Subgroups — #18075885

Order 4864.

680 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊C₄×D₁₉	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#14561476	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	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊C₄×D₁₉	C₄	1	1	yes	characteristic
9	C₂×C₄⋊C₄×D₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄²×D₁₉	—	2	1	no	—
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×(C₂×D₁₉)⋊C₈	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
17	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
18	C₄×Dic₁₉⋊C₄	—	2	1	no	—
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926395	—	2	1	no	—
21	#95×D₁₉	—	2	1	no	—
22	#11926298	—	2	1	no	—
23	#11926298	—	2	1	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	—	2	1	no	—
28	C₂²×C₄×D₁₉	—	2	1	no	—
29	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×Dic₁₉⋊C₄	—	2	1	no	—
41	C₂×Dic₁₉⋊C₄	—	2	1	no	—
42	C₂×C₄×Dic₁₉	—	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×C₄×Dic₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
48	C₂²×C₁₉⋊C₈	—	2	1	no	—
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	C₄⋊C₄×D₁₉	—	2	2	no	—
51	C₄⋊C₄×D₁₉	—	2	2	no	—
52	C₄⋊C₄×D₁₉	—	2	2	no	—
53	C₄⋊C₄×D₁₉	C₈	1	4	yes	complemented
54	C₄²×D₁₉	—	2	1	no	—
55	C₄²×D₁₉	—	2	1	no	—
56	C₄²×D₁₉	—	2	1	no	—
57	C₄²×D₁₉	—	2	1	no	—
58	C₄²×D₁₉	—	4	2	no	—
59	C₄²×D₁₉	—	4	2	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₁₉×#95	—	2	1	no	—
65	C₁₉⋊#95	—	2	1	no	—
66	C₁₉⋊#95	—	2	1	no	—
67	C₁₉⋊#95	—	2	1	no	—
68	(C₂×D₁₉)⋊C₈	—	2	4	no	—
69	(C₂×D₁₉)⋊C₈	—	4	2	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	—	2	1	no	—
81	C₂²×Dic₁₉	—	2	1	no	—
82	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₉	—	2	1	no	—
86	C₂×C₄×D₁₉	—	2	1	no	—
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	—	2	1	no	—
90	C₂×C₄×D₁₉	—	2	1	no	—
91	C₂×C₄×D₁₉	—	2	1	no	—
92	C₂×C₄×D₁₉	—	2	1	no	—
93	C₂×C₄×D₁₉	—	2	4	no	—
94	C₂×C₄×D₁₉	—	2	4	no	—
95	C₂×C₄×D₁₉	—	2	2	no	—
96	C₂×C₄×D₁₉	—	2	1	no	—
97	C₂×C₄×D₁₉	—	2	1	no	—
98	C₂×C₄×D₁₉	—	4	1	no	—
99	C₂×C₄×D₁₉	—	4	2	no	—
100	C₂×C₄×D₁₉	—	4	2	no	—
101	C₂×C₄×D₁₉	—	4	2	no	—
102	C₂×C₄×D₁₉	—	4	2	no	—
103	C₂×C₄×D₁₉	C₂×C₈	1	2	yes	—
104	C₂×C₄×D₁₉	M₁₆	1	2	yes	—
105	C₂×C₄×D₁₉	D₈	1	2	yes	—
106	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
107	C₂×C₈×C₁₉	—	2	2	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	C₂×C₈×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
116	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	#41	1	1	yes	characteristic
120	C₄²×C₁₉	#41	1	1	yes	characteristic
121	C₄²×C₁₉	#41	1	1	yes	characteristic
122	C₄²×C₁₉	#41	1	1	yes	characteristic
123	C₄⋊Dic₁₉	—	2	1	no	—
124	C₄⋊Dic₁₉	—	2	1	no	—
125	C₄⋊Dic₁₉	C₂×C₈	1	2	yes	—
126	C₄⋊Dic₁₉	M₁₆	1	2	yes	—
127	Dic₁₉⋊C₄	—	2	4	no	—
128	Dic₁₉⋊C₄	—	2	4	no	—
129	C₄×Dic₁₉	—	2	1	no	—
130	C₄×Dic₁₉	—	2	1	no	—
131	C₄×Dic₁₉	—	2	1	no	—
132	C₄×Dic₁₉	—	2	1	no	—
133	C₄×Dic₁₉	—	2	1	no	—
134	C₄×Dic₁₉	—	2	1	no	—
