Subgroups — C₁₉×#62392 #18068351

Order 4864.

1712 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3554	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3403	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3388	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3384	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3373	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3371	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3370	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3366	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3263	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3259	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3257	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3256	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3180	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3179	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3176	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3173	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#2961	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#562	—	2	2	no	—
21	C₁₉×#562	—	2	2	no	—
22	C₁₉×#559	C₂²	1	2	yes	—
23	C₁₉×#559	C₂²	1	2	yes	—
24	C₁₉×#559	C₂²	1	2	yes	—
25	C₁₉×#557	C₂²	1	2	yes	—
26	C₁₉×#554	C₂²	1	2	yes	—
27	C₁₉×#554	C₂²	1	2	yes	—
28	C₁₉×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
30	C₁₉×#548	—	2	2	no	—
31	C₁₉×#547	—	2	2	no	—
32	C₁₉×#542	—	2	2	no	—
33	C₁₉×#542	C₂²	1	2	yes	—
34	C₁₉×#542	C₂²	1	2	yes	—
35	C₁₉×#540	C₂²	1	2	yes	—
36	C₁₉×#540	C₂²	1	2	yes	—
37	C₁₉×#539	—	2	2	no	—
38	C₁₉×#539	—	2	2	no	—
39	C₁₉×#536	—	2	2	no	—
40	C₁₉×#533	C₂²	1	1	yes	characteristic
41	C₁₉×#532	C₂²	1	2	yes	—
42	C₁₉×#529	C₂²	1	2	yes	—
43	C₁₉×#501	C₂²	1	2	yes	—
44	C₁₉×#501	C₂²	1	2	yes	—
45	C₁₉×#499	C₂²	1	1	yes	characteristic
46	C₁₉×#498	C₂²	1	1	yes	characteristic
47	C₁₉×#496	C₂²	1	2	yes	—
48	C₁₉×#496	C₂²	1	2	yes	—
49	C₁₉×#495	C₂²	1	1	yes	characteristic
50	C₁₉×#493	C₂²	1	1	yes	characteristic
51	C₁₉×#490	C₂²	1	2	yes	—
52	C₁₉×#490	C₂²	1	2	yes	—
53	C₁₉×#489	C₂²	1	2	yes	—
54	C₁₉×#489	C₂²	1	2	yes	—
55	C₁₉×#488	C₂²	1	2	yes	—
56	C₁₉×#486	C₂²	1	2	yes	—
57	C₁₉×#479	C₂²	1	2	yes	—
58	C₁₉×#479	C₂²	1	2	yes	—
59	C₁₉×#478	C₂²	1	2	yes	—
60	C₁₉×#478	C₂²	1	2	yes	—
61	C₁₉×#478	C₂²	1	2	yes	—
62	C₁₉×#478	C₂²	1	2	yes	—
63	C₁₉×#476	C₂²	1	2	yes	—
64	C₁₉×#476	C₂²	1	2	yes	—
65	C₁₉×#476	C₂²	1	2	yes	—
66	C₁₉×#476	C₂²	1	2	yes	—
67	C₁₉×#475	C₂²	1	2	yes	—
68	C₁₉×#474	C₂²	1	2	yes	—
69	C₁₉×#470	C₂²	1	1	yes	characteristic
70	C₁₉×#469	C₂²	1	1	yes	characteristic
71	C₁₉×#469	C₂²	1	1	yes	characteristic
72	C₁₉×#469	C₂²	1	1	yes	characteristic
73	C₁₉×#469	C₂²	1	2	yes	—
74	C₁₉×#468	C₂²	1	2	yes	—
75	C₁₉×#466	C₂²	1	2	yes	—
76	C₁₉×#466	C₂²	1	2	yes	—
77	C₁₉×#465	C₂²	1	2	yes	—
78	C₁₉×#465	C₂²	1	2	yes	—
79	C₁₉×#464	C₂²	1	2	yes	—
80	C₁₉×#464	C₂²	1	2	yes	—
81	C₁₉×#463	C₂²	1	2	yes	—
82	C₁₉×#463	C₂²	1	2	yes	—
83	C₁₉×#463	C₂²	1	2	yes	—
84	C₁₉×#463	C₂²	1	2	yes	—
85	C₁₉×#460	C₂²	1	2	yes	—
86	C₁₉×#459	C₂²	1	2	yes	—
87	C₁₉×#459	C₂²	1	2	yes	—
