Subgroups — #18090412

Order 4864.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926401	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926401	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926307	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926306	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926306	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₄×D₁₉	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	C₂²×(C₂×D₁₉)⋊C₄	—	2	1	no	—
13	C₂²×(C₂×D₁₉)⋊C₄	—	2	1	no	—
14	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
15	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
16	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
17	#11926401	—	2	2	no	—
18	#11926401	—	2	2	no	—
19	#11926401	—	2	2	no	—
20	#11926401	C₄	1	4	yes	complemented
21	C₂×C₁₉⋊#95	—	2	1	no	—
22	C₂×C₁₉⋊#95	—	2	1	no	—
23	#11926307	—	2	2	no	—
24	#11926306	—	2	2	no	—
25	#11926306	—	2	2	no	—
26	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#340	—	2	2	no	—
30	C₂⁴×D₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂³×Dic₁₉	—	2	1	no	—
35	C₂³×Dic₁₉	—	2	1	no	—
36	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₁₉	—	2	1	no	—
38	C₂²×C₄×D₁₉	—	2	1	no	—
39	C₂²×C₄×D₁₉	—	2	1	no	—
40	C₂²×C₄×D₁₉	—	2	1	no	—
41	C₂²×C₄×D₁₉	—	2	1	no	—
42	C₂²×C₄×D₁₉	—	2	1	no	—
43	C₂²×C₄×D₁₉	—	2	1	no	—
44	C₂²×C₄×D₁₉	—	2	1	no	—
45	C₂²×C₄×D₁₉	—	2	1	no	—
46	C₂²×C₄×D₁₉	—	2	1	no	—
47	C₂²×C₄×D₁₉	—	2	1	no	—
48	C₂²×C₄×D₁₉	—	2	1	no	—
49	C₂²×C₄×D₁₉	C₂×C₄	1	2	yes	—
50	C₂²×C₄×D₁₉	D₄	1	2	yes	—
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	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
71	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
72	C₂×(C₂×D₁₉)⋊C₄	—	4	2	no	—
73	C₂×(C₂×D₁₉)⋊C₄	—	4	2	no	—
74	C₂×(C₂×D₁₉)⋊C₄	—	4	2	no	—
75	C₂×(C₂×D₁₉)⋊C₄	—	4	2	no	—
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	C₂×C₄⋊Dic₁₉	—	2	1	no	—
83	C₂×C₄⋊Dic₁₉	—	2	1	no	—
84	C₂×C₄⋊Dic₁₉	—	2	1	no	—
85	C₂×C₄⋊Dic₁₉	—	2	1	no	—
86	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
87	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
88	C₂²×C₁₉⋊C₈	—	2	1	no	—
89	C₂²×C₁₉⋊C₈	—	2	1	no	—
90	C₂²×C₁₉⋊C₈	—	2	1	no	—
91	C₂²×C₁₉⋊C₈	—	2	1	no	—
92	C₂²×C₁₉⋊C₈	—	2	1	no	—
93	C₂²×C₁₉⋊C₈	—	2	1	no	—
94	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
95	C₁₉⋊#95	—	2	4	no	—
96	C₁₉⋊#95	—	2	4	no	—
97	(C₂×D₁₉)⋊C₈	—	2	8	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂³×D₁₉	—	2	1	no	—
100	C₂³×D₁₉	—	2	1	no	—
101	C₂³×D₁₉	—	2	1	no	—
102	C₂³×D₁₉	—	2	1	no	—
103	C₂³×D₁₉	—	2	1	no	—
104	C₂³×D₁₉	—	2	1	no	—
105	C₂³×D₁₉	—	2	1	no	—
106	C₂³×D₁₉	—	2	1	no	—
107	C₂³×D₁₉	—	2	1	no	—
108	C₂³×D₁₉	—	2	1	no	—
109	C₂³×D₁₉	—	2	1	no	—
110	C₂³×D₁₉	—	2	1	no	—
111	C₂³×D₁₉	C₂²⋊C₄	1	2	yes	—
112	C₂³×D₁₉	SD₁₆	1	2	yes	—
113	C₂³×D₁₉	Q₁₆	1	2	yes	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	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	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
142	C₂²×Dic₁₉	—	2	1	no	—
143	C₂²×Dic₁₉	—	2	1	no	—
144	C₂²×Dic₁₉	—	2	1	no	—
