Subgroups — C₁₉×#62362 #18068321

Order 4864.

1746 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3394	C₂	1	3	yes	maximal, complemented
4	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3381	C₂	1	3	yes	maximal, complemented
6	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3365	C₂	1	3	yes	maximal, complemented
8	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3360	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3248	C₂	1	3	yes	maximal, complemented
12	C₁₉×#3247	C₂	1	3	yes	maximal, complemented
13	C₁₉×#3168	C₂	1	3	yes	maximal, complemented
14	C₁₉×#3167	C₂	1	3	yes	maximal, complemented
15	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	C₂²	1	3	yes	—
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#557	C₂²	1	1	yes	characteristic
19	C₁₉×#557	C₂²	1	3	yes	—
20	C₁₉×#556	C₂²	1	3	yes	—
21	C₁₉×#554	C₂²	1	3	yes	—
22	C₁₉×#552	—	2	3	no	—
23	C₁₉×#550	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₁₉	—	2	1	no	—
25	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#548	—	2	1	no	—
27	C₁₉×#547	—	2	3	no	—
28	C₁₉×#542	—	2	3	no	—
29	C₁₉×#541	—	2	3	no	—
30	C₁₉×#533	C₂²	1	3	yes	—
31	C₁₉×#532	C₂²	1	3	yes	—
32	C₁₉×#529	C₂²	1	3	yes	—
33	C₁₉×#529	C₂²	1	3	yes	—
34	C₁₉×#520	—	2	1	no	—
35	C₁₉×#519	—	2	1	no	—
36	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#499	C₂²	1	3	yes	—
38	C₁₉×#498	C₂²	1	3	yes	—
39	C₁₉×#495	C₂²	1	3	yes	—
40	C₁₉×#492	C₂²	1	3	yes	—
41	C₁₉×#488	C₂²	1	3	yes	—
42	C₁₉×#488	C₂²	1	3	yes	—
43	C₁₉×#487	C₂²	1	3	yes	—
44	C₁₉×#486	C₂²	1	3	yes	—
45	C₁₉×#479	C₂²	1	6	yes	—
46	C₁₉×#478	C₂²	1	6	yes	—
47	C₁₉×#477	C₂²	1	3	yes	—
48	C₁₉×#476	C₂²	1	3	yes	—
49	C₁₉×#475	C₂²	1	3	yes	—
50	C₁₉×#474	C₂²	1	3	yes	—
51	C₁₉×#467	C₂²	1	3	yes	—
52	C₁₉×#466	C₂²	1	3	yes	—
53	C₁₉×#465	C₂²	1	3	yes	—
54	C₁₉×#465	C₂²	1	6	yes	—
55	C₁₉×#465	C₂²	1	1	yes	characteristic
56	C₁₉×#464	C₂²	1	6	yes	—
57	C₁₉×#463	C₂²	1	6	yes	—
58	C₁₉×#462	C₂²	1	3	yes	—
59	C₁₉×#461	C₂²	1	3	yes	—
60	C₁₉×#460	C₂²	1	3	yes	—
61	C₁₉×#459	C₂²	1	3	yes	—
62	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
64	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
65	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
66	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
67	C₄×SD₁₆×C₁₉	C₂²	1	6	yes	—
68	C₄×SD₁₆×C₁₉	C₂²	1	6	yes	—
69	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
70	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
71	C₄×D₈×C₁₉	C₂²	1	3	yes	—
72	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
73	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
74	C₂×#41×C₁₉	—	2	1	no	—
75	C₂×#41×C₁₉	—	2	3	no	—
76	C₂²×Q₈×C₁₉	—	2	1	no	—
77	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
78	C₂×Q₁₆×C₁₉	C₂³	1	3	yes	—
79	C₂×SD₁₆×C₁₉	C₂³	1	3	yes	—
80	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×SD₁₆×C₁₉	C₂³	1	6	yes	—
82	C₂×D₈×C₁₉	C₂³	1	3	yes	—
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
85	C₁₉×C₄⋊Q₈	—	2	3	no	—
