Subgroups — #18075957

Order 4864.

630 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₉×#384	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	#14563612	C₂	1	1	yes	maximal, characteristic
4	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊C₄×D₁₉	—	2	1	no	—
9	C₂×C₄⋊C₄×D₁₉	—	2	1	no	—
10	C₂×C₄⋊C₄×D₁₉	C₄	1	2	yes	—
11	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
15	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
16	#11926414	C₂²	1	1	yes	characteristic
17	#11926413	—	2	1	no	—
18	#11926413	—	2	1	no	—
19	#11926413	C₄	1	2	yes	—
20	#11926298	—	2	1	no	—
21	#11926298	—	2	1	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₉×#384	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₉	—	2	2	no	—
26	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₂×Dic₁₉⋊C₄	—	2	2	no	—
39	C₂×Dic₁₉⋊C₄	—	2	2	no	—
40	C₂×Dic₁₉⋊C₄	—	2	2	no	—
41	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₄⋊C₄×D₁₉	—	4	2	no	—
47	C₄⋊C₄×D₁₉	—	4	2	no	—
48	C₄⋊C₄×D₁₉	—	4	2	no	—
49	C₄⋊C₄×D₁₉	—	4	2	no	—
50	C₄⋊C₄×D₁₉	—	4	4	no	—
51	C₄²×D₁₉	—	2	1	no	—
52	C₄²×D₁₉	—	2	1	no	—
53	C₄²×D₁₉	—	2	1	no	—
54	C₄²×D₁₉	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	(C₂×D₁₉)⋊C₈	—	4	2	no	—
60	(C₂×D₁₉)⋊C₈	—	4	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×Dic₁₉	—	2	2	no	—
71	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×D₁₉	—	2	2	no	—
75	C₂×C₄×D₁₉	—	2	1	no	—
76	C₂×C₄×D₁₉	—	2	1	no	—
77	C₂×C₄×D₁₉	—	2	1	no	—
78	C₂×C₄×D₁₉	—	2	1	no	—
79	C₂×C₄×D₁₉	—	2	1	no	—
80	C₂×C₄×D₁₉	—	2	1	no	—
81	C₂×C₄×D₁₉	—	2	1	no	—
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×C₄×D₁₉	—	2	1	no	—
84	C₂×C₄×D₁₉	—	2	1	no	—
85	C₂×C₄×D₁₉	—	2	2	no	—
86	C₂×C₄×D₁₉	—	4	4	no	—
87	C₂×C₄×D₁₉	—	4	4	no	—
88	C₂×C₄×D₁₉	—	4	4	no	—
89	C₂×C₄×D₁₉	D₈	1	2	yes	—
90	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
91	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
92	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	#41	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	C₄⋊Dic₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	1	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	—	4	2	no	—
113	Dic₁₉⋊C₄	—	4	4	no	—
114	Dic₁₉⋊C₄	—	4	4	no	—
115	Dic₁₉⋊C₄	—	4	4	no	—
116	C₄×Dic₁₉	—	2	1	no	—
117	C₄×Dic₁₉	—	2	1	no	—
118	C₄×Dic₁₉	—	2	1	no	—
119	C₄×Dic₁₉	—	2	1	no	—
120	C₄×Dic₁₉	—	2	1	no	—
121	C₄×Dic₁₉	—	2	1	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	#8724	—	19	1	no	maximal, Sylow
129	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×D₁₉	—	2	1	no	—
131	C₂²×D₁₉	—	2	1	no	—
132	C₂²×D₁₉	—	2	1	no	—
133	C₂²×D₁₉	—	2	1	no	—
