Subgroups — #18090723

Order 4864.

846 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
6	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₈	—	2	2	no	—
13	C₂×Dic₁₉⋊C₈	—	2	2	no	—
14	C₂×Dic₁₉⋊C₈	—	2	2	no	—
15	C₂×C₁₉⋊#95	C₄	1	1	yes	characteristic
16	C₂×C₁₉⋊#95	C₄	1	1	yes	characteristic
17	C₂×C₁₉⋊#95	C₄	1	1	yes	characteristic
18	C₂×C₁₉⋊#95	C₄	1	1	yes	characteristic
19	#11926299	—	2	2	no	—
20	#11926298	—	2	2	no	—
21	#11926298	—	2	2	no	—
22	#11926298	—	2	2	no	—
23	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#336	—	2	2	no	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	D₄	1	2	yes	—
47	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×C₄×Dic₁₉	—	2	1	no	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₂×C₄×Dic₁₉	—	2	1	no	—
60	C₂×C₄×Dic₁₉	—	2	1	no	—
61	C₂×C₄×Dic₁₉	—	2	1	no	—
62	C₂×C₄×Dic₁₉	—	2	1	no	—
63	C₂×C₄×Dic₁₉	—	2	1	no	—
64	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
65	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	C₂²×C₁₉⋊C₈	—	2	1	no	—
69	C₂²×C₁₉⋊C₈	—	2	1	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
79	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
80	C₁₉⋊#95	—	2	2	no	—
81	C₁₉⋊#95	—	2	2	no	—
82	C₁₉⋊#95	—	2	2	no	—
83	C₁₉⋊#95	C₈	1	4	yes	complemented
84	Dic₁₉⋊C₈	—	2	8	no	—
85	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
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	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
99	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×Dic₁₉	—	2	1	no	—
115	C₂²×Dic₁₉	—	2	1	no	—
116	C₂²×Dic₁₉	—	2	1	no	—
117	C₂²×Dic₁₉	—	2	1	no	—
118	C₂²×Dic₁₉	—	2	1	no	—
119	C₂²×Dic₁₉	—	2	1	no	—
120	C₂²×Dic₁₉	—	2	1	no	—
121	C₂²×Dic₁₉	—	2	1	no	—
122	C₂²×Dic₁₉	—	2	1	no	—
123	C₂²×Dic₁₉	—	2	1	no	—
124	C₂²×Dic₁₉	—	2	1	no	—
125	C₂²×Dic₁₉	—	2	1	no	—
126	C₂²×Dic₁₉	—	2	1	no	—
127	C₂²×Dic₁₉	—	2	1	no	—
128	C₂²×Dic₁₉	—	2	1	no	—
129	C₂²×Dic₁₉	—	2	1	no	—
130	C₂²×Dic₁₉	—	2	1	no	—
131	C₂²×Dic₁₉	—	2	1	no	—
132	C₂²×Dic₁₉	—	2	1	no	—
133	C₂²×Dic₁₉	—	2	1	no	—
134	C₂²×Dic₁₉	—	2	1	no	—
135	C₂²×Dic₁₉	—	2	1	no	—
136	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
137	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
138	C₂²×Dic₁₉	C₂×C₈	1	2	yes	—
139	C₂²×Dic₁₉	C₂×C₈	1	2	yes	—
140	C₂²×Dic₁₉	M₁₆	1	2	yes	—
141	C₂²×Dic₁₉	M₁₆	1	2	yes	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	4	1	no	—
149	C₂×C₈×C₁₉	—	4	1	no	—
150	C₂×C₈×C₁₉	—	4	1	no	—
151	C₂×C₈×C₁₉	—	4	1	no	—
152	C₂×C₈×C₁₉	—	4	1	no	—
153	C₂×C₈×C₁₉	—	4	1	no	—
154	C₂×C₈×C₁₉	—	4	1	no	—
155	C₂×C₈×C₁₉	—	4	1	no	—
156	C₄²×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	—	4	1	no	—
158	C₄²×C₁₉	—	4	1	no	—
159	C₄²×C₁₉	—	4	1	no	—
160	C₄×Dic₁₉	—	2	2	no	—
161	C₄×Dic₁₉	—	2	2	no	—
162	C₄×Dic₁₉	—	2	2	no	—
163	C₄×Dic₁₉	—	2	2	no	—
164	C₄×Dic₁₉	—	4	1	no	—
