Subgroups — #18090355

Order 4864.

994 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597292	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926451	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926307	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
6	#14561864	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×#10597292	—	2	2	no	—
13	C₂×#10597292	—	2	2	no	—
14	C₂×#10597292	C₄	1	4	yes	complemented
15	#11926451	—	2	2	no	—
16	#11926451	—	2	2	no	—
17	C₂×C₁₉⋊#95	—	2	1	no	—
18	C₂×C₁₉⋊#95	—	2	1	no	—
19	C₂×C₁₉⋊#95	—	2	1	no	—
20	C₂×C₁₉⋊#95	—	2	1	no	—
21	#11926307	—	2	2	no	—
22	#11926306	—	2	2	no	—
23	#11926298	—	2	2	no	—
24	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	—	2	2	no	—
28	C₂×C₁₉×#103	—	2	2	no	—
29	C₂×C₁₉×#103	—	2	2	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
42	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
43	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×Dic₁₉	—	2	1	no	—
48	C₂³×Dic₁₉	—	2	1	no	—
49	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
50	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₂²×C₈×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
64	C₂×C₄⋊Dic₁₉	—	2	1	no	—
65	C₂×C₄⋊Dic₁₉	—	2	1	no	—
66	C₂×C₄⋊Dic₁₉	—	2	1	no	—
67	C₂×C₄⋊Dic₁₉	—	2	1	no	—
68	C₂×C₄⋊Dic₁₉	—	2	1	no	—
69	C₂×C₄⋊Dic₁₉	—	2	1	no	—
70	C₂×C₄⋊Dic₁₉	—	2	1	no	—
71	C₂×C₄⋊Dic₁₉	—	2	1	no	—
72	C₂×C₄⋊Dic₁₉	—	2	1	no	—
73	C₂×C₄⋊Dic₁₉	—	2	1	no	—
74	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
76	C₂×C₄×Dic₁₉	—	2	1	no	—
77	C₂×C₄×Dic₁₉	—	2	1	no	—
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×C₄×Dic₁₉	—	2	1	no	—
80	C₂×C₄×Dic₁₉	—	2	1	no	—
81	C₂×C₄×Dic₁₉	—	2	1	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	—	2	1	no	—
87	C₂²×C₁₉⋊C₈	—	2	1	no	—
88	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
89	C₁₉×#103	—	2	8	no	—
90	#10597292	—	2	8	no	—
91	C₁₉⋊#95	—	2	4	no	—
92	C₁₉⋊#95	—	2	4	no	—
93	C₁₉⋊#95	—	4	2	no	—
94	C₁₉⋊#95	—	4	2	no	—
95	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	—	4	1	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	—	4	1	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
152	C₂²×Dic₁₉	—	2	1	no	—
153	C₂²×Dic₁₉	—	2	1	no	—
154	C₂²×Dic₁₉	—	2	1	no	—
155	C₂²×Dic₁₉	—	2	1	no	—
156	C₂²×Dic₁₉	—	2	1	no	—
157	C₂²×Dic₁₉	—	2	1	no	—
158	C₂²×Dic₁₉	—	2	1	no	—
159	C₂²×Dic₁₉	—	2	1	no	—
160	C₂²×Dic₁₉	—	2	1	no	—
161	C₂²×Dic₁₉	—	2	1	no	—
162	C₂²×Dic₁₉	—	2	1	no	—
163	C₂²×Dic₁₉	—	2	1	no	—
164	C₂²×Dic₁₉	—	2	2	no	—
165	C₂²×Dic₁₉	—	2	2	no	—
166	C₂²×Dic₁₉	—	4	1	no	—
167	C₂²×Dic₁₉	—	4	1	no	—
168	C₂²×Dic₁₉	—	4	1	no	—
169	C₂²×Dic₁₉	—	4	1	no	—
170	C₂²×Dic₁₉	—	4	1	no	—
171	C₂²×Dic₁₉	—	4	1	no	—
172	C₂²×Dic₁₉	—	4	1	no	—