145	C₂²×Dic₁₉	—	2	1	no	—
146	C₂²×Dic₁₉	—	2	1	no	—
147	C₂²×Dic₁₉	—	2	1	no	—
148	C₂²×Dic₁₉	—	2	2	no	—
149	C₂²×Dic₁₉	—	2	2	no	—
150	C₂²×Dic₁₉	—	4	1	no	—
151	C₂²×Dic₁₉	—	4	1	no	—
152	C₂²×Dic₁₉	—	4	1	no	—
153	C₂²×Dic₁₉	—	4	1	no	—
154	C₂²×Dic₁₉	—	4	1	no	—
155	C₂²×Dic₁₉	—	4	1	no	—
156	C₂²×Dic₁₉	—	4	1	no	—
157	C₂²×Dic₁₉	—	4	1	no	—
158	C₂²×Dic₁₉	—	4	1	no	—
159	C₂²×Dic₁₉	—	4	1	no	—
160	C₂²×Dic₁₉	—	4	1	no	—
161	C₂²×Dic₁₉	—	4	1	no	—
162	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×D₁₉	—	2	2	no	—
164	C₂×C₄×D₁₉	—	2	2	no	—
165	C₂×C₄×D₁₉	—	2	2	no	—
166	C₂×C₄×D₁₉	—	2	2	no	—
167	C₂×C₄×D₁₉	—	2	2	no	—
168	C₂×C₄×D₁₉	—	2	2	no	—
169	C₂×C₄×D₁₉	—	2	2	no	—
170	C₂×C₄×D₁₉	—	2	2	no	—
171	C₂×C₄×D₁₉	—	2	2	no	—
172	C₂×C₄×D₁₉	—	2	2	no	—
173	C₂×C₄×D₁₉	—	2	2	no	—
174	C₂×C₄×D₁₉	—	2	2	no	—
175	C₂×C₄×D₁₉	—	4	1	no	—
176	C₂×C₄×D₁₉	—	4	1	no	—
177	C₂×C₄×D₁₉	—	4	1	no	—
178	C₂×C₄×D₁₉	—	4	1	no	—
179	C₂×C₄×D₁₉	—	4	1	no	—
180	C₂×C₄×D₁₉	—	4	1	no	—
181	C₂×C₄×D₁₉	—	4	1	no	—
182	C₂×C₄×D₁₉	—	4	1	no	—
183	C₂×C₄×D₁₉	—	4	1	no	—
184	C₂×C₄×D₁₉	—	4	1	no	—
185	C₂×C₄×D₁₉	—	4	1	no	—
186	C₂×C₄×D₁₉	—	4	1	no	—
187	C₂×C₄×D₁₉	—	4	1	no	—
188	C₂×C₄×D₁₉	—	4	1	no	—
189	C₂×C₄×D₁₉	—	4	1	no	—
190	C₂×C₄×D₁₉	—	4	1	no	—
191	C₂×C₈×C₁₉	—	2	2	no	—
192	C₂×C₈×C₁₉	—	2	2	no	—
193	C₂×C₈×C₁₉	—	2	2	no	—
194	C₂×C₈×C₁₉	—	4	1	no	—
195	C₂×C₈×C₁₉	—	4	1	no	—
196	C₂×C₈×C₁₉	—	4	1	no	—
197	C₂×C₈×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	4	1	no	—
203	C₄⋊C₄×C₁₉	—	4	1	no	—
204	C₄⋊C₄×C₁₉	—	4	1	no	—
205	C₄⋊C₄×C₁₉	—	4	1	no	—
206	(C₂×D₁₉)⋊C₄	—	4	8	no	—
207	(C₂×D₁₉)⋊C₄	—	4	8	no	—
208	C₄⋊Dic₁₉	—	2	2	no	—
209	C₄⋊Dic₁₉	—	2	2	no	—
210	C₄⋊Dic₁₉	—	2	2	no	—
211	C₄⋊Dic₁₉	—	2	2	no	—
212	C₄⋊Dic₁₉	—	4	1	no	—
213	C₄⋊Dic₁₉	—	4	1	no	—
214	C₄⋊Dic₁₉	—	4	1	no	—
215	C₄⋊Dic₁₉	—	4	1	no	—
216	C₂×C₁₉⋊C₈	—	2	2	no	—
217	C₂×C₁₉⋊C₈	—	2	2	no	—
218	C₂×C₁₉⋊C₈	—	2	2	no	—
219	C₂×C₁₉⋊C₈	—	4	1	no	—
220	C₂×C₁₉⋊C₈	—	4	1	no	—
221	C₂×C₁₉⋊C₈	—	4	1	no	—
222	C₂×C₁₉⋊C₈	—	4	1	no	—
223	#11200	—	19	1	no	maximal, Sylow
224	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₁₉	#120	1	1	yes	characteristic
226	C₂³×C₁₉	#121	1	1	yes	characteristic
227	C₂³×C₁₉	#121	1	1	yes	characteristic
228	C₂³×C₁₉	#123	1	1	yes	characteristic
229	C₂³×C₁₉	#123	1	1	yes	characteristic
230	C₂³×C₁₉	#123	1	1	yes	characteristic
231	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
232	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
233	C₂³×C₁₉	#135	1	1	yes	characteristic
234	C₂³×C₁₉	#135	1	1	yes	characteristic
235	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂³×C₁₉	#137	1	1	yes	characteristic
239	C₂²×D₁₉	—	2	2	no	—
240	C₂²×D₁₉	—	2	2	no	—
241	C₂²×D₁₉	—	2	2	no	—
242	C₂²×D₁₉	—	2	2	no	—
243	C₂²×D₁₉	—	2	2	no	—
244	C₂²×D₁₉	—	2	2	no	—
245	C₂²×D₁₉	—	2	2	no	—
246	C₂²×D₁₉	—	2	2	no	—
247	C₂²×D₁₉	—	2	2	no	—
248	C₂²×D₁₉	—	2	2	no	—
249	C₂²×D₁₉	—	2	2	no	—
250	C₂²×D₁₉	—	2	2	no	—
251	C₂²×D₁₉	—	2	2	no	—
252	C₂²×D₁₉	—	2	2	no	—
253	C₂²×D₁₉	—	2	2	no	—
254	C₂²×D₁₉	—	2	2	no	—
255	C₂²×D₁₉	—	2	2	no	—
256	C₂²×D₁₉	—	2	2	no	—
257	C₂²×D₁₉	—	4	1	no	—
