Subgroups — C₁₉×#60582 #18066541

Order 4864.

2058 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3126	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3121	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3117	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3112	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3108	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3103	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3094	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3091	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3082	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3043	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3004	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2949	C₂	1	2	yes	maximal, complemented
16	C₁₉×#2947	C₂	1	2	yes	maximal, complemented
17	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#137	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
21	C₁₉×#555	—	2	1	no	—
22	C₁₉×#553	—	2	1	no	—
23	C₁₉×#553	—	2	1	no	—
24	C₁₉×#551	—	2	2	no	—
25	C₁₉×#547	—	2	1	no	—
26	C₁₉×#546	—	2	2	no	—
27	C₁₉×#544	C₂²	1	1	yes	characteristic
28	C₁₉×#542	C₂²	1	2	yes	—
29	C₁₉×#540	C₂²	1	2	yes	—
30	C₁₉×#535	C₂²	1	1	yes	characteristic
31	C₁₉×#532	C₂²	1	2	yes	—
32	C₁₉×#529	C₂²	1	2	yes	—
33	C₁₉×#525	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
35	C₁₉×#520	C₂²	1	1	yes	characteristic
36	C₁₉×#519	—	2	2	no	—
37	C₁₉×#519	—	2	1	no	—
38	C₁₉×#519	—	2	1	no	—
39	C₁₉×#519	C₂²	1	2	yes	—
40	C₁₉×#519	C₂²	1	2	yes	—
41	C₁₉×#519	C₂²	1	4	yes	complemented
42	C₁₉×#518	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
44	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
45	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
46	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
47	C₂×C₁₉×#117	—	2	2	no	—
48	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
50	C₁₉×#485	C₂²	1	2	yes	complemented
51	C₁₉×#484	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#483	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#482	C₂²	1	4	yes	—
54	C₁₉×#482	C₂²	1	2	yes	complemented
55	C₁₉×#481	C₂²	1	2	yes	—
56	C₁₉×#481	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#480	C₂²	1	2	yes	—
58	C₁₉×#480	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#479	C₂²	1	4	yes	complemented
60	C₁₉×#479	C₂²	1	4	yes	complemented
61	C₁₉×#477	C₂²	1	4	yes	complemented
62	C₁₉×#475	C₂²	1	4	yes	complemented
63	C₁₉×#464	C₂²	1	4	yes	complemented
64	C₁₉×#464	C₂²	1	4	yes	complemented
65	C₁₉×#460	C₂²	1	4	yes	complemented
66	C₁₉×#460	C₂²	1	4	yes	complemented
67	C₁₉×#451	C₂²	1	2	yes	complemented
68	C₁₉×#451	C₂²	1	2	yes	complemented
69	C₁₉×#448	C₂²	1	2	yes	—
70	C₁₉×#448	C₂²	1	2	yes	—
71	C₁₉×#448	C₂²	1	4	yes	—
72	C₁₉×#448	C₂²	1	2	yes	complemented
73	C₁₉×#448	C₂²	1	2	yes	complemented
74	C₁₉×#441	C₂²	1	4	yes	complemented
75	C₁₉×#440	C₂²	1	4	yes	complemented
76	C₁₉×#440	C₂²	1	4	yes	complemented
77	C₁₉×#440	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
82	C₁₉×#433	C₂²	1	4	yes	complemented
83	C₁₉×#432	C₂²	1	2	yes	complemented
84	C₁₉×#431	C₂²	1	2	yes	complemented
85	C₁₉×#428	C₂²	1	2	yes	—
86	C₁₉×#427	C₂²	1	2	yes	—
87	C₁₉×#424	C₂²	1	2	yes	—
