Subgroups — #18078722

Order 4864.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564442	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926288	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	—	2	1	no	—
9	D₄×C₁₉⋊C₈	—	2	2	no	—
10	D₄×C₁₉⋊C₈	—	2	2	no	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597289	—	2	1	no	—
14	C₂×#10597289	—	2	1	no	—
15	C₂×#10597289	—	2	1	no	—
16	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	#11926414	C₂²	1	1	yes	characteristic
19	#11926306	—	2	1	no	—
20	#11926288	—	2	2	no	—
21	C₂²×D₈×C₁₉	—	2	1	no	—
22	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#459	—	2	2	no	—
25	C₁₉×#459	C₄	1	4	yes	complemented
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂×D₈×C₁₉	—	2	4	no	—
34	C₂×D₈×C₁₉	—	4	2	no	—
35	C₂×D₈×C₁₉	—	4	2	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₁₉×#127	—	2	1	no	—
38	C₁₉×#127	—	2	1	no	—
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#127	C₂×C₄	1	2	yes	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₄×D₄×C₁₉	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	4	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	4	2	no	—
55	C₂²×C₁₉⋊C₈	—	4	2	no	—
56	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
60	C₁₉×#102	—	2	4	no	—
61	#10597289	—	4	2	no	—
62	#10597289	—	4	2	no	—
63	#10597289	—	4	2	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₂⁴×C₁₉	—	2	1	no	—
72	C₂⁴×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	8	1	no	—
91	C₂×D₄×C₁₉	—	8	1	no	—
92	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂×D₄×C₁₉	D₈	1	2	yes	—
94	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×Dic₁₉	—	4	1	no	—
106	D₈×C₁₉	—	4	8	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
112	C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	#41	1	1	yes	characteristic
118	C₄⋊Dic₁₉	—	4	1	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄⋊Dic₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	4	1	no	—
122	C₄⋊Dic₁₉	—	8	1	no	—
123	C₂×C₁₉⋊C₈	—	2	1	no	—
124	C₂×C₁₉⋊C₈	—	2	1	no	—
125	C₂×C₁₉⋊C₈	—	2	1	no	—
126	C₂×C₁₉⋊C₈	—	2	2	no	—
127	C₂×C₁₉⋊C₈	—	2	1	no	—
128	C₂×C₁₉⋊C₈	—	2	1	no	—
129	C₂×C₁₉⋊C₈	—	4	8	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	D₈	1	2	yes	complemented
136	#9221	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	—	8	1	no	—
148	C₂³×C₁₉	—	8	1	no	—
149	C₂³×C₁₉	—	8	1	no	—
150	C₂³×C₁₉	—	8	1	no	—
151	C₂³×C₁₉	#121	1	1	yes	characteristic
152	D₄×C₁₉	—	2	2	no	—
153	D₄×C₁₉	—	2	2	no	—
154	D₄×C₁₉	—	2	2	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	8	2	no	—
160	D₄×C₁₉	—	8	2	no	—
161	D₄×C₁₉	—	8	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	#102	1	4	yes	complemented
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
187	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×Dic₁₉	—	8	1	no	—
190	C₂×Dic₁₉	—	8	1	no	—
191	C₂×Dic₁₉	—	8	1	no	—
192	C₈×C₁₉	—	4	2	no	—
193	C₁₉⋊C₈	—	2	2	no	—
194	C₁₉⋊C₈	—	4	2	no	—
195	C₁₉⋊C₈	—	4	1	no	—
196	C₁₉⋊C₈	—	8	1	no	—
197	C₂×#459	D₁₉	1	1	yes	characteristic
198	C₂×C₈×D₄	—	19	1	no	—
199	#1957	—	19	1	no	—
200	#1802	—	19	1	no	—
201	C₂×#331	—	19	1	no	—
202	#1296	—	19	1	no	—
203	#1277	—	19	1	no	—
204	C₂²×C₁₉	—	2	4	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	8	2	no	—
212	C₂²×C₁₉	—	8	2	no	—
213	C₂²×C₁₉	—	8	2	no	—
214	C₂²×C₁₉	—	16	1	no	—
215	C₂²×C₁₉	—	16	1	no	—