88	C₁₉×#459	C₂²	1	2	yes	—
89	C₁₉×#459	C₂²	1	2	yes	—
90	C₁₉×#459	C₂²	1	2	yes	—
91	C₁₉×#446	C₂²	1	2	yes	—
92	C₁₉×#446	C₂²	1	2	yes	—
93	C₁₉×#446	C₂²	1	2	yes	—
94	C₁₉×#446	C₂²	1	2	yes	—
95	C₁₉×#442	C₂²	1	1	yes	characteristic
96	C₁₉×#442	C₂²	1	1	yes	characteristic
97	C₁₉×#442	C₂²	1	1	yes	characteristic
98	C₁₉×#442	C₂²	1	2	yes	—
99	C₁₉×#442	C₂²	1	2	yes	—
100	C₁₉×#442	C₂²	1	2	yes	—
101	C₁₉×#441	C₂²	1	1	yes	characteristic
102	C₁₉×#440	C₂²	1	2	yes	—
103	C₁₉×#440	C₂²	1	2	yes	—
104	C₁₉×#440	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
106	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
107	C₄×D₈×C₁₉	C₂²	1	2	yes	—
108	C₄×D₈×C₁₉	C₂²	1	2	yes	—
109	C₁₉×#424	C₂²	1	1	yes	characteristic
110	C₁₉×#424	C₂²	1	1	yes	characteristic
111	C₁₉×#423	C₂²	1	1	yes	characteristic
112	C₁₉×#405	C₂²	1	1	yes	characteristic
113	C₁₉×#405	C₂²	1	1	yes	characteristic
114	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
115	C₂×#41×C₁₉	—	2	2	no	—
116	C₂×#41×C₁₉	—	2	2	no	—
117	C₂²×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
122	C₂×D₈×C₁₉	C₂³	1	2	yes	—
123	C₂×D₈×C₁₉	C₂³	1	2	yes	—
124	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₈×C₁₉	C₂³	1	2	yes	—
126	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×C₄⋊Q₈	—	2	2	no	—
133	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
134	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₉×#127	C₂³	1	2	yes	—
138	C₁₉×#127	C₂³	1	2	yes	—
139	C₁₉×#127	C₂³	1	2	yes	—
140	C₁₉×#126	—	2	2	no	—
141	C₁₉×#126	—	2	2	no	—
142	C₁₉×#126	—	2	2	no	—
143	C₁₉×#125	—	2	2	no	—
144	C₁₉×#125	—	2	2	no	—
145	C₁₉×#125	D₄	1	2	yes	—
146	C₁₉×#125	C₂³	1	2	yes	—
147	C₁₉×#125	C₂³	1	2	yes	—
148	C₁₉×#125	C₂³	1	2	yes	—
149	C₁₉×#124	—	2	2	no	—
150	C₁₉×#124	—	2	2	no	—
151	C₁₉×#124	—	2	2	no	—
152	C₁₉×#124	—	2	2	no	—
153	C₁₉×#124	—	2	2	no	—
154	C₁₉×#124	—	2	2	no	—
155	C₁₉×#124	C₂³	1	2	yes	—
156	C₁₉×#124	C₂³	1	2	yes	—
157	C₁₉×#124	C₂³	1	2	yes	—
158	C₁₉×#123	—	2	2	no	—
159	C₁₉×#123	—	2	2	no	—
160	C₁₉×#123	—	2	2	no	—
161	C₁₉×#123	—	2	2	no	—
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×C₂²⋊Q₈	—	2	2	no	—
172	C₁₉×C₂²⋊Q₈	—	2	2	no	—
173	C₁₉×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
182	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
183	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
184	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
185	C₁₉×#121	—	2	2	no	—
186	C₁₉×#121	—	2	2	no	—
187	C₁₉×#121	—	2	2	no	—
188	C₁₉×#121	—	2	2	no	—
189	C₁₉×#121	—	2	2	no	—
190	C₁₉×#121	—	2	2	no	—
191	C₁₉×#121	—	2	2	no	—
192	C₁₉×#121	—	2	2	no	—
193	C₁₉×#121	C₂³	1	2	yes	—
194	C₁₉×#121	C₂³	1	2	yes	—
195	C₁₉×#121	C₂³	1	2	yes	—
196	C₄×Q₈×C₁₉	—	2	2	no	—
197	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
198	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
199	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
200	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
201	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
202	C₄×D₄×C₁₉	—	2	2	no	—
203	C₄×D₄×C₁₉	—	2	2	no	—
204	C₄×D₄×C₁₉	—	2	2	no	—
