Subgroups — #18070591

Order 4864.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926299	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561458	C₂	1	2	yes	maximal, complemented
4	#14561456	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	—	2	1	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	#11926299	—	2	1	no	—
10	#11926299	C₂²	1	2	yes	—
11	#11926299	C₂²	1	2	yes	—
12	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₉	—	2	1	no	—
14	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#390	C₂²	1	1	yes	characteristic
17	C₁₉×#389	C₂²	1	1	yes	characteristic
18	C₁₉×#388	—	2	1	no	—
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#380	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₁₉×#121	—	2	2	no	—
30	C₁₉×#121	C₈	1	4	yes	complemented
31	C₄×D₄×C₁₉	—	4	2	no	—
32	C₄×D₄×C₁₉	—	4	2	no	—
33	C₄×D₄×C₁₉	—	4	2	no	—
34	C₂×C₄⋊C₄×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×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	4	2	no	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	—	2	4	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₂²×C₁₉⋊C₈	—	4	2	no	—
53	C₂²×C₁₉⋊C₈	—	4	2	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
59	C₂⁴×C₁₉	—	2	1	no	—
60	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×D₄×C₁₉	—	2	4	no	—
62	C₂×D₄×C₁₉	—	2	1	no	—
63	C₂×D₄×C₁₉	—	4	1	no	—
64	C₂×D₄×C₁₉	—	4	1	no	—
65	C₂×D₄×C₁₉	—	4	2	no	—
66	C₂×D₄×C₁₉	—	4	2	no	—
67	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	complemented
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	—	4	2	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
86	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
87	C₂²×C₄×C₁₉	D₈	1	2	yes	—
88	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	complemented
98	C₂²⋊C₄×C₁₉	—	2	4	no	—
99	C₂²⋊C₄×C₁₉	—	4	2	no	—
100	C₂²⋊C₄×C₁₉	—	4	2	no	—
101	C₂²⋊C₄×C₁₉	—	4	1	no	—
102	C₂²⋊C₄×C₁₉	—	4	1	no	—
103	C₂²⋊C₄×C₁₉	—	4	1	no	—
104	C₂²⋊C₄×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	2	2	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	—	4	2	no	—
110	C₂×C₁₉⋊C₈	—	2	4	no	—
111	C₂×C₁₉⋊C₈	—	4	8	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	C₂×C₁₉⋊C₈	—	4	2	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	#7586	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
130	C₂³×C₁₉	#102	1	2	yes	—
131	C₂³×C₁₉	#104	1	2	yes	—
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	D₄×C₁₉	—	4	2	no	—
134	D₄×C₁₉	—	4	2	no	—
135	D₄×C₁₉	—	4	8	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	4	no	—
138	C₂×C₄×C₁₉	—	2	1	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	1	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	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	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	—	8	4	no	—
164	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
165	C₂×C₄×C₁₉	#99	1	2	yes	—
166	C₂×C₄×C₁₉	#102	1	2	yes	—
167	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
173	C₁₉⋊C₈	—	4	4	no	—
174	C₁₉⋊C₈	—	8	2	no	—
175	C₄×#121	D₁₉	1	1	yes	characteristic
176	#1797	—	19	1	no	—
177	C₂×#336	—	19	1	no	—
178	#1271	—	19	2	no	—
179	#1270	—	19	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	4	2	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	8	1	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	—	8	1	no	—
193	C₂²×C₁₉	D₄⋊C₈	1	4	yes	—
194	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
196	C₂²×C₁₉	#413	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
198	C₂²×C₁₉	#417	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
200	C₂²×C₁₉	#421	1	1	yes	characteristic
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	8	1	no	—
212	C₄×C₁₉	—	8	1	no	—
213	C₂³×C₈	—	38	1	no	—
214	C₂×#121	Dic₁₉	1	1	yes	characteristic
215	C₂×C₄×D₄	—	2	1	no	—
216	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
217	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
218	C₂×C₄⋊C₈	—	38	1	no	—
219	C₂×C₂²⋊C₈	—	38	1	no	—
220	#390	C₂×D₁₉	1	1	yes	characteristic
221	#389	C₂×D₁₉	1	1	yes	characteristic