135	C₄×Dic₁₉	—	4	1	no	—
136	C₄×Dic₁₉	—	4	1	no	—
137	C₄×Dic₁₉	—	4	2	no	—
138	C₄×Dic₁₉	—	4	2	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	4	1	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	#8706	—	19	1	no	maximal, Sylow
146	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×D₁₉	—	2	1	no	—
148	C₂²×D₁₉	—	2	1	no	—
149	C₂²×D₁₉	—	2	1	no	—
150	C₂²×D₁₉	—	2	1	no	—
151	C₂²×D₁₉	C₂²⋊C₈	1	2	yes	—
152	C₂²×D₁₉	#102	1	2	yes	—
153	C₂²×D₁₉	#104	1	2	yes	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	4	1	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	#117	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×M₁₆	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×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
176	C₂×Dic₁₉	—	2	1	no	—
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	2	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	—	4	1	no	—
188	C₂×Dic₁₉	—	4	1	no	—
189	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
190	C₂×Dic₁₉	#102	1	2	yes	—
191	C₄×D₁₉	—	2	2	no	—
192	C₄×D₁₉	—	2	2	no	—
193	C₄×D₁₉	—	2	2	no	—
194	C₄×D₁₉	—	2	2	no	—
195	C₄×D₁₉	—	2	2	no	—
196	C₄×D₁₉	—	2	2	no	—
197	C₄×D₁₉	—	2	2	no	—
198	C₄×D₁₉	—	2	2	no	—
199	C₄×D₁₉	—	4	2	no	—
200	C₄×D₁₉	—	4	2	no	—
201	C₄×D₁₉	—	4	8	no	—
202	C₄×D₁₉	—	4	8	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₈×C₁₉	—	8	1	no	—
205	C₁₉⋊C₈	—	4	2	no	—
206	C₁₉⋊C₈	—	8	1	no	—
207	C₂×C₄×C₄⋊C₄	—	19	1	no	—
208	#1797	—	19	1	no	—
209	C₄×C₂²⋊C₈	—	19	1	no	—
210	#1279	—	19	1	no	—
211	#1279	—	19	1	no	—
212	#1279	—	19	1	no	—
213	#1279	D₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	#381	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
216	C₂²×C₁₉	#407	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
218	C₂²×C₁₉	#419	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
220	C₂²×C₁₉	#421	1	1	yes	characteristic
221	C₂×D₁₉	—	2	2	no	—
222	C₂×D₁₉	—	2	2	no	—
223	C₂×D₁₉	—	2	2	no	—
224	C₂×D₁₉	—	2	2	no	—
225	C₂×D₁₉	—	2	2	no	—
226	C₂×D₁₉	—	2	2	no	—
227	C₂×D₁₉	D₄⋊C₈	1	4	yes	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	#431	1	1	yes	characteristic
233	C₄×C₁₉	#431	1	1	yes	characteristic
234	C₄×C₁₉	#432	1	1	yes	characteristic
235	C₄×C₁₉	#432	1	1	yes	characteristic
236	C₄×C₁₉	#480	1	1	yes	characteristic
237	C₄×C₁₉	#480	1	1	yes	characteristic
238	C₄×C₁₉	#483	1	1	yes	characteristic
239	C₄×C₁₉	#483	1	1	yes	characteristic
240	Dic₁₉	—	2	2	no	—
241	Dic₁₉	—	2	2	no	—
242	Dic₁₉	—	4	1	no	—
243	Dic₁₉	—	4	2	no	—
244	Dic₁₉	—	4	2	no	—
245	C₂²×C₄⋊C₄	—	19	1	no	—
246	C₂²×C₄⋊C₄	—	19	1	no	—
247	C₂²×C₄²	—	19	1	no	—
248	C₂²×C₄²	—	38	1	no	—
249	C₂×C₄⋊C₈	—	19	1	no	—
250	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	—	38	1	no	—
252	C₂×C₂²⋊C₈	—	38	1	no	—
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	—	19	1	no	—
258	C₄×C₄⋊C₄	—	38	1	no	—
259	C₄×C₄⋊C₄	—	38	1	no	—
260	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
261	C₂×#95	—	38	1	no	—
262	#336	—	38	1	no	—
263	#336	—	38	1	no	—
