Subgroups — C₁₉×#62324 #18068283

Order 4864.

1912 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3546	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3339	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3332	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3324	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3322	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3251	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3198	C₂	1	4	yes	maximal, complemented
13	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3061	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3058	C₂	1	2	yes	maximal, complemented
17	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
20	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
21	C₁₉×#560	—	2	4	no	—
22	C₁₉×#556	C₂²	1	2	yes	—
23	C₁₉×#553	C₂²	1	4	yes	complemented
24	C₁₉×#550	—	2	2	no	—
25	C₁₉×#550	C₂²	1	2	yes	complemented
26	C₁₉×#547	C₂²	1	2	yes	complemented
27	C₁₉×#546	—	2	2	no	—
28	C₁₉×#546	C₂²	1	4	yes	complemented
29	D₄²×C₁₉	C₂²	1	2	yes	—
30	C₁₉×#542	—	2	2	no	—
31	C₁₉×#538	—	2	4	no	—
32	C₁₉×#537	C₂²	1	4	yes	complemented
33	C₁₉×#535	—	2	2	no	—
34	C₁₉×#535	C₂²	1	4	yes	complemented
35	C₁₉×#532	C₂²	1	1	yes	characteristic
36	C₁₉×#532	C₂²	1	2	yes	complemented
37	C₁₉×#529	C₂²	1	2	yes	complemented
38	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#495	C₂²	1	1	yes	characteristic
41	C₁₉×#493	C₂²	1	1	yes	characteristic
42	C₁₉×#488	C₂²	1	2	yes	complemented
43	C₁₉×#486	C₂²	1	2	yes	complemented
44	C₁₉×#485	C₂²	1	4	yes	complemented
45	C₁₉×#482	C₂²	1	4	yes	complemented
46	C₁₉×#481	C₂²	1	4	yes	complemented
47	C₁₉×#480	C₂²	1	4	yes	complemented
48	C₁₉×#478	C₂²	1	4	yes	complemented
49	C₁₉×#475	C₂²	1	2	yes	complemented
50	C₁₉×#474	C₂²	1	2	yes	complemented
51	C₁₉×#469	C₂²	1	4	yes	complemented
52	C₁₉×#469	C₂²	1	4	yes	complemented
53	C₁₉×#468	C₂²	1	4	yes	complemented
54	C₁₉×#468	C₂²	1	4	yes	complemented
55	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#467	C₂²	1	2	yes	complemented
57	C₁₉×#466	C₂²	1	1	yes	characteristic
58	C₁₉×#466	C₂²	1	2	yes	—
59	C₁₉×#466	C₂²	1	2	yes	—
60	C₁₉×#466	C₂²	1	2	yes	complemented
61	C₁₉×#466	C₂²	1	2	yes	complemented
62	C₁₉×#466	C₂²	1	2	yes	complemented
63	C₁₉×#465	C₂²	1	2	yes	complemented
64	C₁₉×#463	C₂²	1	4	yes	complemented
65	C₁₉×#460	C₂²	1	2	yes	complemented
66	C₁₉×#459	C₂²	1	2	yes	—
67	C₁₉×#450	C₂²	1	4	yes	complemented
68	C₁₉×#449	C₂²	1	4	yes	complemented
69	C₁₉×#449	C₂²	1	4	yes	complemented
70	C₁₉×#447	C₂²	1	4	yes	—
71	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
72	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
73	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
74	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
75	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
76	C₁₉×#436	C₂²	1	1	yes	characteristic
77	C₁₉×#436	C₂²	1	2	yes	complemented
78	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
79	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
81	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
82	C₁₉×#427	C₂²	1	2	yes	complemented
83	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
84	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
85	C₁₉×#418	C₂²	1	4	yes	complemented
