Subgroups — C₁₉×#32913 #18038872

Order 4864.

1506 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#449	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1880	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1879	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₁₉×#520	—	2	4	no	—
18	C₁₉×#520	—	2	4	no	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#117	—	2	1	no	—
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#460	—	2	4	no	—
30	C₁₉×#459	—	2	4	no	—
31	C₁₉×#449	—	2	8	no	—
32	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#103	C₂²	1	2	yes	—
35	C₂×C₁₉×#102	C₂²	1	2	yes	—
36	C₂×C₁₉×#102	C₂²	1	2	yes	—
37	C₂×C₁₉×#102	C₂²	1	2	yes	—
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₁₉×#394	—	2	1	no	—
40	C₁₉×#394	—	2	1	no	—
41	C₁₉×#392	—	2	1	no	—
42	C₁₉×#392	—	2	1	no	—
43	C₁₉×#390	C₂²	1	2	yes	—
44	C₁₉×#382	C₂²	1	1	yes	characteristic
45	C₁₉×#340	C₂²	1	2	yes	—
46	C₁₉×#340	C₂²	1	2	yes	—
47	C₁₉×#336	C₂²	1	2	yes	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	—	2	2	no	—
53	C₂×#41×C₁₉	D₄	1	4	yes	complemented
54	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	2	no	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	2	4	no	—
67	C₂×SD₁₆×C₁₉	—	2	4	no	—
68	C₂×SD₁₆×C₁₉	—	2	4	no	—
69	C₂×D₈×C₁₉	—	2	4	no	—
70	C₂×D₈×C₁₉	—	2	4	no	—
71	C₂×D₈×C₁₉	—	2	4	no	—
72	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
74	C₁₉×#127	—	2	2	no	—
75	C₁₉×#127	—	2	2	no	—
76	C₁₉×#121	—	2	4	no	—
77	C₁₉×#121	—	2	4	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	D₄	1	4	yes	complemented
82	C₄×D₄×C₁₉	—	2	8	no	—
83	C₄×D₄×C₁₉	—	2	8	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	D₄	1	4	yes	complemented
88	C₁₉×#117	—	2	8	no	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	—	2	2	no	—
114	C₁₉×C₄⋊C₈	—	2	2	no	—
115	C₁₉×#103	—	2	4	no	—
116	C₁₉×#102	—	2	4	no	—
117	C₁₉×#102	—	2	4	no	—
118	C₁₉×#102	—	2	4	no	—
119	C₁₉×C₂²⋊C₈	—	2	4	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₂⁴×C₁₉	—	2	1	no	—
123	C₂⁴×C₁₉	—	2	2	no	—
124	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
125	#41×C₁₉	—	2	8	no	—
126	#41×C₁₉	—	2	8	no	—
127	#41×C₁₉	—	2	8	no	—
128	#41×C₁₉	—	2	8	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₉	#41	1	2	yes	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	4	4	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	—	4	2	no	—
150	C₂×D₄×C₁₉	—	8	2	no	—
151	C₂×D₄×C₁₉	—	8	2	no	—
152	C₂×D₄×C₁₉	—	8	2	no	—
153	C₂×D₄×C₁₉	—	8	2	no	—
154	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₉	#41	1	2	yes	—
157	C₂²×C₄×C₁₉	—	2	4	no	—
158	C₂²×C₄×C₁₉	—	2	4	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	4	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	4	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	4	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	8	2	no	—
172	C₂²×C₄×C₁₉	—	8	2	no	—
173	C₂²×C₄×C₁₉	—	8	2	no	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₉	#41	1	2	yes	—
181	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
182	SD₁₆×C₁₉	—	4	8	no	—
183	D₈×C₁₉	—	4	8	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	2	2	no	—
189	C₂×C₈×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	4	no	—
191	C₄⋊C₄×C₁₉	—	2	4	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	4	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	4	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	4	4	no	—
