Subgroups — #18077887

Order 4864.

606 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926595	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597392	C₂	1	1	yes	maximal, characteristic
3	#14563612	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561475	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597392	C₄	1	1	yes	characteristic
9	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
10	#11926595	—	2	2	no	—
11	#11926595	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
15	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926451	C₄	1	1	yes	characteristic
18	#11926440	C₄	1	1	yes	characteristic
19	#11926425	—	2	1	no	—
20	#11926415	—	2	1	no	—
21	#11926401	C₄	1	1	yes	characteristic
22	C₄×Dic₁₉⋊C₄	—	2	1	no	—
23	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
25	#11926298	—	2	1	no	—
26	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×Q₈⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₄×Q₈×C₁₉	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	—	2	1	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
45	#10597392	—	2	2	no	—
46	#10597392	—	2	2	no	—
47	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
48	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×Dic₁₉⋊C₄	—	2	1	no	—
52	C₂×Dic₁₉⋊C₄	—	2	1	no	—
53	C₂×C₄×Dic₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
57	C₂²×C₁₉⋊C₈	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	C₄²×D₁₉	—	2	1	no	—
60	C₄²×D₁₉	—	2	1	no	—
61	C₄²×D₁₉	—	2	1	no	—
62	C₄²×D₁₉	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₄×C₈×C₁₉	—	2	1	no	—
66	C₄×C₈×C₁₉	D₄	1	2	yes	—
67	C₁₉⋊#95	—	2	1	no	—
68	C₁₉⋊#95	—	2	1	no	—
69	C₁₉⋊#95	—	2	1	no	—
70	C₁₉⋊#95	—	2	1	no	—
71	C₁₉⋊#95	—	2	1	no	—
72	(C₂×D₁₉)⋊C₈	—	2	4	no	—
73	(C₂×D₁₉)⋊C₈	—	4	2	no	—
74	Dic₁₉⋊C₈	—	2	4	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄×C₁₉⋊C₈	—	2	1	no	—
78	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
79	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×Dic₁₉	—	2	1	no	—
92	C₂²×Dic₁₉	—	2	1	no	—
93	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
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	1	no	—
104	C₂×C₄×D₁₉	—	2	1	no	—
105	C₂×C₄×D₁₉	—	2	1	no	—
106	C₂×C₄×D₁₉	—	2	1	no	—
107	C₂×C₄×D₁₉	—	2	1	no	—
108	C₂×C₄×D₁₉	—	4	1	no	—
109	C₂×C₄×D₁₉	—	4	1	no	—
110	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
111	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₄²×C₁₉	—	4	1	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	#41	1	1	yes	characteristic
127	C₄²×C₁₉	#41	1	1	yes	characteristic
128	(C₂×D₁₉)⋊C₄	—	2	4	no	—
129	(C₂×D₁₉)⋊C₄	—	4	2	no	—
130	C₄⋊Dic₁₉	—	2	1	no	—
131	C₄⋊Dic₁₉	—	2	1	no	—
132	C₄⋊Dic₁₉	—	2	1	no	—
133	C₄⋊Dic₁₉	M₁₆	1	2	yes	—
134	Dic₁₉⋊C₄	—	2	4	no	—
135	Dic₁₉⋊C₄	—	4	2	no	—
136	C₄×Dic₁₉	—	2	1	no	—
137	C₄×Dic₁₉	—	2	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	—	4	1	no	—
143	C₄×Dic₁₉	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	2	2	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	#9075	—	19	1	no	maximal, Sylow
