Subgroups — C₁₉×#62235 #18068194

Order 4864.

1754 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3384	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3370	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3354	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3350	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3347	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3322	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3318	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3306	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3257	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3244	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3122	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3081	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#563	—	2	1	no	—
21	C₁₉×#562	—	2	1	no	—
22	C₁₉×#559	C₂²	1	1	yes	characteristic
23	C₁₉×#556	C₂²	1	1	yes	characteristic
24	C₁₉×#555	C₂²	1	2	yes	—
25	C₁₉×#554	C₂²	1	2	yes	complemented
26	C₁₉×#553	C₂²	1	2	yes	—
27	C₁₉×#553	C₂²	1	2	yes	complemented
28	C₁₉×#551	—	2	2	no	—
29	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#548	—	2	1	no	—
31	C₁₉×#547	—	2	2	no	—
32	C₁₉×#547	C₂²	1	2	yes	complemented
33	C₁₉×#546	—	2	1	no	—
34	C₁₉×#546	C₂²	1	2	yes	—
35	D₄²×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#544	C₂²	1	2	yes	complemented
37	C₁₉×#542	C₂²	1	2	yes	—
38	C₁₉×#540	C₂²	1	2	yes	complemented
39	C₁₉×#539	—	2	2	no	—
40	C₁₉×#539	—	2	1	no	—
41	C₁₉×#538	—	2	2	no	—
42	C₁₉×#537	—	2	1	no	—
43	C₁₉×#532	C₂²	1	1	yes	characteristic
44	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#529	—	2	1	no	—
46	C₁₉×#529	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₉×#124	—	2	1	no	—
49	C₁₉×#518	C₂²	1	2	yes	—
50	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#501	C₂²	1	2	yes	complemented
52	C₁₉×#501	C₂²	1	2	yes	complemented
53	C₁₉×#498	C₂²	1	2	yes	complemented
54	C₁₉×#490	C₂²	1	2	yes	—
55	C₁₉×#489	C₂²	1	2	yes	complemented
56	C₁₉×#488	C₂²	1	2	yes	complemented
57	C₁₉×#485	C₂²	1	2	yes	complemented
58	C₁₉×#483	C₂²	1	2	yes	complemented
59	C₁₉×#482	C₂²	1	2	yes	—
60	C₁₉×#482	C₂²	1	2	yes	complemented
61	C₁₉×#482	C₂²	1	2	yes	complemented
62	C₁₉×#482	C₂²	1	2	yes	complemented
63	C₁₉×#481	C₂²	1	2	yes	—
64	C₁₉×#481	C₂²	1	2	yes	complemented
65	C₁₉×#480	C₂²	1	2	yes	complemented
66	C₁₉×#479	C₂²	1	2	yes	complemented
67	C₁₉×#479	C₂²	1	2	yes	complemented
68	C₁₉×#478	C₂²	1	2	yes	—
69	C₁₉×#478	C₂²	1	2	yes	—
70	C₁₉×#478	C₂²	1	2	yes	—
71	C₁₉×#478	C₂²	1	2	yes	complemented
72	C₁₉×#478	C₂²	1	2	yes	complemented
73	C₁₉×#478	C₂²	1	2	yes	complemented
74	C₁₉×#476	C₂²	1	2	yes	—
75	C₁₉×#476	C₂²	1	2	yes	complemented
76	C₁₉×#476	C₂²	1	2	yes	complemented
77	C₁₉×#476	C₂²	1	2	yes	complemented
78	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#474	C₂²	1	1	yes	characteristic
80	C₁₉×#474	C₂²	1	2	yes	complemented
81	C₁₉×#474	C₂²	1	2	yes	complemented
82	C₁₉×#469	C₂²	1	2	yes	—
83	C₁₉×#469	C₂²	1	2	yes	complemented
84	C₁₉×#469	C₂²	1	2	yes	complemented
85	C₁₉×#468	C₂²	1	2	yes	complemented
86	C₁₉×#466	C₂²	1	2	yes	—
87	C₁₉×#465	C₂²	1	2	yes	complemented
88	C₁₉×#463	C₂²	1	2	yes	complemented
89	C₁₉×#463	C₂²	1	2	yes	complemented
90	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
91	C₁₉×#459	C₂²	1	2	yes	—
92	C₁₉×#459	C₂²	1	1	yes	characteristic
93	C₁₉×#459	C₂²	1	2	yes	complemented
94	C₁₉×#449	C₂²	1	2	yes	—
95	C₁₉×#447	C₂²	1	2	yes	—
96	C₁₉×#447	C₂²	1	2	yes	—
97	C₁₉×#446	C₂²	1	2	yes	complemented
98	C₁₉×#442	C₂²	1	2	yes	—
99	C₁₉×#442	C₂²	1	2	yes	—
100	C₁₉×#442	C₂²	1	2	yes	complemented
101	C₁₉×#440	C₂²	1	2	yes	complemented
102	C₄×D₈×C₁₉	C₂²	1	2	yes	—
103	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
104	C₁₉×#436	C₂²	1	2	yes	complemented
105	C₁₉×#435	C₂²	1	2	yes	—
