Subgroups — #18090721

Order 4864.

846 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926298	C₂	1	2	yes	maximal
3	C₂×#11926298	C₂	1	2	yes	maximal
4	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₁₉	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
10	C₂×C₁₉⋊#95	C₄	1	2	yes	—
11	C₂×C₁₉⋊#95	C₄	1	1	yes	characteristic
12	C₂×C₁₉⋊#95	C₄	1	1	yes	characteristic
13	#11926298	—	2	4	no	—
14	#11926298	—	2	4	no	—
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#336	—	2	2	no	—
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
23	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	2	no	—
30	C₂²×C₈×C₁₉	—	2	2	no	—
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₂²×C₈×C₁₉	D₄	1	2	yes	—
33	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
34	C₂×C₄²×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	D₄	1	2	yes	—
37	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
38	C₂×C₄×Dic₁₉	—	2	2	no	—
39	C₂×C₄×Dic₁₉	—	2	2	no	—
40	C₂×C₄×Dic₁₉	—	2	2	no	—
41	C₂×C₄×Dic₁₉	—	2	2	no	—
42	C₂×C₄×Dic₁₉	—	2	2	no	—
43	C₂×C₄×Dic₁₉	—	2	2	no	—
44	C₂²×C₁₉⋊C₈	—	2	2	no	—
45	C₂²×C₁₉⋊C₈	—	2	2	no	—
46	C₂²×C₁₉⋊C₈	—	2	2	no	—
47	C₂²×C₁₉⋊C₈	—	2	2	no	—
48	C₂²×C₁₉⋊C₈	—	2	2	no	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
51	C₁₉⋊#95	—	2	2	no	—
52	C₁₉⋊#95	—	2	4	no	—
53	C₁₉⋊#95	C₈	1	4	yes	complemented
54	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
55	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
65	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	#41	1	2	yes	—
74	C₂²×C₄×C₁₉	#41	1	2	yes	—
75	C₂²×C₄×C₁₉	#41	1	2	yes	—
76	C₂²×Dic₁₉	—	2	2	no	—
77	C₂²×Dic₁₉	—	2	2	no	—
78	C₂²×Dic₁₉	—	2	2	no	—
79	C₂²×Dic₁₉	—	2	2	no	—
80	C₂²×Dic₁₉	—	2	2	no	—
81	C₂²×Dic₁₉	—	2	2	no	—
82	C₂²×Dic₁₉	—	2	2	no	—
83	C₂²×Dic₁₉	—	2	2	no	—
84	C₂²×Dic₁₉	—	2	2	no	—
85	C₂²×Dic₁₉	—	2	2	no	—
86	C₂²×Dic₁₉	—	2	2	no	—
87	C₂²×Dic₁₉	—	2	2	no	—
88	C₂²×Dic₁₉	C₂×C₈	1	4	yes	—
89	C₂²×Dic₁₉	M₁₆	1	4	yes	—
90	C₂×C₈×C₁₉	—	2	2	no	—
91	C₂×C₈×C₁₉	—	2	4	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	2	4	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	2	no	—
99	C₂×C₈×C₁₉	—	4	2	no	—
100	C₄²×C₁₉	—	2	2	no	—
101	C₄²×C₁₉	—	2	4	no	—
102	C₄²×C₁₉	—	2	2	no	—
103	C₄×Dic₁₉	—	4	2	no	—
104	C₄×Dic₁₉	—	4	2	no	—
105	C₄×Dic₁₉	—	4	2	no	—
106	C₄×Dic₁₉	—	4	2	no	—
107	C₂×C₁₉⋊C₈	—	2	4	no	—
108	C₂×C₁₉⋊C₈	—	2	4	no	—
109	C₂×C₁₉⋊C₈	—	2	4	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	#11255	—	19	1	no	maximal, Sylow
115	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₉	#117	1	2	yes	—
117	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
118	C₂³×C₁₉	C₄×D₄	1	2	yes	—
119	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
120	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
121	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
122	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