151	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×D₁₉	—	2	1	no	—
153	C₂²×D₁₉	—	2	1	no	—
154	C₂²×D₁₉	—	2	1	no	—
155	C₂²×D₁₉	—	2	1	no	—
156	C₂²×D₁₉	—	2	1	no	—
157	C₂²×D₁₉	—	2	1	no	—
158	C₂²×D₁₉	#103	1	2	yes	—
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	4	1	no	—
162	Q₈×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
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	—	2	1	no	—
192	C₂×Dic₁₉	—	2	1	no	—
193	C₂×Dic₁₉	—	2	1	no	—
194	C₂×Dic₁₉	—	4	1	no	—
195	C₂×Dic₁₉	—	4	1	no	—
196	C₂×Dic₁₉	—	4	1	no	—
197	C₂×Dic₁₉	—	4	1	no	—
198	C₂×Dic₁₉	—	4	1	no	—
199	C₂×Dic₁₉	#103	1	2	yes	—
200	C₄×D₁₉	—	2	2	no	—
201	C₄×D₁₉	—	2	2	no	—
202	C₄×D₁₉	—	2	2	no	—
203	C₄×D₁₉	—	2	2	no	—
204	C₄×D₁₉	—	4	2	no	—
205	C₄×D₁₉	—	4	2	no	—
206	C₄×D₁₉	—	4	1	no	—
207	C₄×D₁₉	—	4	1	no	—
208	C₄×D₁₉	—	4	1	no	—
209	C₄×D₁₉	—	4	1	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₈×C₁₉	—	8	1	no	—
212	C₁₉⋊C₈	—	4	2	no	—
213	C₁₉⋊C₈	—	8	1	no	—
214	C₂×#431	—	19	1	no	—
215	C₄×C₂²⋊Q₈	—	19	1	no	—
216	#1797	—	19	1	no	—
217	C₂×Q₈⋊C₈	—	19	1	no	—
218	C₂×Q₈⋊C₈	D₁₉	1	1	yes	characteristic, complemented
219	#1279	—	19	1	no	—
220	#1279	—	19	1	no	—
221	C₂²×C₁₉	#386	1	1	yes	characteristic
222	C₂²×C₁₉	#407	1	1	yes	characteristic
223	C₂²×C₁₉	#408	1	1	yes	characteristic
224	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
225	C₂²×C₁₉	#416	1	1	yes	characteristic
226	C₂²×C₁₉	#421	1	1	yes	characteristic
227	C₂²×C₁₉	#421	1	1	yes	characteristic
228	C₂×D₁₉	—	2	2	no	—
229	C₂×D₁₉	—	2	2	no	—
230	C₂×D₁₉	—	2	2	no	—
231	C₂×D₁₉	—	4	1	no	—
232	C₂×D₁₉	—	4	1	no	—
233	C₂×D₁₉	—	4	1	no	—
234	C₂×D₁₉	—	4	1	no	—
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	8	1	no	—
239	C₄×C₁₉	#435	1	1	yes	characteristic
240	C₄×C₁₉	#435	1	1	yes	characteristic
241	C₄×C₁₉	#436	1	1	yes	characteristic
242	C₄×C₁₉	#436	1	1	yes	characteristic
243	C₄×C₁₉	#465	1	1	yes	characteristic
244	C₄×C₁₉	#465	1	1	yes	characteristic
245	C₄×C₁₉	#467	1	1	yes	characteristic
246	C₄×C₁₉	#467	1	1	yes	characteristic
247	Dic₁₉	—	2	2	no	—
248	Dic₁₉	—	4	1	no	—
249	Dic₁₉	—	4	1	no	—
250	Dic₁₉	—	4	2	no	—
251	Dic₁₉	—	8	1	no	—
252	C₂×C₂²⋊Q₈	—	19	1	no	—
253	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
254	C₂²×C₄²	—	19	1	no	—
255	#431	—	38	2	no	—
256	#431	—	38	2	no	—
257	C₂×C₄⋊C₈	—	19	1	no	—
258	C₂×C₄⋊C₈	—	38	1	no	—
259	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
260	C₂×C₂²⋊C₈	—	38	1	no	—
261	C₂×C₂²⋊C₈	—	38	1	no	—
262	C₂×C₄×C₈	—	19	1	no	—
263	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
264	#391	—	19	1	no	—
265	#389	—	19	1	no	—
266	#387	—	38	1	no	—
267	#385	—	38	1	no	—
268	#380	—	19	1	no	—
269	C₄×C₄⋊C₄	—	19	1	no	—
270	C₄×C₄⋊C₄	—	38	1	no	—
271	C₄×C₂²⋊C₄	—	38	1	no	—
272	#336	—	38	1	no	—
273	Q₈⋊C₈	—	2	2	no	—
274	Q₈⋊C₈	—	38	2	no	—
275	C₂×C₁₉	#1481	1	1	yes	characteristic
276	C₂×C₁₉	#1482	1	1	yes	characteristic
277	C₂×C₁₉	#1487	1	1	yes	characteristic
278	C₂×C₁₉	#1488	1	1	yes	characteristic
