Subgroups — #18077869

Order 4864.

726 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597343	C₂	1	1	yes	maximal, characteristic
3	#14563612	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926276	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926274	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₉	—	2	1	no	—
9	C₂×#10597343	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₁₉	—	2	1	no	—
16	C₄×C₈×D₁₉	—	2	2	no	—
17	C₄×C₈×D₁₉	—	2	2	no	—
18	#11926449	C₄	1	1	yes	characteristic
19	#11926443	C₄	1	1	yes	characteristic
20	#11926429	—	2	1	no	—
21	#11926418	—	2	1	no	—
22	#11926401	C₄	1	1	yes	characteristic
23	C₄×C₄⋊Dic₁₉	—	2	1	no	—
24	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
25	#11926298	—	2	1	no	—
26	#11926276	—	2	2	no	—
27	#11926274	—	2	2	no	—
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
34	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
42	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	—	2	1	no	—
44	C₂×C₄⋊Dic₁₉	—	2	1	no	—
45	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×Dic₁₉⋊C₄	—	2	1	no	—
47	C₂×C₄×Dic₁₉	—	2	1	no	—
48	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂×C₈×D₁₉	—	2	4	no	—
54	C₂×C₈×D₁₉	—	2	4	no	—
55	C₂×C₈×D₁₉	—	2	4	no	—
56	#10597343	—	2	2	no	—
57	#10597343	C₈	1	4	yes	complemented
58	C₄²×D₁₉	—	2	1	no	—
59	C₄²×D₁₉	—	2	1	no	—
60	C₄²×D₁₉	—	2	1	no	—
61	C₄²×D₁₉	—	2	1	no	—
62	C₄×Dic₃₈	—	2	1	no	—
63	C₄×Dic₃₈	—	2	1	no	—
64	C₄×Dic₃₈	—	2	1	no	—
65	C₄×Dic₃₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₄×C₈×C₁₉	—	2	1	no	—
69	C₄×C₈×C₁₉	D₄	1	2	yes	—
70	C₁₉×#95	—	2	1	no	—
71	C₁₉⋊#95	—	2	1	no	—
72	C₁₉⋊#95	—	2	1	no	—
73	C₁₉⋊#95	—	2	1	no	—
74	C₁₉⋊#95	—	2	1	no	—
75	(C₂×D₁₉)⋊C₈	—	4	2	no	—
76	C₈×Dic₁₉	—	2	4	no	—
77	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
79	C₄×C₁₉⋊C₈	—	2	1	no	—
80	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
81	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₁₉	—	2	1	no	—
88	C₂²×Dic₁₉	—	2	1	no	—
89	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₉	—	2	2	no	—
93	C₂×C₄×D₁₉	—	2	1	no	—
94	C₂×C₄×D₁₉	—	2	1	no	—
95	C₂×C₄×D₁₉	—	2	1	no	—
96	C₂×C₄×D₁₉	—	2	1	no	—
97	C₂×C₄×D₁₉	—	2	1	no	—
98	C₂×C₄×D₁₉	—	2	1	no	—
99	C₂×C₄×D₁₉	—	2	1	no	—
100	C₂×C₄×D₁₉	—	2	1	no	—
101	C₂×C₄×D₁₉	—	2	1	no	—
102	C₂×C₄×D₁₉	—	2	1	no	—
103	C₂×C₄×D₁₉	—	2	2	no	—
104	C₂×C₄×D₁₉	C₂×C₈	1	2	yes	—
105	C₂×C₄×D₁₉	M₁₆	1	2	yes	—
106	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
107	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
108	C₂×Dic₃₈	—	2	1	no	—
109	C₂×Dic₃₈	—	2	1	no	—
110	C₂×Dic₃₈	—	2	1	no	—