205	C₄×D₄×C₁₉	—	2	2	no	—
206	C₄×D₄×C₁₉	—	2	2	no	—
207	C₄×D₄×C₁₉	C₂³	1	2	yes	—
208	C₄×D₄×C₁₉	C₂³	1	2	yes	—
209	C₄×D₄×C₁₉	C₂³	1	2	yes	—
210	C₄×D₄×C₁₉	C₂³	1	2	yes	—
211	C₄×D₄×C₁₉	C₂³	1	2	yes	—
212	C₄×D₄×C₁₉	C₂³	1	2	yes	—
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	C₁₉×#117	—	2	2	no	—
217	C₁₉×#117	C₂³	1	1	yes	characteristic
218	C₁₉×#117	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
220	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
222	C₁₉×#107	C₂³	1	2	yes	—
223	C₁₉×#107	C₂³	1	2	yes	—
224	C₁₉×#107	C₂³	1	2	yes	—
225	C₁₉×#106	C₂³	1	2	yes	—
226	C₁₉×#106	C₂³	1	2	yes	—
227	C₁₉×#106	C₂³	1	1	yes	characteristic
228	C₁₉×#106	C₂³	1	2	yes	—
229	C₁₉×#106	C₂³	1	1	yes	characteristic
230	C₁₉×#106	C₂³	1	1	yes	characteristic
231	C₁₉×#106	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	2	yes	—
236	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₉×#103	C₂³	1	2	yes	—
239	C₁₉×#103	C₂³	1	2	yes	—
240	C₁₉×#103	C₂³	1	2	yes	—
241	C₁₉×#103	C₂³	1	2	yes	—
242	C₁₉×#102	C₂³	1	2	yes	—
243	C₁₉×#102	C₂³	1	2	yes	—
244	C₁₉×#102	C₂³	1	2	yes	—
245	C₁₉×#102	C₂³	1	2	yes	—
246	C₁₉×#102	C₂³	1	2	yes	—
247	C₁₉×#102	C₂³	1	2	yes	—
248	C₁₉×#102	C₂³	1	2	yes	—
249	C₁₉×#102	C₂³	1	2	yes	—
250	C₁₉×#102	C₂³	1	2	yes	—
251	C₁₉×#102	C₂³	1	2	yes	—
252	C₁₉×#102	C₂³	1	2	yes	—
253	C₁₉×#102	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	1	yes	characteristic
258	C₁₉×#97	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₁₉	C₂³	1	2	yes	—
261	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
262	#41×C₁₉	—	8	4	no	—
263	#41×C₁₉	—	8	4	no	—
264	C₂×Q₈×C₁₉	—	2	2	no	—
265	C₂×Q₈×C₁₉	—	2	2	no	—
266	C₂×Q₈×C₁₉	—	2	2	no	—
267	C₂×Q₈×C₁₉	—	8	4	no	—
268	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
269	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
270	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
271	C₂×D₄×C₁₉	—	2	2	no	—
272	C₂×D₄×C₁₉	—	2	2	no	—
273	C₂×D₄×C₁₉	—	2	2	no	—
274	C₂×D₄×C₁₉	—	2	2	no	—
275	C₂×D₄×C₁₉	—	2	2	no	—
276	C₂×D₄×C₁₉	—	2	2	no	—
277	C₂×D₄×C₁₉	—	2	2	no	—
278	C₂×D₄×C₁₉	—	2	2	no	—
279	C₂×D₄×C₁₉	—	2	2	no	—
280	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
281	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
282	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₉	—	2	2	no	—
284	C₂²×C₄×C₁₉	—	2	2	no	—
285	C₂²×C₄×C₁₉	—	2	2	no	—
286	C₂²×C₄×C₁₉	—	2	2	no	—
287	C₂²×C₄×C₁₉	—	2	2	no	—
288	C₂²×C₄×C₁₉	—	2	2	no	—
289	C₂²×C₄×C₁₉	—	2	2	no	—
290	C₂²×C₄×C₁₉	—	2	2	no	—
291	C₂²×C₄×C₁₉	—	2	2	no	—
292	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
294	Q₁₆×C₁₉	—	4	1	no	—
295	SD₁₆×C₁₉	—	2	4	no	—
296	SD₁₆×C₁₉	—	4	2	no	—
297	SD₁₆×C₁₉	—	4	2	no	—
298	D₈×C₁₉	—	2	4	no	—
299	D₈×C₁₉	—	4	2	no	—
300	D₈×C₁₉	—	4	1	no	—
301	D₈×C₁₉	—	4	1	no	—
302	D₈×C₁₉	—	4	2	no	—
303	D₈×C₁₉	—	4	1	no	—
304	M₁₆×C₁₉	—	4	1	no	—
305	M₁₆×C₁₉	—	4	1	no	—
306	C₂×C₈×C₁₉	—	2	2	no	—
307	C₂×C₈×C₁₉	—	4	1	no	—
308	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
309	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
312	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
