Subgroups — #18073965

Order 4864.

1006 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562030	C₂	1	2	yes	maximal, complemented
2	#14562026	C₂	1	2	yes	maximal, complemented
3	#14561949	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561949	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926597	C₂²	1	2	yes	—
8	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
9	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
10	#11926270	—	2	1	no	—
11	#11926270	—	2	1	no	—
12	#11926268	—	2	1	no	—
13	#11926268	—	2	1	no	—
14	C₂²×#41×C₁₉	C₄	1	1	yes	characteristic
15	C₁₉×#520	—	2	4	no	—
16	C₁₉×#520	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	—	2	1	no	—
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	C₈	1	4	yes	complemented
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₄×Q₈×C₁₉	—	2	2	no	—
42	C₄×Q₈×C₁₉	—	2	2	no	—
43	C₄×Q₈×C₁₉	—	2	2	no	—
44	C₄×Q₈×C₁₉	D₄	1	4	yes	—
45	C₄×D₄×C₁₉	—	2	8	no	—
46	C₄×D₄×C₁₉	—	2	8	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₄×D₄×C₁₉	—	2	2	no	—
50	C₄×D₄×C₁₉	D₄	1	4	yes	—
51	C₁₉×#117	—	2	8	no	—
52	C₁₉×#117	—	2	2	no	—
53	C₁₉×#117	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	8	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	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
76	C₄×C₁₉⋊C₈	—	2	2	no	—
77	C₄×C₁₉⋊C₈	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	#41×C₁₉	—	2	8	no	—
81	#41×C₁₉	—	2	8	no	—
82	#41×C₁₉	—	2	8	no	—
83	#41×C₁₉	—	2	8	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
88	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
89	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
97	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
98	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	8	2	no	—
113	C₂²×C₄×C₁₉	—	8	2	no	—
114	C₂²×C₄×C₁₉	—	8	2	no	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
119	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₂²⋊C₄×C₁₉	—	2	4	no	—
133	C₂²⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₂²⋊C₄×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	4	no	—
137	C₄²×C₁₉	—	2	1	no	—
138	C₄²×C₁₉	—	2	1	no	—
139	C₄²×C₁₉	—	2	4	no	—
140	C₄²×C₁₉	C₂×D₄	1	2	yes	—
141	C₄²×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×C₁₉⋊C₈	—	4	2	no	—
143	C₂×C₁₉⋊C₈	—	4	2	no	—
144	#8324	—	19	1	no	maximal, Sylow
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
155	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	Q₈×C₁₉	—	2	2	no	—
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	2	no	—
159	Q₈×C₁₉	C₂²⋊C₈	1	4	yes	—
160	D₄×C₁₉	—	2	16	no	—
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	2	2	no	—
163	D₄×C₁₉	—	2	2	no	—
164	D₄×C₁₉	C₂²⋊C₈	1	4	yes	—
165	C₂×C₄×C₁₉	—	2	16	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	8	4	no	—
186	C₂×C₄×C₁₉	—	8	4	no	—
187	C₂×C₄×C₁₉	—	8	4	no	—
188	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#120	1	2	yes	—
192	C₂×C₄×C₁₉	#120	1	2	yes	—
193	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
197	C₁₉⋊C₈	—	8	2	no	—
198	C₁₉⋊C₈	—	8	2	no	—
199	C₂×#520	D₁₉	1	1	yes	characteristic
200	#1479	—	19	2	no	—
201	#1478	—	19	2	no	—
202	#1458	—	19	1	no	—
203	#1458	—	19	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	4	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	4	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	#379	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
218	C₂²×C₁₉	#407	1	1	yes	characteristic
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	4	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
228	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
229	C₄×C₁₉	#407	1	1	yes	characteristic
230	C₄×C₁₉	#407	1	1	yes	characteristic
231	C₂²×#41	Dic₁₉	1	1	yes	characteristic
232	#520	—	2	4	no	—
233	#520	—	2	4	no	—
234	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
236	C₂×C₄×D₄	—	2	1	no	—
