Subgroups — #18079590

Order 4864.

678 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572084	C₂	1	1	yes	maximal, characteristic
2	#14563575	C₂	1	1	yes	maximal, characteristic
3	#14562207	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561999	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561540	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561522	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3007	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597394	—	2	1	no	—
9	C₂×#10597292	—	2	1	no	—
10	C₂×#10597289	—	2	1	no	—
11	#11926511	—	2	2	no	—
12	#11926511	—	2	1	no	—
13	#11926508	—	2	1	no	—
14	#11926508	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
18	#11926404	C₂²	1	1	yes	characteristic
19	#11926281	—	2	1	no	—
20	#11926281	—	2	1	no	—
21	#11926270	—	2	2	no	—
22	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#137	C₄	1	1	yes	characteristic, complemented
24	C₂×C₁₉×#137	C₄	1	1	yes	characteristic, complemented
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₉×#452	—	2	1	no	—
27	C₁₉×#452	—	2	1	no	—
28	C₁₉×#451	—	2	1	no	—
29	C₁₉×#450	—	2	1	no	—
30	C₁₉×#417	C₄	1	1	yes	characteristic, complemented
31	C₁₉×#417	C₄	1	1	yes	characteristic, complemented
32	C₁₉×#407	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	4	2	no	—
36	C₂×#41×C₁₉	—	4	2	no	—
37	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
40	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×#137	—	4	2	no	—
48	C₁₉×#137	—	4	2	no	—
49	C₂×Q₁₆×C₁₉	—	2	1	no	—
50	C₂×Q₁₆×C₁₉	—	2	1	no	—
51	C₂×SD₁₆×C₁₉	—	2	1	no	—
52	C₂×SD₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₁₉×C₂²⋊Q₈	—	2	1	no	—
56	C₁₉×C₂²⋊Q₈	—	2	1	no	—
57	C₁₉×C₂²⋊Q₈	—	2	1	no	—
58	C₁₉×C₂²⋊Q₈	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
63	#10597394	—	4	2	no	—
64	#10597394	—	4	2	no	—
65	C₂×C₄⋊Dic₁₉	—	2	1	no	—
66	C₂×#64520	—	2	2	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂²×C₁₉⋊C₈	—	2	2	no	—
69	C₂²×C₁₉⋊C₈	—	2	1	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₁₉×#103	—	2	1	no	—
72	C₁₉×#103	—	2	1	no	—
73	C₁₉×#102	—	2	1	no	—
74	C₁₉×#102	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₁₉×C₂²⋊C₈	—	2	1	no	—
77	#10597292	—	4	2	no	—
78	#10597289	—	4	2	no	—
79	C₁₉⋊#95	—	2	1	no	—
80	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
81	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
82	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
83	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
84	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
86	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
87	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
88	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	#41	1	1	yes	characteristic
91	#41×C₁₉	—	2	2	no	—
92	#41×C₁₉	—	2	2	no	—
93	#41×C₁₉	—	2	2	no	—
94	#41×C₁₉	—	2	2	no	—
95	#41×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	4	1	no	—
97	#41×C₁₉	—	4	1	no	—
98	#41×C₁₉	—	4	1	no	—
99	#41×C₁₉	—	4	4	no	—
100	#41×C₁₉	—	4	4	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	4	1	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	—	4	1	no	—
108	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×Dic₁₉	—	4	1	no	—
137	Q₁₆×C₁₉	—	4	2	no	—
138	Q₁₆×C₁₉	—	4	2	no	—
139	SD₁₆×C₁₉	—	4	2	no	—
140	SD₁₆×C₁₉	—	4	2	no	—
141	M₁₆×C₁₉	—	4	1	no	—
142	M₁₆×C₁₉	—	4	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	4	1	no	—
151	C₂²⋊Dic₁₉	—	8	1	no	—
152	C₄⋊Dic₁₉	—	4	1	no	—
153	C₄⋊Dic₁₉	—	4	1	no	—
154	#64520	—	4	4	no	—
155	#64520	—	4	1	no	—
156	#64520	—	4	1	no	—
157	C₂×C₁₉⋊C₈	—	2	1	no	—
158	C₂×C₁₉⋊C₈	—	2	2	no	—
159	C₂×C₁₉⋊C₈	—	2	1	no	—
160	C₂×C₁₉⋊C₈	—	4	4	no	—
161	C₂×C₁₉⋊C₈	—	4	1	no	—
162	C₂×C₁₉⋊C₈	—	4	1	no	—
163	C₂×C₁₉⋊C₈	—	4	1	no	—
164	C₂×C₁₉⋊C₈	—	4	1	no	—
165	C₂×C₁₉⋊C₈	—	4	1	no	—
166	#9345	—	19	1	no	maximal, Sylow
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	8	1	no	—