216	C₂²×C₁₉	—	16	1	no	—
217	C₂²×C₁₉	—	16	1	no	—
218	C₂²×C₁₉	#386	1	1	yes	characteristic
219	C₂²×C₁₉	#459	1	1	yes	characteristic
220	C₂²×C₁₉	#463	1	1	yes	characteristic
221	C₂²×C₁₉	#465	1	1	yes	characteristic
222	C₂²×C₁₉	#466	1	1	yes	characteristic
223	C₂²×C₁₉	#471	1	1	yes	characteristic
224	C₂²×C₁₉	#472	1	1	yes	characteristic
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
229	C₄×C₁₉	#416	1	1	yes	characteristic
230	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
231	C₄×C₁₉	#442	1	1	yes	characteristic
232	C₄×C₁₉	#447	1	1	yes	characteristic
233	C₄×C₁₉	#449	1	1	yes	characteristic
234	C₄×C₁₉	#465	1	1	yes	characteristic
235	C₄×C₁₉	#466	1	1	yes	characteristic
236	Dic₁₉	—	16	1	no	—
237	C₂²×D₈	—	2	1	no	—
238	C₂³×C₈	—	38	1	no	—
239	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
241	#459	—	2	2	no	—
242	#459	Dic₁₉	1	4	yes	complemented
243	C₈×D₄	—	38	2	no	—
244	C₈×D₄	—	38	2	no	—
245	C₂×C₄⋊C₈	—	19	1	no	—
246	C₂×C₄⋊C₈	—	19	1	no	—
247	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
248	C₂×#102	—	2	1	no	—
249	C₂×#102	—	38	1	no	—
250	C₂×#102	—	38	1	no	—
251	C₂×#102	—	38	1	no	—
252	C₂×C₂²⋊C₈	—	38	1	no	—
253	C₂×C₄×C₈	—	19	1	no	—
254	#384	—	19	1	no	—
255	#340	—	38	1	no	—
256	#331	—	38	2	no	—
257	C₂×C₁₉	—	4	4	no	—
258	C₂×C₁₉	—	16	2	no	—
259	C₂×C₁₉	#1665	1	1	yes	characteristic
260	C₂×C₁₉	#1667	1	1	yes	characteristic
261	C₂×C₁₉	#1677	1	1	yes	characteristic
262	C₂×C₁₉	#1681	1	1	yes	characteristic
263	C₂×C₁₉	#1879	1	1	yes	characteristic
264	C₂×C₁₉	#1893	1	1	yes	characteristic
265	C₂×C₁₉	#1907	1	1	yes	characteristic
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂×D₈	—	2	4	no	—
272	C₂×D₈	—	4	2	no	—
273	C₂×D₈	—	4	2	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	—	19	1	no	—
276	C₂²×C₈	—	19	1	no	—
277	C₂²×C₈	—	38	4	no	—
278	C₂²×C₈	—	38	1	no	—
279	C₂²×C₈	—	38	1	no	—
280	C₂²×C₈	—	76	2	no	—
281	C₂²×C₈	—	76	2	no	—
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	C₂×Dic₁₉	1	2	yes	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
289	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	—	38	1	no	—
291	C₂×C₄⋊C₄	—	38	1	no	—
292	C₂×C₄⋊C₄	—	38	1	no	—
293	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	19	2	no	—
298	C₄⋊C₈	—	38	1	no	—
299	C₄⋊C₈	—	38	1	no	—
300	C₄⋊C₈	—	38	1	no	—
301	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
302	#102	—	2	4	no	—
303	#102	—	76	2	no	—
304	#102	—	76	2	no	—
305	#102	—	76	2	no	—
306	C₂²⋊C₈	—	38	4	no	—
307	C₄×C₈	—	38	1	no	—
308	C₄×C₈	—	38	1	no	—
309	C₁₉	#9221	1	1	yes	characteristic, complemented, Sylow
310	C₂⁴	—	2	1	no	—
311	C₂⁴	—	4	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	8	1	no	—
330	C₂×D₄	—	8	1	no	—
331	C₂×D₄	#64525	1	2	yes	—
332	C₂×D₄	#64526	1	2	yes	—
333	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	76	1	no	—
342	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
343	C₂²×C₄	#64543	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
345	D₈	—	4	8	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	19	2	no	—
350	C₂×C₈	—	38	1	no	—
351	C₂×C₈	—	38	1	no	—
352	C₂×C₈	—	38	1	no	—
353	C₂×C₈	—	38	2	no	—
354	C₂×C₈	—	38	1	no	—
355	C₂×C₈	—	38	1	no	—
356	C₂×C₈	—	76	8	no	—
357	C₂×C₈	—	76	1	no	—
358	C₂×C₈	—	76	1	no	—
359	C₂×C₈	—	76	1	no	—
360	C₂×C₈	—	76	1	no	—
361	C₂×C₈	—	76	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	76	1	no	—
