Subgroups — C₁₉×#20980 #18026939

Order 4864.

1830 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1897	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1896	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#537	C₄	1	4	yes	complemented
15	C₁₉×#536	—	2	1	no	—
16	C₁₉×#536	C₄	1	2	yes	complemented
17	C₁₉×#535	—	2	1	no	—
18	C₁₉×#535	C₄	1	2	yes	complemented
19	C₁₉×#534	—	2	2	no	—
20	C₁₉×#532	—	2	2	no	—
21	C₁₉×#525	—	2	2	no	—
22	C₁₉×#525	C₂²	1	4	yes	—
23	C₄×#41×C₁₉	—	2	4	no	—
24	C₄×#41×C₁₉	—	2	4	no	—
25	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	—	2	1	no	—
27	C₂×C₄×D₄×C₁₉	—	2	2	no	—
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
31	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₉	C₂²	1	2	yes	complemented
33	C₁₉×#421	—	2	4	no	—
34	C₂×C₁₉×#104	—	2	4	no	—
35	C₂×C₁₉×#104	C₂²	1	2	yes	—
36	C₂×C₁₉×#104	C₂²	1	4	yes	—
37	C₂×C₁₉×#104	C₂²	1	2	yes	—
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#408	—	2	2	no	—
40	C₁₉×#407	C₂²	1	4	yes	complemented
41	C₁₉×#339	C₂²	1	2	yes	complemented
42	C₁₉×#339	C₂²	1	4	yes	complemented
43	C₁₉×#339	C₂²	1	2	yes	complemented
44	C₂×#41×C₁₉	—	2	2	no	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	—	2	1	no	—
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	—	2	2	no	—
54	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×#41×C₁₉	C₂×C₄	1	2	yes	complemented
57	C₂×#41×C₁₉	D₄	1	2	yes	—
58	C₂×#41×C₁₉	D₄	1	2	yes	—
59	C₂×#41×C₁₉	C₂³	1	2	yes	—
60	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
64	C₂²×D₄×C₁₉	D₄	1	2	yes	—
65	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	—	2	2	no	—
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	2	no	—
74	C₂×M₁₆×C₁₉	—	2	2	no	—
75	C₂×M₁₆×C₁₉	—	2	2	no	—
76	C₂×M₁₆×C₁₉	—	2	2	no	—
77	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
78	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	—	2	2	no	—
82	C₁₉×#127	—	2	2	no	—
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	—	2	2	no	—
85	C₁₉×#123	—	2	4	no	—
86	C₁₉×#123	—	2	4	no	—
87	C₁₉×C₂²⋊Q₈	—	2	4	no	—
88	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
89	C₁₉×#121	—	2	4	no	—
90	C₁₉×#121	—	2	8	no	—
91	C₁₉×#121	C₂×C₄	1	8	yes	complemented
92	C₁₉×#120	—	2	4	no	—
93	C₁₉×#120	—	2	4	no	—
94	C₄×Q₈×C₁₉	—	2	8	no	—
95	C₄×D₄×C₁₉	—	2	16	no	—
96	C₄×D₄×C₁₉	—	2	8	no	—
97	C₄×D₄×C₁₉	—	2	8	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	—	2	4	no	—
102	C₁₉×#117	—	2	4	no	—
103	C₁₉×#117	C₂×C₄	1	2	yes	complemented
104	C₁₉×#117	D₄	1	4	yes	complemented
105	C₁₉×#117	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	—	2	2	no	—
114	C₂×C₄²×C₁₉	—	2	2	no	—
115	C₂×C₄²×C₁₉	—	2	1	no	—
116	C₂×C₄²×C₁₉	—	2	4	no	—
117	C₂×C₄²×C₁₉	—	2	4	no	—
118	C₂×C₄²×C₁₉	D₄	1	4	yes	complemented
119	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
122	C₁₉×#104	—	2	4	no	—
123	C₁₉×#104	—	2	4	no	—
124	C₁₉×#104	—	2	8	no	—
125	C₁₉×C₂²⋊C₈	—	2	8	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	#41×C₁₉	—	2	4	no	—
130	#41×C₁₉	—	2	4	no	—
131	#41×C₁₉	—	2	4	no	—
132	#41×C₁₉	—	2	4	no	—
133	#41×C₁₉	—	2	4	no	—
134	#41×C₁₉	—	2	4	no	—
135	#41×C₁₉	—	2	4	no	—
136	#41×C₁₉	—	2	4	no	—
137	#41×C₁₉	—	2	4	no	—
138	#41×C₁₉	—	2	4	no	—
139	#41×C₁₉	—	2	2	no	—
140	#41×C₁₉	—	2	2	no	—
141	#41×C₁₉	—	2	2	no	—
142	#41×C₁₉	—	2	2	no	—
143	#41×C₁₉	—	4	2	no	—
144	#41×C₁₉	—	4	2	no	—
145	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	4	2	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
153	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
154	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
155	C₂×D₄×C₁₉	—	2	4	no	—
156	C₂×D₄×C₁₉	—	2	4	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	8	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	4	2	no	—