134	C₂²×D₁₉	#101	1	2	yes	—
135	C₂²×D₁₉	#102	1	2	yes	—
136	C₂²×D₁₉	#103	1	2	yes	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	2	1	no	—
159	C₂×Dic₁₉	—	2	1	no	—
160	C₂×Dic₁₉	—	2	1	no	—
161	C₂×Dic₁₉	—	2	1	no	—
162	C₂×Dic₁₉	—	4	2	no	—
163	C₂×Dic₁₉	—	4	2	no	—
164	C₂×Dic₁₉	—	4	2	no	—
165	C₂×Dic₁₉	#100	1	2	yes	—
166	C₂×Dic₁₉	#102	1	2	yes	—
167	C₂×Dic₁₉	#103	1	2	yes	—
168	C₄×D₁₉	—	2	4	no	—
169	C₄×D₁₉	—	2	4	no	—
170	C₄×D₁₉	—	2	2	no	—
171	C₄×D₁₉	—	2	2	no	—
172	C₄×D₁₉	—	2	2	no	—
173	C₄×D₁₉	—	2	2	no	—
174	C₄×D₁₉	—	2	2	no	—
175	C₄×D₁₉	—	2	2	no	—
176	C₄×D₁₉	—	2	2	no	—
177	C₄×D₁₉	—	2	2	no	—
178	C₄×D₁₉	—	8	8	no	—
179	C₈×C₁₉	—	8	1	no	—
180	C₈×C₁₉	—	8	1	no	—
181	C₁₉⋊C₈	—	8	1	no	—
182	C₁₉⋊C₈	—	8	1	no	—
183	C₂×#384	—	19	1	no	—
184	#1797	—	19	1	no	—
185	#1797	—	19	1	no	—
186	#1296	—	19	1	no	—
187	#1296	—	19	1	no	—
188	#1296	—	19	1	no	—
189	#1296	D₁₉	1	1	yes	characteristic, complemented
190	C₂²×C₁₉	#381	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
194	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
195	C₂²×C₁₉	#418	1	1	yes	characteristic
196	C₂²×C₁₉	#419	1	1	yes	characteristic
197	C₂×D₁₉	—	2	2	no	—
198	C₂×D₁₉	—	2	2	no	—
199	C₂×D₁₉	—	2	2	no	—
200	C₂×D₁₉	—	2	2	no	—
201	C₂×D₁₉	—	2	2	no	—
202	C₂×D₁₉	—	2	2	no	—
203	C₂×D₁₉	#332	1	4	yes	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	#480	1	1	yes	characteristic
208	C₄×C₁₉	#480	1	1	yes	characteristic
209	C₄×C₁₉	#481	1	1	yes	characteristic
210	C₄×C₁₉	#481	1	1	yes	characteristic
211	C₄×C₁₉	#483	1	1	yes	characteristic
212	C₄×C₁₉	#483	1	1	yes	characteristic
213	C₄×C₁₉	#484	1	1	yes	characteristic
214	C₄×C₁₉	#484	1	1	yes	characteristic
215	Dic₁₉	—	2	2	no	—
216	Dic₁₉	—	2	2	no	—
217	Dic₁₉	—	2	2	no	—
218	Dic₁₉	—	8	2	no	—
219	C₂²×C₄⋊C₄	—	19	2	no	—
220	C₂²×C₄⋊C₄	—	38	1	no	—
221	C₂²×C₄⋊C₄	—	38	1	no	—
222	C₂²×C₄²	—	19	1	no	—
223	C₂×C₄⋊C₈	—	19	1	no	—
224	C₂×C₄⋊C₈	—	19	1	no	—
225	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	—	38	1	no	—
228	C₂×C₂²⋊C₈	—	38	1	no	—
229	#384	—	19	2	no	—
230	#384	—	19	1	no	—
231	#384	—	38	1	no	—
232	#384	—	38	1	no	—
233	#384	C₂×D₁₉	1	1	yes	characteristic
234	#336	—	38	1	no	—
235	#336	—	38	1	no	—
236	C₂×C₁₉	C₂×#332	1	1	yes	characteristic
237	C₂×C₁₉	#1545	1	1	yes	characteristic
238	C₂×C₁₉	#1548	1	1	yes	characteristic
239	C₂×C₁₉	#1556	1	1	yes	characteristic
240	C₂×C₁₉	#1821	1	1	yes	characteristic
241	C₂×C₁₉	#1823	1	1	yes	characteristic
242	C₂×C₁₉	#1824	1	1	yes	characteristic
243	D₁₉	—	2	4	no	—
244	C₂³×C₄	—	19	1	no	—
245	C₂³×C₄	—	19	1	no	—
246	C₂³×C₄	—	19	1	no	—
247	C₂³×C₄	—	38	2	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	38	1	no	—
