Subgroups — C₁₉×#60562 #18066521

Order 4864.

2148 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3116	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3113	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3110	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3107	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3104	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3101	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3095	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3079	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3039	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3007	C₂	1	2	yes	maximal
13	C₄×C₁₉×#137	C₂	1	4	yes	maximal, complemented
14	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#137	C₂²	1	4	yes	—
17	C₁₉×#533	—	2	1	no	—
18	C₁₉×#533	—	2	1	no	—
19	C₁₉×#533	—	2	1	no	—
20	C₁₉×#533	—	2	1	no	—
21	C₁₉×#533	C₂²	1	2	yes	—
22	C₁₉×#533	C₂²	1	2	yes	—
23	C₁₉×#533	C₂²	1	2	yes	complemented
24	C₁₉×#533	C₂²	1	2	yes	complemented
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₉×#125	—	2	1	no	—
28	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
29	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×#41×C₁₉	—	2	1	no	—
31	C₄×#41×C₁₉	—	2	1	no	—
32	C₄×#41×C₁₉	—	2	1	no	—
33	C₄×#41×C₁₉	—	2	1	no	—
34	C₄×#41×C₁₉	C₂²	1	2	yes	—
35	C₄×#41×C₁₉	C₂²	1	2	yes	—
36	C₄×#41×C₁₉	C₂²	1	2	yes	—
37	C₄×#41×C₁₉	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
39	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₁₉	—	2	1	no	—
43	C₂×C₄×D₄×C₁₉	—	2	1	no	—
44	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#117	—	2	1	no	—
47	C₂×C₁₉×#117	—	2	1	no	—
48	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₁₉	—	2	1	no	—
50	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#485	C₂²	1	8	yes	complemented
52	C₁₉×#484	C₂²	1	4	yes	—
53	C₁₉×#483	C₂²	1	4	yes	—
54	C₁₉×#477	C₂²	1	4	yes	complemented
55	C₁₉×#476	C₂²	1	4	yes	complemented
56	C₁₉×#475	C₂²	1	4	yes	complemented
57	C₁₉×#474	C₂²	1	4	yes	complemented
58	C₁₉×#462	C₂²	1	4	yes	complemented
59	C₁₉×#462	C₂²	1	4	yes	complemented
60	C₁₉×#461	C₂²	1	4	yes	complemented
61	C₁₉×#461	C₂²	1	4	yes	complemented
62	C₁₉×#452	C₂²	1	8	yes	—
63	C₁₉×#451	C₂²	1	4	yes	—
64	C₁₉×#450	C₂²	1	4	yes	—
65	C₁₉×#441	C₂²	1	8	yes	complemented
66	C₁₉×#440	C₂²	1	8	yes	complemented
67	C₄×Q₁₆×C₁₉	C₂²	1	8	yes	complemented
68	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	complemented
69	C₁₉×#432	C₂²	1	2	yes	—
70	C₁₉×#432	C₂²	1	2	yes	complemented
71	C₁₉×#431	C₂²	1	2	yes	—
72	C₁₉×#431	C₂²	1	2	yes	complemented
73	C₁₉×#428	C₂²	1	4	yes	complemented
74	C₁₉×#423	C₂²	1	2	yes	complemented
75	C₁₉×#419	C₂²	1	4	yes	complemented
76	C₁₉×#417	C₂²	1	4	yes	—
