Subgroups — C₁₉×#16264 #18022223

Order 4864.

1842 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#398	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1446	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1441	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1440	C₂	1	2	yes	maximal
11	C₁₉×#1439	C₂	1	2	yes	maximal
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
15	C₂×C₁₉×C₂²⋊Q₈	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#398	—	2	8	no	—
27	C₁₉×#395	—	2	4	no	—
28	C₁₉×#385	—	2	4	no	—
29	C₁₉×#380	—	2	4	no	—
30	C₂×C₁₉×#95	C₂²	1	2	yes	—
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂×C₁₉×#95	C₂²	1	2	yes	—
39	C₂×C₁₉×#95	C₂²	1	2	yes	—
40	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₁₉	—	2	4	no	—
43	C₂²×Q₈×C₁₉	—	2	2	no	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	—	4	2	no	—
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	—	2	4	no	—
49	C₂³×C₄×C₁₉	—	2	2	no	—
50	C₂³×C₄×C₁₉	—	4	2	no	—
51	C₂³×C₄×C₁₉	D₄	1	4	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×C₂²⋊Q₈	—	2	32	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	complemented
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	4	no	—
94	C₁₉×#95	—	2	4	no	—
95	C₁₉×#95	—	2	4	no	—
96	C₁₉×#95	—	2	4	no	—
97	C₁₉×#95	—	4	2	no	—
98	C₁₉×#95	—	4	2	no	—
99	C₁₉×#95	—	4	2	no	—
100	C₁₉×#95	D₄	1	4	yes	—
101	C₂⁴×C₁₉	—	2	2	no	—
102	C₂⁴×C₁₉	—	2	1	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	—	2	1	no	—
105	C₂⁴×C₁₉	—	2	2	no	—
106	C₂⁴×C₁₉	—	2	2	no	—
107	C₂⁴×C₁₉	—	2	2	no	—
108	C₂⁴×C₁₉	—	2	1	no	—
109	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
110	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
111	C₂⁴×C₁₉	#41	1	2	yes	—
112	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₂×Q₈×C₁₉	—	2	8	no	—
114	C₂×Q₈×C₁₉	—	4	8	no	—
115	C₂×Q₈×C₁₉	—	4	8	no	—
116	C₂×Q₈×C₁₉	—	4	4	no	—
117	C₂×Q₈×C₁₉	—	4	4	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	8	no	—
152	C₂²×C₄×C₁₉	—	2	8	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	4	4	no	—
171	C₂²×C₄×C₁₉	—	4	8	no	—
172	C₂²×C₄×C₁₉	—	4	8	no	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
181	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
182	C₂²×C₄×C₁₉	#41	1	2	yes	—
183	C₄⋊C₄×C₁₉	—	2	8	no	—
184	C₄⋊C₄×C₁₉	—	2	16	no	—
185	C₄⋊C₄×C₁₉	—	4	8	no	—
186	C₄⋊C₄×C₁₉	—	4	8	no	—
187	C₄⋊C₄×C₁₉	—	4	4	no	—
188	C₄⋊C₄×C₁₉	—	4	4	no	—
189	C₂²⋊C₄×C₁₉	—	2	16	no	—
190	C₂²⋊C₄×C₁₉	—	2	8	no	—
191	C₂²⋊C₄×C₁₉	—	4	8	no	—
192	C₂²⋊C₄×C₁₉	—	4	4	no	—
193	#16264	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	2	2	no	—
200	C₂³×C₁₉	—	2	4	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	2	4	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	2	no	—
207	C₂³×C₁₉	—	2	2	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	—	4	2	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	2	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	2	no	—
216	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
217	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
219	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
221	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
222	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
223	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
224	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
226	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
227	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
228	Q₈×C₁₉	—	4	16	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	4	16	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	2	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	2	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	2	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	4	2	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	2	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	#120	1	4	yes	—
289	C₂×C₄×C₁₉	#121	1	4	yes	—
290	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
291	C₂×#398	C₂×C₁₉	1	2	yes	complemented
292	C₂×#395	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂×#385	C₂×C₁₉	1	1	yes	characteristic
294	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
295	#1446	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1442	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1441	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1441	C₂×C₁₉	1	2	yes	complemented
299	#1440	C₂×C₁₉	1	2	yes	—
300	#1439	C₂×C₁₉	1	2	yes	—
