Subgroups — #18088709

Order 4864.

750 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926500	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926309	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
5	#14563332	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926500	—	2	2	no	—
13	#11926500	—	2	2	no	—
14	C₂×#10597260	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
16	#11926309	C₄	1	4	yes	complemented
17	#11926303	—	2	2	no	—
18	#11926303	—	2	2	no	—
19	#11926299	—	2	1	no	—
20	#11926299	—	2	1	no	—
21	#11926298	C₄	1	4	yes	complemented
22	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₁₉×#427	—	2	2	no	—
26	C₁₉×#427	—	2	2	no	—
27	C₂×C₁₉×#107	C₄	1	2	yes	complemented
28	C₂×C₁₉×#106	C₄	1	2	yes	complemented
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂³×Dic₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#117	—	2	1	no	—
40	C₁₉×#117	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	D₄	1	2	yes	—
46	C₁₉×#117	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄×Dic₁₉	—	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	C₂×C₄	1	2	yes	—
59	C₂×#64520	—	2	1	no	—
60	C₂×#64520	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	C₂×C₄	1	2	yes	—
68	C₂×#64520	C₂×C₄	1	2	yes	—
69	C₂×#64520	D₄	1	2	yes	—
70	C₂×#64520	Q₈	1	2	yes	—
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	C₂×C₄	1	2	yes	—
78	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
79	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
80	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
81	C₁₉×#107	—	2	4	no	—
82	C₁₉×#106	—	2	4	no	—
83	#10597260	—	2	4	no	—
84	C₄×C₁₉⋊C₈	—	2	4	no	—
85	C₂⁴×C₁₉	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×Dic₁₉	—	2	4	no	—
103	C₂²×Dic₁₉	—	2	2	no	—
104	C₂²×Dic₁₉	—	4	2	no	—
105	C₂²×Dic₁₉	—	4	1	no	—
106	C₂²×Dic₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	C₄²	1	2	yes	—
116	C₂×C₈×C₁₉	C₄²	1	2	yes	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
121	C₂²⋊C₄×C₁₉	—	2	2	no	—
122	C₂²⋊C₄×C₁₉	—	2	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	2	2	no	—
126	C₄²×C₁₉	—	2	2	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	—	4	1	no	—
129	C₄×Dic₁₉	—	2	2	no	—
130	C₄×Dic₁₉	—	2	2	no	—
131	C₄×Dic₁₉	—	4	1	no	—
132	C₄×Dic₁₉	—	4	1	no	—
133	#64520	—	2	2	no	—
134	#64520	—	2	2	no	—
135	#64520	—	2	2	no	—
136	#64520	—	2	2	no	—
137	#64520	—	2	2	no	—
138	#64520	—	4	1	no	—
139	#64520	—	4	1	no	—
140	#64520	C₄⋊C₄	1	4	yes	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	2	2	no	—
143	C₂×C₁₉⋊C₈	—	2	2	no	—
144	C₂×C₁₉⋊C₈	—	2	1	no	—
145	C₂×C₁₉⋊C₈	—	2	2	no	—
146	C₂×C₁₉⋊C₈	—	2	1	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	2	2	no	—
150	C₂×C₁₉⋊C₈	—	2	1	no	—
151	C₂×C₁₉⋊C₈	—	2	1	no	—
152	C₂×C₁₉⋊C₈	—	2	2	no	—
153	C₂×C₁₉⋊C₈	—	4	1	no	—
154	C₂×C₁₉⋊C₈	—	4	1	no	—
155	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
156	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
157	#10909	—	19	1	no	maximal, Sylow
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	#117	1	1	yes	characteristic
161	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
163	C₂³×C₁₉	#121	1	1	yes	characteristic
164	C₂³×C₁₉	#123	1	1	yes	characteristic
165	C₂³×C₁₉	#125	1	1	yes	characteristic
166	C₂³×C₁₉	#126	1	1	yes	characteristic
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
201	C₂×Dic₁₉	—	2	4	no	—
202	C₂×Dic₁₉	—	4	4	no	—
203	C₂×Dic₁₉	—	4	4	no	—
204	C₂×Dic₁₉	—	4	2	no	—
205	C₂×Dic₁₉	—	4	2	no	—
206	C₈×C₁₉	—	2	2	no	—
207	C₈×C₁₉	—	2	2	no	—
208	C₁₉⋊C₈	—	2	2	no	—
209	C₁₉⋊C₈	—	2	2	no	—
210	C₁₉⋊C₈	—	2	4	no	—
211	C₁₉⋊C₈	—	4	2	no	—
212	C₂×#427	D₁₉	1	1	yes	characteristic
213	C₂×#405	—	19	1	no	—
214	C₂×#341	—	19	1	no	—
215	C₂×#339	—	19	1	no	—
216	C₂×#339	—	19	1	no	—
217	#1729	—	19	1	no	—
218	C₂×#336	—	19	1	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×C₁₉	#386	1	1	yes	characteristic
