Subgroups — C₁₉×#19471 #18025430

Order 4864.

588 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2984	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1690	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1680	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1670	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1552	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#494	C₂²	1	2	yes	—
16	C₁₉×#487	C₂²	1	2	yes	—
17	C₁₉×#483	—	2	1	no	—
18	C₁₉×#475	—	2	1	no	—
19	C₁₉×#475	—	2	1	no	—
20	C₁₉×#475	C₂²	1	1	yes	characteristic
21	C₁₉×#475	C₂²	1	2	yes	—
22	C₁₉×#475	C₂²	1	1	yes	characteristic
23	C₁₉×#475	C₂²	1	2	yes	—
24	C₁₉×#462	—	2	2	no	—
25	C₁₉×#462	C₂²	1	1	yes	characteristic
26	C₁₉×#462	C₂²	1	1	yes	characteristic
27	C₁₉×#451	—	2	1	no	—
28	C₁₉×#451	—	2	1	no	—
29	C₁₉×#451	—	2	1	no	—
30	C₁₉×#446	—	2	2	no	—
31	C₁₉×#446	C₂²	1	2	yes	—
32	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#441	—	2	1	no	—
34	C₁₉×#441	—	2	1	no	—
35	C₁₉×#432	—	2	1	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#431	—	2	1	no	—
39	C₁₉×#431	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#106	—	2	1	no	—
41	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#103	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#332	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂×Q₁₆×C₁₉	—	2	1	no	—
52	C₂×Q₁₆×C₁₉	—	2	1	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×Q₁₆×C₁₉	—	2	2	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
71	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#117	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#106	—	2	2	no	—
81	C₁₉×#106	—	2	2	no	—
82	C₁₉×#106	—	2	1	no	—
83	C₁₉×#106	—	2	1	no	—
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₄⋊C₈	—	2	1	no	—
87	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
88	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#103	—	2	1	no	—
95	C₁₉×#103	—	2	1	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	1	no	—
99	C₁₉×#103	—	2	1	no	—
100	C₁₉×C₂²⋊C₈	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
103	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₄×C₈×C₁₉	C₂³	1	2	yes	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	8	2	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	Q₁₆×C₁₉	—	4	2	no	—
126	Q₁₆×C₁₉	—	4	2	no	—
127	Q₁₆×C₁₉	—	8	2	no	—
128	Q₁₆×C₁₉	—	8	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	4	2	no	—
134	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²⋊C₄×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	—	2	1	no	—
155	C₄²×C₁₉	—	2	1	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	2	1	no	—
158	C₄²×C₁₉	—	4	1	no	—
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₉	#41	1	1	yes	characteristic
162	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
163	#19471	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	#121	1	1	yes	characteristic
165	Q₈×C₁₉	—	2	1	no	—
166	Q₈×C₁₉	—	2	1	no	—
167	Q₈×C₁₉	—	2	1	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	1	no	—
170	Q₈×C₁₉	—	4	1	no	—
171	Q₈×C₁₉	—	4	2	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	8	2	no	—
175	Q₈×C₁₉	#137	1	2	yes	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
196	C₈×C₁₉	—	2	2	no	—
197	C₈×C₁₉	—	2	2	no	—
198	C₈×C₁₉	—	4	1	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₈×C₁₉	—	4	1	no	—
201	C₈×C₁₉	—	4	2	no	—
202	#3209	C₂×C₁₉	1	1	yes	characteristic
203	#3113	C₂×C₁₉	1	1	yes	characteristic
204	C₂×#475	C₂×C₁₉	1	1	yes	characteristic
205	#2984	C₂×C₁₉	1	1	yes	characteristic
206	#1700	C₂×C₁₉	1	2	yes	complemented
207	#1690	C₂×C₁₉	1	2	yes	complemented
208	#1680	C₂×C₁₉	1	2	yes	complemented
209	#1670	C₂×C₁₉	1	2	yes	complemented
210	#1573	C₂×C₁₉	1	1	yes	characteristic
211	#1556	C₂×C₁₉	1	1	yes	characteristic
212	#1552	C₂×C₁₉	1	1	yes	characteristic
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	#473	1	2	yes	—
216	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	4	1	no	—
223	C₄×C₁₉	—	4	1	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	8	2	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
229	C₄×C₁₉	#575	1	1	yes	characteristic
230	C₄×C₁₉	#577	1	2	yes	—
