Subgroups — C₁₉×#62381 #18068340

Order 4864.

1756 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3397	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3385	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3384	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3362	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3361	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3360	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3358	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3257	C₂	1	4	yes	maximal, complemented
12	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3179	C₂	1	4	yes	maximal, complemented
15	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#563	—	2	2	no	—
19	C₁₉×#562	—	2	2	no	—
20	C₁₉×#559	C₂²	1	2	yes	—
21	Q₈²×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#556	—	2	1	no	—
23	C₁₉×#556	C₂²	1	2	yes	—
24	C₁₉×#554	C₂²	1	2	yes	—
25	C₁₉×#554	C₂²	1	2	yes	—
26	C₁₉×#550	C₂²	1	2	yes	—
27	C₁₉×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₁₉	—	2	1	no	—
29	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
30	C₁₉×#547	—	2	1	no	—
31	C₁₉×#547	—	2	1	no	—
32	C₁₉×#542	—	2	2	no	—
33	C₁₉×#542	C₂²	1	4	yes	—
34	C₁₉×#540	C₂²	1	4	yes	—
35	C₁₉×#537	—	2	2	no	—
36	C₁₉×#537	—	2	2	no	—
37	C₁₉×#536	—	2	2	no	—
38	C₁₉×#533	C₂²	1	1	yes	characteristic
39	C₁₉×#533	C₂²	1	1	yes	characteristic
40	C₁₉×#532	C₂²	1	1	yes	characteristic
41	C₁₉×#532	C₂²	1	1	yes	characteristic
42	C₁₉×#532	C₂²	1	1	yes	characteristic
43	C₁₉×#501	C₂²	1	4	yes	—
44	C₁₉×#500	C₂²	1	1	yes	characteristic
45	C₁₉×#498	C₂²	1	1	yes	characteristic
46	C₁₉×#496	C₂²	1	4	yes	—
47	C₁₉×#493	C₂²	1	1	yes	characteristic
48	C₁₉×#492	C₂²	1	1	yes	characteristic
49	C₁₉×#488	C₂²	1	4	yes	—
50	C₁₉×#487	C₂²	1	1	yes	characteristic
51	C₁₉×#486	C₂²	1	1	yes	characteristic
52	C₁₉×#486	C₂²	1	1	yes	characteristic
53	C₁₉×#486	C₂²	1	1	yes	characteristic
54	C₁₉×#486	C₂²	1	4	yes	—
55	C₁₉×#479	C₂²	1	4	yes	—
56	C₁₉×#478	C₂²	1	4	yes	—
57	C₁₉×#477	C₂²	1	2	yes	—
58	C₁₉×#476	C₂²	1	2	yes	—
59	C₁₉×#476	C₂²	1	2	yes	—
60	C₁₉×#476	C₂²	1	4	yes	—
61	C₁₉×#474	C₂²	1	2	yes	—
62	C₁₉×#474	C₂²	1	4	yes	—
63	C₁₉×#469	C₂²	1	4	yes	—
64	C₁₉×#468	C₂²	1	4	yes	—
65	C₁₉×#466	C₂²	1	2	yes	—
66	C₁₉×#466	C₂²	1	2	yes	—
67	C₁₉×#465	C₂²	1	2	yes	—
68	C₁₉×#465	C₂²	1	2	yes	—
69	C₁₉×#463	C₂²	1	4	yes	—
70	C₁₉×#463	C₂²	1	4	yes	—
71	C₁₉×#461	C₂²	1	2	yes	—
72	C₁₉×#460	C₂²	1	2	yes	—
73	C₁₉×#460	C₂²	1	4	yes	—
74	C₁₉×#459	C₂²	1	2	yes	—
75	C₁₉×#459	C₂²	1	2	yes	—
76	C₁₉×#459	C₂²	1	4	yes	—
77	C₁₉×#446	C₂²	1	2	yes	—
78	C₁₉×#446	C₂²	1	2	yes	—
79	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
80	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
81	C₁₉×#442	C₂²	1	4	yes	—
82	C₁₉×#440	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
86	C₄×D₈×C₁₉	C₂²	1	2	yes	—
87	C₄×D₈×C₁₉	C₂²	1	2	yes	—
88	C₄×D₈×C₁₉	C₂²	1	4	yes	—
89	C₁₉×#424	C₂²	1	2	yes	—
90	C₁₉×#423	C₂²	1	1	yes	characteristic
91	C₁₉×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₉	—	2	2	no	—