86	C₁₉×C₄⋊Q₈	—	2	3	no	—
87	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
88	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
89	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₉×#127	C₂³	1	3	yes	—
91	C₁₉×#126	—	2	6	no	—
92	C₁₉×#126	—	2	3	no	—
93	C₁₉×#126	—	2	3	no	—
94	C₁₉×#125	—	2	6	no	—
95	C₁₉×#125	—	2	3	no	—
96	C₁₉×#125	—	2	3	no	—
97	C₁₉×#125	C₂³	1	3	yes	—
98	C₁₉×#125	C₂³	1	3	yes	—
99	C₁₉×#124	—	2	3	no	—
100	C₁₉×#124	—	2	3	no	—
101	C₁₉×#124	C₂³	1	3	yes	—
102	C₁₉×#124	C₂³	1	3	yes	—
103	C₁₉×#123	—	2	3	no	—
104	C₁₉×#123	—	2	3	no	—
105	C₁₉×#123	—	2	6	no	—
106	C₁₉×C₂²⋊Q₈	—	2	3	no	—
107	C₁₉×C₂²⋊Q₈	—	2	3	no	—
108	C₁₉×C₂²⋊Q₈	—	2	3	no	—
109	C₁₉×C₂²⋊Q₈	—	2	3	no	—
110	C₁₉×C₂²⋊Q₈	—	2	6	no	—
111	C₁₉×C₂²⋊Q₈	C₂³	1	3	yes	—
112	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₉×#121	—	2	3	no	—
114	C₁₉×#121	—	2	3	no	—
115	C₁₉×#121	C₂³	1	3	yes	—
116	C₁₉×#121	C₂³	1	1	yes	characteristic
117	C₄×Q₈×C₁₉	—	2	1	no	—
118	C₄×Q₈×C₁₉	—	2	1	no	—
119	C₄×Q₈×C₁₉	—	2	3	no	—
120	C₄×Q₈×C₁₉	—	2	3	no	—
121	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
122	C₄×Q₈×C₁₉	D₄	1	3	yes	—
123	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
124	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
125	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
126	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
128	C₄×D₄×C₁₉	—	2	3	no	—
129	C₄×D₄×C₁₉	—	2	3	no	—
130	C₄×D₄×C₁₉	—	2	3	no	—
131	C₄×D₄×C₁₉	—	2	3	no	—
132	C₄×D₄×C₁₉	C₂³	1	3	yes	—
133	C₄×D₄×C₁₉	C₂³	1	3	yes	—
134	C₄×D₄×C₁₉	C₂³	1	6	yes	—
135	C₁₉×#117	—	2	3	no	—
136	C₁₉×#117	—	2	3	no	—
137	C₁₉×#117	—	2	3	no	—
138	C₁₉×#117	—	2	3	no	—
139	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
140	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
141	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
142	C₁₉×#107	C₂³	1	3	yes	—
143	C₁₉×#107	C₂³	1	3	yes	—
144	C₁₉×#106	C₂³	1	3	yes	—
145	C₁₉×#106	C₂³	1	1	yes	characteristic
146	C₁₉×#106	C₂³	1	6	yes	—
147	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
150	C₁₉×#103	C₂³	1	3	yes	—
151	C₁₉×#103	C₂³	1	3	yes	—
152	C₁₉×#103	C₂³	1	6	yes	—
153	C₁₉×#103	C₂³	1	3	yes	—
154	C₁₉×#103	C₂³	1	1	yes	characteristic
155	C₁₉×#102	C₂³	1	1	yes	characteristic
156	C₁₉×#102	C₂³	1	3	yes	—
157	C₁₉×#102	C₂³	1	6	yes	—
158	C₁₉×#102	C₂³	1	3	yes	—
159	C₁₉×#102	C₂³	1	3	yes	—
160	C₄×C₈×C₁₉	C₂³	1	3	yes	—
161	C₄×C₈×C₁₉	C₂³	1	3	yes	—
162	C₄×C₈×C₁₉	C₂³	1	3	yes	—
163	C₄×C₈×C₁₉	C₂³	1	3	yes	—
164	#41×C₁₉	—	4	4	no	—
165	#41×C₁₉	—	8	6	no	—
166	C₂×Q₈×C₁₉	—	2	4	no	—
167	C₂×Q₈×C₁₉	—	2	3	no	—
168	C₂×Q₈×C₁₉	—	2	3	no	—
169	C₂×Q₈×C₁₉	—	4	4	no	—
170	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
171	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	3	no	—
176	C₂×D₄×C₁₉	—	2	3	no	—
177	C₂×D₄×C₁₉	—	2	3	no	—
178	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
180	C₂²×C₄×C₁₉	—	2	3	no	—
181	C₂²×C₄×C₁₉	—	2	3	no	—
182	C₂²×C₄×C₁₉	—	2	6	no	—
