Subgroups — C₁₉×#62269 #18068228

Order 4864.

1896 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	C₁₉×#3536	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3335	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3316	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3306	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3282	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3263	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3204	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3195	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3192	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3173	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3060	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#465	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
15	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
16	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#562	—	2	4	no	—
19	C₁₉×#554	C₂²	1	4	yes	complemented
20	C₁₉×#548	C₂²	1	4	yes	—
21	C₁₉×#547	C₂²	1	4	yes	—
22	C₁₉×#546	—	2	4	no	—
23	C₁₉×#546	C₂²	1	4	yes	complemented
24	C₁₉×#543	—	2	2	no	—
25	C₁₉×#542	C₂²	1	4	yes	complemented
26	C₁₉×#539	—	2	2	no	—
27	C₁₉×#538	—	2	2	no	—
28	C₁₉×#537	—	2	2	no	—
29	C₁₉×#537	C₂²	1	4	yes	complemented
30	C₁₉×#525	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₁₉×#121	C₂²	1	2	yes	—
33	C₁₉×#498	C₂²	1	2	yes	complemented
34	C₁₉×#495	C₂²	1	2	yes	complemented
35	C₁₉×#489	C₂²	1	4	yes	complemented
36	C₁₉×#483	C₂²	1	4	yes	complemented
37	C₁₉×#483	C₂²	1	4	yes	complemented
38	C₁₉×#481	C₂²	1	4	yes	—
39	C₁₉×#481	C₂²	1	4	yes	complemented
40	C₁₉×#476	C₂²	1	4	yes	complemented
41	C₁₉×#475	C₂²	1	4	yes	complemented
42	C₁₉×#470	C₂²	1	2	yes	complemented
43	C₁₉×#470	C₂²	1	2	yes	complemented
44	C₁₉×#470	C₂²	1	2	yes	complemented
45	C₁₉×#469	C₂²	1	2	yes	—
46	C₁₉×#469	C₂²	1	2	yes	—
47	C₁₉×#469	C₂²	1	2	yes	complemented
48	C₁₉×#465	C₂²	1	4	yes	—
49	C₁₉×#465	C₂²	1	4	yes	—
50	C₁₉×#465	C₂²	1	4	yes	complemented
51	C₁₉×#465	C₂²	1	4	yes	complemented
52	C₁₉×#465	C₂²	1	4	yes	complemented
53	C₁₉×#464	C₂²	1	4	yes	complemented
54	C₁₉×#463	C₂²	1	4	yes	complemented
55	C₁₉×#452	C₂²	1	4	yes	complemented
56	C₁₉×#451	C₂²	1	4	yes	complemented
57	C₁₉×#449	C₂²	1	4	yes	complemented
58	C₁₉×#447	C₂²	1	4	yes	—
59	C₁₉×#442	C₂²	1	2	yes	complemented
60	C₁₉×#441	C₂²	1	2	yes	complemented
61	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
62	C₁₉×#435	C₂²	1	4	yes	complemented
63	C₈×D₄×C₁₉	C₂²	1	4	yes	complemented
64	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
65	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
66	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#417	C₂²	1	4	yes	complemented
68	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
69	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
70	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#407	C₂²	1	1	yes	characteristic
72	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
73	C₂×#41×C₁₉	—	2	4	no	—
74	C₂×#41×C₁₉	C₂³	1	4	yes	—
75	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₉	—	2	2	no	—
78	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#135	—	4	4	no	—
