Subgroups — #18075439

Order 4864.

524 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926616	C₂	1	1	yes	maximal, characteristic
2	#14563662	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563658	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563623	C₂	1	1	yes	maximal, characteristic
5	#14561502	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926616	—	2	1	no	—
11	#11926616	—	2	1	no	—
12	#11926616	—	2	1	no	—
13	#11926616	—	2	1	no	—
14	C₂×#10597264	—	2	1	no	—
15	C₂×#10597265	—	2	1	no	—
16	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic, complemented
17	C₂×#10597291	—	2	1	no	—
18	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic, complemented
19	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#10597260	C₄	1	1	yes	characteristic, complemented
21	#11926404	C₂²	1	1	yes	characteristic
22	#11926404	C₂²	1	1	yes	characteristic
23	#11926311	—	2	1	no	—
24	#11926306	—	2	1	no	—
25	#11926306	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#99	—	2	1	no	—
28	C₁₉×#380	C₂²	1	1	yes	characteristic
29	C₁₉×#380	C₂²	1	1	yes	characteristic
30	C₁₉×#342	—	2	1	no	—
31	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₄×D₄×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	—	2	1	no	—
36	C₄×D₄×C₁₉	—	2	1	no	—
37	C₄×D₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
47	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×#64520	—	2	1	no	—
51	C₂×#64520	—	2	1	no	—
52	C₂×#64520	—	4	2	no	—
53	C₂²×C₁₉⋊C₈	—	4	2	no	—
54	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
59	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
61	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
62	C₁₉×#99	—	4	2	no	—
63	C₁₉×#95	—	2	1	no	—
64	C₁₉×#95	—	2	1	no	—
65	#10597291	—	4	2	no	—
66	C₁₉⋊#95	—	2	1	no	—
67	C₁₉⋊#95	—	2	1	no	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
72	#10597265	—	4	2	no	—
73	#10597264	—	4	2	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
76	#10597260	—	2	1	no	—
77	#10597260	—	2	1	no	—
78	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	C₂²×Dic₁₉	—	4	1	no	—
104	C₂²×Dic₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₂²⋊C₄×C₁₉	—	4	1	no	—
118	C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	—	2	1	no	—
120	C₄²×C₁₉	—	2	1	no	—
121	C₂²⋊Dic₁₉	—	4	1	no	—
122	C₂²⋊Dic₁₉	—	4	1	no	—
123	C₂²⋊Dic₁₉	—	4	1	no	—
124	C₂²⋊Dic₁₉	—	4	1	no	—
125	C₄⋊Dic₁₉	—	4	1	no	—
126	C₄⋊Dic₁₉	—	4	1	no	—
127	C₄⋊Dic₁₉	—	4	1	no	—
128	C₄⋊Dic₁₉	—	4	1	no	—
129	#64520	—	4	2	no	—
130	#64520	—	4	2	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	1	no	—
135	C₂×C₁₉⋊C₈	—	2	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
145	#8610	—	19	1	no	maximal, Sylow
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂³×C₁₉	#121	1	1	yes	characteristic
155	C₂³×C₁₉	#121	1	1	yes	characteristic
156	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂³×C₁₉	#137	1	1	yes	characteristic
159	C₂³×C₁₉	#137	1	1	yes	characteristic
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	8	1	no	—
184	C₂×C₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	8	1	no	—
186	C₂×C₄×C₁₉	—	8	1	no	—
187	C₂×C₄×C₁₉	—	8	1	no	—
188	C₂×C₄×C₁₉	—	8	1	no	—
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×Dic₁₉	—	8	1	no	—
194	C₂×Dic₁₉	—	8	1	no	—