237	C₂×C₄×D₄	—	2	1	no	—
238	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
240	C₂×#117	—	2	1	no	—
241	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	—	2	1	no	—
243	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
244	#431	—	19	2	no	—
245	#431	—	19	2	no	—
246	Q₈⋊C₈	—	38	4	no	—
247	D₄⋊C₈	—	38	4	no	—
248	#324	—	38	1	no	—
249	#324	—	38	1	no	—
250	#323	—	38	1	no	—
251	#323	—	38	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	4	2	no	—
255	C₂×C₁₉	—	4	4	no	—
256	C₂×C₁₉	#1779	1	1	yes	characteristic
257	C₂×C₁₉	#1795	1	1	yes	characteristic
258	C₂×C₁₉	#1796	1	1	yes	characteristic
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	C₁₉⋊C₈	1	4	yes	complemented
265	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	C₂²⋊D₁₉	1	4	yes	—
277	C₄×D₄	—	2	8	no	—
278	C₄×D₄	—	2	8	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	C₂²⋊D₁₉	1	4	yes	—
283	#117	—	2	8	no	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	8	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
304	C₄⋊C₈	—	38	2	no	—
305	C₄⋊C₈	—	38	2	no	—
306	C₂²⋊C₈	—	38	2	no	—
307	C₂²⋊C₈	—	38	2	no	—
308	C₄×C₈	—	38	2	no	—
309	C₄×C₈	—	38	2	no	—
310	C₁₉	#8324	1	1	yes	characteristic, complemented, Sylow
311	C₂⁴	—	2	1	no	—
312	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
313	#41	—	2	8	no	—
314	#41	—	2	8	no	—
315	#41	—	2	8	no	—
316	#41	—	2	8	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	C₂×C₁₉⋊C₈	1	2	yes	—
321	C₂×Q₈	#64520	1	2	yes	—
322	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂×C₁₉⋊C₈	1	2	yes	—
330	C₂×D₄	#64520	1	2	yes	—
331	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	—	8	2	no	—
347	C₂²×C₄	—	8	2	no	—
348	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
349	C₂²×C₄	#64520	1	2	yes	—
350	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
356	C₂×C₈	—	76	2	no	—
357	C₂×C₈	—	76	2	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
366	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	4	no	—
375	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
376	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
387	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
392	D₄	—	2	16	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
397	C₂×C₄	—	2	16	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
421	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
422	C₂×C₄	C₂×#64520	1	1	yes	characteristic
423	C₂×C₄	C₂×#64520	1	1	yes	characteristic
424	C₂×C₄	C₂×#64520	1	1	yes	characteristic
425	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
427	C₂×C₄	#10597399	1	2	yes	—
428	C₂×C₄	#10597399	1	2	yes	—
429	C₈	—	152	2	no	—
430	C₈	—	152	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	#11926400	1	1	yes	characteristic
444	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
445	C₂²	#11926508	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
455	C₄	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
456	C₄	#11926508	1	1	yes	characteristic
457	C₄	#11926508	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	4	no	—
461	C₂	—	4	2	no	—
462	C₂	#14563545	1	1	yes	characteristic
463	C₂	#14563605	1	1	yes	characteristic
464	C₂	#14563610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#520	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂²×#41×C₁₉	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#520	D₁₉
hypocenter	C₁₉	#8324
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#520

Complements

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

N	H ≅ G/N	type
1. #14562030	C₂	semidirect
2. #14562026	C₂	semidirect
3. #14561949	C₂	semidirect
4. #14561949	C₂	semidirect
32. C₂×#41×C₁₉	C₈	semidirect
264. C₂×#41	C₁₉⋊C₈	semidirect
310. C₁₉	#8324	semidirect

Maximal subgroups

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

subgroup	index
#14562030	2
#14562026	2
#14561949	2
C₂×C₁₉×#520	2
#8324	19