81	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
82	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
83	C₂×SD₁₆×C₁₉	—	4	4	no	—
84	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
85	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
86	C₂×D₈×C₁₉	C₂³	1	2	yes	—
87	C₂×D₈×C₁₉	C₂³	1	2	yes	—
88	C₁₉×#131	—	4	2	no	—
89	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₉	—	4	2	no	—
93	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
98	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₁₉×#126	—	2	4	no	—
100	C₁₉×#125	—	2	4	no	—
101	C₁₉×#124	—	2	4	no	—
102	C₁₉×#124	—	2	4	no	—
103	C₁₉×#124	C₂³	1	4	yes	—
104	C₁₉×#123	—	2	4	no	—
105	C₁₉×#123	—	2	4	no	—
106	C₁₉×#123	—	2	4	no	—
107	C₁₉×#123	—	2	4	no	—
108	C₁₉×#123	D₄	1	2	yes	—
109	C₁₉×C₂²⋊Q₈	—	2	4	no	—
110	C₁₉×C₂²⋊Q₈	—	2	2	no	—
111	C₁₉×C₂²⋊Q₈	—	2	2	no	—
112	C₁₉×C₂²⋊Q₈	—	2	4	no	—
113	C₁₉×C₂²⋊Q₈	—	2	4	no	—
114	C₁₉×C₂²⋊Q₈	—	2	4	no	—
115	C₁₉×C₂²⋊Q₈	—	2	4	no	—
116	C₁₉×C₂²⋊Q₈	—	2	4	no	—
117	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
118	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
119	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
120	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
121	C₁₉×#121	—	2	4	no	—
122	C₁₉×#121	—	2	4	no	—
123	C₁₉×#121	—	2	4	no	—
124	C₁₉×#121	—	2	4	no	—
125	C₁₉×#121	—	2	2	no	—
126	C₁₉×#121	—	2	2	no	—
127	C₁₉×#121	—	2	4	no	—
128	C₁₉×#121	D₄	1	2	yes	—
129	C₁₉×#121	C₂³	1	4	yes	—
130	C₁₉×#121	C₂³	1	4	yes	—
131	C₁₉×#121	C₂³	1	4	yes	—
132	C₁₉×#120	—	2	4	no	—
133	C₁₉×#120	D₄	1	2	yes	—
134	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
135	C₄×D₄×C₁₉	—	2	4	no	—
136	C₄×D₄×C₁₉	—	2	4	no	—
137	C₄×D₄×C₁₉	C₂³	1	4	yes	—
138	C₄×D₄×C₁₉	C₂³	1	4	yes	—
139	C₁₉×#117	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₁₉×#106	C₂³	1	4	yes	—
148	C₁₉×#106	C₂³	1	4	yes	—
149	C₁₉×#106	C₂³	1	2	yes	—
150	C₁₉×#106	C₂³	1	2	yes	—
151	C₁₉×#106	C₂³	1	2	yes	—
152	C₁₉×#106	C₂³	1	2	yes	—
153	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
154	C₁₉×#103	C₂³	1	4	yes	—
155	C₁₉×#103	C₂³	1	4	yes	—
156	C₁₉×#103	C₂³	1	4	yes	—
157	C₁₉×#103	C₂³	1	4	yes	—
158	C₁₉×#102	C₂³	1	4	yes	—
159	C₁₉×#102	C₂³	1	4	yes	—
160	C₁₉×#102	C₂³	1	4	yes	—
161	C₁₉×#102	C₂³	1	4	yes	—
162	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
163	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₁₉×#97	C₂³	1	2	yes	—
165	C₄×C₈×C₁₉	C₂³	1	2	yes	—
166	C₂⁴×C₁₉	—	2	2	no	—
167	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
168	#41×C₁₉	—	4	1	no	—
169	#41×C₁₉	—	4	1	no	—
170	#41×C₁₉	—	4	4	no	—
171	#41×C₁₉	—	4	4	no	—
172	#41×C₁₉	—	8	8	no	—
173	C₂×Q₈×C₁₉	—	2	2	no	—
174	C₂×Q₈×C₁₉	—	2	4	no	—
175	C₂×Q₈×C₁₉	—	4	2	no	—
176	C₂×Q₈×C₁₉	—	4	2	no	—
177	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
179	C₂×D₄×C₁₉	—	2	4	no	—
180	C₂×D₄×C₁₉	—	2	4	no	—
181	C₂×D₄×C₁₉	—	2	4	no	—
182	C₂×D₄×C₁₉	—	2	4	no	—
183	C₂×D₄×C₁₉	—	2	2	no	—
184	C₂×D₄×C₁₉	—	4	2	no	—
185	C₂×D₄×C₁₉	—	4	2	no	—
186	C₂×D₄×C₁₉	—	8	4	no	—
187	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
188	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₁₉	—	2	2	no	—
192	C₂²×C₄×C₁₉	—	2	2	no	—
193	C₂²×C₄×C₁₉	—	2	2	no	—