86	C₁₉×#417	C₂²	1	4	yes	complemented
87	C₁₉×#408	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₁₉	—	2	2	no	—
90	C₂×#41×C₁₉	—	2	2	no	—
91	C₂×#41×C₁₉	C₂³	1	4	yes	—
92	C₂×#41×C₁₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₉	—	2	2	no	—
94	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
95	C₁₉×#135	—	4	4	no	—
96	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
99	C₂×D₈×C₁₉	—	4	4	no	—
100	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×D₈×C₁₉	C₂³	1	2	yes	—
102	C₂×D₈×C₁₉	C₂³	1	2	yes	—
103	C₂×D₈×C₁₉	C₂³	1	4	yes	—
104	C₁₉×#131	—	4	4	no	—
105	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
106	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₉×#127	—	2	2	no	—
115	C₁₉×#127	—	2	4	no	—
116	C₁₉×#127	D₄	1	1	yes	characteristic
117	C₁₉×#127	C₂³	1	2	yes	—
118	C₁₉×#126	—	2	4	no	—
119	C₁₉×#126	—	2	4	no	—
120	C₁₉×#126	—	2	2	no	—
121	C₁₉×#125	C₂³	1	2	yes	—
122	C₁₉×#124	—	2	4	no	—
123	C₁₉×#124	—	2	2	no	—
124	C₁₉×#124	—	2	2	no	—
125	C₁₉×#124	D₄	1	2	yes	—
126	C₁₉×#124	C₂³	1	2	yes	—
127	C₁₉×#123	—	2	2	no	—
128	C₁₉×#123	—	2	4	no	—
129	C₁₉×#123	—	2	4	no	—
130	C₁₉×#123	—	2	4	no	—
131	C₁₉×C₂²⋊Q₈	—	2	4	no	—
132	C₁₉×C₂²⋊Q₈	—	2	2	no	—
133	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₉×#121	—	2	4	no	—
136	C₁₉×#121	—	2	4	no	—
137	C₁₉×#121	—	2	4	no	—
138	C₁₉×#121	—	2	4	no	—
139	C₁₉×#121	—	2	2	no	—
140	C₁₉×#121	—	2	2	no	—
141	C₁₉×#121	—	2	4	no	—
142	C₁₉×#121	—	2	4	no	—
143	C₁₉×#121	D₄	1	1	yes	characteristic
144	C₁₉×#121	D₄	1	1	yes	characteristic
145	C₁₉×#121	D₄	1	2	yes	—
146	C₁₉×#121	C₂³	1	4	yes	—
147	C₁₉×#121	C₂³	1	4	yes	—
148	C₁₉×#121	C₂³	1	4	yes	—
149	C₁₉×#121	C₂³	1	2	yes	—
150	C₁₉×#121	C₂³	1	4	yes	—
151	C₁₉×#120	—	2	4	no	—
152	C₁₉×#120	—	2	4	no	—
153	C₁₉×#120	—	2	4	no	—
154	C₁₉×#120	—	2	4	no	—
155	C₄×Q₈×C₁₉	—	2	2	no	—
156	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
157	C₄×D₄×C₁₉	—	2	2	no	—
158	C₄×D₄×C₁₉	—	2	2	no	—
159	C₄×D₄×C₁₉	—	2	4	no	—
160	C₄×D₄×C₁₉	—	2	2	no	—
161	C₄×D₄×C₁₉	C₂³	1	2	yes	—
162	C₄×D₄×C₁₉	C₂³	1	4	yes	—
163	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₁₉	C₂³	1	2	yes	—
165	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₁₉×#117	—	2	2	no	—
167	C₁₉×#117	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
171	C₁₉×#107	C₂³	1	1	yes	characteristic
172	C₁₉×#107	C₂³	1	2	yes	—
173	C₁₉×#107	C₂³	1	4	yes	—
174	C₁₉×#107	C₂³	1	1	yes	characteristic
175	C₁₉×#107	C₂³	1	2	yes	—
176	C₁₉×#106	C₂³	1	4	yes	—
177	C₁₉×#106	C₂³	1	2	yes	—
178	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
181	C₁₉×#103	C₂³	1	2	yes	—
182	C₁₉×#103	C₂³	1	4	yes	—
183	C₁₉×#103	C₂³	1	2	yes	—
184	C₁₉×#102	C₂³	1	4	yes	—
185	C₁₉×#102	C₂³	1	4	yes	—
186	C₁₉×#102	C₂³	1	2	yes	—
187	C₁₉×#102	C₂³	1	4	yes	—
188	C₁₉×#102	C₂³	1	4	yes	—
189	C₁₉×#102	C₂³	1	2	yes	—
190	C₁₉×#102	C₂³	1	4	yes	—
191	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
199	C₂⁴×C₁₉	—	2	4	no	—
200	#41×C₁₉	—	4	2	no	—
201	#41×C₁₉	—	4	2	no	—
202	#41×C₁₉	—	4	4	no	—
203	#41×C₁₉	—	4	4	no	—
204	#41×C₁₉	—	8	4	no	—
205	#41×C₁₉	—	8	4	no	—
206	C₂×Q₈×C₁₉	—	2	2	no	—
207	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
209	C₂×D₄×C₁₉	—	2	2	no	—
210	C₂×D₄×C₁₉	—	2	4	no	—
211	C₂×D₄×C₁₉	—	2	4	no	—
212	C₂×D₄×C₁₉	—	2	4	no	—
213	C₂×D₄×C₁₉	—	2	4	no	—