258	C₂²×D₁₉	—	4	1	no	—
259	C₂²×D₁₉	—	4	1	no	—
260	C₂²×D₁₉	—	4	1	no	—
261	C₂²×D₁₉	—	4	1	no	—
262	C₂²×D₁₉	—	4	1	no	—
263	C₂²×D₁₉	—	4	1	no	—
264	C₂²×D₁₉	—	4	1	no	—
265	C₂²×D₁₉	—	4	1	no	—
266	C₂²×D₁₉	—	4	1	no	—
267	C₂²×D₁₉	—	4	1	no	—
268	C₂²×D₁₉	—	4	1	no	—
269	C₂²×D₁₉	—	4	1	no	—
270	C₂²×D₁₉	—	4	1	no	—
271	C₂²×D₁₉	—	4	1	no	—
272	C₂²×D₁₉	—	4	1	no	—
273	C₂²×D₁₉	#103	1	4	yes	—
274	C₂×C₄×C₁₉	—	4	2	no	—
275	C₂×C₄×C₁₉	—	4	2	no	—
276	C₂×C₄×C₁₉	—	4	2	no	—
277	C₂×C₄×C₁₉	—	4	2	no	—
278	C₂×C₄×C₁₉	—	4	2	no	—
279	C₂×C₄×C₁₉	—	4	2	no	—
280	C₂×C₄×C₁₉	—	8	1	no	—
281	C₂×C₄×C₁₉	—	8	1	no	—
282	C₂×C₄×C₁₉	—	8	1	no	—
283	C₂×C₄×C₁₉	—	8	1	no	—
284	C₂×C₄×C₁₉	—	8	1	no	—
285	C₂×C₄×C₁₉	—	8	1	no	—
286	C₂×C₄×C₁₉	—	8	1	no	—
287	C₂×C₄×C₁₉	—	8	1	no	—
288	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
289	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
296	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
297	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
298	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
299	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
300	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
301	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
303	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
304	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
305	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
306	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
307	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
308	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
309	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
310	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
311	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
312	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
313	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
314	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
315	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
316	C₂×Dic₁₉	—	2	2	no	—
317	C₂×Dic₁₉	—	2	2	no	—
318	C₂×Dic₁₉	—	2	2	no	—
319	C₂×Dic₁₉	—	4	1	no	—
320	C₂×Dic₁₉	—	4	1	no	—
321	C₂×Dic₁₉	—	4	1	no	—
322	C₂×Dic₁₉	—	4	1	no	—
323	C₂×Dic₁₉	—	4	2	no	—
324	C₂×Dic₁₉	—	4	2	no	—
325	C₂×Dic₁₉	—	4	2	no	—
326	C₂×Dic₁₉	—	4	2	no	—
327	C₂×Dic₁₉	—	4	2	no	—
328	C₂×Dic₁₉	—	4	2	no	—
329	C₂×Dic₁₉	—	8	1	no	—
330	C₂×Dic₁₉	—	8	1	no	—
331	C₂×Dic₁₉	—	8	1	no	—
332	C₂×Dic₁₉	—	8	1	no	—
333	C₂×Dic₁₉	—	8	1	no	—
334	C₂×Dic₁₉	—	8	1	no	—
335	C₂×Dic₁₉	—	8	1	no	—
336	C₂×Dic₁₉	—	8	1	no	—
337	C₄×D₁₉	—	4	2	no	—
338	C₄×D₁₉	—	4	2	no	—
339	C₄×D₁₉	—	4	2	no	—
340	C₄×D₁₉	—	4	2	no	—
341	C₄×D₁₉	—	4	2	no	—
342	C₄×D₁₉	—	4	2	no	—
343	C₄×D₁₉	—	4	2	no	—
344	C₄×D₁₉	—	4	2	no	—
345	C₈×C₁₉	—	4	2	no	—
346	C₁₉⋊C₈	—	4	2	no	—
347	C₂²×C₂²⋊C₈	—	19	1	no	—
348	C₂×#380	—	19	1	no	—
349	C₂×#380	—	19	1	no	—
350	C₂×#340	—	19	1	no	—
351	C₂×#340	—	19	1	no	—
352	C₂×#340	—	19	1	no	—
353	C₂×#340	D₁₉	1	1	yes	characteristic, complemented
354	C₂²×C₁₉	#381	1	1	yes	characteristic
355	C₂²×C₁₉	#386	1	1	yes	characteristic