94	C₂×#41×C₁₉	—	2	2	no	—
95	C₂×#41×C₁₉	—	2	1	no	—
96	C₂×#41×C₁₉	—	2	1	no	—
97	C₂×#41×C₁₉	—	2	1	no	—
98	C₂²×Q₈×C₁₉	—	2	2	no	—
99	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
102	C₂×D₈×C₁₉	C₂³	1	2	yes	—
103	C₂×D₈×C₁₉	C₂³	1	4	yes	—
104	C₂×D₈×C₁₉	C₂³	1	2	yes	—
105	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊Q₈	—	2	4	no	—
109	C₁₉×C₄⋊Q₈	—	2	2	no	—
110	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₉×#127	C₂³	1	1	yes	characteristic
119	C₁₉×#127	C₂³	1	1	yes	characteristic
120	C₁₉×#127	C₂³	1	4	yes	—
121	C₁₉×#127	C₂³	1	1	yes	characteristic
122	C₁₉×#126	—	2	4	no	—
123	C₁₉×#126	—	2	4	no	—
124	C₁₉×#125	—	2	1	no	—
125	C₁₉×#125	D₄	1	2	yes	—
126	C₁₉×#125	C₂³	1	4	yes	—
127	C₁₉×#124	—	2	2	no	—
128	C₁₉×#124	—	2	4	no	—
129	C₁₉×#124	—	2	1	no	—
130	C₁₉×#124	—	2	1	no	—
131	C₁₉×#124	—	2	1	no	—
132	C₁₉×#124	C₂³	1	4	yes	—
133	C₁₉×#123	—	2	4	no	—
134	C₁₉×#123	—	2	4	no	—
135	C₁₉×#123	—	2	4	no	—
136	C₁₉×#123	—	2	4	no	—
137	C₁₉×C₂²⋊Q₈	—	2	2	no	—
138	C₁₉×C₂²⋊Q₈	—	2	2	no	—
139	C₁₉×C₂²⋊Q₈	—	2	2	no	—
140	C₁₉×C₂²⋊Q₈	—	2	1	no	—
141	C₁₉×C₂²⋊Q₈	—	2	2	no	—
142	C₁₉×C₂²⋊Q₈	—	2	4	no	—
143	C₁₉×C₂²⋊Q₈	—	2	4	no	—
144	C₁₉×C₂²⋊Q₈	—	2	4	no	—
145	C₁₉×C₂²⋊Q₈	—	2	4	no	—
146	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
147	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
148	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₉×#121	—	2	1	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	1	no	—
152	C₁₉×#121	—	2	2	no	—
153	C₁₉×#121	—	2	2	no	—
154	C₁₉×#121	—	2	4	no	—
155	C₁₉×#121	—	2	4	no	—
156	C₁₉×#121	—	2	4	no	—
157	C₁₉×#121	—	2	4	no	—
158	C₁₉×#121	C₂³	1	2	yes	—
159	C₁₉×#121	C₂³	1	2	yes	—
160	C₁₉×#121	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₉	—	2	2	no	—
162	C₄×Q₈×C₁₉	—	2	1	no	—
163	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
167	C₄×D₄×C₁₉	—	2	2	no	—
168	C₄×D₄×C₁₉	—	2	1	no	—
169	C₄×D₄×C₁₉	—	2	1	no	—
170	C₄×D₄×C₁₉	—	2	1	no	—
171	C₄×D₄×C₁₉	C₂³	1	2	yes	—
172	C₄×D₄×C₁₉	C₂³	1	2	yes	—
173	C₄×D₄×C₁₉	C₂³	1	4	yes	—
174	C₄×D₄×C₁₉	C₂³	1	4	yes	—
175	C₄×D₄×C₁₉	C₂³	1	2	yes	—
176	C₄×D₄×C₁₉	C₂³	1	4	yes	—
177	C₁₉×#117	—	2	1	no	—
178	C₁₉×#117	—	2	2	no	—
179	C₁₉×#117	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
183	C₁₉×#107	C₂³	1	2	yes	—
184	C₁₉×#107	C₂³	1	2	yes	—
185	C₁₉×#107	C₂³	1	4	yes	—
186	C₁₉×#106	C₂³	1	2	yes	—
187	C₁₉×#106	C₂³	1	2	yes	—
188	C₁₉×#106	C₂³	1	4	yes	—
189	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
190	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
191	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
192	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
193	C₁₉×#103	C₂³	1	2	yes	—
194	C₁₉×#103	C₂³	1	2	yes	—
195	C₁₉×#103	C₂³	1	4	yes	—
196	C₁₉×#102	C₂³	1	2	yes	—
197	C₁₉×#102	C₂³	1	2	yes	—
198	C₁₉×#102	C₂³	1	2	yes	—
199	C₁₉×#102	C₂³	1	2	yes	—
200	C₁₉×#102	C₂³	1	2	yes	—
201	C₁₉×#102	C₂³	1	2	yes	—
202	C₁₉×#102	C₂³	1	4	yes	—
203	C₁₉×#102	C₂³	1	4	yes	—
204	C₁₉×#102	C₂³	1	4	yes	—
205	C₁₉×#97	C₂³	1	4	yes	—
