Subgroups — C₁₉×#19066 #18025025

Order 4864.

852 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1660	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1537	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#563	C₂²	1	4	yes	—
11	C₁₉×#559	—	2	1	no	—
12	Q₈²×C₁₉	—	2	1	no	—
13	C₁₉×#556	—	2	1	no	—
14	C₁₉×#556	—	2	1	no	—
15	D₄×Q₈×C₁₉	—	2	1	no	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#542	—	2	2	no	—
19	C₁₉×#536	—	2	2	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₁₉×#501	—	2	1	no	—
25	C₁₉×#501	—	2	1	no	—
26	C₁₉×#501	C₂²	1	2	yes	—
27	C₁₉×#501	C₂²	1	2	yes	—
28	C₁₉×#501	C₂²	1	2	yes	—
29	C₁₉×#497	C₂²	1	2	yes	—
30	C₁₉×#491	C₂²	1	2	yes	—
31	C₁₉×#489	C₂²	1	2	yes	—
32	C₁₉×#485	—	2	2	no	—
33	C₁₉×#477	—	2	1	no	—
34	C₁₉×#475	—	2	1	no	—
35	C₁₉×#462	—	2	1	no	—
36	C₁₉×#460	—	2	1	no	—
37	C₁₉×#452	—	2	2	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#427	—	2	2	no	—
41	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
42	C₁₉×#330	C₂²	1	4	yes	—
43	C₁₉×#330	C₂²	1	4	yes	—
44	C₁₉×#329	C₂²	1	4	yes	—
45	C₂×#41×C₁₉	D₄	1	2	yes	—
46	C₂²×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₁₆×C₁₉	—	2	2	no	—
48	C₂×SD₁₆×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	—	2	4	no	—
53	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×#127	D₄	1	1	yes	characteristic
61	C₁₉×#126	—	2	4	no	—
62	C₁₉×#126	—	2	4	no	—
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#125	C₂³	1	2	yes	—
65	C₁₉×#125	C₂³	1	2	yes	—
66	C₁₉×#124	—	2	4	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	C₂³	1	2	yes	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	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	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	4	no	—
79	C₁₉×C₂²⋊Q₈	—	2	4	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	D₄	1	2	yes	—
99	C₁₉×#117	D₄	1	2	yes	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	2	no	—
102	C₁₉×#107	—	2	2	no	—
103	C₁₉×#107	—	2	2	no	—
104	C₁₉×#106	—	2	2	no	—
105	C₁₉×#106	—	2	2	no	—
106	C₁₉×#106	—	2	2	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×#103	—	2	2	no	—
110	C₁₉×#103	—	2	2	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	1	no	—
114	C₁₉×C₂²⋊C₈	—	2	1	no	—
115	C₁₉×#97	—	2	1	no	—
116	C₁₉×#97	C₂³	1	2	yes	—
117	C₁₉×#97	C₂³	1	2	yes	—
118	C₁₉×#97	C₂³	1	2	yes	—
119	#41×C₁₉	—	8	2	no	—
120	C₂×Q₈×C₁₉	—	2	4	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	8	4	no	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	Q₁₆×C₁₉	—	8	2	no	—
139	SD₁₆×C₁₉	—	8	2	no	—
140	C₂×C₈×C₁₉	—	2	4	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	4	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	4	1	no	—
161	C₄⋊C₄×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	2	4	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	4	1	no	—
174	C₄²×C₁₉	—	2	4	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	—	4	1	no	—
178	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
182	#19066	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	#120	1	1	yes	characteristic
185	Q₈×C₁₉	—	4	2	no	—
186	Q₈×C₁₉	—	4	2	no	—
187	Q₈×C₁₉	—	4	2	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	4	1	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	Q₈×C₁₉	—	4	2	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	8	4	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	8	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	8	4	no	—
210	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₁₉	—	2	4	no	—
217	C₈×C₁₉	—	4	2	no	—
218	C₈×C₁₉	—	4	2	no	—
219	#3550	C₂×C₁₉	1	1	yes	characteristic
220	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#3216	C₂×C₁₉	1	1	yes	characteristic
222	#3162	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1664	C₂×C₁₉	1	4	yes	complemented
224	#1660	C₂×C₁₉	1	4	yes	complemented
225	#1537	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#1530	C₂×C₁₉	1	1	yes	characteristic
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	4	2	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	8	1	no	—
246	C₄×C₁₉	—	8	1	no	—
247	C₄×C₁₉	#456	1	2	yes	—
248	#563	C₂²×C₁₉	1	4	yes	—
249	#559	—	2	1	no	—
250	Q₈²	—	2	1	no	—
251	#556	—	2	1	no	—
252	#556	—	2	1	no	—
253	D₄×Q₈	—	2	1	no	—
254	D₄×Q₈	—	2	1	no	—
255	#542	—	2	2	no	—
256	#542	—	2	2	no	—
257	#536	—	2	2	no	—
258	#533	C₂²×C₁₉	1	1	yes	characteristic