313	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₁₉	—	2	2	no	—
315	C₄⋊C₄×C₁₉	—	2	2	no	—
316	C₄⋊C₄×C₁₉	—	2	2	no	—
317	C₄⋊C₄×C₁₉	—	2	2	no	—
318	C₄⋊C₄×C₁₉	—	2	2	no	—
319	C₄⋊C₄×C₁₉	—	2	2	no	—
320	C₄⋊C₄×C₁₉	—	2	2	no	—
321	C₄⋊C₄×C₁₉	—	2	2	no	—
322	C₄⋊C₄×C₁₉	—	2	2	no	—
323	C₄⋊C₄×C₁₉	—	2	2	no	—
324	C₄⋊C₄×C₁₉	—	2	2	no	—
325	C₄⋊C₄×C₁₉	—	2	2	no	—
326	C₄⋊C₄×C₁₉	—	2	2	no	—
327	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
328	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
333	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
336	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
339	C₂²⋊C₄×C₁₉	—	2	2	no	—
340	C₂²⋊C₄×C₁₉	—	2	2	no	—
341	C₂²⋊C₄×C₁₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	—	2	2	no	—
350	C₂²⋊C₄×C₁₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₉	—	2	2	no	—
355	C₂²⋊C₄×C₁₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₉	—	2	2	no	—
357	C₂²⋊C₄×C₁₉	—	2	2	no	—
358	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
359	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
360	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₁₉	—	2	2	no	—
362	C₄²×C₁₉	—	2	2	no	—
363	C₄²×C₁₉	—	2	2	no	—
364	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₁₉	C₂⁴	1	2	yes	—
367	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
368	C₄²×C₁₉	C₂⁴	1	2	yes	—
369	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
370	#62392	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂³×C₁₉	—	2	2	no	—
372	C₂³×C₁₉	—	2	2	no	—
373	C₂³×C₁₉	—	2	2	no	—
374	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
375	Q₈×C₁₉	—	2	2	no	—
376	Q₈×C₁₉	—	2	2	no	—
377	Q₈×C₁₉	—	4	2	no	—
378	Q₈×C₁₉	—	4	2	no	—
379	Q₈×C₁₉	—	4	4	no	—
380	Q₈×C₁₉	—	8	2	no	—
381	Q₈×C₁₉	—	8	2	no	—
382	D₄×C₁₉	—	2	2	no	—
383	D₄×C₁₉	—	2	2	no	—
384	D₄×C₁₉	—	2	2	no	—
385	D₄×C₁₉	—	2	2	no	—
386	D₄×C₁₉	—	2	2	no	—
387	D₄×C₁₉	—	2	2	no	—
388	D₄×C₁₉	—	4	4	no	—
389	D₄×C₁₉	—	8	2	no	—
390	D₄×C₁₉	—	8	2	no	—
391	D₄×C₁₉	—	8	2	no	—
392	D₄×C₁₉	—	8	2	no	—
393	D₄×C₁₉	—	8	2	no	—
394	D₄×C₁₉	—	8	2	no	—
395	D₄×C₁₉	—	8	2	no	—
396	D₄×C₁₉	—	8	2	no	—
397	C₂×C₄×C₁₉	—	2	1	no	—
398	C₂×C₄×C₁₉	—	2	1	no	—
399	C₂×C₄×C₁₉	—	2	2	no	—
400	C₂×C₄×C₁₉	—	2	2	no	—
401	C₂×C₄×C₁₉	—	2	2	no	—
402	C₂×C₄×C₁₉	—	2	2	no	—
403	C₂×C₄×C₁₉	—	2	2	no	—
404	C₂×C₄×C₁₉	—	4	2	no	—
405	C₂×C₄×C₁₉	—	4	4	no	—
406	C₂×C₄×C₁₉	—	8	2	no	—
407	C₂×C₄×C₁₉	—	8	2	no	—
408	C₂×C₄×C₁₉	—	8	2	no	—
409	C₂×C₄×C₁₉	—	8	2	no	—
410	C₂×C₄×C₁₉	—	8	2	no	—
411	C₂×C₄×C₁₉	—	8	2	no	—
412	C₂×C₄×C₁₉	—	8	2	no	—
413	C₂×C₄×C₁₉	—	8	2	no	—
414	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
422	C₈×C₁₉	—	2	1	no	—
423	C₈×C₁₉	—	2	2	no	—
424	C₈×C₁₉	—	2	1	no	—
425	C₈×C₁₉	—	2	2	no	—
426	C₈×C₁₉	—	2	1	no	—
427	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
428	#3554	C₂×C₁₉	1	2	yes	complemented
429	#3403	C₂×C₁₉	1	2	yes	complemented
430	#3399	C₂×C₁₉	1	2	yes	complemented
431	#3388	C₂×C₁₉	1	2	yes	complemented
432	#3384	C₂×C₁₉	1	2	yes	complemented
433	#3373	C₂×C₁₉	1	2	yes	complemented
434	#3371	C₂×C₁₉	1	2	yes	complemented