222	#388	—	2	1	no	—
223	#386	—	2	1	no	—
224	#380	Dic₁₉	1	1	yes	characteristic
225	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
226	C₄×C₂²⋊C₄	—	2	1	no	—
227	#336	—	19	2	no	—
228	#336	—	19	2	no	—
229	#336	—	38	1	no	—
230	C₂×C₁₉	—	2	4	no	—
231	C₂×C₁₉	—	8	2	no	—
232	C₂×C₁₉	#1459	1	1	yes	characteristic
233	C₂×C₁₉	C₂×D₄⋊C₈	1	1	yes	characteristic
234	C₂×C₁₉	#1477	1	1	yes	characteristic
235	C₂×C₁₉	#1504	1	1	yes	characteristic
236	C₂×C₁₉	#1519	1	1	yes	characteristic
237	C₂×C₁₉	#1532	1	1	yes	characteristic
238	C₂×C₁₉	#1547	1	1	yes	characteristic
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
243	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂²×C₈	—	38	4	no	—
246	C₂²×C₈	—	38	2	no	—
247	C₂²×C₈	—	38	2	no	—
248	C₂²×C₈	—	76	2	no	—
249	C₂²×C₈	—	76	2	no	—
250	#121	—	2	2	no	—
251	#121	C₁₉⋊C₈	1	4	yes	complemented
252	C₄×D₄	—	4	2	no	—
253	C₄×D₄	—	4	2	no	—
254	C₄×D₄	—	4	2	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	1	no	—
265	C₂×C₄²	—	4	2	no	—
266	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
267	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
268	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
270	C₄⋊C₈	—	76	2	no	—
271	C₂²⋊C₈	—	76	2	no	—
272	#95	—	2	1	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	C₁₉	#7586	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	—	2	1	no	—
277	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	C₂×C₁₉⋊C₈	1	2	yes	complemented
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
300	C₂²×C₄	#64520	1	2	yes	—
301	C₂²×C₄	#64525	1	2	yes	—
302	C₂²×C₄	#64526	1	2	yes	—
303	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂×C₈	—	38	4	no	—
310	C₂×C₈	—	76	8	no	—
311	C₂×C₈	—	76	2	no	—
312	C₂×C₈	—	76	2	no	—
313	C₂×C₈	—	76	2	no	—
314	C₂×C₈	—	76	2	no	—
315	C₂×C₈	—	76	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	C₂×C₁₉⋊C₈	1	2	yes	complemented
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
346	C₂³	#10597289	1	2	yes	—
347	C₂³	#10597294	1	2	yes	—
348	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	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	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	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	—	8	4	no	—
380	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
381	C₂×C₄	#10597289	1	2	yes	—
382	C₂×C₄	#10597291	1	2	yes	—
383	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
384	C₂×C₄	C₂×#64520	1	1	yes	characteristic
385	C₂×C₄	C₂×#64525	1	1	yes	characteristic
386	C₂×C₄	C₂×#64526	1	1	yes	characteristic
387	C₂×C₄	#10597395	1	1	yes	characteristic
388	C₂×C₄	#10597397	1	1	yes	characteristic
389	C₈	—	76	4	no	—
390	C₈	—	152	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	D₄⋊(C₁₉⋊C₈)	1	4	yes	—
405	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
406	C₂²	C₂×#10597291	1	1	yes	characteristic
407	C₂²	#11926528	1	1	yes	characteristic
408	C₂²	C₂×#10597289	1	1	yes	characteristic
409	C₂²	#11926545	1	1	yes	characteristic
410	C₂²	C₂×#10597294	1	1	yes	characteristic
411	C₂²	#11926561	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₂	—	2	4	no	—
425	C₂	—	8	2	no	—
426	C₂	#14561953	1	1	yes	characteristic
427	C₂	C₂×D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
428	C₂	#14562022	1	1	yes	characteristic
429	C₂	#14562139	1	1	yes	characteristic
430	C₂	#14562203	1	1	yes	characteristic
431	C₂	#14562255	1	1	yes	characteristic
432	C₂	#14562312	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
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	#7586
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. #14563615	C₂	semidirect
2. C₂×#11926299	C₂	semidirect
3. #14561458	C₂	semidirect
4. #14561456	C₂	semidirect
30. C₁₉×#121	C₈	semidirect
67. C₂×D₄×C₁₉	C₂×C₈	semidirect
97. C₄⋊C₄×C₁₉	C₂×C₈	semidirect
251. #121	C₁₉⋊C₈	semidirect
275. C₁₉	#7586	semidirect
284. C₂×D₄	C₂×C₁₉⋊C₈	semidirect
321. C₄⋊C₄	C₂×C₁₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
C₂×#11926299	2
#14561458	2
#14561456	2
C₄×C₁₉×#121	2
#7586	19