Subgroups — C₁₉×#62363 #18068322

Order 4864.

1802 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3522	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3396	C₂	1	3	yes	maximal, complemented
3	C₁₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3380	C₂	1	3	yes	maximal, complemented
6	C₁₉×#3362	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3361	C₂	1	6	yes	maximal, complemented
8	C₁₉×#3247	C₂	1	6	yes	maximal, complemented
9	C₁₉×#3169	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3168	C₂	1	3	yes	maximal, complemented
11	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#559	C₂²	1	6	yes	—
13	Q₈²×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#554	C₂²	1	6	yes	—
15	C₁₉×#550	C₂²	1	2	yes	—
16	C₁₉×#548	—	2	2	no	—
17	C₁₉×#547	—	2	6	no	—
18	C₁₉×#542	—	2	6	no	—
19	C₁₉×#532	C₂²	1	6	yes	—
20	C₁₉×#529	C₂²	1	6	yes	—
21	C₁₉×#520	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#500	C₂²	1	3	yes	—
24	C₁₉×#499	C₂²	1	3	yes	—
25	C₁₉×#495	C₂²	1	3	yes	—
26	C₁₉×#493	C₂²	1	3	yes	—
27	C₁₉×#488	C₂²	1	6	yes	—
28	C₁₉×#486	C₂²	1	6	yes	—
29	C₁₉×#478	C₂²	1	12	yes	—
30	C₁₉×#477	C₂²	1	6	yes	—
31	C₁₉×#476	C₂²	1	6	yes	—
32	C₁₉×#467	C₂²	1	1	yes	characteristic
33	C₁₉×#466	C₂²	1	3	yes	—
34	C₁₉×#466	C₂²	1	6	yes	—
35	C₁₉×#465	C₂²	1	6	yes	—
36	C₁₉×#463	C₂²	1	12	yes	—
37	C₁₉×#460	C₂²	1	6	yes	—
38	C₁₉×#459	C₂²	1	6	yes	—
39	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
40	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
42	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
44	C₄×SD₁₆×C₁₉	C₂²	1	6	yes	—
45	C₄×D₈×C₁₉	C₂²	1	3	yes	—
46	C₄×D₈×C₁₉	C₂²	1	6	yes	—
47	C₄×D₈×C₁₉	C₂²	1	6	yes	—
48	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
49	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	6	no	—
52	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
53	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₉	C₂³	1	6	yes	—
55	C₂×D₈×C₁₉	C₂³	1	3	yes	—
56	C₂×D₈×C₁₉	C₂³	1	6	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
59	C₁₉×C₄⋊Q₈	—	2	6	no	—
60	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
61	C₁₉×#127	C₂³	1	6	yes	—
62	C₁₉×#126	—	2	6	no	—
63	C₁₉×#125	C₂³	1	6	yes	—
64	C₁₉×#124	—	2	6	no	—
65	C₁₉×#124	—	2	6	no	—
66	C₁₉×#124	C₂³	1	6	yes	—
67	C₁₉×#123	—	2	6	no	—
68	C₁₉×#123	—	2	12	no	—
69	C₁₉×C₂²⋊Q₈	—	2	6	no	—
70	C₁₉×C₂²⋊Q₈	—	2	12	no	—
71	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
72	C₁₉×#121	—	2	6	no	—
73	C₁₉×#121	—	2	6	no	—
74	C₁₉×#121	C₂³	1	6	yes	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₁₉	D₄	1	3	yes	—
78	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
79	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
81	C₄×D₄×C₁₉	—	2	6	no	—
82	C₄×D₄×C₁₉	—	2	6	no	—
83	C₄×D₄×C₁₉	—	2	6	no	—
84	C₄×D₄×C₁₉	C₂³	1	12	yes	—
85	C₄×D₄×C₁₉	C₂³	1	6	yes	—
86	C₁₉×#117	—	2	6	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
88	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
90	C₁₉×#107	C₂³	1	1	yes	characteristic
91	C₁₉×#107	C₂³	1	3	yes	—
92	C₁₉×#107	C₂³	1	6	yes	—
93	C₁₉×#106	C₂³	1	6	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
95	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
96	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
97	C₁₉×#103	C₂³	1	2	yes	—
98	C₁₉×#103	C₂³	1	6	yes	—
99	C₁₉×#102	C₂³	1	6	yes	—
100	C₁₉×#102	C₂³	1	6	yes	—
101	C₁₉×#102	C₂³	1	12	yes	—
102	C₄×C₈×C₁₉	C₂³	1	3	yes	—
103	C₄×C₈×C₁₉	C₂³	1	3	yes	—