77	C₁₉×#407	C₂²	1	2	yes	—
78	C₄×M₁₆×C₁₉	C₂²	1	2	yes	complemented
79	C₂×#41×C₁₉	—	2	8	no	—
80	C₂×#41×C₁₉	—	2	1	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	C₂³	1	2	yes	—
83	C₂×#41×C₁₉	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₉	—	2	1	no	—
85	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₉	—	2	1	no	—
88	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₉	—	2	1	no	—
90	C₂³×C₄×C₁₉	—	2	1	no	—
91	C₂³×C₄×C₁₉	—	2	1	no	—
92	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×#137	—	2	16	no	—
96	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	—
97	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
98	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
99	C₁₉×C₄⋊Q₈	—	2	1	no	—
100	C₁₉×C₄⋊Q₈	—	2	1	no	—
101	C₁₉×C₄⋊Q₈	—	2	1	no	—
102	C₁₉×C₄⋊Q₈	—	2	1	no	—
103	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₁₉×#125	—	2	2	no	—
108	C₁₉×#125	—	2	2	no	—
109	C₁₉×#125	—	2	2	no	—
110	C₁₉×#125	—	2	2	no	—
111	C₁₉×C₂²⋊Q₈	—	2	2	no	—
112	C₁₉×C₂²⋊Q₈	—	2	2	no	—
113	C₁₉×C₂²⋊Q₈	—	2	2	no	—
114	C₁₉×C₂²⋊Q₈	—	2	2	no	—
115	C₁₉×C₂²⋊Q₈	—	2	2	no	—
116	C₁₉×C₂²⋊Q₈	—	2	2	no	—
117	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
118	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
119	C₄×Q₈×C₁₉	—	2	2	no	—
120	C₄×Q₈×C₁₉	—	2	2	no	—
121	C₄×Q₈×C₁₉	—	2	2	no	—
122	C₄×Q₈×C₁₉	—	2	2	no	—
123	C₄×Q₈×C₁₉	—	2	1	no	—
124	C₄×Q₈×C₁₉	—	2	1	no	—
125	C₄×Q₈×C₁₉	—	2	1	no	—
126	C₄×Q₈×C₁₉	—	2	1	no	—
127	C₄×Q₈×C₁₉	—	2	2	no	—
128	C₄×Q₈×C₁₉	—	2	2	no	—
129	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
130	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
131	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
132	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
133	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
134	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
135	C₄×D₄×C₁₉	—	2	2	no	—
136	C₄×D₄×C₁₉	—	2	2	no	—
137	C₄×D₄×C₁₉	—	2	2	no	—
138	C₄×D₄×C₁₉	—	2	2	no	—
139	C₄×D₄×C₁₉	—	2	2	no	—
140	C₄×D₄×C₁₉	—	2	2	no	—
141	C₄×D₄×C₁₉	—	2	2	no	—
142	C₄×D₄×C₁₉	—	2	2	no	—
143	C₄×D₄×C₁₉	—	2	1	no	—
144	C₄×D₄×C₁₉	—	2	1	no	—
145	C₄×D₄×C₁₉	—	2	1	no	—
146	C₄×D₄×C₁₉	—	2	1	no	—
147	C₄×D₄×C₁₉	C₂³	1	2	yes	—
148	C₄×D₄×C₁₉	C₂³	1	2	yes	—
149	C₄×D₄×C₁₉	C₂³	1	2	yes	—
150	C₄×D₄×C₁₉	C₂³	1	2	yes	—
151	C₁₉×#117	—	2	2	no	—
152	C₁₉×#117	—	2	2	no	—
153	C₁₉×#117	—	2	2	no	—
154	C₁₉×#117	—	2	2	no	—
155	C₁₉×#117	—	2	1	no	—
156	C₁₉×#117	—	2	1	no	—
157	C₁₉×#117	—	2	2	no	—
158	C₁₉×#117	—	2	2	no	—
159	C₁₉×#117	—	2	2	no	—
160	C₁₉×#117	—	2	2	no	—
161	C₁₉×#117	C₂³	1	2	yes	—
162	C₁₉×#117	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂×C₄²×C₁₉	—	2	1	no	—
178	C₂×C₄²×C₁₉	—	2	1	no	—
179	C₂×C₄²×C₁₉	—	2	1	no	—
180	C₂×C₄²×C₁₉	—	2	2	no	—
