Subgroups — C₁₉×#60346 #18066305

Order 4864.

1628 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3531	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2995	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2995	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2994	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2993	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2993	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2992	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2986	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2985	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2969	C₂	1	2	yes	maximal, complemented
12	C₁₉×#2968	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2968	C₂	1	2	yes	maximal, complemented
14	C₁₉×#2967	C₂	1	2	yes	maximal, complemented
15	C₁₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#2962	C₂	1	2	yes	maximal, complemented
18	C₁₉×#2961	C₂	1	2	yes	maximal, complemented
19	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#564	C₄	1	1	yes	characteristic
21	C₁₉×#563	C₄	1	2	yes	—
22	C₁₉×#563	C₄	1	2	yes	—
23	C₁₉×#563	C₄	1	2	yes	—
24	C₁₉×#563	C₄	1	1	yes	characteristic
25	C₁₉×#563	C₄	1	2	yes	—
26	C₁₉×#563	C₄	1	1	yes	characteristic
27	C₁₉×#562	C₄	1	2	yes	—
28	C₁₉×#562	C₄	1	2	yes	—
29	C₁₉×#562	C₄	1	1	yes	characteristic
30	C₁₉×#533	C₂²	1	1	yes	characteristic
31	C₁₉×#533	C₂²	1	2	yes	—
32	C₁₉×#533	C₂²	1	2	yes	—
33	C₁₉×#529	C₂²	1	1	yes	characteristic
34	C₁₉×#529	C₂²	1	1	yes	characteristic
35	C₁₉×#529	C₂²	1	2	yes	—
36	C₁₉×#529	C₂²	1	2	yes	—
37	C₁₉×#529	C₂²	1	2	yes	—
38	C₁₉×#529	C₂²	1	2	yes	—
39	C₁₉×#446	C₂²	1	2	yes	—
40	C₁₉×#446	C₂²	1	2	yes	—
41	C₁₉×#446	C₂²	1	1	yes	characteristic
42	C₁₉×#446	C₂²	1	2	yes	—
43	C₁₉×#446	C₂²	1	2	yes	—
44	C₁₉×#446	C₂²	1	2	yes	—
45	C₁₉×#446	C₂²	1	2	yes	—
46	C₁₉×#446	C₂²	1	2	yes	—
47	C₁₉×#446	C₂²	1	2	yes	—
48	C₁₉×#446	C₂²	1	2	yes	—
49	C₁₉×#446	C₂²	1	2	yes	—
50	C₁₉×#446	C₂²	1	2	yes	—
51	C₁₉×#446	C₂²	1	1	yes	characteristic
52	C₁₉×#446	C₂²	1	2	yes	—
53	C₁₉×#446	C₂²	1	2	yes	—
54	C₁₉×#446	C₂²	1	2	yes	—
55	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
56	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
57	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
59	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
61	C₁₉×#436	C₂²	1	1	yes	characteristic
62	C₁₉×#436	C₂²	1	1	yes	characteristic
63	C₁₉×#436	C₂²	1	2	yes	—
64	C₁₉×#436	C₂²	1	2	yes	—
65	C₁₉×#436	C₂²	1	2	yes	—
66	C₁₉×#436	C₂²	1	2	yes	—
67	C₁₉×#435	C₂²	1	2	yes	—
68	C₁₉×#435	C₂²	1	2	yes	—
69	C₁₉×#435	C₂²	1	2	yes	—
70	C₁₉×#435	C₂²	1	2	yes	—
71	C₁₉×#435	C₂²	1	2	yes	—
72	C₁₉×#435	C₂²	1	2	yes	—
73	C₁₉×#435	C₂²	1	2	yes	—
74	C₁₉×#435	C₂²	1	2	yes	—
75	C₁₉×#435	C₂²	1	2	yes	—
76	C₁₉×#435	C₂²	1	2	yes	—
77	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₁₉	C₂²	1	2	yes	—
79	C₈×D₄×C₁₉	C₂²	1	2	yes	—
80	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
81	C₈×D₄×C₁₉	C₂²	1	2	yes	—
82	C₈×D₄×C₁₉	C₂²	1	2	yes	—
83	C₁₉×#433	C₂²	1	2	yes	—
84	C₁₉×#433	C₂²	1	2	yes	—
85	C₁₉×#433	C₂²	1	2	yes	—
86	C₁₉×#433	C₂²	1	2	yes	—
87	C₁₉×#433	C₂²	1	2	yes	—
88	C₁₉×#433	C₂²	1	2	yes	—
89	C₁₉×#433	C₂²	1	2	yes	—
90	C₁₉×#433	C₂²	1	2	yes	—
91	C₁₉×#433	C₂²	1	2	yes	—
92	C₁₉×#433	C₂²	1	2	yes	—
93	C₁₉×#432	C₂²	1	1	yes	characteristic
94	C₁₉×#432	C₂²	1	1	yes	characteristic
95	C₁₉×#432	C₂²	1	2	yes	—
96	C₁₉×#431	C₂²	1	2	yes	—
97	C₁₉×#431	C₂²	1	2	yes	—
98	C₁₉×#431	C₂²	1	2	yes	—
99	C₁₉×#424	C₂²	1	1	yes	characteristic
100	C₁₉×#424	C₂²	1	1	yes	characteristic
101	C₁₉×#424	C₂²	1	2	yes	—
102	C₁₉×#424	C₂²	1	2	yes	—
103	C₁₉×#424	C₂²	1	2	yes	—
104	C₁₉×#424	C₂²	1	2	yes	—
105	C₁₉×#423	C₂²	1	1	yes	characteristic
106	C₁₉×#423	C₂²	1	2	yes	—
107	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
108	C₁₉×#405	C₂²	1	1	yes	characteristic
109	C₁₉×#405	C₂²	1	1	yes	characteristic
110	C₁₉×#405	C₂²	1	2	yes	—
111	C₁₉×#405	C₂²	1	2	yes	—
112	C₁₉×#405	C₂²	1	2	yes	—
113	C₁₉×#405	C₂²	1	2	yes	—
114	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
115	C₂×C₁₉×#97	C₂²	1	2	yes	—
116	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
117	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
118	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
119	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
121	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
122	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
125	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
127	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