165	C₄×Dic₁₉	—	4	1	no	—
166	C₄×Dic₁₉	—	4	1	no	—
167	C₄×Dic₁₉	—	4	1	no	—
168	C₂×C₁₉⋊C₈	—	2	2	no	—
169	C₂×C₁₉⋊C₈	—	2	2	no	—
170	C₂×C₁₉⋊C₈	—	2	2	no	—
171	C₂×C₁₉⋊C₈	—	2	2	no	—
172	C₂×C₁₉⋊C₈	—	2	2	no	—
173	C₂×C₁₉⋊C₈	—	2	2	no	—
174	C₂×C₁₉⋊C₈	—	4	1	no	—
175	C₂×C₁₉⋊C₈	—	4	1	no	—
176	C₂×C₁₉⋊C₈	—	4	1	no	—
177	C₂×C₁₉⋊C₈	—	4	1	no	—
178	C₂×C₁₉⋊C₈	—	4	1	no	—
179	C₂×C₁₉⋊C₈	—	4	1	no	—
180	C₂×C₁₉⋊C₈	—	4	1	no	—
181	C₂×C₁₉⋊C₈	—	4	1	no	—
182	#11255	—	19	1	no	maximal, Sylow
183	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂³×C₁₉	#117	1	1	yes	characteristic
185	C₂³×C₁₉	#117	1	1	yes	characteristic
186	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
187	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
190	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
191	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
192	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
193	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
194	C₂³×C₁₉	#131	1	1	yes	characteristic
195	C₂³×C₁₉	#131	1	1	yes	characteristic
196	C₂³×C₁₉	#131	1	1	yes	characteristic
197	C₂³×C₁₉	#131	1	1	yes	characteristic
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
240	C₂×Dic₁₉	—	2	2	no	—
241	C₂×Dic₁₉	—	2	2	no	—
242	C₂×Dic₁₉	—	2	2	no	—
243	C₂×Dic₁₉	—	2	2	no	—
244	C₂×Dic₁₉	—	2	2	no	—
245	C₂×Dic₁₉	—	2	2	no	—
246	C₂×Dic₁₉	—	2	2	no	—
247	C₂×Dic₁₉	—	2	2	no	—
248	C₂×Dic₁₉	—	2	2	no	—
249	C₂×Dic₁₉	—	2	2	no	—
250	C₂×Dic₁₉	—	2	2	no	—
251	C₂×Dic₁₉	—	2	2	no	—
252	C₂×Dic₁₉	—	2	2	no	—
253	C₂×Dic₁₉	—	2	2	no	—
254	C₂×Dic₁₉	—	2	2	no	—
255	C₂×Dic₁₉	—	4	1	no	—
256	C₂×Dic₁₉	—	4	1	no	—
257	C₂×Dic₁₉	—	4	1	no	—
258	C₂×Dic₁₉	—	4	1	no	—
259	C₂×Dic₁₉	—	4	1	no	—
260	C₂×Dic₁₉	—	4	1	no	—
261	C₂×Dic₁₉	—	4	1	no	—
262	C₂×Dic₁₉	—	4	1	no	—
263	C₂×Dic₁₉	—	4	1	no	—
264	C₂×Dic₁₉	—	4	1	no	—
265	C₂×Dic₁₉	—	4	1	no	—
266	C₂×Dic₁₉	—	4	1	no	—
267	C₂×Dic₁₉	C₄⋊C₈	1	4	yes	—
268	C₈×C₁₉	—	4	2	no	—
269	C₈×C₁₉	—	4	2	no	—
270	C₁₉⋊C₈	—	4	2	no	—
271	C₁₉⋊C₈	—	4	2	no	—
272	C₂²×C₄⋊C₈	—	19	1	no	—
273	C₂×#336	—	19	1	no	—
274	C₂×#336	—	19	1	no	—
275	C₂×#336	—	19	1	no	—
276	C₂×#336	—	19	1	no	—
277	C₂×#336	D₁₉	1	1	yes	characteristic
278	C₄×#95	—	19	1	no	—
279	C₂²×C₁₉	#382	1	1	yes	characteristic
280	C₂²×C₁₉	#385	1	1	yes	characteristic
281	C₂²×C₁₉	#387	1	1	yes	characteristic
282	C₂²×C₁₉	#387	1	1	yes	characteristic
283	C₂²×C₁₉	#388	1	1	yes	characteristic
284	C₂²×C₁₉	#388	1	1	yes	characteristic
285	C₂²×C₁₉	#389	1	1	yes	characteristic
286	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
287	C₂²×C₁₉	#423	1	1	yes	characteristic
288	C₂²×C₁₉	#424	1	1	yes	characteristic
289	C₂²×C₁₉	#424	1	1	yes	characteristic
290	C₂²×C₁₉	#431	1	1	yes	characteristic
291	C₂²×C₁₉	#431	1	1	yes	characteristic
292	C₂²×C₁₉	#432	1	1	yes	characteristic
293	C₂²×C₁₉	#432	1	1	yes	characteristic