167	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
168	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
169	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
170	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
171	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	8	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	4	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	4	4	no	—
186	C₂²×C₄×C₁₉	—	4	8	no	—
187	C₂²×C₄×C₁₉	—	4	2	no	—
188	C₂²×C₄×C₁₉	—	4	2	no	—
189	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₁₉	#41	1	2	yes	—
200	C₂²×C₄×C₁₉	#41	1	2	yes	—
201	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
202	M₁₆×C₁₉	—	2	2	no	—
203	M₁₆×C₁₉	—	2	2	no	—
204	M₁₆×C₁₉	—	2	2	no	—
205	M₁₆×C₁₉	—	2	2	no	—
206	M₁₆×C₁₉	—	4	2	no	—
207	M₁₆×C₁₉	—	4	2	no	—
208	C₂×C₈×C₁₉	—	2	2	no	—
209	C₂×C₈×C₁₉	—	2	2	no	—
210	C₂×C₈×C₁₉	—	4	2	no	—
211	C₂×C₈×C₁₉	—	4	2	no	—
212	C₄⋊C₄×C₁₉	—	2	8	no	—
213	C₄⋊C₄×C₁₉	—	2	2	no	—
214	C₄⋊C₄×C₁₉	—	2	8	no	—
215	C₄⋊C₄×C₁₉	—	2	4	no	—
216	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
217	C₂²⋊C₄×C₁₉	—	2	8	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	8	no	—
220	C₂²⋊C₄×C₁₉	—	2	4	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	8	no	—
223	C₄²×C₁₉	—	2	8	no	—
224	C₄²×C₁₉	—	2	2	no	—
225	C₄²×C₁₉	—	2	4	no	—
226	C₄²×C₁₉	—	2	1	no	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	—	2	2	no	—
229	C₄²×C₁₉	—	2	2	no	—
230	C₄²×C₁₉	C₂×D₄	1	2	yes	—
231	C₄²×C₁₉	C₂×D₄	1	4	yes	—
232	C₄²×C₁₉	C₂×D₄	1	2	yes	—
233	#20980	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	2	no	—
236	C₂³×C₁₉	—	2	2	no	—
237	C₂³×C₁₉	—	4	2	no	—
238	C₂³×C₁₉	—	4	4	no	—
239	C₂³×C₁₉	—	4	2	no	—
240	C₂³×C₁₉	—	8	2	no	—
241	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
242	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂³×C₁₉	#120	1	2	yes	—
245	C₂³×C₁₉	#123	1	2	yes	—
246	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₁₉	—	2	4	no	—
248	Q₈×C₁₉	—	2	4	no	—
249	Q₈×C₁₉	—	2	2	no	—
250	Q₈×C₁₉	—	2	2	no	—
251	Q₈×C₁₉	—	4	2	no	—
252	D₄×C₁₉	—	2	8	no	—
253	D₄×C₁₉	—	2	8	no	—
254	D₄×C₁₉	—	2	2	no	—
255	D₄×C₁₉	—	2	2	no	—
256	D₄×C₁₉	—	2	4	no	—
257	D₄×C₁₉	—	2	4	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	2	no	—
260	D₄×C₁₉	—	4	4	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	8	8	no	—
263	C₂×C₄×C₁₉	—	2	4	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	—	2	4	no	—
268	C₂×C₄×C₁₉	—	2	4	no	—
269	C₂×C₄×C₁₉	—	2	4	no	—
270	C₂×C₄×C₁₉	—	2	4	no	—
271	C₂×C₄×C₁₉	—	2	4	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	4	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	4	8	no	—
276	C₂×C₄×C₁₉	—	4	16	no	—
277	C₂×C₄×C₁₉	—	4	2	no	—
278	C₂×C₄×C₁₉	—	4	4	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	4	no	—
283	C₂×C₄×C₁₉	—	8	2	no	—
284	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
285	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
288	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
289	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
290	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
291	C₂×C₄×C₁₉	#120	1	2	yes	—
292	C₂×C₄×C₁₉	#121	1	2	yes	—
293	C₂×C₄×C₁₉	#121	1	2	yes	—
294	C₂×C₄×C₁₉	#121	1	2	yes	—
295	C₂×C₄×C₁₉	#121	1	2	yes	—
296	C₂×C₄×C₁₉	#123	1	2	yes	—
297	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
303	C₈×C₁₉	—	4	2	no	—
304	C₈×C₁₉	—	4	2	no	—
305	#3449	C₂×C₁₉	1	1	yes	characteristic
306	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
307	C₂×#421	C₂×C₁₉	1	1	yes	characteristic, complemented
308	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2879	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1897	C₂×C₁₉	1	4	yes	complemented
311	#1896	C₂×C₁₉	1	4	yes	complemented