214	C₂×D₄×C₁₉	—	2	4	no	—
215	C₂×D₄×C₁₉	—	2	2	no	—
216	C₂×D₄×C₁₉	—	2	2	no	—
217	C₂×D₄×C₁₉	—	2	4	no	—
218	C₂×D₄×C₁₉	—	4	4	no	—
219	C₂×D₄×C₁₉	—	4	4	no	—
220	C₂×D₄×C₁₉	—	8	4	no	—
221	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
228	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₁₉	—	2	4	no	—
230	C₂²×C₄×C₁₉	—	2	2	no	—
231	C₂²×C₄×C₁₉	—	2	4	no	—
232	C₂²×C₄×C₁₉	—	2	4	no	—
233	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
238	Q₁₆×C₁₉	—	2	2	no	—
239	SD₁₆×C₁₉	—	4	2	no	—
240	SD₁₆×C₁₉	—	4	4	no	—
241	D₈×C₁₉	—	2	2	no	—
242	D₈×C₁₉	—	2	4	no	—
243	D₈×C₁₉	—	4	4	no	—
244	D₈×C₁₉	—	4	2	no	—
245	M₁₆×C₁₉	—	4	2	no	—
246	M₁₆×C₁₉	—	4	2	no	—
247	M₁₆×C₁₉	—	4	2	no	—
248	C₂×C₈×C₁₉	—	2	2	no	—
249	C₂×C₈×C₁₉	—	2	4	no	—
250	C₂×C₈×C₁₉	—	2	4	no	—
251	C₂×C₈×C₁₉	—	4	1	no	—
252	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
254	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
255	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₄⋊C₄×C₁₉	—	2	4	no	—
259	C₄⋊C₄×C₁₉	—	2	2	no	—
260	C₄⋊C₄×C₁₉	—	2	2	no	—
261	C₄⋊C₄×C₁₉	—	2	2	no	—
262	C₄⋊C₄×C₁₉	—	2	2	no	—
263	C₄⋊C₄×C₁₉	—	2	4	no	—
264	C₄⋊C₄×C₁₉	—	2	2	no	—
265	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
270	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₁₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₉	—	2	2	no	—
274	C₂²⋊C₄×C₁₉	—	2	2	no	—
275	C₂²⋊C₄×C₁₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₉	—	2	2	no	—
277	C₂²⋊C₄×C₁₉	—	2	2	no	—
278	C₂²⋊C₄×C₁₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₉	—	2	2	no	—
282	C₂²⋊C₄×C₁₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
287	C₄²×C₁₉	—	2	2	no	—
288	C₄²×C₁₉	—	2	4	no	—
289	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
292	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
293	#62324	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂³×C₁₉	—	2	2	no	—
295	C₂³×C₁₉	—	2	4	no	—
296	C₂³×C₁₉	—	8	4	no	—
297	C₂³×C₁₉	—	8	4	no	—
298	C₂³×C₁₉	—	8	4	no	—
299	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
300	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
302	Q₈×C₁₉	—	2	2	no	—
303	Q₈×C₁₉	—	2	2	no	—
304	Q₈×C₁₉	—	4	2	no	—
305	Q₈×C₁₉	—	4	4	no	—
306	D₄×C₁₉	—	2	2	no	—
307	D₄×C₁₉	—	2	2	no	—
308	D₄×C₁₉	—	2	2	no	—
309	D₄×C₁₉	—	2	4	no	—
310	D₄×C₁₉	—	2	4	no	—
311	D₄×C₁₉	—	2	2	no	—
312	D₄×C₁₉	—	4	2	no	—
313	D₄×C₁₉	—	4	2	no	—
314	D₄×C₁₉	—	4	2	no	—
315	D₄×C₁₉	—	4	2	no	—
316	D₄×C₁₉	—	4	4	no	—
317	D₄×C₁₉	—	8	2	no	—
318	D₄×C₁₉	—	8	4	no	—
319	D₄×C₁₉	—	8	2	no	—
320	D₄×C₁₉	—	8	4	no	—
321	D₄×C₁₉	—	8	4	no	—
322	D₄×C₁₉	—	8	4	no	—
323	D₄×C₁₉	—	8	4	no	—
324	D₄×C₁₉	—	8	4	no	—
325	C₂×C₄×C₁₉	—	2	2	no	—
326	C₂×C₄×C₁₉	—	2	1	no	—
327	C₂×C₄×C₁₉	—	2	2	no	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	1	no	—
330	C₂×C₄×C₁₉	—	2	2	no	—
331	C₂×C₄×C₁₉	—	2	2	no	—
332	C₂×C₄×C₁₉	—	2	2	no	—
333	C₂×C₄×C₁₉	—	2	2	no	—
334	C₂×C₄×C₁₉	—	2	4	no	—
335	C₂×C₄×C₁₉	—	2	2	no	—
336	C₂×C₄×C₁₉	—	4	1	no	—
337	C₂×C₄×C₁₉	—	4	4	no	—
338	C₂×C₄×C₁₉	—	8	4	no	—
339	C₂×C₄×C₁₉	—	8	4	no	—
340	C₂×C₄×C₁₉	—	8	4	no	—
341	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
349	C₈×C₁₉	—	2	1	no	—
350	C₈×C₁₉	—	2	2	no	—
351	C₈×C₁₉	—	2	2	no	—
352	C₈×C₁₉	—	2	1	no	—
353	C₈×C₁₉	—	2	1	no	—
354	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