106	C₁₉×#435	C₂²	1	2	yes	complemented
107	C₁₉×#433	C₂²	1	2	yes	complemented
108	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
109	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
110	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
111	C₁₉×#428	C₂²	1	2	yes	complemented
112	C₁₉×#427	C₂²	1	2	yes	complemented
113	C₁₉×#424	C₂²	1	2	yes	complemented
114	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
115	C₁₉×#418	C₂²	1	2	yes	—
116	C₁₉×#417	C₂²	1	1	yes	characteristic
117	C₁₉×#417	C₂²	1	1	yes	characteristic
118	C₂×C₁₉×#102	C₂²	1	2	yes	—
119	C₂×#41×C₁₉	—	2	2	no	—
120	C₂×#41×C₁₉	—	2	1	no	—
121	C₂×#41×C₁₉	—	2	1	no	—
122	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₁₉	—	2	1	no	—
124	C₂²×D₄×C₁₉	—	2	1	no	—
125	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
127	C₂×D₈×C₁₉	C₂³	1	2	yes	—
128	C₂×D₈×C₁₉	C₂³	1	2	yes	—
129	C₂×D₈×C₁₉	C₂³	1	2	yes	—
130	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
133	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
134	C₁₉×C₄⋊Q₈	—	2	2	no	—
135	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₉×#127	C₂³	1	1	yes	characteristic
140	C₁₉×#127	C₂³	1	1	yes	characteristic
141	C₁₉×#126	—	2	2	no	—
142	C₁₉×#126	—	2	2	no	—
143	C₁₉×#126	—	2	2	no	—
144	C₁₉×#126	—	2	2	no	—
145	C₁₉×#126	D₄	1	2	yes	—
146	C₁₉×#125	—	2	2	no	—
147	C₁₉×#125	—	2	1	no	—
148	C₁₉×#125	—	2	1	no	—
149	C₁₉×#125	D₄	1	1	yes	characteristic
150	C₁₉×#125	C₂³	1	2	yes	—
151	C₁₉×#125	C₂³	1	2	yes	—
152	C₁₉×#125	C₂³	1	2	yes	—
153	C₁₉×#124	—	2	1	no	—
154	C₁₉×#124	—	2	1	no	—
155	C₁₉×#124	—	2	2	no	—
156	C₁₉×#124	—	2	2	no	—
157	C₁₉×#124	—	2	2	no	—
158	C₁₉×#124	—	2	1	no	—
159	C₁₉×#124	—	2	1	no	—
160	C₁₉×#124	D₄	1	1	yes	characteristic
161	C₁₉×#124	C₂³	1	2	yes	—
162	C₁₉×#123	—	2	2	no	—
163	C₁₉×#123	—	2	2	no	—
164	C₁₉×#123	—	2	2	no	—
165	C₁₉×#123	—	2	2	no	—
166	C₁₉×#123	—	2	2	no	—
167	C₁₉×#123	—	2	2	no	—
168	C₁₉×#123	—	2	2	no	—
169	C₁₉×#123	—	2	2	no	—
170	C₁₉×#123	—	2	2	no	—
171	C₁₉×#123	D₄	1	2	yes	—
172	C₁₉×C₂²⋊Q₈	—	2	2	no	—
173	C₁₉×C₂²⋊Q₈	—	2	1	no	—
174	C₁₉×C₂²⋊Q₈	—	2	2	no	—
175	C₁₉×C₂²⋊Q₈	—	2	2	no	—
176	C₁₉×C₂²⋊Q₈	—	2	2	no	—
177	C₁₉×C₂²⋊Q₈	—	2	2	no	—
178	C₁₉×C₂²⋊Q₈	—	2	2	no	—
179	C₁₉×C₂²⋊Q₈	—	2	2	no	—
180	C₁₉×C₂²⋊Q₈	—	2	2	no	—
181	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
182	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
183	C₁₉×#121	—	2	2	no	—
184	C₁₉×#121	—	2	2	no	—
185	C₁₉×#121	—	2	2	no	—
186	C₁₉×#121	—	2	1	no	—
187	C₁₉×#121	—	2	1	no	—
188	C₁₉×#121	—	2	1	no	—
189	C₁₉×#121	—	2	2	no	—
190	C₁₉×#121	—	2	2	no	—
191	C₁₉×#121	—	2	2	no	—
192	C₁₉×#121	D₄	1	1	yes	characteristic
193	C₁₉×#121	C₂³	1	2	yes	—
194	C₁₉×#121	C₂³	1	2	yes	—
195	C₁₉×#121	C₂³	1	2	yes	—
196	C₁₉×#121	C₂³	1	2	yes	—
197	C₁₉×#121	C₂³	1	2	yes	—
198	C₁₉×#120	—	2	2	no	—
199	C₁₉×#120	—	2	2	no	—
200	C₄×Q₈×C₁₉	—	2	1	no	—
201	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
204	C₄×D₄×C₁₉	—	2	1	no	—
205	C₄×D₄×C₁₉	—	2	1	no	—
206	C₄×D₄×C₁₉	—	2	2	no	—
207	C₄×D₄×C₁₉	—	2	2	no	—
208	C₄×D₄×C₁₉	—	2	1	no	—
209	C₄×D₄×C₁₉	—	2	2	no	—
210	C₄×D₄×C₁₉	—	2	2	no	—
211	C₄×D₄×C₁₉	—	2	1	no	—
212	C₄×D₄×C₁₉	—	2	1	no	—
213	C₄×D₄×C₁₉	C₂³	1	2	yes	—
214	C₄×D₄×C₁₉	C₂³	1	2	yes	—
215	C₄×D₄×C₁₉	C₂³	1	2	yes	—
216	C₄×D₄×C₁₉	C₂³	1	2	yes	—
217	C₄×D₄×C₁₉	C₂³	1	2	yes	—
218	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₁₉	C₂³	1	2	yes	—
221	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₁₉	C₂³	1	2	yes	—
223	C₁₉×#117	—	2	2	no	—
224	C₁₉×#117	—	2	1	no	—
225	C₁₉×#117	C₂³	1	2	yes	—
226	C₁₉×#117	C₂³	1	2	yes	—
227	C₁₉×#117	C₂³	1	1	yes	characteristic
228	C₁₉×#117	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
232	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
236	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
237	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