181	C₂×C₄²×C₁₉	—	2	2	no	—
182	C₂×C₄²×C₁₉	—	2	2	no	—
183	C₂×C₄²×C₁₉	—	2	2	no	—
184	C₂×C₄²×C₁₉	—	2	2	no	—
185	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
197	C₁₉×#107	C₂³	1	8	yes	—
198	C₁₉×#106	C₂³	1	8	yes	—
199	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
200	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
201	C₁₉×#103	C₂³	1	8	yes	—
202	C₁₉×#103	C₂³	1	8	yes	—
203	C₁₉×#103	C₂³	1	8	yes	—
204	C₁₉×#102	C₂³	1	8	yes	—
205	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₁₉×#97	C₂³	1	4	yes	—
208	C₄×C₈×C₁₉	C₂³	1	4	yes	—
209	C₂⁴×C₁₉	—	2	1	no	—
210	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
211	#41×C₁₉	—	2	8	no	—
212	#41×C₁₉	—	2	8	no	—
213	#41×C₁₉	—	2	4	no	—
214	#41×C₁₉	—	2	4	no	—
215	#41×C₁₉	—	2	4	no	—
216	#41×C₁₉	#41	1	8	yes	—
217	C₂×Q₈×C₁₉	—	2	4	no	—
218	C₂×Q₈×C₁₉	—	2	1	no	—
219	C₂×Q₈×C₁₉	—	2	2	no	—
220	C₂×Q₈×C₁₉	—	2	2	no	—
221	C₂×Q₈×C₁₉	—	2	2	no	—
222	C₂×Q₈×C₁₉	—	2	8	no	—
223	C₂×Q₈×C₁₉	—	4	4	no	—
224	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
225	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
226	C₂×D₄×C₁₉	—	2	8	no	—
227	C₂×D₄×C₁₉	—	2	2	no	—
228	C₂×D₄×C₁₉	—	2	2	no	—
229	C₂×D₄×C₁₉	—	2	4	no	—
230	C₂×D₄×C₁₉	—	2	1	no	—
231	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₉	—	2	8	no	—
233	C₂²×C₄×C₁₉	—	2	1	no	—
234	C₂²×C₄×C₁₉	—	2	4	no	—
235	C₂²×C₄×C₁₉	—	2	2	no	—
236	C₂²×C₄×C₁₉	—	2	2	no	—
237	C₂²×C₄×C₁₉	—	2	4	no	—
238	C₂²×C₄×C₁₉	—	2	1	no	—
239	C₂²×C₄×C₁₉	—	2	1	no	—
240	C₂²×C₄×C₁₉	—	2	2	no	—
241	C₂²×C₄×C₁₉	—	2	2	no	—
242	C₂²×C₄×C₁₉	—	2	2	no	—
243	C₂²×C₄×C₁₉	—	2	2	no	—
244	C₂²×C₄×C₁₉	—	2	2	no	—
245	C₂²×C₄×C₁₉	—	2	2	no	—
246	C₂²×C₄×C₁₉	—	4	2	no	—
247	C₂²×C₄×C₁₉	—	4	4	no	—
248	C₂²×C₄×C₁₉	—	4	4	no	—
249	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₁₉	—	2	16	no	—
268	SD₁₆×C₁₉	—	2	16	no	—
269	M₁₆×C₁₉	—	2	8	no	—
270	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
271	C₄⋊C₄×C₁₉	—	2	2	no	—
272	C₄⋊C₄×C₁₉	—	2	2	no	—
273	C₄⋊C₄×C₁₉	—	2	2	no	—
274	C₄⋊C₄×C₁₉	—	2	2	no	—
275	C₄⋊C₄×C₁₉	—	2	2	no	—
276	C₄⋊C₄×C₁₉	—	2	2	no	—
277	C₄⋊C₄×C₁₉	—	2	2	no	—
278	C₄⋊C₄×C₁₉	—	2	2	no	—
279	C₄⋊C₄×C₁₉	—	2	2	no	—
280	C₄⋊C₄×C₁₉	—	2	2	no	—
281	C₄⋊C₄×C₁₉	—	2	4	no	—
282	C₄⋊C₄×C₁₉	—	2	4	no	—
283	C₄⋊C₄×C₁₉	—	2	4	no	—
284	C₄⋊C₄×C₁₉	—	2	4	no	—
285	C₄⋊C₄×C₁₉	—	2	1	no	—
286	C₄⋊C₄×C₁₉	—	2	1	no	—
287	C₄⋊C₄×C₁₉	—	2	2	no	—
288	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
291	C₂²⋊C₄×C₁₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	2	no	—
296	C₂²⋊C₄×C₁₉	—	2	2	no	—
297	C₂²⋊C₄×C₁₉	—	2	2	no	—
298	C₂²⋊C₄×C₁₉	—	2	2	no	—
299	C₄²×C₁₉	—	2	2	no	—
300	C₄²×C₁₉	—	2	2	no	—
301	C₄²×C₁₉	—	2	2	no	—
302	C₄²×C₁₉	—	2	2	no	—
303	C₄²×C₁₉	—	2	2	no	—
304	C₄²×C₁₉	—	2	4	no	—
305	C₄²×C₁₉	—	2	2	no	—
306	C₄²×C₁₉	—	2	4	no	—
