Subgroups — C₁₉×#23557 #18029516

Order 4864.

1110 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2316	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2059	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2059	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2058	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2057	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#544	—	2	4	no	—
15	C₁₉×#544	—	2	4	no	—
16	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×#125	—	2	1	no	—
19	C₂×C₁₉×#125	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#428	—	2	4	no	—
27	C₁₉×#427	—	2	4	no	—
28	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#107	C₂²	1	2	yes	—
30	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#106	C₂²	1	2	yes	—
33	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
34	C₁₉×#389	—	2	1	no	—
35	C₁₉×#389	—	2	1	no	—
36	C₁₉×#389	C₂²	1	2	yes	—
37	C₁₉×#389	C₂²	1	2	yes	—
38	C₁₉×#380	—	2	2	no	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#336	C₂²	1	2	yes	—
44	C₁₉×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	Q₈	1	4	yes	complemented
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	Q₈	1	4	yes	complemented
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	—	2	8	no	—
59	C₁₉×C₄⋊Q₈	—	2	4	no	—
60	C₁₉×C₄⋊Q₈	—	2	4	no	—
61	C₁₉×#125	—	2	8	no	—
62	C₁₉×#125	—	2	4	no	—
63	C₁₉×#125	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	16	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	—	2	2	no	—
68	C₁₉×#117	—	2	2	no	—
69	C₁₉×#117	—	2	2	no	—
70	C₁₉×#117	D₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	complemented
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
96	C₁₉×#107	—	2	2	no	—
97	C₁₉×#107	—	2	2	no	—
98	C₁₉×#107	—	2	4	no	—
99	C₁₉×#106	—	2	2	no	—
100	C₁₉×#106	—	2	2	no	—
101	C₁₉×#106	—	2	4	no	—
102	C₁₉×#95	—	2	2	no	—
103	C₁₉×#95	—	2	2	no	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₉	—	2	8	no	—
106	C₂×Q₈×C₁₉	—	8	2	no	—
107	C₂×Q₈×C₁₉	—	8	2	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	8	1	no	—
117	C₂²×C₄×C₁₉	—	8	1	no	—
118	C₂²×C₄×C₁₉	—	8	1	no	—
119	C₂²×C₄×C₁₉	—	8	1	no	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₁₉	#41	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₁₉	—	2	8	no	—
131	C₂×C₈×C₁₉	—	2	8	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	1	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
139	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
140	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
141	C₄⋊C₄×C₁₉	—	2	8	no	—
142	C₄⋊C₄×C₁₉	—	2	8	no	—
143	C₄⋊C₄×C₁₉	—	2	8	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	8	2	no	—
157	C₄⋊C₄×C₁₉	—	8	2	no	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
159	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	4	2	no	—
165	C₄²×C₁₉	—	2	4	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	4	2	no	—
169	#23557	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	#120	1	2	yes	—
175	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
176	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
177	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₁₉	—	8	8	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	8	4	no	—
204	C₂×C₄×C₁₉	—	8	4	no	—
205	C₂×C₄×C₁₉	#120	1	2	yes	—
206	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
207	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
208	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
210	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
211	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
212	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
218	C₈×C₁₉	—	2	2	no	—
219	C₈×C₁₉	—	2	2	no	—
220	C₈×C₁₉	—	2	4	no	—
221	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
222	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
223	C₂×#427	C₂×C₁₉	1	1	yes	characteristic
224	#2316	C₂×C₁₉	1	1	yes	characteristic
225	#2059	C₂×C₁₉	1	2	yes	complemented
226	#2059	C₂×C₁₉	1	2	yes	complemented
227	#2058	C₂×C₁₉	1	2	yes	complemented
228	#2057	C₂×C₁₉	1	2	yes	complemented
229	#1736	C₂×C₁₉	1	1	yes	characteristic
230	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
231	#1729	C₂×C₁₉	1	1	yes	characteristic
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	#395	1	4	yes	—
239	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
240	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
241	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
242	C₂²×C₁₉	#576	1	1	yes	characteristic
243	C₂²×C₁₉	#577	1	1	yes	characteristic
244	C₂²×C₁₉	#577	1	1	yes	characteristic
245	C₂²×C₁₉	#578	1	1	yes	characteristic
246	C₄×C₁₉	—	4	4	no	—
247	C₄×C₁₉	—	4	2	no	—
248	C₄×C₁₉	—	4	4	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	8	1	no	—
253	C₄×C₁₉	—	8	1	no	—
254	C₄×C₁₉	#395	1	4	yes	—
255	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
256	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
258	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
259	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
260	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
261	#544	—	2	4	no	—
262	#544	—	2	4	no	—
263	C₂×C₄⋊Q₈	—	2	1	no	—
264	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
265	C₂×#125	—	2	1	no	—
266	C₂×#125	C₂²×C₁₉	1	2	yes	—
267	C₂×C₂²⋊Q₈	—	2	2	no	—