129	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
130	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
131	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
132	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
133	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
134	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
135	C₁₉×#126	C₂×C₄	1	2	yes	—
136	C₁₉×#126	C₂×C₄	1	2	yes	—
137	C₁₉×#126	C₂×C₄	1	2	yes	—
138	C₁₉×#126	C₂×C₄	1	2	yes	—
139	C₁₉×#126	C₂×C₄	1	2	yes	—
140	C₁₉×#126	C₂×C₄	1	2	yes	—
141	C₁₉×#126	C₂×C₄	1	2	yes	—
142	C₁₉×#126	C₂×C₄	1	2	yes	—
143	C₁₉×#126	C₂×C₄	1	2	yes	—
144	C₁₉×#126	C₂×C₄	1	2	yes	—
145	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
146	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
147	C₁₉×#125	C₂×C₄	1	2	yes	—
148	C₁₉×#125	C₂×C₄	1	2	yes	—
149	C₁₉×#125	C₂×C₄	1	2	yes	—
150	C₁₉×#125	C₂×C₄	1	2	yes	—
151	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
152	C₁₉×#125	C₂×C₄	1	2	yes	—
153	C₁₉×#125	C₂×C₄	1	2	yes	—
154	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
155	C₁₉×#125	C₂×C₄	1	2	yes	—
156	C₁₉×#125	C₂×C₄	1	2	yes	—
157	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
158	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
159	C₁₉×#124	C₂×C₄	1	2	yes	—
160	C₁₉×#124	C₂×C₄	1	2	yes	—
161	C₁₉×#124	C₂×C₄	1	2	yes	—
162	C₁₉×#124	C₂×C₄	1	2	yes	—
163	C₁₉×#123	C₂×C₄	1	2	yes	—
164	C₁₉×#123	C₂×C₄	1	2	yes	—
165	C₁₉×#123	C₂×C₄	1	2	yes	—
166	C₁₉×#123	C₂×C₄	1	2	yes	—
167	C₁₉×#123	C₂×C₄	1	2	yes	—
168	C₁₉×#123	C₂×C₄	1	2	yes	—
169	C₁₉×#123	C₂×C₄	1	2	yes	—
170	C₁₉×#123	C₂×C₄	1	2	yes	—
171	C₁₉×#123	C₂×C₄	1	2	yes	—
172	C₁₉×#123	C₂×C₄	1	2	yes	—
173	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
174	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
175	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
176	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
177	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
178	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
179	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
180	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
190	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
191	C₁₉×#121	C₂×C₄	1	2	yes	—
192	C₁₉×#121	C₂×C₄	1	2	yes	—
193	C₁₉×#121	C₂×C₄	1	2	yes	—
194	C₁₉×#121	C₂×C₄	1	2	yes	—
195	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
196	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
197	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
198	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
199	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
201	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
202	C₄×D₄×C₁₉	C₂³	1	2	yes	—
203	C₄×D₄×C₁₉	C₂³	1	2	yes	—
204	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
205	C₄×D₄×C₁₉	C₂³	1	2	yes	—
206	C₄×D₄×C₁₉	C₂³	1	2	yes	—
207	C₁₉×#117	C₂³	1	1	yes	characteristic
208	C₁₉×#117	C₂³	1	1	yes	characteristic
209	C₁₉×#117	C₂³	1	2	yes	—
210	C₁₉×#117	C₂³	1	2	yes	—
211	C₁₉×#117	C₂³	1	2	yes	—
212	C₁₉×#117	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
215	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
216	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
219	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
221	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
222	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
223	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
224	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
225	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
226	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
227	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
228	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
229	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
230	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
231	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
232	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
233	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
234	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
236	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
239	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
240	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
241	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₁₉×#97	C₂³	1	2	yes	—
249	C₁₉×#97	C₂³	1	2	yes	—
250	C₁₉×#97	C₂³	1	2	yes	—
251	C₁₉×#97	C₂³	1	2	yes	—
252	C₁₉×#97	C₂³	1	2	yes	—