206	C₂²⋊C₄×C₁₉	—	8	2	no	—
207	C₂²⋊C₄×C₁₉	—	8	2	no	—
208	C₄²×C₁₉	—	2	4	no	—
209	C₄²×C₁₉	—	2	4	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	C₂×D₄	1	2	yes	—
213	C₄²×C₁₉	C₂×D₄	1	2	yes	—
214	#32913	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	2	no	—
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	2	no	—
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	2	2	no	—
222	C₂³×C₁₉	—	4	2	no	—
223	C₂³×C₁₉	—	4	2	no	—
224	C₂³×C₁₉	—	4	2	no	—
225	C₂³×C₁₉	—	4	2	no	—
226	C₂³×C₁₉	—	4	2	no	—
227	C₂³×C₁₉	—	4	2	no	—
228	C₂³×C₁₉	—	4	2	no	—
229	C₂³×C₁₉	—	4	2	no	—
230	C₂³×C₁₉	—	4	2	no	—
231	C₂³×C₁₉	#121	1	2	yes	—
232	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₁₉	—	2	2	no	—
234	Q₈×C₁₉	—	2	2	no	—
235	Q₈×C₁₉	—	2	2	no	—
236	Q₈×C₁₉	#121	1	4	yes	—
237	D₄×C₁₉	—	2	16	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	2	2	no	—
240	D₄×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	8	4	no	—
246	D₄×C₁₉	—	8	4	no	—
247	D₄×C₁₉	—	8	8	no	—
248	D₄×C₁₉	#121	1	4	yes	—
249	C₂×C₄×C₁₉	—	2	16	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	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	—	8	4	no	—
273	C₂×C₄×C₁₉	—	8	4	no	—
274	C₂×C₄×C₁₉	—	8	4	no	—
275	C₂×C₄×C₁₉	#120	1	2	yes	—
276	C₂×C₄×C₁₉	#120	1	2	yes	—
277	C₂×C₄×C₁₉	#121	1	2	yes	—
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
284	C₈×C₁₉	—	4	2	no	—
285	C₈×C₁₉	—	4	2	no	—
286	C₂×#520	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂×#460	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₂×#459	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂×#449	C₂×C₁₉	1	2	yes	complemented
290	#2619	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1880	C₂×C₁₉	1	2	yes	complemented
292	#1879	C₂×C₁₉	1	2	yes	complemented
293	#1874	C₂×C₁₉	1	2	yes	complemented
294	#1805	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1804	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1798	C₂×C₁₉	1	1	yes	characteristic, complemented
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	4	no	—
299	C₂²×C₁₉	—	2	4	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	4	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	4	4	no	—
307	C₂²×C₁₉	—	8	2	no	—
308	C₂²×C₁₉	—	8	2	no	—
309	C₂²×C₁₉	—	8	2	no	—
310	C₂²×C₁₉	—	8	2	no	—
311	C₂²×C₁₉	—	8	2	no	—
312	C₂²×C₁₉	—	8	2	no	—
313	C₂²×C₁₉	—	8	2	no	—
314	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
315	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
316	C₂²×C₁₉	#525	1	1	yes	characteristic
317	C₂²×C₁₉	#576	1	2	yes	—
318	C₂²×C₁₉	#577	1	2	yes	—
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	—	2	4	no	—
321	C₄×C₁₉	—	2	2	no	—
322	C₄×C₁₉	—	2	2	no	—
323	C₄×C₁₉	—	4	1	no	—
324	C₄×C₁₉	—	4	2	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	8	2	no	—
328	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
329	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
330	C₄×C₁₉	#525	1	1	yes	characteristic
331	C₄×C₁₉	#525	1	1	yes	characteristic
332	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
333	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
334	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
335	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#121	C₂²×C₁₉	1	2	yes	—
337	#520	—	2	4	no	—
338	#520	—	2	4	no	—
