Subgroups — #18077091

Order 4864.

688 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926601	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
6	#11926601	—	2	4	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₂×#10597260	—	2	1	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#11926299	—	2	1	no	—
13	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
14	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#390	C₄	1	1	yes	characteristic
19	C₁₉×#389	C₄	1	1	yes	characteristic
20	C₁₉×#388	—	2	1	no	—
21	C₁₉×#386	—	2	1	no	—
22	C₁₉×#380	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₁₉×#121	—	2	2	no	—
32	C₁₉×#121	—	2	2	no	—
33	C₄×D₄×C₁₉	—	2	2	no	—
34	C₄×D₄×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	4	4	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	2	no	—
46	C₂×C₄²×C₁₉	—	2	2	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
58	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
61	#10597260	—	2	4	no	—
62	C₄×C₁₉⋊C₈	—	2	2	no	—
63	C₄×C₁₉⋊C₈	—	2	2	no	—
64	C₂⁴×C₁₉	—	2	1	no	—
65	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	4	no	—
67	C₂×D₄×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	4	2	no	—
71	C₂×D₄×C₁₉	—	4	2	no	—
72	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	4	2	no	—
101	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
102	C₂²⋊C₄×C₁₉	—	2	4	no	—
103	C₂²⋊C₄×C₁₉	—	4	2	no	—
104	C₂²⋊C₄×C₁₉	—	4	2	no	—
105	C₂²⋊C₄×C₁₉	—	4	2	no	—
106	C₂²⋊C₄×C₁₉	—	4	2	no	—
107	C₄²×C₁₉	—	2	2	no	—
108	C₄²×C₁₉	—	2	1	no	—
109	C₄²×C₁₉	—	2	2	no	—
110	C₄²×C₁₉	—	2	1	no	—
111	C₄²×C₁₉	—	4	2	no	—
112	C₄²×C₁₉	C₂×D₄	1	2	yes	—
113	C₄²×C₁₉	#41	1	2	yes	—
114	C₂×C₁₉⋊C₈	—	2	4	no	—
115	C₂×C₁₉⋊C₈	—	2	4	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	C₂×C₁₉⋊C₈	—	4	2	no	—
118	C₂×C₁₉⋊C₈	—	4	2	no	—
119	C₂×C₁₉⋊C₈	—	4	2	no	—
120	#8943	—	19	1	no	maximal, Sylow
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	#104	1	2	yes	—
135	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	D₄×C₁₉	—	2	4	no	—
137	D₄×C₁₉	—	4	8	no	—
138	D₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	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	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	8	2	no	—
165	C₂×C₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	2	yes	—
169	C₂×C₄×C₁₉	#123	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	#131	1	2	yes	—
173	C₂×C₄×C₁₉	#135	1	2	yes	—
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₁₉⋊C₈	—	4	4	no	—
176	C₁₉⋊C₈	—	4	4	no	—
177	C₂×#432	—	19	1	no	—
178	C₄×#121	D₁₉	1	1	yes	characteristic
179	C₄×C₂²⋊C₈	—	19	1	no	—
180	C₂×D₄⋊C₈	—	19	2	no	—
181	#1279	—	19	2	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	1	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	8	1	no	—
193	C₂²×C₁₉	—	8	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	#386	1	1	yes	characteristic
197	C₂²×C₁₉	#407	1	1	yes	characteristic
198	C₂²×C₁₉	#408	1	1	yes	characteristic
199	C₂²×C₁₉	#416	1	1	yes	characteristic
200	C₂²×C₁₉	#418	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
202	C₂²×C₁₉	#421	1	1	yes	characteristic
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	—	8	1	no	—
210	C₄×C₁₉	#435	1	2	yes	—
211	C₄×C₁₉	#436	1	2	yes	—
212	C₄×C₁₉	#449	1	2	yes	—
213	C₄×C₁₉	#482	1	2	yes	—
214	C₂×#121	Dic₁₉	1	1	yes	characteristic
215	C₂×C₄×D₄	—	2	1	no	—
216	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
217	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
218	#432	—	38	4	no	—
219	C₂×C₄⋊C₈	—	19	2	no	—
220	C₂×C₂²⋊C₈	—	38	1	no	—
221	C₂×C₂²⋊C₈	—	38	1	no	—
222	C₂×#97	—	38	1	no	—
223	C₂×C₄×C₈	—	19	2	no	—
224	#390	Dic₁₉	1	1	yes	characteristic