364	C₄⋊C₄	—	76	1	no	—
365	C₄⋊C₄	—	76	1	no	—
366	C₄⋊C₄	—	76	1	no	—
367	C₄⋊C₄	—	152	1	no	—
368	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₄²	D₄×D₁₉	1	1	yes	characteristic
372	C₄²	#64543	1	1	yes	characteristic
373	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	8	1	no	—
384	C₂³	—	8	1	no	—
385	C₂³	—	8	1	no	—
386	C₂³	—	8	1	no	—
387	C₂³	—	8	1	no	—
388	C₂³	—	8	1	no	—
389	C₂³	#10597385	1	1	yes	characteristic
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	1	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	8	1	no	—
403	D₄	#10597289	1	4	yes	complemented
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	152	1	no	—
414	C₂×C₄	—	152	1	no	—
415	C₂×C₄	—	152	1	no	—
416	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
417	C₂×C₄	#10597357	1	1	yes	characteristic
418	C₂×C₄	#10597357	1	1	yes	characteristic
419	C₂×C₄	#10597358	1	1	yes	characteristic
420	C₂×C₄	C₂×#64525	1	1	yes	characteristic
421	C₂×C₄	C₂×#64526	1	1	yes	characteristic
422	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
423	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
424	C₂×C₄	#10597381	1	1	yes	characteristic
425	C₂×C₄	#10597383	1	1	yes	characteristic
426	C₂×C₄	#10597385	1	1	yes	characteristic
427	C₂×C₄	#10597396	1	1	yes	characteristic
428	C₂×C₄	#10597396	1	1	yes	characteristic
429	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
430	C₈	—	4	2	no	—
431	C₈	—	38	2	no	—
432	C₈	—	76	2	no	—
433	C₈	—	76	1	no	—
434	C₈	—	152	1	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	1	no	—
446	C₂²	—	16	1	no	—
447	C₂²	—	16	1	no	—
448	C₂²	—	16	1	no	—
449	C₂²	#11926424	1	1	yes	characteristic
450	C₂²	#11926737	1	1	yes	characteristic
451	C₂²	#11926757	1	1	yes	characteristic
452	C₂²	#11926771	1	1	yes	characteristic
453	C₂²	#11926778	1	1	yes	characteristic
454	C₂²	#11926805	1	1	yes	characteristic
455	C₂²	#11926812	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	304	1	no	—
460	C₄	C₂×#10597289	1	1	yes	characteristic
461	C₄	#11926540	1	1	yes	characteristic
462	C₄	D₈×Dic₁₉	1	1	yes	characteristic
463	C₄	#11926656	1	1	yes	characteristic
464	C₄	#11926676	1	1	yes	characteristic
465	C₄	#11926686	1	1	yes	characteristic
466	C₄	#11926771	1	1	yes	characteristic
467	C₄	#11926778	1	1	yes	characteristic
468	C₂	—	4	4	no	—
469	C₂	—	16	2	no	—
470	C₂	#14562974	1	1	yes	characteristic
471	C₂	#14562988	1	1	yes	characteristic
472	C₂	#14563042	1	1	yes	characteristic
473	C₂	#14563070	1	1	yes	characteristic
474	C₂	#14563985	1	1	yes	characteristic
475	C₂	#14564064	1	1	yes	characteristic
476	C₂	#14564145	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597385
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#459	C₂
socle	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#459	D₁₉
hypocenter	C₁₉	#9221
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₁₉⋊C₈	C₂	semidirect
2. #14564442	C₂	semidirect
3. #14563635	C₂	semidirect
4. C₂×#11926288	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561469	C₂	semidirect
25. C₁₉×#459	C₄	semidirect
135. C₂×C₁₉⋊C₈	D₈	semidirect
165. D₄×C₁₉	#102	semidirect
242. #459	Dic₁₉	semidirect
309. C₁₉	#9221	semidirect
403. D₄	#10597289	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₁₉⋊C₈	2
#14564442	2
#14563635	2
C₂×#11926288	2
#14561519	2
#14561469	2
C₂×C₁₉×#459	2
#9221	19