435	#3370	C₂×C₁₉	1	2	yes	complemented
436	#3366	C₂×C₁₉	1	2	yes	complemented
437	#3263	C₂×C₁₉	1	1	yes	characteristic, complemented
438	#3259	C₂×C₁₉	1	1	yes	characteristic, complemented
439	#3257	C₂×C₁₉	1	2	yes	complemented
440	#3256	C₂×C₁₉	1	1	yes	characteristic, complemented
441	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
442	#3180	C₂×C₁₉	1	2	yes	complemented
443	#3179	C₂×C₁₉	1	2	yes	complemented
444	#3176	C₂×C₁₉	1	1	yes	characteristic, complemented
445	#3173	C₂×C₁₉	1	1	yes	characteristic, complemented
446	#2961	C₂×C₁₉	1	1	yes	characteristic, complemented
447	C₂²×C₁₉	—	2	2	no	—
448	C₂²×C₁₉	—	2	1	no	—
449	C₂²×C₁₉	—	4	2	no	—
450	C₂²×C₁₉	—	4	2	no	—
451	C₂²×C₁₉	—	4	2	no	—
452	C₂²×C₁₉	—	4	2	no	—
453	C₂²×C₁₉	—	4	2	no	—
454	C₂²×C₁₉	—	4	2	no	—
455	C₂²×C₁₉	—	4	2	no	—
456	C₂²×C₁₉	—	4	2	no	—
457	C₂²×C₁₉	—	4	2	no	—
458	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
459	C₄×C₁₉	—	2	2	no	—
460	C₄×C₁₉	—	2	2	no	—
461	C₄×C₁₉	—	2	2	no	—
462	C₄×C₁₉	—	2	2	no	—
463	C₄×C₁₉	—	2	2	no	—
464	C₄×C₁₉	—	2	2	no	—
465	C₄×C₁₉	—	2	1	no	—
466	C₄×C₁₉	—	4	2	no	—
467	C₄×C₁₉	—	4	2	no	—
468	C₄×C₁₉	—	4	2	no	—
469	C₄×C₁₉	—	4	2	no	—
470	C₄×C₁₉	—	4	2	no	—
471	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
472	C₄×C₁₉	#585	1	1	yes	characteristic
473	#562	—	2	2	no	—
474	#562	—	2	2	no	—
475	#559	C₂²×C₁₉	1	2	yes	—
476	#559	C₂²×C₁₉	1	2	yes	—
477	#559	C₂²×C₁₉	1	2	yes	—
478	#557	C₂²×C₁₉	1	2	yes	—
479	#554	C₂²×C₁₉	1	2	yes	—
480	#554	C₂²×C₁₉	1	2	yes	—
481	#550	C₂²×C₁₉	1	2	yes	—
482	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
483	#548	—	2	2	no	—
484	#547	—	2	2	no	—
485	#542	—	2	2	no	—
486	#542	C₂²×C₁₉	1	2	yes	—
487	#542	C₂²×C₁₉	1	2	yes	—
488	#540	C₂²×C₁₉	1	2	yes	—
489	#540	C₂²×C₁₉	1	2	yes	—
490	#539	—	2	2	no	—
491	#539	—	2	2	no	—
492	#536	—	2	2	no	—
493	#533	C₂²×C₁₉	1	1	yes	characteristic
494	#532	C₂²×C₁₉	1	2	yes	—
495	#529	C₂²×C₁₉	1	2	yes	—
496	#501	C₂²×C₁₉	1	2	yes	—
497	#501	C₂²×C₁₉	1	2	yes	—
498	#499	C₂²×C₁₉	1	1	yes	characteristic
499	#498	C₂²×C₁₉	1	1	yes	characteristic
500	#496	C₂²×C₁₉	1	2	yes	—
501	#496	C₂²×C₁₉	1	2	yes	—
502	#495	C₂²×C₁₉	1	1	yes	characteristic
503	#493	C₂²×C₁₉	1	1	yes	characteristic
504	#490	C₂²×C₁₉	1	2	yes	—
505	#490	C₂²×C₁₉	1	2	yes	—
506	#489	C₂²×C₁₉	1	2	yes	—
507	#489	C₂²×C₁₉	1	2	yes	—
508	#488	C₂²×C₁₉	1	2	yes	—
509	#486	C₂²×C₁₉	1	2	yes	—
510	#479	C₂²×C₁₉	1	2	yes	—
511	#479	C₂²×C₁₉	1	2	yes	—
512	#478	C₂²×C₁₉	1	2	yes	—
513	#478	C₂²×C₁₉	1	2	yes	—
514	#478	C₂²×C₁₉	1	2	yes	—
515	#478	C₂²×C₁₉	1	2	yes	—
516	#476	C₂²×C₁₉	1	2	yes	—
517	#476	C₂²×C₁₉	1	2	yes	—
518	#476	C₂²×C₁₉	1	2	yes	—
519	#476	C₂²×C₁₉	1	2	yes	—
520	#475	C₂²×C₁₉	1	2	yes	—
521	#474	C₂²×C₁₉	1	2	yes	—
522	#470	C₂²×C₁₉	1	1	yes	characteristic
523	#469	C₂²×C₁₉	1	1	yes	characteristic
524	#469	C₂²×C₁₉	1	1	yes	characteristic
525	#469	C₂²×C₁₉	1	1	yes	characteristic
526	#469	C₂²×C₁₉	1	2	yes	—
527	#468	C₂²×C₁₉	1	2	yes	—
528	#466	C₂²×C₁₉	1	2	yes	—
529	#466	C₂²×C₁₉	1	2	yes	—
530	#465	C₂²×C₁₉	1	2	yes	—
531	#465	C₂²×C₁₉	1	2	yes	—
532	#464	C₂²×C₁₉	1	2	yes	—
