Subgroups — C₁₉×#18439 #18024398

Order 4864.

964 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2658	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1614	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1469	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#563	—	2	1	no	—
11	C₁₉×#562	—	2	1	no	—
12	C₁₉×#556	—	2	1	no	—
13	C₁₉×#551	—	2	2	no	—
14	D₄×Q₈×C₁₉	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#543	C₂²	1	2	yes	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#542	—	2	2	no	—
20	C₁₉×#538	C₂²	1	2	yes	—
21	C₁₉×#536	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×#529	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#124	—	2	1	no	—
27	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#501	—	2	1	no	—
29	C₁₉×#500	—	2	1	no	—
30	C₁₉×#489	—	2	1	no	—
31	C₁₉×#487	—	2	1	no	—
32	C₁₉×#484	C₂²	1	4	yes	—
33	C₁₉×#484	C₂²	1	2	yes	—
34	C₁₉×#481	C₂²	1	2	yes	—
35	C₁₉×#477	—	2	2	no	—
36	C₁₉×#475	—	2	1	no	—
37	C₁₉×#474	—	2	1	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#431	C₂²	1	1	yes	characteristic
40	C₁₉×#399	—	2	2	no	—
41	C₁₉×#399	C₂²	1	4	yes	—
42	C₁₉×#376	C₂²	1	1	yes	characteristic
43	C₁₉×#328	C₂²	1	2	yes	—
44	C₁₉×#328	C₂²	1	4	yes	—
45	C₁₉×#327	C₂²	1	2	yes	—
46	C₁₉×#323	C₂²	1	4	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	4	4	no	—
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	1	no	—
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#125	D₄	1	1	yes	characteristic
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	—	2	2	no	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	—	2	1	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	4	4	no	—
75	C₁₉×#124	D₄	1	1	yes	characteristic
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	1	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	C₂³	1	1	yes	characteristic
96	C₁₉×#120	—	2	2	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	D₄	1	2	yes	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
118	C₁₉×#107	—	2	2	no	—
119	C₁₉×#107	—	2	4	no	—
120	C₁₉×#106	—	2	2	no	—
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×C₄⋊C₈	—	2	1	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#103	—	2	4	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×#97	—	2	1	no	—
129	C₄×C₈×C₁₉	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	C₂³	1	2	yes	—
132	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
133	#41×C₁₉	—	8	2	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	1	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	—	4	2	no	—
140	C₂×Q₈×C₁₉	—	4	2	no	—
141	C₂×Q₈×C₁₉	—	4	1	no	—
142	C₂×Q₈×C₁₉	—	4	1	no	—
143	C₂×Q₈×C₁₉	—	8	2	no	—
144	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	4	2	no	—
152	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	4	8	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	1	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	—	4	8	no	—
202	C₄²×C₁₉	—	2	4	no	—
203	C₄²×C₁₉	—	2	2	no	—
204	C₄²×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
210	#18439	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	2	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	2	4	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	2	no	—
216	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	4	2	no	—
220	Q₈×C₁₉	—	4	2	no	—
221	Q₈×C₁₉	—	8	1	no	—
222	Q₈×C₁₉	—	8	2	no	—
223	Q₈×C₁₉	—	8	2	no	—
224	Q₈×C₁₉	—	8	2	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	8	2	no	—
230	D₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	8	2	no	—
249	C₂×C₄×C₁₉	—	8	2	no	—
250	C₂×C₄×C₁₉	—	8	2	no	—
251	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₁₉	—	4	2	no	—
258	C₈×C₁₉	—	4	2	no	—
259	#3561	C₂×C₁₉	1	1	yes	characteristic
260	#3239	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#2658	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1618	C₂×C₁₉	1	4	yes	complemented
264	#1614	C₂×C₁₉	1	4	yes	complemented
265	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1500	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1469	C₂×C₁₉	1	1	yes	characteristic, complemented
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	8	4	no	—
277	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
278	C₂²×C₁₉	#578	1	2	yes	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	4	4	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	8	2	no	—
292	C₄×C₁₉	#453	1	2	yes	—
293	#563	—	2	1	no	—
294	#562	—	2	1	no	—
295	#556	—	2	1	no	—
296	#551	—	2	2	no	—
297	D₄×Q₈	—	2	1	no	—
298	#548	—	2	1	no	—
299	#546	—	2	1	no	—
300	#543	C₂²×C₁₉	1	2	yes	—
301	#542	—	2	1	no	—
302	#542	—	2	2	no	—
303	#538	C₂²×C₁₉	1	2	yes	—
304	#536	—	2	1	no	—
305	#533	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊Q₈	—	2	1	no	—
307	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
308	#529	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#124	—	2	1	no	—