88	C₁₉×#419	C₂²	1	2	yes	—
89	C₁₉×#418	C₂²	1	2	yes	—
90	C₁₉×#416	C₂²	1	2	yes	—
91	C₂×C₁₉×#103	C₂²	1	2	yes	—
92	C₁₉×#407	C₂²	1	1	yes	characteristic
93	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₁₉×#405	C₂²	1	2	yes	—
95	C₂×#41×C₁₉	—	2	2	no	—
96	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₉	—	2	8	no	—
98	C₂²×Q₈×C₁₉	—	2	1	no	—
99	C₂²×Q₈×C₁₉	—	2	1	no	—
100	C₂²×Q₈×C₁₉	—	2	1	no	—
101	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
103	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₉	—	2	1	no	—
105	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₉	—	2	1	no	—
107	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#137	—	2	8	no	—
109	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₁₉	—	2	8	no	—
111	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
114	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
115	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
116	C₁₉×C₄⋊Q₈	—	2	1	no	—
117	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₉×#127	C₂³	1	2	yes	—
119	C₁₉×#126	—	2	2	no	—
120	C₁₉×#126	—	2	2	no	—
121	C₁₉×#125	—	2	1	no	—
122	C₁₉×#125	C₂³	1	2	yes	—
123	C₁₉×#124	—	2	2	no	—
124	C₁₉×#124	—	2	2	no	—
125	C₁₉×#124	C₂³	1	2	yes	—
126	C₁₉×#123	—	2	1	no	—
127	C₁₉×#123	—	2	2	no	—
128	C₁₉×#123	—	2	2	no	—
129	C₁₉×#123	—	2	2	no	—
130	C₁₉×#123	—	2	2	no	—
131	C₁₉×C₂²⋊Q₈	—	2	2	no	—
132	C₁₉×C₂²⋊Q₈	—	2	2	no	—
133	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
134	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₉×#121	—	2	1	no	—
136	C₁₉×#121	—	2	1	no	—
137	C₁₉×#121	—	2	2	no	—
138	C₁₉×#121	—	2	1	no	—
139	C₁₉×#121	—	2	1	no	—
140	C₁₉×#121	—	2	2	no	—
141	C₁₉×#121	—	2	2	no	—
142	C₁₉×#121	C₂³	1	2	yes	—
143	C₁₉×#121	C₂³	1	2	yes	—
144	C₁₉×#121	C₂³	1	1	yes	characteristic
145	C₁₉×#121	C₂³	1	1	yes	characteristic
146	C₁₉×#120	—	2	1	no	—
147	C₁₉×#120	—	2	2	no	—
148	C₄×Q₈×C₁₉	—	2	2	no	—
149	C₄×Q₈×C₁₉	—	2	2	no	—
150	C₄×Q₈×C₁₉	—	2	2	no	—
151	C₄×Q₈×C₁₉	—	2	2	no	—
152	C₄×Q₈×C₁₉	—	2	4	no	—
153	C₄×Q₈×C₁₉	—	2	4	no	—
154	C₄×Q₈×C₁₉	—	2	2	no	—
155	C₄×Q₈×C₁₉	—	2	2	no	—
156	C₄×Q₈×C₁₉	—	2	2	no	—
157	C₄×Q₈×C₁₉	—	2	2	no	—
158	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
159	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
162	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
163	C₄×D₄×C₁₉	—	2	1	no	—
164	C₄×D₄×C₁₉	—	2	1	no	—
165	C₄×D₄×C₁₉	—	2	2	no	—
166	C₄×D₄×C₁₉	—	2	1	no	—
167	C₄×D₄×C₁₉	—	2	1	no	—
168	C₄×D₄×C₁₉	—	2	2	no	—
169	C₄×D₄×C₁₉	—	2	2	no	—
170	C₄×D₄×C₁₉	C₂³	1	2	yes	—
171	C₄×D₄×C₁₉	C₂³	1	2	yes	—
172	C₄×D₄×C₁₉	C₂³	1	2	yes	—
173	C₁₉×#117	—	2	1	no	—
174	C₁₉×#117	—	2	1	no	—
175	C₁₉×#117	—	2	1	no	—
176	C₁₉×#117	—	2	4	no	—
177	C₁₉×#117	—	2	4	no	—
178	C₁₉×#117	—	2	4	no	—
179	C₁₉×#117	—	2	4	no	—
180	C₁₉×#117	—	2	2	no	—
181	C₁₉×#117	D₄	1	2	yes	—
182	C₁₉×#117	D₄	1	1	yes	characteristic
183	C₁₉×#117	D₄	1	1	yes	characteristic
184	C₁₉×#117	C₂³	1	2	yes	—
185	C₁₉×#117	C₂³	1	1	yes	characteristic
186	C₁₉×#117	C₂³	1	2	yes	—
187	C₁₉×#117	C₂³	1	1	yes	characteristic
188	C₁₉×#117	C₂³	1	1	yes	characteristic
189	C₁₉×#117	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
202	C₂×C₄²×C₁₉	—	2	2	no	—
203	C₂×C₄²×C₁₉	—	2	2	no	—
