Subgroups — C₁₉×#61723 #18067682

Order 4864.

1734 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#556	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3356	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3328	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3229	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3195	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3104	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3095	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2975	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#556	—	2	4	no	—
11	C₁₉×#556	C₂²	1	8	yes	—
12	C₁₉×#554	—	2	4	no	—
13	C₁₉×#554	C₂²	1	4	yes	—
14	D₄×Q₈×C₁₉	C₂²	1	4	yes	—
15	C₁₉×#544	—	2	1	no	—
16	C₁₉×#543	—	2	2	no	—
17	C₁₉×#533	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#126	—	2	2	no	—
20	C₂×C₁₉×#124	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₁₉×#518	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#117	C₂²	1	2	yes	—
28	C₁₉×#498	C₂²	1	4	yes	complemented
29	C₁₉×#487	C₂²	1	4	yes	complemented
30	C₁₉×#485	C₂²	1	16	yes	complemented
31	C₁₉×#484	C₂²	1	4	yes	—
32	C₁₉×#483	C₂²	1	8	yes	—
33	C₁₉×#483	C₂²	1	8	yes	complemented
34	C₁₉×#477	C₂²	1	4	yes	complemented
35	C₁₉×#475	C₂²	1	8	yes	complemented
36	C₁₉×#470	C₂²	1	16	yes	complemented
37	C₁₉×#462	C₂²	1	4	yes	complemented
38	C₁₉×#451	C₂²	1	4	yes	—
39	C₁₉×#451	C₂²	1	8	yes	complemented
40	C₄×Q₁₆×C₁₉	C₂²	1	8	yes	complemented
41	C₁₉×#436	C₂²	1	8	yes	—
42	C₁₉×#431	C₂²	1	2	yes	—
43	C₁₉×#428	C₂²	1	8	yes	complemented
44	C₁₉×#419	C₂²	1	8	yes	complemented
45	C₁₉×#407	C₂²	1	4	yes	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	—
52	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
53	C₁₉×C₄⋊Q₈	—	2	4	no	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×#126	—	2	16	no	—
59	C₁₉×#125	—	2	4	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#124	—	2	8	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	8	no	—
67	C₁₉×C₂²⋊Q₈	—	2	8	no	—
68	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
69	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
70	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
71	C₄×Q₈×C₁₉	—	2	8	no	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
75	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
76	C₄×D₄×C₁₉	—	2	4	no	—
77	C₄×D₄×C₁₉	—	2	4	no	—
78	C₄×D₄×C₁₉	D₄	1	4	yes	—
79	C₄×D₄×C₁₉	C₂³	1	4	yes	—
80	C₁₉×#117	—	2	4	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
95	C₂×C₄²×C₁₉	—	2	2	no	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	C₂³	1	8	yes	—
99	C₁₉×#106	C₂³	1	16	yes	—
100	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₉×#103	C₂³	1	8	yes	—
102	C₁₉×#103	C₂³	1	16	yes	—
103	C₁₉×#103	C₂³	1	8	yes	—
104	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
106	C₄×C₈×C₁₉	C₂³	1	4	yes	—
107	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	4	2	no	—
113	C₂×Q₈×C₁₉	—	4	8	no	—
114	C₂×Q₈×C₁₉	—	4	4	no	—
115	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
116	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
117	C₂×D₄×C₁₉	—	2	4	no	—
118	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	4	4	no	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
131	Q₁₆×C₁₉	—	4	8	no	—
132	M₁₆×C₁₉	—	4	8	no	—
133	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	8	no	—
136	C₄⋊C₄×C₁₉	—	2	4	no	—
137	C₄⋊C₄×C₁₉	—	2	8	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	4	no	—
146	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
148	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	2	8	no	—
152	C₂²⋊C₄×C₁₉	—	2	8	no	—