339	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₄×D₄	—	2	1	no	—
342	C₂×C₄×D₄	—	2	1	no	—
343	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×#117	—	2	1	no	—
346	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
347	C₂²×C₄⋊C₄	—	2	1	no	—
348	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
349	#460	—	2	4	no	—
350	#459	—	2	4	no	—
351	#449	—	2	8	no	—
352	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×#103	C₂²×C₁₉	1	2	yes	—
355	C₂×#102	C₂²×C₁₉	1	2	yes	—
356	C₂×#102	C₂²×C₁₉	1	2	yes	—
357	C₂×#102	C₂²×C₁₉	1	2	yes	—
358	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
359	#394	—	2	1	no	—
360	#394	—	2	1	no	—
361	#392	—	2	1	no	—
362	#392	—	2	1	no	—
363	#390	C₂²×C₁₉	1	2	yes	—
364	#382	C₂²×C₁₉	1	1	yes	characteristic
365	#340	C₂²×C₁₉	1	2	yes	—
366	#340	C₂²×C₁₉	1	2	yes	—
367	#336	C₂²×C₁₉	1	2	yes	—
368	C₂×C₁₉	—	4	2	no	—
369	C₂×C₁₉	—	4	4	no	—
370	C₂×C₁₉	—	16	2	no	—
371	C₂×C₁₉	#2847	1	1	yes	characteristic
372	C₂×C₁₉	#3008	1	1	yes	characteristic
373	C₂×C₁₉	#3010	1	1	yes	characteristic
374	C₂×C₁₉	#3045	1	2	yes	—
375	C₂×C₁₉	#3119	1	2	yes	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	—	2	2	no	—
379	C₂×#41	—	2	2	no	—
380	C₂×#41	—	2	2	no	—
381	C₂×#41	D₄×C₁₉	1	4	yes	complemented
382	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	—	2	2	no	—
385	C₂²×D₄	—	2	1	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
388	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×SD₁₆	—	2	4	no	—
395	C₂×SD₁₆	—	2	4	no	—
396	C₂×SD₁₆	—	2	4	no	—
397	C₂×D₈	—	2	4	no	—
398	C₂×D₈	—	2	4	no	—
399	C₂×D₈	—	2	4	no	—
400	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
401	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
402	#127	—	2	2	no	—
403	#127	—	2	2	no	—
404	#121	—	2	4	no	—
405	#121	—	2	4	no	—
406	C₄×Q₈	—	2	2	no	—
407	C₄×Q₈	—	2	2	no	—
408	C₄×Q₈	—	2	2	no	—
409	C₄×Q₈	D₄×C₁₉	1	4	yes	complemented
410	C₄×D₄	—	2	8	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	D₄×C₁₉	1	4	yes	complemented
416	#117	—	2	8	no	—
417	#117	—	2	2	no	—
418	#117	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	8	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	2	no	—
424	C₂×C₄⋊C₄	—	2	2	no	—
425	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	2	no	—
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₂²⋊C₄	—	2	2	no	—
435	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
441	C₄⋊C₈	—	2	2	no	—
442	C₄⋊C₈	—	2	2	no	—
443	#103	—	2	4	no	—
444	#102	—	2	4	no	—
445	#102	—	2	4	no	—
446	#102	—	2	4	no	—
447	C₂²⋊C₈	—	2	4	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	C₁₉	#32913	1	1	yes	characteristic, direct product factor, Sylow
451	C₂⁴	—	2	1	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
454	#41	—	2	8	no	—
455	#41	—	2	8	no	—
456	#41	—	2	8	no	—
457	#41	—	2	8	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
462	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
463	C₂×Q₈	#41×C₁₉	1	2	yes	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	4	4	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	8	2	no	—
480	C₂×D₄	—	8	2	no	—
481	C₂×D₄	—	8	2	no	—
482	C₂×D₄	—	8	2	no	—
483	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
484	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂×D₄	#41×C₁₉	1	2	yes	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	8	2	no	—
501	C₂²×C₄	—	8	2	no	—
502	C₂²×C₄	—	8	2	no	—
