Subgroups — #18075221

Order 4864.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597339	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926273	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×#10597339	C₄	1	1	yes	characteristic
10	C₂×#10597339	C₄	1	1	yes	characteristic
11	C₂×C₄²×D₁₉	—	2	1	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	C₂×Dic₁₉⋊C₈	—	2	1	no	—
15	C₂×Dic₁₉⋊C₈	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
18	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
19	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
20	#11926391	—	2	1	no	—
21	#11926391	—	2	1	no	—
22	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
23	#11926298	—	2	1	no	—
24	#11926273	—	2	2	no	—
25	#11926271	—	2	2	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	—	2	1	no	—
31	C₂²×C₄×D₁₉	—	2	1	no	—
32	C₂²×C₄×D₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
40	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
41	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
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×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₉	D₄	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	#10597339	—	2	2	no	—
54	#10597339	—	2	2	no	—
55	#10597339	—	2	2	no	—
56	#10597339	C₈	1	4	yes	complemented
57	C₄×D₇₆	—	2	1	no	—
58	C₄×D₇₆	—	2	1	no	—
59	C₄×D₇₆	D₄	1	2	yes	—
60	C₄×D₇₆	Q₈	1	2	yes	—
61	C₄²×D₁₉	—	4	2	no	—
62	C₄²×D₁₉	—	4	2	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	—	2	1	no	—
67	C₁₉×#95	—	2	1	no	—
68	C₁₉⋊#95	—	2	1	no	—
69	C₁₉⋊#95	—	2	1	no	—
70	Dic₁₉⋊C₈	—	2	4	no	—
71	Dic₁₉⋊C₈	—	4	2	no	—
72	Dic₁₉⋊C₈	—	4	2	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄×C₁₉⋊C₈	—	2	1	no	—
76	C₄×C₁₉⋊C₈	—	2	1	no	—
77	C₂³×D₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×Dic₁₉	—	2	1	no	—
84	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×D₇₆	—	2	1	no	—
89	C₂×D₇₆	—	2	1	no	—
90	C₂×D₇₆	—	2	1	no	—
91	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
92	C₂×D₇₆	C₂×C₈	1	2	yes	—
93	C₂×D₇₆	M₁₆	1	2	yes	—
94	C₂×C₄×D₁₉	—	2	4	no	—
95	C₂×C₄×D₁₉	—	2	2	no	—
96	C₂×C₄×D₁₉	—	2	2	no	—
97	C₂×C₄×D₁₉	—	2	4	no	—
98	C₂×C₄×D₁₉	—	4	2	no	—
99	C₂×C₄×D₁₉	—	4	1	no	—
100	C₂×C₄×D₁₉	—	4	1	no	—
101	C₂×C₄×D₁₉	—	4	1	no	—
102	C₂×C₄×D₁₉	—	4	1	no	—
103	C₂×C₄×D₁₉	—	4	2	no	—
104	C₂×C₄×D₁₉	—	4	2	no	—
105	C₂×C₄×D₁₉	—	4	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
115	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
116	C₄²×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
120	C₄²×C₁₉	#41	1	1	yes	characteristic
121	C₄²×C₁₉	#41	1	1	yes	characteristic
122	(C₂×D₁₉)⋊C₄	—	2	4	no	—
123	(C₂×D₁₉)⋊C₄	—	2	2	no	—
124	(C₂×D₁₉)⋊C₄	—	2	2	no	—
125	(C₂×D₁₉)⋊C₄	—	2	4	no	—
126	C₄⋊Dic₁₉	—	2	1	no	—
127	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
128	C₄×Dic₁₉	—	2	1	no	—
129	C₄×Dic₁₉	—	2	1	no	—
130	C₄×Dic₁₉	—	2	1	no	—
131	C₄×Dic₁₉	—	2	1	no	—
132	C₄×Dic₁₉	—	2	2	no	—
133	C₄×Dic₁₉	—	4	1	no	—
134	C₄×Dic₁₉	—	4	2	no	—
135	C₄×Dic₁₉	—	4	2	no	—
136	C₄×Dic₁₉	C₂×C₈	1	2	yes	—
