Subgroups — #18088008

Order 4864.

1186 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597394	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926561	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926315	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926314	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926308	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563351	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597394	—	2	2	no	—
9	C₂×#10597394	—	2	2	no	—
10	C₂×#10597394	—	2	2	no	—
11	C₂×#10597394	—	2	2	no	—
12	C₂×#10597394	—	2	2	no	—
13	C₂×#10597394	C₄	1	4	yes	complemented
14	C₂²×#64520	—	2	1	no	—
15	C₂²×#64520	C₂²	1	1	yes	characteristic
16	C₂²×#64520	C₂²	1	1	yes	characteristic
17	C₂³×C₁₉⋊C₈	—	2	1	no	—
18	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×#10597372	C₂²	1	1	yes	characteristic
20	#11926561	—	2	2	no	—
21	#11926561	C₄	1	4	yes	complemented
22	C₂×#10597294	—	2	2	no	—
23	#11926315	—	2	2	no	—
24	#11926314	—	2	2	no	—
25	#11926308	—	2	1	no	—
26	#11926308	—	2	1	no	—
27	#11926306	—	2	2	no	—
28	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₁₉×#421	—	2	2	no	—
32	C₁₉×#421	C₄	1	4	yes	complemented
33	C₂×C₁₉×#104	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×#41×C₁₉	D₄	1	2	yes	—
44	C₂×#41×C₁₉	D₄	1	2	yes	—
45	C₂×#41×C₁₉	D₄	1	2	yes	—
46	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₁₉×#117	—	2	1	no	—
61	C₁₉×#117	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
66	#10597394	—	2	8	no	—
67	#10597394	—	2	8	no	—
68	#10597394	—	2	8	no	—
69	#10597394	—	2	8	no	—
70	#10597372	—	2	1	no	—
71	#10597372	—	2	1	no	—
72	#10597372	—	2	1	no	—
73	#10597372	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊Dic₁₉	—	2	1	no	—
75	C₂×C₄×Dic₁₉	—	2	1	no	—
76	C₂×#64520	—	2	4	no	—
77	C₂×#64520	—	2	4	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	—	2	4	no	—
83	C₂×#64520	—	2	1	no	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	C₂×C₄	1	2	yes	—
88	C₂×#64520	C₂×C₄	1	2	yes	—
89	C₂×#64520	D₄	1	2	yes	—
90	C₂×#64520	D₄	1	2	yes	—
91	C₂²×C₁₉⋊C₈	—	2	4	no	—
92	C₂²×C₁₉⋊C₈	—	2	4	no	—
93	C₂²×C₁₉⋊C₈	—	2	1	no	—
94	C₂²×C₁₉⋊C₈	—	2	1	no	—
95	C₂²×C₁₉⋊C₈	—	2	1	no	—
96	C₂²×C₁₉⋊C₈	—	2	1	no	—
97	C₂²×C₁₉⋊C₈	—	2	1	no	—
98	C₂²×C₁₉⋊C₈	—	2	4	no	—
99	C₂²×C₁₉⋊C₈	—	2	1	no	—
100	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
101	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
102	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
103	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
104	C₁₉×#104	—	2	8	no	—
105	#10597294	—	2	8	no	—
106	C₂⁴×C₁₉	—	2	1	no	—
107	C₂⁴×C₁₉	#41	1	1	yes	characteristic
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	2	2	no	—
112	#41×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	2	2	no	—
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	—	2	2	no	—
116	#41×C₁₉	—	2	2	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	C₄²	1	4	yes	—
121	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
122	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
123	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
128	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
129	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
140	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
141	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	4	1	no	—
150	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
164	C₂²×Dic₁₉	—	4	1	no	—
165	M₁₆×C₁₉	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	4	1	no	—
168	M₁₆×C₁₉	—	4	1	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	4	1	no	—
171	C₂×C₈×C₁₉	—	4	1	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	4	1	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	4	1	no	—