301	C₂²×C₁₉	—	2	4	no	—
302	C₂²×C₁₉	—	2	4	no	—
303	C₂²×C₁₉	—	2	4	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	4	4	no	—
308	C₂²×C₁₉	—	4	4	no	—
309	C₂²×C₁₉	—	4	4	no	—
310	C₂²×C₁₉	—	4	4	no	—
311	C₂²×C₁₉	—	4	2	no	—
312	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
313	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
314	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
315	C₂²×C₁₉	#534	1	1	yes	characteristic
316	C₂²×C₁₉	#536	1	1	yes	characteristic
317	C₂²×C₁₉	#536	1	2	yes	—
318	C₂²×C₁₉	#536	1	1	yes	characteristic
319	C₂²×C₁₉	#536	1	2	yes	—
320	C₂²×C₁₉	#537	1	1	yes	characteristic
321	C₂²×C₁₉	#537	1	2	yes	—
322	C₂²×C₁₉	#539	1	2	yes	—
323	C₂²×C₁₉	#541	1	2	yes	—
324	C₂²×C₁₉	#544	1	2	yes	—
325	C₂²×C₁₉	D₄²	1	2	yes	—
326	C₂²×C₁₉	#546	1	2	yes	—
327	C₂²×C₁₉	#546	1	1	yes	characteristic
328	C₂²×C₁₉	#548	1	2	yes	—
329	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
330	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
331	C₂²×C₁₉	#552	1	1	yes	characteristic
332	C₂²×C₁₉	#554	1	1	yes	characteristic
333	C₂²×C₁₉	#562	1	2	yes	—
334	C₂²×C₁₉	#563	1	2	yes	—
335	C₄×C₁₉	—	2	4	no	—
336	C₄×C₁₉	—	2	4	no	—
337	C₄×C₁₉	—	4	4	no	—
338	C₄×C₁₉	—	4	2	no	—
339	C₄×C₁₉	—	4	4	no	—
340	C₄×C₁₉	—	4	2	no	—
341	C₄×C₁₉	—	4	4	no	—
342	C₄×C₁₉	—	8	1	no	—
343	C₄×C₁₉	—	8	2	no	—
344	C₄×C₁₉	—	8	1	no	—
345	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
346	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×C₂²⋊Q₈	—	2	4	no	—
348	C₂×C₂²⋊Q₈	—	2	8	no	—
349	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
351	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
352	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
353	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
354	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
355	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
356	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
357	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
359	#398	—	2	8	no	—
360	#395	—	2	4	no	—
361	#385	—	2	4	no	—
362	#380	—	2	4	no	—
363	C₂×#95	C₂²×C₁₉	1	2	yes	—
364	C₂×#95	C₂²×C₁₉	1	2	yes	—
365	C₂×#95	C₂²×C₁₉	1	2	yes	—
366	C₂×#95	C₂²×C₁₉	1	2	yes	—
367	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×#95	C₂²×C₁₉	1	2	yes	—
371	C₂×#95	C₂²×C₁₉	1	2	yes	—
372	C₂×#95	C₂²×C₁₉	1	2	yes	—
373	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×C₁₉	—	4	4	no	—
375	C₂×C₁₉	#2409	1	1	yes	characteristic
376	C₂×C₁₉	#2410	1	1	yes	characteristic
377	C₂×C₁₉	#2417	1	1	yes	characteristic
378	C₂×C₁₉	#2616	1	1	yes	characteristic
379	C₂×C₁₉	#2621	1	1	yes	characteristic
380	C₂×C₁₉	#2627	1	1	yes	characteristic
381	C₂×C₁₉	#2677	1	2	yes	—
382	C₂×C₁₉	#2681	1	2	yes	—
383	C₂×C₁₉	#2690	1	2	yes	—
384	C₂×C₁₉	#2704	1	2	yes	—
385	C₂×C₁₉	#2814	1	1	yes	characteristic
386	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
387	C₂²×Q₈	—	2	4	no	—
388	C₂²×Q₈	—	2	2	no	—
389	C₂²×Q₈	—	2	2	no	—
390	C₂²×Q₈	—	2	2	no	—
391	C₂²×Q₈	—	4	2	no	—
392	C₂³×C₄	—	2	4	no	—
393	C₂³×C₄	—	2	2	no	—
394	C₂³×C₄	—	2	2	no	—
395	C₂³×C₄	—	4	2	no	—
396	C₂³×C₄	D₄×C₁₉	1	4	yes	—
397	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
399	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
401	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
402	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
403	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂²⋊Q₈	—	2	32	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	4	no	—
411	C₂×C₄⋊C₄	—	2	4	no	—
412	C₂×C₄⋊C₄	—	2	4	no	—
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄⋊C₄	—	2	4	no	—
416	C₂×C₄⋊C₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	4	no	—
418	C₂×C₄⋊C₄	—	2	4	no	—
419	C₂×C₄⋊C₄	—	2	4	no	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	—	4	2	no	—
422	C₂×C₄⋊C₄	—	4	2	no	—
423	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
424	C₂×C₂²⋊C₄	—	2	4	no	—
425	C₂×C₂²⋊C₄	—	2	2	no	—
426	C₂×C₂²⋊C₄	—	2	2	no	—
427	C₂×C₂²⋊C₄	—	2	4	no	—
428	C₂×C₂²⋊C₄	—	2	4	no	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₂²⋊C₄	—	2	4	no	—
432	C₂×C₂²⋊C₄	—	4	2	no	—
433	C₂×C₂²⋊C₄	—	4	2	no	—
434	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	complemented
435	#95	—	2	2	no	—
436	#95	—	2	2	no	—
437	#95	—	2	2	no	—
438	#95	—	2	4	no	—
439	#95	—	2	4	no	—
440	#95	—	2	4	no	—
441	#95	—	2	4	no	—
442	#95	—	4	2	no	—
443	#95	—	4	2	no	—
444	#95	—	4	2	no	—
445	#95	D₄×C₁₉	1	4	yes	—
446	C₁₉	#16264	1	1	yes	characteristic, direct product factor, Sylow
