Subgroups — #18090725

Order 4864.

814 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597264	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
6	#14561865	C₂	1	1	yes	maximal, characteristic
7	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	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×#10597264	—	2	2	no	—
13	C₂×#10597264	—	2	2	no	—
14	C₂×#10597264	—	2	2	no	—
15	C₂×C₁₉⋊#95	—	2	1	no	—
16	C₂×C₁₉⋊#95	—	2	1	no	—
17	#11926306	—	2	2	no	—
18	#11926306	—	2	2	no	—
19	#11926306	C₄	1	4	yes	complemented
20	#11926299	—	2	2	no	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#95	—	2	1	no	—
25	C₂×C₁₉×#95	—	2	1	no	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×Dic₁₉	—	2	1	no	—
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×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	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄⋊Dic₁₉	—	2	1	no	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	—	2	1	no	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	C₂²×C₁₉⋊C₈	—	2	1	no	—
65	C₂²×C₁₉⋊C₈	—	2	1	no	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	C₂²×C₁₉⋊C₈	—	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	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
75	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
76	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
77	C₁₉×#95	—	4	2	no	—
78	C₁₉×#95	—	4	2	no	—
79	C₁₉⋊#95	—	4	2	no	—
80	C₁₉⋊#95	—	4	2	no	—
81	#10597264	—	2	8	no	—
82	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	4	1	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	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	D₈	1	2	yes	—
110	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	C₂²×Dic₁₉	—	2	2	no	—
126	C₂²×Dic₁₉	—	2	2	no	—
127	C₂²×Dic₁₉	—	4	1	no	—
128	C₂²×Dic₁₉	—	4	1	no	—
129	C₂²×Dic₁₉	—	4	1	no	—
130	C₂²×Dic₁₉	—	4	1	no	—
131	C₂²×Dic₁₉	—	4	1	no	—
132	C₂²×Dic₁₉	—	4	1	no	—
133	C₂²×Dic₁₉	—	4	1	no	—
134	C₂²×Dic₁₉	—	4	1	no	—
135	C₂²×Dic₁₉	—	4	1	no	—
136	C₂²×Dic₁₉	—	4	1	no	—
137	C₂²×Dic₁₉	—	4	1	no	—
138	C₂²×Dic₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	—	4	1	no	—
150	C₄²×C₁₉	—	4	1	no	—
151	C₄⋊Dic₁₉	—	2	2	no	—
152	C₄⋊Dic₁₉	—	2	2	no	—
153	C₄⋊Dic₁₉	—	2	2	no	—
154	C₄⋊Dic₁₉	—	2	2	no	—
155	C₄⋊Dic₁₉	—	4	1	no	—
156	C₄⋊Dic₁₉	—	4	1	no	—
157	C₄⋊Dic₁₉	—	4	1	no	—
158	C₄⋊Dic₁₉	—	4	1	no	—
159	C₂×C₁₉⋊C₈	—	2	2	no	—
160	C₂×C₁₉⋊C₈	—	2	2	no	—
161	C₂×C₁₉⋊C₈	—	2	2	no	—
162	C₂×C₁₉⋊C₈	—	2	2	no	—
163	C₂×C₁₉⋊C₈	—	2	2	no	—
164	C₂×C₁₉⋊C₈	—	2	2	no	—
165	C₂×C₁₉⋊C₈	—	2	2	no	—
166	C₂×C₁₉⋊C₈	—	2	2	no	—
167	C₂×C₁₉⋊C₈	—	2	2	no	—