355	#3546	C₂×C₁₉	1	2	yes	complemented
356	#3342	C₂×C₁₉	1	1	yes	characteristic, complemented
357	#3339	C₂×C₁₉	1	2	yes	complemented
358	#3334	C₂×C₁₉	1	1	yes	characteristic, complemented
359	#3332	C₂×C₁₉	1	2	yes	complemented
360	#3324	C₂×C₁₉	1	2	yes	complemented
361	#3322	C₂×C₁₉	1	4	yes	complemented
362	#3287	C₂×C₁₉	1	1	yes	characteristic, complemented
363	#3280	C₂×C₁₉	1	2	yes	complemented
364	D₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
365	#3251	C₂×C₁₉	1	2	yes	complemented
366	#3198	C₂×C₁₉	1	4	yes	complemented
367	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
368	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
369	#3061	C₂×C₁₉	1	2	yes	complemented
370	#3058	C₂×C₁₉	1	2	yes	complemented
371	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
372	C₂²×C₁₉	—	2	1	no	—
373	C₂²×C₁₉	—	2	2	no	—
374	C₂²×C₁₉	—	2	2	no	—
375	C₂²×C₁₉	—	2	1	no	—
376	C₂²×C₁₉	—	2	2	no	—
377	C₂²×C₁₉	—	2	2	no	—
378	C₂²×C₁₉	—	2	1	no	—
379	C₂²×C₁₉	—	2	2	no	—
380	C₂²×C₁₉	—	2	2	no	—
381	C₂²×C₁₉	—	4	4	no	—
382	C₂²×C₁₉	—	4	2	no	—
383	C₂²×C₁₉	—	4	4	no	—
384	C₂²×C₁₉	—	4	2	no	—
385	C₂²×C₁₉	—	4	2	no	—
386	C₂²×C₁₉	—	4	4	no	—
387	C₂²×C₁₉	—	16	8	no	—
388	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
389	C₄×C₁₉	—	2	1	no	—
390	C₄×C₁₉	—	2	1	no	—
391	C₄×C₁₉	—	2	2	no	—
392	C₄×C₁₉	—	2	1	no	—
393	C₄×C₁₉	—	2	2	no	—
394	C₄×C₁₉	—	2	1	no	—
395	C₄×C₁₉	—	4	2	no	—
396	C₄×C₁₉	—	4	2	no	—
397	C₄×C₁₉	—	4	2	no	—
398	C₄×C₁₉	—	4	4	no	—
399	C₄×C₁₉	#576	1	2	yes	—
400	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₄×C₁₉	#585	1	1	yes	characteristic
402	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
403	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
404	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
405	#560	—	2	4	no	—
406	#556	C₂²×C₁₉	1	2	yes	—
407	#553	C₂²×C₁₉	1	4	yes	complemented
408	#550	—	2	2	no	—
409	#550	C₂²×C₁₉	1	2	yes	complemented
410	#547	C₂²×C₁₉	1	2	yes	complemented
411	#546	—	2	2	no	—
412	#546	C₂²×C₁₉	1	4	yes	complemented
413	D₄²	C₂²×C₁₉	1	2	yes	—
414	#542	—	2	2	no	—
415	#538	—	2	4	no	—
416	#537	C₂²×C₁₉	1	4	yes	complemented
417	#535	—	2	2	no	—
418	#535	C₂²×C₁₉	1	4	yes	complemented
419	#532	C₂²×C₁₉	1	1	yes	characteristic
420	#532	C₂²×C₁₉	1	2	yes	complemented
421	#529	C₂²×C₁₉	1	2	yes	complemented
422	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
423	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	#495	C₂²×C₁₉	1	1	yes	characteristic
425	#493	C₂²×C₁₉	1	1	yes	characteristic
426	#488	C₂²×C₁₉	1	2	yes	complemented
427	#486	C₂²×C₁₉	1	2	yes	complemented
428	#485	C₂²×C₁₉	1	4	yes	complemented
429	#482	C₂²×C₁₉	1	4	yes	complemented
430	#481	C₂²×C₁₉	1	4	yes	complemented
431	#480	C₂²×C₁₉	1	4	yes	complemented
432	#478	C₂²×C₁₉	1	4	yes	complemented
433	#475	C₂²×C₁₉	1	2	yes	complemented
434	#474	C₂²×C₁₉	1	2	yes	complemented
435	#469	C₂²×C₁₉	1	4	yes	complemented
436	#469	C₂²×C₁₉	1	4	yes	complemented
437	#468	C₂²×C₁₉	1	4	yes	complemented
438	#468	C₂²×C₁₉	1	4	yes	complemented
439	#467	C₂²×C₁₉	1	2	yes	complemented
440	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
441	#466	C₂²×C₁₉	1	2	yes	—
442	#466	C₂²×C₁₉	1	2	yes	—
443	#466	C₂²×C₁₉	1	1	yes	characteristic
444	#466	C₂²×C₁₉	1	2	yes	complemented
445	#466	C₂²×C₁₉	1	2	yes	complemented