253	C₁₉×#97	C₂³	1	2	yes	—
254	C₁₉×#97	C₂³	1	2	yes	—
255	C₁₉×#97	C₂³	1	2	yes	—
256	C₁₉×#97	C₂³	1	2	yes	—
257	C₁₉×#97	C₂³	1	2	yes	—
258	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₉	C₂³	1	2	yes	—
263	C₄×C₈×C₁₉	C₂³	1	2	yes	—
264	C₄×C₈×C₁₉	C₂³	1	2	yes	—
265	C₄×C₈×C₁₉	C₂³	1	2	yes	—
266	C₄×C₈×C₁₉	C₂³	1	2	yes	—
267	C₄×C₈×C₁₉	C₂³	1	2	yes	—
268	C₄×C₈×C₁₉	C₂³	1	2	yes	—
269	C₄×C₈×C₁₉	C₂³	1	2	yes	—
270	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
271	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
272	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
273	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
274	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
275	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
276	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
277	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
278	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
279	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
280	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
281	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
282	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
285	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
286	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
287	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
288	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
291	M₁₆×C₁₉	—	2	4	no	—
292	M₁₆×C₁₉	—	4	1	no	—
293	M₁₆×C₁₉	—	4	2	no	—
294	M₁₆×C₁₉	—	4	2	no	—
295	M₁₆×C₁₉	—	4	2	no	—
296	M₁₆×C₁₉	—	4	1	no	—
297	C₂×C₈×C₁₉	—	2	2	no	—
298	C₂×C₈×C₁₉	—	2	4	no	—
299	C₂×C₈×C₁₉	—	4	2	no	—
300	C₂×C₈×C₁₉	—	4	1	no	—
301	C₂×C₈×C₁₉	—	4	2	no	—
302	C₂×C₈×C₁₉	—	4	2	no	—
303	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
304	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
305	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
306	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
307	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
308	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
310	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
311	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
312	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
314	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
315	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
316	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
317	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
318	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
319	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
320	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
321	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
322	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
323	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
324	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
325	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
326	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
327	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
328	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
329	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
330	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
331	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
332	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
333	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
334	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
335	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
336	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
337	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
338	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
339	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
340	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
341	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
342	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
343	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
344	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
345	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
346	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
347	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
348	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
349	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
350	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
351	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