168	C₂×C₁₉⋊C₈	—	4	1	no	—
169	C₂×C₁₉⋊C₈	—	4	1	no	—
170	C₂×C₁₉⋊C₈	—	4	1	no	—
171	C₂×C₁₉⋊C₈	—	4	1	no	—
172	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
173	#11256	—	19	1	no	maximal, Sylow
174	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₉	#121	1	1	yes	characteristic
176	C₂³×C₁₉	#121	1	1	yes	characteristic
177	C₂³×C₁₉	#121	1	1	yes	characteristic
178	C₂³×C₁₉	#123	1	1	yes	characteristic
179	C₂³×C₁₉	#123	1	1	yes	characteristic
180	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
181	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
182	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
183	C₂³×C₁₉	#135	1	1	yes	characteristic
184	C₂³×C₁₉	#135	1	1	yes	characteristic
185	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂³×C₁₉	#137	1	1	yes	characteristic
188	C₂³×C₁₉	#137	1	1	yes	characteristic
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	8	1	no	—
210	C₂×C₄×C₁₉	—	8	1	no	—
211	C₂×C₄×C₁₉	—	8	1	no	—
212	C₂×C₄×C₁₉	—	8	1	no	—
213	C₂×C₄×C₁₉	—	8	1	no	—
214	C₂×C₄×C₁₉	—	8	1	no	—
215	C₂×C₄×C₁₉	—	8	1	no	—
216	C₂×C₄×C₁₉	—	8	1	no	—
217	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
245	C₂×Dic₁₉	—	4	2	no	—
246	C₂×Dic₁₉	—	4	2	no	—
247	C₂×Dic₁₉	—	4	2	no	—
248	C₂×Dic₁₉	—	4	2	no	—
249	C₂×Dic₁₉	—	4	2	no	—
250	C₂×Dic₁₉	—	4	2	no	—
251	C₂×Dic₁₉	—	8	1	no	—
252	C₂×Dic₁₉	—	8	1	no	—
253	C₂×Dic₁₉	—	8	1	no	—
254	C₂×Dic₁₉	—	8	1	no	—
255	C₂×Dic₁₉	—	8	1	no	—
256	C₂×Dic₁₉	—	8	1	no	—
257	C₂×Dic₁₉	—	8	1	no	—
258	C₂×Dic₁₉	—	8	1	no	—
259	C₁₉⋊C₈	—	2	4	no	—
260	C₁₉⋊C₈	—	4	2	no	—
261	C₂²×#107	—	19	1	no	—
262	C₂×#340	—	19	1	no	—
263	C₂×#340	—	19	1	no	—
264	C₂×#340	—	19	1	no	—
265	C₂×#336	—	19	1	no	—
266	C₄⋊#95	—	19	1	no	—
267	C₄⋊#95	D₁₉	1	1	yes	characteristic
268	C₂²×C₁₉	#388	1	1	yes	characteristic
269	C₂²×C₁₉	#388	1	1	yes	characteristic
270	C₂²×C₁₉	#389	1	1	yes	characteristic
271	C₂²×C₁₉	#394	1	1	yes	characteristic
272	C₂²×C₁₉	#397	1	1	yes	characteristic
273	C₂²×C₁₉	#398	1	1	yes	characteristic
274	C₂²×C₁₉	#398	1	1	yes	characteristic
275	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
276	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
277	C₂²×C₁₉	#440	1	1	yes	characteristic
278	C₂²×C₁₉	#440	1	1	yes	characteristic
279	C₂²×C₁₉	#459	1	1	yes	characteristic
280	C₂²×C₁₉	#459	1	1	yes	characteristic
281	C₂²×C₁₉	#462	1	1	yes	characteristic
282	C₂²×C₁₉	#462	1	1	yes	characteristic
283	C₂²×C₁₉	#463	1	1	yes	characteristic
284	C₂²×C₁₉	#463	1	1	yes	characteristic
285	C₂²×C₁₉	#464	1	1	yes	characteristic
286	C₂²×C₁₉	#464	1	1	yes	characteristic
287	C₂²×C₁₉	#466	1	1	yes	characteristic