225	#389	Dic₁₉	1	1	yes	characteristic
226	#388	—	2	1	no	—
227	#386	—	2	1	no	—
228	#380	Dic₁₉	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
230	C₄×C₂²⋊C₄	—	2	1	no	—
231	#336	—	38	1	no	—
232	D₄⋊C₈	—	38	4	no	—
233	C₂×C₁₉	—	4	2	no	—
234	C₂×C₁₉	—	8	2	no	—
235	C₂×C₁₉	#1488	1	1	yes	characteristic
236	C₂×C₁₉	#1490	1	1	yes	characteristic
237	C₂×C₁₉	#1494	1	1	yes	characteristic
238	C₂×C₁₉	#1496	1	1	yes	characteristic
239	C₂×C₁₉	#1870	1	1	yes	characteristic
240	C₂×C₁₉	#1871	1	1	yes	characteristic
241	C₂×C₁₉	#1875	1	1	yes	characteristic
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
246	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
248	C₂²×C₈	—	38	2	no	—
249	C₂²×C₈	—	38	2	no	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	4	4	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
268	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
271	C₄⋊C₈	—	19	4	no	—
272	C₄⋊C₈	—	38	2	no	—
273	C₂²⋊C₈	—	38	4	no	—
274	C₂²⋊C₈	—	38	4	no	—
275	#97	—	38	4	no	—
276	C₄×C₈	—	38	2	no	—
277	C₄×C₈	—	38	2	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	C₁₉	#8943	1	1	yes	characteristic, complemented, Sylow
282	C₂⁴	—	2	1	no	—
283	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	#64520	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
315	C₂×C₈	—	38	4	no	—
316	C₂×C₈	—	38	4	no	—
317	C₂×C₈	—	76	2	no	—
318	C₂×C₈	—	76	2	no	—
319	C₂×C₈	—	76	2	no	—
320	C₂×C₈	—	76	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	#64520	1	2	yes	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	2	no	—
336	C₄²	D₄×D₁₉	1	2	yes	—
337	C₄²	#64543	1	2	yes	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	#10597294	1	2	yes	—
352	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
353	D₄	—	2	4	no	—
354	D₄	—	4	8	no	—
355	D₄	—	4	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	C₂×#64520	1	1	yes	characteristic
384	C₂×C₄	C₂×#64520	1	1	yes	characteristic
385	C₂×C₄	#10597378	1	2	yes	—
386	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
387	C₂×C₄	#10597381	1	1	yes	characteristic
388	C₂×C₄	#10597383	1	1	yes	characteristic
389	C₂×C₄	#10597385	1	2	yes	—
390	C₂×C₄	#10597394	1	2	yes	—
391	C₂×C₄	#10597396	1	2	yes	—
392	C₈	—	76	4	no	—
393	C₈	—	76	4	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	#11926424	1	1	yes	characteristic
409	C₂²	#11926508	1	1	yes	characteristic
410	C₂²	#11926511	1	1	yes	characteristic
411	C₂²	#11926540	1	1	yes	characteristic
412	C₂²	#11926549	1	1	yes	characteristic
413	C₂²	C₂×#10597294	1	1	yes	characteristic
414	C₂²	#11926561	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	#11926616	1	2	yes	—
423	C₄	#11926622	1	2	yes	—
424	C₄	#11926687	1	2	yes	—
425	C₄	#11926865	1	2	yes	—
426	C₂	—	4	2	no	—
427	C₂	—	8	2	no	—
428	C₂	#14562069	1	1	yes	characteristic
429	C₂	#14562078	1	1	yes	characteristic
430	C₂	#14562095	1	1	yes	characteristic
431	C₂	#14562104	1	1	yes	characteristic
432	C₂	#14563933	1	1	yes	characteristic
433	C₂	#14563938	1	1	yes	characteristic
434	C₂	#14563958	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#121	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#121	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#121	D₁₉
hypocenter	C₁₉	#8943
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#11926601	C₂	semidirect
2. C₄×C₂²⋊(C₁₉⋊C₈)	C₂	semidirect
3. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561476	C₂	semidirect
60. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
281. C₁₉	#8943	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926601	2
C₄×C₂²⋊(C₁₉⋊C₈)	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561476	2
C₄×C₁₉×#121	2
#8943	19