Subgroups — C₁₉×#18578 #18024537

Order 4864.

1028 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1628	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1627	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1625	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1625	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₉	—	2	1	no	—
13	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
14	C₁₉×#554	—	2	1	no	—
15	C₁₉×#552	—	2	1	no	—
16	C₁₉×#551	—	2	2	no	—
17	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#548	—	2	1	no	—
19	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
20	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#546	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#539	—	2	2	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₁₉×#525	—	2	1	no	—
28	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
29	C₁₉×#520	—	2	1	no	—
30	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#496	—	2	1	no	—
32	C₁₉×#490	—	2	1	no	—
33	C₁₉×#490	—	2	2	no	—
34	C₁₉×#486	C₂²	1	2	yes	complemented
35	C₁₉×#486	C₂²	1	2	yes	complemented
36	C₁₉×#460	C₂²	1	2	yes	complemented
37	C₁₉×#459	—	2	1	no	—
38	C₁₉×#459	—	2	1	no	—
39	C₁₉×#459	C₂²	1	2	yes	—
40	C₁₉×#459	C₂²	1	2	yes	—
41	C₁₉×#459	C₂²	1	2	yes	complemented
42	C₁₉×#450	—	2	1	no	—
43	C₁₉×#447	—	2	1	no	—
44	C₁₉×#432	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₉×#418	—	2	2	no	—
47	C₂×C₁₉×#102	—	2	1	no	—
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#332	C₂²	1	2	yes	complemented
50	C₁₉×#332	C₂²	1	2	yes	complemented
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×D₈×C₁₉	—	2	2	no	—
65	C₂×D₈×C₁₉	—	2	2	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	4	4	no	—
68	C₂×M₁₆×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#127	—	2	1	no	—
75	C₁₉×#127	—	2	1	no	—
76	C₁₉×#127	C₂³	1	2	yes	—
77	C₁₉×#126	—	2	2	no	—
78	C₁₉×#126	—	2	2	no	—
79	C₁₉×#126	—	2	1	no	—
80	C₁₉×#125	—	2	2	no	—
81	C₁₉×#125	D₄	1	1	yes	characteristic
82	C₁₉×#125	D₄	1	2	yes	—
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#124	D₄	1	1	yes	characteristic
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	1	no	—
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	—	2	1	no	—
101	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	D₄	1	1	yes	characteristic
106	C₁₉×#120	—	2	2	no	—
107	C₄×Q₈×C₁₉	—	2	1	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×D₄×C₁₉	—	2	2	no	—
112	C₄×D₄×C₁₉	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	1	no	—
118	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
119	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
120	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₁₉×#117	—	2	2	no	—
124	C₁₉×#117	—	2	1	no	—
125	C₁₉×#117	—	2	1	no	—
126	C₁₉×#117	D₄	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
134	C₁₉×C₄⋊C₈	—	2	1	no	—
135	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
136	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	4	no	—
140	C₁₉×#102	—	2	4	no	—
141	C₁₉×#102	—	2	2	no	—
142	C₁₉×#102	—	2	2	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×#97	—	2	1	no	—
145	C₁₉×#97	—	2	1	no	—
146	C₄×C₈×C₁₉	C₂³	1	2	yes	—
147	C₂⁴×C₁₉	—	2	1	no	—
148	C₂⁴×C₁₉	—	4	1	no	—
149	#41×C₁₉	—	4	2	no	—
150	#41×C₁₉	—	4	2	no	—
151	#41×C₁₉	—	8	2	no	—
152	C₂×Q₈×C₁₉	—	2	2	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	8	2	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	1	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	1	no	—
166	C₂×D₄×C₁₉	—	4	2	no	—
167	C₂×D₄×C₁₉	—	4	4	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	4	1	no	—
170	C₂×D₄×C₁₉	—	4	1	no	—
171	C₂×D₄×C₁₉	—	4	1	no	—
172	C₂×D₄×C₁₉	—	8	2	no	—
173	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	8	2	no	—