288	C₂²×C₁₉	#467	1	1	yes	characteristic
289	C₂²×C₁₉	#469	1	1	yes	characteristic
290	C₂²×C₁₉	#470	1	1	yes	characteristic
291	C₂²×C₁₉	#480	1	1	yes	characteristic
292	C₂²×C₁₉	#480	1	1	yes	characteristic
293	C₂²×C₁₉	#482	1	1	yes	characteristic
294	C₂²×C₁₉	#482	1	1	yes	characteristic
295	C₂²×C₁₉	#484	1	1	yes	characteristic
296	C₂²×C₁₉	#484	1	1	yes	characteristic
297	C₂²×C₁₉	#485	1	1	yes	characteristic
298	C₂²×C₁₉	#485	1	1	yes	characteristic
299	C₂²×C₁₉	#499	1	1	yes	characteristic
300	C₂²×C₁₉	#500	1	1	yes	characteristic
301	C₂²×C₁₉	#501	1	1	yes	characteristic
302	C₂²×C₁₉	#501	1	1	yes	characteristic
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	8	2	no	—
306	C₄×C₁₉	—	8	2	no	—
307	C₄×C₁₉	#382	1	1	yes	characteristic
308	C₄×C₁₉	#385	1	1	yes	characteristic
309	C₄×C₁₉	#387	1	1	yes	characteristic
310	C₄×C₁₉	#387	1	1	yes	characteristic
311	C₄×C₁₉	#393	1	1	yes	characteristic
312	C₄×C₁₉	#400	1	1	yes	characteristic
313	C₄×C₁₉	#400	1	1	yes	characteristic
314	C₄×C₁₉	#400	1	1	yes	characteristic
315	Dic₁₉	—	8	2	no	—
316	Dic₁₉	—	8	2	no	—
317	C₂³×C₈	—	19	1	no	—
318	C₂³×C₈	—	19	1	no	—
319	C₂²×C₄⋊C₄	—	19	1	no	—
320	C₂²×C₄⋊C₄	—	19	1	no	—
321	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
323	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
324	C₂×#107	—	38	2	no	—
325	C₂×#107	—	38	2	no	—
326	C₂×#107	—	38	2	no	—
327	C₂×#95	—	2	1	no	—
328	C₂×#95	—	2	1	no	—
329	C₂×#95	—	38	1	no	—
330	C₂×#95	—	38	1	no	—
331	#340	—	19	4	no	—
332	#340	—	38	2	no	—
333	#340	—	38	2	no	—
334	#336	—	38	2	no	—
335	C₂×C₁₉	#1442	1	1	yes	characteristic
336	C₂×C₁₉	#1925	1	1	yes	characteristic
337	C₂×C₁₉	#1925	1	1	yes	characteristic
338	C₂×C₁₉	#1928	1	1	yes	characteristic
339	C₂×C₁₉	#1928	1	1	yes	characteristic
340	C₂×C₁₉	#1942	1	1	yes	characteristic
341	C₂×C₁₉	#1944	1	1	yes	characteristic
342	C₂×C₁₉	#2054	1	1	yes	characteristic
343	C₂×C₁₉	#2056	1	1	yes	characteristic
344	C₂×C₁₉	#2075	1	1	yes	characteristic
345	C₂×C₁₉	#2076	1	1	yes	characteristic
346	C₂×C₁₉	#2083	1	1	yes	characteristic
347	C₂×C₁₉	#2083	1	1	yes	characteristic
348	C₂×C₁₉	#2085	1	1	yes	characteristic
349	C₂×C₁₉	#2085	1	1	yes	characteristic
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	—	38	1	no	—
353	C₂³×C₄	—	38	1	no	—
354	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
355	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
356	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
357	C₂²×C₈	—	19	2	no	—
358	C₂²×C₈	—	19	2	no	—
359	C₂²×C₈	—	19	2	no	—
360	C₂²×C₈	—	19	2	no	—
361	C₂²×C₈	—	38	1	no	—
362	C₂²×C₈	—	38	1	no	—
363	C₂²×C₈	—	38	1	no	—