153	C₂²⋊C₄×C₁₉	—	2	8	no	—
154	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
155	C₄²×C₁₉	—	2	8	no	—
156	C₄²×C₁₉	—	2	4	no	—
157	C₄²×C₁₉	—	2	4	no	—
158	C₄²×C₁₉	C₂×D₄	1	2	yes	—
159	C₄²×C₁₉	C₂⁴	1	2	yes	—
160	#61723	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂³×C₁₉	—	2	4	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
165	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	4	no	—
167	Q₈×C₁₉	—	2	8	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	8	no	—
170	Q₈×C₁₉	—	8	2	no	—
171	Q₈×C₁₉	—	8	4	no	—
172	D₄×C₁₉	—	2	8	no	—
173	C₂×C₄×C₁₉	—	2	8	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	8	4	no	—
187	C₂×C₄×C₁₉	—	8	4	no	—
188	C₂×C₄×C₁₉	#137	1	4	yes	—
189	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
194	C₈×C₁₉	—	2	8	no	—
195	#3501	C₂×C₁₉	1	1	yes	characteristic
196	C₂×#556	C₂×C₁₉	1	1	yes	characteristic
197	#3356	C₂×C₁₉	1	8	yes	complemented
198	#3328	C₂×C₁₉	1	8	yes	complemented
199	#3229	C₂×C₁₉	1	2	yes	complemented
200	#3195	C₂×C₁₉	1	4	yes	complemented
201	#3104	C₂×C₁₉	1	2	yes	complemented
202	#3095	C₂×C₁₉	1	4	yes	complemented
203	#2975	C₂×C₁₉	1	1	yes	characteristic
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	4	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	8	4	no	—
210	C₂²×C₁₉	C₂×#137	1	2	yes	—
211	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	4	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	4	4	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	C₂×#137	1	4	yes	—
221	C₄×C₁₉	#585	1	2	yes	—
222	#556	—	2	4	no	—
223	#556	C₂²×C₁₉	1	8	yes	—
224	#554	—	2	4	no	—
225	#554	C₂²×C₁₉	1	4	yes	—
226	D₄×Q₈	C₂²×C₁₉	1	4	yes	—
227	#544	—	2	1	no	—
228	#543	—	2	2	no	—
229	#533	C₂²×C₁₉	1	2	yes	—
230	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×#126	—	2	2	no	—
232	C₂×#124	—	2	1	no	—
233	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
234	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
235	#518	—	2	1	no	—
236	C₂×C₄×Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#117	C₂²×C₁₉	1	2	yes	—
240	#498	C₂²×C₁₉	1	4	yes	complemented
241	#487	C₂²×C₁₉	1	4	yes	complemented
242	#485	C₂²×C₁₉	1	16	yes	complemented
243	#484	C₂²×C₁₉	1	4	yes	—
244	#483	C₂²×C₁₉	1	8	yes	—
245	#483	C₂²×C₁₉	1	8	yes	complemented
246	#477	C₂²×C₁₉	1	4	yes	complemented
247	#475	C₂²×C₁₉	1	8	yes	complemented
248	#470	C₂²×C₁₉	1	16	yes	complemented
249	#462	C₂²×C₁₉	1	4	yes	complemented
250	#451	C₂²×C₁₉	1	4	yes	—
251	#451	C₂²×C₁₉	1	8	yes	complemented
252	C₄×Q₁₆	C₂²×C₁₉	1	8	yes	complemented
253	#436	C₂²×C₁₉	1	8	yes	—
254	#431	C₂²×C₁₉	1	2	yes	—
255	#428	C₂²×C₁₉	1	8	yes	complemented
256	#419	C₂²×C₁₉	1	8	yes	complemented
257	#407	C₂²×C₁₉	1	4	yes	—
258	C₂×C₁₉	—	2	2	no	—
259	C₂×C₁₉	—	4	4	no	—
260	C₂×C₁₉	#3485	1	1	yes	characteristic
261	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
262	C₂×C₁₉	#3586	1	1	yes	characteristic
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
265	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
266	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
268	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	—
269	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
273	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
274	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
275	#126	—	2	16	no	—
276	#125	—	2	4	no	—
277	#125	—	2	2	no	—
278	#124	—	2	8	no	—
279	C₂²⋊Q₈	—	2	4	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	8	no	—
284	C₂²⋊Q₈	—	2	8	no	—
285	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
286	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