195	C₂×Dic₁₉	—	8	1	no	—
196	C₂×Dic₁₉	—	8	1	no	—
197	C₂×Dic₁₉	—	8	1	no	—
198	C₂×Dic₁₉	—	8	1	no	—
199	C₁₉⋊C₈	—	2	1	no	—
200	C₁₉⋊C₈	—	2	1	no	—
201	C₁₉⋊C₈	—	2	1	no	—
202	C₁₉⋊C₈	—	4	1	no	—
203	C₁₉⋊C₈	—	4	1	no	—
204	C₁₉⋊C₈	#99	1	2	yes	complemented
205	C₂×#435	—	19	1	no	—
206	#1808	—	19	1	no	—
207	#1807	—	19	1	no	—
208	#1799	—	19	1	no	—
209	#1799	D₁₉	1	1	yes	characteristic
210	#1289	—	19	1	no	—
211	#1289	—	19	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	—	4	1	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	#380	1	1	yes	characteristic
228	C₂²×C₁₉	#428	1	1	yes	characteristic
229	C₂²×C₁₉	#428	1	1	yes	characteristic
230	C₂²×C₁₉	#468	1	1	yes	characteristic
231	C₂²×C₁₉	#468	1	1	yes	characteristic
232	C₂²×C₁₉	#469	1	1	yes	characteristic
233	C₂²×C₁₉	#470	1	1	yes	characteristic
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	4	1	no	—
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	—	4	1	no	—
240	C₄×C₁₉	—	16	1	no	—
241	C₄×C₁₉	—	16	1	no	—
242	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
243	C₄×C₁₉	#410	1	1	yes	characteristic
244	Dic₁₉	—	16	1	no	—
245	Dic₁₉	—	16	1	no	—
246	C₂²×M₁₆	—	19	1	no	—
247	C₂³×C₈	—	19	1	no	—
248	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
249	#435	—	38	1	no	—
250	#435	—	38	1	no	—
251	#435	—	38	1	no	—
252	#435	—	38	1	no	—
253	C₂×#107	—	38	1	no	—
254	C₂×#106	—	38	1	no	—
255	C₂×C₄⋊C₈	—	19	1	no	—
256	C₂×#99	—	2	1	no	—
257	C₂×#99	—	38	1	no	—
258	C₂×C₂²⋊C₈	—	19	1	no	—
259	C₂×C₂²⋊C₈	—	19	1	no	—
260	C₂×#97	—	19	1	no	—
261	#380	—	19	1	no	—
262	#380	—	19	1	no	—
263	#380	C₂×D₁₉	1	1	yes	characteristic
264	#380	C₂×D₁₉	1	1	yes	characteristic
265	#342	—	2	1	no	—
266	#342	—	38	1	no	—
267	#340	—	38	1	no	—
268	#340	—	38	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	—	2	1	no	—
273	C₂×C₁₉	—	2	1	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	8	1	no	—
276	C₂×C₁₉	#1799	1	1	yes	characteristic
277	C₂×C₁₉	#1809	1	1	yes	characteristic
278	C₂×C₁₉	#1812	1	1	yes	characteristic
279	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
281	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
282	C₂×M₁₆	—	38	1	no	—
283	C₂×M₁₆	—	38	1	no	—
284	C₂×M₁₆	—	76	2	no	—
285	C₂²×C₈	—	19	1	no	—
286	C₂²×C₈	—	19	1	no	—
287	C₂²×C₈	—	19	1	no	—
288	C₂²×C₈	—	19	1	no	—
289	C₂²×C₈	—	19	1	no	—
290	C₂²×C₈	—	19	1	no	—
291	C₂²×C₈	—	19	1	no	—
292	C₂²×C₈	—	19	1	no	—
293	C₂²×C₈	—	76	2	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	38	1	no	—
301	C₂×C₄⋊C₄	—	38	1	no	—
302	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	38	1	no	—
306	C₂×C₂²⋊C₄	—	38	1	no	—
307	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
310	#107	—	76	2	no	—
311	#106	—	76	2	no	—
312	C₄⋊C₈	—	38	1	no	—
313	C₄⋊C₈	—	38	1	no	—
314	#99	—	4	2	no	—
315	#99	—	76	2	no	—
316	C₂²⋊C₈	—	38	1	no	—
317	C₂²⋊C₈	—	38	1	no	—
318	C₂²⋊C₈	—	38	1	no	—
319	C₂²⋊C₈	—	38	1	no	—
320	#97	—	38	1	no	—
321	#97	—	38	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	38	1	no	—
325	#95	—	38	1	no	—
326	C₁₉	#8610	1	1	yes	characteristic, complemented, Sylow
327	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
328	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	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	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	76	1	no	—