183	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
184	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
185	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
186	Q₁₆×C₁₉	—	4	3	no	—
187	SD₁₆×C₁₉	—	2	6	no	—
188	SD₁₆×C₁₉	—	2	2	no	—
189	SD₁₆×C₁₉	—	4	6	no	—
190	D₈×C₁₉	—	4	3	no	—
191	C₂×C₈×C₁₉	—	2	2	no	—
192	C₂×C₈×C₁₉	—	4	3	no	—
193	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
194	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
195	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
196	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	—	2	3	no	—
198	C₄⋊C₄×C₁₉	—	2	3	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	3	no	—
201	C₄⋊C₄×C₁₉	—	2	3	no	—
202	C₄⋊C₄×C₁₉	—	2	3	no	—
203	C₄⋊C₄×C₁₉	—	2	3	no	—
204	C₄⋊C₄×C₁₉	—	2	3	no	—
205	C₄⋊C₄×C₁₉	—	2	3	no	—
206	C₄⋊C₄×C₁₉	—	2	3	no	—
207	C₄⋊C₄×C₁₉	—	2	6	no	—
208	C₄⋊C₄×C₁₉	—	2	3	no	—
209	C₄⋊C₄×C₁₉	—	2	3	no	—
210	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
212	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
213	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
214	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
215	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
216	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₉	—	2	3	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	3	no	—
221	C₂²⋊C₄×C₁₉	—	2	3	no	—
222	C₂²⋊C₄×C₁₉	—	2	3	no	—
223	C₂²⋊C₄×C₁₉	—	2	3	no	—
224	C₂²⋊C₄×C₁₉	—	2	3	no	—
225	C₂²⋊C₄×C₁₉	—	2	3	no	—
226	C₂²⋊C₄×C₁₉	—	2	6	no	—
227	C₂²⋊C₄×C₁₉	—	2	3	no	—
228	C₄²×C₁₉	—	2	6	no	—
229	C₄²×C₁₉	—	2	3	no	—
230	C₄²×C₁₉	—	2	3	no	—
231	C₄²×C₁₉	C₂×D₄	1	3	yes	—
232	C₄²×C₁₉	C₂×D₄	1	3	yes	—
233	C₄²×C₁₉	C₂⁴	1	3	yes	—
234	C₄²×C₁₉	C₂⁴	1	3	yes	—
235	#62362	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂³×C₁₉	—	2	1	no	—
237	C₂³×C₁₉	—	2	3	no	—
238	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₉	—	2	6	no	—
240	Q₈×C₁₉	—	2	1	no	—
241	Q₈×C₁₉	—	2	3	no	—
242	Q₈×C₁₉	—	2	3	no	—
243	Q₈×C₁₉	—	2	1	no	—
244	Q₈×C₁₉	—	4	6	no	—
245	Q₈×C₁₉	—	8	3	no	—
246	Q₈×C₁₉	#135	1	4	yes	—
247	D₄×C₁₉	—	2	1	no	—
248	D₄×C₁₉	—	2	3	no	—
249	D₄×C₁₉	—	2	1	no	—
250	D₄×C₁₉	—	2	3	no	—
251	D₄×C₁₉	—	4	2	no	—
252	D₄×C₁₉	—	4	6	no	—
253	D₄×C₁₉	—	4	6	no	—
254	D₄×C₁₉	—	8	3	no	—
255	C₂×C₄×C₁₉	—	2	6	no	—
256	C₂×C₄×C₁₉	—	2	6	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	3	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	3	no	—
263	C₂×C₄×C₁₉	—	2	3	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	4	6	no	—
266	C₂×C₄×C₁₉	—	4	6	no	—
267	C₂×C₄×C₁₉	—	8	6	no	—
268	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
269	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
272	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
273	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
274	C₈×C₁₉	—	2	1	no	—
275	C₈×C₁₉	—	2	3	no	—
276	C₈×C₁₉	—	2	3	no	—
277	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