177	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
178	C₂³×C₁₉	#121	1	1	yes	characteristic
179	C₂³×C₁₉	#123	1	1	yes	characteristic
180	Q₈×C₁₉	—	2	1	no	—
181	Q₈×C₁₉	—	2	1	no	—
182	Q₈×C₁₉	—	2	1	no	—
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	4	1	no	—
185	Q₈×C₁₉	—	4	1	no	—
186	Q₈×C₁₉	—	8	1	no	—
187	Q₈×C₁₉	#99	1	2	yes	—
188	D₄×C₁₉	—	2	4	no	—
189	D₄×C₁₉	—	2	1	no	—
190	D₄×C₁₉	—	2	1	no	—
191	D₄×C₁₉	—	2	1	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	#99	1	2	yes	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	8	1	no	—
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
221	C₂×Dic₁₉	—	8	1	no	—
222	C₂×Dic₁₉	—	8	1	no	—
223	C₂×Dic₁₉	—	8	1	no	—
224	C₈×C₁₉	—	4	1	no	—
225	C₈×C₁₉	—	4	1	no	—
226	C₁₉⋊C₈	—	4	1	no	—
227	C₁₉⋊C₈	—	4	2	no	—
228	C₁₉⋊C₈	—	4	1	no	—
229	C₁₉⋊C₈	—	8	1	no	—
230	#3007	D₁₉	1	1	yes	characteristic
231	#2880	—	19	1	no	—
232	#1788	—	19	1	no	—
233	#1520	—	19	1	no	—
234	#1472	—	19	1	no	—
235	#1305	—	19	1	no	—
236	#1298	—	19	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	1	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	8	1	no	—
252	C₂²×C₁₉	—	8	1	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	#386	1	1	yes	characteristic
256	C₂²×C₁₉	#471	1	1	yes	characteristic
257	C₂²×C₁₉	#473	1	1	yes	characteristic
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	2	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	4	1	no	—
263	C₄×C₁₉	—	8	1	no	—
264	C₄×C₁₉	—	8	1	no	—
265	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
266	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
267	Dic₁₉	—	16	1	no	—
268	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
269	C₂×#137	Dic₁₉	1	1	yes	characteristic, complemented
270	C₂×#137	Dic₁₉	1	1	yes	characteristic, complemented
271	C₂×#131	—	38	1	no	—
272	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
273	#452	—	2	1	no	—
274	#452	—	2	1	no	—
275	#451	—	2	1	no	—
276	#450	—	2	1	no	—
277	#417	Dic₁₉	1	1	yes	characteristic, complemented
278	#417	Dic₁₉	1	1	yes	characteristic, complemented
279	C₂×#103	—	38	1	no	—
280	C₂×#102	—	38	1	no	—
281	#408	—	38	2	no	—
282	#408	—	38	1	no	—
283	#407	—	19	1	no	—
284	#407	—	38	1	no	—
285	#407	C₂×D₁₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	—	19	1	no	—
287	C₂×C₂²⋊C₈	—	19	1	no	—
288	C₂×C₂²⋊C₈	—	38	1	no	—
289	#380	—	19	1	no	—
290	#328	—	38	1	no	—
291	#328	—	38	1	no	—
292	#324	—	38	2	no	—
293	C₂×C₁₉	—	2	1	no	—
294	C₂×C₁₉	—	2	1	no	—
295	C₂×C₁₉	—	4	1	no	—
296	C₂×C₁₉	—	4	1	no	—
297	C₂×C₁₉	—	4	2	no	—
298	C₂×C₁₉	—	8	1	no	—
299	C₂×C₁₉	#1881	1	1	yes	characteristic
300	C₂×C₁₉	#1898	1	1	yes	characteristic
301	C₂×C₁₉	#1908	1	1	yes	characteristic
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	4	2	no	—
305	C₂×#41	—	4	2	no	—
306	C₂×#41	C₂×Dic₁₉	1	1	yes	characteristic
307	C₂×#41	C₂×Dic₁₉	1	1	yes	characteristic
308	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
310	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
311	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
316	#137	—	4	2	no	—
317	#137	—	4	2	no	—
318	C₂×Q₁₆	—	2	1	no	—
319	C₂×Q₁₆	—	2	1	no	—
320	C₂×SD₁₆	—	2	1	no	—
321	C₂×SD₁₆	—	2	1	no	—
322	#131	—	76	2	no	—
323	#131	—	76	2	no	—
324	C₂×M₁₆	—	38	2	no	—
325	C₂×M₁₆	—	38	1	no	—
326	C₂×M₁₆	C₂×Dic₁₉	1	1	yes	characteristic
327	C₂×M₁₆	C₂×Dic₁₉	1	1	yes	characteristic
328	C₂²×C₈	—	38	2	no	—
329	C₂²×C₈	—	38	1	no	—
330	C₂²×C₈	—	38	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	2	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	38	1	no	—
337	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	38	1	no	—
340	#103	—	2	1	no	—
341	#103	—	2	1	no	—
342	#103	—	76	2	no	—
343	#102	—	2	1	no	—
344	#102	—	2	1	no	—
345	#102	—	76	2	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	19	2	no	—
349	C₂²⋊C₈	—	19	1	no	—
350	C₂²⋊C₈	—	19	1	no	—
351	C₂²⋊C₈	—	38	2	no	—
352	C₂²⋊C₈	—	38	2	no	—