307	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
320	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
321	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
322	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
323	#60562	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂³×C₁₉	—	2	4	no	—
325	C₂³×C₁₉	—	2	2	no	—
326	C₂³×C₁₉	—	2	2	no	—
327	C₂³×C₁₉	—	2	2	no	—
328	C₂³×C₁₉	—	4	1	no	—
329	C₂³×C₁₉	—	4	2	no	—
330	C₂³×C₁₉	—	4	2	no	—
331	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
333	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₁₉	—	2	4	no	—
335	Q₈×C₁₉	—	2	2	no	—
336	Q₈×C₁₉	—	2	8	no	—
337	Q₈×C₁₉	—	4	4	no	—
338	Q₈×C₁₉	—	4	4	no	—
339	Q₈×C₁₉	—	4	4	no	—
340	Q₈×C₁₉	C₂×#41	1	4	yes	—
341	D₄×C₁₉	—	2	8	no	—
342	D₄×C₁₉	—	2	4	no	—
343	D₄×C₁₉	—	2	8	no	—
344	D₄×C₁₉	—	2	2	no	—
345	D₄×C₁₉	C₂×#41	1	4	yes	—
346	C₂×C₄×C₁₉	—	2	4	no	—
347	C₂×C₄×C₁₉	—	2	8	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	2	2	no	—
350	C₂×C₄×C₁₉	—	2	2	no	—
351	C₂×C₄×C₁₉	—	2	2	no	—
352	C₂×C₄×C₁₉	—	2	8	no	—
353	C₂×C₄×C₁₉	—	2	2	no	—
354	C₂×C₄×C₁₉	—	2	2	no	—
355	C₂×C₄×C₁₉	—	2	2	no	—
356	C₂×C₄×C₁₉	—	2	2	no	—
357	C₂×C₄×C₁₉	—	2	2	no	—
358	C₂×C₄×C₁₉	—	2	2	no	—
359	C₂×C₄×C₁₉	—	2	2	no	—
360	C₂×C₄×C₁₉	—	2	2	no	—
361	C₂×C₄×C₁₉	—	2	2	no	—
362	C₂×C₄×C₁₉	—	2	2	no	—
363	C₂×C₄×C₁₉	—	2	2	no	—
364	C₂×C₄×C₁₉	—	2	2	no	—
365	C₂×C₄×C₁₉	—	2	4	no	—
366	C₂×C₄×C₁₉	—	2	4	no	—
367	C₂×C₄×C₁₉	—	4	1	no	—
368	C₂×C₄×C₁₉	—	4	1	no	—
369	C₂×C₄×C₁₉	—	4	1	no	—
370	C₂×C₄×C₁₉	—	4	4	no	—
371	C₂×C₄×C₁₉	—	4	2	no	—
372	C₂×C₄×C₁₉	—	4	4	no	—
373	C₂×C₄×C₁₉	—	4	4	no	—
374	C₂×C₄×C₁₉	—	4	2	no	—
375	C₂×C₄×C₁₉	—	4	4	no	—
376	C₂×C₄×C₁₉	—	4	4	no	—
377	C₂×C₄×C₁₉	—	4	4	no	—
378	C₂×C₄×C₁₉	#137	1	4	yes	complemented
379	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
391	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
392	C₈×C₁₉	—	2	8	no	—
393	C₂×#533	C₂×C₁₉	1	1	yes	characteristic, complemented
394	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
395	#3116	C₂×C₁₉	1	4	yes	complemented
396	#3113	C₂×C₁₉	1	2	yes	complemented
397	#3110	C₂×C₁₉	1	2	yes	complemented
398	#3107	C₂×C₁₉	1	4	yes	complemented
399	#3104	C₂×C₁₉	1	2	yes	complemented
400	#3101	C₂×C₁₉	1	2	yes	complemented
401	#3095	C₂×C₁₉	1	2	yes	complemented
402	#3079	C₂×C₁₉	1	2	yes	complemented
403	#3039	C₂×C₁₉	1	2	yes	complemented
404	#3007	C₂×C₁₉	1	2	yes	—
405	C₄×#137	C₂×C₁₉	1	4	yes	complemented
406	#2920	C₂×C₁₉	1	1	yes	characteristic, complemented
407	C₂²×C₁₉	—	2	1	no	—
408	C₂²×C₁₉	—	2	1	no	—
409	C₂²×C₁₉	—	2	1	no	—
410	C₂²×C₁₉	—	2	1	no	—
411	C₂²×C₁₉	—	2	1	no	—
412	C₂²×C₁₉	—	2	4	no	—
413	C₂²×C₁₉	—	2	1	no	—
414	C₂²×C₁₉	—	2	1	no	—
415	C₂²×C₁₉	—	4	4	no	—
416	C₂²×C₁₉	—	4	8	no	—
417	C₂²×C₁₉	—	4	2	no	—