278	#3523	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#3522	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#3394	C₂×C₁₉	1	3	yes	complemented
281	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#3381	C₂×C₁₉	1	3	yes	complemented
283	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3365	C₂×C₁₉	1	3	yes	complemented
285	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3360	C₂×C₁₉	1	3	yes	complemented
287	#3358	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#3248	C₂×C₁₉	1	3	yes	complemented
289	#3247	C₂×C₁₉	1	3	yes	complemented
290	#3168	C₂×C₁₉	1	3	yes	complemented
291	#3167	C₂×C₁₉	1	3	yes	complemented
292	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	3	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	3	no	—
299	C₂²×C₁₉	—	4	3	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	#577	1	2	yes	—
302	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	3	no	—
305	C₄×C₁₉	—	2	3	no	—
306	C₄×C₁₉	—	2	3	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	3	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	3	no	—
311	C₄×C₁₉	—	4	3	no	—
312	C₄×C₁₉	—	4	1	no	—
313	C₄×C₁₉	C₂×#135	1	6	yes	—
314	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₄×C₁₉	#585	1	1	yes	characteristic
316	#559	C₂²×C₁₉	1	3	yes	—
317	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
318	#557	C₂²×C₁₉	1	1	yes	characteristic
319	#557	C₂²×C₁₉	1	3	yes	—
320	#556	C₂²×C₁₉	1	3	yes	—
321	#554	C₂²×C₁₉	1	3	yes	—
322	#552	—	2	3	no	—
323	#550	C₂²×C₁₉	1	1	yes	characteristic
324	D₄×Q₈	—	2	1	no	—
325	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	#548	—	2	1	no	—
327	#547	—	2	3	no	—
328	#542	—	2	3	no	—
329	#541	—	2	3	no	—
330	#533	C₂²×C₁₉	1	3	yes	—
331	#532	C₂²×C₁₉	1	3	yes	—
332	#529	C₂²×C₁₉	1	3	yes	—
333	#529	C₂²×C₁₉	1	3	yes	—
334	#520	—	2	1	no	—
335	#519	—	2	1	no	—
336	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
337	#499	C₂²×C₁₉	1	3	yes	—
338	#498	C₂²×C₁₉	1	3	yes	—
339	#495	C₂²×C₁₉	1	3	yes	—
340	#492	C₂²×C₁₉	1	3	yes	—
341	#488	C₂²×C₁₉	1	3	yes	—
342	#488	C₂²×C₁₉	1	3	yes	—
343	#487	C₂²×C₁₉	1	3	yes	—
344	#486	C₂²×C₁₉	1	3	yes	—
345	#479	C₂²×C₁₉	1	6	yes	—
346	#478	C₂²×C₁₉	1	6	yes	—
347	#477	C₂²×C₁₉	1	3	yes	—
348	#476	C₂²×C₁₉	1	3	yes	—
349	#475	C₂²×C₁₉	1	3	yes	—
350	#474	C₂²×C₁₉	1	3	yes	—
351	#467	C₂²×C₁₉	1	3	yes	—
352	#466	C₂²×C₁₉	1	3	yes	—
353	#465	C₂²×C₁₉	1	3	yes	—
354	#465	C₂²×C₁₉	1	6	yes	—
355	#465	C₂²×C₁₉	1	1	yes	characteristic
356	#464	C₂²×C₁₉	1	6	yes	—
357	#463	C₂²×C₁₉	1	6	yes	—
358	#462	C₂²×C₁₉	1	3	yes	—
359	#461	C₂²×C₁₉	1	3	yes	—
360	#460	C₂²×C₁₉	1	3	yes	—
361	#459	C₂²×C₁₉	1	3	yes	—
362	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
363	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
364	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
365	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
366	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
367	C₄×SD₁₆	C₂²×C₁₉	1	6	yes	—
368	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