194	C₂²×C₄×C₁₉	—	2	4	no	—
195	C₂²×C₄×C₁₉	—	2	4	no	—
196	C₂²×C₄×C₁₉	—	2	4	no	—
197	C₂²×C₄×C₁₉	—	4	1	no	—
198	C₂²×C₄×C₁₉	—	4	1	no	—
199	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
204	Q₁₆×C₁₉	—	4	2	no	—
205	Q₁₆×C₁₉	—	4	2	no	—
206	SD₁₆×C₁₉	—	2	8	no	—
207	SD₁₆×C₁₉	—	4	4	no	—
208	D₈×C₁₉	—	4	2	no	—
209	D₈×C₁₉	—	4	2	no	—
210	M₁₆×C₁₉	—	4	1	no	—
211	M₁₆×C₁₉	—	4	2	no	—
212	M₁₆×C₁₉	—	4	1	no	—
213	C₂×C₈×C₁₉	—	2	2	no	—
214	C₂×C₈×C₁₉	—	2	4	no	—
215	C₂×C₈×C₁₉	—	2	4	no	—
216	C₂×C₈×C₁₉	—	4	2	no	—
217	C₂×C₈×C₁₉	—	4	1	no	—
218	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
219	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
220	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
221	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
222	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₄⋊C₄×C₁₉	—	2	4	no	—
224	C₄⋊C₄×C₁₉	—	2	4	no	—
225	C₄⋊C₄×C₁₉	—	2	2	no	—
226	C₄⋊C₄×C₁₉	—	2	4	no	—
227	C₄⋊C₄×C₁₉	—	2	2	no	—
228	C₄⋊C₄×C₁₉	—	2	4	no	—
229	C₄⋊C₄×C₁₉	—	2	4	no	—
230	C₄⋊C₄×C₁₉	—	2	4	no	—
231	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
232	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
235	C₂²⋊C₄×C₁₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
245	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
247	C₄²×C₁₉	—	2	4	no	—
248	C₄²×C₁₉	C₂⁴	1	2	yes	—
249	#62269	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₉	—	2	4	no	—
251	C₂³×C₁₉	—	2	4	no	—
252	C₂³×C₁₉	—	4	1	no	—
253	C₂³×C₁₉	—	4	4	no	—
254	C₂³×C₁₉	—	8	2	no	—
255	C₂³×C₁₉	—	8	2	no	—
256	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
258	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
259	Q₈×C₁₉	—	2	4	no	—
260	Q₈×C₁₉	—	2	4	no	—
261	Q₈×C₁₉	—	4	1	no	—
262	Q₈×C₁₉	—	8	2	no	—
263	Q₈×C₁₉	—	8	4	no	—
264	D₄×C₁₉	—	2	8	no	—
265	D₄×C₁₉	—	2	4	no	—
266	D₄×C₁₉	—	2	4	no	—
267	D₄×C₁₉	—	4	1	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	8	no	—
270	D₄×C₁₉	—	8	2	no	—
271	D₄×C₁₉	—	8	4	no	—
272	D₄×C₁₉	—	8	4	no	—
273	D₄×C₁₉	—	8	4	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	4	no	—
281	C₂×C₄×C₁₉	—	2	4	no	—
282	C₂×C₄×C₁₉	—	2	4	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	4	no	—
286	C₂×C₄×C₁₉	—	8	4	no	—
287	C₂×C₄×C₁₉	—	8	4	no	—
288	C₂×C₄×C₁₉	—	8	2	no	—
289	C₂×C₄×C₁₉	—	8	2	no	—
290	C₂×C₄×C₁₉	—	8	4	no	—
291	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
292	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
296	C₈×C₁₉	—	2	1	no	—
297	C₈×C₁₉	—	2	2	no	—
298	C₈×C₁₉	—	2	2	no	—
299	C₈×C₁₉	—	2	2	no	—
300	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
301	#3536	C₂×C₁₉	1	2	yes	complemented
302	#3335	C₂×C₁₉	1	4	yes	complemented
303	#3316	C₂×C₁₉	1	4	yes	complemented
304	#3306	C₂×C₁₉	1	4	yes	complemented
305	#3282	C₂×C₁₉	1	4	yes	complemented
306	#3263	C₂×C₁₉	1	2	yes	complemented
307	#3204	C₂×C₁₉	1	2	yes	complemented
308	#3195	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#3192	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#3173	C₂×C₁₉	1	2	yes	complemented
311	#3060	C₂×C₁₉	1	2	yes	complemented
312	C₂×#465	C₂×C₁₉	1	2	yes	complemented
313	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	2	no	—
318	C₂²×C₁₉	—	2	4	no	—
319	C₂²×C₁₉	—	2	2	no	—