206	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
207	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₉	C₂³	1	4	yes	—
211	#41×C₁₉	—	8	2	no	—
212	#41×C₁₉	—	8	2	no	—
213	#41×C₁₉	—	8	2	no	—
214	#41×C₁₉	—	8	4	no	—
215	#41×C₁₉	—	8	4	no	—
216	C₂×Q₈×C₁₉	—	2	1	no	—
217	C₂×Q₈×C₁₉	—	2	1	no	—
218	C₂×Q₈×C₁₉	—	2	1	no	—
219	C₂×Q₈×C₁₉	—	2	4	no	—
220	C₂×Q₈×C₁₉	—	2	1	no	—
221	C₂×Q₈×C₁₉	—	8	4	no	—
222	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
225	C₂×D₄×C₁₉	—	2	2	no	—
226	C₂×D₄×C₁₉	—	2	2	no	—
227	C₂×D₄×C₁₉	—	2	2	no	—
228	C₂×D₄×C₁₉	—	2	1	no	—
229	C₂×D₄×C₁₉	—	2	1	no	—
230	C₂×D₄×C₁₉	—	2	1	no	—
231	C₂×D₄×C₁₉	—	2	4	no	—
232	C₂×D₄×C₁₉	—	2	4	no	—
233	C₂×D₄×C₁₉	—	2	1	no	—
234	C₂×D₄×C₁₉	—	2	1	no	—
235	C₂×D₄×C₁₉	—	2	1	no	—
236	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
237	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
238	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₉	—	2	2	no	—
240	C₂²×C₄×C₁₉	—	2	2	no	—
241	C₂²×C₄×C₁₉	—	2	2	no	—
242	C₂²×C₄×C₁₉	—	2	4	no	—
243	C₂²×C₄×C₁₉	—	2	4	no	—
244	C₂²×C₄×C₁₉	—	2	4	no	—
245	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₁₉	—	2	4	no	—
249	SD₁₆×C₁₉	—	4	2	no	—
250	SD₁₆×C₁₉	—	4	4	no	—
251	D₈×C₁₉	—	2	4	no	—
252	D₈×C₁₉	—	4	2	no	—
253	D₈×C₁₉	—	4	4	no	—
254	M₁₆×C₁₉	—	4	2	no	—
255	C₂×C₈×C₁₉	—	2	2	no	—
256	C₂×C₈×C₁₉	—	4	1	no	—
257	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
261	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₄⋊C₄×C₁₉	—	2	1	no	—
263	C₄⋊C₄×C₁₉	—	2	1	no	—
264	C₄⋊C₄×C₁₉	—	2	4	no	—
265	C₄⋊C₄×C₁₉	—	2	4	no	—
266	C₄⋊C₄×C₁₉	—	2	1	no	—
267	C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₄⋊C₄×C₁₉	—	2	2	no	—
271	C₄⋊C₄×C₁₉	—	2	4	no	—
272	C₄⋊C₄×C₁₉	—	2	4	no	—
273	C₄⋊C₄×C₁₉	—	2	2	no	—
274	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
280	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
284	C₂²⋊C₄×C₁₉	—	2	2	no	—
285	C₂²⋊C₄×C₁₉	—	2	4	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	4	no	—
290	C₂²⋊C₄×C₁₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₉	—	2	2	no	—
293	C₂²⋊C₄×C₁₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
297	C₄²×C₁₉	—	2	2	no	—
298	C₄²×C₁₉	—	2	4	no	—
299	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
302	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
303	C₄²×C₁₉	C₂⁴	1	4	yes	—
304	#62381	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
305	C₂³×C₁₉	—	2	2	no	—
306	C₂³×C₁₉	—	2	2	no	—
307	C₂³×C₁₉	—	2	2	no	—
308	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₁₉	—	2	4	no	—
310	Q₈×C₁₉	—	2	4	no	—
311	Q₈×C₁₉	—	2	2	no	—
312	Q₈×C₁₉	—	2	2	no	—
313	Q₈×C₁₉	—	4	2	no	—
314	Q₈×C₁₉	—	8	4	no	—
315	Q₈×C₁₉	—	8	1	no	—
316	Q₈×C₁₉	—	8	1	no	—
317	Q₈×C₁₉	—	8	1	no	—
318	D₄×C₁₉	—	2	2	no	—
319	D₄×C₁₉	—	2	2	no	—
320	D₄×C₁₉	—	2	2	no	—
321	D₄×C₁₉	—	2	2	no	—
322	D₄×C₁₉	—	2	2	no	—
323	D₄×C₁₉	—	2	2	no	—
324	D₄×C₁₉	—	4	2	no	—
325	D₄×C₁₉	—	4	2	no	—
326	D₄×C₁₉	—	4	2	no	—
327	D₄×C₁₉	—	8	1	no	—
328	D₄×C₁₉	—	8	1	no	—
329	D₄×C₁₉	—	8	4	no	—
330	D₄×C₁₉	—	8	1	no	—