418	C₂²×C₁₉	—	4	2	no	—
419	C₂²×C₁₉	#525	1	2	yes	—
420	C₂²×C₁₉	C₂×#137	1	2	yes	—
421	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₁₉	—	2	1	no	—
423	C₄×C₁₉	—	2	4	no	—
424	C₄×C₁₉	—	2	1	no	—
425	C₄×C₁₉	—	2	1	no	—
426	C₄×C₁₉	—	2	1	no	—
427	C₄×C₁₉	—	2	1	no	—
428	C₄×C₁₉	—	2	1	no	—
429	C₄×C₁₉	—	2	1	no	—
430	C₄×C₁₉	—	4	4	no	—
431	C₄×C₁₉	—	4	2	no	—
432	C₄×C₁₉	—	4	2	no	—
433	C₄×C₁₉	—	4	4	no	—
434	C₄×C₁₉	#525	1	2	yes	—
435	C₄×C₁₉	C₂×#137	1	2	yes	—
436	C₄×C₁₉	C₂×#137	1	2	yes	—
437	C₄×C₁₉	#575	1	2	yes	—
438	C₄×C₁₉	C₂²×#41	1	2	yes	—
439	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
440	C₂×#137	C₂²×C₁₉	1	4	yes	—
441	#533	—	2	1	no	—
442	#533	—	2	1	no	—
443	#533	—	2	1	no	—
444	#533	—	2	1	no	—
445	#533	C₂²×C₁₉	1	2	yes	—
446	#533	C₂²×C₁₉	1	2	yes	—
447	#533	C₂²×C₁₉	1	2	yes	complemented
448	#533	C₂²×C₁₉	1	2	yes	complemented
449	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
450	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
451	C₂×#125	—	2	1	no	—
452	C₂×C₂²⋊Q₈	—	2	1	no	—
453	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
454	C₄×#41	—	2	1	no	—
455	C₄×#41	—	2	1	no	—
456	C₄×#41	—	2	1	no	—
457	C₄×#41	—	2	1	no	—
458	C₄×#41	C₂²×C₁₉	1	2	yes	—
459	C₄×#41	C₂²×C₁₉	1	2	yes	—
460	C₄×#41	C₂²×C₁₉	1	2	yes	—
461	C₄×#41	C₂²×C₁₉	1	2	yes	—
462	C₂×C₄×Q₈	—	2	1	no	—
463	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
464	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
465	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
466	C₂×C₄×D₄	—	2	1	no	—
467	C₂×C₄×D₄	—	2	1	no	—
468	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
470	C₂×#117	—	2	1	no	—
471	C₂×#117	—	2	1	no	—
472	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
473	C₂²×C₄²	—	2	1	no	—
474	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
475	#485	C₂²×C₁₉	1	8	yes	complemented
476	#484	C₂²×C₁₉	1	4	yes	—
477	#483	C₂²×C₁₉	1	4	yes	—
478	#477	C₂²×C₁₉	1	4	yes	complemented
479	#476	C₂²×C₁₉	1	4	yes	complemented
480	#475	C₂²×C₁₉	1	4	yes	complemented
481	#474	C₂²×C₁₉	1	4	yes	complemented
482	#462	C₂²×C₁₉	1	4	yes	complemented
483	#462	C₂²×C₁₉	1	4	yes	complemented
484	#461	C₂²×C₁₉	1	4	yes	complemented
485	#461	C₂²×C₁₉	1	4	yes	complemented
486	#452	C₂²×C₁₉	1	8	yes	—
487	#451	C₂²×C₁₉	1	4	yes	—
488	#450	C₂²×C₁₉	1	4	yes	—
489	#441	C₂²×C₁₉	1	8	yes	complemented
490	#440	C₂²×C₁₉	1	8	yes	complemented
491	C₄×Q₁₆	C₂²×C₁₉	1	8	yes	complemented
492	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	complemented
493	#432	C₂²×C₁₉	1	2	yes	—
494	#432	C₂²×C₁₉	1	2	yes	complemented
495	#431	C₂²×C₁₉	1	2	yes	—
496	#431	C₂²×C₁₉	1	2	yes	complemented
497	#428	C₂²×C₁₉	1	4	yes	complemented
498	#423	C₂²×C₁₉	1	2	yes	complemented
499	#419	C₂²×C₁₉	1	4	yes	complemented
