Subgroups — C₁₉×#11315 #18017274

Order 4864.

770 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#95	—	2	1	no	—
16	C₂×C₁₉×#95	—	2	1	no	—
17	C₂×C₁₉×#95	—	2	1	no	—
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₁₉×#340	—	2	2	no	—
20	C₁₉×#340	—	2	2	no	—
21	C₁₉×#340	—	2	2	no	—
22	C₁₉×#340	C₄	1	4	yes	complemented
23	C₁₉×#336	—	2	2	no	—
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	—	2	1	no	—
43	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₉	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	—	2	1	no	—
74	C₂×C₄²×C₁₉	—	2	1	no	—
75	C₁₉×#95	—	4	2	no	—
76	C₁₉×#95	—	4	2	no	—
77	C₁₉×#95	—	4	2	no	—
78	C₁₉×#95	—	4	2	no	—
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	D₈	1	2	yes	—
121	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	4	1	no	—
143	C₂×C₈×C₁₉	—	4	1	no	—
144	C₂×C₈×C₁₉	—	4	1	no	—
145	C₂×C₈×C₁₉	—	4	1	no	—
146	C₂×C₈×C₁₉	—	4	1	no	—
147	C₂×C₈×C₁₉	—	4	1	no	—
148	C₂×C₈×C₁₉	—	4	1	no	—
149	C₂×C₈×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	4	1	no	—
159	C₄⋊C₄×C₁₉	—	4	1	no	—
160	C₄⋊C₄×C₁₉	—	4	1	no	—
161	C₄⋊C₄×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	—	4	1	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	1	no	—
166	C₄²×C₁₉	—	4	1	no	—
167	C₄²×C₁₉	—	4	1	no	—
168	C₄²×C₁₉	—	4	1	no	—
169	C₄²×C₁₉	—	4	1	no	—
170	#11315	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₁₉	#121	1	1	yes	characteristic
173	C₂³×C₁₉	#121	1	1	yes	characteristic
174	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂³×C₁₉	#123	1	1	yes	characteristic
176	C₂³×C₁₉	#123	1	1	yes	characteristic
177	C₂³×C₁₉	#124	1	1	yes	characteristic
178	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
179	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
180	C₂³×C₁₉	#135	1	1	yes	characteristic
181	C₂³×C₁₉	#135	1	1	yes	characteristic
182	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂³×C₁₉	#137	1	1	yes	characteristic
184	C₂³×C₁₉	#137	1	1	yes	characteristic
185	C₂³×C₁₉	#137	1	1	yes	characteristic
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	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	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	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	8	1	no	—
213	C₂×C₄×C₁₉	—	8	1	no	—
214	C₂×C₄×C₁₉	—	8	1	no	—
215	C₂×C₄×C₁₉	—	8	1	no	—
216	C₂×C₄×C₁₉	—	8	1	no	—
217	C₂×C₄×C₁₉	—	8	1	no	—
218	C₂×C₄×C₁₉	—	8	1	no	—
219	C₂×C₄×C₁₉	—	8	1	no	—
220	C₂×C₄×C₁₉	—	8	1	no	—
221	C₂×C₄×C₁₉	—	8	1	no	—
222	C₂×C₄×C₁₉	—	8	1	no	—
223	C₂×C₄×C₁₉	—	8	1	no	—
224	C₂×C₄×C₁₉	—	8	1	no	—
225	C₂×C₄×C₁₉	—	8	1	no	—
226	C₂×C₄×C₁₉	—	8	1	no	—
227	C₂×C₄×C₁₉	—	8	1	no	—
228	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
256	C₈×C₁₉	—	4	2	no	—
257	C₈×C₁₉	—	4	2	no	—
258	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
259	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
260	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
261	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
262	C₂×#336	C₂×C₁₉	1	1	yes	characteristic
263	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
264	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
