Subgroups — #18090352

Order 4864.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597289	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597289	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926306	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926299	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561865	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#390	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×#10597289	—	2	2	no	—
13	C₂×#10597289	—	2	2	no	—
14	C₂×#10597289	—	2	2	no	—
15	C₂×#10597289	—	2	2	no	—
16	C₂×#10597289	—	2	2	no	—
17	C₂×#10597289	C₄	1	4	yes	complemented
18	C₂×C₁₉⋊#95	—	2	1	no	—
19	C₂×C₁₉⋊#95	—	2	1	no	—
20	#11926306	—	2	2	no	—
21	#11926306	—	2	2	no	—
22	#11926299	—	2	2	no	—
23	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
26	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#390	—	2	2	no	—
29	C₁₉×#390	—	2	2	no	—
30	C₂⁵×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₉	D₄	1	2	yes	—
44	C₂²×D₄×C₁₉	D₄	1	2	yes	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×Dic₁₉	—	2	1	no	—
50	C₂³×Dic₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	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	—	2	1	no	—
75	C₂×C₄⋊Dic₁₉	—	2	1	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	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
81	C₂²×C₁₉⋊C₈	—	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	—	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	C₂×C₄	1	2	yes	—
94	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
95	#10597289	—	2	8	no	—
96	#10597289	—	2	8	no	—
97	C₁₉⋊#95	—	4	2	no	—
98	C₁₉⋊#95	—	4	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	2	no	—
101	C₂⁴×C₁₉	—	2	2	no	—
102	C₂⁴×C₁₉	—	4	1	no	—
103	C₂⁴×C₁₉	—	4	1	no	—
104	C₂⁴×C₁₉	—	4	1	no	—
105	C₂⁴×C₁₉	—	4	1	no	—
106	C₂⁴×C₁₉	—	4	1	no	—
107	C₂⁴×C₁₉	—	4	1	no	—
108	C₂⁴×C₁₉	—	4	1	no	—
109	C₂⁴×C₁₉	—	4	1	no	—
110	C₂⁴×C₁₉	—	4	1	no	—
111	C₂⁴×C₁₉	—	4	1	no	—
112	C₂⁴×C₁₉	—	4	1	no	—
113	C₂⁴×C₁₉	—	4	1	no	—
114	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	—	4	1	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	—	4	1	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	—	4	1	no	—
158	C₂²×C₄×C₁₉	—	4	1	no	—
159	C₂²×C₄×C₁₉	—	4	1	no	—
160	C₂²×C₄×C₁₉	—	4	1	no	—
161	C₂²×C₄×C₁₉	—	4	1	no	—
162	C₂²×C₄×C₁₉	D₈	1	2	yes	—
163	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
178	C₂²×Dic₁₉	—	2	2	no	—
179	C₂²×Dic₁₉	—	2	2	no	—
180	C₂²×Dic₁₉	—	4	1	no	—
181	C₂²×Dic₁₉	—	4	1	no	—
182	C₂²×Dic₁₉	—	4	1	no	—
183	C₂²×Dic₁₉	—	4	1	no	—
184	C₂²×Dic₁₉	—	4	1	no	—
185	C₂²×Dic₁₉	—	4	1	no	—
186	C₂²×Dic₁₉	—	4	1	no	—
187	C₂²×Dic₁₉	—	4	1	no	—
188	C₂²×Dic₁₉	—	4	1	no	—
189	C₂²×Dic₁₉	—	4	1	no	—
190	C₂²×Dic₁₉	—	4	1	no	—
191	C₂²×Dic₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₄⋊C₄×C₁₉	—	4	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	8	no	—