204	C₂×C₄²×C₁₉	—	2	1	no	—
205	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
206	C₁₉×#107	C₂³	1	2	yes	—
207	C₁₉×#107	C₂³	1	2	yes	—
208	C₁₉×#107	C₂³	1	4	yes	—
209	C₁₉×#106	C₂³	1	2	yes	—
210	C₁₉×#106	C₂³	1	2	yes	—
211	C₁₉×#106	C₂³	1	4	yes	—
212	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
214	C₁₉×#103	C₂³	1	4	yes	—
215	C₁₉×#103	C₂³	1	4	yes	—
216	C₁₉×#103	C₂³	1	2	yes	—
217	C₁₉×#103	C₂³	1	2	yes	—
218	C₁₉×#103	C₂³	1	4	yes	—
219	C₁₉×#103	C₂³	1	4	yes	—
220	C₁₉×#102	C₂³	1	2	yes	—
221	C₁₉×#102	C₂³	1	2	yes	—
222	C₁₉×#102	C₂³	1	4	yes	—
223	C₁₉×#102	C₂³	1	4	yes	—
224	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₁₉×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₁₉	C₂³	1	4	yes	—
231	C₂⁴×C₁₉	—	2	1	no	—
232	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
233	#41×C₁₉	—	2	4	no	—
234	#41×C₁₉	—	8	4	no	—
235	C₂×Q₈×C₁₉	—	2	8	no	—
236	C₂×Q₈×C₁₉	—	2	8	no	—
237	C₂×Q₈×C₁₉	—	2	8	no	—
238	C₂×Q₈×C₁₉	—	2	8	no	—
239	C₂×Q₈×C₁₉	—	2	8	no	—
240	C₂×Q₈×C₁₉	—	2	2	no	—
241	C₂×Q₈×C₁₉	—	2	2	no	—
242	C₂×Q₈×C₁₉	—	2	2	no	—
243	C₂×Q₈×C₁₉	—	2	2	no	—
244	C₂×Q₈×C₁₉	—	2	4	no	—
245	C₂×Q₈×C₁₉	#41	1	8	yes	complemented
246	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
248	C₂×D₄×C₁₉	—	2	1	no	—
249	C₂×D₄×C₁₉	—	2	1	no	—
250	C₂×D₄×C₁₉	—	2	2	no	—
251	C₂×D₄×C₁₉	—	2	1	no	—
252	C₂×D₄×C₁₉	—	2	2	no	—
253	C₂×D₄×C₁₉	—	2	1	no	—
254	C₂×D₄×C₁₉	—	2	2	no	—
255	C₂×D₄×C₁₉	—	2	2	no	—
256	C₂×D₄×C₁₉	—	2	4	no	—
257	C₂×D₄×C₁₉	—	8	2	no	—
258	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₉	—	2	8	no	—
261	C₂²×C₄×C₁₉	—	2	2	no	—
262	C₂²×C₄×C₁₉	—	2	2	no	—
263	C₂²×C₄×C₁₉	—	2	2	no	—
264	C₂²×C₄×C₁₉	—	2	4	no	—
265	C₂²×C₄×C₁₉	—	2	1	no	—
266	C₂²×C₄×C₁₉	—	2	1	no	—
267	C₂²×C₄×C₁₉	—	2	1	no	—
268	C₂²×C₄×C₁₉	—	2	1	no	—
269	C₂²×C₄×C₁₉	—	2	2	no	—
270	C₂²×C₄×C₁₉	—	2	2	no	—
271	C₂²×C₄×C₁₉	—	2	2	no	—
272	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
280	Q₁₆×C₁₉	—	2	8	no	—
281	SD₁₆×C₁₉	—	2	8	no	—
282	SD₁₆×C₁₉	—	2	8	no	—
283	SD₁₆×C₁₉	—	2	8	no	—
284	M₁₆×C₁₉	—	2	4	no	—
285	C₂×C₈×C₁₉	—	2	4	no	—
286	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
288	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
289	C₄⋊C₄×C₁₉	—	2	1	no	—
290	C₄⋊C₄×C₁₉	—	2	4	no	—
291	C₄⋊C₄×C₁₉	—	2	4	no	—
292	C₄⋊C₄×C₁₉	—	2	4	no	—
293	C₄⋊C₄×C₁₉	—	2	4	no	—
294	C₄⋊C₄×C₁₉	—	2	2	no	—
295	C₄⋊C₄×C₁₉	—	2	1	no	—
296	C₄⋊C₄×C₁₉	—	2	1	no	—
297	C₄⋊C₄×C₁₉	—	2	1	no	—
298	C₄⋊C₄×C₁₉	—	2	2	no	—
299	C₄⋊C₄×C₁₉	—	2	2	no	—
300	C₄⋊C₄×C₁₉	—	2	2	no	—
301	C₄⋊C₄×C₁₉	—	2	1	no	—
302	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
313	C₂²⋊C₄×C₁₉	—	2	1	no	—
314	C₂²⋊C₄×C₁₉	—	2	2	no	—
315	C₂²⋊C₄×C₁₉	—	2	2	no	—
316	C₂²⋊C₄×C₁₉	—	2	1	no	—
317	C₂²⋊C₄×C₁₉	—	2	1	no	—
318	C₂²⋊C₄×C₁₉	—	2	2	no	—
319	C₂²⋊C₄×C₁₉	—	2	2	no	—
320	C₂²⋊C₄×C₁₉	—	2	2	no	—
321	C₂²⋊C₄×C₁₉	—	2	2	no	—
322	C₂²⋊C₄×C₁₉	—	2	2	no	—
323	C₂²⋊C₄×C₁₉	—	2	2	no	—
324	C₂²⋊C₄×C₁₉	—	2	1	no	—
325	C₂²⋊C₄×C₁₉	—	2	2	no	—
326	C₂²⋊C₄×C₁₉	—	2	1	no	—
327	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
331	C₄²×C₁₉	—	2	4	no	—
332	C₄²×C₁₉	—	2	4	no	—
333	C₄²×C₁₉	—	2	4	no	—
334	C₄²×C₁₉	—	2	4	no	—
335	C₄²×C₁₉	—	2	2	no	—
336	C₄²×C₁₉	—	2	2	no	—
337	C₄²×C₁₉	—	2	2	no	—
338	C₄²×C₁₉	—	2	1	no	—
339	C₄²×C₁₉	C₂×D₄	1	2	yes	—