352	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
353	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
354	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
355	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
356	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
357	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
358	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
359	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
360	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
361	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
362	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
363	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
364	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
365	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
366	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
367	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
368	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
369	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
370	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
371	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
372	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
373	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
374	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
375	C₄²×C₁₉	C₂⁴	1	2	yes	—
376	C₄²×C₁₉	C₂⁴	1	2	yes	—
377	C₄²×C₁₉	C₂⁴	1	2	yes	—
378	C₄²×C₁₉	C₂⁴	1	2	yes	—
379	#60346	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
381	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
382	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
383	Q₈×C₁₉	—	4	2	no	—
384	Q₈×C₁₉	—	4	2	no	—
385	Q₈×C₁₉	—	4	1	no	—
386	Q₈×C₁₉	—	4	2	no	—
387	Q₈×C₁₉	—	4	1	no	—
388	Q₈×C₁₉	—	4	2	no	—
389	D₄×C₁₉	—	4	1	no	—
390	D₄×C₁₉	—	4	2	no	—
391	D₄×C₁₉	—	4	2	no	—
392	D₄×C₁₉	—	4	1	no	—
393	D₄×C₁₉	—	4	2	no	—
394	D₄×C₁₉	—	4	2	no	—
395	C₂×C₄×C₁₉	—	2	1	no	—
396	C₂×C₄×C₁₉	—	2	2	no	—
397	C₂×C₄×C₁₉	—	2	2	no	—
398	C₂×C₄×C₁₉	—	2	2	no	—
399	C₂×C₄×C₁₉	—	2	1	no	—
400	C₂×C₄×C₁₉	—	2	2	no	—
401	C₂×C₄×C₁₉	—	4	1	no	—
402	C₂×C₄×C₁₉	—	4	1	no	—
403	C₂×C₄×C₁₉	—	4	2	no	—
404	C₂×C₄×C₁₉	—	4	2	no	—
405	C₂×C₄×C₁₉	—	4	2	no	—
406	C₂×C₄×C₁₉	—	4	2	no	—
407	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
408	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
409	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
410	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
411	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
412	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
413	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
414	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
417	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
418	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
419	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
420	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
423	C₈×C₁₉	—	2	1	no	—
424	C₈×C₁₉	—	2	2	no	—
425	C₈×C₁₉	—	2	2	no	—
426	C₈×C₁₉	—	2	1	no	—
427	C₈×C₁₉	—	2	2	no	—
428	C₈×C₁₉	—	2	2	no	—
429	C₈×C₁₉	—	2	1	no	—
430	C₈×C₁₉	—	2	2	no	—
431	C₈×C₁₉	—	2	2	no	—
432	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
433	#3531	C₂×C₁₉	1	1	yes	characteristic
434	#2995	C₂×C₁₉	1	1	yes	characteristic, complemented
435	#2995	C₂×C₁₉	1	1	yes	characteristic, complemented
436	#2994	C₂×C₁₉	1	2	yes	complemented
437	#2993	C₂×C₁₉	1	2	yes	complemented
438	#2993	C₂×C₁₉	1	2	yes	complemented
439	#2992	C₂×C₁₉	1	2	yes	complemented
440	#2987	C₂×C₁₉	1	1	yes	characteristic, complemented
441	#2986	C₂×C₁₉	1	2	yes	complemented
442	#2985	C₂×C₁₉	1	2	yes	complemented
443	#2969	C₂×C₁₉	1	2	yes	complemented
444	#2968	C₂×C₁₉	1	2	yes	complemented
445	#2968	C₂×C₁₉	1	2	yes	complemented
446	#2967	C₂×C₁₉	1	2	yes	complemented
447	#2966	C₂×C₁₉	1	1	yes	characteristic, complemented
448	#2966	C₂×C₁₉	1	1	yes	characteristic, complemented
449	#2962	C₂×C₁₉	1	2	yes	complemented
450	#2961	C₂×C₁₉	1	2	yes	complemented
451	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
452	C₂²×C₁₉	—	2	1	no	—
453	C₂²×C₁₉	—	2	2	no	—
454	C₂²×C₁₉	—	2	2	no	—
455	C₂²×C₁₉	—	2	1	no	—
456	C₂²×C₁₉	—	2	1	no	—
457	C₂²×C₁₉	—	2	2	no	—
458	C₂²×C₁₉	—	2	2	no	—
459	C₂²×C₁₉	—	2	2	no	—
460	C₂²×C₁₉	—	2	2	no	—
461	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
462	C₄×C₁₉	—	2	1	no	—
463	C₄×C₁₉	—	2	2	no	—
464	C₄×C₁₉	—	2	2	no	—
465	C₄×C₁₉	—	2	1	no	—
466	C₄×C₁₉	—	2	1	no	—
467	C₄×C₁₉	—	2	2	no	—