251	C₂²×C₈	—	38	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	19	2	no	—
255	C₂×C₄⋊C₄	—	38	2	no	—
256	C₂×C₄⋊C₄	—	38	2	no	—
257	C₂×C₄⋊C₄	—	38	2	no	—
258	C₂×C₄⋊C₄	—	38	1	no	—
259	C₂×C₄⋊C₄	—	38	1	no	—
260	C₂×C₄⋊C₄	—	76	2	no	—
261	C₂×C₄⋊C₄	—	76	2	no	—
262	C₂×C₄⋊C₄	—	76	2	no	—
263	C₂×C₄⋊C₄	—	76	2	no	—
264	C₂×C₄⋊C₄	—	76	4	no	—
265	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
266	C₂×C₄²	—	19	1	no	—
267	C₂×C₄²	—	19	1	no	—
268	C₂×C₄²	—	19	1	no	—
269	C₂×C₄²	—	38	1	no	—
270	C₂×C₄²	—	38	1	no	—
271	C₂×C₄²	—	38	1	no	—
272	C₂×C₄²	—	38	1	no	—
273	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	38	1	no	—
279	C₄⋊C₈	—	38	1	no	—
280	C₄⋊C₈	—	38	1	no	—
281	C₄⋊C₈	—	38	1	no	—
282	C₂²⋊C₈	—	76	2	no	—
283	C₂²⋊C₈	—	76	2	no	—
284	C₁₉	#8724	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	—	19	1	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	19	1	no	—
288	C₂²×C₄	—	19	1	no	—
289	C₂²×C₄	—	19	1	no	—
290	C₂²×C₄	—	19	2	no	—
291	C₂²×C₄	—	19	2	no	—
292	C₂²×C₄	—	19	2	no	—
293	C₂²×C₄	—	19	2	no	—
294	C₂²×C₄	—	38	2	no	—
295	C₂²×C₄	—	38	2	no	—
296	C₂²×C₄	—	38	1	no	—
297	C₂²×C₄	—	38	1	no	—
298	C₂²×C₄	—	38	1	no	—
299	C₂²×C₄	—	38	1	no	—
300	C₂²×C₄	—	38	1	no	—
301	C₂²×C₄	—	38	1	no	—
302	C₂²×C₄	—	38	1	no	—
303	C₂²×C₄	—	38	1	no	—
304	C₂²×C₄	—	38	1	no	—
305	C₂²×C₄	—	38	1	no	—
306	C₂²×C₄	—	38	2	no	—
307	C₂²×C₄	—	76	4	no	—
308	C₂²×C₄	—	76	4	no	—
309	C₂²×C₄	—	76	4	no	—
310	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	76	1	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₂×C₈	—	76	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	76	2	no	—
331	C₄⋊C₄	—	76	4	no	—
332	C₄⋊C₄	—	76	4	no	—
333	C₄⋊C₄	—	76	4	no	—
334	C₄⋊C₄	—	76	1	no	—
335	C₄⋊C₄	—	76	1	no	—
336	C₄⋊C₄	—	76	1	no	—
337	C₄⋊C₄	—	76	1	no	—
338	C₄²	—	38	1	no	—
339	C₄²	—	38	1	no	—
340	C₄²	—	38	1	no	—
341	C₄²	—	38	1	no	—
342	C₄²	—	38	1	no	—
343	C₄²	—	38	1	no	—
344	C₄²	#64541	1	1	yes	characteristic
345	C₄²	#64541	1	1	yes	characteristic
346	C₄²	#64543	1	1	yes	characteristic
347	C₄²	#64545	1	1	yes	characteristic
348	C₂³	—	19	2	no	—
349	C₂³	—	19	2	no	—
350	C₂³	—	19	2	no	—
351	C₂³	—	38	1	no	—
352	C₂³	—	38	1	no	—
353	C₂³	—	38	1	no	—
354	C₂³	—	38	1	no	—
355	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	19	2	no	—
362	C₂×C₄	—	19	2	no	—
363	C₂×C₄	—	19	2	no	—
364	C₂×C₄	—	38	4	no	—
365	C₂×C₄	—	38	4	no	—
366	C₂×C₄	—	38	1	no	—
367	C₂×C₄	—	38	1	no	—
368	C₂×C₄	—	38	1	no	—
369	C₂×C₄	—	38	1	no	—
370	C₂×C₄	—	38	1	no	—
371	C₂×C₄	—	38	1	no	—
372	C₂×C₄	—	38	2	no	—
373	C₂×C₄	—	38	2	no	—
374	C₂×C₄	—	38	2	no	—