312	#1733	C₂×C₁₉	1	1	yes	characteristic, complemented
313	C₂×#339	C₂×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	2	8	no	—
318	C₂²×C₁₉	—	2	4	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	4	no	—
322	C₂²×C₁₉	—	4	4	no	—
323	C₂²×C₁₉	—	4	4	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	8	4	no	—
326	C₂²×C₁₉	#386	1	2	yes	—
327	C₂²×C₁₉	#386	1	2	yes	—
328	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
330	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
331	C₄×C₁₉	—	2	4	no	—
332	C₄×C₁₉	—	2	4	no	—
333	C₄×C₁₉	—	4	4	no	—
334	C₄×C₁₉	—	4	2	no	—
335	C₄×C₁₉	—	4	4	no	—
336	C₄×C₁₉	—	4	2	no	—
337	C₄×C₁₉	#386	1	2	yes	—
338	C₄×C₁₉	#386	1	2	yes	—
339	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
340	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
342	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
343	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
344	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
346	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
347	#537	C₄×C₁₉	1	4	yes	complemented
348	#536	—	2	1	no	—
349	#536	C₄×C₁₉	1	2	yes	complemented
350	#535	—	2	1	no	—
351	#535	C₄×C₁₉	1	2	yes	complemented
352	#534	—	2	2	no	—
353	#532	—	2	2	no	—
354	#525	—	2	2	no	—
355	#525	C₂²×C₁₉	1	4	yes	—
356	C₄×#41	—	2	4	no	—
357	C₄×#41	—	2	4	no	—
358	C₂×C₄×Q₈	—	2	1	no	—
359	C₂×C₄×D₄	—	2	1	no	—
360	C₂×C₄×D₄	—	2	2	no	—
361	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
364	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
365	C₂²×C₄²	C₂²×C₁₉	1	2	yes	complemented
366	#421	—	2	4	no	—
367	C₂×#104	—	2	4	no	—
368	C₂×#104	C₂²×C₁₉	1	2	yes	—
369	C₂×#104	C₂²×C₁₉	1	2	yes	—
370	C₂×#104	C₂²×C₁₉	1	4	yes	—
371	#408	—	2	2	no	—
372	#408	—	2	2	no	—
373	#407	C₂²×C₁₉	1	4	yes	complemented
374	#339	C₂²×C₁₉	1	2	yes	complemented
375	#339	C₂²×C₁₉	1	4	yes	complemented
376	#339	C₂²×C₁₉	1	2	yes	complemented
377	C₂×C₁₉	—	2	1	no	—
378	C₂×C₁₉	—	2	1	no	—
379	C₂×C₁₉	—	2	2	no	—
380	C₂×C₁₉	—	2	2	no	—
381	C₂×C₁₉	—	4	4	no	—
382	C₂×C₁₉	—	8	2	no	—
383	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
384	C₂×C₁₉	#2901	1	2	yes	—
385	C₂×#41	—	2	2	no	—
386	C₂×#41	—	2	2	no	—
387	C₂×#41	—	2	1	no	—
388	C₂×#41	—	2	1	no	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	—	2	2	no	—
391	C₂×#41	—	2	2	no	—
392	C₂×#41	—	2	2	no	—
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
396	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
397	C₂×#41	C₂×C₄×C₁₉	1	2	yes	complemented
398	C₂×#41	D₄×C₁₉	1	2	yes	—
399	C₂×#41	D₄×C₁₉	1	2	yes	—
400	C₂×#41	C₂³×C₁₉	1	2	yes	—
401	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
402	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
405	C₂²×D₄	D₄×C₁₉	1	2	yes	—
406	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	2	no	—
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
411	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	2	no	—
415	C₂×M₁₆	—	2	2	no	—
416	C₂×M₁₆	—	2	2	no	—
417	C₂×M₁₆	—	2	2	no	—
418	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
419	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
420	C₂²×C₈	—	2	1	no	—
421	C₂²×C₈	—	2	1	no	—
422	C₄⋊Q₈	—	2	2	no	—
423	#127	—	2	2	no	—
424	#124	—	2	2	no	—
425	#124	—	2	2	no	—
426	#123	—	2	4	no	—
427	#123	—	2	4	no	—
428	C₂²⋊Q₈	—	2	4	no	—
429	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
430	#121	—	2	4	no	—
431	#121	—	2	8	no	—
432	#121	C₂×C₄×C₁₉	1	8	yes	complemented
433	#120	—	2	4	no	—
434	#120	—	2	4	no	—
435	C₄×Q₈	—	2	8	no	—
436	C₄×D₄	—	2	16	no	—
437	C₄×D₄	—	2	8	no	—
438	C₄×D₄	—	2	8	no	—
439	#117	—	2	2	no	—
440	#117	—	2	1	no	—
441	#117	—	2	1	no	—
442	#117	—	2	4	no	—
443	#117	—	2	4	no	—
444	#117	C₂×C₄×C₁₉	1	2	yes	complemented
