₂×Q₈×C₁₉	—	2	8	no	—
125	C₂×Q₈×C₁₉	—	2	16	no	—
126	C₂×Q₈×C₁₉	—	2	4	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	4	no	—
129	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
130	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
131	C₂×D₄×C₁₉	—	2	32	no	—
132	C₂×D₄×C₁₉	—	2	32	no	—
133	C₂×D₄×C₁₉	—	2	16	no	—
134	C₂×D₄×C₁₉	—	2	8	no	—
135	C₂×D₄×C₁₉	—	2	16	no	—
136	C₂×D₄×C₁₉	—	2	8	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	16	no	—
139	C₂×D₄×C₁₉	—	2	4	no	—
140	C₂×D₄×C₁₉	—	2	16	no	—
141	C₂×D₄×C₁₉	—	2	4	no	—
142	C₂×D₄×C₁₉	—	2	4	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
145	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₁₉	—	2	8	no	—
147	C₂²×C₄×C₁₉	—	2	32	no	—
148	C₂²×C₄×C₁₉	—	2	32	no	—
149	C₂²×C₄×C₁₉	—	2	16	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	4	no	—
153	C₂²×C₄×C₁₉	—	2	8	no	—
154	C₂²×C₄×C₁₉	—	2	4	no	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	4	no	—
157	C₂²×C₄×C₁₉	—	2	8	no	—
158	C₂²×C₄×C₁₉	—	2	4	no	—
159	C₂²×C₄×C₁₉	—	2	16	no	—
160	C₂²×C₄×C₁₉	—	2	8	no	—
161	C₂²×C₄×C₁₉	—	2	4	no	—
162	C₂²×C₄×C₁₉	—	2	8	no	—
163	C₂²×C₄×C₁₉	—	2	8	no	—
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	4	no	—
166	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
173	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
185	M₁₆×C₁₉	—	2	8	no	—
186	M₁₆×C₁₉	—	4	4	no	—
187	C₂×C₈×C₁₉	—	2	4	no	—
188	C₂×C₈×C₁₉	—	4	4	no	—
189	C₄⋊C₄×C₁₉	—	4	4	no	—
190	C₂²⋊C₄×C₁₉	—	4	8	no	—
191	C₂²⋊C₄×C₁₉	—	4	4	no	—
192	C₄²×C₁₉	—	2	8	no	—
193	#20605	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	4	no	—
196	C₂³×C₁₉	—	2	16	no	—
197	C₂³×C₁₉	—	2	4	no	—
198	C₂³×C₁₉	—	2	4	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	2	8	no	—
202	C₂³×C₁₉	—	2	4	no	—
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	4	2	no	—
208	C₂³×C₁₉	—	4	16	no	—
209	C₂³×C₁₉	—	4	32	no	—
210	C₂³×C₁₉	—	4	8	no	—
211	C₂³×C₁₉	—	4	8	no	—
212	C₂³×C₁₉	—	4	8	no	—
213	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂³×C₁₉	#120	1	4	yes	—
218	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₁₉	—	2	16	no	—
220	Q₈×C₁₉	—	2	4	no	—
221	Q₈×C₁₉	—	2	8	no	—
222	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
223	D₄×C₁₉	—	2	32	no	—
224	D₄×C₁₉	—	2	16	no	—
225	D₄×C₁₉	—	2	16	no	—
226	D₄×C₁₉	—	2	16	no	—
227	D₄×C₁₉	—	2	4	no	—
228	D₄×C₁₉	—	2	8	no	—
229	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
230	C₂×C₄×C₁₉	—	2	16	no	—
231	C₂×C₄×C₁₉	—	2	32	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	8	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	16	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	16	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	4	8	no	—
249	C₂×C₄×C₁₉	—	4	4	no	—
250	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
253	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
254	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#120	1	4	yes	—
257	C₂×C₄×C₁₉	#120	1	4	yes	—
258	C₂×C₄×C₁₉	#120	1	4	yes	—
259	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₈×C₁₉	—	4	4	no	—
263	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic
264	C₂×#421	C₂×C₁₉	1	4	yes	complemented
265	C₂×#407	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1789	C₂×C₁₉	1	8	yes	complemented
268	C₂²×C₁₉	—	2	8	no	—
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	2	2	no	—
272	C₂²×C₁₉	—	2	2	no	—
273	C₂²×C₁₉	—	2	2	no	—
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	8	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	8	no	—
280	C₂²×C₁₉	—	4	8	no	—
281	C₂²×C₁₉	—	4	4	no	—
282	C₂²×C₁₉	—	4	16	no	—
283	C₂²×C₁₉	—	4	32	no	—
284	C₂²×C₁₉	—	4	8	no	—
285	C₂²×C₁₉	#379	1	2	yes	—
286	C₂²×C₁₉	#379	1	2	yes	—
287	C₂²×C₁₉	#421	1	4	yes	complemented
288	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₁₉	C₂×#120	1	2	yes	—
290	C₄×C₁₉	—	2	2	no	—
291	C₄×C₁₉	—	2	8	no	—
292	C₄×C₁₉	—	2	2	no	—
293	C₄×C₁₉	—	8	4	no	—
294	C₄×C₁₉	#379	1	2	yes	—
295	C₄×C₁₉	#379	1	2	yes	—
296	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
297	C₄×C₁₉	C₂×#120	1	2	yes	—
298	C₂²×#41	—	2	16	no	—
299	C₂²×#41	—	2	2	no	—
300	C₂²×#41	—	2	1	no	—
301	C₂²×#41	—	2	2	no	—
302	C₂²×#41	—	2	1	no	—
303	C₂²×#41	C₄×C₁₉	1	4	yes	complemented
304	C₂²×#41	C₄×C₁₉	1	2	yes	complemented
305	C₂²×#41	C₂²×C₁₉	1	4	yes	—
306	C₂²×#41	C₂²×C₁₉	1	2	yes	—
307	C₂³×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
308	C₂³×D₄	—	2	1	no	—
309	C₂³×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
310	C₂⁴×C₄	—	2	1	no	—