369	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
370	C₄×SD₁₆	C₂²×C₁₉	1	6	yes	—
371	C₄×D₈	C₂²×C₁₉	1	3	yes	—
372	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
373	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
374	C₂×C₁₉	—	2	2	no	—
375	C₂×C₁₉	—	8	1	no	—
376	C₂×C₁₉	—	8	3	no	—
377	C₂×C₁₉	#3497	1	1	yes	characteristic
378	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
379	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
380	C₂×#41	—	2	1	no	—
381	C₂×#41	—	2	3	no	—
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
384	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
385	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
386	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×SD₁₆	C₂³×C₁₉	1	6	yes	—
388	C₂×D₈	C₂³×C₁₉	1	3	yes	—
389	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
391	C₄⋊Q₈	—	2	3	no	—
392	C₄⋊Q₈	—	2	3	no	—
393	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
394	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
395	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
396	#127	C₂³×C₁₉	1	3	yes	—
397	#126	—	2	6	no	—
398	#126	—	2	3	no	—
399	#126	—	2	3	no	—
400	#125	—	2	6	no	—
401	#125	—	2	3	no	—
402	#125	—	2	3	no	—
403	#125	C₂³×C₁₉	1	3	yes	—
404	#125	C₂³×C₁₉	1	3	yes	—
405	#124	—	2	3	no	—
406	#124	—	2	3	no	—
407	#124	C₂³×C₁₉	1	3	yes	—
408	#124	C₂³×C₁₉	1	3	yes	—
409	#123	—	2	3	no	—
410	#123	—	2	3	no	—
411	#123	—	2	6	no	—
412	C₂²⋊Q₈	—	2	3	no	—
413	C₂²⋊Q₈	—	2	3	no	—
414	C₂²⋊Q₈	—	2	3	no	—
415	C₂²⋊Q₈	—	2	3	no	—
416	C₂²⋊Q₈	—	2	6	no	—
417	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂³×C₁₉	1	3	yes	—
419	#121	—	2	3	no	—
420	#121	—	2	3	no	—
421	#121	C₂³×C₁₉	1	1	yes	characteristic
422	#121	C₂³×C₁₉	1	3	yes	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	—	2	3	no	—
426	C₄×Q₈	—	2	3	no	—
427	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
428	C₄×Q₈	D₄×C₁₉	1	3	yes	—
429	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
430	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
431	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
432	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
434	C₄×D₄	—	2	3	no	—
435	C₄×D₄	—	2	3	no	—
436	C₄×D₄	—	2	3	no	—
437	C₄×D₄	—	2	3	no	—
438	C₄×D₄	C₂³×C₁₉	1	3	yes	—
439	C₄×D₄	C₂³×C₁₉	1	3	yes	—
440	C₄×D₄	C₂³×C₁₉	1	6	yes	—
441	#117	—	2	3	no	—
442	#117	—	2	3	no	—
443	#117	—	2	3	no	—
444	#117	—	2	3	no	—
445	C₂×C₄⋊C₄	—	2	3	no	—
446	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
447	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
448	#107	C₂³×C₁₉	1	3	yes	—
449	#107	C₂³×C₁₉	1	3	yes	—
450	#106	C₂³×C₁₉	1	3	yes	—
451	#106	C₂³×C₁₉	1	1	yes	characteristic
452	#106	C₂³×C₁₉	1	6	yes	—
453	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
454	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
455	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
456	#103	C₂³×C₁₉	1	3	yes	—
457	#103	C₂³×C₁₉	1	3	yes	—