279	C₂×C₁₉	#1870	1	1	yes	characteristic
280	C₂×C₁₉	#1892	1	1	yes	characteristic
281	C₂×C₁₉	#1897	1	1	yes	characteristic
282	D₁₉	—	4	2	no	—
283	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
284	C₂³×C₄	—	19	1	no	—
285	C₂³×C₄	—	19	1	no	—
286	C₂³×C₄	—	19	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	38	1	no	—
290	C₂²×C₈	—	38	1	no	—
291	C₂²⋊Q₈	—	38	2	no	—
292	C₂²⋊Q₈	—	38	2	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	19	1	no	—
299	C₂×C₄⋊C₄	—	19	1	no	—
300	C₂×C₄⋊C₄	—	38	1	no	—
301	C₂×C₄⋊C₄	—	38	1	no	—
302	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	38	1	no	—
304	C₂×C₂²⋊C₄	—	38	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	19	1	no	—
307	C₂×C₄²	—	19	1	no	—
308	C₂×C₄²	—	19	1	no	—
309	C₂×C₄²	—	38	1	no	—
310	C₂×C₄²	—	38	1	no	—
311	C₂×C₄²	—	38	1	no	—
312	C₂×C₄²	—	38	1	no	—
313	C₂×C₄²	—	38	1	no	—
314	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	38	4	no	—
318	C₄⋊C₈	—	38	1	no	—
319	C₄⋊C₈	—	38	1	no	—
320	C₂²⋊C₈	—	38	4	no	—
321	C₂²⋊C₈	—	76	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	19	2	no	—
324	C₄×C₈	—	38	1	no	—
325	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
326	#95	—	38	1	no	—
327	#95	—	38	1	no	—
328	#95	—	38	1	no	—
329	#95	—	38	1	no	—
330	#95	—	38	1	no	—
331	C₁₉	#9075	1	1	yes	characteristic, complemented, Sylow
332	C₂⁴	—	19	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	#64515	1	2	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	19	1	no	—
342	C₂²×C₄	—	19	2	no	—
343	C₂²×C₄	—	19	2	no	—
344	C₂²×C₄	—	19	1	no	—
345	C₂²×C₄	—	19	1	no	—
346	C₂²×C₄	—	38	1	no	—
347	C₂²×C₄	—	38	1	no	—
348	C₂²×C₄	—	38	1	no	—
349	C₂²×C₄	—	38	1	no	—
350	C₂²×C₄	—	38	1	no	—
351	C₂²×C₄	—	38	1	no	—
352	C₂²×C₄	—	38	1	no	—
353	C₂²×C₄	—	38	1	no	—
354	C₂²×C₄	—	38	1	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	—	76	1	no	—
361	C₂²×C₄	—	76	1	no	—
362	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
363	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
364	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	38	2	no	—
372	C₂×C₈	—	76	1	no	—
373	C₂×C₈	—	76	1	no	—
374	C₂×C₈	—	76	1	no	—
375	C₂×C₈	—	76	1	no	—
376	C₂×C₈	—	76	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	19	2	no	—
382	C₄⋊C₄	—	38	4	no	—
383	C₄⋊C₄	—	38	1	no	—
384	C₄⋊C₄	—	38	1	no	—
385	C₄⋊C₄	—	38	1	no	—
386	C₄⋊C₄	—	76	2	no	—
387	C₂²⋊C₄	—	38	4	no	—
388	C₂²⋊C₄	—	76	2	no	—
389	C₄²	—	4	1	no	—
390	C₄²	—	4	1	no	—
391	C₄²	—	38	1	no	—
392	C₄²	—	38	1	no	—
393	C₄²	—	38	1	no	—
394	C₄²	—	38	1	no	—
395	C₄²	—	38	1	no	—
396	C₄²	—	38	1	no	—
397	C₄²	—	76	1	no	—
398	C₄²	—	76	1	no	—
399	C₄²	#64541	1	1	yes	characteristic
400	C₄²	D₄×D₁₉	1	1	yes	characteristic
401	C₄²	#64543	1	1	yes	characteristic
402	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
403	C₂³	—	19	2	no	—
404	C₂³	—	38	1	no	—
405	C₂³	—	38	1	no	—
406	C₂³	—	38	1	no	—
407	C₂³	—	38	1	no	—
408	C₂³	—	38	1	no	—
409	C₂³	—	38	1	no	—
410	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	2	2	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	19	2	no	—