356	C₂²×C₁₉	#386	1	1	yes	characteristic
357	C₂²×C₁₉	#394	1	1	yes	characteristic
358	C₂²×C₁₉	#394	1	1	yes	characteristic
359	C₂²×C₁₉	#397	1	1	yes	characteristic
360	C₂²×C₁₉	#397	1	1	yes	characteristic
361	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
362	C₂²×C₁₉	#416	1	1	yes	characteristic
363	C₂²×C₁₉	#417	1	1	yes	characteristic
364	C₂²×C₁₉	#418	1	1	yes	characteristic
365	C₂²×C₁₉	#449	1	1	yes	characteristic
366	C₂²×C₁₉	#449	1	1	yes	characteristic
367	C₂²×C₁₉	#450	1	1	yes	characteristic
368	C₂²×C₁₉	#451	1	1	yes	characteristic
369	C₂²×C₁₉	#465	1	1	yes	characteristic
370	C₂²×C₁₉	#465	1	1	yes	characteristic
371	C₂²×C₁₉	#467	1	1	yes	characteristic
372	C₂²×C₁₉	#467	1	1	yes	characteristic
373	C₂²×C₁₉	#468	1	1	yes	characteristic
374	C₂²×C₁₉	#468	1	1	yes	characteristic
375	C₂²×C₁₉	#469	1	1	yes	characteristic
376	C₂²×C₁₉	#469	1	1	yes	characteristic
377	C₂²×C₁₉	#481	1	1	yes	characteristic
378	C₂²×C₁₉	#481	1	1	yes	characteristic
379	C₂²×C₁₉	#482	1	1	yes	characteristic
380	C₂²×C₁₉	#482	1	1	yes	characteristic
381	C₂²×C₁₉	#482	1	1	yes	characteristic
382	C₂²×C₁₉	#482	1	1	yes	characteristic
383	C₂²×C₁₉	#483	1	1	yes	characteristic
384	C₂²×C₁₉	#484	1	1	yes	characteristic
385	C₂²×C₁₉	#484	1	1	yes	characteristic
386	C₂²×C₁₉	#484	1	1	yes	characteristic
387	C₂²×C₁₉	#485	1	1	yes	characteristic
388	C₂²×C₁₉	#485	1	1	yes	characteristic
389	C₂×D₁₉	—	2	4	no	—
390	C₂×D₁₉	—	2	4	no	—
391	C₂×D₁₉	—	2	4	no	—
392	C₂×D₁₉	—	4	2	no	—
393	C₂×D₁₉	—	4	2	no	—
394	C₂×D₁₉	—	4	2	no	—
395	C₂×D₁₉	—	4	2	no	—
396	C₂×D₁₉	—	4	2	no	—
397	C₂×D₁₉	—	4	2	no	—
398	C₂×D₁₉	—	4	2	no	—
399	C₂×D₁₉	—	4	2	no	—
400	C₂×D₁₉	—	4	2	no	—
401	C₂×D₁₉	—	4	2	no	—
402	C₂×D₁₉	—	4	2	no	—
403	C₂×D₁₉	—	4	2	no	—
404	C₄×C₁₉	—	8	2	no	—
405	C₄×C₁₉	—	8	2	no	—
406	C₄×C₁₉	#388	1	1	yes	characteristic
407	C₄×C₁₉	#388	1	1	yes	characteristic
408	C₄×C₁₉	#388	1	1	yes	characteristic
409	C₄×C₁₉	#388	1	1	yes	characteristic
410	C₄×C₁₉	#394	1	1	yes	characteristic
411	C₄×C₁₉	#394	1	1	yes	characteristic
412	C₄×C₁₉	#397	1	1	yes	characteristic
413	C₄×C₁₉	#397	1	1	yes	characteristic
414	Dic₁₉	—	4	2	no	—
415	Dic₁₉	—	8	2	no	—
416	Dic₁₉	—	8	2	no	—
417	C₂⁴×C₄	—	19	1	no	—
418	C₂³×C₈	—	19	1	no	—
419	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	—	19	1	no	—
421	C₂²×C₄⋊C₄	—	19	1	no	—
422	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
423	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
424	C₂²×C₂²⋊C₄	—	38	1	no	—
425	C₂²×C₂²⋊C₄	—	38	1	no	—
426	C₂×C₂²⋊C₈	—	38	2	no	—
427	C₂×C₂²⋊C₈	—	38	2	no	—
428	C₂×C₂²⋊C₈	—	38	2	no	—
429	#380	—	19	4	no	—
430	#380	—	38	2	no	—
431	#380	—	38	2	no	—
432	#380	—	38	2	no	—
433	C₂×#95	—	38	1	no	—
434	C₂×#95	—	38	1	no	—
435	#340	—	2	2	no	—
436	#340	—	38	2	no	—
437	#340	—	38	2	no	—
438	#340	—	38	2	no	—
439	C₂×C₁₉	#1440	1	1	yes	characteristic
440	C₂×C₁₉	#1824	1	1	yes	characteristic
441	C₂×C₁₉	#1825	1	1	yes	characteristic
442	C₂×C₁₉	#1872	1	1	yes	characteristic
443	C₂×C₁₉	#1875	1	1	yes	characteristic
444	C₂×C₁₉	#1892	1	1	yes	characteristic