446	#466	C₂²×C₁₉	1	2	yes	complemented
447	#465	C₂²×C₁₉	1	2	yes	complemented
448	#463	C₂²×C₁₉	1	4	yes	complemented
449	#460	C₂²×C₁₉	1	2	yes	complemented
450	#459	C₂²×C₁₉	1	2	yes	—
451	#450	C₂²×C₁₉	1	4	yes	complemented
452	#449	C₂²×C₁₉	1	4	yes	complemented
453	#449	C₂²×C₁₉	1	4	yes	complemented
454	#447	C₂²×C₁₉	1	4	yes	—
455	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
456	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
457	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
458	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
459	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
460	#436	C₂²×C₁₉	1	1	yes	characteristic
461	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
462	#436	C₂²×C₁₉	1	2	yes	complemented
463	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
464	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
465	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
466	#427	C₂²×C₁₉	1	2	yes	complemented
467	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
468	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
469	#418	C₂²×C₁₉	1	4	yes	complemented
470	#417	C₂²×C₁₉	1	4	yes	complemented
471	#408	C₂²×C₁₉	1	2	yes	complemented
472	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
473	C₂×C₁₉	—	4	1	no	—
474	C₂×C₁₉	—	4	2	no	—
475	C₂×C₁₉	—	4	2	no	—
476	C₂×C₁₉	—	8	4	no	—
477	C₂×C₁₉	—	8	2	no	—
478	C₂×C₁₉	#3496	1	1	yes	characteristic
479	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
480	C₂×C₁₉	#3584	1	1	yes	characteristic
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	2	2	no	—
483	C₂×#41	C₂³×C₁₉	1	4	yes	—
484	C₂×#41	C₂³×C₁₉	1	2	yes	—
485	C₂²×D₄	—	2	2	no	—
486	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
487	#135	—	4	4	no	—
488	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
489	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
490	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
491	C₂×D₈	—	4	4	no	—
492	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
493	C₂×D₈	C₂³×C₁₉	1	2	yes	—
494	C₂×D₈	C₂³×C₁₉	1	4	yes	—
495	C₂×D₈	C₂³×C₁₉	1	2	yes	—
496	#131	—	4	4	no	—
497	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
498	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
499	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
500	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
502	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
503	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
504	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
506	#127	—	2	2	no	—
507	#127	—	2	4	no	—
508	#127	D₄×C₁₉	1	1	yes	characteristic
509	#127	C₂³×C₁₉	1	2	yes	—
510	#126	—	2	4	no	—
511	#126	—	2	4	no	—
512	#126	—	2	2	no	—
513	#125	C₂³×C₁₉	1	2	yes	—
514	#124	—	2	4	no	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	D₄×C₁₉	1	2	yes	—
518	#124	C₂³×C₁₉	1	2	yes	—
519	#123	—	2	2	no	—
520	#123	—	2	4	no	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
526	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#121	—	2	4	no	—
530	#121	—	2	4	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	4	no	—
534	#121	—	2	4	no	—
535	#121	D₄×C₁₉	1	1	yes	characteristic
536	#121	D₄×C₁₉	1	1	yes	characteristic
537	#121	D₄×C₁₉	1	2	yes	—