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	SD₁₆×C₁₉	—	8	2	no	—
190	D₈×C₁₉	—	4	4	no	—
191	D₈×C₁₉	—	4	4	no	—
192	D₈×C₁₉	—	8	2	no	—
193	M₁₆×C₁₉	—	4	2	no	—
194	C₂×C₈×C₁₉	—	2	2	no	—
195	C₂×C₈×C₁₉	—	2	2	no	—
196	C₂×C₈×C₁₉	—	2	2	no	—
197	C₂×C₈×C₁₉	—	4	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	2	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	2	1	no	—
230	C₂²⋊C₄×C₁₉	—	2	1	no	—
231	C₂²⋊C₄×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	—	2	2	no	—
233	C₄²×C₁₉	—	2	2	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
239	#18578	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	1	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	4	2	no	—
244	C₂³×C₁₉	—	4	2	no	—
245	C₂³×C₁₉	—	4	2	no	—
246	C₂³×C₁₉	—	8	1	no	—
247	C₂³×C₁₉	—	8	2	no	—
248	C₂³×C₁₉	—	8	2	no	—
249	C₂³×C₁₉	—	8	2	no	—
250	C₂³×C₁₉	#120	1	1	yes	characteristic
251	Q₈×C₁₉	—	2	2	no	—
252	Q₈×C₁₉	—	4	1	no	—
253	Q₈×C₁₉	—	4	1	no	—
254	Q₈×C₁₉	—	4	2	no	—
255	Q₈×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	2	1	no	—
257	D₄×C₁₉	—	2	1	no	—
258	D₄×C₁₉	—	2	1	no	—
259	D₄×C₁₉	—	2	2	no	—
260	D₄×C₁₉	—	4	2	no	—
261	D₄×C₁₉	—	4	4	no	—
262	D₄×C₁₉	—	4	4	no	—
263	D₄×C₁₉	—	4	2	no	—
264	D₄×C₁₉	—	4	2	no	—
265	D₄×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	4	2	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	8	2	no	—
269	D₄×C₁₉	—	8	2	no	—
270	D₄×C₁₉	—	8	2	no	—
271	D₄×C₁₉	—	8	2	no	—
272	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	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	1	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	1	no	—
283	C₂×C₄×C₁₉	—	2	1	no	—
284	C₂×C₄×C₁₉	—	4	4	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	2	no	—
289	C₂×C₄×C₁₉	—	8	1	no	—
290	C₂×C₄×C₁₉	—	8	1	no	—
291	C₂×C₄×C₁₉	—	8	1	no	—
292	C₂×C₄×C₁₉	—	8	2	no	—
293	C₂×C₄×C₁₉	—	8	2	no	—
294	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
296	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂²×D₄	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	C₈×C₁₉	—	4	2	no	—
301	C₈×C₁₉	—	4	2	no	—
302	C₈×C₁₉	—	4	2	no	—
303	#3520	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
306	C₂×#459	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#1628	C₂×C₁₉	1	2	yes	complemented
308	#1627	C₂×C₁₉	1	2	yes	complemented
309	#1625	C₂×C₁₉	1	2	yes	complemented
310	#1625	C₂×C₁₉	1	2	yes	complemented
311	#1552	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1483	C₂×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	1	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	8	4	no	—
326	C₂²×C₁₉	—	8	2	no	—
327	C₂²×C₁₉	—	8	2	no	—
328	C₂²×C₁₉	—	8	2	no	—
329	C₂²×C₁₉	—	16	4	no	—
330	C₂²×C₁₉	#454	1	2	yes	—
331	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	2	1	no	—
334	C₄×C₁₉	—	2	1	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	4	1	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	4	1	no	—
340	C₄×C₁₉	—	4	2	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	1	no	—
343	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₄×C₁₉	#575	1	1	yes	characteristic
345	C₄×C₁₉	#576	1	2	yes	—
346	C₂²×D₈	—	2	1	no	—
347	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#554	—	2	1	no	—
349	#552	—	2	1	no	—
350	#551	—	2	2	no	—
351	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#548	—	2	1	no	—
353	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#546	—	2	1	no	—
356	#542	—	2	1	no	—
357	#539	—	2	2	no	—
358	#533	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
360	#529	C₂²×C₁₉	1	1	yes	characteristic
361	#525	—	2	1	no	—
362	C₂×C₂²⋊Q₈	—	2	1	no	—
363	#520	—	2	1	no	—
364	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
365	#496	—	2	1	no	—
366	#490	—	2	2	no	—
367	#490	—	2	1	no	—
368	#486	C₂²×C₁₉	1	2	yes	complemented
369	#486	C₂²×C₁₉	1	2	yes	complemented