458	#103	C₂³×C₁₉	1	6	yes	—
459	#103	C₂³×C₁₉	1	3	yes	—
460	#103	C₂³×C₁₉	1	1	yes	characteristic
461	#102	C₂³×C₁₉	1	1	yes	characteristic
462	#102	C₂³×C₁₉	1	3	yes	—
463	#102	C₂³×C₁₉	1	6	yes	—
464	#102	C₂³×C₁₉	1	3	yes	—
465	#102	C₂³×C₁₉	1	3	yes	—
466	C₄×C₈	C₂³×C₁₉	1	3	yes	—
467	C₄×C₈	C₂³×C₁₉	1	3	yes	—
468	C₄×C₈	C₂³×C₁₉	1	3	yes	—
469	C₄×C₈	C₂³×C₁₉	1	3	yes	—
470	C₁₉	#62362	1	1	yes	characteristic, direct product factor, Sylow
471	#41	—	4	4	no	—
472	#41	—	8	6	no	—
473	C₂×Q₈	—	2	4	no	—
474	C₂×Q₈	—	2	3	no	—
475	C₂×Q₈	—	2	3	no	—
476	C₂×Q₈	—	4	4	no	—
477	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
478	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
480	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	3	no	—
483	C₂×D₄	—	2	3	no	—
484	C₂×D₄	—	2	3	no	—
485	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
486	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
487	C₂²×C₄	—	2	3	no	—
488	C₂²×C₄	—	2	3	no	—
489	C₂²×C₄	—	2	6	no	—
490	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
491	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
492	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
493	Q₁₆	—	4	3	no	—
494	SD₁₆	—	2	6	no	—
495	SD₁₆	—	2	2	no	—
496	SD₁₆	—	4	6	no	—
497	D₈	—	4	3	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	4	3	no	—
500	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
501	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
502	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
503	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
504	C₄⋊C₄	—	2	3	no	—
505	C₄⋊C₄	—	2	3	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	3	no	—
508	C₄⋊C₄	—	2	3	no	—
509	C₄⋊C₄	—	2	3	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	—	2	3	no	—
514	C₄⋊C₄	—	2	6	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
518	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
519	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
520	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
521	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
522	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
523	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
524	C₂²⋊C₄	—	2	3	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	3	no	—
528	C₂²⋊C₄	—	2	3	no	—
529	C₂²⋊C₄	—	2	3	no	—
530	C₂²⋊C₄	—	2	3	no	—
531	C₂²⋊C₄	—	2	3	no	—
532	C₂²⋊C₄	—	2	3	no	—
533	C₂²⋊C₄	—	2	6	no	—
534	C₂²⋊C₄	—	2	3	no	—
535	C₄²	—	2	6	no	—
536	C₄²	—	2	3	no	—
537	C₄²	—	2	3	no	—
538	C₄²	C₂×D₄×C₁₉	1	3	yes	—
539	C₄²	C₂×D₄×C₁₉	1	3	yes	—
540	C₄²	C₂⁴×C₁₉	1	3	yes	—
541	C₄²	C₂⁴×C₁₉	1	3	yes	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	3	no	—
544	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
545	Q₈	—	2	6	no	—
546	Q₈	—	2	1	no	—
547	Q₈	—	2	3	no	—
548	Q₈	—	2	3	no	—
549	Q₈	—	2	1	no	—
550	Q₈	—	4	6	no	—
551	Q₈	—	8	3	no	—
552	Q₈	C₁₉×#135	1	4	yes	—
553	D₄	—	2	1	no	—
554	D₄	—	2	3	no	—
555	D₄	—	2	1	no	—