176	C₄²×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	—	4	1	no	—
178	C₂²⋊Dic₁₉	—	2	2	no	—
179	C₂²⋊Dic₁₉	—	4	1	no	—
180	C₄⋊Dic₁₉	—	2	2	no	—
181	C₄⋊Dic₁₉	—	4	1	no	—
182	C₄×Dic₁₉	—	2	2	no	—
183	C₄×Dic₁₉	—	4	1	no	—
184	#64520	—	2	16	no	—
185	#64520	—	2	2	no	—
186	#64520	—	2	2	no	—
187	#64520	—	2	2	no	—
188	#64520	—	2	2	no	—
189	#64520	—	2	2	no	—
190	#64520	—	4	1	no	—
191	#64520	—	4	1	no	—
192	#64520	C₂²⋊C₄	1	4	yes	—
193	C₂×C₁₉⋊C₈	—	2	16	no	—
194	C₂×C₁₉⋊C₈	—	2	2	no	—
195	C₂×C₁₉⋊C₈	—	2	2	no	—
196	C₂×C₁₉⋊C₈	—	2	2	no	—
197	C₂×C₁₉⋊C₈	—	2	2	no	—
198	C₂×C₁₉⋊C₈	—	2	2	no	—
199	C₂×C₁₉⋊C₈	—	2	1	no	—
200	C₂×C₁₉⋊C₈	—	2	1	no	—
201	C₂×C₁₉⋊C₈	—	2	2	no	—
202	C₂×C₁₉⋊C₈	—	2	2	no	—
203	C₂×C₁₉⋊C₈	—	2	1	no	—
204	C₂×C₁₉⋊C₈	—	2	1	no	—
205	C₂×C₁₉⋊C₈	—	2	2	no	—
206	C₂×C₁₉⋊C₈	—	4	1	no	—
207	C₂×C₁₉⋊C₈	—	4	1	no	—
208	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
209	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
210	#10773	—	19	1	no	maximal, Sylow
211	C₂³×C₁₉	—	2	2	no	—
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	2	2	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	4	no	—
216	C₂³×C₁₉	#117	1	1	yes	characteristic
217	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₁₉	#121	1	1	yes	characteristic
220	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
221	C₂³×C₁₉	#123	1	1	yes	characteristic
222	C₂³×C₁₉	#123	1	1	yes	characteristic
223	Q₈×C₁₉	—	2	2	no	—
224	Q₈×C₁₉	—	2	2	no	—
225	Q₈×C₁₉	—	2	2	no	—
226	Q₈×C₁₉	#95	1	4	yes	—
227	D₄×C₁₉	—	2	4	no	—
228	D₄×C₁₉	—	2	4	no	—
229	D₄×C₁₉	—	2	4	no	—
230	D₄×C₁₉	—	2	4	no	—
231	D₄×C₁₉	—	2	2	no	—
232	D₄×C₁₉	—	2	2	no	—
233	D₄×C₁₉	—	2	2	no	—
234	D₄×C₁₉	#95	1	4	yes	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
272	C₂×Dic₁₉	—	4	2	no	—
273	C₂×Dic₁₉	—	8	2	no	—
274	C₈×C₁₉	—	4	2	no	—
275	C₁₉⋊C₈	—	2	2	no	—
276	C₁₉⋊C₈	—	2	4	no	—
277	C₁₉⋊C₈	—	2	2	no	—
278	C₁₉⋊C₈	—	4	2	no	—
279	C₂²×#131	—	19	1	no	—
280	C₂×#421	—	19	1	no	—
281	C₂×#421	D₁₉	1	1	yes	characteristic
282	C₂×#344	—	19	1	no	—
283	C₂×#344	—	19	1	no	—
284	C₂×#341	—	19	1	no	—
285	#1735	—	19	1	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	4	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	4	no	—
295	C₂²×C₁₉	—	4	4	no	—
296	C₂²×C₁₉	—	4	4	no	—
297	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₁₉	#380	1	1	yes	characteristic
299	C₂²×C₁₉	#381	1	1	yes	characteristic
300	C₂²×C₁₉	#385	1	1	yes	characteristic
301	C₂²×C₁₉	#385	1	1	yes	characteristic
302	C₂²×C₁₉	#386	1	1	yes	characteristic
303	C₂²×C₁₉	#386	1	1	yes	characteristic
304	C₄×C₁₉	—	2	4	no	—
305	C₄×C₁₉	—	8	2	no	—
306	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
307	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
308	C₄×C₁₉	#379	1	1	yes	characteristic
309	C₄×C₁₉	#380	1	1	yes	characteristic
310	C₄×C₁₉	#385	1	1	yes	characteristic
311	C₄×C₁₉	#385	1	1	yes	characteristic
312	C₄×C₁₉	#386	1	1	yes	characteristic
313	C₄×C₁₉	#386	1	1	yes	characteristic
314	Dic₁₉	—	8	2	no	—
315	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
316	C₂×#131	—	19	4	no	—
317	C₂×#131	—	38	2	no	—
318	C₂×#131	—	38	2	no	—
319	C₂×#131	—	38	2	no	—
320	C₂×#131	—	38	2	no	—
321	C₂×#131	—	38	2	no	—
322	C₂²×M₁₆	—	19	1	no	—
323	C₂²×M₁₆	—	19	1	no	—
324	C₂²×M₁₆	—	38	1	no	—
325	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
326	C₂³×C₈	—	19	1	no	—
327	C₂³×C₈	—	38	1	no	—
328	C₂×#117	—	19	1	no	—
329	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
330	#421	—	2	2	no	—
331	#421	—	19	4	no	—
332	#421	—	38	2	no	—
333	#421	Dic₁₉	1	4	yes	complemented
334	C₂×#104	—	2	2	no	—
335	C₂×#104	—	38	2	no	—
336	#344	—	38	2	no	—
337	#344	—	38	2	no	—
338	#341	—	38	1	no	—
339	#341	—	38	1	no	—
340	#340	—	38	2	no	—
341	C₂×C₁₉	—	2	1	no	—
342	C₂×C₁₉	—	2	1	no	—
343	C₂×C₁₉	—	2	1	no	—