197	C₂²⋊C₄×C₁₉	—	4	8	no	—
198	C₄²×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	4	1	no	—
200	C₄²×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄⋊Dic₁₉	—	2	2	no	—
203	C₄⋊Dic₁₉	—	2	2	no	—
204	C₄⋊Dic₁₉	—	2	2	no	—
205	C₄⋊Dic₁₉	—	2	2	no	—
206	C₄⋊Dic₁₉	—	4	1	no	—
207	C₄⋊Dic₁₉	—	4	1	no	—
208	C₄⋊Dic₁₉	—	4	1	no	—
209	C₄⋊Dic₁₉	—	4	1	no	—
210	C₂×C₁₉⋊C₈	—	2	2	no	—
211	C₂×C₁₉⋊C₈	—	2	2	no	—
212	C₂×C₁₉⋊C₈	—	2	2	no	—
213	C₂×C₁₉⋊C₈	—	2	2	no	—
214	C₂×C₁₉⋊C₈	—	2	2	no	—
215	C₂×C₁₉⋊C₈	—	2	2	no	—
216	C₂×C₁₉⋊C₈	—	4	1	no	—
217	C₂×C₁₉⋊C₈	—	4	1	no	—
218	C₂×C₁₉⋊C₈	—	4	1	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	C₂×C₁₉⋊C₈	—	4	1	no	—
224	#11189	—	19	1	no	maximal, Sylow
225	C₂³×C₁₉	—	2	4	no	—
226	C₂³×C₁₉	—	4	2	no	—
227	C₂³×C₁₉	—	4	2	no	—
228	C₂³×C₁₉	—	4	2	no	—
229	C₂³×C₁₉	—	4	2	no	—
230	C₂³×C₁₉	—	4	2	no	—
231	C₂³×C₁₉	—	4	2	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	—	4	2	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	—	4	2	no	—
238	C₂³×C₁₉	—	4	2	no	—
239	C₂³×C₁₉	—	4	2	no	—
240	C₂³×C₁₉	—	4	2	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	4	2	no	—
243	C₂³×C₁₉	—	4	2	no	—
244	C₂³×C₁₉	—	8	1	no	—
245	C₂³×C₁₉	—	8	1	no	—
246	C₂³×C₁₉	—	8	1	no	—
247	C₂³×C₁₉	—	8	1	no	—
248	C₂³×C₁₉	—	8	1	no	—
249	C₂³×C₁₉	—	8	1	no	—
250	C₂³×C₁₉	—	8	1	no	—
251	C₂³×C₁₉	—	8	1	no	—
252	C₂³×C₁₉	—	8	1	no	—
253	C₂³×C₁₉	—	8	1	no	—
254	C₂³×C₁₉	—	8	1	no	—
255	C₂³×C₁₉	—	8	1	no	—
256	C₂³×C₁₉	—	8	1	no	—
257	C₂³×C₁₉	—	8	1	no	—
258	C₂³×C₁₉	—	8	1	no	—
259	C₂³×C₁₉	—	8	1	no	—
260	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
261	C₂³×C₁₉	#120	1	1	yes	characteristic
262	C₂³×C₁₉	#121	1	1	yes	characteristic
263	C₂³×C₁₉	#121	1	1	yes	characteristic
264	C₂³×C₁₉	#121	1	1	yes	characteristic
265	C₂³×C₁₉	#123	1	1	yes	characteristic
266	C₂³×C₁₉	#124	1	1	yes	characteristic
267	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
268	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
269	C₂³×C₁₉	#135	1	1	yes	characteristic
270	C₂³×C₁₉	#135	1	1	yes	characteristic
271	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂³×C₁₉	#137	1	1	yes	characteristic
275	D₄×C₁₉	—	2	4	no	—
276	D₄×C₁₉	—	2	4	no	—
277	D₄×C₁₉	—	4	2	no	—
278	D₄×C₁₉	—	4	2	no	—
279	D₄×C₁₉	—	4	2	no	—
280	D₄×C₁₉	—	4	2	no	—
281	D₄×C₁₉	—	4	2	no	—
282	D₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	—	4	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	8	1	no	—
301	C₂×C₄×C₁₉	—	8	1	no	—
302	C₂×C₄×C₁₉	—	8	1	no	—
303	C₂×C₄×C₁₉	—	8	1	no	—
304	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
306	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
307	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
311	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
312	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
313	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
314	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