229	C₂²×C₁₉	#387	1	1	yes	characteristic
230	C₂²×C₁₉	#387	1	1	yes	characteristic
231	C₂²×C₁₉	#387	1	1	yes	characteristic
232	C₂²×C₁₉	#388	1	1	yes	characteristic
233	C₂²×C₁₉	#389	1	1	yes	characteristic
234	C₂²×C₁₉	#443	1	2	yes	—
235	C₂²×C₁₉	#444	1	2	yes	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	—	8	2	no	—
238	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
239	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₁₉	#385	1	1	yes	characteristic
241	C₄×C₁₉	#385	1	1	yes	characteristic
242	C₄×C₁₉	#387	1	1	yes	characteristic
243	C₄×C₁₉	#388	1	1	yes	characteristic
244	C₄×C₁₉	#389	1	1	yes	characteristic
245	C₄×C₁₉	#391	1	1	yes	characteristic
246	Dic₁₉	—	4	4	no	—
247	C₂²×M₁₆	—	19	1	no	—
248	C₂²×M₁₆	—	19	1	no	—
249	C₂³×C₈	—	19	1	no	—
250	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
251	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
252	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
253	C₂²×C₄²	—	19	1	no	—
254	#427	—	2	2	no	—
255	#427	—	2	2	no	—
256	C₂×#107	Dic₁₉	1	2	yes	complemented
257	C₂×#106	Dic₁₉	1	2	yes	complemented
258	#405	—	38	2	no	—
259	#405	—	38	2	no	—
260	C₂×#97	—	38	1	no	—
261	C₂×C₄×C₈	—	38	1	no	—
262	#341	—	19	4	no	—
263	#339	—	38	2	no	—
264	#339	—	38	2	no	—
265	#336	—	19	4	no	—
266	#336	—	38	1	no	—
267	#336	—	38	1	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	#1436	1	1	yes	characteristic
273	C₂×C₁₉	#1772	1	1	yes	characteristic
274	C₂×C₁₉	#1773	1	1	yes	characteristic
275	C₂×C₁₉	#1876	1	2	yes	—
276	C₂×C₁₉	#1922	1	2	yes	—
277	C₂³×C₄	—	38	1	no	—
278	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
279	C₂×M₁₆	—	19	2	no	—
280	C₂×M₁₆	—	19	2	no	—
281	C₂×M₁₆	—	19	2	no	—
282	C₂×M₁₆	—	19	2	no	—
283	C₂×M₁₆	—	38	1	no	—
284	C₂×M₁₆	—	38	1	no	—
285	C₂×M₁₆	—	38	1	no	—
286	C₂×M₁₆	—	38	1	no	—
287	C₂×M₁₆	—	38	1	no	—
288	C₂×M₁₆	—	38	1	no	—
289	C₂×M₁₆	—	38	1	no	—
290	C₂×M₁₆	—	38	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	—	19	2	no	—
296	C₂²×C₈	—	19	1	no	—
297	C₂²×C₈	—	19	1	no	—
298	C₂²×C₈	—	19	2	no	—
299	C₂²×C₈	—	38	1	no	—
300	C₂²×C₈	—	38	1	no	—
301	C₂²×C₈	—	38	1	no	—
302	C₂²×C₈	—	38	1	no	—
303	C₂²×C₈	—	38	1	no	—
304	C₂²×C₈	—	38	1	no	—
305	C₂²×C₈	C₄×D₁₉	1	2	yes	—
306	C₂²×C₈	C₄×D₁₉	1	2	yes	—
307	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
308	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
309	#117	—	2	1	no	—
310	#117	—	2	1	no	—
311	#117	—	2	1	no	—
312	#117	—	2	1	no	—
313	#117	—	2	1	no	—
314	#117	—	2	1	no	—
315	#117	C₂²⋊D₁₉	1	2	yes	—
316	#117	C₂²⋊D₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
318	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	19	2	no	—
324	C₂×C₄²	—	38	1	no	—
325	C₂×C₄²	—	38	1	no	—
326	C₂×C₄²	—	38	1	no	—
327	C₂×C₄²	—	38	1	no	—
328	C₂×C₄²	—	38	1	no	—
329	#107	—	2	4	no	—
330	#106	—	2	4	no	—
331	#97	—	38	4	no	—
332	C₄×C₈	—	38	4	no	—
333	C₁₉	#10909	1	1	yes	characteristic, complemented, Sylow
334	C₂⁴	#64543	1	1	yes	characteristic
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	38	4	no	—
338	C₂²×C₄	—	38	2	no	—
339	C₂²×C₄	—	76	2	no	—
340	C₂²×C₄	—	76	1	no	—
341	C₂²×C₄	—	76	1	no	—
342	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
344	C₂²×C₄	#64541	1	1	yes	characteristic
345	C₂²×C₄	#64541	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
348	C₂²×C₄	#64543	1	1	yes	characteristic
349	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
350	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
351	C₂²×C₄	#64545	1	1	yes	characteristic
352	C₂²×C₄	#64545	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	M₁₆	—	19	4	no	—
357	M₁₆	—	38	2	no	—
358	M₁₆	—	38	2	no	—
359	M₁₆	—	38	2	no	—
360	M₁₆	—	38	2	no	—
361	M₁₆	—	38	2	no	—
362	M₁₆	—	76	1	no	—
363	M₁₆	—	76	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	19	2	no	—
373	C₂×C₈	—	19	2	no	—
374	C₂×C₈	—	38	1	no	—
375	C₂×C₈	—	38	2	no	—
376	C₂×C₈	—	38	1	no	—
377	C₂×C₈	—	38	2	no	—