238	C₂×C₄²×C₁₉	—	2	1	no	—
239	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
240	C₁₉×#107	C₂³	1	2	yes	—
241	C₁₉×#107	C₂³	1	2	yes	—
242	C₁₉×#107	C₂³	1	2	yes	—
243	C₁₉×#107	C₂³	1	2	yes	—
244	C₁₉×#107	C₂³	1	2	yes	—
245	C₁₉×#106	C₂³	1	2	yes	—
246	C₁₉×#106	C₂³	1	2	yes	—
247	C₁₉×#106	C₂³	1	2	yes	—
248	C₁₉×#106	C₂³	1	2	yes	—
249	C₁₉×#106	C₂³	1	2	yes	—
250	C₁₉×#106	C₂³	1	2	yes	—
251	C₁₉×#106	C₂³	1	2	yes	—
252	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₉×#103	C₂³	1	2	yes	—
259	C₁₉×#103	C₂³	1	2	yes	—
260	C₁₉×#103	C₂³	1	2	yes	—
261	C₁₉×#102	C₂³	1	2	yes	—
262	C₁₉×#102	C₂³	1	2	yes	—
263	C₁₉×#102	C₂³	1	2	yes	—
264	C₁₉×#102	C₂³	1	2	yes	—
265	C₁₉×#102	C₂³	1	2	yes	—
266	C₁₉×#102	C₂³	1	2	yes	—
267	C₁₉×#102	C₂³	1	2	yes	—
268	C₁₉×#102	C₂³	1	2	yes	—
269	C₁₉×#102	C₂³	1	2	yes	—
270	C₁₉×#102	C₂³	1	2	yes	—
271	C₁₉×#102	C₂³	1	2	yes	—
272	C₁₉×#102	C₂³	1	2	yes	—
273	C₁₉×#102	C₂³	1	2	yes	—
274	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₉×#97	C₂³	1	2	yes	—
278	C₁₉×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₁₉	C₂³	1	2	yes	—
280	C₂⁴×C₁₉	—	2	2	no	—
281	#41×C₁₉	—	2	2	no	—
282	#41×C₁₉	—	4	1	no	—
283	#41×C₁₉	—	8	2	no	—
284	#41×C₁₉	—	8	4	no	—
285	#41×C₁₉	—	8	2	no	—
286	C₂×Q₈×C₁₉	—	2	1	no	—
287	C₂×Q₈×C₁₉	—	2	2	no	—
288	C₂×Q₈×C₁₉	—	2	2	no	—
289	C₂×Q₈×C₁₉	—	2	1	no	—
290	C₂×Q₈×C₁₉	—	8	2	no	—
291	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
293	C₂×D₄×C₁₉	—	2	4	no	—
294	C₂×D₄×C₁₉	—	2	1	no	—
295	C₂×D₄×C₁₉	—	2	2	no	—
296	C₂×D₄×C₁₉	—	2	2	no	—
297	C₂×D₄×C₁₉	—	2	2	no	—
298	C₂×D₄×C₁₉	—	2	2	no	—
299	C₂×D₄×C₁₉	—	2	2	no	—
300	C₂×D₄×C₁₉	—	2	2	no	—
301	C₂×D₄×C₁₉	—	2	1	no	—
302	C₂×D₄×C₁₉	—	2	1	no	—
303	C₂×D₄×C₁₉	—	2	1	no	—
304	C₂×D₄×C₁₉	—	2	1	no	—
305	C₂×D₄×C₁₉	—	4	2	no	—
306	C₂×D₄×C₁₉	—	8	2	no	—
307	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
309	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
310	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
311	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₉	—	2	1	no	—
313	C₂²×C₄×C₁₉	—	2	1	no	—
314	C₂²×C₄×C₁₉	—	2	2	no	—
315	C₂²×C₄×C₁₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
328	SD₁₆×C₁₉	—	4	2	no	—
329	D₈×C₁₉	—	2	4	no	—
330	D₈×C₁₉	—	4	2	no	—
331	D₈×C₁₉	—	4	2	no	—
332	M₁₆×C₁₉	—	4	1	no	—
333	M₁₆×C₁₉	—	4	2	no	—
334	M₁₆×C₁₉	—	4	1	no	—
335	C₂×C₈×C₁₉	—	4	2	no	—
336	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
337	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
338	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
339	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₁₉	—	2	2	no	—
341	C₄⋊C₄×C₁₉	—	2	2	no	—
342	C₄⋊C₄×C₁₉	—	2	2	no	—
343	C₄⋊C₄×C₁₉	—	2	2	no	—
344	C₄⋊C₄×C₁₉	—	2	2	no	—
345	C₄⋊C₄×C₁₉	—	2	2	no	—
346	C₄⋊C₄×C₁₉	—	2	1	no	—
347	C₄⋊C₄×C₁₉	—	2	2	no	—
348	C₄⋊C₄×C₁₉	—	2	1	no	—
349	C₄⋊C₄×C₁₉	—	2	1	no	—
350	C₄⋊C₄×C₁₉	—	2	1	no	—
351	C₄⋊C₄×C₁₉	—	2	2	no	—
352	C₄⋊C₄×C₁₉	—	2	1	no	—
353	C₄⋊C₄×C₁₉	—	2	1	no	—
354	C₄⋊C₄×C₁₉	—	2	2	no	—
355	C₄⋊C₄×C₁₉	—	2	2	no	—
356	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
368	C₂²⋊C₄×C₁₉	—	2	2	no	—
369	C₂²⋊C₄×C₁₉	—	2	2	no	—
370	C₂²⋊C₄×C₁₉	—	2	1	no	—
371	C₂²⋊C₄×C₁₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₉	—	2	1	no	—
373	C₂²⋊C₄×C₁₉	—	2	2	no	—
374	C₂²⋊C₄×C₁₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₉	—	2	2	no	—
378	C₂²⋊C₄×C₁₉	—	2	1	no	—
379	C₂²⋊C₄×C₁₉	—	2	2	no	—
380	C₂²⋊C₄×C₁₉	—	2	2	no	—
381	C₂²⋊C₄×C₁₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₉	—	2	2	no	—
383	C₂²⋊C₄×C₁₉	—	2	2	no	—
384	C₂²⋊C₄×C₁₉	—	2	2	no	—
385	C₂²⋊C₄×C₁₉	—	2	2	no	—
386	C₂²⋊C₄×C₁₉	—	2	2	no	—
387	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
392	C₄²×C₁₉	—	2	1	no	—
393	C₄²×C₁₉	—	2	1	no	—
394	C₄²×C₁₉	—	2	1	no	—
395	C₄²×C₁₉	—	2	2	no	—
396	C₄²×C₁₉	—	2	2	no	—