315	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
316	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
317	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
318	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
319	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
320	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
321	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
322	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
323	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
324	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
325	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
326	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
327	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
328	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
329	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
330	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
331	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
332	C₂×Dic₁₉	—	4	2	no	—
333	C₂×Dic₁₉	—	4	2	no	—
334	C₂×Dic₁₉	—	4	2	no	—
335	C₂×Dic₁₉	—	4	2	no	—
336	C₂×Dic₁₉	—	4	2	no	—
337	C₂×Dic₁₉	—	4	2	no	—
338	C₂×Dic₁₉	—	8	1	no	—
339	C₂×Dic₁₉	—	8	1	no	—
340	C₂×Dic₁₉	—	8	1	no	—
341	C₂×Dic₁₉	—	8	1	no	—
342	C₂×Dic₁₉	—	8	1	no	—
343	C₂×Dic₁₉	—	8	1	no	—
344	C₂×Dic₁₉	—	8	1	no	—
345	C₂×Dic₁₉	—	8	1	no	—
346	C₁₉⋊C₈	—	4	2	no	—
347	C₁₉⋊C₈	—	4	2	no	—
348	C₂²×#102	—	19	1	no	—
349	C₂²×#102	—	19	1	no	—
350	C₂×#390	D₁₉	1	1	yes	characteristic
351	C₂×#340	—	19	1	no	—
352	C₂×#340	—	19	1	no	—
353	C₂×#336	—	19	1	no	—
354	C₄⋊#95	—	19	1	no	—
355	C₂²×C₁₉	—	4	4	no	—
356	C₂²×C₁₉	—	4	4	no	—
357	C₂²×C₁₉	—	4	4	no	—
358	C₂²×C₁₉	—	8	2	no	—
359	C₂²×C₁₉	—	8	2	no	—
360	C₂²×C₁₉	—	8	2	no	—
361	C₂²×C₁₉	—	8	2	no	—
362	C₂²×C₁₉	—	8	2	no	—
363	C₂²×C₁₉	—	8	2	no	—
364	C₂²×C₁₉	—	8	2	no	—
365	C₂²×C₁₉	—	8	2	no	—
366	C₂²×C₁₉	—	8	2	no	—
367	C₂²×C₁₉	—	8	2	no	—
368	C₂²×C₁₉	—	8	2	no	—
369	C₂²×C₁₉	—	8	2	no	—
370	C₂²×C₁₉	#386	1	1	yes	characteristic
371	C₂²×C₁₉	#388	1	1	yes	characteristic
372	C₂²×C₁₉	#388	1	1	yes	characteristic
373	C₂²×C₁₉	#394	1	1	yes	characteristic
374	C₂²×C₁₉	#394	1	1	yes	characteristic
375	C₂²×C₁₉	#394	1	1	yes	characteristic
376	C₂²×C₁₉	#397	1	1	yes	characteristic
377	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
378	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
379	C₂²×C₁₉	#440	1	1	yes	characteristic
380	C₂²×C₁₉	#442	1	1	yes	characteristic
381	C₂²×C₁₉	#447	1	1	yes	characteristic
382	C₂²×C₁₉	#449	1	1	yes	characteristic
383	C₂²×C₁₉	#450	1	1	yes	characteristic
384	C₂²×C₁₉	#452	1	1	yes	characteristic
385	C₂²×C₁₉	#459	1	1	yes	characteristic
386	C₂²×C₁₉	#459	1	1	yes	characteristic
387	C₂²×C₁₉	#460	1	1	yes	characteristic
388	C₂²×C₁₉	#461	1	1	yes	characteristic
389	C₂²×C₁₉	#463	1	1	yes	characteristic
390	C₂²×C₁₉	#463	1	1	yes	characteristic
391	C₂²×C₁₉	#463	1	1	yes	characteristic