331	D₄×C₁₉	—	8	4	no	—
332	D₄×C₁₉	—	8	2	no	—
333	D₄×C₁₉	—	8	2	no	—
334	D₄×C₁₉	—	8	2	no	—
335	C₂×C₄×C₁₉	—	2	2	no	—
336	C₂×C₄×C₁₉	—	2	2	no	—
337	C₂×C₄×C₁₉	—	2	1	no	—
338	C₂×C₄×C₁₉	—	2	1	no	—
339	C₂×C₄×C₁₉	—	2	2	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	2	no	—
342	C₂×C₄×C₁₉	—	2	2	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	4	4	no	—
345	C₂×C₄×C₁₉	—	4	4	no	—
346	C₂×C₄×C₁₉	—	4	4	no	—
347	C₂×C₄×C₁₉	—	8	4	no	—
348	C₂×C₄×C₁₉	—	8	4	no	—
349	C₂×C₄×C₁₉	—	8	4	no	—
350	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
355	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
358	C₈×C₁₉	—	2	1	no	—
359	C₈×C₁₉	—	2	1	no	—
360	C₈×C₁₉	—	2	1	no	—
361	C₈×C₁₉	—	2	4	no	—
362	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
363	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
364	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
365	#3399	C₂×C₁₉	1	2	yes	complemented
366	#3397	C₂×C₁₉	1	2	yes	complemented
367	#3385	C₂×C₁₉	1	2	yes	complemented
368	#3384	C₂×C₁₉	1	2	yes	complemented
369	#3362	C₂×C₁₉	1	2	yes	complemented
370	#3361	C₂×C₁₉	1	2	yes	complemented
371	#3360	C₂×C₁₉	1	2	yes	complemented
372	#3358	C₂×C₁₉	1	2	yes	complemented
373	#3257	C₂×C₁₉	1	4	yes	complemented
374	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
375	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
376	#3179	C₂×C₁₉	1	4	yes	complemented
377	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
378	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
379	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
380	C₂²×C₁₉	—	2	1	no	—
381	C₂²×C₁₉	—	2	1	no	—
382	C₂²×C₁₉	—	2	1	no	—
383	C₂²×C₁₉	—	4	2	no	—
384	C₂²×C₁₉	—	4	2	no	—
385	C₂²×C₁₉	—	4	2	no	—
386	C₂²×C₁₉	—	4	2	no	—
387	C₂²×C₁₉	—	4	2	no	—
388	C₂²×C₁₉	—	4	2	no	—
389	C₂²×C₁₉	—	4	2	no	—
390	C₂²×C₁₉	—	4	2	no	—
391	C₂²×C₁₉	—	4	2	no	—
392	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₁₉	—	2	1	no	—
394	C₄×C₁₉	—	2	1	no	—
395	C₄×C₁₉	—	2	4	no	—
396	C₄×C₁₉	—	2	1	no	—
397	C₄×C₁₉	—	2	4	no	—
398	C₄×C₁₉	—	4	2	no	—
399	C₄×C₁₉	—	4	2	no	—
400	C₄×C₁₉	—	4	2	no	—
401	C₄×C₁₉	—	4	2	no	—
402	C₄×C₁₉	—	4	2	no	—
403	C₄×C₁₉	#576	1	2	yes	—
404	C₄×C₁₉	#577	1	2	yes	—
405	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
406	C₄×C₁₉	#585	1	1	yes	characteristic
407	#563	—	2	2	no	—
408	#562	—	2	2	no	—
409	#559	C₂²×C₁₉	1	2	yes	—
410	Q₈²	C₂²×C₁₉	1	2	yes	—
411	#556	—	2	1	no	—
412	#556	C₂²×C₁₉	1	2	yes	—
413	#554	C₂²×C₁₉	1	2	yes	—
414	#554	C₂²×C₁₉	1	2	yes	—
415	#550	C₂²×C₁₉	1	2	yes	—
416	#550	C₂²×C₁₉	1	2	yes	—
417	D₄×Q₈	—	2	1	no	—
418	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
419	#547	—	2	1	no	—
420	#547	—	2	1	no	—
421	#542	—	2	2	no	—
422	#542	C₂²×C₁₉	1	4	yes	—
423	#540	C₂²×C₁₉	1	4	yes	—
424	#537	—	2	2	no	—
425	#537	—	2	2	no	—
426	#536	—	2	2	no	—
427	#533	C₂²×C₁₉	1	1	yes	characteristic
428	#533	C₂²×C₁₉	1	1	yes	characteristic
429	#532	C₂²×C₁₉	1	1	yes	characteristic
430	#532	C₂²×C₁₉	1	1	yes	characteristic
431	#532	C₂²×C₁₉	1	1	yes	characteristic