445	#117	D₄×C₁₉	1	4	yes	complemented
446	#117	C₂³×C₁₉	1	2	yes	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	2	no	—
449	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	2	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	—	2	2	no	—
456	C₂×C₄²	—	2	2	no	—
457	C₂×C₄²	—	2	4	no	—
458	C₂×C₄²	—	2	4	no	—
459	C₂×C₄²	D₄×C₁₉	1	4	yes	complemented
460	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
463	#104	—	2	4	no	—
464	#104	—	2	4	no	—
465	#104	—	2	8	no	—
466	C₂²⋊C₈	—	2	8	no	—
467	C₁₉	#20980	1	1	yes	characteristic, direct product factor, Sylow
468	C₂⁴	—	2	1	no	—
469	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
470	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
471	#41	—	2	4	no	—
472	#41	—	2	4	no	—
473	#41	—	2	4	no	—
474	#41	—	2	4	no	—
475	#41	—	2	4	no	—
476	#41	—	2	4	no	—
477	#41	—	2	4	no	—
478	#41	—	2	4	no	—
479	#41	—	2	4	no	—
480	#41	—	2	4	no	—
481	#41	—	2	2	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	—	2	2	no	—
485	#41	—	4	2	no	—
486	#41	—	4	2	no	—
487	#41	—	4	2	no	—
488	#41	—	4	2	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
495	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
496	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	8	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	4	2	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
510	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
511	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
512	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
513	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	8	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
532	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
535	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
536	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
540	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
541	C₂²×C₄	#41×C₁₉	1	2	yes	—
542	C₂²×C₄	#41×C₁₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
544	M₁₆	—	2	2	no	—
545	M₁₆	—	2	2	no	—
546	M₁₆	—	2	2	no	—
547	M₁₆	—	2	2	no	—
548	M₁₆	—	4	2	no	—
549	M₁₆	—	4	2	no	—
550	C₂×C₈	—	2	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	4	2	no	—
553	C₂×C₈	—	4	2	no	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	8	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	8	no	—
565	C₄²	—	2	8	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	C₂×D₄×C₁₉	1	2	yes	—
573	C₄²	C₂×D₄×C₁₉	1	4	yes	—
574	C₄²	C₂×D₄×C₁₉	1	2	yes	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	4	2	no	—
579	C₂³	—	4	4	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	8	2	no	—
582	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
583	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
584	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
585	C₂³	C₁₉×#120	1	2	yes	—
586	C₂³	C₁₉×#123	1	2	yes	—
587	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
588	Q₈	—	2	4	no	—
589	Q₈	—	2	4	no	—
590	Q₈	—	2	2	no	—
591	Q₈	—	2	2	no	—
592	Q₈	—	4	2	no	—
593	D₄	—	2	8	no	—
594	D₄	—	2	8	no	—
595	D₄	—	2	4	no	—
596	D₄	—	2	4	no	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	4	4	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	8	8	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	4	8	no	—
617	C₂×C₄	—	4	16	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	4	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	8	2	no	—
625	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
626	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
627	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
628	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
629	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