173	C₂²×Dic₁₉	—	4	1	no	—
174	C₂²×Dic₁₉	—	4	1	no	—
175	C₂²×Dic₁₉	—	4	1	no	—
176	C₂²×Dic₁₉	—	4	1	no	—
177	C₂²×Dic₁₉	—	4	1	no	—
178	C₂²×Dic₁₉	SD₁₆	1	2	yes	—
179	C₂²×Dic₁₉	Q₁₆	1	2	yes	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	2	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	4	1	no	—
184	C₂×C₈×C₁₉	—	4	1	no	—
185	C₂×C₈×C₁₉	—	4	1	no	—
186	C₂×C₈×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊Dic₁₉	—	2	2	no	—
192	C₄⋊Dic₁₉	—	2	2	no	—
193	C₄⋊Dic₁₉	—	2	2	no	—
194	C₄⋊Dic₁₉	—	2	2	no	—
195	C₄⋊Dic₁₉	—	4	1	no	—
196	C₄⋊Dic₁₉	—	4	1	no	—
197	C₄⋊Dic₁₉	—	4	1	no	—
198	C₄⋊Dic₁₉	—	4	1	no	—
199	C₄×Dic₁₉	—	4	1	no	—
200	C₄×Dic₁₉	—	4	1	no	—
201	C₄×Dic₁₉	—	4	1	no	—
202	C₄×Dic₁₉	—	4	1	no	—
203	C₂×C₁₉⋊C₈	—	2	2	no	—
204	C₂×C₁₉⋊C₈	—	2	2	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	—	4	1	no	—
209	C₂×C₁₉⋊C₈	—	4	1	no	—
210	#11190	—	19	1	no	maximal, Sylow
211	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
212	C₂³×C₁₉	#120	1	1	yes	characteristic
213	C₂³×C₁₉	#121	1	1	yes	characteristic
214	C₂³×C₁₉	#121	1	1	yes	characteristic
215	C₂³×C₁₉	#121	1	1	yes	characteristic
216	C₂³×C₁₉	#123	1	1	yes	characteristic
217	C₂³×C₁₉	#124	1	1	yes	characteristic
218	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
219	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
220	C₂³×C₁₉	#135	1	1	yes	characteristic
221	C₂³×C₁₉	#135	1	1	yes	characteristic
222	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂³×C₁₉	#137	1	1	yes	characteristic
224	C₂³×C₁₉	#137	1	1	yes	characteristic
225	C₂³×C₁₉	#137	1	1	yes	characteristic
226	Q₈×C₁₉	—	2	4	no	—
227	Q₈×C₁₉	—	2	4	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	Q₈×C₁₉	—	4	2	no	—
230	Q₈×C₁₉	—	4	2	no	—
231	Q₈×C₁₉	—	4	2	no	—
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	8	1	no	—
245	C₂×C₄×C₁₉	—	8	1	no	—
246	C₂×C₄×C₁₉	—	8	1	no	—
247	C₂×C₄×C₁₉	—	8	1	no	—
248	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
272	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
273	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
276	C₂×Dic₁₉	—	2	2	no	—
277	C₂×Dic₁₉	—	2	2	no	—
278	C₂×Dic₁₉	—	2	2	no	—
279	C₂×Dic₁₉	—	2	2	no	—
280	C₂×Dic₁₉	—	2	2	no	—
281	C₂×Dic₁₉	—	2	2	no	—
282	C₂×Dic₁₉	—	4	1	no	—
283	C₂×Dic₁₉	—	4	1	no	—
284	C₂×Dic₁₉	—	4	1	no	—
285	C₂×Dic₁₉	—	4	1	no	—
286	C₂×Dic₁₉	—	4	1	no	—
287	C₂×Dic₁₉	—	4	1	no	—
288	C₂×Dic₁₉	—	4	1	no	—
289	C₂×Dic₁₉	—	4	1	no	—
290	C₂×Dic₁₉	—	4	2	no	—
291	C₂×Dic₁₉	—	4	2	no	—
292	C₂×Dic₁₉	—	4	2	no	—
293	C₂×Dic₁₉	—	4	2	no	—
294	C₂×Dic₁₉	—	4	2	no	—
295	C₂×Dic₁₉	—	4	2	no	—
296	C₂×Dic₁₉	—	8	1	no	—
297	C₂×Dic₁₉	—	8	1	no	—
298	C₂×Dic₁₉	—	8	1	no	—
299	C₂×Dic₁₉	—	8	1	no	—
300	C₂×Dic₁₉	—	8	1	no	—
301	C₂×Dic₁₉	—	8	1	no	—