538	#121	C₂³×C₁₉	1	2	yes	—
539	#121	C₂³×C₁₉	1	4	yes	—
540	#121	C₂³×C₁₉	1	4	yes	—
541	#121	C₂³×C₁₉	1	4	yes	—
542	#121	C₂³×C₁₉	1	4	yes	—
543	#120	—	2	4	no	—
544	#120	—	2	4	no	—
545	#120	—	2	4	no	—
546	#120	—	2	4	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	C₂³×C₁₉	1	2	yes	—
554	C₄×D₄	C₂³×C₁₉	1	4	yes	—
555	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₁₉	1	2	yes	—
557	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
558	#117	—	2	2	no	—
559	#117	C₂³×C₁₉	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
561	C₂×C₂²⋊C₄	—	2	4	no	—
562	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
563	#107	C₂³×C₁₉	1	1	yes	characteristic
564	#107	C₂³×C₁₉	1	2	yes	—
565	#107	C₂³×C₁₉	1	4	yes	—
566	#107	C₂³×C₁₉	1	1	yes	characteristic
567	#107	C₂³×C₁₉	1	2	yes	—
568	#106	C₂³×C₁₉	1	4	yes	—
569	#106	C₂³×C₁₉	1	2	yes	—
570	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
571	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
572	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
573	#103	C₂³×C₁₉	1	2	yes	—
574	#103	C₂³×C₁₉	1	4	yes	—
575	#103	C₂³×C₁₉	1	2	yes	—
576	#102	C₂³×C₁₉	1	4	yes	—
577	#102	C₂³×C₁₉	1	4	yes	—
578	#102	C₂³×C₁₉	1	2	yes	—
579	#102	C₂³×C₁₉	1	4	yes	—
580	#102	C₂³×C₁₉	1	4	yes	—
581	#102	C₂³×C₁₉	1	2	yes	—
582	#102	C₂³×C₁₉	1	4	yes	—
583	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
585	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
586	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
587	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
588	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
589	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
590	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
591	C₁₉	#62324	1	1	yes	characteristic, direct product factor, Sylow
592	C₂⁴	—	2	4	no	—
593	#41	—	4	2	no	—
594	#41	—	4	2	no	—
595	#41	—	4	4	no	—
596	#41	—	4	4	no	—
597	#41	—	8	4	no	—
598	#41	—	8	4	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
601	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	8	4	no	—
614	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
615	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
616	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
617	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
619	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
620	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
621	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
631	Q₁₆	—	2	2	no	—
632	SD₁₆	—	4	2	no	—
633	SD₁₆	—	4	4	no	—
634	D₈	—	2	2	no	—
635	D₈	—	2	4	no	—
636	D₈	—	4	4	no	—
637	D₈	—	4	2	no	—
638	M₁₆	—	4	2	no	—
639	M₁₆	—	4	2	no	—
640	M₁₆	—	4	2	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	4	no	—
643	C₂×C₈	—	2	4	no	—
644	C₂×C₈	—	4	1	no	—
645	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
646	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
647	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
648	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
649	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
650	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
659	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
660	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
661	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