364	C₂²×C₈	—	38	1	no	—
365	C₂²×C₈	—	38	1	no	—
366	C₂²×C₈	—	38	1	no	—
367	C₂²×C₈	—	38	1	no	—
368	C₂²×C₈	—	38	1	no	—
369	C₂²×C₈	—	38	1	no	—
370	C₂²×C₈	—	38	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	19	2	no	—
382	C₂×C₄⋊C₄	—	19	2	no	—
383	C₂×C₄⋊C₄	—	38	1	no	—
384	C₂×C₄⋊C₄	—	38	1	no	—
385	C₂×C₄⋊C₄	—	38	1	no	—
386	C₂×C₄⋊C₄	—	38	1	no	—
387	C₂×C₄⋊C₄	—	38	1	no	—
388	C₂×C₄⋊C₄	—	38	1	no	—
389	C₂×C₄⋊C₄	—	38	1	no	—
390	C₂×C₄⋊C₄	—	38	1	no	—
391	C₂×C₄⋊C₄	—	38	1	no	—
392	C₂×C₄⋊C₄	—	38	1	no	—
393	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
394	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	#107	—	38	8	no	—
402	#95	—	4	2	no	—
403	#95	—	4	2	no	—
404	#95	—	76	2	no	—
405	#95	—	76	2	no	—
406	C₁₉	#11256	1	1	yes	characteristic, complemented, Sylow
407	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	38	2	no	—
435	C₂²×C₄	—	38	2	no	—
436	C₂²×C₄	—	76	1	no	—
437	C₂²×C₄	—	76	1	no	—
438	C₂²×C₄	—	76	1	no	—
439	C₂²×C₄	—	76	1	no	—
440	C₂²×C₄	—	76	1	no	—
441	C₂²×C₄	—	76	1	no	—
442	C₂²×C₄	—	76	1	no	—
443	C₂²×C₄	—	76	1	no	—
444	C₂²×C₄	—	76	1	no	—
445	C₂²×C₄	—	76	1	no	—
446	C₂²×C₄	—	76	1	no	—
447	C₂²×C₄	—	76	1	no	—
448	C₂²×C₄	#64525	1	2	yes	—
449	C₂²×C₄	#64528	1	2	yes	—
450	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
452	C₂²×C₄	#64541	1	1	yes	characteristic
453	C₂²×C₄	#64541	1	1	yes	characteristic
454	C₂²×C₄	#64541	1	1	yes	characteristic
455	C₂²×C₄	#64541	1	1	yes	characteristic
456	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
458	C₂²×C₄	#64543	1	1	yes	characteristic
459	C₂²×C₄	#64543	1	1	yes	characteristic
460	C₂²×C₄	#64543	1	1	yes	characteristic
461	C₂²×C₄	#64543	1	1	yes	characteristic
462	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
463	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
464	C₂×C₈	—	19	4	no	—
465	C₂×C₈	—	38	2	no	—
466	C₂×C₈	—	38	2	no	—
467	C₂×C₈	—	38	2	no	—
468	C₂×C₈	—	38	2	no	—
469	C₂×C₈	—	38	2	no	—
470	C₂×C₈	—	38	2	no	—
471	C₂×C₈	—	38	2	no	—
472	C₂×C₈	—	38	2	no	—
473	C₂×C₈	—	38	2	no	—
474	C₂×C₈	—	76	1	no	—
475	C₂×C₈	—	76	1	no	—
476	C₂×C₈	—	76	1	no	—
477	C₂×C₈	—	76	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	38	2	no	—
487	C₄⋊C₄	—	38	2	no	—
488	C₄⋊C₄	—	38	2	no	—
489	C₄⋊C₄	—	38	2	no	—
490	C₄⋊C₄	—	76	1	no	—
491	C₄⋊C₄	—	76	1	no	—
492	C₄⋊C₄	—	76	1	no	—
493	C₄⋊C₄	—	76	1	no	—
494	C₄²	—	4	1	no	—
495	C₄²	—	4	1	no	—
496	C₄²	—	4	1	no	—
497	C₄²	—	4	1	no	—
498	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
499	C₂³	#10597375	1	1	yes	characteristic
500	C₂³	#10597376	1	1	yes	characteristic
501	C₂³	C₂×#64525	1	1	yes	characteristic