432	#501	C₂²×C₁₉	1	4	yes	—
433	#500	C₂²×C₁₉	1	1	yes	characteristic
434	#498	C₂²×C₁₉	1	1	yes	characteristic
435	#496	C₂²×C₁₉	1	4	yes	—
436	#493	C₂²×C₁₉	1	1	yes	characteristic
437	#492	C₂²×C₁₉	1	1	yes	characteristic
438	#488	C₂²×C₁₉	1	4	yes	—
439	#487	C₂²×C₁₉	1	1	yes	characteristic
440	#486	C₂²×C₁₉	1	1	yes	characteristic
441	#486	C₂²×C₁₉	1	4	yes	—
442	#486	C₂²×C₁₉	1	1	yes	characteristic
443	#486	C₂²×C₁₉	1	1	yes	characteristic
444	#479	C₂²×C₁₉	1	4	yes	—
445	#478	C₂²×C₁₉	1	4	yes	—
446	#477	C₂²×C₁₉	1	2	yes	—
447	#476	C₂²×C₁₉	1	2	yes	—
448	#476	C₂²×C₁₉	1	4	yes	—
449	#476	C₂²×C₁₉	1	2	yes	—
450	#474	C₂²×C₁₉	1	2	yes	—
451	#474	C₂²×C₁₉	1	4	yes	—
452	#469	C₂²×C₁₉	1	4	yes	—
453	#468	C₂²×C₁₉	1	4	yes	—
454	#466	C₂²×C₁₉	1	2	yes	—
455	#466	C₂²×C₁₉	1	2	yes	—
456	#465	C₂²×C₁₉	1	2	yes	—
457	#465	C₂²×C₁₉	1	2	yes	—
458	#463	C₂²×C₁₉	1	4	yes	—
459	#463	C₂²×C₁₉	1	4	yes	—
460	#461	C₂²×C₁₉	1	2	yes	—
461	#460	C₂²×C₁₉	1	4	yes	—
462	#460	C₂²×C₁₉	1	2	yes	—
463	#459	C₂²×C₁₉	1	2	yes	—
464	#459	C₂²×C₁₉	1	4	yes	—
465	#459	C₂²×C₁₉	1	2	yes	—
466	#446	C₂²×C₁₉	1	2	yes	—
467	#446	C₂²×C₁₉	1	2	yes	—
468	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
469	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
470	#442	C₂²×C₁₉	1	4	yes	—
471	#440	C₂²×C₁₉	1	4	yes	—
472	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
473	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
474	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
475	C₄×D₈	C₂²×C₁₉	1	2	yes	—
476	C₄×D₈	C₂²×C₁₉	1	4	yes	—
477	C₄×D₈	C₂²×C₁₉	1	2	yes	—
478	#424	C₂²×C₁₉	1	2	yes	—
479	#423	C₂²×C₁₉	1	1	yes	characteristic
480	#405	C₂²×C₁₉	1	2	yes	—
481	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
482	C₂×C₁₉	—	4	1	no	—
483	C₂×C₁₉	—	8	2	no	—
484	C₂×C₁₉	—	8	2	no	—
485	C₂×C₁₉	—	8	2	no	—
486	C₂×C₁₉	#3497	1	1	yes	characteristic
487	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
488	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	2	1	no	—
494	C₂²×Q₈	—	2	2	no	—
495	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
498	C₂×D₈	C₂³×C₁₉	1	2	yes	—
499	C₂×D₈	C₂³×C₁₉	1	4	yes	—
500	C₂×D₈	C₂³×C₁₉	1	2	yes	—
501	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
502	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
504	C₄⋊Q₈	—	2	4	no	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
507	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
512	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
514	#127	C₂³×C₁₉	1	1	yes	characteristic
515	#127	C₂³×C₁₉	1	1	yes	characteristic
516	#127	C₂³×C₁₉	1	1	yes	characteristic
517	#127	C₂³×C₁₉	1	4	yes	—
518	#126	—	2	4	no	—
519	#126	—	2	4	no	—
520	#125	—	2	1	no	—
521	#125	D₄×C₁₉	1	2	yes	—
522	#125	C₂³×C₁₉	1	4	yes	—
523	#124	—	2	2	no	—
524	#124	—	2	4	no	—
525	#124	—	2	1	no	—
526	#124	—	2	1	no	—
527	#124	—	2	1	no	—
528	#124	C₂³×C₁₉	1	4	yes	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	#123	—	2	4	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
543	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