445	C₂×C₁₉	#1895	1	1	yes	characteristic
446	C₂×C₁₉	#2034	1	1	yes	characteristic
447	C₂×C₁₉	#2034	1	1	yes	characteristic
448	C₂×C₁₉	#2036	1	1	yes	characteristic
449	C₂×C₁₉	#2036	1	1	yes	characteristic
450	C₂×C₁₉	#2076	1	1	yes	characteristic
451	C₂×C₁₉	#2076	1	1	yes	characteristic
452	C₂×C₁₉	#2077	1	1	yes	characteristic
453	C₂×C₁₉	#2077	1	1	yes	characteristic
454	D₁₉	—	4	4	no	—
455	C₂⁵	—	19	1	no	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	—	19	1	no	—
459	C₂³×C₄	—	19	2	no	—
460	C₂³×C₄	—	19	2	no	—
461	C₂³×C₄	—	38	1	no	—
462	C₂³×C₄	—	38	1	no	—
463	C₂³×C₄	—	38	1	no	—
464	C₂³×C₄	—	38	1	no	—
465	C₂³×C₄	—	38	1	no	—
466	C₂³×C₄	—	38	1	no	—
467	C₂³×C₄	—	38	1	no	—
468	C₂³×C₄	—	38	1	no	—
469	C₂³×C₄	—	38	1	no	—
470	C₂³×C₄	—	38	1	no	—
471	C₂³×C₄	—	38	1	no	—
472	C₂³×C₄	—	38	1	no	—
473	C₂³×C₄	—	38	1	no	—
474	C₂³×C₄	—	38	1	no	—
475	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
476	C₂²×C₈	—	2	1	no	—
477	C₂²×C₈	—	2	1	no	—
478	C₂²×C₈	—	2	1	no	—
479	C₂²×C₈	—	2	1	no	—
480	C₂²×C₈	—	2	1	no	—
481	C₂²×C₈	—	2	1	no	—
482	C₂²×C₈	—	19	2	no	—
483	C₂²×C₈	—	38	1	no	—
484	C₂²×C₈	—	38	1	no	—
485	C₂²×C₈	—	38	1	no	—
486	C₂²×C₈	—	38	1	no	—
487	C₂²×C₈	—	38	1	no	—
488	C₂²×C₈	—	38	1	no	—
489	C₂²×C₈	D₇₆	1	2	yes	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	19	2	no	—
501	C₂×C₄⋊C₄	—	19	2	no	—
502	C₂×C₄⋊C₄	—	38	1	no	—
503	C₂×C₄⋊C₄	—	38	1	no	—
504	C₂×C₄⋊C₄	—	38	1	no	—
505	C₂×C₄⋊C₄	—	38	1	no	—
506	C₂×C₄⋊C₄	—	38	1	no	—
507	C₂×C₄⋊C₄	—	38	1	no	—
508	C₂×C₄⋊C₄	—	38	1	no	—
509	C₂×C₄⋊C₄	—	38	1	no	—
510	C₂×C₄⋊C₄	—	38	1	no	—
511	C₂×C₄⋊C₄	—	38	1	no	—
512	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
514	C₂×C₂²⋊C₄	—	38	4	no	—
515	C₂×C₂²⋊C₄	—	38	4	no	—
516	C₂×C₂²⋊C₄	—	76	2	no	—
517	C₂×C₂²⋊C₄	—	76	2	no	—
518	C₂×C₂²⋊C₄	—	76	2	no	—
519	C₂×C₂²⋊C₄	—	76	2	no	—
520	C₂²⋊C₈	—	38	8	no	—
521	#95	—	38	4	no	—
522	#95	—	38	4	no	—
523	C₁₉	#11200	1	1	yes	characteristic, complemented, Sylow
524	C₂⁴	—	19	2	no	—
525	C₂⁴	—	19	2	no	—
526	C₂⁴	—	19	2	no	—
527	C₂⁴	—	38	1	no	—
528	C₂⁴	—	38	1	no	—
529	C₂⁴	—	38	1	no	—
530	C₂⁴	—	38	1	no	—
531	C₂⁴	—	38	1	no	—
532	C₂⁴	—	38	1	no	—
533	C₂⁴	—	38	1	no	—
534	C₂⁴	—	38	1	no	—
535	C₂⁴	—	38	1	no	—
536	C₂⁴	—	38	1	no	—
537	C₂⁴	—	38	1	no	—
538	C₂⁴	—	38	1	no	—
539	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	4	1	no	—
543	C₂²×C₄	—	4	1	no	—
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	—	4	1	no	—
546	C₂²×C₄	—	4	1	no	—
547	C₂²×C₄	—	4	1	no	—
548	C₂²×C₄	—	4	1	no	—
549	C₂²×C₄	—	4	1	no	—
550	C₂²×C₄	—	4	1	no	—
551	C₂²×C₄	—	4	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	—	19	2	no	—
555	C₂²×C₄	—	38	1	no	—
556	C₂²×C₄	—	38	1	no	—
557	C₂²×C₄	—	38	1	no	—
558	C₂²×C₄	—	38	1	no	—
559	C₂²×C₄	—	38	1	no	—
560	C₂²×C₄	—	38	1	no	—
561	C₂²×C₄	—	38	2	no	—
562	C₂²×C₄	—	38	2	no	—
563	C₂²×C₄	—	38	2	no	—
564	C₂²×C₄	—	38	2	no	—
565	C₂²×C₄	—	38	2	no	—
566	C₂²×C₄	—	38	2	no	—
567	C₂²×C₄	—	38	2	no	—
568	C₂²×C₄	—	38	2	no	—
569	C₂²×C₄	—	38	2	no	—
570	C₂²×C₄	—	38	2	no	—
571	C₂²×C₄	—	38	2	no	—
572	C₂²×C₄	—	38	2	no	—
