Subgroups — C₁₉×#18270 #18024229

Order 4864.

1000 conjugacy classes of subgroups.

The subgroup lattice has 616 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	1	yes	maximal, characteristic
2	C₁₉×#3092	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1610	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1609	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1507	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1501	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1472	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#562	—	2	2	no	—
11	C₁₉×#554	—	2	1	no	—
12	C₁₉×#548	—	2	1	no	—
13	C₁₉×#547	—	2	1	no	—
14	C₁₉×#546	—	2	1	no	—
15	C₁₉×#546	—	2	2	no	—
16	C₁₉×#543	—	2	1	no	—
17	C₁₉×#542	—	2	1	no	—
18	C₁₉×#539	C₂²	1	2	yes	—
19	C₁₉×#538	—	2	1	no	—
20	C₁₉×#537	—	2	1	no	—
21	C₁₉×#537	C₂²	1	2	yes	—
22	C₁₉×#525	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#484	—	2	1	no	—
27	C₁₉×#483	C₂²	1	2	yes	complemented
28	C₁₉×#481	—	2	1	no	—
29	C₁₉×#480	—	2	2	no	—
30	C₁₉×#480	C₂²	1	4	yes	—
31	C₁₉×#480	C₂²	1	2	yes	complemented
32	C₁₉×#428	—	2	1	no	—
33	C₂×C₁₉×#107	—	2	1	no	—
34	C₁₉×#417	—	2	1	no	—
35	C₂×C₁₉×#102	—	2	1	no	—
36	C₁₉×#407	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₉×#398	C₂²	1	4	yes	complemented
39	C₁₉×#391	—	2	1	no	—
40	C₁₉×#385	—	2	2	no	—
41	C₁₉×#384	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#328	C₂²	1	2	yes	complemented
44	C₁₉×#327	C₂²	1	4	yes	—
45	C₁₉×#327	C₂²	1	2	yes	complemented
46	C₁₉×#324	C₂²	1	4	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#124	—	2	2	no	—
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×#124	—	2	2	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×#123	—	2	1	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
80	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×#121	—	2	1	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	D₄	1	2	yes	—
90	C₁₉×#121	D₄	1	1	yes	characteristic
91	C₁₉×#121	C₂³	1	2	yes	—
92	C₁₉×#121	C₂³	1	1	yes	characteristic
93	C₁₉×#120	—	2	2	no	—
94	C₁₉×#120	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₁₉×#117	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
117	C₂×C₄²×C₁₉	—	2	1	no	—
118	C₁₉×#107	—	2	4	no	—
119	C₁₉×#107	—	2	2	no	—
120	C₁₉×#106	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#102	—	2	4	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×C₂²⋊C₈	—	2	1	no	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×#95	—	2	4	no	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₂⁴×C₁₉	—	2	1	no	—
131	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
132	#41×C₁₉	—	4	2	no	—
133	#41×C₁₉	—	8	4	no	—
134	#41×C₁₉	—	8	2	no	—
135	C₂×Q₈×C₁₉	—	2	2	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	4	2	no	—
139	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	—	8	2	no	—
150	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	4	1	no	—
161	C₂²×C₄×C₁₉	—	4	1	no	—
162	C₂²×C₄×C₁₉	—	8	2	no	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	M₁₆×C₁₉	—	4	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	8	4	no	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	2	2	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	4	2	no	—
212	#18270	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂³×C₁₉	—	2	2	no	—
214	C₂³×C₁₉	—	2	2	no	—
215	C₂³×C₁₉	—	2	2	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	2	no	—
219	C₂³×C₁₉	—	8	1	no	—
220	C₂³×C₁₉	—	8	1	no	—
221	C₂³×C₁₉	#120	1	1	yes	characteristic
222	C₂³×C₁₉	#120	1	1	yes	characteristic
223	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	2	no	—
226	Q₈×C₁₉	—	8	1	no	—
227	Q₈×C₁₉	—	8	2	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	4	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	2	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	8	2	no	—
235	D₄×C₁₉	—	8	1	no	—
236	D₄×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	8	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	4	no	—
258	C₂×C₄×C₁₉	—	8	1	no	—
259	C₂×C₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	—	8	2	no	—
264	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₁₉	—	4	2	no	—
269	C₈×C₁₉	—	4	2	no	—
270	#3536	C₂×C₁₉	1	1	yes	characteristic
271	#3092	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂×#480	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#2502	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1610	C₂×C₁₉	1	4	yes	complemented
275	#1609	C₂×C₁₉	1	4	yes	complemented
276	#1507	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1501	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1472	C₂×C₁₉	1	1	yes	characteristic, complemented
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	4	4	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	16	2	no	—
294	C₂²×C₁₉	#456	1	2	yes	—
295	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
296	C₂²×C₁₉	#576	1	2	yes	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	4	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	2	no	—
307	C₄×C₁₉	—	8	2	no	—
308	C₄×C₁₉	#458	1	2	yes	—
309	#562	—	2	2	no	—
310	#554	—	2	1	no	—
311	#548	—	2	1	no	—
312	#547	—	2	1	no	—
313	#546	—	2	1	no	—
314	#546	—	2	2	no	—
315	#543	—	2	1	no	—
316	#542	—	2	1	no	—
317	#539	C₂²×C₁₉	1	2	yes	—
318	#538	—	2	1	no	—
319	#537	—	2	1	no	—
