Subgroups — C₁₉×#61379 #18067338

Order 4864.

1674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3502	C₂	1	2	yes	maximal
2	C₁₉×#3390	C₂	1	8	yes	maximal, complemented
3	C₁₉×#3387	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3163	C₂	1	2	yes	maximal
5	C₁₉×#3162	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#3082	C₂	1	4	yes	maximal
7	C₁₉×#3078	C₂	1	2	yes	maximal
8	C₁₉×#2961	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2950	C₂	1	2	yes	maximal
10	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
11	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	Q₈²×C₁₉	—	2	2	no	—
13	Q₈²×C₁₉	C₂²	1	4	yes	—
14	C₁₉×#557	—	2	2	no	—
15	C₁₉×#557	—	2	4	no	—
16	C₁₉×#557	C₂²	1	8	yes	—
17	C₁₉×#557	C₂²	1	4	yes	—
18	C₁₉×#544	—	2	4	no	—
19	C₁₉×#544	C₂²	1	4	yes	—
20	C₁₉×#533	—	2	4	no	—
21	C₁₉×#533	C₂²	1	2	yes	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₁₉×#519	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#501	C₂²	1	4	yes	—
26	C₁₉×#501	C₂²	1	8	yes	—
27	C₁₉×#501	C₂²	1	4	yes	—
28	C₁₉×#499	C₂²	1	4	yes	—
29	C₁₉×#498	C₂²	1	4	yes	—
30	C₁₉×#479	C₂²	1	8	yes	—
31	C₁₉×#479	C₂²	1	8	yes	—
32	C₁₉×#479	C₂²	1	8	yes	—
33	C₁₉×#477	C₂²	1	4	yes	—
34	C₁₉×#477	C₂²	1	8	yes	—
35	C₁₉×#475	C₂²	1	4	yes	—
36	C₁₉×#475	C₂²	1	8	yes	—
37	C₁₉×#446	C₂²	1	8	yes	—
38	C₁₉×#441	C₂²	1	8	yes	—
39	C₁₉×#441	C₂²	1	4	yes	—
40	C₁₉×#441	C₂²	1	4	yes	—
41	C₄×Q₁₆×C₁₉	C₂²	1	8	yes	—
42	C₁₉×#428	C₂²	1	4	yes	—
43	C₁₉×#427	C₂²	1	2	yes	—
44	C₁₉×#427	C₂²	1	2	yes	—
45	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
46	C₁₉×#424	C₂²	1	2	yes	—
47	C₁₉×#423	C₂²	1	1	yes	characteristic
48	C₁₉×#419	C₂²	1	4	yes	—
49	C₂×C₁₉×#103	C₂²	1	2	yes	—
50	C₁₉×#405	C₂²	1	2	yes	—
51	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₁₉	Q₈	1	8	yes	complemented
54	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
55	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	—	2	4	no	—
59	C₁₉×C₄⋊Q₈	—	2	8	no	—
60	C₁₉×C₄⋊Q₈	—	2	4	no	—
61	C₁₉×C₄⋊Q₈	—	2	8	no	—
62	C₁₉×C₄⋊Q₈	—	2	4	no	—
63	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
64	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
66	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₉×#125	—	2	8	no	—
68	C₁₉×#125	—	2	8	no	—
69	C₁₉×#125	—	2	8	no	—
70	C₁₉×#125	—	2	4	no	—
71	C₁₉×#125	D₄	1	2	yes	—
72	C₁₉×#125	C₂³	1	8	yes	—
73	C₁₉×#125	C₂³	1	4	yes	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	8	no	—
77	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
78	C₄×Q₈×C₁₉	—	2	4	no	—
79	C₄×Q₈×C₁₉	—	2	4	no	—
80	C₄×Q₈×C₁₉	—	2	4	no	—
81	C₄×Q₈×C₁₉	—	2	8	no	—
82	C₄×Q₈×C₁₉	—	2	4	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	2	no	—
87	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
88	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
89	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
90	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
91	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
92	C₁₉×#117	—	2	8	no	—
93	C₁₉×#117	C₂³	1	4	yes	—
94	C₁₉×#117	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₉	—	2	2	no	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#107	C₂³	1	4	yes	—
100	C₁₉×#107	C₂³	1	4	yes	—
101	C₁₉×#107	C₂³	1	8	yes	—
102	C₁₉×#106	C₂³	1	4	yes	—
103	C₁₉×#106	C₂³	1	2	yes	—
104	C₁₉×#106	C₂³	1	2	yes	—
105	C₁₉×#106	C₂³	1	2	yes	—
106	C₁₉×#106	C₂³	1	2	yes	—
107	C₁₉×#106	C₂³	1	8	yes	—
108	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
110	C₁₉×#103	C₂³	1	8	yes	—
111	C₁₉×#103	C₂³	1	8	yes	—
112	C₁₉×#103	C₂³	1	8	yes	—
113	C₁₉×#97	C₂³	1	4	yes	—
114	C₁₉×#97	C₂³	1	4	yes	—
115	C₄×C₈×C₁₉	C₂³	1	4	yes	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	8	no	—
120	C₂×Q₈×C₁₉	—	2	4	no	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
122	C₂×Q₈×C₁₉	C₂×Q₈	1	8	yes	—
123	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₁₉	C₂×Q₈	1	16	yes	—