294	C₂²×C₁₉	#433	1	1	yes	characteristic
295	C₂²×C₁₉	#433	1	1	yes	characteristic
296	C₂²×C₁₉	#433	1	1	yes	characteristic
297	C₂²×C₁₉	#433	1	1	yes	characteristic
298	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
299	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
300	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
301	C₂²×C₁₉	#435	1	1	yes	characteristic
302	C₂²×C₁₉	#435	1	1	yes	characteristic
303	C₂²×C₁₉	#435	1	1	yes	characteristic
304	C₂²×C₁₉	#435	1	1	yes	characteristic
305	C₂²×C₁₉	#435	1	1	yes	characteristic
306	C₂²×C₁₉	#435	1	1	yes	characteristic
307	C₂²×C₁₉	#436	1	1	yes	characteristic
308	C₂²×C₁₉	#436	1	1	yes	characteristic
309	C₂²×C₁₉	#436	1	1	yes	characteristic
310	C₂²×C₁₉	C₈×Q₈	1	1	yes	characteristic
311	C₂²×C₁₉	#446	1	1	yes	characteristic
312	C₂²×C₁₉	#446	1	1	yes	characteristic
313	C₂²×C₁₉	#446	1	1	yes	characteristic
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	#393	1	1	yes	characteristic
317	C₄×C₁₉	#394	1	1	yes	characteristic
318	C₄×C₁₉	#397	1	1	yes	characteristic
319	C₄×C₁₉	#398	1	1	yes	characteristic
320	C₄×C₁₉	#398	1	1	yes	characteristic
321	C₄×C₁₉	#400	1	1	yes	characteristic
322	C₄×C₁₉	#400	1	1	yes	characteristic
323	C₄×C₁₉	#400	1	1	yes	characteristic
324	Dic₁₉	—	2	4	no	—
325	Dic₁₉	—	4	2	no	—
326	Dic₁₉	—	4	2	no	—
327	Dic₁₉	—	4	2	no	—
328	C₂³×C₈	—	19	1	no	—
329	C₂³×C₈	—	19	1	no	—
330	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
331	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
332	C₂²×C₄²	—	19	1	no	—
333	C₂²×C₄²	—	19	1	no	—
334	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
335	C₂×C₄⋊C₈	—	38	2	no	—
336	C₂×C₄⋊C₈	—	38	2	no	—
337	C₂×C₄⋊C₈	—	38	2	no	—
338	C₂×#95	—	19	1	no	—
339	C₂×#95	—	19	1	no	—
340	C₂×#95	—	19	1	no	—
341	C₂×#95	—	19	1	no	—
342	#336	—	2	2	no	—
343	#336	—	38	2	no	—
344	#336	—	38	2	no	—
345	#336	—	38	2	no	—
346	#336	—	38	2	no	—
347	C₂×C₁₉	#1442	1	1	yes	characteristic
348	C₂×C₁₉	#1831	1	1	yes	characteristic
349	C₂×C₁₉	#1832	1	1	yes	characteristic
350	C₂×C₁₉	#1850	1	1	yes	characteristic
351	C₂×C₁₉	#1851	1	1	yes	characteristic
352	C₂×C₁₉	#1916	1	1	yes	characteristic
353	C₂×C₁₉	#1916	1	1	yes	characteristic
354	C₂×C₁₉	#1917	1	1	yes	characteristic
355	C₂×C₁₉	#1917	1	1	yes	characteristic
356	C₂×C₁₉	#1923	1	1	yes	characteristic
357	C₂×C₁₉	#1923	1	1	yes	characteristic
358	C₂×C₁₉	#1924	1	1	yes	characteristic
359	C₂×C₁₉	#1924	1	1	yes	characteristic
360	C₂×C₁₉	#1939	1	1	yes	characteristic
361	C₂×C₁₉	#1940	1	1	yes	characteristic
362	C₂³×C₄	—	19	1	no	—
363	C₂³×C₄	—	19	1	no	—
364	C₂³×C₄	—	19	1	no	—
365	C₂³×C₄	—	19	1	no	—
366	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
367	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
368	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	19	2	no	—
382	C₂²×C₈	—	19	2	no	—