370	#460	C₂²×C₁₉	1	2	yes	complemented
371	#459	—	2	1	no	—
372	#459	—	2	1	no	—
373	#459	C₂²×C₁₉	1	2	yes	—
374	#459	C₂²×C₁₉	1	2	yes	—
375	#459	C₂²×C₁₉	1	2	yes	complemented
376	#450	—	2	1	no	—
377	#447	—	2	1	no	—
378	#432	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
380	#418	—	2	2	no	—
381	C₂×#102	—	2	1	no	—
382	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
383	#332	C₂²×C₁₉	1	2	yes	complemented
384	#332	C₂²×C₁₉	1	2	yes	complemented
385	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
386	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
387	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
388	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
389	C₂×C₁₉	—	2	2	no	—
390	C₂×C₁₉	—	4	2	no	—
391	C₂×C₁₉	—	8	1	no	—
392	C₂×C₁₉	—	8	1	no	—
393	C₂×C₁₉	—	16	2	no	—
394	C₂×C₁₉	#3006	1	1	yes	characteristic
395	C₂×C₁₉	#3008	1	1	yes	characteristic
396	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
397	C₂×#41	—	2	1	no	—
398	C₂×#41	—	2	1	no	—
399	C₂²×Q₈	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
404	C₂³×C₄	—	2	1	no	—
405	C₂×SD₁₆	—	2	2	no	—
406	C₂×D₈	—	2	2	no	—
407	C₂×D₈	—	2	2	no	—
408	C₂×D₈	—	2	2	no	—
409	C₂×D₈	—	4	4	no	—
410	C₂×M₁₆	—	2	1	no	—
411	C₂²×C₈	—	2	1	no	—
412	C₄⋊Q₈	—	2	1	no	—
413	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
415	#127	—	2	1	no	—
416	#127	—	2	1	no	—
417	#127	—	2	1	no	—
418	#127	C₂³×C₁₉	1	2	yes	—
419	#126	—	2	2	no	—
420	#126	—	2	2	no	—
421	#126	—	2	1	no	—
422	#125	—	2	2	no	—
423	#125	D₄×C₁₉	1	1	yes	characteristic
424	#125	D₄×C₁₉	1	2	yes	—
425	#124	—	2	2	no	—
426	#124	—	2	1	no	—
427	#124	D₄×C₁₉	1	1	yes	characteristic
428	#123	—	2	2	no	—
429	#123	—	2	2	no	—
430	#123	—	2	1	no	—
431	#123	—	2	2	no	—
432	#123	—	2	2	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	—	2	2	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	1	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	C₂²⋊Q₈	—	2	1	no	—
439	C₂²⋊Q₈	—	2	1	no	—
440	C₂²⋊Q₈	—	2	1	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	1	no	—
443	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
444	#121	—	2	2	no	—
445	#121	—	2	1	no	—
446	#121	—	2	1	no	—
447	#121	D₄×C₁₉	1	1	yes	characteristic
448	#120	—	2	2	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	—	2	1	no	—
458	C₄×D₄	—	2	1	no	—
459	C₄×D₄	—	2	1	no	—
460	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
461	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
462	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
463	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
464	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
465	#117	—	2	2	no	—
466	#117	—	2	1	no	—
467	#117	—	2	1	no	—
468	#117	D₄×C₁₉	1	2	yes	—
469	C₂×C₄⋊C₄	—	2	2	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	—	2	2	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
476	C₄⋊C₈	—	2	1	no	—
477	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
478	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
479	#102	—	2	2	no	—
480	#102	—	2	2	no	—
481	#102	—	2	4	no	—
482	#102	—	2	4	no	—
483	#102	—	2	2	no	—
484	#102	—	2	2	no	—
485	C₂²⋊C₈	—	2	1	no	—
486	#97	—	2	1	no	—
487	#97	—	2	1	no	—
488	C₄×C₈	C₂³×C₁₉	1	2	yes	—
489	C₁₉	#18578	1	1	yes	characteristic, direct product factor, Sylow
490	C₂⁴	—	2	1	no	—
491	C₂⁴	—	4	1	no	—
492	#41	—	4	2	no	—
493	#41	—	4	2	no	—
494	#41	—	8	2	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	8	2	no	—
499	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	4	1	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	4	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	4	1	no	—
513	C₂×D₄	—	4	1	no	—
514	C₂×D₄	—	4	1	no	—
515	C₂×D₄	—	8	2	no	—
516	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	8	2	no	—
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	SD₁₆	—	8	2	no	—