311	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
313	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
314	#421	—	2	16	no	—
315	C₂×#104	C₂²×C₁₉	1	16	yes	complemented
316	#407	—	2	1	no	—
317	#407	—	2	1	no	—
318	#407	C₂²×C₁₉	1	4	yes	complemented
319	C₂×C₂²⋊C₈	—	2	2	no	—
320	#381	—	2	1	no	—
321	#380	—	2	2	no	—
322	#379	—	2	1	no	—
323	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
324	C₂×C₁₉	—	2	2	no	—
325	C₂×C₁₉	—	2	2	no	—
326	C₂×C₁₉	—	2	4	no	—
327	C₂×C₁₉	—	2	2	no	—
328	C₂×C₁₉	—	4	2	no	—
329	C₂×C₁₉	—	4	8	no	—
330	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
331	C₂×C₁₉	C₂×#421	1	2	yes	—
332	C₂⁵	—	2	1	no	—
333	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
334	C₂×#41	—	2	16	no	—
335	C₂×#41	—	2	32	no	—
336	C₂×#41	—	2	32	no	—
337	C₂×#41	—	2	16	no	—
338	C₂×#41	—	2	32	no	—
339	C₂×#41	—	2	32	no	—
340	C₂×#41	—	2	8	no	—
341	C₂×#41	—	2	8	no	—
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	2	4	no	—
344	C₂×#41	—	2	4	no	—
345	C₂×#41	—	2	4	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	8	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
351	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
352	C₂×#41	D₄×C₁₉	1	16	yes	—
353	C₂×#41	C₂³×C₁₉	1	4	yes	—
354	C₂²×Q₈	—	2	8	no	—
355	C₂²×Q₈	—	2	2	no	—
356	C₂²×Q₈	—	2	1	no	—
357	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
358	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
359	C₂²×D₄	—	2	16	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	—	2	4	no	—
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	2	8	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
368	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
369	C₂³×C₄	—	2	16	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	4	no	—
372	C₂³×C₄	—	2	2	no	—
373	C₂³×C₄	—	2	4	no	—
374	C₂³×C₄	—	2	2	no	—
375	C₂³×C₄	—	2	8	no	—
376	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
377	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
378	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
379	C₂³×C₄	D₄×C₁₉	1	2	yes	—
380	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
381	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
382	C₂³×C₄	D₄×C₁₉	1	2	yes	—
383	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×M₁₆	—	2	2	no	—
387	C₂×M₁₆	—	2	8	no	—
388	C₂×M₁₆	C₂³×C₁₉	1	4	yes	complemented
389	C₂²×C₈	—	2	2	no	—
390	#117	—	2	8	no	—
391	C₂×C₄⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	4	no	—
394	C₂×C₄²	C₂³×C₁₉	1	4	yes	complemented
395	#104	—	2	32	no	—
396	C₂²⋊C₈	—	2	4	no	—
397	C₂²⋊C₈	—	2	4	no	—
398	#95	—	2	4	no	—
399	C₁₉	#20605	1	1	yes	characteristic, direct product factor, Sylow
400	C₂⁴	—	2	8	no	—
401	C₂⁴	—	2	4	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	4	4	no	—
405	C₂⁴	—	4	8	no	—
406	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
407	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
408	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
409	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
410	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
411	#41	—	2	32	no	—
412	#41	—	2	32	no	—
413	#41	—	2	32	no	—
414	#41	—	2	32	no	—
415	#41	—	2	32	no	—
416	#41	—	2	16	no	—
417	#41	—	2	16	no	—
418	#41	—	2	8	no	—
419	#41	—	2	16	no	—
420	#41	—	2	16	no	—
421	#41	—	2	8	no	—
422	#41	C₂²⋊C₄×C₁₉	1	16	yes	complemented
423	#41	C₂×D₄×C₁₉	1	16	yes	—
424	C₂×Q₈	—	2	16	no	—
425	C₂×Q₈	—	2	8	no	—
426	C₂×Q₈	—	2	16	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
431	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
432	C₂×D₄	—	2	32	no	—
433	C₂×D₄	—	2	32	no	—
434	C₂×D₄	—	2	16	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	16	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	16	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	16	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
446	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
447	C₂²×C₄	—	2	8	no	—
448	C₂²×C₄	—	2	32	no	—
449	C₂²×C₄	—	2	32	no	—
450	C₂²×C₄	—	2	16	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	16	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
469	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
471	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
472	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
473	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
474	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
475	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