264	C₂×C₁₉	C₂×D₄⋊C₈	1	1	yes	characteristic
265	C₂×C₁₉	#1479	1	1	yes	characteristic
266	C₂×C₁₉	#1486	1	1	yes	characteristic
267	C₂×C₁₉	#1491	1	1	yes	characteristic
268	C₂×C₁₉	#1817	1	1	yes	characteristic
269	C₂×C₁₉	#1823	1	1	yes	characteristic
270	C₂×C₁₉	#1826	1	1	yes	characteristic
271	D₁₉	—	2	4	no	—
272	C₂³×C₄	—	19	1	no	—
273	C₂³×C₄	—	19	1	no	—
274	C₂³×C₄	—	19	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	C₂×C₄⋊C₄	—	19	1	no	—
282	C₂×C₄⋊C₄	—	19	1	no	—
283	C₂×C₄⋊C₄	—	19	4	no	—
284	C₂×C₄⋊C₄	—	38	2	no	—
285	C₂×C₄⋊C₄	—	38	2	no	—
286	C₂×C₄⋊C₄	—	38	1	no	—
287	C₂×C₄⋊C₄	—	38	1	no	—
288	C₂×C₄⋊C₄	—	38	2	no	—
289	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	19	1	no	—
293	C₂×C₄²	—	19	1	no	—
294	C₂×C₄²	—	19	1	no	—
295	C₂×C₄²	—	38	1	no	—
296	C₂×C₄²	—	38	1	no	—
297	C₂×C₄²	—	38	1	no	—
298	C₂×C₄²	—	38	1	no	—
299	C₂×C₄²	—	38	1	no	—
300	C₂×C₄²	—	38	1	no	—
301	C₂×C₄²	—	38	1	no	—
302	C₂×C₄²	—	76	2	no	—
303	C₂×C₄²	—	76	2	no	—
304	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	38	1	no	—
308	C₄⋊C₈	—	38	1	no	—
309	C₂²⋊C₈	—	38	4	no	—
310	C₂²⋊C₈	—	76	2	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	38	1	no	—
314	C₄×C₈	—	38	1	no	—
315	#95	—	2	1	no	—
316	#95	—	38	1	no	—
317	#95	—	38	1	no	—
318	#95	—	38	1	no	—
319	C₁₉	#8706	1	1	yes	characteristic, complemented, Sylow
320	C₂⁴	—	19	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	19	1	no	—
324	C₂²×C₄	—	19	1	no	—
325	C₂²×C₄	—	19	2	no	—
326	C₂²×C₄	—	19	2	no	—
327	C₂²×C₄	—	19	2	no	—
328	C₂²×C₄	—	19	2	no	—
329	C₂²×C₄	—	19	1	no	—
330	C₂²×C₄	—	38	2	no	—
331	C₂²×C₄	—	38	4	no	—
332	C₂²×C₄	—	38	4	no	—
333	C₂²×C₄	—	38	1	no	—
334	C₂²×C₄	—	38	1	no	—
335	C₂²×C₄	—	38	1	no	—
336	C₂²×C₄	—	38	1	no	—
337	C₂²×C₄	—	38	1	no	—
338	C₂²×C₄	—	38	1	no	—
339	C₂²×C₄	—	38	1	no	—
340	C₂²×C₄	—	38	1	no	—
341	C₂²×C₄	—	38	1	no	—
342	C₂²×C₄	—	38	1	no	—
343	C₂²×C₄	—	38	1	no	—
344	C₂²×C₄	—	38	1	no	—
345	C₂²×C₄	—	76	1	no	—
346	C₂²×C₄	—	76	2	no	—
347	C₂²×C₄	—	76	2	no	—
348	C₂²×C₄	—	76	2	no	—
349	C₂²×C₄	—	76	2	no	—
350	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	38	2	no	—
360	C₂×C₈	—	76	1	no	—
361	C₂×C₈	—	76	1	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	19	2	no	—
368	C₄⋊C₄	—	19	2	no	—
369	C₄⋊C₄	—	38	4	no	—
370	C₄⋊C₄	—	38	4	no	—
371	C₄⋊C₄	—	38	1	no	—
372	C₄⋊C₄	—	38	1	no	—
373	C₄⋊C₄	C₈×D₁₉	1	2	yes	—
374	C₄⋊C₄	#64515	1	2	yes	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	—	38	1	no	—
378	C₄²	—	38	1	no	—
379	C₄²	—	38	1	no	—
380	C₄²	—	38	1	no	—
381	C₄²	—	38	1	no	—
382	C₄²	—	38	1	no	—
383	C₄²	—	76	2	no	—
384	C₄²	—	76	2	no	—
385	C₄²	—	76	1	no	—
386	C₄²	—	76	1	no	—
387	C₄²	#64541	1	1	yes	characteristic
388	C₄²	#64541	1	1	yes	characteristic
389	C₄²	#64543	1	1	yes	characteristic
390	C₄²	#64545	1	1	yes	characteristic
391	C₂³	—	19	2	no	—
392	C₂³	—	19	2	no	—
393	C₂³	—	19	2	no	—
394	C₂³	—	38	1	no	—
395	C₂³	—	38	1	no	—
396	C₂³	—	38	1	no	—
397	C₂³	—	38	1	no	—
398	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	19	2	no	—