573	C₂²×C₄	—	38	2	no	—
574	C₂²×C₄	—	38	2	no	—
575	C₂²×C₄	—	76	1	no	—
576	C₂²×C₄	—	76	1	no	—
577	C₂²×C₄	—	76	1	no	—
578	C₂²×C₄	—	76	1	no	—
579	C₂²×C₄	—	76	1	no	—
580	C₂²×C₄	—	76	1	no	—
581	C₂²×C₄	—	76	1	no	—
582	C₂²×C₄	—	76	1	no	—
583	C₂²×C₄	—	76	1	no	—
584	C₂²×C₄	—	76	1	no	—
585	C₂²×C₄	—	76	1	no	—
586	C₂²×C₄	—	76	1	no	—
587	C₂²×C₄	—	76	1	no	—
588	C₂²×C₄	—	76	1	no	—
589	C₂²×C₄	—	76	1	no	—
590	C₂²×C₄	—	76	1	no	—
591	C₂²×C₄	—	76	1	no	—
592	C₂²×C₄	—	76	1	no	—
593	C₂²×C₄	—	76	1	no	—
594	C₂²×C₄	—	76	1	no	—
595	C₂²×C₄	—	76	1	no	—
596	C₂²×C₄	—	76	1	no	—
597	C₂²×C₄	—	76	1	no	—
598	C₂²×C₄	—	76	1	no	—
599	C₂²×C₄	—	76	1	no	—
600	C₂²×C₄	—	76	1	no	—
601	C₂²×C₄	—	76	1	no	—
602	C₂²×C₄	—	76	1	no	—
603	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
605	C₂²×C₄	#64541	1	1	yes	characteristic
606	C₂²×C₄	#64541	1	1	yes	characteristic
607	C₂²×C₄	#64541	1	1	yes	characteristic
608	C₂²×C₄	#64541	1	1	yes	characteristic
609	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
610	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
611	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
612	C₂²×C₄	#64543	1	1	yes	characteristic
613	C₂²×C₄	#64543	1	1	yes	characteristic
614	C₂²×C₄	#64545	1	1	yes	characteristic
615	C₂²×C₄	#64545	1	1	yes	characteristic
616	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	2	2	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	—	4	1	no	—
621	C₂×C₈	—	4	1	no	—
622	C₂×C₈	—	4	1	no	—
623	C₂×C₈	—	4	1	no	—
624	C₂×C₈	—	38	2	no	—
625	C₂×C₈	—	38	2	no	—
626	C₂×C₈	—	38	2	no	—
627	C₂×C₈	—	76	1	no	—
628	C₂×C₈	—	76	1	no	—
629	C₂×C₈	—	76	1	no	—
630	C₂×C₈	—	76	1	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₄⋊C₄	—	4	1	no	—
637	C₄⋊C₄	—	4	1	no	—
638	C₄⋊C₄	—	4	1	no	—
639	C₄⋊C₄	—	38	2	no	—
640	C₄⋊C₄	—	38	2	no	—
641	C₄⋊C₄	—	38	2	no	—
642	C₄⋊C₄	—	38	2	no	—
643	C₄⋊C₄	—	76	1	no	—
644	C₄⋊C₄	—	76	1	no	—
645	C₄⋊C₄	—	76	1	no	—
646	C₄⋊C₄	—	76	1	no	—
647	C₂²⋊C₄	—	76	8	no	—
648	C₂²⋊C₄	—	76	8	no	—
649	C₂³	—	19	4	no	—
650	C₂³	—	38	2	no	—
651	C₂³	—	38	2	no	—
652	C₂³	—	38	2	no	—
653	C₂³	—	38	2	no	—
654	C₂³	—	38	2	no	—
655	C₂³	—	38	2	no	—
656	C₂³	—	38	2	no	—
657	C₂³	—	38	2	no	—
658	C₂³	—	38	2	no	—
659	C₂³	—	38	2	no	—
660	C₂³	—	38	2	no	—
661	C₂³	—	38	2	no	—
662	C₂³	—	38	2	no	—
663	C₂³	—	38	2	no	—
664	C₂³	—	38	2	no	—
665	C₂³	—	38	2	no	—
666	C₂³	—	38	2	no	—
667	C₂³	—	38	2	no	—
668	C₂³	—	76	1	no	—
669	C₂³	—	76	1	no	—
670	C₂³	—	76	1	no	—
671	C₂³	—	76	1	no	—
672	C₂³	—	76	1	no	—
673	C₂³	—	76	1	no	—
674	C₂³	—	76	1	no	—
675	C₂³	—	76	1	no	—
676	C₂³	—	76	1	no	—
677	C₂³	—	76	1	no	—
678	C₂³	—	76	1	no	—
679	C₂³	—	76	1	no	—
680	C₂³	—	76	1	no	—
681	C₂³	—	76	1	no	—
682	C₂³	—	76	1	no	—
683	C₂³	—	76	1	no	—
684	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
685	C₂³	#10597329	1	1	yes	characteristic
686	C₂³	#10597329	1	1	yes	characteristic
687	C₂³	#10597330	1	1	yes	characteristic
688	C₂³	#10597340	1	1	yes	characteristic
689	C₂³	#10597341	1	1	yes	characteristic
690	C₂³	#10597357	1	1	yes	characteristic