123	C₂³×C₁₉	#131	1	1	yes	characteristic
124	C₂³×C₁₉	#131	1	1	yes	characteristic
125	C₂³×C₁₉	#131	1	2	yes	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
136	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#121	1	2	yes	—
139	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
141	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#123	1	2	yes	—
144	C₂×C₄×C₁₉	#123	1	2	yes	—
145	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#124	1	2	yes	—
148	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#125	1	2	yes	—
150	C₂×C₄×C₁₉	#125	1	2	yes	—
151	C₂×C₄×C₁₉	#126	1	2	yes	—
152	C₂×C₄×C₁₉	#126	1	2	yes	—
153	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
154	C₂×Dic₁₉	—	2	4	no	—
155	C₂×Dic₁₉	—	2	4	no	—
156	C₂×Dic₁₉	—	2	4	no	—
157	C₂×Dic₁₉	—	2	4	no	—
158	C₂×Dic₁₉	—	2	4	no	—
159	C₂×Dic₁₉	—	2	4	no	—
160	C₂×Dic₁₉	—	4	2	no	—
161	C₂×Dic₁₉	—	4	2	no	—
162	C₂×Dic₁₉	—	4	2	no	—
163	C₂×Dic₁₉	—	4	2	no	—
164	C₂×Dic₁₉	—	4	2	no	—
165	C₂×Dic₁₉	—	4	2	no	—
166	C₂×Dic₁₉	—	4	2	no	—
167	C₂×Dic₁₉	—	4	2	no	—
168	C₈×C₁₉	—	4	2	no	—
169	C₈×C₁₉	—	4	2	no	—
170	C₁₉⋊C₈	—	4	4	no	—
171	C₂²×C₄⋊C₈	—	19	1	no	—
172	C₂×#336	—	19	2	no	—
173	C₂×#336	—	19	2	no	—
174	C₂×#336	D₁₉	1	1	yes	characteristic
175	C₄×#95	—	19	1	no	—
176	C₂²×C₁₉	#382	1	1	yes	characteristic
177	C₂²×C₁₉	#385	1	1	yes	characteristic
178	C₂²×C₁₉	#387	1	2	yes	—
179	C₂²×C₁₉	#388	1	2	yes	—
180	C₂²×C₁₉	#389	1	1	yes	characteristic
181	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
182	C₂²×C₁₉	#423	1	1	yes	characteristic
183	C₂²×C₁₉	#424	1	1	yes	characteristic
184	C₂²×C₁₉	#424	1	1	yes	characteristic
185	C₂²×C₁₉	#431	1	2	yes	—
186	C₂²×C₁₉	#432	1	2	yes	—
187	C₂²×C₁₉	#433	1	2	yes	—
188	C₂²×C₁₉	#433	1	2	yes	—
189	C₂²×C₁₉	C₈×D₄	1	2	yes	—
190	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
191	C₂²×C₁₉	#435	1	2	yes	—
192	C₂²×C₁₉	#435	1	2	yes	—
193	C₂²×C₁₉	#435	1	2	yes	—
194	C₂²×C₁₉	#436	1	2	yes	—
195	C₂²×C₁₉	#436	1	1	yes	characteristic
196	C₂²×C₁₉	C₈×Q₈	1	1	yes	characteristic
197	C₂²×C₁₉	#446	1	2	yes	—
198	C₂²×C₁₉	#446	1	1	yes	characteristic
199	C₄×C₁₉	—	2	4	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	#393	1	1	yes	characteristic
202	C₄×C₁₉	#394	1	1	yes	characteristic
203	C₄×C₁₉	#397	1	1	yes	characteristic
204	C₄×C₁₉	#398	1	2	yes	—
205	C₄×C₁₉	#400	1	1	yes	characteristic
206	C₄×C₁₉	#400	1	2	yes	—
207	Dic₁₉	—	4	4	no	—
208	Dic₁₉	—	4	4	no	—
209	C₂³×C₈	—	19	2	no	—
210	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
211	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
212	C₂²×C₄²	—	19	2	no	—
213	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	38	4	no	—
215	C₂×C₄⋊C₈	—	38	2	no	—
216	C₂×#95	—	19	1	no	—
217	C₂×#95	—	19	2	no	—
218	C₂×#95	—	19	1	no	—
219	#336	—	2	2	no	—
220	#336	—	38	4	no	—
221	#336	—	38	4	no	—
222	C₂×C₁₉	#1442	1	1	yes	characteristic
223	C₂×C₁₉	#1831	1	1	yes	characteristic