320	C₂²×C₁₉	—	4	4	no	—
321	C₂²×C₁₉	—	4	4	no	—
322	C₂²×C₁₉	—	4	4	no	—
323	C₂²×C₁₉	—	4	4	no	—
324	C₂²×C₁₉	—	16	4	no	—
325	C₂²×C₁₉	#577	1	4	yes	—
326	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
327	C₄×C₁₉	—	2	1	no	—
328	C₄×C₁₉	—	2	2	no	—
329	C₄×C₁₉	—	2	2	no	—
330	C₄×C₁₉	—	2	4	no	—
331	C₄×C₁₉	—	4	4	no	—
332	C₄×C₁₉	—	4	4	no	—
333	C₄×C₁₉	—	4	4	no	—
334	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₄×C₁₉	#585	1	1	yes	characteristic
336	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
337	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
338	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
340	#562	—	2	4	no	—
341	#554	C₂²×C₁₉	1	4	yes	complemented
342	#548	C₂²×C₁₉	1	4	yes	—
343	#547	C₂²×C₁₉	1	4	yes	—
344	#546	—	2	4	no	—
345	#546	C₂²×C₁₉	1	4	yes	complemented
346	#543	—	2	2	no	—
347	#542	C₂²×C₁₉	1	4	yes	complemented
348	#539	—	2	2	no	—
349	#538	—	2	2	no	—
350	#537	—	2	2	no	—
351	#537	C₂²×C₁₉	1	4	yes	complemented
352	#525	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
354	C₂×#121	C₂²×C₁₉	1	2	yes	—
355	#498	C₂²×C₁₉	1	2	yes	complemented
356	#495	C₂²×C₁₉	1	2	yes	complemented
357	#489	C₂²×C₁₉	1	4	yes	complemented
358	#483	C₂²×C₁₉	1	4	yes	complemented
359	#483	C₂²×C₁₉	1	4	yes	complemented
360	#481	C₂²×C₁₉	1	4	yes	—
361	#481	C₂²×C₁₉	1	4	yes	complemented
362	#476	C₂²×C₁₉	1	4	yes	complemented
363	#475	C₂²×C₁₉	1	4	yes	complemented
364	#470	C₂²×C₁₉	1	2	yes	complemented
365	#470	C₂²×C₁₉	1	2	yes	complemented
366	#470	C₂²×C₁₉	1	2	yes	complemented
367	#469	C₂²×C₁₉	1	2	yes	—
368	#469	C₂²×C₁₉	1	2	yes	—
369	#469	C₂²×C₁₉	1	2	yes	complemented
370	#465	C₂²×C₁₉	1	4	yes	—
371	#465	C₂²×C₁₉	1	4	yes	—
372	#465	C₂²×C₁₉	1	4	yes	complemented
373	#465	C₂²×C₁₉	1	4	yes	complemented
374	#465	C₂²×C₁₉	1	4	yes	complemented
375	#464	C₂²×C₁₉	1	4	yes	complemented
376	#463	C₂²×C₁₉	1	4	yes	complemented
377	#452	C₂²×C₁₉	1	4	yes	complemented
378	#451	C₂²×C₁₉	1	4	yes	complemented
379	#449	C₂²×C₁₉	1	4	yes	complemented
380	#447	C₂²×C₁₉	1	4	yes	—
381	#442	C₂²×C₁₉	1	2	yes	complemented
382	#441	C₂²×C₁₉	1	2	yes	complemented
383	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
384	#435	C₂²×C₁₉	1	4	yes	complemented
385	C₈×D₄	C₂²×C₁₉	1	4	yes	complemented
386	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
387	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
388	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
389	#417	C₂²×C₁₉	1	4	yes	complemented
390	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
391	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
392	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
393	#407	C₂²×C₁₉	1	1	yes	characteristic
394	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
395	C₂×C₁₉	—	2	4	no	—
396	C₂×C₁₉	—	4	2	no	—
397	C₂×C₁₉	—	4	1	no	—
398	C₂×C₁₉	—	8	4	no	—
399	C₂×C₁₉	#3496	1	1	yes	characteristic
400	C₂×C₁₉	C₂×#577	1	2	yes	—
401	C₂×#41	—	2	4	no	—
402	C₂×#41	C₂³×C₁₉	1	4	yes	—
403	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
404	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
405	C₂²×D₄	—	2	2	no	—
406	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