468	C₄×C₁₉	—	2	2	no	—
469	C₄×C₁₉	—	2	2	no	—
470	C₄×C₁₉	—	2	2	no	—
471	C₄×C₁₉	—	2	1	no	—
472	C₄×C₁₉	—	2	1	no	—
473	C₄×C₁₉	—	2	2	no	—
474	C₄×C₁₉	—	2	2	no	—
475	C₄×C₁₉	—	2	2	no	—
476	C₄×C₁₉	—	2	2	no	—
477	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
478	C₄×C₁₉	#585	1	1	yes	characteristic
479	#564	C₄×C₁₉	1	1	yes	characteristic
480	#563	C₄×C₁₉	1	2	yes	—
481	#563	C₄×C₁₉	1	2	yes	—
482	#563	C₄×C₁₉	1	2	yes	—
483	#563	C₄×C₁₉	1	1	yes	characteristic
484	#563	C₄×C₁₉	1	2	yes	—
485	#563	C₄×C₁₉	1	1	yes	characteristic
486	#562	C₄×C₁₉	1	2	yes	—
487	#562	C₄×C₁₉	1	2	yes	—
488	#562	C₄×C₁₉	1	1	yes	characteristic
489	#533	C₂²×C₁₉	1	1	yes	characteristic
490	#533	C₂²×C₁₉	1	2	yes	—
491	#533	C₂²×C₁₉	1	2	yes	—
492	#529	C₂²×C₁₉	1	1	yes	characteristic
493	#529	C₂²×C₁₉	1	1	yes	characteristic
494	#529	C₂²×C₁₉	1	2	yes	—
495	#529	C₂²×C₁₉	1	2	yes	—
496	#529	C₂²×C₁₉	1	2	yes	—
497	#529	C₂²×C₁₉	1	2	yes	—
498	#446	C₂²×C₁₉	1	2	yes	—
499	#446	C₂²×C₁₉	1	2	yes	—
500	#446	C₂²×C₁₉	1	1	yes	characteristic
501	#446	C₂²×C₁₉	1	2	yes	—
502	#446	C₂²×C₁₉	1	2	yes	—
503	#446	C₂²×C₁₉	1	2	yes	—
504	#446	C₂²×C₁₉	1	2	yes	—
505	#446	C₂²×C₁₉	1	2	yes	—
506	#446	C₂²×C₁₉	1	2	yes	—
507	#446	C₂²×C₁₉	1	2	yes	—
508	#446	C₂²×C₁₉	1	2	yes	—
509	#446	C₂²×C₁₉	1	2	yes	—
510	#446	C₂²×C₁₉	1	1	yes	characteristic
511	#446	C₂²×C₁₉	1	2	yes	—
512	#446	C₂²×C₁₉	1	2	yes	—
513	#446	C₂²×C₁₉	1	2	yes	—
514	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
515	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
516	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
517	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
518	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
519	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
520	#436	C₂²×C₁₉	1	1	yes	characteristic
521	#436	C₂²×C₁₉	1	1	yes	characteristic
522	#436	C₂²×C₁₉	1	2	yes	—
523	#436	C₂²×C₁₉	1	2	yes	—
524	#436	C₂²×C₁₉	1	2	yes	—
525	#436	C₂²×C₁₉	1	2	yes	—
526	#435	C₂²×C₁₉	1	2	yes	—
527	#435	C₂²×C₁₉	1	2	yes	—
528	#435	C₂²×C₁₉	1	2	yes	—
529	#435	C₂²×C₁₉	1	2	yes	—
530	#435	C₂²×C₁₉	1	2	yes	—
531	#435	C₂²×C₁₉	1	2	yes	—
532	#435	C₂²×C₁₉	1	2	yes	—
533	#435	C₂²×C₁₉	1	2	yes	—
534	#435	C₂²×C₁₉	1	2	yes	—
535	#435	C₂²×C₁₉	1	2	yes	—
536	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
537	C₈×D₄	C₂²×C₁₉	1	2	yes	—
538	C₈×D₄	C₂²×C₁₉	1	2	yes	—
539	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
540	C₈×D₄	C₂²×C₁₉	1	2	yes	—
541	C₈×D₄	C₂²×C₁₉	1	2	yes	—
542	#433	C₂²×C₁₉	1	2	yes	—
543	#433	C₂²×C₁₉	1	2	yes	—
544	#433	C₂²×C₁₉	1	2	yes	—
545	#433	C₂²×C₁₉	1	2	yes	—
546	#433	C₂²×C₁₉	1	2	yes	—
547	#433	C₂²×C₁₉	1	2	yes	—
548	#433	C₂²×C₁₉	1	2	yes	—
549	#433	C₂²×C₁₉	1	2	yes	—
550	#433	C₂²×C₁₉	1	2	yes	—
551	#433	C₂²×C₁₉	1	2	yes	—
552	#432	C₂²×C₁₉	1	1	yes	characteristic
553	#432	C₂²×C₁₉	1	1	yes	characteristic
554	#432	C₂²×C₁₉	1	2	yes	—
555	#431	C₂²×C₁₉	1	2	yes	—
556	#431	C₂²×C₁₉	1	2	yes	—
557	#431	C₂²×C₁₉	1	2	yes	—
558	#424	C₂²×C₁₉	1	1	yes	characteristic
559	#424	C₂²×C₁₉	1	1	yes	characteristic
560	#424	C₂²×C₁₉	1	2	yes	—
561	#424	C₂²×C₁₉	1	2	yes	—
562	#424	C₂²×C₁₉	1	2	yes	—
563	#424	C₂²×C₁₉	1	2	yes	—
564	#423	C₂²×C₁₉	1	1	yes	characteristic
565	#423	C₂²×C₁₉	1	2	yes	—
566	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
567	#405	C₂²×C₁₉	1	1	yes	characteristic
568	#405	C₂²×C₁₉	1	1	yes	characteristic
569	#405	C₂²×C₁₉	1	2	yes	—
570	#405	C₂²×C₁₉	1	2	yes	—
571	#405	C₂²×C₁₉	1	2	yes	—
572	#405	C₂²×C₁₉	1	2	yes	—
573	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
574	C₂×#97	C₂²×C₁₉	1	2	yes	—
575	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
576	C₂×C₁₉	—	4	1	no	—
577	C₂×C₁₉	—	4	2	no	—
578	C₂×C₁₉	—	4	2	no	—
579	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
580	C₂×C₁₉	#3573	1	1	yes	characteristic
581	C₂×C₁₉	#3573	1	1	yes	characteristic
582	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
583	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
584	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
586	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
587	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
588	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
589	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
590	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
591	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
592	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
593	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
594	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