340	C₄²×C₁₉	C₂×D₄	1	2	yes	—
341	C₄²×C₁₉	C₂⁴	1	2	yes	—
342	C₄²×C₁₉	C₂⁴	1	2	yes	—
343	#60582	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₁₉	—	2	2	no	—
345	C₂³×C₁₉	—	2	2	no	—
346	C₂³×C₁₉	—	2	2	no	—
347	C₂³×C₁₉	—	2	1	no	—
348	C₂³×C₁₉	—	4	1	no	—
349	C₂³×C₁₉	—	4	2	no	—
350	C₂³×C₁₉	—	8	1	no	—
351	C₂³×C₁₉	—	8	1	no	—
352	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
353	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
354	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
355	Q₈×C₁₉	—	2	8	no	—
356	Q₈×C₁₉	—	2	8	no	—
357	Q₈×C₁₉	—	2	8	no	—
358	Q₈×C₁₉	—	2	4	no	—
359	Q₈×C₁₉	—	2	2	no	—
360	Q₈×C₁₉	—	8	2	no	—
361	Q₈×C₁₉	C₂×#41	1	8	yes	—
362	D₄×C₁₉	—	2	4	no	—
363	D₄×C₁₉	—	2	2	no	—
364	D₄×C₁₉	—	4	2	no	—
365	D₄×C₁₉	—	4	4	no	—
366	D₄×C₁₉	—	4	2	no	—
367	D₄×C₁₉	—	4	2	no	—
368	D₄×C₁₉	—	8	2	no	—
369	D₄×C₁₉	—	8	2	no	—
370	D₄×C₁₉	—	8	1	no	—
371	D₄×C₁₉	—	8	2	no	—
372	C₂×C₄×C₁₉	—	2	8	no	—
373	C₂×C₄×C₁₉	—	2	8	no	—
374	C₂×C₄×C₁₉	—	2	8	no	—
375	C₂×C₄×C₁₉	—	2	2	no	—
376	C₂×C₄×C₁₉	—	2	4	no	—
377	C₂×C₄×C₁₉	—	2	4	no	—
378	C₂×C₄×C₁₉	—	2	2	no	—
379	C₂×C₄×C₁₉	—	2	2	no	—
380	C₂×C₄×C₁₉	—	2	2	no	—
381	C₂×C₄×C₁₉	—	2	2	no	—
382	C₂×C₄×C₁₉	—	2	2	no	—
383	C₂×C₄×C₁₉	—	2	2	no	—
384	C₂×C₄×C₁₉	—	2	1	no	—
385	C₂×C₄×C₁₉	—	2	1	no	—
386	C₂×C₄×C₁₉	—	2	1	no	—
387	C₂×C₄×C₁₉	—	2	2	no	—
388	C₂×C₄×C₁₉	—	4	2	no	—
389	C₂×C₄×C₁₉	—	4	2	no	—
390	C₂×C₄×C₁₉	—	4	2	no	—
391	C₂×C₄×C₁₉	—	4	2	no	—
392	C₂×C₄×C₁₉	—	8	2	no	—
393	C₂×C₄×C₁₉	—	8	2	no	—
394	C₂×C₄×C₁₉	—	8	2	no	—
395	C₂×C₄×C₁₉	—	8	1	no	—
396	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
404	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
405	C₈×C₁₉	—	2	2	no	—
406	C₈×C₁₉	—	2	2	no	—
407	C₈×C₁₉	—	2	4	no	—
408	#3494	C₂×C₁₉	1	1	yes	characteristic
409	C₂×#519	C₂×C₁₉	1	1	yes	characteristic, complemented
410	#3126	C₂×C₁₉	1	4	yes	complemented
411	#3121	C₂×C₁₉	1	4	yes	complemented
412	#3117	C₂×C₁₉	1	2	yes	complemented
413	#3112	C₂×C₁₉	1	2	yes	complemented
414	#3108	C₂×C₁₉	1	2	yes	complemented
415	#3103	C₂×C₁₉	1	2	yes	complemented
416	#3094	C₂×C₁₉	1	1	yes	characteristic, complemented
417	#3091	C₂×C₁₉	1	1	yes	characteristic, complemented
418	#3082	C₂×C₁₉	1	2	yes	complemented
419	#3043	C₂×C₁₉	1	2	yes	complemented
420	#3004	C₂×C₁₉	1	1	yes	characteristic, complemented
421	C₂×#448	C₂×C₁₉	1	1	yes	characteristic, complemented
422	#2949	C₂×C₁₉	1	2	yes	complemented
423	#2947	C₂×C₁₉	1	2	yes	complemented
424	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
425	C₂²×C₁₉	—	2	1	no	—
426	C₂²×C₁₉	—	2	1	no	—
427	C₂²×C₁₉	—	2	1	no	—
428	C₂²×C₁₉	—	2	1	no	—
429	C₂²×C₁₉	—	2	1	no	—
430	C₂²×C₁₉	—	2	1	no	—
431	C₂²×C₁₉	—	2	1	no	—
432	C₂²×C₁₉	—	4	4	no	—
433	C₂²×C₁₉	—	4	2	no	—
434	C₂²×C₁₉	—	4	1	no	—
435	C₂²×C₁₉	—	4	1	no	—
436	C₂²×C₁₉	—	4	2	no	—
437	C₂²×C₁₉	—	4	1	no	—
438	C₂²×C₁₉	—	4	2	no	—
439	C₂²×C₁₉	—	16	2	no	—
440	C₂²×C₁₉	#525	1	2	yes	—
441	C₂²×C₁₉	#577	1	2	yes	—
442	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
443	C₄×C₁₉	—	2	2	no	—
444	C₄×C₁₉	—	2	2	no	—
445	C₄×C₁₉	—	2	8	no	—
446	C₄×C₁₉	—	2	1	no	—
447	C₄×C₁₉	—	2	1	no	—
448	C₄×C₁₉	—	2	2	no	—
449	C₄×C₁₉	—	2	2	no	—
450	C₄×C₁₉	—	4	2	no	—
451	C₄×C₁₉	—	4	1	no	—
452	C₄×C₁₉	—	4	1	no	—
453	C₄×C₁₉	—	4	2	no	—