344	C₂²×C₄	—	76	1	no	—
345	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
346	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
347	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	#64543	1	1	yes	characteristic
353	C₂²×C₄	#64543	1	1	yes	characteristic
354	M₁₆	—	76	2	no	—
355	M₁₆	—	76	2	no	—
356	C₂×C₈	—	19	1	no	—
357	C₂×C₈	—	19	1	no	—
358	C₂×C₈	—	19	1	no	—
359	C₂×C₈	—	19	1	no	—
360	C₂×C₈	—	38	2	no	—
361	C₂×C₈	—	38	2	no	—
362	C₂×C₈	—	38	2	no	—
363	C₂×C₈	—	38	1	no	—
364	C₂×C₈	—	38	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₂×C₈	—	76	1	no	—
367	C₂×C₈	—	76	1	no	—
368	C₂×C₈	—	76	1	no	—
369	C₂×C₈	—	76	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	76	1	no	—
377	C₄⋊C₄	—	76	1	no	—
378	C₄⋊C₄	—	76	1	no	—
379	C₄⋊C₄	—	76	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	76	1	no	—
389	C₂²⋊C₄	—	76	1	no	—
390	C₂²⋊C₄	—	76	1	no	—
391	C₂²⋊C₄	—	76	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
402	C₂³	#10597378	1	1	yes	characteristic
403	C₂³	#10597385	1	1	yes	characteristic
404	C₂³	#10597385	1	1	yes	characteristic
405	C₂³	#10597388	1	1	yes	characteristic
406	C₂³	#10597395	1	1	yes	characteristic
407	C₂³	#10597397	1	1	yes	characteristic
408	D₄	—	4	1	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	8	1	no	—
432	C₂×C₄	—	8	1	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	—	8	1	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	152	1	no	—
438	C₂×C₄	—	152	1	no	—
439	C₂×C₄	—	152	1	no	—
440	C₂×C₄	—	152	1	no	—
441	C₂×C₄	—	152	1	no	—
442	C₂×C₄	—	152	1	no	—
443	C₂×C₄	#10597323	1	1	yes	characteristic
444	C₂×C₄	#10597324	1	1	yes	characteristic
445	C₂×C₄	#10597324	1	1	yes	characteristic
446	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
447	C₈	—	19	2	no	—
448	C₈	—	38	1	no	—
449	C₈	—	38	1	no	—
450	C₈	—	38	1	no	—
451	C₈	—	76	1	no	—
452	C₈	—	76	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	#11926402	1	1	yes	characteristic
469	C₂²	#11926584	1	1	yes	characteristic
470	C₂²	#11926587	1	1	yes	characteristic
471	C₂²	#11926788	1	1	yes	characteristic
472	C₂²	#11926792	1	1	yes	characteristic
473	C₂²	#11926795	1	1	yes	characteristic
474	C₂²	#11926800	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	16	1	no	—
482	C₄	—	16	1	no	—
483	C₄	—	304	1	no	—
484	C₄	—	304	1	no	—
485	C₄	#99×D₁₉	1	1	yes	characteristic
486	C₄	#11926516	1	1	yes	characteristic
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	8	1	no	—
494	C₂	#14563621	1	1	yes	characteristic
495	C₂	#14563666	1	1	yes	characteristic
496	C₂	#14563679	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1799	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1799	D₁₉
hypocenter	C₁₉	#8610
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1799

Complements

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

N	H ≅ G/N	type
2. #14563662	C₂	semidirect
3. #14563658	C₂	semidirect
5. #14561502	C₂	semidirect
6. #14561502	C₂	semidirect
8. C₂²×#64520	C₄	semidirect
16. C₂×C₄⋊(C₁₉⋊C₈)	C₄	semidirect
18. C₂×C₂²⋊(C₁₉⋊C₈)	C₄	semidirect
20. C₂×#10597260	C₄	semidirect
204. C₁₉⋊C₈	#99	semidirect
326. C₁₉	#8610	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926616	2
#14563662	2
#14563658	2
#14563623	2
#14561502	2
C₁₉×#1799	2
#8610	19