476	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
480	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
486	M₁₆	—	2	8	no	—
487	M₁₆	—	4	4	no	—
488	C₂×C₈	—	2	4	no	—
489	C₂×C₈	—	4	4	no	—
490	C₄⋊C₄	—	4	4	no	—
491	C₂²⋊C₄	—	4	8	no	—
492	C₂²⋊C₄	—	4	4	no	—
493	C₄²	—	2	8	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	16	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	8	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	16	no	—
509	C₂³	—	4	32	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	8	no	—
512	C₂³	—	4	8	no	—
513	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
514	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
515	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
516	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
517	C₂³	C₁₉×#120	1	4	yes	—
518	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
519	Q₈	—	2	16	no	—
520	Q₈	—	2	8	no	—
521	Q₈	—	2	4	no	—
522	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
523	D₄	—	2	32	no	—
524	D₄	—	2	16	no	—
525	D₄	—	2	16	no	—
526	D₄	—	2	16	no	—
527	D₄	—	2	8	no	—
528	D₄	—	2	4	no	—
529	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
530	C₂×C₄	—	2	16	no	—
531	C₂×C₄	—	2	32	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	16	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	16	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	8	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
551	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
552	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
554	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
555	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
556	C₂×C₄	C₁₉×#120	1	4	yes	—
557	C₂×C₄	C₁₉×#120	1	4	yes	—
558	C₂×C₄	C₁₉×#120	1	4	yes	—
559	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
561	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
562	C₈	—	4	4	no	—
563	C₂²	—	2	8	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	8	no	—
575	C₂²	—	4	8	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	16	no	—
578	C₂²	—	4	32	no	—
579	C₂²	—	4	8	no	—
580	C₂²	C₁₉×#379	1	2	yes	—
581	C₂²	C₁₉×#379	1	2	yes	—
582	C₂²	C₁₉×#421	1	4	yes	complemented
583	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
584	C₂²	C₂×C₁₉×#120	1	2	yes	—
585	C₄	—	2	2	no	—
586	C₄	—	2	8	no	—
587	C₄	—	2	2	no	—
588	C₄	—	8	4	no	—
589	C₄	C₁₉×#379	1	2	yes	—
590	C₄	C₁₉×#379	1	2	yes	—
591	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
592	C₄	C₂×C₁₉×#120	1	2	yes	—
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	2	4	no	—
596	C₂	—	2	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	4	8	no	—
599	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
600	C₂	C₂×C₁₉×#421	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₂³×#41×C₁₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#421	C₂	semidirect
3. C₂×C₁₉×#407	C₂	semidirect
4. C₁₉×#2280	C₂	semidirect
5. C₁₉×#1789	C₂	semidirect
11. C₂²×#41×C₁₉	C₄	semidirect
12. C₂²×#41×C₁₉	C₄	semidirect
15. C₂³×Q₈×C₁₉	C₄	semidirect
17. C₂³×D₄×C₁₉	C₄	semidirect
20. C₂²×M₁₆×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#117	C₂²	semidirect
23. C₂×C₁₉×#104	C₂²	semidirect
26. C₁₉×#407	C₂²	semidirect
31. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
88. C₂×M₁₆×C₁₉	C₂³	semidirect
94. C₂×C₄²×C₁₉	C₂³	semidirect
121. #41×C₁₉	C₂²⋊C₄	semidirect
129. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
144. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
193. #20605	C₁₉	direct (N × H)
264. C₂×#421	C₂×C₁₉	semidirect
265. C₂×#407	C₂×C₁₉	semidirect
266. #2280	C₂×C₁₉	semidirect
267. #1789	C₂×C₁₉	semidirect
287. C₂²×C₁₉	#421	semidirect
303. C₂²×#41	C₄×C₁₉	semidirect
304. C₂²×#41	C₄×C₁₉	semidirect
307. C₂³×Q₈	C₄×C₁₉	semidirect
309. C₂³×D₄	C₄×C₁₉	semidirect
312. C₂²×M₁₆	C₂²×C₁₉	semidirect
313. C₂×#117	C₂²×C₁₉	semidirect
315. C₂×#104	C₂²×C₁₉	semidirect
318. #407	C₂²×C₁₉	semidirect
323. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
388. C₂×M₁₆	C₂³×C₁₉	semidirect
394. C₂×C₄²	C₂³×C₁₉	semidirect
399. C₁₉	#20605	direct (N × H)
422. #41	C₂²⋊C₄×C₁₉	semidirect
430. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
445. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
582. C₂²	C₁₉×#421	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×#421	2
C₂×C₁₉×#407	2
C₁₉×#2280	2
C₁₉×#1789	2
#20605	19

Subgroups — C19×#20605 #18026564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20605 #18026564