454	C₄×C₁₉	—	4	2	no	—
455	C₄×C₁₉	—	4	1	no	—
456	C₄×C₁₉	#525	1	2	yes	—
457	C₄×C₁₉	C₂²×#41	1	2	yes	—
458	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×#137	C₂²×C₁₉	1	2	yes	—
460	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
461	#555	—	2	1	no	—
462	#553	—	2	1	no	—
463	#553	—	2	1	no	—
464	#551	—	2	2	no	—
465	#547	—	2	1	no	—
466	#546	—	2	2	no	—
467	#544	C₂²×C₁₉	1	1	yes	characteristic
468	#542	C₂²×C₁₉	1	2	yes	—
469	#540	C₂²×C₁₉	1	2	yes	—
470	#535	C₂²×C₁₉	1	1	yes	characteristic
471	#532	C₂²×C₁₉	1	2	yes	—
472	#529	C₂²×C₁₉	1	2	yes	—
473	#525	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
475	#520	C₂²×C₁₉	1	1	yes	characteristic
476	#519	—	2	2	no	—
477	#519	—	2	1	no	—
478	#519	—	2	1	no	—
479	#519	C₂²×C₁₉	1	2	yes	—
480	#519	C₂²×C₁₉	1	2	yes	—
481	#519	C₂²×C₁₉	1	4	yes	complemented
482	#518	C₂²×C₁₉	1	1	yes	characteristic
483	C₂×C₄×Q₈	—	2	1	no	—
484	C₂×C₄×Q₈	—	2	1	no	—
485	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
486	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
487	C₂×#117	—	2	2	no	—
488	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
489	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
490	#485	C₂²×C₁₉	1	2	yes	complemented
491	#484	C₂²×C₁₉	1	1	yes	characteristic, complemented
492	#483	C₂²×C₁₉	1	1	yes	characteristic, complemented
493	#482	C₂²×C₁₉	1	4	yes	—
494	#482	C₂²×C₁₉	1	2	yes	complemented
495	#481	C₂²×C₁₉	1	2	yes	—
496	#481	C₂²×C₁₉	1	1	yes	characteristic, complemented
497	#480	C₂²×C₁₉	1	2	yes	—
498	#480	C₂²×C₁₉	1	1	yes	characteristic, complemented
499	#479	C₂²×C₁₉	1	4	yes	complemented
500	#479	C₂²×C₁₉	1	4	yes	complemented
501	#477	C₂²×C₁₉	1	4	yes	complemented
502	#475	C₂²×C₁₉	1	4	yes	complemented
503	#464	C₂²×C₁₉	1	4	yes	complemented
504	#464	C₂²×C₁₉	1	4	yes	complemented
505	#460	C₂²×C₁₉	1	4	yes	complemented
506	#460	C₂²×C₁₉	1	4	yes	complemented
507	#451	C₂²×C₁₉	1	2	yes	complemented
508	#451	C₂²×C₁₉	1	2	yes	complemented
509	#448	C₂²×C₁₉	1	2	yes	—
510	#448	C₂²×C₁₉	1	2	yes	—
511	#448	C₂²×C₁₉	1	4	yes	—
512	#448	C₂²×C₁₉	1	2	yes	complemented
513	#448	C₂²×C₁₉	1	2	yes	complemented
514	#441	C₂²×C₁₉	1	4	yes	complemented
515	#440	C₂²×C₁₉	1	4	yes	complemented
516	#440	C₂²×C₁₉	1	4	yes	complemented
517	#440	C₂²×C₁₉	1	4	yes	complemented
518	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	complemented
519	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
520	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
521	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
522	#433	C₂²×C₁₉	1	4	yes	complemented
523	#432	C₂²×C₁₉	1	2	yes	complemented
524	#431	C₂²×C₁₉	1	2	yes	complemented
525	#428	C₂²×C₁₉	1	2	yes	—
526	#427	C₂²×C₁₉	1	2	yes	—
527	#424	C₂²×C₁₉	1	2	yes	—
528	#419	C₂²×C₁₉	1	2	yes	—
529	#418	C₂²×C₁₉	1	2	yes	—
530	#416	C₂²×C₁₉	1	2	yes	—
531	C₂×#103	C₂²×C₁₉	1	2	yes	—
532	#407	C₂²×C₁₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
534	#405	C₂²×C₁₉	1	2	yes	—
535	C₂×C₁₉	—	2	2	no	—
536	C₂×C₁₉	—	2	2	no	—
537	C₂×C₁₉	—	4	1	no	—
538	C₂×C₁₉	—	8	1	no	—
539	C₂×C₁₉	—	8	2	no	—
540	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
541	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
542	C₂×C₁₉	#3586	1	1	yes	characteristic