302	C₂×Dic₁₉	—	8	1	no	—
303	C₂×Dic₁₉	—	8	1	no	—
304	C₈×C₁₉	—	4	2	no	—
305	C₁₉⋊C₈	—	4	2	no	—
306	C₂²×#103	—	19	1	no	—
307	C₂²×#103	D₁₉	1	1	yes	characteristic
308	C₂×#391	—	19	1	no	—
309	C₂×#340	—	19	1	no	—
310	C₂×#340	—	19	1	no	—
311	C₂×#336	—	19	1	no	—
312	C₄⋊#95	—	19	1	no	—
313	C₂²×C₁₉	#386	1	1	yes	characteristic
314	C₂²×C₁₉	#388	1	1	yes	characteristic
315	C₂²×C₁₉	#388	1	1	yes	characteristic
316	C₂²×C₁₉	#394	1	1	yes	characteristic
317	C₂²×C₁₉	#394	1	1	yes	characteristic
318	C₂²×C₁₉	#394	1	1	yes	characteristic
319	C₂²×C₁₉	#397	1	1	yes	characteristic
320	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
321	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
322	C₂²×C₁₉	#440	1	1	yes	characteristic
323	C₂²×C₁₉	#441	1	1	yes	characteristic
324	C₂²×C₁₉	#448	1	1	yes	characteristic
325	C₂²×C₁₉	#449	1	1	yes	characteristic
326	C₂²×C₁₉	#451	1	1	yes	characteristic
327	C₂²×C₁₉	#452	1	1	yes	characteristic
328	C₂²×C₁₉	#460	1	1	yes	characteristic
329	C₂²×C₁₉	#461	1	1	yes	characteristic
330	C₂²×C₁₉	#462	1	1	yes	characteristic
331	C₂²×C₁₉	#462	1	1	yes	characteristic
332	C₂²×C₁₉	#463	1	1	yes	characteristic
333	C₂²×C₁₉	#464	1	1	yes	characteristic
334	C₂²×C₁₉	#464	1	1	yes	characteristic
335	C₂²×C₁₉	#464	1	1	yes	characteristic
336	C₂²×C₁₉	#465	1	1	yes	characteristic
337	C₂²×C₁₉	#467	1	1	yes	characteristic
338	C₂²×C₁₉	#468	1	1	yes	characteristic
339	C₂²×C₁₉	#470	1	1	yes	characteristic
340	C₂²×C₁₉	#483	1	1	yes	characteristic
341	C₂²×C₁₉	#484	1	1	yes	characteristic
342	C₂²×C₁₉	#485	1	1	yes	characteristic
343	C₂²×C₁₉	#485	1	1	yes	characteristic
344	C₂²×C₁₉	#487	1	1	yes	characteristic
345	C₂²×C₁₉	#488	1	1	yes	characteristic
346	C₂²×C₁₉	#489	1	1	yes	characteristic
347	C₂²×C₁₉	#491	1	1	yes	characteristic
348	C₄×C₁₉	—	4	4	no	—
349	C₄×C₁₉	—	8	2	no	—
350	C₄×C₁₉	#381	1	1	yes	characteristic
351	C₄×C₁₉	#386	1	1	yes	characteristic
352	C₄×C₁₉	#388	1	1	yes	characteristic
353	C₄×C₁₉	#388	1	1	yes	characteristic
354	C₄×C₁₉	#394	1	1	yes	characteristic
355	C₄×C₁₉	#397	1	1	yes	characteristic
356	C₄×C₁₉	#397	1	1	yes	characteristic
357	C₄×C₁₉	#397	1	1	yes	characteristic
358	Dic₁₉	—	4	2	no	—
359	Dic₁₉	—	4	2	no	—
360	Dic₁₉	—	8	2	no	—
361	Dic₁₉	—	8	2	no	—
362	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
363	C₂³×C₈	—	19	1	no	—
364	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
365	C₂²×C₄⋊C₄	—	19	1	no	—
366	C₂²×C₄⋊C₄	—	19	1	no	—
367	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
368	C₂²×C₄²	—	19	1	no	—
369	C₂×#103	—	2	2	no	—
370	C₂×#103	—	2	2	no	—
371	C₂×#103	—	2	2	no	—
372	C₂×#103	—	19	4	no	—
373	C₂×#103	—	38	2	no	—
374	C₂×#103	—	38	2	no	—
375	#391	—	38	2	no	—
376	#391	—	38	2	no	—