383	C₂²×C₈	—	38	1	no	—
384	C₂²×C₈	—	38	1	no	—
385	C₂²×C₈	—	38	1	no	—
386	C₂²×C₈	—	38	1	no	—
387	C₂²×C₈	—	38	1	no	—
388	C₂²×C₈	—	38	1	no	—
389	C₂²×C₈	—	38	1	no	—
390	C₂²×C₈	—	38	1	no	—
391	C₂²×C₈	—	38	1	no	—
392	C₂²×C₈	—	38	1	no	—
393	C₂²×C₈	—	38	1	no	—
394	C₂²×C₈	—	38	1	no	—
395	C₂²×C₈	Dic₃₈	1	2	yes	—
396	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	19	2	no	—
404	C₂×C₄²	—	19	2	no	—
405	C₂×C₄²	—	38	1	no	—
406	C₂×C₄²	—	38	1	no	—
407	C₂×C₄²	—	38	1	no	—
408	C₂×C₄²	—	38	1	no	—
409	C₂×C₄²	—	38	1	no	—
410	C₂×C₄²	—	38	1	no	—
411	C₂×C₄²	—	38	1	no	—
412	C₂×C₄²	—	38	1	no	—
413	C₂×C₄²	—	38	1	no	—
414	C₂×C₄²	—	38	1	no	—
415	C₄⋊C₈	—	38	8	no	—
416	#95	—	19	4	no	—
417	#95	—	38	2	no	—
418	#95	—	38	2	no	—
419	#95	—	38	2	no	—
420	C₁₉	#11255	1	1	yes	characteristic, complemented, Sylow
421	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	19	2	no	—
435	C₂²×C₄	—	19	2	no	—
436	C₂²×C₄	—	19	2	no	—
437	C₂²×C₄	—	19	2	no	—
438	C₂²×C₄	—	19	2	no	—
439	C₂²×C₄	—	19	2	no	—
440	C₂²×C₄	—	38	1	no	—
441	C₂²×C₄	—	38	1	no	—
442	C₂²×C₄	—	38	1	no	—
443	C₂²×C₄	—	38	1	no	—
444	C₂²×C₄	—	38	1	no	—
445	C₂²×C₄	—	38	1	no	—
446	C₂²×C₄	—	38	1	no	—
447	C₂²×C₄	—	38	1	no	—
448	C₂²×C₄	—	38	1	no	—
449	C₂²×C₄	—	38	1	no	—
450	C₂²×C₄	—	38	1	no	—
451	C₂²×C₄	—	38	1	no	—
452	C₂²×C₄	—	38	1	no	—
453	C₂²×C₄	—	38	1	no	—
454	C₂²×C₄	—	38	1	no	—
455	C₂²×C₄	—	38	1	no	—
456	C₂²×C₄	—	38	1	no	—
457	C₂²×C₄	—	38	1	no	—
458	C₂²×C₄	—	38	1	no	—
459	C₂²×C₄	—	38	1	no	—
460	C₂²×C₄	—	38	1	no	—
461	C₂²×C₄	—	38	1	no	—
462	C₂²×C₄	C₈×D₁₉	1	2	yes	—
463	C₂²×C₄	#64515	1	2	yes	—
464	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
465	C₂²×C₄	#64541	1	1	yes	characteristic
466	C₂²×C₄	#64541	1	1	yes	characteristic
467	C₂²×C₄	#64541	1	1	yes	characteristic
468	C₂²×C₄	#64541	1	1	yes	characteristic
469	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
470	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
471	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
472	C₂²×C₄	#64543	1	1	yes	characteristic
473	C₂²×C₄	#64543	1	1	yes	characteristic
474	C₂²×C₄	#64543	1	1	yes	characteristic
475	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
476	C₂²×C₄	#64545	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	1	no	—
488	C₂×C₈	—	4	1	no	—
489	C₂×C₈	—	4	1	no	—
490	C₂×C₈	—	4	1	no	—
491	C₂×C₈	—	4	1	no	—
492	C₂×C₈	—	38	2	no	—
493	C₂×C₈	—	38	2	no	—
494	C₂×C₈	—	38	2	no	—
495	C₂×C₈	—	38	2	no	—
496	C₂×C₈	—	38	2	no	—
497	C₂×C₈	—	38	2	no	—
498	C₂×C₈	—	76	1	no	—
499	C₂×C₈	—	76	1	no	—
500	C₂×C₈	—	76	1	no	—
501	C₂×C₈	—	76	1	no	—
502	C₂×C₈	—	76	1	no	—
503	C₂×C₈	—	76	1	no	—
504	C₂×C₈	—	76	1	no	—
505	C₂×C₈	—	76	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	—	4	1	no	—
510	C₄²	—	38	2	no	—
511	C₄²	—	38	2	no	—
512	C₄²	—	38	2	no	—
513	C₄²	—	38	2	no	—
514	C₄²	—	76	1	no	—