137	C₄×Dic₁₉	M₁₆	1	2	yes	—
138	C₄×Dic₁₉	D₈	1	2	yes	—
139	C₄×Dic₁₉	SD₁₆	1	2	yes	—
140	C₂×C₁₉⋊C₈	—	2	2	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	#8563	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×D₁₉	—	2	2	no	—
149	C₂²×D₁₉	—	2	2	no	—
150	C₂²×D₁₉	—	2	2	no	—
151	C₂²×D₁₉	—	4	1	no	—
152	C₂²×D₁₉	—	4	1	no	—
153	C₂²×D₁₉	—	4	1	no	—
154	C₂²×D₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
177	C₂×Dic₁₉	—	2	1	no	—
178	C₂×Dic₁₉	—	2	1	no	—
179	C₂×Dic₁₉	—	2	1	no	—
180	C₂×Dic₁₉	—	2	1	no	—
181	C₂×Dic₁₉	—	2	2	no	—
182	C₂×Dic₁₉	—	2	1	no	—
183	C₂×Dic₁₉	—	2	1	no	—
184	C₂×Dic₁₉	—	2	1	no	—
185	C₂×Dic₁₉	—	4	1	no	—
186	C₂×Dic₁₉	—	4	1	no	—
187	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
188	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
189	C₂×Dic₁₉	#102	1	2	yes	—
190	C₂×Dic₁₉	#102	1	2	yes	—
191	C₂×Dic₁₉	#104	1	2	yes	—
192	D₇₆	—	2	2	no	—
193	D₇₆	—	2	2	no	—
194	D₇₆	—	2	2	no	—
195	D₇₆	C₄⋊C₈	1	4	yes	complemented
196	C₄×D₁₉	—	4	8	no	—
197	C₄×D₁₉	—	4	2	no	—
198	C₄×D₁₉	—	4	2	no	—
199	C₄×D₁₉	—	4	2	no	—
200	C₄×D₁₉	—	4	2	no	—
201	C₄×D₁₉	—	4	8	no	—
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	—	8	1	no	—
204	C₁₉⋊C₈	—	4	2	no	—
205	C₁₉⋊C₈	—	8	1	no	—
206	C₄²×D₄	—	19	1	no	—
207	#1842	—	19	1	no	—
208	C₄×C₄⋊C₈	—	19	1	no	—
209	C₂×D₄⋊C₈	—	19	1	no	—
210	C₂×D₄⋊C₈	—	19	1	no	—
211	#1279	—	19	1	no	—
212	#1279	D₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	#380	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
215	C₂²×C₁₉	#407	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
217	C₂²×C₁₉	#417	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
219	C₂²×C₁₉	#421	1	1	yes	characteristic
220	C₂×D₁₉	—	2	4	no	—
221	C₂×D₁₉	—	4	2	no	—
222	C₂×D₁₉	—	4	2	no	—
223	C₂×D₁₉	—	4	2	no	—
224	C₂×D₁₉	—	4	2	no	—
225	C₂×D₁₉	—	4	2	no	—
226	C₂×D₁₉	—	4	2	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
232	C₄×C₁₉	#423	1	1	yes	characteristic
233	C₄×C₁₉	#431	1	1	yes	characteristic
234	C₄×C₁₉	#432	1	1	yes	characteristic
235	C₄×C₁₉	#459	1	1	yes	characteristic
236	C₄×C₁₉	#461	1	1	yes	characteristic
237	C₄×C₁₉	#474	1	1	yes	characteristic
238	C₄×C₁₉	#476	1	1	yes	characteristic
239	Dic₁₉	—	2	2	no	—
240	Dic₁₉	—	2	2	no	—
241	Dic₁₉	—	4	2	no	—
242	Dic₁₉	—	4	1	no	—
243	Dic₁₉	D₄⋊C₈	1	4	yes	complemented
244	C₂×C₄×D₄	—	19	1	no	—
245	C₂×C₄×D₄	—	19	1	no	—
246	C₂×C₄×D₄	—	19	1	no	—
247	C₂²×C₄²	—	38	1	no	—
248	C₂×C₄⋊C₈	—	19	1	no	—
249	C₂×C₄⋊C₈	—	38	1	no	—
250	C₂×C₄⋊C₈	—	38	1	no	—
251	C₂×C₄⋊C₈	—	38	1	no	—
252	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
253	C₂×C₄×C₈	—	19	1	no	—
254	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
255	C₄×C₄⋊C₄	—	19	1	no	—
256	C₄×C₄⋊C₄	—	19	1	no	—
257	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	—	38	1	no	—
259	C₄×C₂²⋊C₄	—	38	1	no	—
260	C₄×C₂²⋊C₄	—	38	1	no	—
261	C₄³	—	19	1	no	—
262	#336	—	38	1	no	—
263	D₄⋊C₈	—	38	2	no	—
264	D₄⋊C₈	—	38	2	no	—
265	C₂×C₁₉	C₂×D₄⋊C₈	1	1	yes	characteristic
266	C₂×C₁₉	#1477	1	1	yes	characteristic
267	C₂×C₁₉	#1486	1	1	yes	characteristic
268	C₂×C₁₉	#1489	1	1	yes	characteristic