265	C₂²×C₁₉	#387	1	1	yes	characteristic
266	C₂²×C₁₉	#388	1	1	yes	characteristic
267	C₂²×C₁₉	#388	1	1	yes	characteristic
268	C₂²×C₁₉	#396	1	1	yes	characteristic
269	C₂²×C₁₉	#397	1	1	yes	characteristic
270	C₂²×C₁₉	#397	1	1	yes	characteristic
271	C₂²×C₁₉	#400	1	1	yes	characteristic
272	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
273	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
274	C₂²×C₁₉	#440	1	1	yes	characteristic
275	C₂²×C₁₉	#441	1	1	yes	characteristic
276	C₂²×C₁₉	#459	1	1	yes	characteristic
277	C₂²×C₁₉	#461	1	1	yes	characteristic
278	C₂²×C₁₉	#464	1	1	yes	characteristic
279	C₂²×C₁₉	#464	1	1	yes	characteristic
280	C₂²×C₁₉	#465	1	1	yes	characteristic
281	C₂²×C₁₉	#466	1	1	yes	characteristic
282	C₂²×C₁₉	#468	1	1	yes	characteristic
283	C₂²×C₁₉	#470	1	1	yes	characteristic
284	C₂²×C₁₉	#474	1	1	yes	characteristic
285	C₂²×C₁₉	#475	1	1	yes	characteristic
286	C₂²×C₁₉	#478	1	1	yes	characteristic
287	C₂²×C₁₉	#479	1	1	yes	characteristic
288	C₂²×C₁₉	#480	1	1	yes	characteristic
289	C₂²×C₁₉	#480	1	1	yes	characteristic
290	C₂²×C₁₉	#481	1	1	yes	characteristic
291	C₂²×C₁₉	#482	1	1	yes	characteristic
292	C₂²×C₁₉	#483	1	1	yes	characteristic
293	C₂²×C₁₉	#485	1	1	yes	characteristic
294	C₂²×C₁₉	#485	1	1	yes	characteristic
295	C₂²×C₁₉	#485	1	1	yes	characteristic
296	C₂²×C₁₉	#486	1	1	yes	characteristic
297	C₂²×C₁₉	#488	1	1	yes	characteristic
298	C₂²×C₁₉	#489	1	1	yes	characteristic
299	C₂²×C₁₉	#491	1	1	yes	characteristic
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	8	2	no	—
303	C₄×C₁₉	—	8	2	no	—
304	C₄×C₁₉	—	8	2	no	—
305	C₄×C₁₉	—	8	2	no	—
306	C₄×C₁₉	#383	1	1	yes	characteristic
307	C₄×C₁₉	#387	1	1	yes	characteristic
308	C₄×C₁₉	#387	1	1	yes	characteristic
309	C₄×C₁₉	#388	1	1	yes	characteristic
310	C₄×C₁₉	#397	1	1	yes	characteristic
311	C₄×C₁₉	#400	1	1	yes	characteristic
312	C₄×C₁₉	#400	1	1	yes	characteristic
313	C₄×C₁₉	#401	1	1	yes	characteristic
314	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
320	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#95	—	2	1	no	—
322	C₂×#95	—	2	1	no	—
323	C₂×#95	—	2	1	no	—
324	C₂×#95	—	2	1	no	—
325	#340	—	2	2	no	—
326	#340	—	2	2	no	—
327	#340	—	2	2	no	—
328	#340	C₄×C₁₉	1	4	yes	complemented
329	#336	—	2	2	no	—
330	C₂×C₁₉	#1443	1	1	yes	characteristic
331	C₂×C₁₉	#1918	1	1	yes	characteristic
332	C₂×C₁₉	#1919	1	1	yes	characteristic
333	C₂×C₁₉	#1925	1	1	yes	characteristic
334	C₂×C₁₉	#1927	1	1	yes	characteristic
335	C₂×C₁₉	#1934	1	1	yes	characteristic
336	C₂×C₁₉	#1935	1	1	yes	characteristic
337	C₂×C₁₉	#2066	1	1	yes	characteristic
338	C₂×C₁₉	#2067	1	1	yes	characteristic
339	C₂×C₁₉	#2071	1	1	yes	characteristic
340	C₂×C₁₉	#2074	1	1	yes	characteristic
341	C₂×C₁₉	#2075	1	1	yes	characteristic
342	C₂×C₁₉	#2077	1	1	yes	characteristic
343	C₂×C₁₉	#2099	1	1	yes	characteristic
344	C₂×C₁₉	#2101	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
350	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
365	C₂²×C₈	D₄×C₁₉	1	2	yes	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
387	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
388	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