533	#464	C₂²×C₁₉	1	2	yes	—
534	#463	C₂²×C₁₉	1	2	yes	—
535	#463	C₂²×C₁₉	1	2	yes	—
536	#463	C₂²×C₁₉	1	2	yes	—
537	#463	C₂²×C₁₉	1	2	yes	—
538	#460	C₂²×C₁₉	1	2	yes	—
539	#459	C₂²×C₁₉	1	2	yes	—
540	#459	C₂²×C₁₉	1	2	yes	—
541	#459	C₂²×C₁₉	1	2	yes	—
542	#459	C₂²×C₁₉	1	2	yes	—
543	#459	C₂²×C₁₉	1	2	yes	—
544	#446	C₂²×C₁₉	1	2	yes	—
545	#446	C₂²×C₁₉	1	2	yes	—
546	#446	C₂²×C₁₉	1	2	yes	—
547	#446	C₂²×C₁₉	1	2	yes	—
548	#442	C₂²×C₁₉	1	1	yes	characteristic
549	#442	C₂²×C₁₉	1	2	yes	—
550	#442	C₂²×C₁₉	1	1	yes	characteristic
551	#442	C₂²×C₁₉	1	1	yes	characteristic
552	#442	C₂²×C₁₉	1	2	yes	—
553	#442	C₂²×C₁₉	1	2	yes	—
554	#441	C₂²×C₁₉	1	1	yes	characteristic
555	#440	C₂²×C₁₉	1	2	yes	—
556	#440	C₂²×C₁₉	1	2	yes	—
557	#440	C₂²×C₁₉	1	2	yes	—
558	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
559	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
560	C₄×D₈	C₂²×C₁₉	1	2	yes	—
561	C₄×D₈	C₂²×C₁₉	1	2	yes	—
562	#424	C₂²×C₁₉	1	1	yes	characteristic
563	#424	C₂²×C₁₉	1	1	yes	characteristic
564	#423	C₂²×C₁₉	1	1	yes	characteristic
565	#405	C₂²×C₁₉	1	1	yes	characteristic
566	#405	C₂²×C₁₉	1	1	yes	characteristic
567	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
568	C₂×C₁₉	—	4	1	no	—
569	C₂×C₁₉	—	8	2	no	—
570	C₂×C₁₉	—	8	2	no	—
571	C₂×C₁₉	—	8	2	no	—
572	C₂×C₁₉	#3497	1	1	yes	characteristic
573	C₂×C₁₉	#3585	1	2	yes	—
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	2	2	no	—
576	C₂²×Q₈	—	2	2	no	—
577	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
578	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
581	C₂×D₈	C₂³×C₁₉	1	2	yes	—
582	C₂×D₈	C₂³×C₁₉	1	2	yes	—
583	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
584	C₂×D₈	C₂³×C₁₉	1	2	yes	—
585	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
586	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
587	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
588	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
589	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
590	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
591	C₄⋊Q₈	—	2	2	no	—
592	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
593	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
594	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
595	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
596	#127	C₂³×C₁₉	1	2	yes	—
597	#127	C₂³×C₁₉	1	2	yes	—
598	#127	C₂³×C₁₉	1	2	yes	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	D₄×C₁₉	1	2	yes	—
605	#125	C₂³×C₁₉	1	2	yes	—
606	#125	C₂³×C₁₉	1	2	yes	—
607	#125	C₂³×C₁₉	1	2	yes	—
608	#124	—	2	2	no	—
609	#124	—	2	2	no	—
610	#124	—	2	2	no	—
611	#124	—	2	2	no	—
612	#124	—	2	2	no	—
613	#124	—	2	2	no	—
614	#124	C₂³×C₁₉	1	2	yes	—
615	#124	C₂³×C₁₉	1	2	yes	—
616	#124	C₂³×C₁₉	1	2	yes	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
642	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
644	#121	—	2	2	no	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	C₂³×C₁₉	1	2	yes	—
653	#121	C₂³×C₁₉	1	2	yes	—
654	#121	C₂³×C₁₉	1	2	yes	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