269	C₂×C₁₉	#1797	1	1	yes	characteristic
270	C₂×C₁₉	#1802	1	1	yes	characteristic
271	C₂×C₁₉	#1806	1	1	yes	characteristic
272	D₁₉	—	4	4	no	—
273	C₂²×D₄	—	19	1	no	—
274	C₂³×C₄	—	38	1	no	—
275	C₂³×C₄	—	38	1	no	—
276	C₂³×C₄	—	38	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	38	1	no	—
280	C₂²×C₈	—	38	1	no	—
281	C₄×D₄	—	19	4	no	—
282	C₄×D₄	—	19	2	no	—
283	C₄×D₄	—	19	2	no	—
284	C₄×D₄	—	38	2	no	—
285	C₄×D₄	—	38	2	no	—
286	C₄×D₄	—	38	2	no	—
287	C₄×D₄	—	38	1	no	—
288	C₄×D₄	—	38	1	no	—
289	C₂×C₄⋊C₄	—	19	1	no	—
290	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	38	1	no	—
293	C₂×C₂²⋊C₄	—	38	1	no	—
294	C₂×C₂²⋊C₄	—	38	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	19	1	no	—
297	C₂×C₄²	—	19	1	no	—
298	C₂×C₄²	—	19	1	no	—
299	C₂×C₄²	—	19	1	no	—
300	C₂×C₄²	—	19	1	no	—
301	C₂×C₄²	—	19	1	no	—
302	C₂×C₄²	—	38	1	no	—
303	C₂×C₄²	—	38	1	no	—
304	C₂×C₄²	—	76	2	no	—
305	C₂×C₄²	—	76	2	no	—
306	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	38	4	no	—
310	C₄⋊C₈	—	38	1	no	—
311	C₄⋊C₈	—	38	1	no	—
312	C₄⋊C₈	—	76	2	no	—
313	C₄⋊C₈	—	76	2	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	38	1	no	—
317	C₄×C₈	—	38	1	no	—
318	#95	—	2	1	no	—
319	#95	—	38	1	no	—
320	#95	—	38	1	no	—
321	C₁₉	#8563	1	1	yes	characteristic, complemented, Sylow
322	C₂⁴	—	38	1	no	—
323	C₂×D₄	—	19	2	no	—
324	C₂×D₄	—	19	2	no	—
325	C₂×D₄	—	19	2	no	—
326	C₂×D₄	—	38	1	no	—
327	C₂×D₄	—	38	1	no	—
328	C₂×D₄	—	38	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	19	1	no	—
332	C₂²×C₄	—	19	1	no	—
333	C₂²×C₄	—	19	1	no	—
334	C₂²×C₄	—	19	1	no	—
335	C₂²×C₄	—	38	4	no	—
336	C₂²×C₄	—	38	4	no	—
337	C₂²×C₄	—	38	1	no	—
338	C₂²×C₄	—	38	2	no	—
339	C₂²×C₄	—	38	2	no	—
340	C₂²×C₄	—	76	2	no	—
341	C₂²×C₄	—	76	2	no	—
342	C₂²×C₄	—	76	2	no	—
343	C₂²×C₄	—	76	2	no	—
344	C₂²×C₄	—	76	1	no	—
345	C₂²×C₄	—	76	1	no	—
346	C₂²×C₄	—	76	1	no	—
347	C₂²×C₄	—	76	1	no	—
348	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	38	2	no	—
358	C₂×C₈	—	76	1	no	—
359	C₂×C₈	—	76	1	no	—
360	C₂×C₈	—	76	1	no	—
361	C₂×C₈	—	76	1	no	—
362	C₂×C₈	—	76	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	19	2	no	—
366	C₄⋊C₄	—	38	1	no	—
367	C₄⋊C₄	C₈×D₁₉	1	2	yes	—
368	C₄⋊C₄	#64515	1	2	yes	—
369	C₂²⋊C₄	—	38	4	no	—
370	C₂²⋊C₄	—	38	4	no	—
371	C₂²⋊C₄	—	38	2	no	—
372	C₂²⋊C₄	—	38	2	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	4	1	no	—
375	C₄²	—	19	2	no	—
376	C₄²	—	19	2	no	—
377	C₄²	—	19	2	no	—
378	C₄²	—	19	2	no	—
379	C₄²	—	38	2	no	—
380	C₄²	—	38	1	no	—
381	C₄²	—	38	1	no	—
382	C₄²	—	38	1	no	—
383	C₄²	—	38	1	no	—
384	C₄²	—	76	1	no	—
385	C₄²	—	76	2	no	—
386	C₄²	—	76	2	no	—
387	C₄²	#64541	1	1	yes	characteristic
388	C₄²	#64541	1	1	yes	characteristic
389	C₄²	D₄×D₁₉	1	1	yes	characteristic
390	C₄²	Q₈×D₁₉	1	1	yes	characteristic
391	C₂³	—	38	2	no	—
392	C₂³	—	38	2	no	—
393	C₂³	—	38	2	no	—
394	C₂³	—	76	1	no	—
395	C₂³	—	76	1	no	—
396	C₂³	—	76	1	no	—
397	C₂³	—	76	1	no	—
398	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
399	D₄	—	19	4	no	—
400	D₄	—	38	2	no	—
401	D₄	—	38	2	no	—