344	C₂×C₁₉	—	2	1	no	—
345	C₂×C₁₉	—	2	1	no	—
346	C₂×C₁₉	—	2	1	no	—
347	C₂×C₁₉	—	4	4	no	—
348	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
349	C₂×C₁₉	#1814	1	2	yes	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	C₄×D₁₉	1	2	yes	—
357	C₂×#41	C₄×D₁₉	1	2	yes	—
358	C₂×#41	D₇₆	1	2	yes	—
359	C₂×#41	C₂×Dic₁₉	1	2	yes	—
360	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
361	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
362	C₂²×Q₈	Dic₃₈	1	1	yes	characteristic
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
367	#131	—	38	8	no	—
368	#131	—	38	8	no	—
369	#131	—	38	8	no	—
370	#131	—	38	8	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	19	2	no	—
377	C₂×M₁₆	—	19	2	no	—
378	C₂×M₁₆	—	19	2	no	—
379	C₂×M₁₆	—	19	2	no	—
380	C₂×M₁₆	—	38	4	no	—
381	C₂×M₁₆	—	38	4	no	—
382	C₂×M₁₆	—	38	4	no	—
383	C₂×M₁₆	—	38	1	no	—
384	C₂×M₁₆	—	38	1	no	—
385	C₂×M₁₆	—	38	1	no	—
386	C₂×M₁₆	—	38	1	no	—
387	C₂×M₁₆	—	38	1	no	—
388	C₂×M₁₆	—	38	1	no	—
389	C₂×M₁₆	—	38	1	no	—
390	C₂×M₁₆	—	38	1	no	—
391	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	19	2	no	—
394	C₂²×C₈	—	19	1	no	—
395	C₂²×C₈	—	19	1	no	—
396	C₂²×C₈	—	19	2	no	—
397	C₂²×C₈	—	38	4	no	—
398	C₂²×C₈	—	38	4	no	—
399	C₂²×C₈	—	38	4	no	—
400	C₂²×C₈	—	38	1	no	—
401	C₂²×C₈	—	38	1	no	—
402	C₂²×C₈	—	38	1	no	—
403	C₂²×C₈	—	38	1	no	—
404	C₂²×C₈	—	38	1	no	—
405	C₂²×C₈	—	38	1	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	19	2	no	—
410	#117	—	38	1	no	—
411	#117	—	38	1	no	—
412	#117	—	38	1	no	—
413	#117	C₂×Dic₁₉	1	2	yes	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	38	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	38	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	38	1	no	—
420	#104	—	2	8	no	—
421	#104	—	38	8	no	—
422	C₁₉	#10773	1	1	yes	characteristic, complemented, Sylow
423	C₂⁴	—	2	1	no	—
424	C₂⁴	#64543	1	1	yes	characteristic
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	C₄×Dic₁₉	1	4	yes	—
438	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
439	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
440	#41	C₂²⋊Dic₁₉	1	4	yes	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
445	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
446	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
457	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
458	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	76	1	no	—
468	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
472	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
473	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
476	C₂²×C₄	#64543	1	1	yes	characteristic
477	C₂²×C₄	#64543	1	1	yes	characteristic
478	C₂²×C₄	#64543	1	1	yes	characteristic
479	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	4	1	no	—
485	M₁₆	—	4	1	no	—
486	M₁₆	—	19	4	no	—
487	M₁₆	—	38	16	no	—
488	M₁₆	—	38	2	no	—
489	M₁₆	—	38	2	no	—
490	M₁₆	—	38	2	no	—
491	M₁₆	—	38	2	no	—
492	M₁₆	—	38	2	no	—
493	M₁₆	—	76	1	no	—
494	M₁₆	—	76	1	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	4	1	no	—
497	C₂×C₈	—	4	1	no	—
498	C₂×C₈	—	19	2	no	—
499	C₂×C₈	—	19	2	no	—
500	C₂×C₈	—	38	16	no	—
501	C₂×C₈	—	38	1	no	—
502	C₂×C₈	—	38	1	no	—
503	C₂×C₈	—	38	2	no	—
504	C₂×C₈	—	38	2	no	—
505	C₂×C₈	—	38	2	no	—
506	C₂×C₈	—	38	2	no	—
507	C₂×C₈	—	38	1	no	—
508	C₂×C₈	—	38	1	no	—
509	C₂×C₈	—	38	2	no	—
510	C₂×C₈	—	38	2	no	—
511	C₂×C₈	—	38	2	no	—
512	C₂×C₈	—	38	2	no	—
513	C₂×C₈	—	76	1	no	—
514	C₂×C₈	—	76	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	—	38	2	no	—
518	C₄⋊C₄	—	76	1	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	38	2	no	—
522	C₂²⋊C₄	—	76	1	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	38	2	no	—
526	C₄²	—	76	1	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	4	no	—