111	C₂×Dic₃₈	—	2	1	no	—
112	C₂×Dic₃₈	—	2	1	no	—
113	C₂×Dic₃₈	C₂×C₈	1	2	yes	complemented
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	complemented
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	#41	1	1	yes	characteristic
129	C₄²×C₁₉	#41	1	1	yes	characteristic
130	(C₂×D₁₉)⋊C₄	—	2	4	no	—
131	(C₂×D₁₉)⋊C₄	—	4	2	no	—
132	C₄⋊Dic₁₉	—	2	4	no	—
133	C₄⋊Dic₁₉	—	2	1	no	—
134	C₄⋊Dic₁₉	—	2	1	no	—
135	C₄⋊Dic₁₉	—	4	2	no	—
136	Dic₁₉⋊C₄	—	4	1	no	—
137	Dic₁₉⋊C₄	—	4	1	no	—
138	C₄×Dic₁₉	—	2	1	no	—
139	C₄×Dic₁₉	—	2	1	no	—
140	C₄×Dic₁₉	—	2	1	no	—
141	C₄×Dic₁₉	—	2	1	no	—
142	C₄×Dic₁₉	—	2	1	no	—
143	C₄×Dic₁₉	—	2	1	no	—
144	C₄×Dic₁₉	—	4	1	no	—
145	C₄×Dic₁₉	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	C₂×C₁₉⋊C₈	—	4	1	no	—
151	C₂×C₁₉⋊C₈	—	4	1	no	—
152	C₈×D₁₉	—	2	16	no	—
153	#9071	—	19	1	no	maximal, Sylow
154	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×D₁₉	—	2	1	no	—
156	C₂²×D₁₉	—	2	1	no	—
157	C₂²×D₁₉	—	2	1	no	—
158	C₂²×D₁₉	—	2	1	no	—
159	C₂²×D₁₉	C₂²⋊C₈	1	2	yes	—
160	C₂²×D₁₉	#103	1	2	yes	—
161	C₂²×D₁₉	#104	1	2	yes	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
184	C₂×Dic₁₉	—	2	1	no	—
185	C₂×Dic₁₉	—	2	1	no	—
186	C₂×Dic₁₉	—	2	1	no	—
187	C₂×Dic₁₉	—	2	1	no	—
188	C₂×Dic₁₉	—	2	1	no	—
189	C₂×Dic₁₉	—	2	1	no	—
190	C₂×Dic₁₉	—	2	2	no	—
191	C₂×Dic₁₉	—	4	1	no	—
192	C₂×Dic₁₉	—	4	1	no	—
193	C₂×Dic₁₉	—	4	1	no	—
194	C₂×Dic₁₉	—	4	1	no	—
195	C₂×Dic₁₉	—	4	1	no	—
196	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
197	C₂×Dic₁₉	#103	1	2	yes	—
198	C₂×Dic₁₉	#104	1	2	yes	—
199	C₄×D₁₉	—	2	4	no	—
200	C₄×D₁₉	—	2	4	no	—
201	C₄×D₁₉	—	2	2	no	—
202	C₄×D₁₉	—	2	2	no	—
203	C₄×D₁₉	—	2	2	no	—
204	C₄×D₁₉	—	2	2	no	—
205	C₄×D₁₉	—	2	2	no	—
206	C₄×D₁₉	—	2	2	no	—
207	C₄×D₁₉	—	2	2	no	—
208	C₄×D₁₉	—	2	2	no	—
209	Dic₃₈	—	2	2	no	—
210	Dic₃₈	—	2	2	no	—
211	Dic₃₈	—	4	1	no	—
212	Dic₃₈	—	4	1	no	—
213	C₈×C₁₉	—	2	4	no	—
214	C₈×C₁₉	—	8	1	no	—
215	C₁₉⋊C₈	—	2	4	no	—
216	C₁₉⋊C₈	—	8	1	no	—
217	C₂²×C₄×C₈	—	19	1	no	—
218	C₄×C₂²⋊Q₈	—	19	1	no	—
219	#1797	—	19	1	no	—
220	C₂×Q₈⋊C₈	—	19	1	no	—
221	C₂×Q₈⋊C₈	—	19	1	no	—
222	#1279	—	19	1	no	—
223	#1279	D₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	#386	1	1	yes	characteristic
225	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
226	C₂²×C₁₉	#408	1	1	yes	characteristic
227	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
228	C₂²×C₁₉	#416	1	1	yes	characteristic
229	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
231	C₂×D₁₉	—	2	2	no	—
232	C₂×D₁₉	—	2	2	no	—
233	C₂×D₁₉	—	2	2	no	—
234	C₂×D₁₉	—	2	2	no	—
235	C₂×D₁₉	—	2	2	no	—
236	C₂×D₁₉	—	2	2	no	—