402	D₄	—	38	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	19	2	no	—
412	C₂×C₄	—	19	2	no	—
413	C₂×C₄	—	19	2	no	—
414	C₂×C₄	—	19	2	no	—
415	C₂×C₄	—	19	2	no	—
416	C₂×C₄	—	38	1	no	—
417	C₂×C₄	—	38	1	no	—
418	C₂×C₄	—	38	1	no	—
419	C₂×C₄	—	38	1	no	—
420	C₂×C₄	—	38	1	no	—
421	C₂×C₄	—	38	1	no	—
422	C₂×C₄	—	38	2	no	—
423	C₂×C₄	—	38	1	no	—
424	C₂×C₄	—	76	8	no	—
425	C₂×C₄	—	76	8	no	—
426	C₂×C₄	—	76	1	no	—
427	C₂×C₄	—	76	1	no	—
428	C₂×C₄	—	76	2	no	—
429	C₂×C₄	—	76	2	no	—
430	C₂×C₄	—	76	2	no	—
431	C₂×C₄	—	76	2	no	—
432	C₂×C₄	#10597318	1	1	yes	characteristic
433	C₂×C₄	#10597330	1	1	yes	characteristic
434	C₂×C₄	#10597330	1	1	yes	characteristic
435	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
436	C₂×C₄	#10597342	1	1	yes	characteristic
437	C₂×C₄	#10597342	1	1	yes	characteristic
438	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂×#64515	1	1	yes	characteristic
440	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
441	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
442	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
443	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
444	C₂×C₄	#10597360	1	1	yes	characteristic
445	C₂×C₄	#10597364	1	1	yes	characteristic
446	C₈	—	4	2	no	—
447	C₈	—	8	1	no	—
448	C₈	—	76	2	no	—
449	C₈	—	152	1	no	—
450	C₂²	—	38	4	no	—
451	C₂²	—	76	2	no	—
452	C₂²	—	76	2	no	—
453	C₂²	—	76	2	no	—
454	C₂²	—	76	2	no	—
455	C₂²	—	76	2	no	—
456	C₂²	—	76	2	no	—
457	C₂²	#11926403	1	1	yes	characteristic
458	C₂²	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
459	C₂²	#11926506	1	1	yes	characteristic
460	C₂²	#102×D₁₉	1	1	yes	characteristic
461	C₂²	#11926544	1	1	yes	characteristic
462	C₂²	#104×D₁₉	1	1	yes	characteristic
463	C₂²	#11926559	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	19	4	no	—
469	C₄	—	38	2	no	—
470	C₄	—	38	2	no	—
471	C₄	—	76	1	no	—
472	C₄	—	76	2	no	—
473	C₄	C₄⋊C₈×D₁₉	1	1	yes	characteristic
474	C₄	#11926566	1	1	yes	characteristic
475	C₄	#11926595	1	1	yes	characteristic
476	C₄	#11926599	1	1	yes	characteristic
477	C₄	#11926738	1	1	yes	characteristic
478	C₄	#11926748	1	1	yes	characteristic
479	C₄	#11926823	1	1	yes	characteristic
480	C₄	#11926833	1	1	yes	characteristic
481	C₂	—	76	4	no	—
482	C₂	D₁₉×D₄⋊C₈	1	1	yes	characteristic
483	C₂	#14562021	1	1	yes	characteristic
484	C₂	#14562058	1	1	yes	characteristic
485	C₂	#14562073	1	1	yes	characteristic
486	C₂	#14563614	1	1	yes	characteristic
487	C₂	#14563634	1	1	yes	characteristic
488	C₂	#14563654	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	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8563
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
2. #14563786	C₂	semidirect
3. C₄×Dic₁₉⋊C₈	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
56. #10597339	C₈	semidirect
195. D₇₆	C₄⋊C₈	semidirect
212. #1279	D₁₉	semidirect
243. Dic₁₉	D₄⋊C₈	semidirect
321. C₁₉	#8563	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597339	2
#14563786	2
C₄×Dic₁₉⋊C₈	2
C₂×#11926273	2
C₂×#11926271	2
#14561476	2
C₁₉×#1279	2
#8563	19