595	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
596	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
597	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
598	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
599	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
600	#126	C₂×C₄×C₁₉	1	2	yes	—
601	#126	C₂×C₄×C₁₉	1	2	yes	—
602	#126	C₂×C₄×C₁₉	1	2	yes	—
603	#126	C₂×C₄×C₁₉	1	2	yes	—
604	#126	C₂×C₄×C₁₉	1	2	yes	—
605	#126	C₂×C₄×C₁₉	1	2	yes	—
606	#126	C₂×C₄×C₁₉	1	2	yes	—
607	#126	C₂×C₄×C₁₉	1	2	yes	—
608	#126	C₂×C₄×C₁₉	1	2	yes	—
609	#126	C₂×C₄×C₁₉	1	2	yes	—
610	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
611	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
612	#125	C₂×C₄×C₁₉	1	2	yes	—
613	#125	C₂×C₄×C₁₉	1	2	yes	—
614	#125	C₂×C₄×C₁₉	1	2	yes	—
615	#125	C₂×C₄×C₁₉	1	2	yes	—
616	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
617	#125	C₂×C₄×C₁₉	1	2	yes	—
618	#125	C₂×C₄×C₁₉	1	2	yes	—
619	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
620	#125	C₂×C₄×C₁₉	1	2	yes	—
621	#125	C₂×C₄×C₁₉	1	2	yes	—
622	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
623	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
624	#124	C₂×C₄×C₁₉	1	2	yes	—
625	#124	C₂×C₄×C₁₉	1	2	yes	—
626	#124	C₂×C₄×C₁₉	1	2	yes	—
627	#124	C₂×C₄×C₁₉	1	2	yes	—
628	#123	C₂×C₄×C₁₉	1	2	yes	—
629	#123	C₂×C₄×C₁₉	1	2	yes	—
630	#123	C₂×C₄×C₁₉	1	2	yes	—
631	#123	C₂×C₄×C₁₉	1	2	yes	—
632	#123	C₂×C₄×C₁₉	1	2	yes	—
633	#123	C₂×C₄×C₁₉	1	2	yes	—
634	#123	C₂×C₄×C₁₉	1	2	yes	—
635	#123	C₂×C₄×C₁₉	1	2	yes	—
636	#123	C₂×C₄×C₁₉	1	2	yes	—
637	#123	C₂×C₄×C₁₉	1	2	yes	—
638	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
639	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
640	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
641	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
642	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
643	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
644	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
645	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
646	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
647	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
648	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
649	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
650	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
651	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
652	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
653	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
654	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
655	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
656	#121	C₂×C₄×C₁₉	1	2	yes	—
657	#121	C₂×C₄×C₁₉	1	2	yes	—
658	#121	C₂×C₄×C₁₉	1	2	yes	—
659	#121	C₂×C₄×C₁₉	1	2	yes	—
660	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
661	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
662	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
663	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
664	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
665	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
666	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
667	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
668	C₄×D₄	C₂³×C₁₉	1	2	yes	—
669	C₄×D₄	C₂³×C₁₉	1	2	yes	—
670	C₄×D₄	C₂³×C₁₉	1	2	yes	—
671	C₄×D₄	C₂³×C₁₉	1	2	yes	—
672	#117	C₂³×C₁₉	1	2	yes	—
673	#117	C₂³×C₁₉	1	2	yes	—
674	#117	C₂³×C₁₉	1	2	yes	—
675	#117	C₂³×C₁₉	1	1	yes	characteristic
676	#117	C₂³×C₁₉	1	2	yes	—
677	#117	C₂³×C₁₉	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
680	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
681	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
682	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
683	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
684	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
685	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
686	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
687	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
688	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
689	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
690	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
691	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
692	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
693	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
694	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