237	C₂×D₁₉	Q₈⋊C₈	1	4	yes	complemented
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	8	1	no	—
242	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
243	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
244	C₄×C₁₉	#435	1	1	yes	characteristic
245	C₄×C₁₉	#435	1	1	yes	characteristic
246	C₄×C₁₉	#465	1	1	yes	characteristic
247	C₄×C₁₉	#465	1	1	yes	characteristic
248	C₄×C₁₉	#467	1	1	yes	characteristic
249	C₄×C₁₉	#467	1	1	yes	characteristic
250	Dic₁₉	—	2	2	no	—
251	Dic₁₉	—	2	2	no	—
252	Dic₁₉	—	2	2	no	—
253	Dic₁₉	—	4	2	no	—
254	Dic₁₉	—	8	1	no	—
255	C₂³×C₈	—	38	1	no	—
256	C₂×C₂²⋊Q₈	—	19	1	no	—
257	C₂×C₄×Q₈	—	19	1	no	—
258	C₂²×C₄²	—	19	1	no	—
259	C₂×C₄⋊C₈	—	19	1	no	—
260	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	—	38	1	no	—
262	C₂×C₄×C₈	—	19	1	no	—
263	C₂×C₄×C₈	—	38	2	no	—
264	C₂×C₄×C₈	—	38	1	no	—
265	C₂×C₄×C₈	—	38	2	no	—
266	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
267	#391	—	19	1	no	—
268	#389	—	19	1	no	—
269	#387	—	38	1	no	—
270	#385	—	38	1	no	—
271	#380	—	19	1	no	—
272	C₄×C₄⋊C₄	—	38	1	no	—
273	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
274	C₄×C₂²⋊C₄	—	38	1	no	—
275	#336	—	38	1	no	—
276	Q₈⋊C₈	—	38	2	no	—
277	Q₈⋊C₈	—	38	2	no	—
278	C₂×C₁₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
279	C₂×C₁₉	#1476	1	1	yes	characteristic
280	C₂×C₁₉	#1493	1	1	yes	characteristic
281	C₂×C₁₉	#1494	1	1	yes	characteristic
282	C₂×C₁₉	#1869	1	1	yes	characteristic
283	C₂×C₁₉	#1892	1	1	yes	characteristic
284	C₂×C₁₉	#1896	1	1	yes	characteristic
285	D₁₉	—	2	4	no	—
286	C₂²×Q₈	—	19	1	no	—
287	C₂³×C₄	—	19	1	no	—
288	C₂³×C₄	—	19	1	no	—
289	C₂³×C₄	—	19	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	38	4	no	—
293	C₂²×C₈	—	38	4	no	—
294	C₂²×C₈	—	38	4	no	—
295	C₂²×C₈	—	38	1	no	—
296	C₂²×C₈	—	38	1	no	—
297	C₂²⋊Q₈	—	19	4	no	—
298	C₂²⋊Q₈	—	38	2	no	—
299	C₄×Q₈	—	38	1	no	—
300	C₄×Q₈	—	38	1	no	—
301	C₄×Q₈	—	38	1	no	—
302	C₄×Q₈	—	38	1	no	—
303	C₂×C₄⋊C₄	—	19	1	no	—
304	C₂×C₄⋊C₄	—	38	1	no	—
305	C₂×C₄⋊C₄	—	38	1	no	—
306	C₂×C₄⋊C₄	—	38	1	no	—
307	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	38	1	no	—
310	C₂×C₂²⋊C₄	—	38	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	19	1	no	—
313	C₂×C₄²	—	19	1	no	—
314	C₂×C₄²	—	19	1	no	—
315	C₂×C₄²	—	38	1	no	—
316	C₂×C₄²	—	38	1	no	—
317	C₂×C₄²	—	38	1	no	—
318	C₂×C₄²	—	38	1	no	—
319	C₂×C₄²	—	38	1	no	—
320	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	38	1	no	—
324	C₄⋊C₈	—	38	1	no	—
325	C₂²⋊C₈	—	76	2	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	—	19	2	no	—
328	C₄×C₈	—	38	4	no	—
329	C₄×C₈	—	38	1	no	—
330	C₄×C₈	D₇₆	1	2	yes	—