543	C₂×#41	—	2	2	no	—
544	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
545	C₂²×Q₈	—	2	8	no	—
546	C₂²×Q₈	—	2	1	no	—
547	C₂²×Q₈	—	2	1	no	—
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
550	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
551	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
554	C₂³×C₄	—	2	1	no	—
555	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
556	#137	—	2	8	no	—
557	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
558	C₂×SD₁₆	—	2	8	no	—
559	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
560	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
561	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
562	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
563	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
566	#127	C₂³×C₁₉	1	2	yes	—
567	#126	—	2	2	no	—
568	#126	—	2	2	no	—
569	#125	—	2	1	no	—
570	#125	C₂³×C₁₉	1	2	yes	—
571	#124	—	2	2	no	—
572	#124	—	2	2	no	—
573	#124	C₂³×C₁₉	1	2	yes	—
574	#123	—	2	1	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
582	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
583	#121	—	2	1	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	C₂³×C₁₉	1	2	yes	—
591	#121	C₂³×C₁₉	1	2	yes	—
592	#121	C₂³×C₁₉	1	1	yes	characteristic
593	#121	C₂³×C₁₉	1	1	yes	characteristic
594	#120	—	2	1	no	—
595	#120	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	4	no	—
601	C₄×Q₈	—	2	4	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
607	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
608	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
609	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
610	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	C₂³×C₁₉	1	2	yes	—
619	C₄×D₄	C₂³×C₁₉	1	2	yes	—
620	C₄×D₄	C₂³×C₁₉	1	2	yes	—
621	#117	—	2	1	no	—
622	#117	—	2	1	no	—
623	#117	—	2	1	no	—
624	#117	—	2	4	no	—
625	#117	—	2	4	no	—
626	#117	—	2	4	no	—
627	#117	—	2	4	no	—
628	#117	—	2	2	no	—
629	#117	D₄×C₁₉	1	2	yes	—
630	#117	D₄×C₁₉	1	1	yes	characteristic
631	#117	D₄×C₁₉	1	1	yes	characteristic
632	#117	C₂³×C₁₉	1	2	yes	—
633	#117	C₂³×C₁₉	1	2	yes	—
634	#117	C₂³×C₁₉	1	1	yes	characteristic
635	#117	C₂³×C₁₉	1	1	yes	characteristic
636	#117	C₂³×C₁₉	1	1	yes	characteristic
637	#117	C₂³×C₁₉	1	2	yes	—
638	C₂×C₄⋊C₄	—	2	2	no	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
650	C₂×C₄²	—	2	2	no	—
651	C₂×C₄²	—	2	2	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
654	#107	C₂³×C₁₉	1	2	yes	—
655	#107	C₂³×C₁₉	1	2	yes	—
656	#107	C₂³×C₁₉	1	4	yes	—
657	#106	C₂³×C₁₉	1	2	yes	—
658	#106	C₂³×C₁₉	1	2	yes	—
659	#106	C₂³×C₁₉	1	4	yes	—
660	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
661	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
662	#103	C₂³×C₁₉	1	4	yes	—
663	#103	C₂³×C₁₉	1	4	yes	—
664	#103	C₂³×C₁₉	1	2	yes	—
665	#103	C₂³×C₁₉	1	2	yes	—
666	#103	C₂³×C₁₉	1	4	yes	—
667	#103	C₂³×C₁₉	1	4	yes	—
668	#102	C₂³×C₁₉	1	2	yes	—
669	#102	C₂³×C₁₉	1	2	yes	—
670	#102	C₂³×C₁₉	1	4	yes	—
671	#102	C₂³×C₁₉	1	4	yes	—
672	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
673	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
674	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