104	C₄×C₈×C₁₉	C₂³	1	3	yes	—
105	C₄×C₈×C₁₉	C₂³	1	3	yes	—
106	#41×C₁₉	—	4	8	no	—
107	#41×C₁₉	—	8	12	no	—
108	C₂×Q₈×C₁₉	—	2	4	no	—
109	C₂×Q₈×C₁₉	—	2	6	no	—
110	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
111	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
113	C₂×D₄×C₁₉	—	2	6	no	—
114	C₂×D₄×C₁₉	—	2	6	no	—
115	C₂×D₄×C₁₉	—	2	6	no	—
116	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₁₉	—	2	6	no	—
118	C₂²×C₄×C₁₉	—	2	12	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	Q₁₆×C₁₉	—	2	2	no	—
123	SD₁₆×C₁₉	—	4	6	no	—
124	D₈×C₁₉	—	2	6	no	—
125	D₈×C₁₉	—	4	6	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	4	3	no	—
128	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
129	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
130	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₄⋊C₄×C₁₉	—	2	6	no	—
133	C₄⋊C₄×C₁₉	—	2	6	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	6	no	—
136	C₄⋊C₄×C₁₉	—	2	6	no	—
137	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
138	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
139	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
140	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	6	no	—
144	C₂²⋊C₄×C₁₉	—	2	6	no	—
145	C₂²⋊C₄×C₁₉	—	2	6	no	—
146	C₂²⋊C₄×C₁₉	—	2	6	no	—
147	C₂²⋊C₄×C₁₉	—	2	12	no	—
148	C₄²×C₁₉	—	2	6	no	—
149	C₄²×C₁₉	C₂×D₄	1	3	yes	—
150	C₄²×C₁₉	C₂×D₄	1	3	yes	—
151	C₄²×C₁₉	C₂⁴	1	3	yes	—
152	C₄²×C₁₉	C₂⁴	1	3	yes	—
153	#62363	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	6	no	—
155	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₉	—	2	6	no	—
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	2	no	—
159	Q₈×C₁₉	—	8	6	no	—
160	Q₈×C₁₉	#135	1	4	yes	—
161	D₄×C₁₉	—	2	6	no	—
162	D₄×C₁₉	—	2	6	no	—
163	D₄×C₁₉	—	4	12	no	—
164	D₄×C₁₉	—	4	12	no	—
165	D₄×C₁₉	—	8	6	no	—
166	C₂×C₄×C₁₉	—	2	6	no	—
167	C₂×C₄×C₁₉	—	2	6	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	6	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	12	no	—
174	C₂×C₄×C₁₉	—	8	12	no	—
175	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
177	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
178	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
179	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
180	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
181	C₈×C₁₉	—	2	1	no	—
182	C₈×C₁₉	—	2	3	no	—
183	C₈×C₁₉	—	2	3	no	—
184	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
185	#3522	C₂×C₁₉	1	2	yes	complemented
186	#3396	C₂×C₁₉	1	3	yes	complemented
187	#3391	C₂×C₁₉	1	1	yes	characteristic, complemented
188	Q₈×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#3380	C₂×C₁₉	1	3	yes	complemented
190	#3362	C₂×C₁₉	1	2	yes	complemented
191	#3361	C₂×C₁₉	1	6	yes	complemented
192	#3247	C₂×C₁₉	1	6	yes	complemented
193	#3169	C₂×C₁₉	1	3	yes	complemented
194	#3168	C₂×C₁₉	1	3	yes	complemented
195	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	4	6	no	—
199	C₂²×C₁₉	—	4	6	no	—
200	C₂²×C₁₉	—	4	6	no	—
201	C₂²×C₁₉	#576	1	2	yes	—
202	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	3	no	—
205	C₄×C₁₉	—	2	3	no	—
206	C₄×C₁₉	—	2	3	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	4	6	no	—
210	C₄×C₁₉	C₂×#135	1	6	yes	—
211	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
212	C₄×C₁₉	#585	1	1	yes	characteristic
213	#559	C₂²×C₁₉	1	6	yes	—
214	Q₈²	C₂²×C₁₉	1	2	yes	—
215	#554	C₂²×C₁₉	1	6	yes	—
216	#550	C₂²×C₁₉	1	2	yes	—
217	#548	—	2	2	no	—