677	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
678	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
679	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	4	no	—
682	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
684	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
685	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
686	C₂³	—	2	2	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	8	4	no	—
689	C₂³	—	8	4	no	—
690	C₂³	—	8	4	no	—
691	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
692	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
693	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
694	Q₈	—	2	2	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	4	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	4	no	—
702	D₄	—	2	4	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	4	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	2	no	—
711	D₄	—	8	4	no	—
712	D₄	—	8	4	no	—
713	D₄	—	8	4	no	—
714	D₄	—	8	4	no	—
715	D₄	—	8	2	no	—
716	D₄	—	8	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	8	4	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	—	8	4	no	—
733	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
740	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
741	C₈	—	2	1	no	—
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	2	1	no	—
745	C₈	—	2	1	no	—
746	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	4	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	16	8	no	—
763	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
764	C₄	—	2	2	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	4	no	—
773	C₄	—	4	2	no	—
774	C₄	C₁₉×#576	1	2	yes	—
775	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
776	C₄	C₁₉×#585	1	1	yes	characteristic
777	C₂	—	4	2	no	—
778	C₂	—	4	1	no	—
779	C₂	—	4	2	no	—
780	C₂	—	8	2	no	—
781	C₂	—	8	4	no	—
782	C₂	C₁₉×#3496	1	1	yes	characteristic
783	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
784	C₂	C₁₉×#3584	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3546	C₂	semidirect
2. C₁₉×#3342	C₂	semidirect
3. C₁₉×#3339	C₂	semidirect
4. C₁₉×#3334	C₂	semidirect
5. C₁₉×#3332	C₂	semidirect
6. C₁₉×#3324	C₂	semidirect
7. C₁₉×#3322	C₂	semidirect
8. C₁₉×#3287	C₂	semidirect
9. C₁₉×#3280	C₂	semidirect
10. D₄×D₈×C₁₉	C₂	semidirect
11. C₁₉×#3251	C₂	semidirect
12. C₁₉×#3198	C₂	semidirect
13. C₁₉×#3169	C₂	semidirect
14. C₁₉×#3168	C₂	semidirect
15. C₁₉×#3061	C₂	semidirect
16. C₁₉×#3058	C₂	semidirect
17. C₁₉×#2931	C₂	semidirect
18. C₂×C₁₉×#135	C₂²	semidirect
20. C₂×C₁₉×#131	C₂²	semidirect
23. C₁₉×#553	C₂²	semidirect
25. C₁₉×#550	C₂²	semidirect
26. C₁₉×#547	C₂²	semidirect
28. C₁₉×#546	C₂²	semidirect
32. C₁₉×#537	C₂²	semidirect
34. C₁₉×#535	C₂²	semidirect
36. C₁₉×#532	C₂²	semidirect
37. C₁₉×#529	C₂²	semidirect
38. C₁₉×#500	C₂²	semidirect
39. C₁₉×#499	C₂²	semidirect
42. C₁₉×#488	C₂²	semidirect
43. C₁₉×#486	C₂²	semidirect
44. C₁₉×#485	C₂²	semidirect
45. C₁₉×#482	C₂²	semidirect
46. C₁₉×#481	C₂²	semidirect
47. C₁₉×#480	C₂²	semidirect
48. C₁₉×#478	C₂²	semidirect
49. C₁₉×#475	C₂²	semidirect
50. C₁₉×#474	C₂²	semidirect
51. C₁₉×#469	C₂²	semidirect
52. C₁₉×#469	C₂²	semidirect
53. C₁₉×#468	C₂²	semidirect