377	C₂×#95	—	38	1	no	—
378	C₂×#95	—	38	1	no	—
379	C₂×#95	—	38	1	no	—
380	C₂×#95	—	38	1	no	—
381	#340	—	38	2	no	—
382	#340	—	38	2	no	—
383	#336	—	38	2	no	—
384	C₂×C₁₉	#1440	1	1	yes	characteristic
385	C₂×C₁₉	#1878	1	1	yes	characteristic
386	C₂×C₁₉	#1880	1	1	yes	characteristic
387	C₂×C₁₉	#1927	1	1	yes	characteristic
388	C₂×C₁₉	#1928	1	1	yes	characteristic
389	C₂×C₁₉	#1933	1	1	yes	characteristic
390	C₂×C₁₉	#1935	1	1	yes	characteristic
391	C₂×C₁₉	#2035	1	1	yes	characteristic
392	C₂×C₁₉	#2036	1	1	yes	characteristic
393	C₂×C₁₉	#2042	1	1	yes	characteristic
394	C₂×C₁₉	#2043	1	1	yes	characteristic
395	C₂×C₁₉	#2055	1	1	yes	characteristic
396	C₂×C₁₉	#2056	1	1	yes	characteristic
397	C₂×C₁₉	#2072	1	1	yes	characteristic
398	C₂×C₁₉	#2074	1	1	yes	characteristic
399	C₂²×Q₈	—	2	1	no	—
400	C₂²×Q₈	—	2	1	no	—
401	C₂²×Q₈	—	2	1	no	—
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×Q₈	—	2	1	no	—
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×Q₈	—	2	1	no	—
406	C₂²×Q₈	—	2	1	no	—
407	C₂²×Q₈	—	2	1	no	—
408	C₂²×Q₈	—	2	1	no	—
409	C₂²×Q₈	—	2	1	no	—
410	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
411	C₂²×Q₈	D₇₆	1	2	yes	—
412	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
413	C₂³×C₄	—	2	1	no	—
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	19	1	no	—
416	C₂³×C₄	—	19	1	no	—
417	C₂³×C₄	—	38	1	no	—
418	C₂³×C₄	—	38	1	no	—
419	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
420	C₂²×C₈	—	2	1	no	—
421	C₂²×C₈	—	2	1	no	—
422	C₂²×C₈	—	2	1	no	—
423	C₂²×C₈	—	2	1	no	—
424	C₂²×C₈	—	2	1	no	—
425	C₂²×C₈	—	2	1	no	—
426	C₂²×C₈	—	19	2	no	—
427	C₂²×C₈	—	38	1	no	—
428	C₂²×C₈	—	38	1	no	—
429	C₂²×C₈	—	38	1	no	—
430	C₂²×C₈	—	38	1	no	—
431	C₂²×C₈	—	38	1	no	—
432	C₂²×C₈	—	38	1	no	—
433	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	19	2	no	—
440	C₂×C₄⋊C₄	—	19	2	no	—
441	C₂×C₄⋊C₄	—	38	1	no	—
442	C₂×C₄⋊C₄	—	38	1	no	—
443	C₂×C₄⋊C₄	—	38	1	no	—
444	C₂×C₄⋊C₄	—	38	1	no	—
445	C₂×C₄⋊C₄	—	38	1	no	—
446	C₂×C₄⋊C₄	—	38	1	no	—
447	C₂×C₄⋊C₄	—	38	1	no	—
448	C₂×C₄⋊C₄	—	38	1	no	—
449	C₂×C₄⋊C₄	—	38	1	no	—
450	C₂×C₄⋊C₄	—	38	1	no	—
451	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
452	C₂×C₄²	—	38	1	no	—
453	C₂×C₄²	—	38	1	no	—
454	C₂×C₄²	—	38	1	no	—
455	C₂×C₄²	—	38	1	no	—
456	C₂×C₄²	—	38	1	no	—
457	C₂×C₄²	—	38	1	no	—
458	#103	—	2	8	no	—
459	#103	—	38	8	no	—
460	#95	—	38	4	no	—
461	#95	—	38	4	no	—
462	#95	—	76	2	no	—
463	#95	—	76	2	no	—
464	C₁₉	#11190	1	1	yes	characteristic, complemented, Sylow
465	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	2	no	—
481	C₂×Q₈	—	4	1	no	—
482	C₂×Q₈	—	4	1	no	—
483	C₂×Q₈	—	4	1	no	—
484	C₂×Q₈	—	4	1	no	—
485	C₂×Q₈	—	4	1	no	—
486	C₂×Q₈	—	4	1	no	—
487	C₂×Q₈	—	4	1	no	—