544	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
545	#121	—	2	1	no	—
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	2	4	no	—
551	#121	—	2	4	no	—
552	#121	—	2	4	no	—
553	#121	—	2	4	no	—
554	#121	C₂³×C₁₉	1	2	yes	—
555	#121	C₂³×C₁₉	1	2	yes	—
556	#121	C₂³×C₁₉	1	2	yes	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
560	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
561	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
562	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	C₂³×C₁₉	1	2	yes	—
568	C₄×D₄	C₂³×C₁₉	1	2	yes	—
569	C₄×D₄	C₂³×C₁₉	1	2	yes	—
570	C₄×D₄	C₂³×C₁₉	1	4	yes	—
571	C₄×D₄	C₂³×C₁₉	1	4	yes	—
572	C₄×D₄	C₂³×C₁₉	1	4	yes	—
573	#117	—	2	1	no	—
574	#117	—	2	2	no	—
575	#117	C₂³×C₁₉	1	2	yes	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
579	#107	C₂³×C₁₉	1	2	yes	—
580	#107	C₂³×C₁₉	1	2	yes	—
581	#107	C₂³×C₁₉	1	4	yes	—
582	#106	C₂³×C₁₉	1	2	yes	—
583	#106	C₂³×C₁₉	1	2	yes	—
584	#106	C₂³×C₁₉	1	4	yes	—
585	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
586	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
587	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
588	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
589	#103	C₂³×C₁₉	1	2	yes	—
590	#103	C₂³×C₁₉	1	2	yes	—
591	#103	C₂³×C₁₉	1	4	yes	—
592	#102	C₂³×C₁₉	1	2	yes	—
593	#102	C₂³×C₁₉	1	2	yes	—
594	#102	C₂³×C₁₉	1	2	yes	—
595	#102	C₂³×C₁₉	1	2	yes	—
596	#102	C₂³×C₁₉	1	2	yes	—
597	#102	C₂³×C₁₉	1	2	yes	—
598	#102	C₂³×C₁₉	1	4	yes	—
599	#102	C₂³×C₁₉	1	4	yes	—
600	#102	C₂³×C₁₉	1	4	yes	—
601	#97	C₂³×C₁₉	1	4	yes	—
602	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
603	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
604	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
605	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₁₉	1	4	yes	—
607	C₁₉	#62381	1	1	yes	characteristic, direct product factor, Sylow
608	#41	—	8	2	no	—
609	#41	—	8	2	no	—
610	#41	—	8	2	no	—
611	#41	—	8	4	no	—
612	#41	—	8	4	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	8	4	no	—
619	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
620	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
634	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
635	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
645	SD₁₆	—	2	4	no	—
646	SD₁₆	—	4	2	no	—
647	SD₁₆	—	4	4	no	—
648	D₈	—	2	4	no	—
649	D₈	—	4	2	no	—
650	D₈	—	4	4	no	—
651	M₁₆	—	4	2	no	—
652	C₂×C₈	—	2	2	no	—
653	C₂×C₈	—	4	1	no	—
654	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
655	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
656	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
657	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
658	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
672	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
673	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
676	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