532	C₂³	#10597323	1	1	yes	characteristic
533	C₂³	#10597324	1	1	yes	characteristic
534	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
535	C₂³	#10597332	1	1	yes	characteristic
536	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
537	C₂³	#10597381	1	1	yes	characteristic
538	C₂³	#10597385	1	1	yes	characteristic
539	Q₈	—	2	2	no	—
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	C₁₉⋊#95	1	4	yes	—
543	D₄	—	2	4	no	—
544	D₄	—	2	4	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	4	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	C₁₉⋊#95	1	4	yes	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	76	2	no	—
561	C₂×C₄	—	152	2	no	—
562	C₂×C₄	#10597323	1	1	yes	characteristic
563	C₂×C₄	#10597324	1	1	yes	characteristic
564	C₂×C₄	#10597324	1	1	yes	characteristic
565	C₂×C₄	#10597324	1	1	yes	characteristic
566	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
567	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
568	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
570	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
571	C₂×C₄	#10597328	1	1	yes	characteristic
572	C₂×C₄	#10597328	1	1	yes	characteristic
573	C₂×C₄	#10597332	1	1	yes	characteristic
574	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
575	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
576	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
577	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
578	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
579	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
580	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
581	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
582	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
583	C₂×C₄	#10597381	1	1	yes	characteristic
584	C₂×C₄	#10597383	1	1	yes	characteristic
585	C₂×C₄	#10597383	1	1	yes	characteristic
586	C₂×C₄	#10597385	1	1	yes	characteristic
587	C₂×C₄	#10597385	1	1	yes	characteristic
588	C₂×C₄	#10597385	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
590	C₈	—	4	2	no	—
591	C₈	—	38	2	no	—
592	C₈	—	38	2	no	—
593	C₈	—	38	4	no	—
594	C₈	—	76	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	4	no	—
606	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
607	C₂²	#11926402	1	1	yes	characteristic
608	C₂²	#11926405	1	1	yes	characteristic
609	C₂²	#11926416	1	1	yes	characteristic
610	C₂²	#11926419	1	1	yes	characteristic
611	C₂²	#11926421	1	1	yes	characteristic
612	C₂²	#11926424	1	1	yes	characteristic
613	C₄	—	2	4	no	—
614	C₄	—	8	2	no	—
615	C₄	—	152	2	no	—
616	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
617	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
618	C₄	#11926399	1	1	yes	characteristic
619	C₄	#11926402	1	1	yes	characteristic
620	C₄	#11926416	1	1	yes	characteristic
621	C₄	#11926419	1	1	yes	characteristic
622	C₄	#11926421	1	1	yes	characteristic
623	C₄	#11926424	1	1	yes	characteristic
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	4	4	no	—
631	C₂	#14561857	1	1	yes	characteristic
632	C₂	#14563687	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#421	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#421	D₁₉
hypocenter	C₁₉	#10773
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#421

Complements

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

N	H ≅ G/N	type
3. C₂×#11926315	C₂	semidirect
4. C₂×#11926314	C₂	semidirect
5. C₂×#11926308	C₂	semidirect
6. #14563351	C₂	semidirect
13. C₂×#10597394	C₄	semidirect
21. #11926561	C₄	semidirect
32. C₁₉×#421	C₄	semidirect
333. #421	Dic₁₉	semidirect
422. C₁₉	#10773	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597394	2
C₂×#11926561	2
C₂×#11926315	2
C₂×#11926314	2
C₂×#11926308	2
#14563351	2
C₂×C₁₉×#421	2
#10773	19