657	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
658	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
659	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
660	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	C₂³×C₁₉	1	2	yes	—
667	C₄×D₄	C₂³×C₁₉	1	2	yes	—
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	C₄×D₄	C₂³×C₁₉	1	2	yes	—
673	C₄×D₄	C₂³×C₁₉	1	2	yes	—
674	C₄×D₄	C₂³×C₁₉	1	2	yes	—
675	#117	—	2	2	no	—
676	#117	C₂³×C₁₉	1	1	yes	characteristic
677	#117	C₂³×C₁₉	1	1	yes	characteristic
678	C₂×C₄⋊C₄	—	2	2	no	—
679	C₂×C₄⋊C₄	—	2	2	no	—
680	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
681	#107	C₂³×C₁₉	1	2	yes	—
682	#107	C₂³×C₁₉	1	2	yes	—
683	#107	C₂³×C₁₉	1	2	yes	—
684	#106	C₂³×C₁₉	1	2	yes	—
685	#106	C₂³×C₁₉	1	2	yes	—
686	#106	C₂³×C₁₉	1	1	yes	characteristic
687	#106	C₂³×C₁₉	1	2	yes	—
688	#106	C₂³×C₁₉	1	1	yes	characteristic
689	#106	C₂³×C₁₉	1	1	yes	characteristic
690	#106	C₂³×C₁₉	1	1	yes	characteristic
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	2	yes	—
695	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
696	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
697	#103	C₂³×C₁₉	1	2	yes	—
698	#103	C₂³×C₁₉	1	2	yes	—
699	#103	C₂³×C₁₉	1	2	yes	—
700	#103	C₂³×C₁₉	1	2	yes	—
701	#102	C₂³×C₁₉	1	2	yes	—
702	#102	C₂³×C₁₉	1	2	yes	—
703	#102	C₂³×C₁₉	1	2	yes	—
704	#102	C₂³×C₁₉	1	2	yes	—
705	#102	C₂³×C₁₉	1	2	yes	—
706	#102	C₂³×C₁₉	1	2	yes	—
707	#102	C₂³×C₁₉	1	2	yes	—
708	#102	C₂³×C₁₉	1	2	yes	—
709	#102	C₂³×C₁₉	1	2	yes	—
710	#102	C₂³×C₁₉	1	2	yes	—
711	#102	C₂³×C₁₉	1	2	yes	—
712	#102	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	1	yes	characteristic
717	#97	C₂³×C₁₉	1	1	yes	characteristic
718	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
719	C₄×C₈	C₂³×C₁₉	1	2	yes	—
720	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
721	C₁₉	#62392	1	1	yes	characteristic, direct product factor, Sylow
722	#41	—	8	4	no	—
723	#41	—	8	4	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	8	4	no	—
728	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
729	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
741	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
742	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
754	Q₁₆	—	4	1	no	—
755	SD₁₆	—	2	4	no	—
756	SD₁₆	—	4	2	no	—
757	SD₁₆	—	4	2	no	—
758	D₈	—	2	4	no	—
759	D₈	—	4	2	no	—
760	D₈	—	4	1	no	—
761	D₈	—	4	1	no	—
762	D₈	—	4	2	no	—
763	D₈	—	4	1	no	—
764	M₁₆	—	4	1	no	—
765	M₁₆	—	4	1	no	—
766	C₂×C₈	—	2	2	no	—
767	C₂×C₈	—	4	1	no	—
768	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
769	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
770	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
771	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
772	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
773	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
788	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
789	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
793	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