500	#417	C₂²×C₁₉	1	4	yes	—
501	#407	C₂²×C₁₉	1	2	yes	—
502	C₄×M₁₆	C₂²×C₁₉	1	2	yes	complemented
503	C₂×C₁₉	—	2	2	no	—
504	C₂×C₁₉	—	2	2	no	—
505	C₂×C₁₉	—	4	1	no	—
506	C₂×C₁₉	—	4	4	no	—
507	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
508	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
509	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
510	C₂×#41	—	2	8	no	—
511	C₂×#41	—	2	1	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	C₂³×C₁₉	1	2	yes	—
514	C₂×#41	C₂³×C₁₉	1	2	yes	—
515	C₂²×Q₈	—	2	1	no	—
516	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
524	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
526	#137	—	2	16	no	—
527	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	—
528	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
529	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
549	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
561	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
562	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
563	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
564	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
565	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	C₂³×C₁₉	1	2	yes	—
579	C₄×D₄	C₂³×C₁₉	1	2	yes	—
580	C₄×D₄	C₂³×C₁₉	1	2	yes	—
581	C₄×D₄	C₂³×C₁₉	1	2	yes	—
582	#117	—	2	2	no	—
583	#117	—	2	2	no	—
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	#117	—	2	1	no	—
587	#117	—	2	1	no	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	C₂³×C₁₉	1	2	yes	—
593	#117	C₂³×C₁₉	1	2	yes	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
604	C₂×C₂²⋊C₄	—	2	2	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₄²	—	2	1	no	—
609	C₂×C₄²	—	2	2	no	—
610	C₂×C₄²	—	2	1	no	—
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	—	2	2	no	—
613	C₂×C₄²	—	2	2	no	—
614	C₂×C₄²	—	2	2	no	—
615	C₂×C₄²	—	2	2	no	—
616	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
617	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
618	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
619	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
620	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
621	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
628	#107	C₂³×C₁₉	1	8	yes	—
629	#106	C₂³×C₁₉	1	8	yes	—
630	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
631	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
632	#103	C₂³×C₁₉	1	8	yes	—
633	#103	C₂³×C₁₉	1	8	yes	—
634	#103	C₂³×C₁₉	1	8	yes	—
635	#102	C₂³×C₁₉	1	8	yes	—
636	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
637	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
638	#97	C₂³×C₁₉	1	4	yes	—
639	C₄×C₈	C₂³×C₁₉	1	4	yes	—