268	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
273	#428	—	2	4	no	—
274	#427	—	2	4	no	—
275	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#107	C₂²×C₁₉	1	2	yes	—
277	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×#106	C₂²×C₁₉	1	2	yes	—
280	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
281	#389	—	2	1	no	—
282	#389	—	2	1	no	—
283	#389	C₂²×C₁₉	1	2	yes	—
284	#389	C₂²×C₁₉	1	2	yes	—
285	#380	—	2	2	no	—
286	#340	C₂²×C₁₉	1	2	yes	—
287	#340	C₂²×C₁₉	1	2	yes	—
288	#340	C₂²×C₁₉	1	2	yes	—
289	#340	C₂²×C₁₉	1	2	yes	—
290	#336	C₂²×C₁₉	1	2	yes	—
291	#336	C₂²×C₁₉	1	2	yes	—
292	C₂×C₁₉	—	2	4	no	—
293	C₂×C₁₉	C₂×#395	1	1	yes	characteristic
294	C₂×C₁₉	#3012	1	1	yes	characteristic
295	C₂×C₁₉	#3013	1	1	yes	characteristic
296	C₂×C₁₉	#3081	1	1	yes	characteristic
297	C₂×C₁₉	#3082	1	1	yes	characteristic
298	C₂×C₁₉	#3163	1	1	yes	characteristic
299	C₂×C₁₉	#3164	1	1	yes	characteristic
300	C₂²×Q₈	—	2	2	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	Q₈×C₁₉	1	4	yes	complemented
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	Q₈×C₁₉	1	4	yes	complemented
310	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
313	C₄⋊Q₈	—	2	8	no	—
314	C₄⋊Q₈	—	2	4	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	#125	—	2	8	no	—
317	#125	—	2	4	no	—
318	#125	—	2	4	no	—
319	C₂²⋊Q₈	—	2	16	no	—
320	#117	—	2	2	no	—
321	#117	—	2	2	no	—
322	#117	—	2	2	no	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	#117	D₄×C₁₉	1	4	yes	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
338	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	complemented
339	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
351	#107	—	2	2	no	—
352	#107	—	2	2	no	—
353	#107	—	2	4	no	—
354	#106	—	2	2	no	—
355	#106	—	2	2	no	—
356	#106	—	2	4	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	C₁₉	#23557	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	8	2	no	—
363	C₂×Q₈	—	8	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	8	1	no	—
373	C₂²×C₄	—	8	1	no	—
374	C₂²×C₄	—	8	1	no	—
375	C₂²×C₄	—	8	1	no	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
383	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
384	C₂²×C₄	#41×C₁₉	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
386	M₁₆	—	2	8	no	—
387	C₂×C₈	—	2	8	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
395	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
396	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	8	2	no	—
413	C₄⋊C₄	—	8	2	no	—
414	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
415	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	4	2	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	C₁₉×#120	1	2	yes	—
430	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
431	C₂³	C₁₉×C₄⋊Q₈	1	2	yes	—
432	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
433	Q₈	—	8	8	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	8	4	no	—
459	C₂×C₄	—	8	4	no	—
460	C₂×C₄	C₁₉×#120	1	2	yes	—
461	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
462	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
463	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
464	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
465	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
466	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
467	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
469	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	2	4	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	C₁₉×#395	1	4	yes	—
483	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
484	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
485	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
486	C₂²	C₁₉×#576	1	1	yes	characteristic
487	C₂²	C₁₉×#577	1	1	yes	characteristic
488	C₂²	C₁₉×#577	1	1	yes	characteristic
489	C₂²	C₁₉×#578	1	1	yes	characteristic
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	1	no	—
498	C₄	C₁₉×#395	1	4	yes	—
499	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
500	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
501	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
502	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
503	C₂	—	2	4	no	—
504	C₂	C₂×C₁₉×#395	1	1	yes	characteristic
505	C₂	C₁₉×#3012	1	1	yes	characteristic
506	C₂	C₁₉×#3013	1	1	yes	characteristic
507	C₂	C₁₉×#3081	1	1	yes	characteristic
508	C₂	C₁₉×#3082	1	1	yes	characteristic
509	C₂	C₁₉×#3163	1	1	yes	characteristic
510	C₂	C₁₉×#3164	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2059	C₂	semidirect
6. C₁₉×#2059	C₂	semidirect
7. C₁₉×#2058	C₂	semidirect
8. C₁₉×#2057	C₂	semidirect
51. C₂×M₁₆×C₁₉	Q₈	semidirect
54. C₂²×C₈×C₁₉	Q₈	semidirect
83. C₂×C₄⋊C₄×C₁₉	Q₈	semidirect
169. #23557	C₁₉	direct (N × H)
225. #2059	C₂×C₁₉	semidirect
226. #2059	C₂×C₁₉	semidirect
227. #2058	C₂×C₁₉	semidirect
228. #2057	C₂×C₁₉	semidirect
306. C₂×M₁₆	Q₈×C₁₉	semidirect
309. C₂²×C₈	Q₈×C₁₉	semidirect
338. C₂×C₄⋊C₄	Q₈×C₁₉	semidirect
359. C₁₉	#23557	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#544	2
C₂×C₁₉×#428	2
C₂×C₁₉×#427	2
C₁₉×#2316	2
C₁₉×#2059	2
C₁₉×#2058	2
C₁₉×#2057	2
C₁₉×#1736	2
C₂×C₁₉×#340	2
C₁₉×#1729	2
#23557	19

Subgroups — C19×#23557 #18029516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23557 #18029516