331	#95	—	2	1	no	—
332	#95	—	38	1	no	—
333	#95	—	38	1	no	—
334	#95	—	38	1	no	—
335	#95	—	38	1	no	—
336	C₁₉	#9071	1	1	yes	characteristic, complemented, Sylow
337	C₂⁴	—	19	1	no	—
338	C₂×Q₈	—	19	2	no	—
339	C₂×Q₈	—	38	1	no	—
340	C₂×Q₈	—	38	1	no	—
341	C₂×Q₈	—	38	1	no	—
342	C₂×Q₈	—	38	1	no	—
343	C₂×Q₈	—	38	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	19	1	no	—
347	C₂²×C₄	—	19	1	no	—
348	C₂²×C₄	—	19	1	no	—
349	C₂²×C₄	—	19	2	no	—
350	C₂²×C₄	—	19	2	no	—
351	C₂²×C₄	—	19	2	no	—
352	C₂²×C₄	—	19	2	no	—
353	C₂²×C₄	—	38	2	no	—
354	C₂²×C₄	—	38	2	no	—
355	C₂²×C₄	—	38	1	no	—
356	C₂²×C₄	—	38	1	no	—
357	C₂²×C₄	—	38	1	no	—
358	C₂²×C₄	—	38	1	no	—
359	C₂²×C₄	—	38	1	no	—
360	C₂²×C₄	—	38	1	no	—
361	C₂²×C₄	—	38	1	no	—
362	C₂²×C₄	—	38	1	no	—
363	C₂²×C₄	—	38	1	no	—
364	C₂²×C₄	—	38	1	no	—
365	C₂²×C₄	—	38	1	no	—
366	C₂²×C₄	—	38	1	no	—
367	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
368	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	38	16	no	—
377	C₂×C₈	—	38	2	no	—
378	C₂×C₈	—	38	2	no	—
379	C₂×C₈	—	38	2	no	—
380	C₂×C₈	—	76	1	no	—
381	C₂×C₈	—	76	1	no	—
382	C₂×C₈	—	76	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	38	4	no	—
387	C₄⋊C₄	—	38	1	no	—
388	C₄⋊C₄	—	38	1	no	—
389	C₄⋊C₄	—	76	2	no	—
390	C₄⋊C₄	—	76	1	no	—
391	C₄⋊C₄	—	76	1	no	—
392	C₄⋊C₄	C₈×D₁₉	1	2	yes	complemented
393	C₂²⋊C₄	—	38	4	no	—
394	C₂²⋊C₄	—	76	2	no	—
395	C₄²	—	4	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	38	1	no	—
398	C₄²	—	38	1	no	—
399	C₄²	—	38	1	no	—
400	C₄²	—	38	1	no	—
401	C₄²	—	38	1	no	—
402	C₄²	—	38	1	no	—
403	C₄²	—	76	1	no	—
404	C₄²	—	76	1	no	—
405	C₄²	C₂×D₇₆	1	1	yes	characteristic
406	C₄²	#64541	1	1	yes	characteristic
407	C₄²	D₄×D₁₉	1	1	yes	characteristic
408	C₄²	#64545	1	1	yes	characteristic
409	C₂³	—	19	2	no	—
410	C₂³	—	19	2	no	—
411	C₂³	—	19	2	no	—
412	C₂³	—	38	1	no	—
413	C₂³	—	38	1	no	—
414	C₂³	—	38	1	no	—
415	C₂³	—	38	1	no	—
416	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
417	Q₈	—	38	2	no	—
418	Q₈	—	38	2	no	—
419	Q₈	—	76	1	no	—
420	Q₈	—	76	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	19	2	no	—
430	C₂×C₄	—	19	2	no	—
431	C₂×C₄	—	19	2	no	—
432	C₂×C₄	—	38	4	no	—
433	C₂×C₄	—	38	4	no	—
434	C₂×C₄	—	38	1	no	—
435	C₂×C₄	—	38	1	no	—
436	C₂×C₄	—	38	1	no	—
437	C₂×C₄	—	38	1	no	—
438	C₂×C₄	—	38	1	no	—
439	C₂×C₄	—	38	1	no	—
440	C₂×C₄	—	38	2	no	—
441	C₂×C₄	—	38	2	no	—
442	C₂×C₄	—	38	2	no	—
443	C₂×C₄	—	38	2	no	—
444	C₂×C₄	—	38	2	no	—
445	C₂×C₄	—	38	2	no	—
446	C₂×C₄	—	38	2	no	—
447	C₂×C₄	—	38	2	no	—
448	C₂×C₄	—	38	2	no	—
449	C₂×C₄	—	76	1	no	—
450	C₂×C₄	—	76	1	no	—
451	C₂×C₄	—	76	1	no	—