407	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
408	#135	—	4	4	no	—
409	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
410	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
411	C₂×SD₁₆	—	4	4	no	—
412	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
413	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
414	C₂×D₈	C₂³×C₁₉	1	2	yes	—
415	C₂×D₈	C₂³×C₁₉	1	2	yes	—
416	#131	—	4	2	no	—
417	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
419	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
420	C₂²×C₈	—	4	2	no	—
421	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
423	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
424	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
426	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
427	#126	—	2	4	no	—
428	#125	—	2	4	no	—
429	#124	—	2	4	no	—
430	#124	—	2	4	no	—
431	#124	C₂³×C₁₉	1	4	yes	—
432	#123	—	2	4	no	—
433	#123	—	2	4	no	—
434	#123	—	2	4	no	—
435	#123	—	2	4	no	—
436	#123	D₄×C₁₉	1	2	yes	—
437	C₂²⋊Q₈	—	2	4	no	—
438	C₂²⋊Q₈	—	2	2	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	4	no	—
441	C₂²⋊Q₈	—	2	4	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	—	2	4	no	—
444	C₂²⋊Q₈	—	2	4	no	—
445	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
446	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
447	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
448	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
449	#121	—	2	4	no	—
450	#121	—	2	4	no	—
451	#121	—	2	4	no	—
452	#121	—	2	4	no	—
453	#121	—	2	2	no	—
454	#121	—	2	2	no	—
455	#121	—	2	4	no	—
456	#121	D₄×C₁₉	1	2	yes	—
457	#121	C₂³×C₁₉	1	4	yes	—
458	#121	C₂³×C₁₉	1	4	yes	—
459	#121	C₂³×C₁₉	1	4	yes	—
460	#120	—	2	4	no	—
461	#120	D₄×C₁₉	1	2	yes	—
462	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
463	C₄×D₄	—	2	4	no	—
464	C₄×D₄	—	2	4	no	—
465	C₄×D₄	C₂³×C₁₉	1	4	yes	—
466	C₄×D₄	C₂³×C₁₉	1	4	yes	—
467	#117	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	—	2	2	no	—
469	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
472	C₂×C₂²⋊C₄	—	2	2	no	—
473	C₂×C₂²⋊C₄	—	2	2	no	—
474	C₂×C₂²⋊C₄	—	2	4	no	—
475	#106	C₂³×C₁₉	1	4	yes	—
476	#106	C₂³×C₁₉	1	4	yes	—
477	#106	C₂³×C₁₉	1	2	yes	—
478	#106	C₂³×C₁₉	1	2	yes	—
479	#106	C₂³×C₁₉	1	2	yes	—
480	#106	C₂³×C₁₉	1	2	yes	—
481	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
482	#103	C₂³×C₁₉	1	4	yes	—
483	#103	C₂³×C₁₉	1	4	yes	—
484	#103	C₂³×C₁₉	1	4	yes	—
485	#103	C₂³×C₁₉	1	4	yes	—
486	#102	C₂³×C₁₉	1	4	yes	—
487	#102	C₂³×C₁₉	1	4	yes	—
488	#102	C₂³×C₁₉	1	4	yes	—
489	#102	C₂³×C₁₉	1	4	yes	—
490	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
491	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
492	#97	C₂³×C₁₉	1	2	yes	—
493	C₄×C₈	C₂³×C₁₉	1	2	yes	—
494	C₁₉	#62269	1	1	yes	characteristic, direct product factor, Sylow
495	C₂⁴	—	2	2	no	—
496	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
497	#41	—	4	1	no	—
498	#41	—	4	1	no	—
499	#41	—	4	4	no	—
500	#41	—	4	4	no	—
501	#41	—	8	8	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	2	no	—
506	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂×D₄	—	8	4	no	—
516	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