630	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
631	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
632	C₂×C₄	C₁₉×#120	1	2	yes	—
633	C₂×C₄	C₁₉×#121	1	2	yes	—
634	C₂×C₄	C₁₉×#121	1	2	yes	—
635	C₂×C₄	C₁₉×#121	1	2	yes	—
636	C₂×C₄	C₁₉×#121	1	2	yes	—
637	C₂×C₄	C₁₉×#123	1	2	yes	—
638	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
640	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
642	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
643	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
644	C₈	—	4	2	no	—
645	C₈	—	4	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	8	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	4	4	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	8	4	no	—
658	C₂²	C₁₉×#386	1	2	yes	—
659	C₂²	C₁₉×#386	1	2	yes	—
660	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
661	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
662	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
663	C₄	—	2	4	no	—
664	C₄	—	2	4	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	4	no	—
669	C₄	C₁₉×#386	1	2	yes	—
670	C₄	C₁₉×#386	1	2	yes	—
671	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
672	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
673	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
674	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
675	C₂	—	2	1	no	—
676	C₂	—	2	1	no	—
677	C₂	—	2	2	no	—
678	C₂	—	2	2	no	—
679	C₂	—	4	4	no	—
680	C₂	—	8	2	no	—
681	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
682	C₂	C₁₉×#2901	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	C₁₉×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₁₉	C₂	semidirect
3. C₂×C₁₉×#421	C₂	semidirect
4. C₂²×C₁₉×#104	C₂	semidirect
5. C₁₉×#2879	C₂	semidirect
6. C₁₉×#1897	C₂	semidirect
7. C₁₉×#1896	C₂	semidirect
8. C₁₉×#1733	C₂	semidirect
9. C₂×C₁₉×#339	C₂	semidirect
14. C₁₉×#537	C₄	semidirect
16. C₁₉×#536	C₄	semidirect
18. C₁₉×#535	C₄	semidirect
30. C₂×C₁₉×#117	C₂²	semidirect
32. C₂²×C₄²×C₁₉	C₂²	semidirect
40. C₁₉×#407	C₂²	semidirect
41. C₁₉×#339	C₂²	semidirect
42. C₁₉×#339	C₂²	semidirect
43. C₁₉×#339	C₂²	semidirect
56. C₂×#41×C₁₉	C₂×C₄	semidirect
60. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
63. C₂²×D₄×C₁₉	C₂×C₄	semidirect
88. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₁₉×#121	C₂×C₄	semidirect
103. C₁₉×#117	C₂×C₄	semidirect
104. C₁₉×#117	D₄	semidirect
108. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
118. C₂×C₄²×C₁₉	D₄	semidirect
233. #20980	C₁₉	direct (N × H)
306. C₂×C₄×#41	C₂×C₁₉	semidirect
307. C₂×#421	C₂×C₁₉	semidirect
308. C₂²×#104	C₂×C₁₉	semidirect
309. #2879	C₂×C₁₉	semidirect
310. #1897	C₂×C₁₉	semidirect
311. #1896	C₂×C₁₉	semidirect
312. #1733	C₂×C₁₉	semidirect
313. C₂×#339	C₂×C₁₉	semidirect
347. #537	C₄×C₁₉	semidirect
349. #536	C₄×C₁₉	semidirect
351. #535	C₄×C₁₉	semidirect
363. C₂×#117	C₂²×C₁₉	semidirect
365. C₂²×C₄²	C₂²×C₁₉	semidirect
373. #407	C₂²×C₁₉	semidirect
374. #339	C₂²×C₁₉	semidirect
375. #339	C₂²×C₁₉	semidirect
376. #339	C₂²×C₁₉	semidirect
397. C₂×#41	C₂×C₄×C₁₉	semidirect
401. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
404. C₂²×D₄	C₂×C₄×C₁₉	semidirect
429. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
432. #121	C₂×C₄×C₁₉	semidirect
444. #117	C₂×C₄×C₁₉	semidirect
445. #117	D₄×C₁₉	semidirect
449. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
459. C₂×C₄²	D₄×C₁₉	semidirect
467. C₁₉	#20980	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3449	2
C₂×C₄×#41×C₁₉	2
C₂×C₁₉×#421	2
C₂²×C₁₉×#104	2
C₁₉×#2879	2
C₁₉×#1897	2
C₁₉×#1896	2
C₁₉×#1733	2
C₂×C₁₉×#339	2
#20980	19

Subgroups — C19×#20980 #18026939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20980 #18026939