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	1	no	—
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	—	2	2	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	2	2	no	—
454	C₂⁴	—	2	1	no	—
455	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
456	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
457	C₂⁴	#41×C₁₉	1	2	yes	—
458	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
459	C₂×Q₈	—	2	8	no	—
460	C₂×Q₈	—	4	8	no	—
461	C₂×Q₈	—	4	8	no	—
462	C₂×Q₈	—	4	4	no	—
463	C₂×Q₈	—	4	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	2	8	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	8	no	—
518	C₂²×C₄	—	4	8	no	—
519	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
520	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
521	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
522	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
523	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
524	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
526	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
527	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
528	C₂²×C₄	#41×C₁₉	1	2	yes	—
529	C₄⋊C₄	—	2	8	no	—
530	C₄⋊C₄	—	2	16	no	—
531	C₄⋊C₄	—	4	8	no	—
532	C₄⋊C₄	—	4	8	no	—
533	C₄⋊C₄	—	4	4	no	—
534	C₄⋊C₄	—	4	4	no	—
535	C₂²⋊C₄	—	2	16	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	4	8	no	—
538	C₂²⋊C₄	—	4	4	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
562	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
563	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
564	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
566	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
567	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
568	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
569	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
571	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
572	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
573	Q₈	—	4	16	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	16	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	C₁₉×#120	1	4	yes	—
634	C₂×C₄	C₁₉×#121	1	4	yes	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
647	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
648	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
649	C₂²	C₁₉×#534	1	1	yes	characteristic
650	C₂²	C₁₉×#536	1	1	yes	characteristic
651	C₂²	C₁₉×#536	1	2	yes	—
652	C₂²	C₁₉×#536	1	2	yes	—
653	C₂²	C₁₉×#536	1	1	yes	characteristic
654	C₂²	C₁₉×#537	1	1	yes	characteristic
655	C₂²	C₁₉×#537	1	2	yes	—
656	C₂²	C₁₉×#539	1	2	yes	—
657	C₂²	C₁₉×#541	1	2	yes	—
658	C₂²	C₁₉×#544	1	2	yes	—
659	C₂²	D₄²×C₁₉	1	2	yes	—
660	C₂²	C₁₉×#546	1	2	yes	—
661	C₂²	C₁₉×#546	1	1	yes	characteristic
662	C₂²	C₁₉×#548	1	2	yes	—
663	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
664	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
665	C₂²	C₁₉×#552	1	1	yes	characteristic
666	C₂²	C₁₉×#554	1	1	yes	characteristic
667	C₂²	C₁₉×#562	1	2	yes	—
668	C₂²	C₁₉×#563	1	2	yes	—
669	C₄	—	2	4	no	—
670	C₄	—	2	4	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	4	no	—
675	C₄	—	4	4	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	2	no	—
678	C₄	—	8	1	no	—
679	C₂	—	4	4	no	—
680	C₂	C₁₉×#2409	1	1	yes	characteristic
681	C₂	C₁₉×#2410	1	1	yes	characteristic
682	C₂	C₁₉×#2417	1	1	yes	characteristic
683	C₂	C₁₉×#2616	1	1	yes	characteristic
684	C₂	C₁₉×#2621	1	1	yes	characteristic
685	C₂	C₁₉×#2627	1	1	yes	characteristic
686	C₂	C₁₉×#2677	1	2	yes	—
687	C₂	C₁₉×#2681	1	2	yes	—
688	C₂	C₁₉×#2690	1	2	yes	—
689	C₂	C₁₉×#2704	1	2	yes	—
690	C₂	C₁₉×#2814	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#398	C₂	semidirect
3. C₂×C₁₉×#395	C₂	semidirect
6. C₁₉×#1446	C₂	semidirect
7. C₁₉×#1442	C₂	semidirect
8. C₁₉×#1441	C₂	semidirect
9. C₁₉×#1441	C₂	semidirect
89. C₂×C₂²⋊C₄×C₁₉	Q₈	semidirect
193. #16264	C₁₉	direct (N × H)
291. C₂×#398	C₂×C₁₉	semidirect
292. C₂×#395	C₂×C₁₉	semidirect
295. #1446	C₂×C₁₉	semidirect
296. #1442	C₂×C₁₉	semidirect
297. #1441	C₂×C₁₉	semidirect
298. #1441	C₂×C₁₉	semidirect
434. C₂×C₂²⋊C₄	Q₈×C₁₉	semidirect
446. C₁₉	#16264	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₂×C₁₉×#398	2
C₂×C₁₉×#395	2
C₂×C₁₉×#385	2
C₂×C₁₉×#380	2
C₁₉×#1446	2
C₁₉×#1442	2
C₁₉×#1441	2
C₁₉×#1440	2
C₁₉×#1439	2
#16264	19

Subgroups — C19×#16264 #18022223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16264 #18022223