353	C₂²⋊C₈	—	38	1	no	—
354	C₂²⋊C₈	—	38	1	no	—
355	C₂²⋊C₈	—	38	1	no	—
356	C₂²⋊C₈	—	38	1	no	—
357	#95	—	38	1	no	—
358	C₁₉	#9345	1	1	yes	characteristic, complemented, Sylow
359	C₂⁴	—	2	1	no	—
360	C₂⁴	#64543	1	1	yes	characteristic
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	4	1	no	—
366	#41	—	4	1	no	—
367	#41	—	4	1	no	—
368	#41	—	4	1	no	—
369	#41	—	4	4	no	—
370	#41	—	4	4	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	4	1	no	—
376	C₂×Q₈	—	4	1	no	—
377	C₂×Q₈	—	4	1	no	—
378	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
379	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
389	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	76	1	no	—
401	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
402	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
403	C₂²×C₄	#64543	1	1	yes	characteristic
404	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
407	Q₁₆	—	4	2	no	—
408	Q₁₆	—	4	2	no	—
409	SD₁₆	—	4	2	no	—
410	SD₁₆	—	4	2	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	4	1	no	—
413	M₁₆	—	76	4	no	—
414	M₁₆	—	76	1	no	—
415	M₁₆	—	76	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	38	1	no	—
419	C₂×C₈	—	38	2	no	—
420	C₂×C₈	—	38	1	no	—
421	C₂×C₈	—	76	4	no	—
422	C₂×C₈	—	76	1	no	—
423	C₂×C₈	—	76	1	no	—
424	C₂×C₈	—	76	1	no	—
425	C₂×C₈	—	76	1	no	—
426	C₂×C₈	—	76	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	76	1	no	—
432	C₄⋊C₄	—	76	1	no	—
433	C₂²⋊C₄	—	4	1	no	—
434	C₂²⋊C₄	—	4	1	no	—
435	C₂²⋊C₄	—	152	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	8	1	no	—
446	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
447	C₂³	#10597381	1	1	yes	characteristic
448	C₂³	#10597385	1	1	yes	characteristic
449	Q₈	—	2	1	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	2	1	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	1	no	—
454	Q₈	—	4	1	no	—
455	Q₈	—	8	1	no	—
456	Q₈	#10597291	1	2	yes	—
457	D₄	—	2	4	no	—
458	D₄	—	2	1	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	#10597291	1	2	yes	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	—	152	1	no	—
487	C₂×C₄	—	152	1	no	—
488	C₂×C₄	—	152	1	no	—
489	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
490	C₂×C₄	#10597383	1	1	yes	characteristic
491	C₂×C₄	#10597385	1	1	yes	characteristic
492	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
493	C₈	—	4	1	no	—
494	C₈	—	4	1	no	—
495	C₈	—	76	1	no	—
496	C₈	—	76	2	no	—
497	C₈	—	76	1	no	—
498	C₈	—	152	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	#11926424	1	1	yes	characteristic
518	C₂²	#11926809	1	1	yes	characteristic
519	C₂²	#11926817	1	1	yes	characteristic
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	8	1	no	—
526	C₄	—	8	1	no	—
527	C₄	—	304	1	no	—
528	C₄	C₂×#10597291	1	1	yes	characteristic
529	C₄	C₂×#10597291	1	1	yes	characteristic
530	C₂	—	2	1	no	—
531	C₂	—	2	1	no	—
532	C₂	—	4	1	no	—
533	C₂	—	4	1	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	1	no	—
536	C₂	#14563999	1	1	yes	characteristic
537	C₂	#14564089	1	1	yes	characteristic
538	C₂	#14564152	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#3007	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#3007	D₁₉
hypocenter	C₁₉	#9345
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3007

Complements

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

N	H ≅ G/N	type
3. #14562207	C₂	semidirect
4. #14561999	C₂	semidirect
5. #14561540	C₂	semidirect
6. #14561522	C₂	semidirect
23. C₂×C₁₉×#137	C₄	semidirect
24. C₂×C₁₉×#137	C₄	semidirect
30. C₁₉×#417	C₄	semidirect
31. C₁₉×#417	C₄	semidirect
269. C₂×#137	Dic₁₉	semidirect
270. C₂×#137	Dic₁₉	semidirect
277. #417	Dic₁₉	semidirect
278. #417	Dic₁₉	semidirect
358. C₁₉	#9345	semidirect

Maximal subgroups

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

subgroup	index
#14572084	2
#14563575	2
#14562207	2
#14561999	2
#14561540	2
#14561522	2
C₁₉×#3007	2
#9345	19