375	C₂×C₄	—	38	2	no	—
376	C₂×C₄	—	38	2	no	—
377	C₂×C₄	—	38	2	no	—
378	C₂×C₄	—	38	2	no	—
379	C₂×C₄	—	38	2	no	—
380	C₂×C₄	—	76	2	no	—
381	C₂×C₄	—	76	2	no	—
382	C₂×C₄	—	76	2	no	—
383	C₂×C₄	—	152	8	no	—
384	C₂×C₄	#10597318	1	1	yes	characteristic
385	C₂×C₄	#10597329	1	1	yes	characteristic
386	C₂×C₄	#10597329	1	1	yes	characteristic
387	C₂×C₄	#10597338	1	1	yes	characteristic
388	C₂×C₄	#10597340	1	1	yes	characteristic
389	C₂×C₄	#10597340	1	1	yes	characteristic
390	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
391	C₂×C₄	#10597357	1	1	yes	characteristic
392	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
393	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
394	C₂×C₄	#10597360	1	1	yes	characteristic
395	C₂×C₄	#10597361	1	1	yes	characteristic
396	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
397	C₂×C₄	#10597364	1	1	yes	characteristic
398	C₈	—	8	1	no	—
399	C₈	—	8	1	no	—
400	C₈	—	152	1	no	—
401	C₈	—	152	1	no	—
402	C₂²	—	19	4	no	—
403	C₂²	—	38	2	no	—
404	C₂²	—	38	2	no	—
405	C₂²	—	38	2	no	—
406	C₂²	—	38	2	no	—
407	C₂²	—	38	2	no	—
408	C₂²	—	38	2	no	—
409	C₂²	#11926406	1	1	yes	characteristic
410	C₂²	#100×D₁₉	1	1	yes	characteristic
411	C₂²	#101×D₁₉	1	1	yes	characteristic
412	C₂²	#102×D₁₉	1	1	yes	characteristic
413	C₂²	#103×D₁₉	1	1	yes	characteristic
414	C₂²	#11926547	1	1	yes	characteristic
415	C₂²	#11926551	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	8	2	no	—
419	C₄	—	38	2	no	—
420	C₄	—	38	2	no	—
421	C₄	—	38	2	no	—
422	C₄	—	152	2	no	—
423	C₄	#11926856	1	1	yes	characteristic
424	C₄	#11926859	1	1	yes	characteristic
425	C₄	#11926861	1	1	yes	characteristic
426	C₄	#11926864	1	1	yes	characteristic
427	C₄	#11926873	1	1	yes	characteristic
428	C₄	#11926876	1	1	yes	characteristic
429	C₄	#11926878	1	1	yes	characteristic
430	C₄	#11926881	1	1	yes	characteristic
431	C₂	—	38	4	no	—
432	C₂	D₁₉×#332	1	1	yes	characteristic
433	C₂	#14562301	1	1	yes	characteristic
434	C₂	#14562314	1	1	yes	characteristic
435	C₂	#14562350	1	1	yes	characteristic
436	C₂	#14563714	1	1	yes	characteristic
437	C₂	#14563720	1	1	yes	characteristic
438	C₂	#14563724	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#8724
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. #14561519	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561518	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
189. #1296	D₁₉	semidirect
284. C₁₉	#8724	semidirect

Maximal subgroups

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

subgroup	index
D₁₉×#384	2
#14563612	2
#14561519	2
#14561518	2
C₁₉×#1296	2
#8724	19