502	C₂³	#10597378	1	1	yes	characteristic
503	C₂³	#10597381	1	1	yes	characteristic
504	C₂³	#10597384	1	1	yes	characteristic
505	C₂³	#10597385	1	1	yes	characteristic
506	C₂³	#10597388	1	1	yes	characteristic
507	C₂³	C₂×#64528	1	1	yes	characteristic
508	C₂³	#10597390	1	1	yes	characteristic
509	C₂³	#10597395	1	1	yes	characteristic
510	C₂³	#10597396	1	1	yes	characteristic
511	C₂³	#10597396	1	1	yes	characteristic
512	C₂³	#10597397	1	1	yes	characteristic
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	1	no	—
534	C₂×C₄	—	8	1	no	—
535	C₂×C₄	—	8	1	no	—
536	C₂×C₄	—	8	1	no	—
537	C₂×C₄	—	8	1	no	—
538	C₂×C₄	—	8	1	no	—
539	C₂×C₄	—	8	1	no	—
540	C₂×C₄	—	8	1	no	—
541	C₂×C₄	—	76	2	no	—
542	C₂×C₄	—	76	2	no	—
543	C₂×C₄	—	76	2	no	—
544	C₂×C₄	—	76	2	no	—
545	C₂×C₄	—	76	2	no	—
546	C₂×C₄	—	76	2	no	—
547	C₂×C₄	—	152	1	no	—
548	C₂×C₄	—	152	1	no	—
549	C₂×C₄	—	152	1	no	—
550	C₂×C₄	—	152	1	no	—
551	C₂×C₄	—	152	1	no	—
552	C₂×C₄	—	152	1	no	—
553	C₂×C₄	—	152	1	no	—
554	C₂×C₄	—	152	1	no	—
555	C₂×C₄	#10597318	1	1	yes	characteristic
556	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
557	C₂×C₄	#10597321	1	1	yes	characteristic
558	C₂×C₄	#10597322	1	1	yes	characteristic
559	C₂×C₄	#10597323	1	1	yes	characteristic
560	C₂×C₄	#10597325	1	1	yes	characteristic
561	C₂×C₄	#10597325	1	1	yes	characteristic
562	C₂×C₄	#10597325	1	1	yes	characteristic
563	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
564	C₂×C₄	#10597328	1	1	yes	characteristic
565	C₂×C₄	#10597329	1	1	yes	characteristic
566	C₂×C₄	#10597329	1	1	yes	characteristic
567	C₂×C₄	#10597331	1	1	yes	characteristic
568	C₂×C₄	#10597331	1	1	yes	characteristic
569	C₂×C₄	#10597331	1	1	yes	characteristic
570	C₂×C₄	#10597332	1	1	yes	characteristic
571	C₂×C₄	#10597333	1	1	yes	characteristic
572	C₂×C₄	#10597335	1	1	yes	characteristic
573	C₂×C₄	#10597335	1	1	yes	characteristic
574	C₂×C₄	#10597335	1	1	yes	characteristic
575	C₂×C₄	#10597335	1	1	yes	characteristic
576	C₂×C₄	#10597335	1	1	yes	characteristic
577	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
578	C₂×C₄	#10597342	1	1	yes	characteristic
579	C₂×C₄	#10597342	1	1	yes	characteristic
580	C₂×C₄	#10597342	1	1	yes	characteristic
581	C₂×C₄	#10597343	1	1	yes	characteristic
582	C₂×C₄	#10597343	1	1	yes	characteristic
583	C₈	—	38	4	no	—
584	C₈	—	76	2	no	—
585	C₂²	#11926432	1	1	yes	characteristic
586	C₂²	#11926435	1	1	yes	characteristic
587	C₂²	#11926439	1	1	yes	characteristic
588	C₂²	#11926460	1	1	yes	characteristic
589	C₂²	#11926472	1	1	yes	characteristic
590	C₂²	#11926474	1	1	yes	characteristic