389	C₂×C₄⋊C₄	Q₈×C₁₉	1	2	yes	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	#95	—	4	2	no	—
397	#95	—	4	2	no	—
398	#95	—	4	2	no	—
399	#95	—	4	2	no	—
400	C₁₉	#11315	1	1	yes	characteristic, direct product factor, Sylow
401	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	D₈×C₁₉	1	2	yes	—
443	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	4	1	no	—
465	C₂×C₈	—	4	1	no	—
466	C₂×C₈	—	4	1	no	—
467	C₂×C₈	—	4	1	no	—
468	C₂×C₈	—	4	1	no	—
469	C₂×C₈	—	4	1	no	—
470	C₂×C₈	—	4	1	no	—
471	C₂×C₈	—	4	1	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	—	4	1	no	—
490	C₄²	—	4	1	no	—
491	C₄²	—	4	1	no	—
492	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
493	C₂³	C₁₉×#121	1	1	yes	characteristic
494	C₂³	C₁₉×#121	1	1	yes	characteristic
495	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
496	C₂³	C₁₉×#123	1	1	yes	characteristic
497	C₂³	C₁₉×#123	1	1	yes	characteristic
498	C₂³	C₁₉×#124	1	1	yes	characteristic
499	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
500	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
501	C₂³	C₁₉×#135	1	1	yes	characteristic
502	C₂³	C₁₉×#135	1	1	yes	characteristic
503	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₂³	C₁₉×#137	1	1	yes	characteristic
505	C₂³	C₁₉×#137	1	1	yes	characteristic
506	C₂³	C₁₉×#137	1	1	yes	characteristic
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	1	no	—
534	C₂×C₄	—	8	1	no	—
535	C₂×C₄	—	8	1	no	—
536	C₂×C₄	—	8	1	no	—
537	C₂×C₄	—	8	1	no	—
538	C₂×C₄	—	8	1	no	—
539	C₂×C₄	—	8	1	no	—
540	C₂×C₄	—	8	1	no	—
541	C₂×C₄	—	8	1	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	—	8	1	no	—
544	C₂×C₄	—	8	1	no	—
545	C₂×C₄	—	8	1	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	—	8	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
550	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
551	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
552	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
554	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
555	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
556	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
557	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
558	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
559	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
560	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
561	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
562	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
563	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
564	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
565	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
566	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
567	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
568	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
569	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
570	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
571	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
572	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