218	#547	—	2	6	no	—
219	#542	—	2	6	no	—
220	#532	C₂²×C₁₉	1	6	yes	—
221	#529	C₂²×C₁₉	1	6	yes	—
222	#520	—	2	2	no	—
223	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
224	#500	C₂²×C₁₉	1	3	yes	—
225	#499	C₂²×C₁₉	1	3	yes	—
226	#495	C₂²×C₁₉	1	3	yes	—
227	#493	C₂²×C₁₉	1	3	yes	—
228	#488	C₂²×C₁₉	1	6	yes	—
229	#486	C₂²×C₁₉	1	6	yes	—
230	#478	C₂²×C₁₉	1	12	yes	—
231	#477	C₂²×C₁₉	1	6	yes	—
232	#476	C₂²×C₁₉	1	6	yes	—
233	#467	C₂²×C₁₉	1	1	yes	characteristic
234	#466	C₂²×C₁₉	1	3	yes	—
235	#466	C₂²×C₁₉	1	6	yes	—
236	#465	C₂²×C₁₉	1	6	yes	—
237	#463	C₂²×C₁₉	1	12	yes	—
238	#460	C₂²×C₁₉	1	6	yes	—
239	#459	C₂²×C₁₉	1	6	yes	—
240	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
241	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
243	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
245	C₄×SD₁₆	C₂²×C₁₉	1	6	yes	—
246	C₄×D₈	C₂²×C₁₉	1	6	yes	—
247	C₄×D₈	C₂²×C₁₉	1	3	yes	—
248	C₄×D₈	C₂²×C₁₉	1	6	yes	—
249	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
250	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	8	6	no	—
253	C₂×C₁₉	#3497	1	1	yes	characteristic
254	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
255	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	6	no	—
258	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
259	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×SD₁₆	C₂³×C₁₉	1	6	yes	—
261	C₂×D₈	C₂³×C₁₉	1	3	yes	—
262	C₂×D₈	C₂³×C₁₉	1	6	yes	—
263	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
265	C₄⋊Q₈	—	2	6	no	—
266	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
267	#127	C₂³×C₁₉	1	6	yes	—
268	#126	—	2	6	no	—
269	#125	C₂³×C₁₉	1	6	yes	—
270	#124	—	2	6	no	—
271	#124	—	2	6	no	—
272	#124	C₂³×C₁₉	1	6	yes	—
273	#123	—	2	6	no	—
274	#123	—	2	12	no	—
275	C₂²⋊Q₈	—	2	6	no	—
276	C₂²⋊Q₈	—	2	12	no	—
277	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
278	#121	—	2	6	no	—
279	#121	—	2	6	no	—
280	#121	C₂³×C₁₉	1	6	yes	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
283	C₄×Q₈	D₄×C₁₉	1	3	yes	—
284	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
285	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
287	C₄×D₄	—	2	6	no	—
288	C₄×D₄	—	2	6	no	—
289	C₄×D₄	—	2	6	no	—
290	C₄×D₄	C₂³×C₁₉	1	6	yes	—
291	C₄×D₄	C₂³×C₁₉	1	12	yes	—
292	#117	—	2	6	no	—
293	C₂×C₄⋊C₄	—	2	6	no	—
294	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
295	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
296	#107	C₂³×C₁₉	1	1	yes	characteristic
297	#107	C₂³×C₁₉	1	3	yes	—
298	#107	C₂³×C₁₉	1	6	yes	—
299	#106	C₂³×C₁₉	1	6	yes	—
300	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
301	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
302	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
303	#103	C₂³×C₁₉	1	2	yes	—
304	#103	C₂³×C₁₉	1	6	yes	—
305	#102	C₂³×C₁₉	1	6	yes	—
306	#102	C₂³×C₁₉	1	6	yes	—
307	#102	C₂³×C₁₉	1	12	yes	—
308	C₄×C₈	C₂³×C₁₉	1	3	yes	—
309	C₄×C₈	C₂³×C₁₉	1	3	yes	—
310	C₄×C₈	C₂³×C₁₉	1	3	yes	—
311	C₄×C₈	C₂³×C₁₉	1	3	yes	—
312	C₁₉	#62363	1	1	yes	characteristic, direct product factor, Sylow
313	#41	—	4	8	no	—
314	#41	—	8	12	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	6	no	—
317	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
318	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
320	C₂×D₄	—	2	6	no	—
321	C₂×D₄	—	2	6	no	—
322	C₂×D₄	—	2	6	no	—
323	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
324	C₂²×C₄	—	2	6	no	—
325	C₂²×C₄	—	2	12	no	—