392	C₂²×C₁₉	#464	1	1	yes	characteristic
393	C₂²×C₁₉	#465	1	1	yes	characteristic
394	C₂²×C₁₉	#466	1	1	yes	characteristic
395	C₂²×C₁₉	#468	1	1	yes	characteristic
396	C₂²×C₁₉	#469	1	1	yes	characteristic
397	C₂²×C₁₉	#480	1	1	yes	characteristic
398	C₂²×C₁₉	#481	1	1	yes	characteristic
399	C₂²×C₁₉	#482	1	1	yes	characteristic
400	C₂²×C₁₉	#482	1	1	yes	characteristic
401	C₂²×C₁₉	#486	1	1	yes	characteristic
402	C₂²×C₁₉	#488	1	1	yes	characteristic
403	C₂²×C₁₉	#489	1	1	yes	characteristic
404	C₂²×C₁₉	#490	1	1	yes	characteristic
405	C₄×C₁₉	—	4	2	no	—
406	C₄×C₁₉	—	4	2	no	—
407	C₄×C₁₉	—	8	2	no	—
408	C₄×C₁₉	#381	1	1	yes	characteristic
409	C₄×C₁₉	#386	1	1	yes	characteristic
410	C₄×C₁₉	#388	1	1	yes	characteristic
411	C₄×C₁₉	#388	1	1	yes	characteristic
412	C₄×C₁₉	#394	1	1	yes	characteristic
413	C₄×C₁₉	#397	1	1	yes	characteristic
414	C₄×C₁₉	#397	1	1	yes	characteristic
415	C₄×C₁₉	#397	1	1	yes	characteristic
416	Dic₁₉	—	8	2	no	—
417	Dic₁₉	—	8	2	no	—
418	C₂³×D₄	C₂×D₁₉	1	1	yes	characteristic
419	C₂³×C₈	—	19	1	no	—
420	C₂³×C₈	—	19	1	no	—
421	C₂²×C₄⋊C₄	—	19	1	no	—
422	C₂²×C₄⋊C₄	—	19	1	no	—
423	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
424	C₂²×C₂²⋊C₄	—	2	1	no	—
425	C₂²×C₂²⋊C₄	—	2	1	no	—
426	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
427	C₂×#102	—	19	4	no	—
428	C₂×#102	—	38	2	no	—
429	C₂×#102	—	38	2	no	—
430	C₂×#102	—	38	2	no	—
431	C₂×#102	—	38	2	no	—
432	C₂×#102	—	38	2	no	—
433	#390	—	2	2	no	—
434	#390	—	2	2	no	—
435	C₂×#95	—	38	1	no	—
436	C₂×#95	—	38	1	no	—
437	#340	—	38	2	no	—
438	#340	—	38	2	no	—
439	#336	—	38	2	no	—
440	C₂×C₁₉	—	8	4	no	—
441	C₂×C₁₉	#1440	1	1	yes	characteristic
442	C₂×C₁₉	#1877	1	1	yes	characteristic
443	C₂×C₁₉	#1879	1	1	yes	characteristic
444	C₂×C₁₉	#1925	1	1	yes	characteristic
445	C₂×C₁₉	#1926	1	1	yes	characteristic
446	C₂×C₁₉	#1934	1	1	yes	characteristic
447	C₂×C₁₉	#1936	1	1	yes	characteristic
448	C₂×C₁₉	#2033	1	1	yes	characteristic
449	C₂×C₁₉	#2034	1	1	yes	characteristic
450	C₂×C₁₉	#2041	1	1	yes	characteristic
451	C₂×C₁₉	#2042	1	1	yes	characteristic
452	C₂×C₁₉	#2054	1	1	yes	characteristic
453	C₂×C₁₉	#2055	1	1	yes	characteristic
454	C₂×C₁₉	#2071	1	1	yes	characteristic
455	C₂×C₁₉	#2073	1	1	yes	characteristic
456	C₂⁵	—	2	1	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	C₄×D₁₉	1	2	yes	—
469	C₂²×D₄	D₇₆	1	2	yes	—
470	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	38	1	no	—
473	C₂³×C₄	—	38	1	no	—
474	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
475	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
476	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
477	C₂²×C₈	—	19	2	no	—
478	C₂²×C₈	—	19	2	no	—
479	C₂²×C₈	—	38	1	no	—
480	C₂²×C₈	—	38	1	no	—
481	C₂²×C₈	—	38	1	no	—
482	C₂²×C₈	—	38	1	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	—	38	1	no	—
490	C₂²×C₈	—	38	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	—	19	2	no	—