573	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
574	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
575	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
576	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
577	C₈	—	4	2	no	—
578	C₈	—	4	2	no	—
579	C₂²	C₁₉×#387	1	1	yes	characteristic
580	C₂²	C₁₉×#388	1	1	yes	characteristic
581	C₂²	C₁₉×#388	1	1	yes	characteristic
582	C₂²	C₁₉×#396	1	1	yes	characteristic
583	C₂²	C₁₉×#397	1	1	yes	characteristic
584	C₂²	C₁₉×#397	1	1	yes	characteristic
585	C₂²	C₁₉×#400	1	1	yes	characteristic
586	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
587	C₂²	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
588	C₂²	C₁₉×#440	1	1	yes	characteristic
589	C₂²	C₁₉×#441	1	1	yes	characteristic
590	C₂²	C₁₉×#459	1	1	yes	characteristic
591	C₂²	C₁₉×#461	1	1	yes	characteristic
592	C₂²	C₁₉×#464	1	1	yes	characteristic
593	C₂²	C₁₉×#464	1	1	yes	characteristic
594	C₂²	C₁₉×#465	1	1	yes	characteristic
595	C₂²	C₁₉×#466	1	1	yes	characteristic
596	C₂²	C₁₉×#468	1	1	yes	characteristic
597	C₂²	C₁₉×#470	1	1	yes	characteristic
598	C₂²	C₁₉×#474	1	1	yes	characteristic
599	C₂²	C₁₉×#475	1	1	yes	characteristic
600	C₂²	C₁₉×#478	1	1	yes	characteristic
601	C₂²	C₁₉×#479	1	1	yes	characteristic
602	C₂²	C₁₉×#480	1	1	yes	characteristic
603	C₂²	C₁₉×#480	1	1	yes	characteristic
604	C₂²	C₁₉×#481	1	1	yes	characteristic
605	C₂²	C₁₉×#482	1	1	yes	characteristic
606	C₂²	C₁₉×#483	1	1	yes	characteristic
607	C₂²	C₁₉×#485	1	1	yes	characteristic
608	C₂²	C₁₉×#485	1	1	yes	characteristic
609	C₂²	C₁₉×#485	1	1	yes	characteristic
610	C₂²	C₁₉×#486	1	1	yes	characteristic
611	C₂²	C₁₉×#488	1	1	yes	characteristic
612	C₂²	C₁₉×#489	1	1	yes	characteristic
613	C₂²	C₁₉×#491	1	1	yes	characteristic
614	C₄	—	4	2	no	—
615	C₄	—	4	2	no	—
616	C₄	—	8	2	no	—
617	C₄	—	8	2	no	—
618	C₄	—	8	2	no	—
619	C₄	—	8	2	no	—
620	C₄	C₁₉×#383	1	1	yes	characteristic
621	C₄	C₁₉×#387	1	1	yes	characteristic
622	C₄	C₁₉×#387	1	1	yes	characteristic
623	C₄	C₁₉×#388	1	1	yes	characteristic
624	C₄	C₁₉×#397	1	1	yes	characteristic
625	C₄	C₁₉×#400	1	1	yes	characteristic
626	C₄	C₁₉×#400	1	1	yes	characteristic
627	C₄	C₁₉×#401	1	1	yes	characteristic
628	C₂	C₁₉×#1443	1	1	yes	characteristic
629	C₂	C₁₉×#1918	1	1	yes	characteristic
630	C₂	C₁₉×#1919	1	1	yes	characteristic
631	C₂	C₁₉×#1925	1	1	yes	characteristic
632	C₂	C₁₉×#1927	1	1	yes	characteristic
633	C₂	C₁₉×#1934	1	1	yes	characteristic
634	C₂	C₁₉×#1935	1	1	yes	characteristic
635	C₂	C₁₉×#2066	1	1	yes	characteristic
636	C₂	C₁₉×#2067	1	1	yes	characteristic
637	C₂	C₁₉×#2071	1	1	yes	characteristic
638	C₂	C₁₉×#2074	1	1	yes	characteristic
639	C₂	C₁₉×#2075	1	1	yes	characteristic
640	C₂	C₁₉×#2077	1	1	yes	characteristic
641	C₂	C₁₉×#2099	1	1	yes	characteristic
642	C₂	C₁₉×#2101	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
22. C₁₉×#340	C₄	semidirect
170. #11315	C₁₉	direct (N × H)
328. #340	C₄×C₁₉	semidirect
400. C₁₉	#11315	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×#340	2
C₂×C₁₉×#336	2
C₁₉×C₄⋊#95	2
#11315	19

Subgroups — C19×#11315 #18017274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11315 #18017274