397	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
400	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
401	C₄²×C₁₉	C₂⁴	1	2	yes	—
402	#62235	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₁₉	—	2	1	no	—
404	C₂³×C₁₉	—	2	2	no	—
405	C₂³×C₁₉	—	2	2	no	—
406	C₂³×C₁₉	—	4	4	no	—
407	C₂³×C₁₉	—	8	2	no	—
408	C₂³×C₁₉	—	8	2	no	—
409	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
410	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
411	Q₈×C₁₉	—	2	1	no	—
412	Q₈×C₁₉	—	2	1	no	—
413	Q₈×C₁₉	—	4	1	no	—
414	Q₈×C₁₉	—	4	2	no	—
415	Q₈×C₁₉	—	8	2	no	—
416	Q₈×C₁₉	—	8	1	no	—
417	Q₈×C₁₉	—	8	2	no	—
418	D₄×C₁₉	—	2	2	no	—
419	D₄×C₁₉	—	2	2	no	—
420	D₄×C₁₉	—	2	1	no	—
421	D₄×C₁₉	—	2	2	no	—
422	D₄×C₁₉	—	2	2	no	—
423	D₄×C₁₉	—	4	1	no	—
424	D₄×C₁₉	—	4	2	no	—
425	D₄×C₁₉	—	4	4	no	—
426	D₄×C₁₉	—	4	2	no	—
427	D₄×C₁₉	—	4	2	no	—
428	D₄×C₁₉	—	4	4	no	—
429	D₄×C₁₉	—	8	1	no	—
430	D₄×C₁₉	—	8	1	no	—
431	D₄×C₁₉	—	8	1	no	—
432	D₄×C₁₉	—	8	2	no	—
433	D₄×C₁₉	—	8	2	no	—
434	D₄×C₁₉	—	8	2	no	—
435	D₄×C₁₉	—	8	2	no	—
436	D₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
437	C₂×C₄×C₁₉	—	2	2	no	—
438	C₂×C₄×C₁₉	—	2	1	no	—
439	C₂×C₄×C₁₉	—	2	2	no	—
440	C₂×C₄×C₁₉	—	2	1	no	—
441	C₂×C₄×C₁₉	—	2	1	no	—
442	C₂×C₄×C₁₉	—	2	1	no	—
443	C₂×C₄×C₁₉	—	2	1	no	—
444	C₂×C₄×C₁₉	—	2	2	no	—
445	C₂×C₄×C₁₉	—	2	2	no	—
446	C₂×C₄×C₁₉	—	2	2	no	—
447	C₂×C₄×C₁₉	—	2	2	no	—
448	C₂×C₄×C₁₉	—	4	1	no	—
449	C₂×C₄×C₁₉	—	4	1	no	—
450	C₂×C₄×C₁₉	—	4	2	no	—
451	C₂×C₄×C₁₉	—	4	2	no	—
452	C₂×C₄×C₁₉	—	4	2	no	—
453	C₂×C₄×C₁₉	—	8	1	no	—
454	C₂×C₄×C₁₉	—	8	2	no	—
455	C₂×C₄×C₁₉	—	8	2	no	—
456	C₂×C₄×C₁₉	—	8	2	no	—
457	C₂×C₄×C₁₉	—	8	2	no	—
458	C₂×C₄×C₁₉	—	8	2	no	—
459	C₂×C₄×C₁₉	—	8	2	no	—
460	C₂×C₄×C₁₉	—	8	1	no	—
461	C₂×C₄×C₁₉	—	8	2	no	—
462	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
471	C₈×C₁₉	—	2	2	no	—
472	C₈×C₁₉	—	2	2	no	—
473	C₈×C₁₉	—	2	2	no	—
474	C₈×C₁₉	—	2	2	no	—
475	#3559	C₂×C₁₉	1	1	yes	characteristic, complemented
476	#3514	C₂×C₁₉	1	1	yes	characteristic, complemented
477	#3384	C₂×C₁₉	1	2	yes	complemented
478	#3370	C₂×C₁₉	1	2	yes	complemented
479	#3354	C₂×C₁₉	1	2	yes	complemented
480	#3350	C₂×C₁₉	1	2	yes	complemented
481	#3347	C₂×C₁₉	1	2	yes	complemented
482	#3322	C₂×C₁₉	1	2	yes	complemented
483	#3318	C₂×C₁₉	1	2	yes	complemented
484	#3306	C₂×C₁₉	1	2	yes	complemented
485	#3257	C₂×C₁₉	1	2	yes	complemented
486	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
487	#3244	C₂×C₁₉	1	2	yes	complemented
488	#3234	C₂×C₁₉	1	1	yes	characteristic, complemented
489	#3122	C₂×C₁₉	1	2	yes	complemented
490	#3115	C₂×C₁₉	1	1	yes	characteristic, complemented
491	#3081	C₂×C₁₉	1	2	yes	complemented
492	#3080	C₂×C₁₉	1	1	yes	characteristic, complemented
493	#2995	C₂×C₁₉	1	1	yes	characteristic, complemented
494	C₂²×C₁₉	—	2	1	no	—
495	C₂²×C₁₉	—	2	1	no	—
496	C₂²×C₁₉	—	2	2	no	—
497	C₂²×C₁₉	—	2	2	no	—
498	C₂²×C₁₉	—	2	1	no	—
499	C₂²×C₁₉	—	2	2	no	—
500	C₂²×C₁₉	—	2	2	no	—
501	C₂²×C₁₉	—	4	1	no	—
502	C₂²×C₁₉	—	4	1	no	—
503	C₂²×C₁₉	—	4	2	no	—
504	C₂²×C₁₉	—	4	2	no	—
505	C₂²×C₁₉	—	4	2	no	—
506	C₂²×C₁₉	—	4	2	no	—
507	C₂²×C₁₉	—	4	2	no	—
508	C₂²×C₁₉	—	4	2	no	—
509	C₂²×C₁₉	—	16	4	no	—
510	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₁₉	—	2	1	no	—
512	C₄×C₁₉	—	2	1	no	—
513	C₄×C₁₉	—	2	1	no	—
514	C₄×C₁₉	—	2	1	no	—
515	C₄×C₁₉	—	2	2	no	—
516	C₄×C₁₉	—	2	2	no	—
517	C₄×C₁₉	—	2	1	no	—
518	C₄×C₁₉	—	2	2	no	—
519	C₄×C₁₉	—	4	2	no	—
520	C₄×C₁₉	—	4	1	no	—
521	C₄×C₁₉	—	4	1	no	—
522	C₄×C₁₉	—	4	2	no	—
523	C₄×C₁₉	—	4	2	no	—
524	C₄×C₁₉	—	4	2	no	—
525	C₄×C₁₉	—	4	1	no	—
526	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	C₄×C₁₉	#585	1	1	yes	characteristic
528	#563	—	2	1	no	—
529	#562	—	2	1	no	—
530	#559	C₂²×C₁₉	1	1	yes	characteristic
531	#556	C₂²×C₁₉	1	1	yes	characteristic
532	#555	C₂²×C₁₉	1	2	yes	—
533	#554	C₂²×C₁₉	1	2	yes	complemented