54. C₁₉×#468	C₂²	semidirect
55. C₁₉×#467	C₂²	semidirect
56. C₁₉×#467	C₂²	semidirect
60. C₁₉×#466	C₂²	semidirect
61. C₁₉×#466	C₂²	semidirect
62. C₁₉×#466	C₂²	semidirect
63. C₁₉×#465	C₂²	semidirect
64. C₁₉×#463	C₂²	semidirect
65. C₁₉×#460	C₂²	semidirect
67. C₁₉×#450	C₂²	semidirect
68. C₁₉×#449	C₂²	semidirect
69. C₁₉×#449	C₂²	semidirect
71. C₄×Q₁₆×C₁₉	C₂²	semidirect
72. C₄×SD₁₆×C₁₉	C₂²	semidirect
74. C₄×D₈×C₁₉	C₂²	semidirect
75. C₄×D₈×C₁₉	C₂²	semidirect
77. C₁₉×#436	C₂²	semidirect
78. C₁₉×#436	C₂²	semidirect
80. C₈×D₄×C₁₉	C₂²	semidirect
81. C₈×D₄×C₁₉	C₂²	semidirect
82. C₁₉×#427	C₂²	semidirect
83. C₂×C₁₉×#107	C₂²	semidirect
84. C₁₉×#423	C₂²	semidirect
85. C₁₉×#418	C₂²	semidirect
86. C₁₉×#417	C₂²	semidirect
87. C₁₉×#408	C₂²	semidirect
88. C₂×C₄×C₈×C₁₉	C₂²	semidirect
293. #62324	C₁₉	direct (N × H)
355. #3546	C₂×C₁₉	semidirect
356. #3342	C₂×C₁₉	semidirect
357. #3339	C₂×C₁₉	semidirect
358. #3334	C₂×C₁₉	semidirect
359. #3332	C₂×C₁₉	semidirect
360. #3324	C₂×C₁₉	semidirect
361. #3322	C₂×C₁₉	semidirect
362. #3287	C₂×C₁₉	semidirect
363. #3280	C₂×C₁₉	semidirect
364. D₄×D₈	C₂×C₁₉	semidirect
365. #3251	C₂×C₁₉	semidirect
366. #3198	C₂×C₁₉	semidirect
367. #3169	C₂×C₁₉	semidirect
368. #3168	C₂×C₁₉	semidirect
369. #3061	C₂×C₁₉	semidirect
370. #3058	C₂×C₁₉	semidirect
371. #2931	C₂×C₁₉	semidirect
402. C₂×#135	C₂²×C₁₉	semidirect
404. C₂×#131	C₂²×C₁₉	semidirect
407. #553	C₂²×C₁₉	semidirect
409. #550	C₂²×C₁₉	semidirect
410. #547	C₂²×C₁₉	semidirect
412. #546	C₂²×C₁₉	semidirect
416. #537	C₂²×C₁₉	semidirect
418. #535	C₂²×C₁₉	semidirect
420. #532	C₂²×C₁₉	semidirect
421. #529	C₂²×C₁₉	semidirect
422. #500	C₂²×C₁₉	semidirect
423. #499	C₂²×C₁₉	semidirect
426. #488	C₂²×C₁₉	semidirect
427. #486	C₂²×C₁₉	semidirect
428. #485	C₂²×C₁₉	semidirect
429. #482	C₂²×C₁₉	semidirect
430. #481	C₂²×C₁₉	semidirect
431. #480	C₂²×C₁₉	semidirect
432. #478	C₂²×C₁₉	semidirect
433. #475	C₂²×C₁₉	semidirect
434. #474	C₂²×C₁₉	semidirect
435. #469	C₂²×C₁₉	semidirect
436. #469	C₂²×C₁₉	semidirect
437. #468	C₂²×C₁₉	semidirect
438. #468	C₂²×C₁₉	semidirect
439. #467	C₂²×C₁₉	semidirect
440. #467	C₂²×C₁₉	semidirect
444. #466	C₂²×C₁₉	semidirect
445. #466	C₂²×C₁₉	semidirect
446. #466	C₂²×C₁₉	semidirect
447. #465	C₂²×C₁₉	semidirect
448. #463	C₂²×C₁₉	semidirect
449. #460	C₂²×C₁₉	semidirect
451. #450	C₂²×C₁₉	semidirect
452. #449	C₂²×C₁₉	semidirect
453. #449	C₂²×C₁₉	semidirect
455. C₄×Q₁₆	C₂²×C₁₉	semidirect
456. C₄×SD₁₆	C₂²×C₁₉	semidirect
458. C₄×D₈	C₂²×C₁₉	semidirect
459. C₄×D₈	C₂²×C₁₉	semidirect
461. #436	C₂²×C₁₉	semidirect
462. #436	C₂²×C₁₉	semidirect
464. C₈×D₄	C₂²×C₁₉	semidirect
465. C₈×D₄	C₂²×C₁₉	semidirect
466. #427	C₂²×C₁₉	semidirect
467. C₂×#107	C₂²×C₁₉	semidirect
468. #423	C₂²×C₁₉	semidirect
469. #418	C₂²×C₁₉	semidirect
470. #417	C₂²×C₁₉	semidirect
471. #408	C₂²×C₁₉	semidirect
472. C₂×C₄×C₈	C₂²×C₁₉	semidirect
591. C₁₉	#62324	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×#3546	2
C₁₉×#3342	2
C₁₉×#3339	2
C₁₉×#3334	2
C₁₉×#3332	2
C₁₉×#3324	2
C₁₉×#3322	2
C₁₉×#3287	2
C₁₉×#3280	2
D₄×D₈×C₁₉	2
C₁₉×#3251	2
C₁₉×#3198	2
C₁₉×#3169	2
C₁₉×#3168	2
C₁₉×#3061	2
C₁₉×#3058	2
C₁₉×#2931	2
#62324	19

Subgroups — C19×#62324 #18068283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62324 #18068283