695	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
696	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
697	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
698	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
699	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
700	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
701	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
702	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
703	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
704	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
706	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
707	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
713	#97	C₂³×C₁₉	1	2	yes	—
714	#97	C₂³×C₁₉	1	2	yes	—
715	#97	C₂³×C₁₉	1	2	yes	—
716	#97	C₂³×C₁₉	1	2	yes	—
717	#97	C₂³×C₁₉	1	2	yes	—
718	#97	C₂³×C₁₉	1	2	yes	—
719	#97	C₂³×C₁₉	1	2	yes	—
720	#97	C₂³×C₁₉	1	2	yes	—
721	#97	C₂³×C₁₉	1	2	yes	—
722	#97	C₂³×C₁₉	1	2	yes	—
723	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
724	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
725	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
726	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
727	C₄×C₈	C₂³×C₁₉	1	2	yes	—
728	C₄×C₈	C₂³×C₁₉	1	2	yes	—
729	C₄×C₈	C₂³×C₁₉	1	2	yes	—
730	C₄×C₈	C₂³×C₁₉	1	2	yes	—
731	C₄×C₈	C₂³×C₁₉	1	2	yes	—
732	C₄×C₈	C₂³×C₁₉	1	2	yes	—
733	C₄×C₈	C₂³×C₁₉	1	2	yes	—
734	C₄×C₈	C₂³×C₁₉	1	2	yes	—
735	C₁₉	#60346	1	1	yes	characteristic, direct product factor, Sylow
736	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
737	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
738	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
739	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
740	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
741	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
742	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
743	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
744	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
745	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
746	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
747	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
748	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
749	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
750	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
751	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
752	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
753	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
757	M₁₆	—	2	4	no	—
758	M₁₆	—	4	1	no	—
759	M₁₆	—	4	2	no	—
760	M₁₆	—	4	2	no	—
761	M₁₆	—	4	2	no	—
762	M₁₆	—	4	1	no	—
763	C₂×C₈	—	2	2	no	—
764	C₂×C₈	—	2	4	no	—
765	C₂×C₈	—	4	2	no	—
766	C₂×C₈	—	4	1	no	—
767	C₂×C₈	—	4	2	no	—
768	C₂×C₈	—	4	2	no	—
769	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
770	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
771	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
772	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
773	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
774	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
775	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
776	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
777	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
778	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
780	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
781	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
782	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
784	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
786	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
787	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
788	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
790	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
794	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
795	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
796	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
797	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
800	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
801	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
802	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
803	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
804	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
805	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