320	#537	C₂²×C₁₉	1	2	yes	—
321	#525	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
325	#484	—	2	1	no	—
326	#483	C₂²×C₁₉	1	2	yes	complemented
327	#481	—	2	1	no	—
328	#480	—	2	2	no	—
329	#480	C₂²×C₁₉	1	4	yes	—
330	#480	C₂²×C₁₉	1	2	yes	complemented
331	#428	—	2	1	no	—
332	C₂×#107	—	2	1	no	—
333	#417	—	2	1	no	—
334	C₂×#102	—	2	1	no	—
335	#407	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
337	#398	C₂²×C₁₉	1	4	yes	complemented
338	#391	—	2	1	no	—
339	#385	—	2	2	no	—
340	#384	—	2	1	no	—
341	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
342	#328	C₂²×C₁₉	1	2	yes	complemented
343	#327	C₂²×C₁₉	1	4	yes	—
344	#327	C₂²×C₁₉	1	2	yes	complemented
345	#324	C₂²×C₁₉	1	4	yes	complemented
346	C₂×C₁₉	—	2	2	no	—
347	C₂×C₁₉	—	2	2	no	—
348	C₂×C₁₉	—	4	1	no	—
349	C₂×C₁₉	—	8	1	no	—
350	C₂×C₁₉	—	8	2	no	—
351	C₂×C₁₉	#3008	1	1	yes	characteristic
352	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
353	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
357	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	#126	—	2	2	no	—
366	#125	—	2	2	no	—
367	#124	—	2	2	no	—
368	#124	—	2	1	no	—
369	#124	—	2	2	no	—
370	#123	—	2	2	no	—
371	#123	—	2	2	no	—
372	#123	—	2	2	no	—
373	#123	—	2	1	no	—
374	#123	—	2	2	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
387	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
388	#121	—	2	1	no	—
389	#121	—	2	2	no	—
390	#121	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	2	no	—
396	#121	D₄×C₁₉	1	2	yes	—
397	#121	D₄×C₁₉	1	1	yes	characteristic
398	#121	C₂³×C₁₉	1	2	yes	—
399	#121	C₂³×C₁₉	1	1	yes	characteristic
400	#120	—	2	2	no	—
401	#120	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	2	no	—
408	#117	D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	4	no	—
416	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
420	C₂×C₂²⋊C₄	—	2	2	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
424	C₂×C₄²	—	2	1	no	—
425	#107	—	2	4	no	—
426	#107	—	2	2	no	—
427	#106	—	2	2	no	—
428	#103	—	2	2	no	—
429	#102	—	2	4	no	—
430	#102	—	2	2	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
434	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
435	#95	—	2	4	no	—
436	#95	C₂³×C₁₉	1	2	yes	—
437	C₁₉	#18270	1	1	yes	characteristic, direct product factor, Sylow
438	C₂⁴	—	2	1	no	—
439	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
440	#41	—	4	2	no	—
441	#41	—	8	4	no	—
442	#41	—	8	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	—	8	2	no	—
458	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	8	2	no	—
471	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
479	M₁₆	—	4	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	4	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	8	4	no	—
499	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
501	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	4	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	8	1	no	—
527	C₂³	—	8	1	no	—
528	C₂³	C₁₉×#120	1	1	yes	characteristic
529	C₂³	C₁₉×#120	1	1	yes	characteristic
530	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
531	Q₈	—	4	1	no	—
532	Q₈	—	4	2	no	—
533	Q₈	—	8	1	no	—
534	Q₈	—	8	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	8	2	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	8	1	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	—	8	2	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
572	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
575	C₈	—	4	2	no	—
576	C₈	—	4	2	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	16	2	no	—
592	C₂²	C₁₉×#456	1	2	yes	—
593	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
594	C₂²	C₁₉×#576	1	2	yes	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	4	4	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	2	no	—
605	C₄	—	8	2	no	—
606	C₄	C₁₉×#458	1	2	yes	—
607	C₂	—	2	2	no	—
608	C₂	—	2	2	no	—
609	C₂	—	4	1	no	—
610	C₂	—	8	2	no	—
611	C₂	—	8	1	no	—
612	C₂	C₁₉×#3008	1	1	yes	characteristic
613	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
614	C₂	C₂×C₁₉×#458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3536	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3092	C₂	semidirect
3. C₂×C₁₉×#480	C₂	semidirect
4. C₁₉×#2502	C₂	semidirect
5. C₁₉×#1610	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1507	C₂	semidirect
8. C₁₉×#1501	C₂	semidirect
9. C₁₉×#1472	C₂	semidirect
27. C₁₉×#483	C₂²	semidirect
31. C₁₉×#480	C₂²	semidirect
38. C₁₉×#398	C₂²	semidirect
43. C₁₉×#328	C₂²	semidirect
45. C₁₉×#327	C₂²	semidirect
46. C₁₉×#324	C₂²	semidirect
212. #18270	C₁₉	direct (N × H)
271. #3092	C₂×C₁₉	semidirect
272. C₂×#480	C₂×C₁₉	semidirect
273. #2502	C₂×C₁₉	semidirect
274. #1610	C₂×C₁₉	semidirect
275. #1609	C₂×C₁₉	semidirect
276. #1507	C₂×C₁₉	semidirect
277. #1501	C₂×C₁₉	semidirect
278. #1472	C₂×C₁₉	semidirect
326. #483	C₂²×C₁₉	semidirect
330. #480	C₂²×C₁₉	semidirect
337. #398	C₂²×C₁₉	semidirect
342. #328	C₂²×C₁₉	semidirect
344. #327	C₂²×C₁₉	semidirect
345. #324	C₂²×C₁₉	semidirect
437. C₁₉	#18270	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×#3092	2
C₂×C₁₉×#480	2
C₁₉×#2502	2
C₁₉×#1610	2
C₁₉×#1609	2
C₁₉×#1507	2
C₁₉×#1501	2
C₁₉×#1472	2
#18270	19

Subgroups — C19×#18270 #18024229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18270 #18024229