556	D₄	—	2	3	no	—
557	D₄	—	4	6	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	6	no	—
560	D₄	—	8	3	no	—
561	C₂×C₄	—	2	6	no	—
562	C₂×C₄	—	2	6	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	3	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	3	no	—
569	C₂×C₄	—	2	3	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	6	no	—
572	C₂×C₄	—	4	6	no	—
573	C₂×C₄	—	8	6	no	—
574	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
575	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
577	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
578	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
579	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
580	C₈	—	2	1	no	—
581	C₈	—	2	3	no	—
582	C₈	—	2	3	no	—
583	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	3	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	3	no	—
590	C₂²	—	4	3	no	—
591	C₂²	—	4	1	no	—
592	C₂²	C₁₉×#577	1	2	yes	—
593	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	3	no	—
596	C₄	—	2	3	no	—
597	C₄	—	2	3	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	3	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	3	no	—
602	C₄	—	4	3	no	—
603	C₄	—	4	1	no	—
604	C₄	C₂×C₁₉×#135	1	6	yes	—
605	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
606	C₄	C₁₉×#585	1	1	yes	characteristic
607	C₂	—	2	2	no	—
608	C₂	—	8	1	no	—
609	C₂	—	8	3	no	—
610	C₂	C₁₉×#3497	1	1	yes	characteristic
611	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
612	C₂	C₂×C₁₉×#577	1	1	yes	characteristic

	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 ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3523	C₂	semidirect
2. C₁₉×#3522	C₂	semidirect
3. C₁₉×#3394	C₂	semidirect
4. C₁₉×#3392	C₂	semidirect
5. C₁₉×#3381	C₂	semidirect
6. Q₈×SD₁₆×C₁₉	C₂	semidirect
7. C₁₉×#3365	C₂	semidirect
8. C₁₉×#3363	C₂	semidirect
9. C₁₉×#3360	C₂	semidirect
10. C₁₉×#3358	C₂	semidirect
11. C₁₉×#3248	C₂	semidirect
12. C₁₉×#3247	C₂	semidirect
13. C₁₉×#3168	C₂	semidirect
14. C₁₉×#3167	C₂	semidirect
15. C₂×C₈×Q₈×C₁₉	C₂	semidirect
235. #62362	C₁₉	direct (N × H)
278. #3523	C₂×C₁₉	semidirect
279. #3522	C₂×C₁₉	semidirect
280. #3394	C₂×C₁₉	semidirect
281. #3392	C₂×C₁₉	semidirect
282. #3381	C₂×C₁₉	semidirect
283. Q₈×SD₁₆	C₂×C₁₉	semidirect
284. #3365	C₂×C₁₉	semidirect
285. #3363	C₂×C₁₉	semidirect
286. #3360	C₂×C₁₉	semidirect
287. #3358	C₂×C₁₉	semidirect
288. #3248	C₂×C₁₉	semidirect
289. #3247	C₂×C₁₉	semidirect
290. #3168	C₂×C₁₉	semidirect
291. #3167	C₂×C₁₉	semidirect
292. C₂×C₈×Q₈	C₂×C₁₉	semidirect
470. C₁₉	#62362	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×#3523	2
C₁₉×#3522	2
C₁₉×#3394	2
C₁₉×#3392	2
C₁₉×#3381	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3365	2
C₁₉×#3363	2
C₁₉×#3360	2
C₁₉×#3358	2
C₁₉×#3248	2
C₁₉×#3247	2
C₁₉×#3168	2
C₁₉×#3167	2
C₂×C₈×Q₈×C₁₉	2
#62362	19

Subgroups — C19×#62362 #18068321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62362 #18068321