517	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
518	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
533	Q₁₆	—	4	2	no	—
534	Q₁₆	—	4	2	no	—
535	SD₁₆	—	2	8	no	—
536	SD₁₆	—	4	4	no	—
537	D₈	—	4	2	no	—
538	D₈	—	4	2	no	—
539	M₁₆	—	4	1	no	—
540	M₁₆	—	4	2	no	—
541	M₁₆	—	4	1	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	2	4	no	—
544	C₂×C₈	—	2	4	no	—
545	C₂×C₈	—	4	2	no	—
546	C₂×C₈	—	4	1	no	—
547	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
548	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
549	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
550	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
551	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
561	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
562	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
563	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	—	2	4	no	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
574	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
575	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
576	C₄²	—	2	4	no	—
577	C₄²	C₂⁴×C₁₉	1	2	yes	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	8	2	no	—
583	C₂³	—	8	2	no	—
584	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
585	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
586	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
587	Q₈	—	2	4	no	—
588	Q₈	—	2	4	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	8	2	no	—
591	Q₈	—	8	4	no	—
592	D₄	—	2	8	no	—
593	D₄	—	2	4	no	—
594	D₄	—	2	4	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	8	no	—
598	D₄	—	8	2	no	—
599	D₄	—	8	4	no	—
600	D₄	—	8	4	no	—
601	D₄	—	8	4	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	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	—	4	2	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	4	no	—
614	C₂×C₄	—	8	4	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	—	8	2	no	—
617	C₂×C₄	—	8	2	no	—
618	C₂×C₄	—	8	4	no	—
619	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
620	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
623	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
624	C₈	—	2	1	no	—
625	C₈	—	2	2	no	—
626	C₈	—	2	2	no	—
627	C₈	—	2	2	no	—
628	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	16	4	no	—
640	C₂²	C₁₉×#577	1	4	yes	—
641	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
642	C₄	—	2	1	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	2	no	—
645	C₄	—	2	4	no	—
646	C₄	—	4	4	no	—
647	C₄	—	4	4	no	—
648	C₄	—	4	4	no	—
649	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
650	C₄	C₁₉×#585	1	1	yes	characteristic
651	C₂	—	2	4	no	—
652	C₂	—	4	1	no	—
653	C₂	—	4	2	no	—
654	C₂	—	8	4	no	—
655	C₂	C₁₉×#3496	1	1	yes	characteristic
656	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3536	C₂	semidirect
2. C₁₉×#3335	C₂	semidirect
3. C₁₉×#3316	C₂	semidirect
4. C₁₉×#3306	C₂	semidirect
5. C₁₉×#3282	C₂	semidirect
6. C₁₉×#3263	C₂	semidirect
7. C₁₉×#3204	C₂	semidirect
8. C₁₉×#3195	C₂	semidirect
9. C₁₉×#3192	C₂	semidirect
10. C₁₉×#3173	C₂	semidirect
11. C₁₉×#3060	C₂	semidirect
12. C₂×C₁₉×#465	C₂	semidirect
13. C₁₉×#2929	C₂	semidirect