806	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
807	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
808	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
809	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
810	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
811	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
812	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
817	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
818	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
831	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
833	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
834	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
835	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
836	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
837	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
838	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
839	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
840	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
841	C₄²	C₂⁴×C₁₉	1	2	yes	—
842	C₄²	C₂⁴×C₁₉	1	2	yes	—
843	C₄²	C₂⁴×C₁₉	1	2	yes	—
844	C₄²	C₂⁴×C₁₉	1	2	yes	—
845	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
846	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
847	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
848	Q₈	—	4	1	no	—
849	Q₈	—	4	1	no	—
850	Q₈	—	4	2	no	—
851	Q₈	—	4	2	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	4	2	no	—
854	D₄	—	4	1	no	—
855	D₄	—	4	1	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
873	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
874	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
875	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
876	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
877	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
878	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
879	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
880	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
881	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
882	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
883	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
884	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
887	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
888	C₈	—	2	1	no	—
889	C₈	—	2	2	no	—
890	C₈	—	2	2	no	—
891	C₈	—	2	1	no	—
892	C₈	—	2	2	no	—
893	C₈	—	2	2	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	2	no	—
896	C₈	—	2	2	no	—
897	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
908	C₄	—	2	1	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	1	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
924	C₄	C₁₉×#585	1	1	yes	characteristic
925	C₂	—	4	1	no	—
926	C₂	—	4	2	no	—
927	C₂	—	4	2	no	—
928	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
929	C₂	C₁₉×#3573	1	1	yes	characteristic
930	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3531	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2995	C₂	semidirect
3. C₁₉×#2995	C₂	semidirect
4. C₁₉×#2994	C₂	semidirect
5. C₁₉×#2993	C₂	semidirect
6. C₁₉×#2993	C₂	semidirect
7. C₁₉×#2992	C₂	semidirect
8. C₁₉×#2987	C₂	semidirect
9. C₁₉×#2986	C₂	semidirect
10. C₁₉×#2985	C₂	semidirect
11. C₁₉×#2969	C₂	semidirect
12. C₁₉×#2968	C₂	semidirect
13. C₁₉×#2968	C₂	semidirect
14. C₁₉×#2967	C₂	semidirect
15. C₁₉×#2966	C₂	semidirect
16. C₁₉×#2966	C₂	semidirect
17. C₁₉×#2962	C₂	semidirect
18. C₁₉×#2961	C₂	semidirect
19. C₁₉×#2960	C₂	semidirect
379. #60346	C₁₉	direct (N × H)
434. #2995	C₂×C₁₉	semidirect
435. #2995	C₂×C₁₉	semidirect
436. #2994	C₂×C₁₉	semidirect
437. #2993	C₂×C₁₉	semidirect
438. #2993	C₂×C₁₉	semidirect
439. #2992	C₂×C₁₉	semidirect
440. #2987	C₂×C₁₉	semidirect
441. #2986	C₂×C₁₉	semidirect
442. #2985	C₂×C₁₉	semidirect
443. #2969	C₂×C₁₉	semidirect
444. #2968	C₂×C₁₉	semidirect
445. #2968	C₂×C₁₉	semidirect
446. #2967	C₂×C₁₉	semidirect
447. #2966	C₂×C₁₉	semidirect
448. #2966	C₂×C₁₉	semidirect
449. #2962	C₂×C₁₉	semidirect
450. #2961	C₂×C₁₉	semidirect
451. #2960	C₂×C₁₉	semidirect
735. C₁₉	#60346	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3531	2
C₁₉×#2995	2
C₁₉×#2994	2
C₁₉×#2993	2
C₁₉×#2992	2
C₁₉×#2987	2
C₁₉×#2986	2
C₁₉×#2985	2
C₁₉×#2969	2
C₁₉×#2968	2
C₁₉×#2967	2
C₁₉×#2966	2
C₁₉×#2962	2
C₁₉×#2961	2
C₁₉×#2960	2
#60346	19

Subgroups — C19×#60346 #18066305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60346 #18066305