677	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	4	no	—
696	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
697	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
698	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
699	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
700	C₄²	C₂⁴×C₁₉	1	4	yes	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
705	Q₈	—	2	4	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	8	4	no	—
711	Q₈	—	8	1	no	—
712	Q₈	—	8	1	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	2	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	1	no	—
724	D₄	—	8	1	no	—
725	D₄	—	8	4	no	—
726	D₄	—	8	1	no	—
727	D₄	—	8	4	no	—
728	D₄	—	8	2	no	—
729	D₄	—	8	2	no	—
730	D₄	—	8	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	—	8	4	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
747	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
751	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
753	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
754	C₈	—	2	1	no	—
755	C₈	—	2	1	no	—
756	C₈	—	2	1	no	—
757	C₈	—	2	4	no	—
758	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	4	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	C₁₉×#576	1	2	yes	—
783	C₄	C₁₉×#577	1	2	yes	—
784	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
785	C₄	C₁₉×#585	1	1	yes	characteristic
786	C₂	—	4	1	no	—
787	C₂	—	8	2	no	—
788	C₂	—	8	2	no	—
789	C₂	—	8	2	no	—
790	C₂	C₁₉×#3497	1	1	yes	characteristic
791	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
792	C₂	C₂×C₁₉×#577	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3550	C₂	semidirect
2. C₁₉×#3548	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3397	C₂	semidirect
5. C₁₉×#3385	C₂	semidirect
6. C₁₉×#3384	C₂	semidirect
7. C₁₉×#3362	C₂	semidirect
8. C₁₉×#3361	C₂	semidirect
9. C₁₉×#3360	C₂	semidirect
10. C₁₉×#3358	C₂	semidirect
11. C₁₉×#3257	C₂	semidirect
12. C₁₉×#3254	C₂	semidirect
13. C₁₉×#3253	C₂	semidirect
14. C₁₉×#3179	C₂	semidirect
15. C₁₉×#3169	C₂	semidirect
16. C₁₉×#3167	C₂	semidirect
17. C₁₉×#2960	C₂	semidirect
304. #62381	C₁₉	direct (N × H)
363. #3550	C₂×C₁₉	semidirect
364. #3548	C₂×C₁₉	semidirect
365. #3399	C₂×C₁₉	semidirect
366. #3397	C₂×C₁₉	semidirect
367. #3385	C₂×C₁₉	semidirect
368. #3384	C₂×C₁₉	semidirect
369. #3362	C₂×C₁₉	semidirect
370. #3361	C₂×C₁₉	semidirect
371. #3360	C₂×C₁₉	semidirect
372. #3358	C₂×C₁₉	semidirect
373. #3257	C₂×C₁₉	semidirect
374. #3254	C₂×C₁₉	semidirect
375. #3253	C₂×C₁₉	semidirect
376. #3179	C₂×C₁₉	semidirect
377. #3169	C₂×C₁₉	semidirect
378. #3167	C₂×C₁₉	semidirect
379. #2960	C₂×C₁₉	semidirect
607. C₁₉	#62381	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×#3550	2
C₁₉×#3548	2
C₁₉×#3399	2
C₁₉×#3397	2
C₁₉×#3385	2
C₁₉×#3384	2
C₁₉×#3362	2
C₁₉×#3361	2
C₁₉×#3360	2
C₁₉×#3358	2
C₁₉×#3257	2
C₁₉×#3254	2
C₁₉×#3253	2
C₁₉×#3179	2
C₁₉×#3169	2
C₁₉×#3167	2
C₁₉×#2960	2
#62381	19

Subgroups — C19×#62381 #18068340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62381 #18068340