591	C₂²	#11926475	1	1	yes	characteristic
592	C₂²	C₄×#64525	1	1	yes	characteristic
593	C₂²	C₄×#64528	1	1	yes	characteristic
594	C₂²	#11926642	1	1	yes	characteristic
595	C₂²	#11926644	1	1	yes	characteristic
596	C₂²	#11926736	1	1	yes	characteristic
597	C₂²	#11926739	1	1	yes	characteristic
598	C₂²	#11926751	1	1	yes	characteristic
599	C₂²	#11926754	1	1	yes	characteristic
600	C₂²	#11926756	1	1	yes	characteristic
601	C₂²	#11926759	1	1	yes	characteristic
602	C₂²	#11926763	1	1	yes	characteristic
603	C₂²	#11926766	1	1	yes	characteristic
604	C₂²	#11926778	1	1	yes	characteristic
605	C₂²	#11926783	1	1	yes	characteristic
606	C₂²	#11926795	1	1	yes	characteristic
607	C₂²	#11926800	1	1	yes	characteristic
608	C₂²	#11926855	1	1	yes	characteristic
609	C₂²	#11926857	1	1	yes	characteristic
610	C₂²	#11926865	1	1	yes	characteristic
611	C₂²	#11926868	1	1	yes	characteristic
612	C₂²	#11926877	1	1	yes	characteristic
613	C₂²	#11926879	1	1	yes	characteristic
614	C₂²	#11926882	1	1	yes	characteristic
615	C₂²	#11926885	1	1	yes	characteristic
616	C₂²	#11926943	1	1	yes	characteristic
617	C₂²	#11926947	1	1	yes	characteristic
618	C₂²	#11926950	1	1	yes	characteristic
619	C₂²	#11926954	1	1	yes	characteristic
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	8	2	no	—
623	C₄	—	8	2	no	—
624	C₄	—	152	2	no	—
625	C₄	—	152	2	no	—
626	C₄	#11926408	1	1	yes	characteristic
627	C₄	#11926418	1	1	yes	characteristic
628	C₄	#11926426	1	1	yes	characteristic
629	C₄	#11926429	1	1	yes	characteristic
630	C₄	#11926457	1	1	yes	characteristic
631	C₄	#11926484	1	1	yes	characteristic
632	C₄	#11926485	1	1	yes	characteristic
633	C₄	#11926485	1	1	yes	characteristic
634	C₂	#14561890	1	1	yes	characteristic
635	C₂	#14564252	1	1	yes	characteristic
636	C₂	#14564255	1	1	yes	characteristic
637	C₂	#14564273	1	1	yes	characteristic
638	C₂	#14564276	1	1	yes	characteristic
639	C₂	#14564365	1	1	yes	characteristic
640	C₂	#14564375	1	1	yes	characteristic
641	C₂	#14564945	1	1	yes	characteristic
642	C₂	#14564957	1	1	yes	characteristic
643	C₂	#14565061	1	1	yes	characteristic
644	C₂	#14565066	1	1	yes	characteristic
645	C₂	#14565106	1	1	yes	characteristic
646	C₂	#14565107	1	1	yes	characteristic
647	C₂	#14565116	1	1	yes	characteristic
648	C₂	#14565117	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄⋊#95	D₁₉
hypocenter	C₁₉	#11256
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
19. #11926306	C₄	semidirect
406. C₁₉	#11256	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597264	2
C₂×#11926306	2
C₂×#11926299	2
#14561865	2
C₁₉×C₄⋊#95	2
#11256	19