287	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
288	C₄×Q₈	—	2	8	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
292	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	—	2	4	no	—
295	C₄×D₄	D₄×C₁₉	1	4	yes	—
296	C₄×D₄	C₂³×C₁₉	1	4	yes	—
297	#117	—	2	4	no	—
298	#117	—	2	2	no	—
299	#117	C₂³×C₁₉	1	8	yes	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
315	#107	C₂³×C₁₉	1	8	yes	—
316	#106	C₂³×C₁₉	1	16	yes	—
317	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
318	#103	C₂³×C₁₉	1	8	yes	—
319	#103	C₂³×C₁₉	1	16	yes	—
320	#103	C₂³×C₁₉	1	8	yes	—
321	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
322	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
323	C₄×C₈	C₂³×C₁₉	1	4	yes	—
324	C₁₉	#61723	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	8	no	—
332	C₂×Q₈	—	4	4	no	—
333	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
334	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
349	Q₁₆	—	4	8	no	—
350	M₁₆	—	4	8	no	—
351	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
365	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
366	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
367	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	4	no	—
376	C₄²	C₂×D₄×C₁₉	1	2	yes	—
377	C₄²	C₂⁴×C₁₉	1	2	yes	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
382	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	2	8	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	8	no	—
387	Q₈	—	8	4	no	—
388	Q₈	—	8	2	no	—
389	D₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	8	4	no	—
404	C₂×C₄	—	8	4	no	—
405	C₂×C₄	C₁₉×#137	1	4	yes	—
406	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
410	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
411	C₈	—	2	8	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	8	4	no	—
418	C₂²	C₂×C₁₉×#137	1	2	yes	—
419	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	4	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₄	C₂×C₁₉×#137	1	4	yes	—
429	C₄	C₁₉×#585	1	2	yes	—
430	C₂	—	2	2	no	—
431	C₂	—	4	4	no	—
432	C₂	C₁₉×#3485	1	1	yes	characteristic
433	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
434	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3356	C₂	semidirect
4. C₁₉×#3328	C₂	semidirect
5. C₁₉×#3229	C₂	semidirect
6. C₁₉×#3195	C₂	semidirect
7. C₁₉×#3104	C₂	semidirect
8. C₁₉×#3095	C₂	semidirect
28. C₁₉×#498	C₂²	semidirect
29. C₁₉×#487	C₂²	semidirect
30. C₁₉×#485	C₂²	semidirect
33. C₁₉×#483	C₂²	semidirect
34. C₁₉×#477	C₂²	semidirect
35. C₁₉×#475	C₂²	semidirect
36. C₁₉×#470	C₂²	semidirect
37. C₁₉×#462	C₂²	semidirect
39. C₁₉×#451	C₂²	semidirect
40. C₄×Q₁₆×C₁₉	C₂²	semidirect
43. C₁₉×#428	C₂²	semidirect
44. C₁₉×#419	C₂²	semidirect
160. #61723	C₁₉	direct (N × H)
197. #3356	C₂×C₁₉	semidirect
198. #3328	C₂×C₁₉	semidirect
199. #3229	C₂×C₁₉	semidirect
200. #3195	C₂×C₁₉	semidirect
201. #3104	C₂×C₁₉	semidirect
202. #3095	C₂×C₁₉	semidirect
240. #498	C₂²×C₁₉	semidirect
241. #487	C₂²×C₁₉	semidirect
242. #485	C₂²×C₁₉	semidirect
245. #483	C₂²×C₁₉	semidirect
246. #477	C₂²×C₁₉	semidirect
247. #475	C₂²×C₁₉	semidirect
248. #470	C₂²×C₁₉	semidirect
249. #462	C₂²×C₁₉	semidirect
251. #451	C₂²×C₁₉	semidirect
252. C₄×Q₁₆	C₂²×C₁₉	semidirect
255. #428	C₂²×C₁₉	semidirect
256. #419	C₂²×C₁₉	semidirect
324. C₁₉	#61723	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×#3501	2
C₂×C₁₉×#556	2
C₁₉×#3356	2
C₁₉×#3328	2
C₁₉×#3229	2
C₁₉×#3195	2
C₁₉×#3104	2
C₁₉×#3095	2
C₁₉×#2975	2
#61723	19

Subgroups — C19×#61723 #18067682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61723 #18067682