691	C₂³	#10597358	1	1	yes	characteristic
692	C₂³	SD₁₆×D₁₉	1	1	yes	characteristic
693	C₂³	#10597360	1	1	yes	characteristic
694	C₂³	#10597360	1	1	yes	characteristic
695	C₂³	#10597362	1	1	yes	characteristic
696	C₂³	Q₁₆×D₁₉	1	1	yes	characteristic
697	C₂³	#10597364	1	1	yes	characteristic
698	C₂³	#10597383	1	1	yes	characteristic
699	C₂×C₄	—	4	2	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	4	2	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	—	8	1	no	—
707	C₂×C₄	—	8	1	no	—
708	C₂×C₄	—	8	1	no	—
709	C₂×C₄	—	8	1	no	—
710	C₂×C₄	—	8	1	no	—
711	C₂×C₄	—	8	1	no	—
712	C₂×C₄	—	8	1	no	—
713	C₂×C₄	—	38	2	no	—
714	C₂×C₄	—	38	2	no	—
715	C₂×C₄	—	38	2	no	—
716	C₂×C₄	—	76	1	no	—
717	C₂×C₄	—	76	1	no	—
718	C₂×C₄	—	76	1	no	—
719	C₂×C₄	—	76	1	no	—
720	C₂×C₄	—	76	2	no	—
721	C₂×C₄	—	76	2	no	—
722	C₂×C₄	—	76	2	no	—
723	C₂×C₄	—	76	2	no	—
724	C₂×C₄	—	76	2	no	—
725	C₂×C₄	—	76	2	no	—
726	C₂×C₄	—	76	2	no	—
727	C₂×C₄	—	76	2	no	—
728	C₂×C₄	—	76	2	no	—
729	C₂×C₄	—	76	2	no	—
730	C₂×C₄	—	76	2	no	—
731	C₂×C₄	—	76	2	no	—
732	C₂×C₄	—	76	2	no	—
733	C₂×C₄	—	76	2	no	—
734	C₂×C₄	—	152	1	no	—
735	C₂×C₄	—	152	1	no	—
736	C₂×C₄	—	152	1	no	—
737	C₂×C₄	—	152	1	no	—
738	C₂×C₄	—	152	1	no	—
739	C₂×C₄	—	152	1	no	—
740	C₂×C₄	—	152	1	no	—
741	C₂×C₄	—	152	1	no	—
742	C₂×C₄	#10597318	1	1	yes	characteristic
743	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
744	C₂×C₄	#10597321	1	1	yes	characteristic
745	C₂×C₄	#10597322	1	1	yes	characteristic
746	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
747	C₂×C₄	#10597328	1	1	yes	characteristic
748	C₂×C₄	#10597329	1	1	yes	characteristic
749	C₂×C₄	#10597330	1	1	yes	characteristic
750	C₂×C₄	#10597330	1	1	yes	characteristic
751	C₂×C₄	#10597331	1	1	yes	characteristic
752	C₂×C₄	#10597331	1	1	yes	characteristic
753	C₂×C₄	#10597332	1	1	yes	characteristic
754	C₂×C₄	#10597338	1	1	yes	characteristic
755	C₂×C₄	#10597339	1	1	yes	characteristic
756	C₂×C₄	#10597340	1	1	yes	characteristic
757	C₂×C₄	#10597340	1	1	yes	characteristic
758	C₂×C₄	#10597340	1	1	yes	characteristic
759	C₂×C₄	#10597340	1	1	yes	characteristic
760	C₂×C₄	#10597341	1	1	yes	characteristic
761	C₂×C₄	#10597344	1	1	yes	characteristic
762	C₂×C₄	#10597344	1	1	yes	characteristic
763	C₂×C₄	#10597344	1	1	yes	characteristic
764	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
765	C₂×C₄	#10597375	1	1	yes	characteristic
766	C₂×C₄	#10597376	1	1	yes	characteristic
767	C₂×C₄	#10597384	1	1	yes	characteristic
768	C₂×C₄	#10597385	1	1	yes	characteristic
769	C₂×C₄	#10597393	1	1	yes	characteristic
770	C₈	—	4	2	no	—
771	C₈	—	76	2	no	—
772	C₂²	—	38	4	no	—
773	C₂²	—	38	4	no	—
774	C₂²	—	38	4	no	—
775	C₂²	—	76	2	no	—
776	C₂²	—	76	2	no	—
777	C₂²	—	76	2	no	—
778	C₂²	—	76	2	no	—
779	C₂²	—	76	2	no	—
780	C₂²	—	76	2	no	—
781	C₂²	—	76	2	no	—
782	C₂²	—	76	2	no	—
783	C₂²	—	76	2	no	—
784	C₂²	—	76	2	no	—
785	C₂²	—	76	2	no	—
786	C₂²	—	76	2	no	—
787	C₂²	#11926406	1	1	yes	characteristic
788	C₂²	#11926420	1	1	yes	characteristic
789	C₂²	#11926422	1	1	yes	characteristic