534	#553	C₂²×C₁₉	1	2	yes	—
535	#553	C₂²×C₁₉	1	2	yes	complemented
536	#551	—	2	2	no	—
537	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
538	#548	—	2	1	no	—
539	#547	—	2	2	no	—
540	#547	C₂²×C₁₉	1	2	yes	complemented
541	#546	—	2	1	no	—
542	#546	C₂²×C₁₉	1	2	yes	—
543	D₄²	C₂²×C₁₉	1	1	yes	characteristic
544	#544	C₂²×C₁₉	1	2	yes	complemented
545	#542	C₂²×C₁₉	1	2	yes	—
546	#540	C₂²×C₁₉	1	2	yes	complemented
547	#539	—	2	2	no	—
548	#539	—	2	1	no	—
549	#538	—	2	2	no	—
550	#537	—	2	1	no	—
551	#532	C₂²×C₁₉	1	1	yes	characteristic
552	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
553	#529	—	2	1	no	—
554	#529	C₂²×C₁₉	1	1	yes	characteristic
555	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
556	C₂×#124	—	2	1	no	—
557	#518	C₂²×C₁₉	1	2	yes	—
558	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
559	#501	C₂²×C₁₉	1	2	yes	complemented
560	#501	C₂²×C₁₉	1	2	yes	complemented
561	#498	C₂²×C₁₉	1	2	yes	complemented
562	#490	C₂²×C₁₉	1	2	yes	—
563	#489	C₂²×C₁₉	1	2	yes	complemented
564	#488	C₂²×C₁₉	1	2	yes	complemented
565	#485	C₂²×C₁₉	1	2	yes	complemented
566	#483	C₂²×C₁₉	1	2	yes	complemented
567	#482	C₂²×C₁₉	1	2	yes	—
568	#482	C₂²×C₁₉	1	2	yes	complemented
569	#482	C₂²×C₁₉	1	2	yes	complemented
570	#482	C₂²×C₁₉	1	2	yes	complemented
571	#481	C₂²×C₁₉	1	2	yes	—
572	#481	C₂²×C₁₉	1	2	yes	complemented
573	#480	C₂²×C₁₉	1	2	yes	complemented
574	#479	C₂²×C₁₉	1	2	yes	complemented
575	#479	C₂²×C₁₉	1	2	yes	complemented
576	#478	C₂²×C₁₉	1	2	yes	—
577	#478	C₂²×C₁₉	1	2	yes	—
578	#478	C₂²×C₁₉	1	2	yes	—
579	#478	C₂²×C₁₉	1	2	yes	complemented
580	#478	C₂²×C₁₉	1	2	yes	complemented
581	#478	C₂²×C₁₉	1	2	yes	complemented
582	#476	C₂²×C₁₉	1	2	yes	—
583	#476	C₂²×C₁₉	1	2	yes	complemented
584	#476	C₂²×C₁₉	1	2	yes	complemented
585	#476	C₂²×C₁₉	1	2	yes	complemented
586	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
587	#474	C₂²×C₁₉	1	1	yes	characteristic
588	#474	C₂²×C₁₉	1	2	yes	complemented
589	#474	C₂²×C₁₉	1	2	yes	complemented
590	#469	C₂²×C₁₉	1	2	yes	—
591	#469	C₂²×C₁₉	1	2	yes	complemented
592	#469	C₂²×C₁₉	1	2	yes	complemented
593	#468	C₂²×C₁₉	1	2	yes	complemented
594	#466	C₂²×C₁₉	1	2	yes	—
595	#465	C₂²×C₁₉	1	2	yes	complemented
596	#463	C₂²×C₁₉	1	2	yes	complemented
597	#463	C₂²×C₁₉	1	2	yes	complemented
598	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
599	#459	C₂²×C₁₉	1	2	yes	—
600	#459	C₂²×C₁₉	1	1	yes	characteristic
601	#459	C₂²×C₁₉	1	2	yes	complemented
602	#449	C₂²×C₁₉	1	2	yes	—
603	#447	C₂²×C₁₉	1	2	yes	—
604	#447	C₂²×C₁₉	1	2	yes	—
605	#446	C₂²×C₁₉	1	2	yes	complemented
606	#442	C₂²×C₁₉	1	2	yes	—
607	#442	C₂²×C₁₉	1	2	yes	—
608	#442	C₂²×C₁₉	1	2	yes	complemented
609	#440	C₂²×C₁₉	1	2	yes	complemented
610	C₄×D₈	C₂²×C₁₉	1	2	yes	—
611	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
612	#436	C₂²×C₁₉	1	2	yes	complemented
613	#435	C₂²×C₁₉	1	2	yes	—
614	#435	C₂²×C₁₉	1	2	yes	complemented
615	#433	C₂²×C₁₉	1	2	yes	complemented
616	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
617	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
618	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
619	#428	C₂²×C₁₉	1	2	yes	complemented
620	#427	C₂²×C₁₉	1	2	yes	complemented
621	#424	C₂²×C₁₉	1	2	yes	complemented
622	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
623	#418	C₂²×C₁₉	1	2	yes	—
624	#417	C₂²×C₁₉	1	1	yes	characteristic
625	#417	C₂²×C₁₉	1	1	yes	characteristic
626	C₂×#102	C₂²×C₁₉	1	2	yes	—
627	C₂×C₁₉	—	4	1	no	—
628	C₂×C₁₉	—	4	2	no	—
629	C₂×C₁₉	—	4	2	no	—
630	C₂×C₁₉	—	8	2	no	—
631	C₂×C₁₉	—	8	2	no	—
632	C₂×C₁₉	#3489	1	1	yes	characteristic
633	C₂×C₁₉	#3585	1	1	yes	characteristic
634	C₂×C₁₉	#3585	1	1	yes	characteristic
635	C₂×#41	—	2	2	no	—
636	C₂×#41	—	2	1	no	—
637	C₂×#41	—	2	1	no	—
638	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