14. C₂×C₁₉×#135	C₂²	semidirect
15. C₂²×SD₁₆×C₁₉	C₂²	semidirect
16. C₂×C₁₉×#131	C₂²	semidirect
19. C₁₉×#554	C₂²	semidirect
23. C₁₉×#546	C₂²	semidirect
25. C₁₉×#542	C₂²	semidirect
29. C₁₉×#537	C₂²	semidirect
33. C₁₉×#498	C₂²	semidirect
34. C₁₉×#495	C₂²	semidirect
35. C₁₉×#489	C₂²	semidirect
36. C₁₉×#483	C₂²	semidirect
37. C₁₉×#483	C₂²	semidirect
39. C₁₉×#481	C₂²	semidirect
40. C₁₉×#476	C₂²	semidirect
41. C₁₉×#475	C₂²	semidirect
42. C₁₉×#470	C₂²	semidirect
43. C₁₉×#470	C₂²	semidirect
44. C₁₉×#470	C₂²	semidirect
47. C₁₉×#469	C₂²	semidirect
50. C₁₉×#465	C₂²	semidirect
51. C₁₉×#465	C₂²	semidirect
52. C₁₉×#465	C₂²	semidirect
53. C₁₉×#464	C₂²	semidirect
54. C₁₉×#463	C₂²	semidirect
55. C₁₉×#452	C₂²	semidirect
56. C₁₉×#451	C₂²	semidirect
57. C₁₉×#449	C₂²	semidirect
59. C₁₉×#442	C₂²	semidirect
60. C₁₉×#441	C₂²	semidirect
61. C₄×SD₁₆×C₁₉	C₂²	semidirect
62. C₁₉×#435	C₂²	semidirect
63. C₈×D₄×C₁₉	C₂²	semidirect
64. C₂×C₁₉×#106	C₂²	semidirect
65. C₂×C₁₉×#106	C₂²	semidirect
66. C₁₉×#424	C₂²	semidirect
67. C₁₉×#417	C₂²	semidirect
68. C₂×C₁₉×#103	C₂²	semidirect
69. C₂×C₁₉×#102	C₂²	semidirect
70. C₁₉×#408	C₂²	semidirect
72. C₁₉×#405	C₂²	semidirect
249. #62269	C₁₉	direct (N × H)
301. #3536	C₂×C₁₉	semidirect
302. #3335	C₂×C₁₉	semidirect
303. #3316	C₂×C₁₉	semidirect
304. #3306	C₂×C₁₉	semidirect
305. #3282	C₂×C₁₉	semidirect
306. #3263	C₂×C₁₉	semidirect
307. #3204	C₂×C₁₉	semidirect
308. #3195	C₂×C₁₉	semidirect
309. #3192	C₂×C₁₉	semidirect
310. #3173	C₂×C₁₉	semidirect
311. #3060	C₂×C₁₉	semidirect
312. C₂×#465	C₂×C₁₉	semidirect
313. #2929	C₂×C₁₉	semidirect
336. C₂×#135	C₂²×C₁₉	semidirect
337. C₂²×SD₁₆	C₂²×C₁₉	semidirect
338. C₂×#131	C₂²×C₁₉	semidirect
341. #554	C₂²×C₁₉	semidirect
345. #546	C₂²×C₁₉	semidirect
347. #542	C₂²×C₁₉	semidirect
351. #537	C₂²×C₁₉	semidirect
355. #498	C₂²×C₁₉	semidirect
356. #495	C₂²×C₁₉	semidirect
357. #489	C₂²×C₁₉	semidirect
358. #483	C₂²×C₁₉	semidirect
359. #483	C₂²×C₁₉	semidirect
361. #481	C₂²×C₁₉	semidirect
362. #476	C₂²×C₁₉	semidirect
363. #475	C₂²×C₁₉	semidirect
364. #470	C₂²×C₁₉	semidirect
365. #470	C₂²×C₁₉	semidirect
366. #470	C₂²×C₁₉	semidirect
369. #469	C₂²×C₁₉	semidirect
372. #465	C₂²×C₁₉	semidirect
373. #465	C₂²×C₁₉	semidirect
374. #465	C₂²×C₁₉	semidirect
375. #464	C₂²×C₁₉	semidirect
376. #463	C₂²×C₁₉	semidirect
377. #452	C₂²×C₁₉	semidirect
378. #451	C₂²×C₁₉	semidirect
379. #449	C₂²×C₁₉	semidirect
381. #442	C₂²×C₁₉	semidirect
382. #441	C₂²×C₁₉	semidirect
383. C₄×SD₁₆	C₂²×C₁₉	semidirect
384. #435	C₂²×C₁₉	semidirect
385. C₈×D₄	C₂²×C₁₉	semidirect
386. C₂×#106	C₂²×C₁₉	semidirect
387. C₂×#106	C₂²×C₁₉	semidirect
388. #424	C₂²×C₁₉	semidirect
389. #417	C₂²×C₁₉	semidirect
390. C₂×#103	C₂²×C₁₉	semidirect
391. C₂×#102	C₂²×C₁₉	semidirect
392. #408	C₂²×C₁₉	semidirect
394. #405	C₂²×C₁₉	semidirect
494. C₁₉	#62269	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×#3536	2
C₁₉×#3335	2
C₁₉×#3316	2
C₁₉×#3306	2
C₁₉×#3282	2
C₁₉×#3263	2
C₁₉×#3204	2
C₁₉×#3195	2
C₁₉×#3192	2
C₁₉×#3173	2
C₁₉×#3060	2
C₂×C₁₉×#465	2
C₁₉×#2929	2
#62269	19

Subgroups — C19×#62269 #18068228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62269 #18068228