224	C₂×C₁₉	#1832	1	1	yes	characteristic
225	C₂×C₁₉	#1850	1	1	yes	characteristic
226	C₂×C₁₉	#1851	1	1	yes	characteristic
227	C₂×C₁₉	#1916	1	2	yes	—
228	C₂×C₁₉	#1917	1	2	yes	—
229	C₂×C₁₉	#1923	1	2	yes	—
230	C₂×C₁₉	#1924	1	2	yes	—
231	C₂×C₁₉	#1939	1	1	yes	characteristic
232	C₂×C₁₉	#1940	1	1	yes	characteristic
233	C₂³×C₄	—	19	2	no	—
234	C₂³×C₄	—	19	2	no	—
235	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
236	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
237	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	19	4	no	—
247	C₂²×C₈	—	38	2	no	—
248	C₂²×C₈	—	38	2	no	—
249	C₂²×C₈	—	38	2	no	—
250	C₂²×C₈	—	38	2	no	—
251	C₂²×C₈	—	38	2	no	—
252	C₂²×C₈	—	38	2	no	—
253	C₂²×C₈	Dic₃₈	1	2	yes	—
254	C₂²×C₈	D₇₆	1	2	yes	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	38	2	no	—
258	C₂×C₄²	—	38	2	no	—
259	C₂×C₄²	—	38	2	no	—
260	C₂×C₄²	—	38	2	no	—
261	C₂×C₄²	—	38	2	no	—
262	C₂×C₄²	—	38	2	no	—
263	C₂×C₄²	Dic₃₈	1	2	yes	—
264	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
265	C₄⋊C₈	—	38	8	no	—
266	#95	—	19	4	no	—
267	#95	—	38	4	no	—
268	#95	—	38	2	no	—
269	C₁₉	#11255	1	1	yes	characteristic, complemented, Sylow
270	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	19	4	no	—
278	C₂²×C₄	—	19	4	no	—
279	C₂²×C₄	—	38	2	no	—
280	C₂²×C₄	—	38	2	no	—
281	C₂²×C₄	—	38	2	no	—
282	C₂²×C₄	—	38	2	no	—
283	C₂²×C₄	—	38	2	no	—
284	C₂²×C₄	—	38	2	no	—
285	C₂²×C₄	—	38	2	no	—
286	C₂²×C₄	—	38	2	no	—
287	C₂²×C₄	—	38	2	no	—
288	C₂²×C₄	—	38	2	no	—
289	C₂²×C₄	—	38	2	no	—
290	C₂²×C₄	—	38	2	no	—
291	C₂²×C₄	C₈×D₁₉	1	2	yes	—
292	C₂²×C₄	#64515	1	2	yes	—
293	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
294	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
295	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
296	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
298	C₂²×C₄	#64541	1	1	yes	characteristic
299	C₂²×C₄	#64541	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₁₉	1	2	yes	—
301	C₂²×C₄	#64543	1	2	yes	—
302	C₂²×C₄	#64543	1	2	yes	—
303	C₂²×C₄	#64545	1	2	yes	—
304	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	38	4	no	—
316	C₂×C₈	—	38	4	no	—
317	C₂×C₈	—	38	4	no	—
318	C₂×C₈	—	76	2	no	—
319	C₂×C₈	—	76	2	no	—
320	C₂×C₈	—	76	2	no	—
321	C₂×C₈	—	76	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	76	2	no	—
326	C₄²	—	76	2	no	—
327	C₄²	—	76	2	no	—
328	C₄²	—	76	2	no	—
329	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
330	C₂³	C₄×D₇₆	1	1	yes	characteristic
331	C₂³	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
332	C₂³	#10597338	1	2	yes	—
333	C₂³	C₂×C₈×D₁₉	1	1	yes	characteristic
334	C₂³	C₂×#64515	1	1	yes	characteristic
335	C₂³	#10597347	1	1	yes	characteristic
336	C₂³	#10597347	1	1	yes	characteristic
337	C₂³	M₁₆×D₁₉	1	2	yes	—
338	C₂³	#10597353	1	2	yes	—
339	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	38	4	no	—
350	C₂×C₄	—	38	4	no	—