677	#97	C₂³×C₁₉	1	4	yes	—
678	C₄×C₈	C₂³×C₁₉	1	4	yes	—
679	C₁₉	#60582	1	1	yes	characteristic, direct product factor, Sylow
680	C₂⁴	—	2	1	no	—
681	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
682	#41	—	2	4	no	—
683	#41	—	8	4	no	—
684	C₂×Q₈	—	2	8	no	—
685	C₂×Q₈	—	2	8	no	—
686	C₂×Q₈	—	2	8	no	—
687	C₂×Q₈	—	2	8	no	—
688	C₂×Q₈	—	2	8	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	#41×C₁₉	1	8	yes	complemented
695	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
696	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	8	2	no	—
707	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
708	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
709	C₂²×C₄	—	2	8	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
729	Q₁₆	—	2	8	no	—
730	SD₁₆	—	2	8	no	—
731	SD₁₆	—	2	8	no	—
732	SD₁₆	—	2	8	no	—
733	M₁₆	—	2	4	no	—
734	C₂×C₈	—	2	4	no	—
735	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
736	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
737	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
752	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
755	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
756	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
761	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
780	C₄²	—	2	4	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	1	no	—
788	C₄²	C₂×D₄×C₁₉	1	2	yes	—
789	C₄²	C₂×D₄×C₁₉	1	2	yes	—
790	C₄²	C₂⁴×C₁₉	1	2	yes	—
791	C₄²	C₂⁴×C₁₉	1	2	yes	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	4	1	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	8	1	no	—
799	C₂³	—	8	1	no	—
800	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
801	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
802	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
803	Q₈	—	2	8	no	—
804	Q₈	—	2	8	no	—
805	Q₈	—	2	8	no	—
806	Q₈	—	2	4	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	C₂×#41×C₁₉	1	8	yes	—
810	D₄	—	2	4	no	—
811	D₄	—	2	2	no	—
812	D₄	—	4	2	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	2	no	—
819	D₄	—	8	1	no	—
820	C₂×C₄	—	2	8	no	—
821	C₂×C₄	—	2	8	no	—
822	C₂×C₄	—	2	8	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	1	no	—
844	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
851	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
852	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	2	2	no	—
855	C₈	—	2	4	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	16	2	no	—
871	C₂²	C₁₉×#525	1	2	yes	—
872	C₂²	C₁₉×#577	1	2	yes	—
873	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
874	C₄	—	2	8	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	C₁₉×#525	1	2	yes	—
888	C₄	C₂²×#41×C₁₉	1	2	yes	—
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	2	no	—
893	C₂	—	8	1	no	—
894	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
895	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
896	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#519	C₂	semidirect
3. C₁₉×#3126	C₂	semidirect
4. C₁₉×#3121	C₂	semidirect
5. C₁₉×#3117	C₂	semidirect
6. C₁₉×#3112	C₂	semidirect
7. C₁₉×#3108	C₂	semidirect
8. C₁₉×#3103	C₂	semidirect
9. C₁₉×#3094	C₂	semidirect