640	C₁₉	#60562	1	1	yes	characteristic, direct product factor, Sylow
641	C₂⁴	—	2	1	no	—
642	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
643	#41	—	2	8	no	—
644	#41	—	2	8	no	—
645	#41	—	2	4	no	—
646	#41	—	2	4	no	—
647	#41	—	2	4	no	—
648	#41	#41×C₁₉	1	8	yes	—
649	C₂×Q₈	—	2	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	8	no	—
655	C₂×Q₈	—	4	4	no	—
656	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
657	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
658	C₂×D₄	—	2	8	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
664	C₂²×C₄	—	2	8	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	4	no	—
680	C₂²×C₄	—	4	4	no	—
681	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
699	Q₁₆	—	2	16	no	—
700	SD₁₆	—	2	16	no	—
701	M₁₆	—	2	8	no	—
702	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
721	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
741	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
751	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
752	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
753	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
754	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
755	C₂³	—	2	4	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
763	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
764	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
765	Q₈	—	2	4	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	8	no	—
768	Q₈	—	4	4	no	—
769	Q₈	—	4	4	no	—
770	Q₈	—	4	4	no	—
771	Q₈	C₂×#41×C₁₉	1	4	yes	—
772	D₄	—	2	8	no	—
773	D₄	—	2	4	no	—
774	D₄	—	2	8	no	—
775	D₄	—	2	2	no	—
776	D₄	C₂×#41×C₁₉	1	4	yes	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	8	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	8	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	C₁₉×#137	1	4	yes	complemented
810	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
821	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
822	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
823	C₈	—	2	8	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	8	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	C₁₉×#525	1	2	yes	—
837	C₂²	C₂×C₁₉×#137	1	2	yes	—
838	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	2	4	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	4	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	4	no	—
851	C₄	C₁₉×#525	1	2	yes	—
852	C₄	C₂×C₁₉×#137	1	2	yes	—
853	C₄	C₂×C₁₉×#137	1	2	yes	—
854	C₄	C₁₉×#575	1	2	yes	—
855	C₄	C₂²×#41×C₁₉	1	2	yes	—
856	C₂	—	2	2	no	—
857	C₂	—	2	2	no	—
858	C₂	—	4	1	no	—
859	C₂	—	4	4	no	—
860	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
861	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