503	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
509	C₂²×C₄	#41×C₁₉	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
511	SD₁₆	—	4	8	no	—
512	D₈	—	4	8	no	—
513	C₂×C₈	—	2	2	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
529	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	4	4	no	—
535	C₂²⋊C₄	—	8	2	no	—
536	C₂²⋊C₄	—	8	2	no	—
537	C₄²	—	2	4	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	C₂×D₄×C₁₉	1	2	yes	—
542	C₄²	C₂×D₄×C₁₉	1	2	yes	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	C₁₉×#121	1	2	yes	—
560	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	C₁₉×#121	1	4	yes	—
565	D₄	—	2	16	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	4	no	—
574	D₄	—	8	4	no	—
575	D₄	—	8	8	no	—
576	D₄	C₁₉×#121	1	4	yes	—
577	C₂×C₄	—	2	16	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	8	4	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	C₁₉×#120	1	2	yes	—
604	C₂×C₄	C₁₉×#120	1	2	yes	—
605	C₂×C₄	C₁₉×#121	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
610	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
612	C₈	—	4	2	no	—
613	C₈	—	4	2	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	4	no	—
624	C₂²	—	8	2	no	—
625	C₂²	—	8	2	no	—
626	C₂²	—	8	2	no	—
627	C₂²	—	8	2	no	—
628	C₂²	—	8	2	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	8	2	no	—
631	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
632	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
633	C₂²	C₁₉×#525	1	1	yes	characteristic
634	C₂²	C₁₉×#576	1	2	yes	—
635	C₂²	C₁₉×#577	1	2	yes	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	4	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	1	no	—
644	C₄	—	8	2	no	—
645	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
646	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
647	C₄	C₁₉×#525	1	1	yes	characteristic
648	C₄	C₁₉×#525	1	1	yes	characteristic
649	C₂	—	4	2	no	—
650	C₂	—	4	4	no	—
651	C₂	—	16	2	no	—
652	C₂	C₁₉×#2847	1	1	yes	characteristic
653	C₂	C₁₉×#3008	1	1	yes	characteristic
654	C₂	C₁₉×#3010	1	1	yes	characteristic
655	C₂	C₁₉×#3045	1	2	yes	—
656	C₂	C₁₉×#3119	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#520	C₂	semidirect
2. C₂×C₁₉×#460	C₂	semidirect
3. C₂×C₁₉×#459	C₂	semidirect
4. C₂×C₁₉×#449	C₂	semidirect
5. C₁₉×#2619	C₂	semidirect
6. C₁₉×#1880	C₂	semidirect
7. C₁₉×#1879	C₂	semidirect
8. C₁₉×#1874	C₂	semidirect
9. C₁₉×#1805	C₂	semidirect
10. C₁₉×#1804	C₂	semidirect
11. C₁₉×#1798	C₂	semidirect
53. C₂×#41×C₁₉	D₄	semidirect
81. C₄×Q₈×C₁₉	D₄	semidirect
87. C₄×D₄×C₁₉	D₄	semidirect
214. #32913	C₁₉	direct (N × H)
286. C₂×#520	C₂×C₁₉	semidirect
287. C₂×#460	C₂×C₁₉	semidirect
288. C₂×#459	C₂×C₁₉	semidirect
289. C₂×#449	C₂×C₁₉	semidirect
290. #2619	C₂×C₁₉	semidirect
291. #1880	C₂×C₁₉	semidirect
292. #1879	C₂×C₁₉	semidirect
293. #1874	C₂×C₁₉	semidirect
294. #1805	C₂×C₁₉	semidirect
295. #1804	C₂×C₁₉	semidirect
296. #1798	C₂×C₁₉	semidirect
381. C₂×#41	D₄×C₁₉	semidirect
409. C₄×Q₈	D₄×C₁₉	semidirect
415. C₄×D₄	D₄×C₁₉	semidirect
450. C₁₉	#32913	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×#520	2
C₂×C₁₉×#460	2
C₂×C₁₉×#459	2
C₂×C₁₉×#449	2
C₁₉×#2619	2
C₁₉×#1880	2
C₁₉×#1879	2
C₁₉×#1874	2
C₁₉×#1805	2
C₁₉×#1804	2
C₁₉×#1798	2
#32913	19

Subgroups — C19×#32913 #18038872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32913 #18038872