10. C₁₉×#3091	C₂	semidirect
11. C₁₉×#3082	C₂	semidirect
12. C₁₉×#3043	C₂	semidirect
13. C₁₉×#3004	C₂	semidirect
14. C₂×C₁₉×#448	C₂	semidirect
15. C₁₉×#2949	C₂	semidirect
16. C₁₉×#2947	C₂	semidirect
17. C₁₉×#2924	C₂	semidirect
41. C₁₉×#519	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
46. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
50. C₁₉×#485	C₂²	semidirect
51. C₁₉×#484	C₂²	semidirect
52. C₁₉×#483	C₂²	semidirect
54. C₁₉×#482	C₂²	semidirect
56. C₁₉×#481	C₂²	semidirect
58. C₁₉×#480	C₂²	semidirect
59. C₁₉×#479	C₂²	semidirect
60. C₁₉×#479	C₂²	semidirect
61. C₁₉×#477	C₂²	semidirect
62. C₁₉×#475	C₂²	semidirect
63. C₁₉×#464	C₂²	semidirect
64. C₁₉×#464	C₂²	semidirect
65. C₁₉×#460	C₂²	semidirect
66. C₁₉×#460	C₂²	semidirect
67. C₁₉×#451	C₂²	semidirect
68. C₁₉×#451	C₂²	semidirect
72. C₁₉×#448	C₂²	semidirect
73. C₁₉×#448	C₂²	semidirect
74. C₁₉×#441	C₂²	semidirect
75. C₁₉×#440	C₂²	semidirect
76. C₁₉×#440	C₂²	semidirect
77. C₁₉×#440	C₂²	semidirect
78. C₄×Q₁₆×C₁₉	C₂²	semidirect
79. C₄×SD₁₆×C₁₉	C₂²	semidirect
80. C₄×SD₁₆×C₁₉	C₂²	semidirect
81. C₄×SD₁₆×C₁₉	C₂²	semidirect
82. C₁₉×#433	C₂²	semidirect
83. C₁₉×#432	C₂²	semidirect
84. C₁₉×#431	C₂²	semidirect
245. C₂×Q₈×C₁₉	#41	semidirect
343. #60582	C₁₉	direct (N × H)
409. C₂×#519	C₂×C₁₉	semidirect
410. #3126	C₂×C₁₉	semidirect
411. #3121	C₂×C₁₉	semidirect
412. #3117	C₂×C₁₉	semidirect
413. #3112	C₂×C₁₉	semidirect
414. #3108	C₂×C₁₉	semidirect
415. #3103	C₂×C₁₉	semidirect
416. #3094	C₂×C₁₉	semidirect
417. #3091	C₂×C₁₉	semidirect
418. #3082	C₂×C₁₉	semidirect
419. #3043	C₂×C₁₉	semidirect
420. #3004	C₂×C₁₉	semidirect
421. C₂×#448	C₂×C₁₉	semidirect
422. #2949	C₂×C₁₉	semidirect
423. #2947	C₂×C₁₉	semidirect
424. #2924	C₂×C₁₉	semidirect
481. #519	C₂²×C₁₉	semidirect
485. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
486. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
490. #485	C₂²×C₁₉	semidirect
491. #484	C₂²×C₁₉	semidirect
492. #483	C₂²×C₁₉	semidirect
494. #482	C₂²×C₁₉	semidirect
496. #481	C₂²×C₁₉	semidirect
498. #480	C₂²×C₁₉	semidirect
499. #479	C₂²×C₁₉	semidirect
500. #479	C₂²×C₁₉	semidirect
501. #477	C₂²×C₁₉	semidirect
502. #475	C₂²×C₁₉	semidirect
503. #464	C₂²×C₁₉	semidirect
504. #464	C₂²×C₁₉	semidirect
505. #460	C₂²×C₁₉	semidirect
506. #460	C₂²×C₁₉	semidirect
507. #451	C₂²×C₁₉	semidirect
508. #451	C₂²×C₁₉	semidirect
512. #448	C₂²×C₁₉	semidirect
513. #448	C₂²×C₁₉	semidirect
514. #441	C₂²×C₁₉	semidirect
515. #440	C₂²×C₁₉	semidirect
516. #440	C₂²×C₁₉	semidirect
517. #440	C₂²×C₁₉	semidirect
518. C₄×Q₁₆	C₂²×C₁₉	semidirect
519. C₄×SD₁₆	C₂²×C₁₉	semidirect
520. C₄×SD₁₆	C₂²×C₁₉	semidirect
521. C₄×SD₁₆	C₂²×C₁₉	semidirect
522. #433	C₂²×C₁₉	semidirect
523. #432	C₂²×C₁₉	semidirect
524. #431	C₂²×C₁₉	semidirect
679. C₁₉	#60582	direct (N × H)
694. C₂×Q₈	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3494	2
C₂×C₁₉×#519	2
C₁₉×#3126	2
C₁₉×#3121	2
C₁₉×#3117	2
C₁₉×#3112	2
C₁₉×#3108	2
C₁₉×#3103	2
C₁₉×#3094	2
C₁₉×#3091	2
C₁₉×#3082	2
C₁₉×#3043	2
C₁₉×#3004	2
C₂×C₁₉×#448	2
C₁₉×#2949	2
C₁₉×#2947	2
C₁₉×#2924	2
#60582	19

Subgroups — C19×#60582 #18066541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60582 #18066541