424	C₂×C₄	—	38	1	no	—
425	C₂×C₄	—	38	1	no	—
426	C₂×C₄	—	38	2	no	—
427	C₂×C₄	—	38	2	no	—
428	C₂×C₄	—	38	2	no	—
429	C₂×C₄	—	38	2	no	—
430	C₂×C₄	—	38	1	no	—
431	C₂×C₄	—	38	1	no	—
432	C₂×C₄	—	38	1	no	—
433	C₂×C₄	—	38	1	no	—
434	C₂×C₄	—	38	2	no	—
435	C₂×C₄	—	38	1	no	—
436	C₂×C₄	—	38	1	no	—
437	C₂×C₄	—	76	2	no	—
438	C₂×C₄	—	76	2	no	—
439	C₂×C₄	—	76	1	no	—
440	C₂×C₄	—	76	1	no	—
441	C₂×C₄	—	76	1	no	—
442	C₂×C₄	—	76	1	no	—
443	C₂×C₄	—	76	1	no	—
444	C₂×C₄	—	76	1	no	—
445	C₂×C₄	—	76	1	no	—
446	C₂×C₄	—	76	1	no	—
447	C₂×C₄	—	76	1	no	—
448	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
449	C₂×C₄	#10597329	1	1	yes	characteristic
450	C₂×C₄	#10597330	1	1	yes	characteristic
451	C₂×C₄	C₂×#64515	1	1	yes	characteristic
452	C₂×C₄	#10597347	1	1	yes	characteristic
453	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
454	C₂×C₄	#10597353	1	1	yes	characteristic
455	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
456	C₂×C₄	#10597362	1	1	yes	characteristic
457	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
458	C₂×C₄	#10597365	1	1	yes	characteristic
459	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
460	C₂×C₄	#10597383	1	1	yes	characteristic
461	C₂×C₄	#10597384	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	8	1	no	—
464	C₈	—	76	2	no	—
465	C₈	—	152	1	no	—
466	C₂²	—	38	2	no	—
467	C₂²	—	38	2	no	—
468	C₂²	—	38	2	no	—
469	C₂²	—	76	1	no	—
470	C₂²	—	76	1	no	—
471	C₂²	—	76	1	no	—
472	C₂²	—	76	1	no	—
473	C₂²	#11926420	1	1	yes	characteristic
474	C₂²	#11926506	1	1	yes	characteristic
475	C₂²	#11926509	1	1	yes	characteristic
476	C₂²	#103×D₁₉	1	1	yes	characteristic
477	C₂²	#11926539	1	1	yes	characteristic
478	C₂²	#11926559	1	1	yes	characteristic
479	C₂²	#11926559	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	38	2	no	—
485	C₄	—	76	2	no	—
486	C₄	—	76	1	no	—
487	C₄	—	76	1	no	—
488	C₄	—	152	1	no	—
489	C₄	#11926612	1	1	yes	characteristic
490	C₄	#11926615	1	1	yes	characteristic
491	C₄	#11926619	1	1	yes	characteristic
492	C₄	#11926620	1	1	yes	characteristic
493	C₄	#11926770	1	1	yes	characteristic
494	C₄	#11926776	1	1	yes	characteristic
495	C₄	#11926782	1	1	yes	characteristic
496	C₄	#11926784	1	1	yes	characteristic
497	C₂	—	76	2	no	—
498	C₂	#14562036	1	1	yes	characteristic
499	C₂	#14562042	1	1	yes	characteristic
500	C₂	#14562062	1	1	yes	characteristic
501	C₂	#14562068	1	1	yes	characteristic
502	C₂	#14563929	1	1	yes	characteristic
503	C₂	#14564055	1	1	yes	characteristic
504	C₂	#14564080	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₈⋊C₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#9075
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
5. #14561475	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
218. C₂×Q₈⋊C₈	D₁₉	semidirect
331. C₁₉	#9075	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926595	2
C₄×#10597392	2
#14563612	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561475	2
#14561474	2
C₂×C₁₉×Q₈⋊C₈	2
#9075	19