408	C₂×C₄	—	19	2	no	—
409	C₂×C₄	—	38	1	no	—
410	C₂×C₄	—	38	1	no	—
411	C₂×C₄	—	38	1	no	—
412	C₂×C₄	—	38	1	no	—
413	C₂×C₄	—	38	2	no	—
414	C₂×C₄	—	38	2	no	—
415	C₂×C₄	—	38	2	no	—
416	C₂×C₄	—	38	2	no	—
417	C₂×C₄	—	38	2	no	—
418	C₂×C₄	—	38	2	no	—
419	C₂×C₄	—	38	2	no	—
420	C₂×C₄	—	38	2	no	—
421	C₂×C₄	—	38	1	no	—
422	C₂×C₄	—	38	1	no	—
423	C₂×C₄	—	38	1	no	—
424	C₂×C₄	—	38	2	no	—
425	C₂×C₄	—	38	2	no	—
426	C₂×C₄	—	76	2	no	—
427	C₂×C₄	—	76	2	no	—
428	C₂×C₄	—	76	8	no	—
429	C₂×C₄	—	76	8	no	—
430	C₂×C₄	—	76	1	no	—
431	C₂×C₄	—	76	1	no	—
432	C₂×C₄	—	76	1	no	—
433	C₂×C₄	—	76	1	no	—
434	C₂×C₄	#10597318	1	1	yes	characteristic
435	C₂×C₄	#10597329	1	1	yes	characteristic
436	C₂×C₄	#10597329	1	1	yes	characteristic
437	C₂×C₄	#10597338	1	1	yes	characteristic
438	C₂×C₄	#10597340	1	1	yes	characteristic
439	C₂×C₄	#10597340	1	1	yes	characteristic
440	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#64515	1	1	yes	characteristic
442	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
443	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
444	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
445	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
446	C₂×C₄	#10597361	1	1	yes	characteristic
447	C₂×C₄	#10597364	1	1	yes	characteristic
448	C₈	—	4	2	no	—
449	C₈	—	8	1	no	—
450	C₈	—	76	2	no	—
451	C₈	—	152	1	no	—
452	C₂²	—	19	4	no	—
453	C₂²	—	38	2	no	—
454	C₂²	—	38	2	no	—
455	C₂²	—	38	2	no	—
456	C₂²	—	38	2	no	—
457	C₂²	—	38	2	no	—
458	C₂²	—	38	2	no	—
459	C₂²	#11926406	1	1	yes	characteristic
460	C₂²	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
461	C₂²	#11926506	1	1	yes	characteristic
462	C₂²	#102×D₁₉	1	1	yes	characteristic
463	C₂²	#11926551	1	1	yes	characteristic
464	C₂²	#104×D₁₉	1	1	yes	characteristic
465	C₂²	#11926559	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	38	2	no	—
471	C₄	—	38	2	no	—
472	C₄	—	76	2	no	—
473	C₄	—	76	1	no	—
474	C₄	—	76	2	no	—
475	C₄	#11926595	1	1	yes	characteristic
476	C₄	#11926596	1	1	yes	characteristic
477	C₄	#11926599	1	1	yes	characteristic
478	C₄	#11926600	1	1	yes	characteristic
479	C₄	#11926856	1	1	yes	characteristic
480	C₄	#11926859	1	1	yes	characteristic
481	C₄	#11926873	1	1	yes	characteristic
482	C₄	#11926876	1	1	yes	characteristic
483	C₂	—	38	4	no	—
484	C₂	D₁₉×D₄⋊C₈	1	1	yes	characteristic
485	C₂	#14562028	1	1	yes	characteristic
486	C₂	#14562058	1	1	yes	characteristic
487	C₂	#14562080	1	1	yes	characteristic
488	C₂	#14563702	1	1	yes	characteristic
489	C₂	#14563720	1	1	yes	characteristic
490	C₂	#14563733	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	#8706
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. #14561476	C₂	semidirect
5. #14561475	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
53. C₄⋊C₄×D₁₉	C₈	semidirect
213. #1279	D₁₉	semidirect
319. C₁₉	#8706	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊C₄×D₁₉	2
#14563612	2
C₄×(C₂×D₁₉)⋊C₈	2
#14561476	2
#14561475	2
#14561474	2
C₁₉×#1279	2
#8706	19