378	C₂×C₈	—	38	2	no	—
379	C₂×C₈	—	38	2	no	—
380	C₂×C₈	—	38	1	no	—
381	C₂×C₈	—	38	1	no	—
382	C₂×C₈	—	38	2	no	—
383	C₂×C₈	—	38	2	no	—
384	C₂×C₈	—	38	2	no	—
385	C₂×C₈	—	38	2	no	—
386	C₂×C₈	—	76	1	no	—
387	C₂×C₈	—	76	1	no	—
388	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
389	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	38	2	no	—
403	C₄²	—	38	2	no	—
404	C₄²	—	76	1	no	—
405	C₄²	—	76	1	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	#10597333	1	1	yes	characteristic
409	C₂³	#10597335	1	1	yes	characteristic
410	C₂³	#10597338	1	1	yes	characteristic
411	C₂³	#10597344	1	1	yes	characteristic
412	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
413	C₂³	#10597381	1	1	yes	characteristic
414	C₂³	#10597385	1	1	yes	characteristic
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	38	4	no	—
422	C₂×C₄	—	76	4	no	—
423	C₂×C₄	—	76	4	no	—
424	C₂×C₄	—	76	2	no	—
425	C₂×C₄	—	76	2	no	—
426	C₂×C₄	#10597333	1	1	yes	characteristic
427	C₂×C₄	#10597335	1	1	yes	characteristic
428	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
429	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
430	C₂×C₄	#10597338	1	1	yes	characteristic
431	C₂×C₄	#10597339	1	1	yes	characteristic
432	C₂×C₄	#10597339	1	1	yes	characteristic
433	C₂×C₄	#10597340	1	1	yes	characteristic
434	C₂×C₄	#10597340	1	1	yes	characteristic
435	C₂×C₄	#10597342	1	1	yes	characteristic
436	C₂×C₄	#10597342	1	1	yes	characteristic
437	C₂×C₄	#10597344	1	1	yes	characteristic
438	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
439	C₂×C₄	#10597372	1	1	yes	characteristic
440	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
441	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
442	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
444	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
445	C₂×C₄	#10597383	1	1	yes	characteristic
446	C₂×C₄	#10597385	1	1	yes	characteristic
447	C₂×C₄	#10597390	1	1	yes	characteristic
448	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
449	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
450	C₂×C₄	#10597392	1	1	yes	characteristic
451	C₂×C₄	#10597392	1	1	yes	characteristic
452	C₂×C₄	#10597393	1	1	yes	characteristic
453	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	38	2	no	—
457	C₈	—	38	2	no	—
458	C₈	—	38	4	no	—
459	C₈	—	76	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
469	C₂²	#11926424	1	1	yes	characteristic
470	C₂²	#11926425	1	1	yes	characteristic
471	C₂²	#11926425	1	1	yes	characteristic
472	C₂²	#11926430	1	1	yes	characteristic
473	C₂²	#11926434	1	1	yes	characteristic
474	C₂²	#11926439	1	1	yes	characteristic
475	C₂²	#11926661	1	2	yes	—
476	C₂²	#11926666	1	2	yes	—
477	C₄	—	4	4	no	—
478	C₄	—	8	2	no	—
479	C₄	—	76	4	no	—
480	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
481	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
482	C₄	#11926415	1	1	yes	characteristic
483	C₄	#11926415	1	1	yes	characteristic
484	C₄	#11926430	1	1	yes	characteristic
485	C₄	#11926434	1	1	yes	characteristic
486	C₄	#11926439	1	1	yes	characteristic
487	C₄	#11926451	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	#14561867	1	1	yes	characteristic
493	C₂	#14563516	1	1	yes	characteristic
494	C₂	#14563521	1	1	yes	characteristic
495	C₂	#14563964	1	2	yes	—
496	C₂	#14564236	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#427	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#427	D₁₉
hypocenter	C₁₉	#10909
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
16. #11926309	C₄	semidirect
21. #11926298	C₄	semidirect
27. C₂×C₁₉×#107	C₄	semidirect
28. C₂×C₁₉×#106	C₄	semidirect
256. C₂×#107	Dic₁₉	semidirect
257. C₂×#106	Dic₁₉	semidirect
333. C₁₉	#10909	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926500	2
C₂×#11926309	2
C₂×#11926303	2
#14563332	2
C₂×#11926298	2
C₂×C₁₉×#427	2
#10909	19