452	C₂×C₄	—	76	1	no	—
453	C₂×C₄	—	76	1	no	—
454	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
455	C₂×C₄	#10597328	1	1	yes	characteristic
456	C₂×C₄	#10597330	1	1	yes	characteristic
457	C₂×C₄	#10597339	1	1	yes	characteristic
458	C₂×C₄	#10597340	1	1	yes	characteristic
459	C₂×C₄	#10597341	1	1	yes	characteristic
460	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
461	C₂×C₄	#10597347	1	1	yes	characteristic
462	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
463	C₂×C₄	#10597353	1	1	yes	characteristic
464	C₂×C₄	#10597358	1	1	yes	characteristic
465	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
466	C₂×C₄	#10597362	1	1	yes	characteristic
467	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
468	C₈	—	2	4	no	—
469	C₈	—	8	1	no	—
470	C₈	—	38	4	no	—
471	C₈	—	152	1	no	—
472	C₂²	—	19	4	no	—
473	C₂²	—	38	2	no	—
474	C₂²	—	38	2	no	—
475	C₂²	—	38	2	no	—
476	C₂²	—	38	2	no	—
477	C₂²	—	38	2	no	—
478	C₂²	—	38	2	no	—
479	C₂²	#11926422	1	1	yes	characteristic
480	C₂²	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
481	C₂²	#11926509	1	1	yes	characteristic
482	C₂²	#103×D₁₉	1	1	yes	characteristic
483	C₂²	#11926537	1	1	yes	characteristic
484	C₂²	#104×D₁₉	1	1	yes	characteristic
485	C₂²	#104×D₁₉	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	8	1	no	—
490	C₄	—	38	2	no	—
491	C₄	—	38	2	no	—
492	C₄	—	38	2	no	—
493	C₄	—	76	2	no	—
494	C₄	—	152	1	no	—
495	C₄	#11926609	1	1	yes	characteristic
496	C₄	C₈×D₇₆	1	1	yes	characteristic
497	C₄	#11926614	1	1	yes	characteristic
498	C₄	#11926617	1	1	yes	characteristic
499	C₄	#11926772	1	1	yes	characteristic
500	C₄	#11926774	1	1	yes	characteristic
501	C₄	#11926784	1	1	yes	characteristic
502	C₄	#11926786	1	1	yes	characteristic
503	C₂	—	38	4	no	—
504	C₂	D₁₉×Q₈⋊C₈	1	1	yes	characteristic
505	C₂	#14562014	1	1	yes	characteristic
506	C₂	#14562088	1	1	yes	characteristic
507	C₂	#14562092	1	1	yes	characteristic
508	C₂	#14563926	1	1	yes	characteristic
509	C₂	#14564057	1	1	yes	characteristic
510	C₂	#14564077	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#9071
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. C₂×#11926276	C₂	semidirect
5. C₂×#11926274	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
57. #10597343	C₈	semidirect
113. C₂×Dic₃₈	C₂×C₈	semidirect
123. C₄⋊C₄×C₁₉	C₂×C₈	semidirect
223. #1279	D₁₉	semidirect
237. C₂×D₁₉	Q₈⋊C₈	semidirect
336. C₁₉	#9071	semidirect
392. C₄⋊C₄	C₈×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×D₁₉	2
C₄×#10597343	2
#14563612	2
C₂×#11926276	2
C₂×#11926274	2
#14561476	2
C₁₉×#1279	2
#9071	19