351	C₂×C₄	—	38	4	no	—
352	C₂×C₄	—	38	4	no	—
353	C₂×C₄	—	38	4	no	—
354	C₂×C₄	—	38	4	no	—
355	C₂×C₄	—	76	2	no	—
356	C₂×C₄	—	76	2	no	—
357	C₂×C₄	—	76	2	no	—
358	C₂×C₄	—	76	2	no	—
359	C₂×C₄	—	76	2	no	—
360	C₂×C₄	—	76	2	no	—
361	C₂×C₄	—	76	2	no	—
362	C₂×C₄	—	76	2	no	—
363	C₂×C₄	Dic₁₉⋊C₈	1	4	yes	—
364	C₂×C₄	#10597315	1	1	yes	characteristic
365	C₂×C₄	#10597316	1	1	yes	characteristic
366	C₂×C₄	#10597324	1	2	yes	—
367	C₂×C₄	#10597324	1	2	yes	—
368	C₂×C₄	#10597325	1	2	yes	—
369	C₂×C₄	#10597331	1	2	yes	—
370	C₂×C₄	#10597332	1	2	yes	—
371	C₂×C₄	#10597336	1	2	yes	—
372	C₂×C₄	#10597336	1	2	yes	—
373	C₂×C₄	#10597340	1	2	yes	—
374	C₂×C₄	#10597341	1	2	yes	—
375	C₂×C₄	#10597344	1	2	yes	—
376	C₂×C₄	#10597370	1	1	yes	characteristic
377	C₂×C₄	#10597376	1	1	yes	characteristic
378	C₂×C₄	#10597381	1	1	yes	characteristic
379	C₂×C₄	#10597382	1	1	yes	characteristic
380	C₂×C₄	#10597383	1	1	yes	characteristic
381	C₂×C₄	#10597393	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	76	4	no	—
385	C₂²	#11926409	1	1	yes	characteristic
386	C₂²	#11926416	1	1	yes	characteristic
387	C₂²	#11926431	1	2	yes	—
388	C₂²	#11926436	1	2	yes	—
389	C₂²	#11926442	1	1	yes	characteristic
390	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
391	C₂²	#11926567	1	1	yes	characteristic
392	C₂²	#11926570	1	1	yes	characteristic
393	C₂²	#11926572	1	1	yes	characteristic
394	C₂²	#11926596	1	2	yes	—
395	C₂²	#11926600	1	2	yes	—
396	C₂²	#11926604	1	2	yes	—
397	C₂²	#11926604	1	2	yes	—
398	C₂²	(C₂²⋊D₁₉)⋊C₈	1	2	yes	—
399	C₂²	C₈×D₇₆	1	1	yes	characteristic
400	C₂²	#11926612	1	2	yes	—
401	C₂²	#11926617	1	2	yes	—
402	C₂²	#11926618	1	2	yes	—
403	C₂²	#11926619	1	2	yes	—
404	C₂²	#11926623	1	1	yes	characteristic
405	C₂²	C₈×Dic₃₈	1	1	yes	characteristic
406	C₂²	#11926672	1	2	yes	—
407	C₂²	#11926674	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	4	2	no	—
410	C₄	—	76	4	no	—
411	C₄	—	76	4	no	—
412	C₄	#11926456	1	1	yes	characteristic
413	C₄	#11926461	1	1	yes	characteristic
414	C₄	#11926469	1	1	yes	characteristic
415	C₄	#11926476	1	2	yes	—
416	C₄	#11926483	1	1	yes	characteristic
417	C₄	#11926486	1	2	yes	—
418	C₂	#14561891	1	1	yes	characteristic
419	C₂	#14563751	1	1	yes	characteristic
420	C₂	#14563754	1	1	yes	characteristic
421	C₂	#14563812	1	1	yes	characteristic
422	C₂	#14563817	1	1	yes	characteristic
423	C₂	#14564195	1	2	yes	—
424	C₂	#14564202	1	2	yes	—
425	C₂	#14564242	1	2	yes	—
426	C₂	#14564249	1	2	yes	—
427	C₂	#14564353	1	1	yes	characteristic
428	C₂	#14564358	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Fitting	C₂×C₁₉×#336	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#336	D₁₉
hypocenter	C₁₉	#11255
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
53. C₁₉⋊#95	C₈	semidirect
269. C₁₉	#11255	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₁₉⋊C₈)	2
C₂×#11926298	2
C₄×C₁₉⋊#95	2
C₂×C₁₉×#336	2
#11255	19