231	#533	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	#494	C₂²×C₁₉	1	2	yes	—
235	#487	C₂²×C₁₉	1	2	yes	—
236	#483	—	2	1	no	—
237	#475	—	2	1	no	—
238	#475	—	2	1	no	—
239	#475	C₂²×C₁₉	1	2	yes	—
240	#475	C₂²×C₁₉	1	2	yes	—
241	#475	C₂²×C₁₉	1	1	yes	characteristic
242	#475	C₂²×C₁₉	1	1	yes	characteristic
243	#462	—	2	2	no	—
244	#462	C₂²×C₁₉	1	1	yes	characteristic
245	#462	C₂²×C₁₉	1	1	yes	characteristic
246	#451	—	2	1	no	—
247	#451	—	2	1	no	—
248	#451	—	2	1	no	—
249	#446	—	2	2	no	—
250	#446	C₂²×C₁₉	1	2	yes	—
251	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
252	#441	—	2	1	no	—
253	#441	—	2	1	no	—
254	#432	—	2	1	no	—
255	#432	C₂²×C₁₉	1	1	yes	characteristic
256	#432	C₂²×C₁₉	1	1	yes	characteristic
257	#431	—	2	1	no	—
258	#431	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#106	—	2	1	no	—
260	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#103	—	2	1	no	—
262	#335	C₂²×C₁₉	1	2	yes	—
263	#334	C₂²×C₁₉	1	2	yes	—
264	#332	C₂²×C₁₉	1	2	yes	—
265	#332	C₂²×C₁₉	1	2	yes	—
266	#332	C₂²×C₁₉	1	2	yes	—
267	#332	C₂²×C₁₉	1	2	yes	—
268	C₂×C₁₉	—	2	2	no	—
269	C₂×C₁₉	#3043	1	1	yes	characteristic
270	C₂×C₁₉	#3056	1	1	yes	characteristic
271	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	2	1	no	—
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	—	2	2	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
283	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
285	#125	—	2	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
293	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
294	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
303	#106	—	2	2	no	—
304	#106	—	2	2	no	—
305	#106	—	2	1	no	—
306	#106	—	2	1	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
311	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
312	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
314	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
315	#103	—	2	2	no	—
316	#103	—	2	2	no	—
317	#103	—	2	1	no	—
318	#103	—	2	1	no	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#103	—	2	1	no	—
322	#103	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
326	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
327	#97	—	2	2	no	—
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	C₄×C₈	—	2	2	no	—
331	C₄×C₈	C₂³×C₁₉	1	2	yes	—
332	C₁₉	#19471	1	1	yes	characteristic, direct product factor, Sylow
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	4	1	no	—
339	C₂×Q₈	—	4	1	no	—
340	C₂×Q₈	—	8	2	no	—
341	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
349	Q₁₆	—	4	2	no	—
350	Q₁₆	—	4	2	no	—
351	Q₁₆	—	8	2	no	—
352	Q₁₆	—	8	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₂²⋊C₄	—	4	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₄²	#41×C₁₉	1	1	yes	characteristic
386	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
387	C₂³	C₁₉×#121	1	1	yes	characteristic
388	Q₈	—	2	1	no	—
389	Q₈	—	2	1	no	—
390	Q₈	—	2	1	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	1	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	8	2	no	—
398	Q₈	C₁₉×#137	1	2	yes	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
415	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	C₁₉×#473	1	2	yes	—
428	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
441	C₄	C₁₉×#575	1	1	yes	characteristic
442	C₄	C₁₉×#577	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	C₁₉×#3043	1	1	yes	characteristic
445	C₂	C₁₉×#3056	1	1	yes	characteristic
446	C₂	C₂×C₁₉×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#121
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
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1690	C₂	semidirect
7. C₁₉×#1680	C₂	semidirect
8. C₁₉×#1670	C₂	semidirect
163. #19471	C₁₉	direct (N × H)
206. #1700	C₂×C₁₉	semidirect
207. #1690	C₂×C₁₉	semidirect
208. #1680	C₂×C₁₉	semidirect
209. #1670	C₂×C₁₉	semidirect
332. C₁₉	#19471	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×#3209	2
C₁₉×#3113	2
C₂×C₁₉×#475	2
C₁₉×#2984	2
C₁₉×#1700	2
C₁₉×#1690	2
C₁₉×#1680	2
C₁₉×#1670	2
C₁₉×#1573	2
C₁₉×#1556	2
C₁₉×#1552	2
#19471	19

Subgroups — C19×#19471 #18025430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19471 #18025430