497	C₂×C₄⋊C₄	—	19	2	no	—
498	C₂×C₄⋊C₄	—	38	1	no	—
499	C₂×C₄⋊C₄	—	38	1	no	—
500	C₂×C₄⋊C₄	—	38	1	no	—
501	C₂×C₄⋊C₄	—	38	1	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	C₂²⋊D₁₉	1	2	yes	—
509	C₂×C₂²⋊C₄	—	2	4	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	4	2	no	—
512	C₂×C₂²⋊C₄	—	4	2	no	—
513	C₂×C₂²⋊C₄	—	4	2	no	—
514	C₂×C₂²⋊C₄	—	4	2	no	—
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	—	2	1	no	—
521	#102	—	38	8	no	—
522	#102	—	38	8	no	—
523	#95	—	76	2	no	—
524	#95	—	76	2	no	—
525	C₁₉	#11189	1	1	yes	characteristic, complemented, Sylow
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	4	1	no	—
530	C₂⁴	—	4	1	no	—
531	C₂⁴	—	4	1	no	—
532	C₂⁴	—	4	1	no	—
533	C₂⁴	—	4	1	no	—
534	C₂⁴	—	4	1	no	—
535	C₂⁴	—	4	1	no	—
536	C₂⁴	—	4	1	no	—
537	C₂⁴	—	4	1	no	—
538	C₂⁴	—	4	1	no	—
539	C₂⁴	—	4	1	no	—
540	C₂⁴	—	4	1	no	—
541	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	4	1	no	—
558	C₂×D₄	—	4	1	no	—
559	C₂×D₄	—	4	1	no	—
560	C₂×D₄	—	4	1	no	—
561	C₂×D₄	—	4	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	4	1	no	—
584	C₂²×C₄	—	4	1	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	38	2	no	—
590	C₂²×C₄	—	38	2	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	#64525	1	2	yes	—
604	C₂²×C₄	#64526	1	2	yes	—
605	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₇₆	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	#64543	1	1	yes	characteristic
612	C₂²×C₄	#64543	1	1	yes	characteristic
613	C₂²×C₄	#64543	1	1	yes	characteristic
614	C₂²×C₄	#64543	1	1	yes	characteristic
615	C₂²×C₄	#64543	1	1	yes	characteristic
616	C₂²×C₄	#64543	1	1	yes	characteristic
617	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
618	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
619	C₂×C₈	—	38	2	no	—
620	C₂×C₈	—	38	2	no	—
621	C₂×C₈	—	38	2	no	—
622	C₂×C₈	—	38	2	no	—
623	C₂×C₈	—	38	2	no	—
624	C₂×C₈	—	38	2	no	—
625	C₂×C₈	—	76	1	no	—
626	C₂×C₈	—	76	1	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	C₂×C₈	—	76	1	no	—
632	C₂×C₈	—	76	1	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	—	38	2	no	—
638	C₄⋊C₄	—	38	2	no	—
639	C₄⋊C₄	—	38	2	no	—
640	C₄⋊C₄	—	38	2	no	—
641	C₄⋊C₄	—	76	1	no	—
642	C₄⋊C₄	—	76	1	no	—
643	C₄⋊C₄	—	76	1	no	—
644	C₄⋊C₄	—	76	1	no	—
645	C₂²⋊C₄	—	4	8	no	—
646	C₂²⋊C₄	—	4	8	no	—
647	C₄²	—	4	1	no	—
648	C₄²	—	4	1	no	—
649	C₄²	—	4	1	no	—
650	C₄²	—	4	1	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	—	4	2	no	—
657	C₂³	—	4	2	no	—
658	C₂³	—	4	2	no	—
659	C₂³	—	4	2	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	4	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	8	1	no	—
671	C₂³	—	8	1	no	—
672	C₂³	—	8	1	no	—
673	C₂³	—	8	1	no	—
674	C₂³	—	8	1	no	—
675	C₂³	—	8	1	no	—
676	C₂³	—	8	1	no	—
677	C₂³	—	8	1	no	—
678	C₂³	—	8	1	no	—
679	C₂³	—	8	1	no	—
680	C₂³	—	8	1	no	—
681	C₂³	—	8	1	no	—
682	C₂³	—	8	1	no	—