515	C₄²	—	76	1	no	—
516	C₄²	—	76	1	no	—
517	C₄²	—	76	1	no	—
518	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
519	C₂³	#10597318	1	1	yes	characteristic
520	C₂³	#10597323	1	1	yes	characteristic
521	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
522	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
523	C₂³	#10597339	1	1	yes	characteristic
524	C₂³	C₂×C₈×D₁₉	1	1	yes	characteristic
525	C₂³	C₂×#64515	1	1	yes	characteristic
526	C₂³	#10597347	1	1	yes	characteristic
527	C₂³	#10597347	1	1	yes	characteristic
528	C₂³	M₁₆×D₁₉	1	1	yes	characteristic
529	C₂³	M₁₆×D₁₉	1	1	yes	characteristic
530	C₂³	#10597353	1	1	yes	characteristic
531	C₂³	#10597353	1	1	yes	characteristic
532	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	19	4	no	—
548	C₂×C₄	—	38	2	no	—
549	C₂×C₄	—	38	2	no	—
550	C₂×C₄	—	38	2	no	—
551	C₂×C₄	—	38	2	no	—
552	C₂×C₄	—	38	2	no	—
553	C₂×C₄	—	38	2	no	—
554	C₂×C₄	—	38	2	no	—
555	C₂×C₄	—	38	2	no	—
556	C₂×C₄	—	38	2	no	—
557	C₂×C₄	—	38	2	no	—
558	C₂×C₄	—	38	2	no	—
559	C₂×C₄	—	38	2	no	—
560	C₂×C₄	—	38	2	no	—
561	C₂×C₄	—	38	2	no	—
562	C₂×C₄	—	38	2	no	—
563	C₂×C₄	—	76	1	no	—
564	C₂×C₄	—	76	1	no	—
565	C₂×C₄	—	76	1	no	—
566	C₂×C₄	—	76	1	no	—
567	C₂×C₄	—	76	1	no	—
568	C₂×C₄	—	76	1	no	—
569	C₂×C₄	—	76	1	no	—
570	C₂×C₄	—	76	1	no	—
571	C₂×C₄	—	76	1	no	—
572	C₂×C₄	—	76	1	no	—
573	C₂×C₄	—	76	1	no	—
574	C₂×C₄	—	76	1	no	—
575	C₂×C₄	#10597316	1	1	yes	characteristic
576	C₂×C₄	#10597322	1	1	yes	characteristic
577	C₂×C₄	#10597324	1	1	yes	characteristic
578	C₂×C₄	#10597324	1	1	yes	characteristic
579	C₂×C₄	#10597325	1	1	yes	characteristic
580	C₂×C₄	#10597329	1	1	yes	characteristic
581	C₂×C₄	#10597329	1	1	yes	characteristic
582	C₂×C₄	#10597330	1	1	yes	characteristic
583	C₂×C₄	#10597330	1	1	yes	characteristic
584	C₂×C₄	#10597331	1	1	yes	characteristic
585	C₂×C₄	#10597331	1	1	yes	characteristic
586	C₂×C₄	#10597331	1	1	yes	characteristic
587	C₂×C₄	#10597334	1	1	yes	characteristic
588	C₂×C₄	#10597335	1	1	yes	characteristic
589	C₂×C₄	#10597335	1	1	yes	characteristic
590	C₂×C₄	#10597335	1	1	yes	characteristic
591	C₂×C₄	#10597336	1	1	yes	characteristic
592	C₂×C₄	#10597340	1	1	yes	characteristic
593	C₂×C₄	#10597340	1	1	yes	characteristic
594	C₂×C₄	#10597342	1	1	yes	characteristic
595	C₂×C₄	#10597344	1	1	yes	characteristic
596	C₂×C₄	#10597344	1	1	yes	characteristic
597	C₂×C₄	#10597370	1	1	yes	characteristic
598	C₂×C₄	#10597375	1	1	yes	characteristic
599	C₂×C₄	#10597382	1	1	yes	characteristic
600	C₂×C₄	#10597383	1	1	yes	characteristic
601	C₂×C₄	#10597385	1	1	yes	characteristic
602	C₂×C₄	#10597392	1	1	yes	characteristic
603	C₈	—	4	2	no	—
604	C₈	—	4	2	no	—
605	C₈	—	76	2	no	—
606	C₈	—	76	2	no	—
607	C₂²	#11926408	1	1	yes	characteristic
608	C₂²	#11926415	1	1	yes	characteristic