533	D₈	—	4	4	no	—
534	D₈	—	4	4	no	—
535	D₈	—	8	2	no	—
536	M₁₆	—	4	2	no	—
537	C₂×C₈	—	2	2	no	—
538	C₂×C₈	—	2	2	no	—
539	C₂×C₈	—	2	2	no	—
540	C₂×C₈	—	4	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
556	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
559	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	2	no	—
577	C₄²	—	2	1	no	—
578	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
579	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
580	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
581	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	8	1	no	—
589	C₂³	—	8	2	no	—
590	C₂³	—	8	2	no	—
591	C₂³	—	8	2	no	—
592	C₂³	C₁₉×#120	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	4	1	no	—
595	Q₈	—	4	1	no	—
596	Q₈	—	4	2	no	—
597	Q₈	—	8	2	no	—
598	D₄	—	2	1	no	—
599	D₄	—	2	1	no	—
600	D₄	—	2	1	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	4	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	8	2	no	—
611	D₄	—	8	2	no	—
612	D₄	—	8	2	no	—
613	D₄	—	8	2	no	—
614	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	8	1	no	—
632	C₂×C₄	—	8	1	no	—
633	C₂×C₄	—	8	1	no	—
634	C₂×C₄	—	8	2	no	—
635	C₂×C₄	—	8	2	no	—
636	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
637	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
638	C₂×C₄	C₁₉×#120	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	C₈	—	4	2	no	—
643	C₈	—	4	2	no	—
644	C₈	—	4	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	8	4	no	—
657	C₂²	—	8	2	no	—
658	C₂²	—	8	2	no	—
659	C₂²	—	8	2	no	—
660	C₂²	—	16	4	no	—
661	C₂²	C₁₉×#454	1	2	yes	—
662	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
675	C₄	C₁₉×#575	1	1	yes	characteristic
676	C₄	C₁₉×#576	1	2	yes	—
677	C₂	—	2	2	no	—
678	C₂	—	4	2	no	—
679	C₂	—	8	1	no	—
680	C₂	—	8	1	no	—
681	C₂	—	16	2	no	—
682	C₂	C₁₉×#3006	1	1	yes	characteristic
683	C₂	C₁₉×#3008	1	1	yes	characteristic
684	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3520	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#3138	C₂	semidirect
4. C₂×C₁₉×#459	C₂	semidirect
5. C₁₉×#1628	C₂	semidirect
6. C₁₉×#1627	C₂	semidirect
7. C₁₉×#1625	C₂	semidirect
8. C₁₉×#1625	C₂	semidirect
9. C₁₉×#1552	C₂	semidirect
10. C₁₉×#1490	C₂	semidirect
11. C₁₉×#1483	C₂	semidirect
13. C₁₉×#556	C₂²	semidirect
17. D₄×Q₈×C₁₉	C₂²	semidirect
19. C₁₉×#547	C₂²	semidirect
20. C₁₉×#547	C₂²	semidirect
34. C₁₉×#486	C₂²	semidirect
35. C₁₉×#486	C₂²	semidirect
36. C₁₉×#460	C₂²	semidirect
41. C₁₉×#459	C₂²	semidirect
49. C₁₉×#332	C₂²	semidirect
50. C₁₉×#332	C₂²	semidirect
51. C₁₉×Q₈⋊C₈	C₂²	semidirect
52. C₁₉×D₄⋊C₈	C₂²	semidirect
53. C₁₉×D₄⋊C₈	C₂²	semidirect
54. C₁₉×D₄⋊C₈	C₂²	semidirect
239. #18578	C₁₉	direct (N × H)
303. #3520	C₂×C₁₉	semidirect
304. #3217	C₂×C₁₉	semidirect
305. #3138	C₂×C₁₉	semidirect
306. C₂×#459	C₂×C₁₉	semidirect
307. #1628	C₂×C₁₉	semidirect
308. #1627	C₂×C₁₉	semidirect
309. #1625	C₂×C₁₉	semidirect
310. #1625	C₂×C₁₉	semidirect
311. #1552	C₂×C₁₉	semidirect
312. #1490	C₂×C₁₉	semidirect
313. #1483	C₂×C₁₉	semidirect
347. #556	C₂²×C₁₉	semidirect
351. D₄×Q₈	C₂²×C₁₉	semidirect
353. #547	C₂²×C₁₉	semidirect
354. #547	C₂²×C₁₉	semidirect
368. #486	C₂²×C₁₉	semidirect
369. #486	C₂²×C₁₉	semidirect
370. #460	C₂²×C₁₉	semidirect
375. #459	C₂²×C₁₉	semidirect
383. #332	C₂²×C₁₉	semidirect
384. #332	C₂²×C₁₉	semidirect
385. Q₈⋊C₈	C₂²×C₁₉	semidirect
386. D₄⋊C₈	C₂²×C₁₉	semidirect
387. D₄⋊C₈	C₂²×C₁₉	semidirect
388. D₄⋊C₈	C₂²×C₁₉	semidirect
489. C₁₉	#18578	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×#3520	2
C₁₉×#3217	2
C₁₉×#3138	2
C₂×C₁₉×#459	2
C₁₉×#1628	2
C₁₉×#1627	2
C₁₉×#1625	2
C₁₉×#1552	2
C₁₉×#1490	2
C₁₉×#1483	2
#18578	19

Subgroups — C19×#18578 #18024537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18578 #18024537