488	C₂×Q₈	—	4	1	no	—
489	C₂×Q₈	—	4	1	no	—
490	C₂×Q₈	—	4	1	no	—
491	C₂×Q₈	—	4	1	no	—
492	C₂×Q₈	—	4	1	no	—
493	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	—	4	1	no	—
504	C₂²×C₄	—	4	1	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	19	2	no	—
509	C₂²×C₄	—	19	2	no	—
510	C₂²×C₄	—	38	1	no	—
511	C₂²×C₄	—	38	1	no	—
512	C₂²×C₄	—	38	1	no	—
513	C₂²×C₄	—	38	1	no	—
514	C₂²×C₄	—	38	1	no	—
515	C₂²×C₄	—	38	1	no	—
516	C₂²×C₄	—	38	1	no	—
517	C₂²×C₄	—	38	1	no	—
518	C₂²×C₄	—	38	1	no	—
519	C₂²×C₄	—	38	1	no	—
520	C₂²×C₄	—	38	1	no	—
521	C₂²×C₄	—	38	1	no	—
522	C₂²×C₄	—	38	2	no	—
523	C₂²×C₄	—	38	2	no	—
524	C₂²×C₄	—	76	1	no	—
525	C₂²×C₄	—	76	1	no	—
526	C₂²×C₄	—	76	1	no	—
527	C₂²×C₄	—	76	1	no	—
528	C₂²×C₄	—	76	1	no	—
529	C₂²×C₄	—	76	1	no	—
530	C₂²×C₄	—	76	1	no	—
531	C₂²×C₄	—	76	1	no	—
532	C₂²×C₄	—	76	1	no	—
533	C₂²×C₄	—	76	1	no	—
534	C₂²×C₄	—	76	1	no	—
535	C₂²×C₄	—	76	1	no	—
536	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
538	C₂²×C₄	#64541	1	1	yes	characteristic
539	C₂²×C₄	#64541	1	1	yes	characteristic
540	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
541	C₂²×C₄	#64543	1	1	yes	characteristic
542	C₂²×C₄	#64543	1	1	yes	characteristic
543	C₂²×C₄	#64543	1	1	yes	characteristic
544	C₂²×C₄	#64543	1	1	yes	characteristic
545	C₂²×C₄	#64543	1	1	yes	characteristic
546	C₂²×C₄	#64543	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
549	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
550	C₂×C₈	—	2	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	2	2	no	—
553	C₂×C₈	—	4	1	no	—
554	C₂×C₈	—	4	1	no	—
555	C₂×C₈	—	4	1	no	—
556	C₂×C₈	—	4	1	no	—
557	C₂×C₈	—	38	2	no	—
558	C₂×C₈	—	38	2	no	—
559	C₂×C₈	—	38	2	no	—
560	C₂×C₈	—	76	1	no	—
561	C₂×C₈	—	76	1	no	—
562	C₂×C₈	—	76	1	no	—
563	C₂×C₈	—	76	1	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	4	1	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	—	38	2	no	—
569	C₄⋊C₄	—	38	2	no	—
570	C₄⋊C₄	—	38	2	no	—
571	C₄⋊C₄	—	38	2	no	—
572	C₄⋊C₄	—	76	1	no	—
573	C₄⋊C₄	—	76	1	no	—
574	C₄⋊C₄	—	76	1	no	—
575	C₄⋊C₄	—	76	1	no	—
576	C₄²	—	76	1	no	—
577	C₄²	—	76	1	no	—
578	C₄²	—	76	1	no	—
579	C₄²	—	76	1	no	—
580	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
581	C₂³	#10597328	1	1	yes	characteristic
582	C₂³	#10597329	1	1	yes	characteristic
583	C₂³	#10597331	1	1	yes	characteristic
584	C₂³	SD₁₆×D₁₉	1	1	yes	characteristic
585	C₂³	#10597360	1	1	yes	characteristic
586	C₂³	#10597361	1	1	yes	characteristic
587	C₂³	#10597362	1	1	yes	characteristic
588	C₂³	Q₁₆×D₁₉	1	1	yes	characteristic
589	C₂³	#10597364	1	1	yes	characteristic
590	C₂³	#10597364	1	1	yes	characteristic
591	C₂³	#10597365	1	1	yes	characteristic
592	C₂³	#10597384	1	1	yes	characteristic