609	C₂²	#11926427	1	1	yes	characteristic
610	C₂²	#11926428	1	1	yes	characteristic
611	C₂²	#11926433	1	1	yes	characteristic
612	C₂²	#11926438	1	1	yes	characteristic
613	C₂²	#11926441	1	1	yes	characteristic
614	C₂²	C₄⋊C₈×D₁₉	1	1	yes	characteristic
615	C₂²	#11926566	1	1	yes	characteristic
616	C₂²	#11926569	1	1	yes	characteristic
617	C₂²	#11926569	1	1	yes	characteristic
618	C₂²	#11926594	1	1	yes	characteristic
619	C₂²	#11926595	1	1	yes	characteristic
620	C₂²	#11926598	1	1	yes	characteristic
621	C₂²	#11926599	1	1	yes	characteristic
622	C₂²	#11926602	1	1	yes	characteristic
623	C₂²	#11926602	1	1	yes	characteristic
624	C₂²	#11926603	1	1	yes	characteristic
625	C₂²	#11926606	1	1	yes	characteristic
626	C₂²	(C₂²⋊D₁₉)⋊C₈	1	1	yes	characteristic
627	C₂²	C₈×C₂²⋊D₁₉	1	1	yes	characteristic
628	C₂²	#11926609	1	1	yes	characteristic
629	C₂²	#11926612	1	1	yes	characteristic
630	C₂²	#11926613	1	1	yes	characteristic
631	C₂²	#11926614	1	1	yes	characteristic
632	C₂²	#11926614	1	1	yes	characteristic
633	C₂²	#11926615	1	1	yes	characteristic
634	C₂²	#11926618	1	1	yes	characteristic
635	C₂²	#11926619	1	1	yes	characteristic
636	C₂²	#11926620	1	1	yes	characteristic
637	C₂²	#11926621	1	1	yes	characteristic
638	C₂²	C₈×Dic₃₈	1	1	yes	characteristic
639	C₂²	#11926672	1	1	yes	characteristic
640	C₂²	#11926672	1	1	yes	characteristic
641	C₂²	#11926674	1	1	yes	characteristic
642	C₄	—	4	2	no	—
643	C₄	—	4	2	no	—
644	C₄	—	38	4	no	—
645	C₄	—	76	2	no	—
646	C₄	—	76	2	no	—
647	C₄	—	76	2	no	—
648	C₄	#11926456	1	1	yes	characteristic
649	C₄	#11926459	1	1	yes	characteristic
650	C₄	#11926473	1	1	yes	characteristic
651	C₄	#11926477	1	1	yes	characteristic
652	C₄	#11926478	1	1	yes	characteristic
653	C₄	#11926482	1	1	yes	characteristic
654	C₄	#11926485	1	1	yes	characteristic
655	C₄	#11926486	1	1	yes	characteristic
656	C₂	#14561893	1	1	yes	characteristic
657	C₂	#14563750	1	1	yes	characteristic
658	C₂	#14563753	1	1	yes	characteristic
659	C₂	#14563811	1	1	yes	characteristic
660	C₂	#14563816	1	1	yes	characteristic
661	C₂	#14564191	1	1	yes	characteristic
662	C₂	#14564192	1	1	yes	characteristic
663	C₂	#14564198	1	1	yes	characteristic
664	C₂	#14564199	1	1	yes	characteristic
665	C₂	#14564239	1	1	yes	characteristic
666	C₂	#14564244	1	1	yes	characteristic
667	C₂	#14564246	1	1	yes	characteristic
668	C₂	#14564251	1	1	yes	characteristic
669	C₂	#14564352	1	1	yes	characteristic
670	C₂	#14564357	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Fitting	C₂×C₁₉×#336	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#336	D₁₉
hypocenter	C₁₉	#11255
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
83. C₁₉⋊#95	C₈	semidirect
420. C₁₉	#11255	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₉⋊C₈	2
C₂×#11926299	2
C₂×#11926298	2
C₄×C₁₉⋊#95	2
C₂×C₁₉×#336	2
#11255	19