639	C₂²×Q₈	—	2	1	no	—
640	C₂²×D₄	—	2	1	no	—
641	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
643	C₂×D₈	C₂³×C₁₉	1	2	yes	—
644	C₂×D₈	C₂³×C₁₉	1	2	yes	—
645	C₂×D₈	C₂³×C₁₉	1	2	yes	—
646	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
647	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
648	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
649	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
654	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
655	#127	C₂³×C₁₉	1	1	yes	characteristic
656	#127	C₂³×C₁₉	1	1	yes	characteristic
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	D₄×C₁₉	1	2	yes	—
662	#125	—	2	2	no	—
663	#125	—	2	1	no	—
664	#125	—	2	1	no	—
665	#125	D₄×C₁₉	1	1	yes	characteristic
666	#125	C₂³×C₁₉	1	2	yes	—
667	#125	C₂³×C₁₉	1	2	yes	—
668	#125	C₂³×C₁₉	1	2	yes	—
669	#124	—	2	1	no	—
670	#124	—	2	1	no	—
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	—	2	2	no	—
674	#124	—	2	1	no	—
675	#124	—	2	1	no	—
676	#124	D₄×C₁₉	1	1	yes	characteristic
677	#124	C₂³×C₁₉	1	2	yes	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	D₄×C₁₉	1	2	yes	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	1	no	—
703	#121	—	2	1	no	—
704	#121	—	2	1	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	D₄×C₁₉	1	1	yes	characteristic
709	#121	C₂³×C₁₉	1	2	yes	—
710	#121	C₂³×C₁₉	1	2	yes	—
711	#121	C₂³×C₁₉	1	2	yes	—
712	#121	C₂³×C₁₉	1	2	yes	—
713	#121	C₂³×C₁₉	1	2	yes	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₁₉	1	2	yes	—
732	C₄×D₄	C₂³×C₁₉	1	2	yes	—
733	C₄×D₄	C₂³×C₁₉	1	2	yes	—
734	C₄×D₄	C₂³×C₁₉	1	2	yes	—
735	C₄×D₄	C₂³×C₁₉	1	2	yes	—
736	C₄×D₄	C₂³×C₁₉	1	2	yes	—
737	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
738	C₄×D₄	C₂³×C₁₉	1	2	yes	—
739	#117	—	2	2	no	—
740	#117	—	2	1	no	—
741	#117	C₂³×C₁₉	1	1	yes	characteristic
742	#117	C₂³×C₁₉	1	2	yes	—
743	#117	C₂³×C₁₉	1	2	yes	—
744	#117	C₂³×C₁₉	1	2	yes	—
745	C₂×C₄⋊C₄	—	2	1	no	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	2	no	—
748	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
751	C₂×C₂²⋊C₄	—	2	2	no	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₄²	—	2	1	no	—
755	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
756	#107	C₂³×C₁₉	1	2	yes	—
757	#107	C₂³×C₁₉	1	2	yes	—
758	#107	C₂³×C₁₉	1	2	yes	—
759	#107	C₂³×C₁₉	1	2	yes	—
760	#107	C₂³×C₁₉	1	2	yes	—
761	#106	C₂³×C₁₉	1	2	yes	—
762	#106	C₂³×C₁₉	1	2	yes	—
763	#106	C₂³×C₁₉	1	2	yes	—
764	#106	C₂³×C₁₉	1	2	yes	—
765	#106	C₂³×C₁₉	1	2	yes	—
766	#106	C₂³×C₁₉	1	2	yes	—
767	#106	C₂³×C₁₉	1	2	yes	—
768	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
769	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
770	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
772	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
773	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
774	#103	C₂³×C₁₉	1	2	yes	—
775	#103	C₂³×C₁₉	1	2	yes	—
776	#103	C₂³×C₁₉	1	2	yes	—
777	#102	C₂³×C₁₉	1	2	yes	—
778	#102	C₂³×C₁₉	1	2	yes	—
779	#102	C₂³×C₁₉	1	2	yes	—
780	#102	C₂³×C₁₉	1	2	yes	—
781	#102	C₂³×C₁₉	1	2	yes	—
782	#102	C₂³×C₁₉	1	2	yes	—
783	#102	C₂³×C₁₉	1	2	yes	—
784	#102	C₂³×C₁₉	1	2	yes	—
785	#102	C₂³×C₁₉	1	2	yes	—
786	#102	C₂³×C₁₉	1	2	yes	—
787	#102	C₂³×C₁₉	1	2	yes	—
788	#102	C₂³×C₁₉	1	2	yes	—
789	#102	C₂³×C₁₉	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
793	#97	C₂³×C₁₉	1	2	yes	—
794	#97	C₂³×C₁₉	1	2	yes	—
795	C₄×C₈	C₂³×C₁₉	1	2	yes	—
796	C₁₉	#62235	1	1	yes	characteristic, direct product factor, Sylow
797	C₂⁴	—	2	2	no	—
798	#41	—	2	2	no	—
799	#41	—	4	1	no	—
800	#41	—	8	2	no	—
801	#41	—	8	4	no	—
802	#41	—	8	2	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	8	2	no	—
808	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
809	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	8	2	no	—