790	C₂²	#11926459	1	1	yes	characteristic
791	C₂²	#11926461	1	1	yes	characteristic
792	C₂²	#11926471	1	1	yes	characteristic
793	C₂²	#11926473	1	1	yes	characteristic
794	C₂²	#103×D₁₉	1	1	yes	characteristic
795	C₂²	#11926537	1	1	yes	characteristic
796	C₂²	#11926544	1	1	yes	characteristic
797	C₂²	#11926547	1	1	yes	characteristic
798	C₂²	#11926686	1	1	yes	characteristic
799	C₂²	#11926688	1	1	yes	characteristic
800	C₂²	#11926693	1	1	yes	characteristic
801	C₂²	#11926698	1	1	yes	characteristic
802	C₂²	#11926772	1	1	yes	characteristic
803	C₂²	#11926774	1	1	yes	characteristic
804	C₂²	#11926784	1	1	yes	characteristic
805	C₂²	#11926786	1	1	yes	characteristic
806	C₂²	#11926791	1	1	yes	characteristic
807	C₂²	#11926793	1	1	yes	characteristic
808	C₂²	#11926796	1	1	yes	characteristic
809	C₂²	#11926798	1	1	yes	characteristic
810	C₂²	#11926861	1	1	yes	characteristic
811	C₂²	#11926864	1	1	yes	characteristic
812	C₂²	#11926866	1	1	yes	characteristic
813	C₂²	#11926866	1	1	yes	characteristic
814	C₂²	#11926867	1	1	yes	characteristic
815	C₂²	#11926870	1	1	yes	characteristic
816	C₂²	#11926873	1	1	yes	characteristic
817	C₂²	#11926878	1	1	yes	characteristic
818	C₂²	#11926878	1	1	yes	characteristic
819	C₂²	#11926881	1	1	yes	characteristic
820	C₂²	#11926883	1	1	yes	characteristic
821	C₂²	#11926887	1	1	yes	characteristic
822	C₄	—	8	2	no	—
823	C₄	—	8	2	no	—
824	C₄	—	76	2	no	—
825	C₄	—	152	2	no	—
826	C₄	—	152	2	no	—
827	C₄	#11926433	1	1	yes	characteristic
828	C₄	#11926434	1	1	yes	characteristic
829	C₄	#11926435	1	1	yes	characteristic
830	C₄	#11926436	1	1	yes	characteristic
831	C₄	#11926460	1	1	yes	characteristic
832	C₄	#11926462	1	1	yes	characteristic
833	C₄	#11926470	1	1	yes	characteristic
834	C₄	#11926473	1	1	yes	characteristic
835	C₂	—	76	4	no	—
836	C₂	#14561883	1	1	yes	characteristic
837	C₂	#14563724	1	1	yes	characteristic
838	C₂	#14563728	1	1	yes	characteristic
839	C₂	#14563939	1	1	yes	characteristic
840	C₂	#14563954	1	1	yes	characteristic
841	C₂	#14564057	1	1	yes	characteristic
842	C₂	#14564072	1	1	yes	characteristic
843	C₂	#14564822	1	1	yes	characteristic
844	C₂	#14564826	1	1	yes	characteristic
845	C₂	#14564836	1	1	yes	characteristic
846	C₂	#14564840	1	1	yes	characteristic
847	C₂	#14565065	1	1	yes	characteristic
848	C₂	#14565067	1	1	yes	characteristic
849	C₂	#14565070	1	1	yes	characteristic
850	C₂	#14565073	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#340	C₂
socle	C₂⁴×C₁₉	C₂×D₄
prime radical	C₂⁴×D₁₉	D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#340	D₁₉
hypocenter	C₁₉	#11200
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
4. C₂×#11926307	C₂	semidirect
5. C₂×#11926306	C₂	semidirect
6. C₂×#11926306	C₂	semidirect
7. C₂×C₁₉×#340	C₂	semidirect
20. #11926401	C₄	semidirect
353. C₂×#340	D₁₉	semidirect
523. C₁₉	#11200	semidirect

Maximal subgroups

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

subgroup	index
C₂²×(C₂×D₁₉)⋊C₈	2
C₂×#11926401	2
C₂×#11926307	2
C₂×#11926306	2
C₂×C₁₉×#340	2
#11200	19