862	C₂	C₂×C₁₉×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂³×D₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#533	C₂	semidirect
3. C₁₉×#3116	C₂	semidirect
4. C₁₉×#3113	C₂	semidirect
5. C₁₉×#3110	C₂	semidirect
6. C₁₉×#3107	C₂	semidirect
7. C₁₉×#3104	C₂	semidirect
8. C₁₉×#3101	C₂	semidirect
9. C₁₉×#3095	C₂	semidirect
10. C₁₉×#3079	C₂	semidirect
11. C₁₉×#3039	C₂	semidirect
13. C₄×C₁₉×#137	C₂	semidirect
14. C₁₉×#2920	C₂	semidirect
23. C₁₉×#533	C₂²	semidirect
24. C₁₉×#533	C₂²	semidirect
25. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
51. C₁₉×#485	C₂²	semidirect
54. C₁₉×#477	C₂²	semidirect
55. C₁₉×#476	C₂²	semidirect
56. C₁₉×#475	C₂²	semidirect
57. C₁₉×#474	C₂²	semidirect
58. C₁₉×#462	C₂²	semidirect
59. C₁₉×#462	C₂²	semidirect
60. C₁₉×#461	C₂²	semidirect
61. C₁₉×#461	C₂²	semidirect
65. C₁₉×#441	C₂²	semidirect
66. C₁₉×#440	C₂²	semidirect
67. C₄×Q₁₆×C₁₉	C₂²	semidirect
68. C₄×SD₁₆×C₁₉	C₂²	semidirect
70. C₁₉×#432	C₂²	semidirect
72. C₁₉×#431	C₂²	semidirect
73. C₁₉×#428	C₂²	semidirect
74. C₁₉×#423	C₂²	semidirect
75. C₁₉×#419	C₂²	semidirect
78. C₄×M₁₆×C₁₉	C₂²	semidirect
323. #60562	C₁₉	direct (N × H)
378. C₂×C₄×C₁₉	#137	semidirect
393. C₂×#533	C₂×C₁₉	semidirect
395. #3116	C₂×C₁₉	semidirect
396. #3113	C₂×C₁₉	semidirect
397. #3110	C₂×C₁₉	semidirect
398. #3107	C₂×C₁₉	semidirect
399. #3104	C₂×C₁₉	semidirect
400. #3101	C₂×C₁₉	semidirect
401. #3095	C₂×C₁₉	semidirect
402. #3079	C₂×C₁₉	semidirect
403. #3039	C₂×C₁₉	semidirect
405. C₄×#137	C₂×C₁₉	semidirect
406. #2920	C₂×C₁₉	semidirect
447. #533	C₂²×C₁₉	semidirect
448. #533	C₂²×C₁₉	semidirect
449. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
450. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
465. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
475. #485	C₂²×C₁₉	semidirect
478. #477	C₂²×C₁₉	semidirect
479. #476	C₂²×C₁₉	semidirect
480. #475	C₂²×C₁₉	semidirect
481. #474	C₂²×C₁₉	semidirect
482. #462	C₂²×C₁₉	semidirect
483. #462	C₂²×C₁₉	semidirect
484. #461	C₂²×C₁₉	semidirect
485. #461	C₂²×C₁₉	semidirect
489. #441	C₂²×C₁₉	semidirect
490. #440	C₂²×C₁₉	semidirect
491. C₄×Q₁₆	C₂²×C₁₉	semidirect
492. C₄×SD₁₆	C₂²×C₁₉	semidirect
494. #432	C₂²×C₁₉	semidirect
496. #431	C₂²×C₁₉	semidirect
497. #428	C₂²×C₁₉	semidirect
498. #423	C₂²×C₁₉	semidirect
499. #419	C₂²×C₁₉	semidirect
502. C₄×M₁₆	C₂²×C₁₉	semidirect
640. C₁₉	#60562	direct (N × H)
809. C₂×C₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#533	2
C₂×C₄×#41×C₁₉	2
C₁₉×#3116	2
C₁₉×#3113	2
C₁₉×#3110	2
C₁₉×#3107	2
C₁₉×#3104	2
C₁₉×#3101	2
C₁₉×#3095	2
C₁₉×#3079	2
C₁₉×#3039	2
C₁₉×#3007	2
C₄×C₁₉×#137	2
C₁₉×#2920	2
#60562	19

Subgroups — C19×#60562 #18066521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60562 #18066521