259	#533	C₂²×C₁₉	1	1	yes	characteristic
260	#533	C₂²×C₁₉	1	1	yes	characteristic
261	#532	C₂²×C₁₉	1	1	yes	characteristic
262	#501	—	2	1	no	—
263	#501	—	2	1	no	—
264	#501	C₂²×C₁₉	1	2	yes	—
265	#501	C₂²×C₁₉	1	2	yes	—
266	#501	C₂²×C₁₉	1	2	yes	—
267	#497	C₂²×C₁₉	1	2	yes	—
268	#491	C₂²×C₁₉	1	2	yes	—
269	#489	C₂²×C₁₉	1	2	yes	—
270	#485	—	2	2	no	—
271	#477	—	2	1	no	—
272	#475	—	2	1	no	—
273	#462	—	2	1	no	—
274	#460	—	2	1	no	—
275	#452	—	2	2	no	—
276	#432	C₂²×C₁₉	1	1	yes	characteristic
277	#432	C₂²×C₁₉	1	1	yes	characteristic
278	#427	—	2	2	no	—
279	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
280	#330	C₂²×C₁₉	1	4	yes	—
281	#330	C₂²×C₁₉	1	4	yes	—
282	#329	C₂²×C₁₉	1	4	yes	—
283	C₂×C₁₉	—	4	1	no	—
284	C₂×C₁₉	—	8	2	no	—
285	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
286	C₂×C₁₉	#3019	1	1	yes	characteristic
287	C₂×C₁₉	#3020	1	1	yes	characteristic
288	C₂×#41	D₄×C₁₉	1	2	yes	—
289	C₂²×Q₈	—	2	2	no	—
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	4	no	—
296	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
297	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
298	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
299	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
300	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
301	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
303	#127	D₄×C₁₉	1	1	yes	characteristic
304	#126	—	2	4	no	—
305	#126	—	2	4	no	—
306	#125	—	2	1	no	—
307	#125	C₂³×C₁₉	1	2	yes	—
308	#125	C₂³×C₁₉	1	2	yes	—
309	#124	—	2	4	no	—
310	#124	—	2	2	no	—
311	#124	—	2	2	no	—
312	#124	C₂³×C₁₉	1	2	yes	—
313	#123	—	2	4	no	—
314	#123	—	2	4	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	#121	—	2	1	no	—
326	#121	—	2	1	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×Q₈	—	2	1	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	2	1	no	—
339	#117	—	2	2	no	—
340	#117	—	2	1	no	—
341	#117	D₄×C₁₉	1	2	yes	—
342	#117	D₄×C₁₉	1	2	yes	—
343	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
344	#107	—	2	2	no	—
345	#107	—	2	2	no	—
346	#107	—	2	2	no	—
347	#106	—	2	2	no	—
348	#106	—	2	2	no	—
349	#106	—	2	2	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	#103	—	2	2	no	—
353	#103	—	2	2	no	—
354	#103	—	2	2	no	—
355	#102	—	2	2	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₂²⋊C₈	—	2	1	no	—
358	#97	—	2	1	no	—
359	#97	C₂³×C₁₉	1	2	yes	—
360	#97	C₂³×C₁₉	1	2	yes	—
361	#97	C₂³×C₁₉	1	2	yes	—
362	C₁₉	#19066	1	1	yes	characteristic, direct product factor, Sylow
363	#41	—	8	2	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	8	4	no	—
372	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	Q₁₆	—	8	2	no	—
383	SD₁₆	—	8	2	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
407	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	4	1	no	—
422	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
426	C₂³	—	2	2	no	—
427	C₂³	C₁₉×#120	1	1	yes	characteristic
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	8	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	8	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	4	no	—
453	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
454	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
455	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
459	C₈	—	2	4	no	—
460	C₈	—	4	2	no	—
461	C₈	—	4	2	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	1	no	—
481	C₄	C₁₉×#456	1	2	yes	—
482	C₂	—	4	1	no	—
483	C₂	—	8	2	no	—
484	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
485	C₂	C₁₉×#3019	1	1	yes	characteristic
486	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
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
2. C₁₉×#3237	C₂	semidirect
4. C₁₉×#3162	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1660	C₂	semidirect
7. C₁₉×#1537	C₂	semidirect
8. C₁₉×#1531	C₂	semidirect
182. #19066	C₁₉	direct (N × H)
220. #3237	C₂×C₁₉	semidirect
222. #3162	C₂×C₁₉	semidirect
223. #1664	C₂×C₁₉	semidirect
224. #1660	C₂×C₁₉	semidirect
225. #1537	C₂×C₁₉	semidirect
226. #1531	C₂×C₁₉	semidirect
362. C₁₉	#19066	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×#3550	2
C₁₉×#3237	2
C₁₉×#3216	2
C₁₉×#3162	2
C₁₉×#1664	2
C₁₉×#1660	2
C₁₉×#1537	2
C₁₉×#1531	2
C₁₉×#1530	2
#19066	19

Subgroups — C19×#19066 #18025025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19066 #18025025