129	M₁₆×C₁₉	—	2	4	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
132	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
133	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
134	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	4	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	8	no	—
139	C₄⋊C₄×C₁₉	—	2	8	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	8	no	—
144	C₄⋊C₄×C₁₉	—	2	8	no	—
145	C₄⋊C₄×C₁₉	—	2	4	no	—
146	C₄⋊C₄×C₁₉	—	2	8	no	—
147	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
151	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
155	C₄²×C₁₉	—	2	4	no	—
156	C₄²×C₁₉	—	2	4	no	—
157	C₄²×C₁₉	—	2	8	no	—
158	C₄²×C₁₉	—	2	8	no	—
159	C₄²×C₁₉	—	2	4	no	—
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₉	C₂⁴	1	2	yes	—
163	C₄²×C₁₉	C₂⁴	1	4	yes	—
164	#61379	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	8	no	—
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	4	4	no	—
169	Q₈×C₁₉	—	4	4	no	—
170	Q₈×C₁₉	—	8	2	no	—
171	Q₈×C₁₉	—	8	8	no	—
172	Q₈×C₁₉	C₂²×Q₈	1	8	yes	—
173	C₂×C₄×C₁₉	—	2	8	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	8	2	no	—
180	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
183	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
185	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
186	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
187	C₈×C₁₉	—	2	2	no	—
188	C₈×C₁₉	—	2	4	no	—
189	C₈×C₁₉	C₂²×Q₈	1	4	yes	—
190	#3502	C₂×C₁₉	1	2	yes	—
191	#3390	C₂×C₁₉	1	8	yes	complemented
192	#3387	C₂×C₁₉	1	8	yes	complemented
193	#3163	C₂×C₁₉	1	2	yes	—
194	#3162	C₂×C₁₉	1	1	yes	characteristic
195	#3082	C₂×C₁₉	1	4	yes	—
196	#3078	C₂×C₁₉	1	2	yes	—
197	#2961	C₂×C₁₉	1	1	yes	characteristic
198	#2950	C₂×C₁₉	1	2	yes	—
199	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
202	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	2	8	no	—
206	C₄×C₁₉	—	2	8	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	4	4	no	—
210	C₄×C₁₉	D₄×Q₈	1	2	yes	—
211	C₄×C₁₉	C₂³×Q₈	1	1	yes	characteristic
212	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
213	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
214	Q₈²	—	2	2	no	—
215	Q₈²	C₂²×C₁₉	1	4	yes	—
216	#557	—	2	2	no	—
217	#557	—	2	4	no	—
218	#557	C₂²×C₁₉	1	8	yes	—
219	#557	C₂²×C₁₉	1	4	yes	—
220	#544	—	2	4	no	—
221	#544	C₂²×C₁₉	1	4	yes	—
222	#533	—	2	4	no	—
223	#533	C₂²×C₁₉	1	2	yes	—
224	#533	C₂²×C₁₉	1	1	yes	characteristic
225	#519	C₂²×C₁₉	1	4	yes	—
226	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
227	#501	C₂²×C₁₉	1	4	yes	—
228	#501	C₂²×C₁₉	1	8	yes	—
229	#501	C₂²×C₁₉	1	4	yes	—
230	#499	C₂²×C₁₉	1	4	yes	—
231	#498	C₂²×C₁₉	1	4	yes	—
232	#479	C₂²×C₁₉	1	8	yes	—
233	#479	C₂²×C₁₉	1	8	yes	—
234	#479	C₂²×C₁₉	1	8	yes	—
235	#477	C₂²×C₁₉	1	4	yes	—
236	#477	C₂²×C₁₉	1	8	yes	—
237	#475	C₂²×C₁₉	1	4	yes	—
238	#475	C₂²×C₁₉	1	8	yes	—
239	#446	C₂²×C₁₉	1	8	yes	—
240	#441	C₂²×C₁₉	1	4	yes	—
241	#441	C₂²×C₁₉	1	8	yes	—
242	#441	C₂²×C₁₉	1	4	yes	—
243	C₄×Q₁₆	C₂²×C₁₉	1	8	yes	—
244	#428	C₂²×C₁₉	1	4	yes	—
245	#427	C₂²×C₁₉	1	2	yes	—
246	#427	C₂²×C₁₉	1	2	yes	—
247	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
248	#424	C₂²×C₁₉	1	2	yes	—
249	#423	C₂²×C₁₉	1	1	yes	characteristic
250	#419	C₂²×C₁₉	1	4	yes	—
251	C₂×#103	C₂²×C₁₉	1	2	yes	—
252	#405	C₂²×C₁₉	1	2	yes	—
253	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×C₁₉	—	2	2	no	—
255	C₂×C₁₉	C₂×D₄×Q₈	1	1	yes	characteristic
256	C₂×C₁₉	#3586	1	2	yes	—
257	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
258	C₂×Q₁₆	Q₈×C₁₉	1	8	yes	complemented
259	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
260	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	4	no	—
264	C₄⋊Q₈	—	2	8	no	—
265	C₄⋊Q₈	—	2	4	no	—
266	C₄⋊Q₈	—	2	8	no	—
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
269	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
270	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