310	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
311	#501	—	2	1	no	—
312	#500	—	2	1	no	—
313	#489	—	2	1	no	—
314	#487	—	2	1	no	—
315	#484	C₂²×C₁₉	1	2	yes	—
316	#484	C₂²×C₁₉	1	4	yes	—
317	#481	C₂²×C₁₉	1	2	yes	—
318	#477	—	2	2	no	—
319	#475	—	2	1	no	—
320	#474	—	2	1	no	—
321	#432	C₂²×C₁₉	1	1	yes	characteristic
322	#431	C₂²×C₁₉	1	1	yes	characteristic
323	#399	—	2	2	no	—
324	#399	C₂²×C₁₉	1	4	yes	—
325	#376	C₂²×C₁₉	1	1	yes	characteristic
326	#328	C₂²×C₁₉	1	2	yes	—
327	#328	C₂²×C₁₉	1	4	yes	—
328	#327	C₂²×C₁₉	1	2	yes	—
329	#323	C₂²×C₁₉	1	4	yes	—
330	C₂×C₁₉	—	2	2	no	—
331	C₂×C₁₉	—	8	1	no	—
332	C₂×C₁₉	—	8	2	no	—
333	C₂×C₁₉	#3011	1	1	yes	characteristic
334	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
335	C₂×C₁₉	#3028	1	1	yes	characteristic
336	C₂×#41	—	2	1	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
340	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	4	4	no	—
348	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
349	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
350	#126	—	2	2	no	—
351	#126	—	2	2	no	—
352	#126	—	2	2	no	—
353	#126	—	2	1	no	—
354	#125	—	2	1	no	—
355	#125	D₄×C₁₉	1	1	yes	characteristic
356	#124	—	2	1	no	—
357	#124	—	2	2	no	—
358	#124	—	2	2	no	—
359	#124	—	2	1	no	—
360	#124	—	2	1	no	—
361	#124	—	2	1	no	—
362	#124	—	2	1	no	—
363	#124	—	4	4	no	—
364	#124	D₄×C₁₉	1	1	yes	characteristic
365	#123	—	2	2	no	—
366	#123	—	2	2	no	—
367	#123	—	2	2	no	—
368	#123	—	2	1	no	—
369	#123	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	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	C₂³×C₁₉	1	1	yes	characteristic
380	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
381	#121	—	2	1	no	—
382	#121	—	2	2	no	—
383	#121	—	2	2	no	—
384	#121	C₂³×C₁₉	1	1	yes	characteristic
385	#120	—	2	2	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
389	C₄×Q₈	D₄×C₁₉	1	2	yes	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
395	#117	—	2	2	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	4	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
401	C₂×C₂²⋊C₄	—	2	2	no	—
402	C₂×C₂²⋊C₄	—	2	4	no	—
403	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
407	#107	—	2	2	no	—
408	#107	—	2	4	no	—
409	#106	—	2	2	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	#103	—	2	2	no	—
413	#103	—	2	4	no	—
414	#102	—	2	2	no	—
415	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
416	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
417	#97	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	C₂³×C₁₉	1	2	yes	—
421	C₁₉	#18439	1	1	yes	characteristic, direct product factor, Sylow
422	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
423	#41	—	8	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	4	2	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	—	4	1	no	—
432	C₂×Q₈	—	4	1	no	—
433	C₂×Q₈	—	8	2	no	—
434	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	4	8	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	4	8	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	1	no	—
496	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂³	—	2	2	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
506	Q₈	—	4	1	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	8	1	no	—
511	Q₈	—	8	2	no	—
512	Q₈	—	8	2	no	—
513	Q₈	—	8	2	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	8	1	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
541	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
542	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
543	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	8	4	no	—
557	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
558	C₂²	C₁₉×#578	1	2	yes	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	8	2	no	—
572	C₄	C₁₉×#453	1	2	yes	—
573	C₂	—	2	2	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	1	no	—
576	C₂	C₁₉×#3011	1	1	yes	characteristic
577	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
578	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3561	C₂
LCS	G ▷ C₂²×C₄ ▷ 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
2. C₁₉×#3239	C₂	semidirect
3. C₁₉×#3230	C₂	semidirect
4. C₁₉×#2658	C₂	semidirect
5. C₁₉×#1618	C₂	semidirect
6. C₁₉×#1614	C₂	semidirect
7. C₁₉×#1506	C₂	semidirect
8. C₁₉×#1500	C₂	semidirect
9. C₁₉×#1469	C₂	semidirect
210. #18439	C₁₉	direct (N × H)
260. #3239	C₂×C₁₉	semidirect
261. #3230	C₂×C₁₉	semidirect
262. #2658	C₂×C₁₉	semidirect
263. #1618	C₂×C₁₉	semidirect
264. #1614	C₂×C₁₉	semidirect
265. #1506	C₂×C₁₉	semidirect
266. #1500	C₂×C₁₉	semidirect
267. #1469	C₂×C₁₉	semidirect
421. C₁₉	#18439	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×#3561	2
C₁₉×#3239	2
C₁₉×#3230	2
C₁₉×#2658	2
C₁₉×#1618	2
C₁₉×#1614	2
C₁₉×#1506	2
C₁₉×#1500	2
C₁₉×#1469	2
#18439	19

Subgroups — C19×#18439 #18024398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18439 #18024398