593	C₂³	#10597385	1	1	yes	characteristic
594	C₂³	#10597385	1	1	yes	characteristic
595	Q₈	—	2	4	no	—
596	Q₈	—	2	4	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	4	2	no	—
599	Q₈	—	4	2	no	—
600	Q₈	—	4	2	no	—
601	Q₈	—	4	2	no	—
602	Q₈	—	4	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	8	1	no	—
614	C₂×C₄	—	8	1	no	—
615	C₂×C₄	—	8	1	no	—
616	C₂×C₄	—	8	1	no	—
617	C₂×C₄	—	38	2	no	—
618	C₂×C₄	—	38	2	no	—
619	C₂×C₄	—	38	2	no	—
620	C₂×C₄	—	38	2	no	—
621	C₂×C₄	—	38	2	no	—
622	C₂×C₄	—	38	2	no	—
623	C₂×C₄	—	76	1	no	—
624	C₂×C₄	—	76	1	no	—
625	C₂×C₄	—	76	1	no	—
626	C₂×C₄	—	76	1	no	—
627	C₂×C₄	—	76	1	no	—
628	C₂×C₄	—	76	1	no	—
629	C₂×C₄	—	76	1	no	—
630	C₂×C₄	—	76	1	no	—
631	C₂×C₄	—	76	2	no	—
632	C₂×C₄	—	76	2	no	—
633	C₂×C₄	—	76	2	no	—
634	C₂×C₄	—	76	2	no	—
635	C₂×C₄	—	76	2	no	—
636	C₂×C₄	—	76	2	no	—
637	C₂×C₄	—	152	1	no	—
638	C₂×C₄	—	152	1	no	—
639	C₂×C₄	—	152	1	no	—
640	C₂×C₄	—	152	1	no	—
641	C₂×C₄	—	152	1	no	—
642	C₂×C₄	—	152	1	no	—
643	C₂×C₄	—	152	1	no	—
644	C₂×C₄	—	152	1	no	—
645	C₂×C₄	#10597323	1	1	yes	characteristic
646	C₂×C₄	#10597323	1	1	yes	characteristic
647	C₂×C₄	#10597325	1	1	yes	characteristic
648	C₂×C₄	#10597325	1	1	yes	characteristic
649	C₂×C₄	#10597325	1	1	yes	characteristic
650	C₂×C₄	#10597325	1	1	yes	characteristic
651	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
652	C₂×C₄	#10597329	1	1	yes	characteristic
653	C₂×C₄	#10597331	1	1	yes	characteristic
654	C₂×C₄	#10597332	1	1	yes	characteristic
655	C₂×C₄	#10597332	1	1	yes	characteristic
656	C₂×C₄	#10597332	1	1	yes	characteristic
657	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
658	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
659	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
660	C₂×C₄	#10597375	1	1	yes	characteristic
661	C₂×C₄	#10597376	1	1	yes	characteristic
662	C₂×C₄	#10597376	1	1	yes	characteristic
663	C₂×C₄	#10597381	1	1	yes	characteristic
664	C₂×C₄	#10597381	1	1	yes	characteristic
665	C₂×C₄	#10597381	1	1	yes	characteristic
666	C₂×C₄	#10597381	1	1	yes	characteristic
667	C₂×C₄	#10597382	1	1	yes	characteristic
668	C₂×C₄	#10597382	1	1	yes	characteristic
669	C₂×C₄	#10597384	1	1	yes	characteristic
670	C₂×C₄	#10597385	1	1	yes	characteristic
671	C₂×C₄	#10597385	1	1	yes	characteristic
672	C₂×C₄	#10597399	1	1	yes	characteristic
673	C₈	—	4	2	no	—
674	C₈	—	76	2	no	—
675	C₂²	#11926421	1	1	yes	characteristic
676	C₂²	#11926432	1	1	yes	characteristic
677	C₂²	#11926438	1	1	yes	characteristic
678	C₂²	#11926458	1	1	yes	characteristic
679	C₂²	#11926460	1	1	yes	characteristic
680	C₂²	#11926460	1	1	yes	characteristic
681	C₂²	#11926472	1	1	yes	characteristic
682	C₂²	#11926629	1	1	yes	characteristic