794	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
797	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
819	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
825	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
826	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
827	C₄²	C₂⁴×C₁₉	1	2	yes	—
828	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
829	C₄²	C₂⁴×C₁₉	1	2	yes	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	2	no	—
837	Q₈	—	4	2	no	—
838	Q₈	—	4	4	no	—
839	Q₈	—	8	2	no	—
840	Q₈	—	8	2	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	4	4	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	2	no	—
850	D₄	—	8	2	no	—
851	D₄	—	8	2	no	—
852	D₄	—	8	2	no	—
853	D₄	—	8	2	no	—
854	D₄	—	8	2	no	—
855	D₄	—	8	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
874	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
880	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
881	C₈	—	2	1	no	—
882	C₈	—	2	2	no	—
883	C₈	—	2	1	no	—
884	C₈	—	2	2	no	—
885	C₈	—	2	1	no	—
886	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
887	C₂²	—	2	1	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
899	C₄	—	2	1	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
912	C₄	C₁₉×#585	1	1	yes	characteristic
913	C₂	—	4	1	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	—	8	2	no	—
917	C₂	C₁₉×#3497	1	1	yes	characteristic
918	C₂	C₁₉×#3585	1	2	yes	—

	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3554	C₂	semidirect
2. C₁₉×#3403	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3388	C₂	semidirect
5. C₁₉×#3384	C₂	semidirect
6. C₁₉×#3373	C₂	semidirect
7. C₁₉×#3371	C₂	semidirect
8. C₁₉×#3370	C₂	semidirect
9. C₁₉×#3366	C₂	semidirect
10. C₁₉×#3263	C₂	semidirect
11. C₁₉×#3259	C₂	semidirect
12. C₁₉×#3257	C₂	semidirect
13. C₁₉×#3256	C₂	semidirect
14. C₁₉×#3253	C₂	semidirect
15. C₁₉×#3180	C₂	semidirect
16. C₁₉×#3179	C₂	semidirect
17. C₁₉×#3176	C₂	semidirect
18. C₁₉×#3173	C₂	semidirect
19. C₁₉×#2961	C₂	semidirect
370. #62392	C₁₉	direct (N × H)
428. #3554	C₂×C₁₉	semidirect
429. #3403	C₂×C₁₉	semidirect
430. #3399	C₂×C₁₉	semidirect
431. #3388	C₂×C₁₉	semidirect
432. #3384	C₂×C₁₉	semidirect
433. #3373	C₂×C₁₉	semidirect
434. #3371	C₂×C₁₉	semidirect
435. #3370	C₂×C₁₉	semidirect
436. #3366	C₂×C₁₉	semidirect
437. #3263	C₂×C₁₉	semidirect
438. #3259	C₂×C₁₉	semidirect
439. #3257	C₂×C₁₉	semidirect
440. #3256	C₂×C₁₉	semidirect
441. #3253	C₂×C₁₉	semidirect
442. #3180	C₂×C₁₉	semidirect
443. #3179	C₂×C₁₉	semidirect
444. #3176	C₂×C₁₉	semidirect
445. #3173	C₂×C₁₉	semidirect
446. #2961	C₂×C₁₉	semidirect
721. C₁₉	#62392	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×#3554	2
C₁₉×#3403	2
C₁₉×#3399	2
C₁₉×#3388	2
C₁₉×#3384	2
C₁₉×#3373	2
C₁₉×#3371	2
C₁₉×#3370	2
C₁₉×#3366	2
C₁₉×#3263	2
C₁₉×#3259	2
C₁₉×#3257	2
C₁₉×#3256	2
C₁₉×#3253	2
C₁₉×#3180	2
C₁₉×#3179	2
C₁₉×#3176	2
C₁₉×#3173	2
C₁₉×#2961	2
#62392	19

Subgroups — C19×#62392 #18068351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62392 #18068351