326	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
328	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
329	Q₁₆	—	2	2	no	—
330	SD₁₆	—	4	6	no	—
331	D₈	—	2	6	no	—
332	D₈	—	4	6	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	3	no	—
335	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
336	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
337	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
338	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
339	C₄⋊C₄	—	2	6	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	6	no	—
343	C₄⋊C₄	—	2	6	no	—
344	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
345	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
346	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
347	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
348	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	6	no	—
351	C₂²⋊C₄	—	2	6	no	—
352	C₂²⋊C₄	—	2	6	no	—
353	C₂²⋊C₄	—	2	6	no	—
354	C₂²⋊C₄	—	2	12	no	—
355	C₄²	—	2	6	no	—
356	C₄²	C₂×D₄×C₁₉	1	3	yes	—
357	C₄²	C₂×D₄×C₁₉	1	3	yes	—
358	C₄²	C₂⁴×C₁₉	1	3	yes	—
359	C₄²	C₂⁴×C₁₉	1	3	yes	—
360	C₂³	—	2	6	no	—
361	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
362	Q₈	—	2	6	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	2	no	—
365	Q₈	—	8	6	no	—
366	Q₈	C₁₉×#135	1	4	yes	—
367	D₄	—	2	6	no	—
368	D₄	—	2	6	no	—
369	D₄	—	4	12	no	—
370	D₄	—	4	12	no	—
371	D₄	—	8	6	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	12	no	—
380	C₂×C₄	—	8	12	no	—
381	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
383	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
384	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
385	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
386	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	2	3	no	—
389	C₈	—	2	3	no	—
390	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	6	no	—
394	C₂²	—	4	6	no	—
395	C₂²	—	4	6	no	—
396	C₂²	C₁₉×#576	1	2	yes	—
397	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	3	no	—
400	C₄	—	2	3	no	—
401	C₄	—	2	3	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	6	no	—
405	C₄	C₂×C₁₉×#135	1	6	yes	—
406	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
407	C₄	C₁₉×#585	1	1	yes	characteristic
408	C₂	—	2	2	no	—
409	C₂	—	8	6	no	—
410	C₂	C₁₉×#3497	1	1	yes	characteristic
411	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
412	C₂	C₂×C₁₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3522	C₂	semidirect
2. C₁₉×#3396	C₂	semidirect
3. C₁₉×#3391	C₂	semidirect
4. Q₈×Q₁₆×C₁₉	C₂	semidirect
5. C₁₉×#3380	C₂	semidirect
6. C₁₉×#3362	C₂	semidirect
7. C₁₉×#3361	C₂	semidirect
8. C₁₉×#3247	C₂	semidirect
9. C₁₉×#3169	C₂	semidirect
10. C₁₉×#3168	C₂	semidirect
11. C₂×C₈×Q₈×C₁₉	C₂	semidirect
153. #62363	C₁₉	direct (N × H)
185. #3522	C₂×C₁₉	semidirect
186. #3396	C₂×C₁₉	semidirect
187. #3391	C₂×C₁₉	semidirect
188. Q₈×Q₁₆	C₂×C₁₉	semidirect
189. #3380	C₂×C₁₉	semidirect
190. #3362	C₂×C₁₉	semidirect
191. #3361	C₂×C₁₉	semidirect
192. #3247	C₂×C₁₉	semidirect
193. #3169	C₂×C₁₉	semidirect
194. #3168	C₂×C₁₉	semidirect
195. C₂×C₈×Q₈	C₂×C₁₉	semidirect
312. C₁₉	#62363	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×#3522	2
C₁₉×#3396	2
C₁₉×#3391	2
Q₈×Q₁₆×C₁₉	2
C₁₉×#3380	2
C₁₉×#3362	2
C₁₉×#3361	2
C₁₉×#3247	2
C₁₉×#3169	2
C₁₉×#3168	2
C₂×C₈×Q₈×C₁₉	2
#62363	19

Subgroups — C19×#62363 #18068322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62363 #18068322