683	C₂²	#11926636	1	1	yes	characteristic
684	C₂²	#11926647	1	1	yes	characteristic
685	C₂²	#11926648	1	1	yes	characteristic
686	C₂²	#11926684	1	1	yes	characteristic
687	C₂²	#11926692	1	1	yes	characteristic
688	C₂²	#11926701	1	1	yes	characteristic
689	C₂²	#11926709	1	1	yes	characteristic
690	C₂²	#11926742	1	1	yes	characteristic
691	C₂²	#11926747	1	1	yes	characteristic
692	C₂²	#11926752	1	1	yes	characteristic
693	C₂²	#11926752	1	1	yes	characteristic
694	C₂²	#11926761	1	1	yes	characteristic
695	C₂²	#11926764	1	1	yes	characteristic
696	C₂²	#11926768	1	1	yes	characteristic
697	C₂²	#11926768	1	1	yes	characteristic
698	C₂²	#11926770	1	1	yes	characteristic
699	C₂²	#11926782	1	1	yes	characteristic
700	C₂²	#11926787	1	1	yes	characteristic
701	C₂²	#11926799	1	1	yes	characteristic
702	C₂²	#11926873	1	1	yes	characteristic
703	C₂²	#11926878	1	1	yes	characteristic
704	C₂²	#11926883	1	1	yes	characteristic
705	C₂²	#11926884	1	1	yes	characteristic
706	C₂²	#11926893	1	1	yes	characteristic
707	C₂²	#11926900	1	1	yes	characteristic
708	C₂²	#11926905	1	1	yes	characteristic
709	C₂²	#11926911	1	1	yes	characteristic
710	C₄	—	4	4	no	—
711	C₄	—	8	2	no	—
712	C₄	—	76	2	no	—
713	C₄	—	76	2	no	—
714	C₄	—	152	2	no	—
715	C₄	—	152	2	no	—
716	C₄	#11926405	1	1	yes	characteristic
717	C₄	#11926423	1	1	yes	characteristic
718	C₄	#11926432	1	1	yes	characteristic
719	C₄	#11926438	1	1	yes	characteristic
720	C₄	#11926458	1	1	yes	characteristic
721	C₄	#11926469	1	1	yes	characteristic
722	C₄	#11926469	1	1	yes	characteristic
723	C₄	#11926472	1	1	yes	characteristic
724	C₂	#14561882	1	1	yes	characteristic
725	C₂	#14563974	1	1	yes	characteristic
726	C₂	#14563988	1	1	yes	characteristic
727	C₂	#14564272	1	1	yes	characteristic
728	C₂	#14564279	1	1	yes	characteristic
729	C₂	#14564308	1	1	yes	characteristic
730	C₂	#14564322	1	1	yes	characteristic
731	C₂	#14564830	1	1	yes	characteristic
732	C₂	#14564837	1	1	yes	characteristic
733	C₂	#14564873	1	1	yes	characteristic
734	C₂	#14564880	1	1	yes	characteristic
735	C₂	#14564948	1	1	yes	characteristic
736	C₂	#14564955	1	1	yes	characteristic
737	C₂	#14565046	1	1	yes	characteristic
738	C₂	#14565056	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#103	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#103	D₁₉
hypocenter	C₁₉	#11190
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#103

Complements

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

N	H ≅ G/N	type
14. C₂×#10597292	C₄	semidirect
464. C₁₉	#11190	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597292	2
C₂×#11926451	2
C₂×#11926307	2
C₂×#11926306	2
C₂×#11926298	2
#14561864	2
C₂²×C₁₉×#103	2
#11190	19