824	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
825	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
826	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
827	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
828	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
842	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
845	SD₁₆	—	4	2	no	—
846	D₈	—	2	4	no	—
847	D₈	—	4	2	no	—
848	D₈	—	4	2	no	—
849	M₁₆	—	4	1	no	—
850	M₁₆	—	4	2	no	—
851	M₁₆	—	4	1	no	—
852	C₂×C₈	—	4	2	no	—
853	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
854	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
855	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
856	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
874	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
875	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
876	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
879	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
884	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	1	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
908	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
909	C₄²	—	2	1	no	—
910	C₄²	—	2	1	no	—
911	C₄²	—	2	1	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
915	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
916	C₄²	C₂⁴×C₁₉	1	2	yes	—
917	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
918	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	4	4	no	—
923	C₂³	—	8	2	no	—
924	C₂³	—	8	2	no	—
925	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
926	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
927	Q₈	—	2	1	no	—
928	Q₈	—	2	1	no	—
929	Q₈	—	4	1	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	8	2	no	—
932	Q₈	—	8	1	no	—
933	Q₈	—	8	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	2	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	4	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	1	no	—
947	D₄	—	8	1	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	2	no	—
950	D₄	—	8	2	no	—
951	D₄	—	8	2	no	—
952	D₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	1	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	1	no	—
978	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
984	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
985	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
986	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	—	2	2	no	—
990	C₈	—	2	2	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	16	4	no	—
1007	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1008	C₄	—	2	1	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
1024	C₄	C₁₉×#585	1	1	yes	characteristic
1025	C₂	—	4	2	no	—
1026	C₂	—	4	1	no	—
1027	C₂	—	4	2	no	—
1028	C₂	—	8	2	no	—
1029	C₂	—	8	2	no	—
1030	C₂	C₁₉×#3489	1	1	yes	characteristic
1031	C₂	C₁₉×#3585	1	1	yes	characteristic
1032	C₂	C₁₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3559	C₂	semidirect
2. C₁₉×#3514	C₂	semidirect
3. C₁₉×#3384	C₂	semidirect
4. C₁₉×#3370	C₂	semidirect
5. C₁₉×#3354	C₂	semidirect
6. C₁₉×#3350	C₂	semidirect
7. C₁₉×#3347	C₂	semidirect
8. C₁₉×#3322	C₂	semidirect
9. C₁₉×#3318	C₂	semidirect
10. C₁₉×#3306	C₂	semidirect
11. C₁₉×#3257	C₂	semidirect
12. C₁₉×#3253	C₂	semidirect
13. C₁₉×#3244	C₂	semidirect
14. C₁₉×#3234	C₂	semidirect
15. C₁₉×#3122	C₂	semidirect
16. C₁₉×#3115	C₂	semidirect
17. C₁₉×#3081	C₂	semidirect
18. C₁₉×#3080	C₂	semidirect
19. C₁₉×#2995	C₂	semidirect
25. C₁₉×#554	C₂²	semidirect
27. C₁₉×#553	C₂²	semidirect
32. C₁₉×#547	C₂²	semidirect
36. C₁₉×#544	C₂²	semidirect
38. C₁₉×#540	C₂²	semidirect
44. C₁₉×#532	C₂²	semidirect
47. C₂×C₁₉×#125	C₂²	semidirect
51. C₁₉×#501	C₂²	semidirect
52. C₁₉×#501	C₂²	semidirect
53. C₁₉×#498	C₂²	semidirect