683	C₂³	—	8	1	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
687	C₂³	#10597376	1	1	yes	characteristic
688	C₂³	C₂×#64525	1	1	yes	characteristic
689	C₂³	#10597378	1	1	yes	characteristic
690	C₂³	#10597378	1	1	yes	characteristic
691	C₂³	C₂×#64526	1	1	yes	characteristic
692	C₂³	#10597381	1	1	yes	characteristic
693	C₂³	#10597382	1	1	yes	characteristic
694	C₂³	#10597384	1	1	yes	characteristic
695	C₂³	#10597385	1	1	yes	characteristic
696	C₂³	#10597395	1	1	yes	characteristic
697	C₂³	#10597396	1	1	yes	characteristic
698	C₂³	#10597396	1	1	yes	characteristic
699	C₂³	#10597397	1	1	yes	characteristic
700	C₂³	#10597399	1	1	yes	characteristic
701	D₄	—	2	4	no	—
702	D₄	—	2	4	no	—
703	D₄	—	4	2	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	8	1	no	—
727	C₂×C₄	—	8	1	no	—
728	C₂×C₄	—	8	1	no	—
729	C₂×C₄	—	8	1	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	—	76	2	no	—
735	C₂×C₄	—	76	2	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	—	152	1	no	—
743	C₂×C₄	—	152	1	no	—
744	C₂×C₄	#10597323	1	1	yes	characteristic
745	C₂×C₄	#10597323	1	1	yes	characteristic
746	C₂×C₄	#10597325	1	1	yes	characteristic
747	C₂×C₄	#10597325	1	1	yes	characteristic
748	C₂×C₄	#10597325	1	1	yes	characteristic
749	C₂×C₄	#10597325	1	1	yes	characteristic
750	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
751	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
752	C₂×C₄	#10597328	1	1	yes	characteristic
753	C₂×C₄	#10597329	1	1	yes	characteristic
754	C₂×C₄	#10597329	1	1	yes	characteristic
755	C₂×C₄	#10597331	1	1	yes	characteristic
756	C₂×C₄	#10597331	1	1	yes	characteristic
757	C₂×C₄	#10597332	1	1	yes	characteristic
758	C₂×C₄	#10597332	1	1	yes	characteristic
759	C₂×C₄	#10597332	1	1	yes	characteristic
760	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
761	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
762	C₂×C₄	#10597375	1	1	yes	characteristic
763	C₂×C₄	#10597376	1	1	yes	characteristic
764	C₂×C₄	#10597381	1	1	yes	characteristic
765	C₂×C₄	#10597381	1	1	yes	characteristic
766	C₂×C₄	#10597381	1	1	yes	characteristic
767	C₂×C₄	#10597382	1	1	yes	characteristic
768	C₂×C₄	#10597384	1	1	yes	characteristic
769	C₂×C₄	#10597385	1	1	yes	characteristic
770	C₂×C₄	#10597385	1	1	yes	characteristic
771	C₂×C₄	#10597385	1	1	yes	characteristic
772	C₈	—	76	2	no	—
773	C₈	—	76	2	no	—
774	C₂²	—	4	4	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	8	2	no	—
778	C₂²	—	8	2	no	—
779	C₂²	—	8	2	no	—
780	C₂²	—	8	2	no	—
781	C₂²	—	8	2	no	—
782	C₂²	—	8	2	no	—
783	C₂²	—	8	2	no	—
784	C₂²	—	8	2	no	—
785	C₂²	—	8	2	no	—
786	C₂²	—	8	2	no	—
787	C₂²	—	8	2	no	—
788	C₂²	—	8	2	no	—
789	C₂²	#11926423	1	1	yes	characteristic
790	C₂²	#11926432	1	1	yes	characteristic
791	C₂²	#11926438	1	1	yes	characteristic
792	C₂²	#11926458	1	1	yes	characteristic
793	C₂²	#11926458	1	1	yes	characteristic
794	C₂²	#11926460	1	1	yes	characteristic