271	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
272	#125	—	2	8	no	—
273	#125	—	2	8	no	—
274	#125	—	2	8	no	—
275	#125	—	2	4	no	—
276	#125	D₄×C₁₉	1	2	yes	—
277	#125	C₂³×C₁₉	1	4	yes	—
278	#125	C₂³×C₁₉	1	8	yes	—
279	C₂²⋊Q₈	—	2	2	no	—
280	C₂²⋊Q₈	—	2	2	no	—
281	C₂²⋊Q₈	—	2	8	no	—
282	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	—	2	8	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
293	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
294	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
295	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
296	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
297	#117	—	2	8	no	—
298	#117	C₂³×C₁₉	1	4	yes	—
299	#117	C₂³×C₁₉	1	2	yes	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
304	#107	C₂³×C₁₉	1	4	yes	—
305	#107	C₂³×C₁₉	1	4	yes	—
306	#107	C₂³×C₁₉	1	8	yes	—
307	#106	C₂³×C₁₉	1	4	yes	—
308	#106	C₂³×C₁₉	1	2	yes	—
309	#106	C₂³×C₁₉	1	2	yes	—
310	#106	C₂³×C₁₉	1	2	yes	—
311	#106	C₂³×C₁₉	1	2	yes	—
312	#106	C₂³×C₁₉	1	8	yes	—
313	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
314	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
315	#103	C₂³×C₁₉	1	8	yes	—
316	#103	C₂³×C₁₉	1	8	yes	—
317	#103	C₂³×C₁₉	1	8	yes	—
318	#97	C₂³×C₁₉	1	4	yes	—
319	#97	C₂³×C₁₉	1	4	yes	—
320	C₄×C₈	C₂³×C₁₉	1	4	yes	—
321	C₁₉	#61379	1	1	yes	characteristic, direct product factor, Sylow
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
328	C₂×Q₈	C₂×Q₈×C₁₉	1	8	yes	—
329	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
334	Q₁₆	C₂×Q₈×C₁₉	1	16	yes	—
335	M₁₆	—	2	4	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
338	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
339	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
340	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
354	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
355	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
356	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
357	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
358	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	8	no	—
364	C₄²	—	2	8	no	—
365	C₄²	—	2	4	no	—
366	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₄²	C₂⁴×C₁₉	1	4	yes	—
369	C₄²	C₂⁴×C₁₉	1	2	yes	—
370	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
371	Q₈	—	2	8	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	4	4	no	—
374	Q₈	—	4	4	no	—
375	Q₈	—	8	2	no	—
376	Q₈	—	8	8	no	—
377	Q₈	C₂²×Q₈×C₁₉	1	8	yes	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
386	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
388	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
390	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
391	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	2	4	no	—
394	C₈	C₂²×Q₈×C₁₉	1	4	yes	—
395	C₂²	—	2	2	no	—
396	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
397	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
398	C₄	—	2	8	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	8	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	4	no	—
405	C₄	D₄×Q₈×C₁₉	1	2	yes	—
406	C₄	C₂³×Q₈×C₁₉	1	1	yes	characteristic
407	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂	—	2	2	no	—
409	C₂	C₂×D₄×Q₈×C₁₉	1	1	yes	characteristic
410	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂³×C₁₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3390	C₂	semidirect
3. C₁₉×#3387	C₂	semidirect
53. C₂×Q₁₆×C₁₉	Q₈	semidirect
164. #61379	C₁₉	direct (N × H)
191. #3390	C₂×C₁₉	semidirect
192. #3387	C₂×C₁₉	semidirect
258. C₂×Q₁₆	Q₈×C₁₉	semidirect
321. C₁₉	#61379	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×#3502	2
C₁₉×#3390	2
C₁₉×#3387	2
C₁₉×#3163	2
C₁₉×#3162	2
C₁₉×#3082	2
C₁₉×#3078	2
C₁₉×#2961	2
C₁₉×#2950	2
C₂×C₁₉×#441	2
#61379	19

Subgroups — C19×#61379 #18067338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61379 #18067338