55. C₁₉×#489	C₂²	semidirect
56. C₁₉×#488	C₂²	semidirect
57. C₁₉×#485	C₂²	semidirect
58. C₁₉×#483	C₂²	semidirect
60. C₁₉×#482	C₂²	semidirect
61. C₁₉×#482	C₂²	semidirect
62. C₁₉×#482	C₂²	semidirect
64. C₁₉×#481	C₂²	semidirect
65. C₁₉×#480	C₂²	semidirect
66. C₁₉×#479	C₂²	semidirect
67. C₁₉×#479	C₂²	semidirect
71. C₁₉×#478	C₂²	semidirect
72. C₁₉×#478	C₂²	semidirect
73. C₁₉×#478	C₂²	semidirect
75. C₁₉×#476	C₂²	semidirect
76. C₁₉×#476	C₂²	semidirect
77. C₁₉×#476	C₂²	semidirect
78. C₁₉×#475	C₂²	semidirect
80. C₁₉×#474	C₂²	semidirect
81. C₁₉×#474	C₂²	semidirect
83. C₁₉×#469	C₂²	semidirect
84. C₁₉×#469	C₂²	semidirect
85. C₁₉×#468	C₂²	semidirect
87. C₁₉×#465	C₂²	semidirect
88. C₁₉×#463	C₂²	semidirect
89. C₁₉×#463	C₂²	semidirect
90. C₁₉×#460	C₂²	semidirect
93. C₁₉×#459	C₂²	semidirect
97. C₁₉×#446	C₂²	semidirect
100. C₁₉×#442	C₂²	semidirect
101. C₁₉×#440	C₂²	semidirect
103. C₄×D₈×C₁₉	C₂²	semidirect
104. C₁₉×#436	C₂²	semidirect
106. C₁₉×#435	C₂²	semidirect
107. C₁₉×#433	C₂²	semidirect
108. C₁₉×#432	C₂²	semidirect
109. C₁₉×#428	C₂²	semidirect
110. C₁₉×#428	C₂²	semidirect
111. C₁₉×#428	C₂²	semidirect
112. C₁₉×#427	C₂²	semidirect
113. C₁₉×#424	C₂²	semidirect
114. C₁₉×#423	C₂²	semidirect
402. #62235	C₁₉	direct (N × H)
475. #3559	C₂×C₁₉	semidirect
476. #3514	C₂×C₁₉	semidirect
477. #3384	C₂×C₁₉	semidirect
478. #3370	C₂×C₁₉	semidirect
479. #3354	C₂×C₁₉	semidirect
480. #3350	C₂×C₁₉	semidirect
481. #3347	C₂×C₁₉	semidirect
482. #3322	C₂×C₁₉	semidirect
483. #3318	C₂×C₁₉	semidirect
484. #3306	C₂×C₁₉	semidirect
485. #3257	C₂×C₁₉	semidirect
486. #3253	C₂×C₁₉	semidirect
487. #3244	C₂×C₁₉	semidirect
488. #3234	C₂×C₁₉	semidirect
489. #3122	C₂×C₁₉	semidirect
490. #3115	C₂×C₁₉	semidirect
491. #3081	C₂×C₁₉	semidirect
492. #3080	C₂×C₁₉	semidirect
493. #2995	C₂×C₁₉	semidirect
533. #554	C₂²×C₁₉	semidirect
535. #553	C₂²×C₁₉	semidirect
540. #547	C₂²×C₁₉	semidirect
544. #544	C₂²×C₁₉	semidirect
546. #540	C₂²×C₁₉	semidirect
552. #532	C₂²×C₁₉	semidirect
555. C₂×#125	C₂²×C₁₉	semidirect
559. #501	C₂²×C₁₉	semidirect
560. #501	C₂²×C₁₉	semidirect
561. #498	C₂²×C₁₉	semidirect
563. #489	C₂²×C₁₉	semidirect
564. #488	C₂²×C₁₉	semidirect
565. #485	C₂²×C₁₉	semidirect
566. #483	C₂²×C₁₉	semidirect
568. #482	C₂²×C₁₉	semidirect
569. #482	C₂²×C₁₉	semidirect
570. #482	C₂²×C₁₉	semidirect
572. #481	C₂²×C₁₉	semidirect
573. #480	C₂²×C₁₉	semidirect
574. #479	C₂²×C₁₉	semidirect
575. #479	C₂²×C₁₉	semidirect
579. #478	C₂²×C₁₉	semidirect
580. #478	C₂²×C₁₉	semidirect
581. #478	C₂²×C₁₉	semidirect
583. #476	C₂²×C₁₉	semidirect
584. #476	C₂²×C₁₉	semidirect
585. #476	C₂²×C₁₉	semidirect
586. #475	C₂²×C₁₉	semidirect
588. #474	C₂²×C₁₉	semidirect
589. #474	C₂²×C₁₉	semidirect
591. #469	C₂²×C₁₉	semidirect
592. #469	C₂²×C₁₉	semidirect
593. #468	C₂²×C₁₉	semidirect
595. #465	C₂²×C₁₉	semidirect
596. #463	C₂²×C₁₉	semidirect
597. #463	C₂²×C₁₉	semidirect
598. #460	C₂²×C₁₉	semidirect
601. #459	C₂²×C₁₉	semidirect
605. #446	C₂²×C₁₉	semidirect
608. #442	C₂²×C₁₉	semidirect
609. #440	C₂²×C₁₉	semidirect
611. C₄×D₈	C₂²×C₁₉	semidirect
612. #436	C₂²×C₁₉	semidirect
614. #435	C₂²×C₁₉	semidirect
615. #433	C₂²×C₁₉	semidirect
616. #432	C₂²×C₁₉	semidirect
617. #428	C₂²×C₁₉	semidirect
618. #428	C₂²×C₁₉	semidirect
619. #428	C₂²×C₁₉	semidirect
620. #427	C₂²×C₁₉	semidirect
621. #424	C₂²×C₁₉	semidirect
622. #423	C₂²×C₁₉	semidirect
796. C₁₉	#62235	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×#3559	2
C₁₉×#3514	2
C₁₉×#3384	2
C₁₉×#3370	2
C₁₉×#3354	2
C₁₉×#3350	2
C₁₉×#3347	2
C₁₉×#3322	2
C₁₉×#3318	2
C₁₉×#3306	2
C₁₉×#3257	2
C₁₉×#3253	2
C₁₉×#3244	2
C₁₉×#3234	2
C₁₉×#3122	2
C₁₉×#3115	2
C₁₉×#3081	2
C₁₉×#3080	2
C₁₉×#2995	2
#62235	19

Subgroups — C19×#62235 #18068194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62235 #18068194