795	C₂²	#11926469	1	1	yes	characteristic
796	C₂²	C₄×#64525	1	1	yes	characteristic
797	C₂²	C₄×#64526	1	1	yes	characteristic
798	C₂²	#11926644	1	1	yes	characteristic
799	C₂²	#11926654	1	1	yes	characteristic
800	C₂²	#11926678	1	1	yes	characteristic
801	C₂²	#11926689	1	1	yes	characteristic
802	C₂²	#11926695	1	1	yes	characteristic
803	C₂²	#11926706	1	1	yes	characteristic
804	C₂²	#11926736	1	1	yes	characteristic
805	C₂²	#11926739	1	1	yes	characteristic
806	C₂²	#11926741	1	1	yes	characteristic
807	C₂²	#11926749	1	1	yes	characteristic
808	C₂²	#11926756	1	1	yes	characteristic
809	C₂²	#11926759	1	1	yes	characteristic
810	C₂²	#11926759	1	1	yes	characteristic
811	C₂²	#11926763	1	1	yes	characteristic
812	C₂²	#11926771	1	1	yes	characteristic
813	C₂²	#11926778	1	1	yes	characteristic
814	C₂²	#11926788	1	1	yes	characteristic
815	C₂²	#11926795	1	1	yes	characteristic
816	C₂²	#11926855	1	1	yes	characteristic
817	C₂²	#11926860	1	1	yes	characteristic
818	C₂²	#11926865	1	1	yes	characteristic
819	C₂²	#11926865	1	1	yes	characteristic
820	C₂²	#11926890	1	1	yes	characteristic
821	C₂²	#11926898	1	1	yes	characteristic
822	C₂²	#11926903	1	1	yes	characteristic
823	C₂²	#11926908	1	1	yes	characteristic
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	8	2	no	—
827	C₄	—	152	2	no	—
828	C₄	—	152	2	no	—
829	C₄	#11926405	1	1	yes	characteristic
830	C₄	#11926421	1	1	yes	characteristic
831	C₄	#11926432	1	1	yes	characteristic
832	C₄	#11926438	1	1	yes	characteristic
833	C₄	#11926460	1	1	yes	characteristic
834	C₄	#11926469	1	1	yes	characteristic
835	C₄	#11926472	1	1	yes	characteristic
836	C₄	#11926472	1	1	yes	characteristic
837	C₂	—	8	4	no	—
838	C₂	#14561882	1	1	yes	characteristic
839	C₂	#14563969	1	1	yes	characteristic
840	C₂	#14563983	1	1	yes	characteristic
841	C₂	#14564252	1	1	yes	characteristic
842	C₂	#14564259	1	1	yes	characteristic
843	C₂	#14564321	1	1	yes	characteristic
844	C₂	#14564335	1	1	yes	characteristic
845	C₂	#14564814	1	1	yes	characteristic
846	C₂	#14564821	1	1	yes	characteristic
847	C₂	#14564866	1	1	yes	characteristic
848	C₂	#14564871	1	1	yes	characteristic
849	C₂	#14564945	1	1	yes	characteristic
850	C₂	#14564952	1	1	yes	characteristic
851	C₂	#14565038	1	1	yes	characteristic
852	C₂	#14565048	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#390	C₂
socle	C₂⁴×C₁₉	C₂×D₄
prime radical	C₂³×D₄×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#390	D₁₉
hypocenter	C₁₉	#11189
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#390

Complements

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

N	H ≅ G/N	type
3. C₂×#11926306	C₂	semidirect
4. C₂×#11926306	C₂	semidirect
5. C₂×#11926299	C₂	semidirect
6. #14561865	C₂	semidirect
17. C₂×#10597289	C₄	semidirect
525. C₁₉	#11189	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597289	2
C₂×#11926306	2
C₂×#11926299	2
#14561865	2
C₂×C₁₉×#390	2
#11189	19