Subgroups — C₁₉×#22529 #18028488

Order 4864.

1004 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1995	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1986	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1806	C₂	1	2	yes	maximal
9	C₁₉×#1806	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1759	C₂	1	2	yes	maximal
11	C₄×C₁₉×#104	C₂	1	1	yes	maximal, characteristic
12	Q₈²×C₁₉	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#557	C₄	1	2	yes	complemented
14	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#554	—	2	2	no	—
16	C₁₉×#554	—	2	1	no	—
17	C₁₉×#554	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#554	C₄	1	2	yes	complemented
19	D₄×Q₈×C₁₉	—	2	1	no	—
20	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#533	—	2	1	no	—
22	C₁₉×#533	—	2	2	no	—
23	C₁₉×#533	C₂²	1	1	yes	characteristic
24	C₁₉×#533	C₂²	1	2	yes	—
25	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×#41×C₁₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#446	—	2	1	no	—
30	C₁₉×#446	—	2	2	no	—
31	C₈×Q₈×C₁₉	—	2	1	no	—
32	C₁₉×#423	C₂²	1	1	yes	characteristic
33	C₁₉×#423	C₂²	1	2	yes	—
34	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#104	C₂²	1	2	yes	—
36	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
39	C₁₉×#391	—	2	1	no	—
40	C₁₉×#389	—	2	1	no	—
41	C₁₉×#387	—	2	2	no	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#376	C₂²	1	2	yes	—
45	C₄³×C₁₉	C₂²	1	1	yes	characteristic
46	C₁₉×#339	C₂²	1	1	yes	characteristic
47	C₁₉×#339	C₂²	1	2	yes	—
48	C₁₉×#339	C₂²	1	2	yes	—
49	C₁₉×#339	C₂²	1	2	yes	—
50	C₁₉×#339	C₂²	1	2	yes	—
51	C₁₉×#339	C₂²	1	2	yes	—
52	C₁₉×#339	C₂²	1	1	yes	characteristic
53	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
56	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
58	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
65	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#125	C₂×C₄	1	2	yes	—
71	C₁₉×#125	C₂×C₄	1	2	yes	—
72	C₁₉×#125	C₂×C₄	1	2	yes	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	2	no	—
89	C₄×Q₈×C₁₉	—	2	2	no	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
95	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	D₄	1	2	yes	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
109	C₁₉×#117	—	2	2	no	—
110	C₁₉×#117	—	2	1	no	—
111	C₁₉×#117	C₂³	1	1	yes	characteristic
112	C₁₉×#117	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₉	—	2	1	no	—
120	C₂×C₄²×C₁₉	—	2	2	no	—
121	C₂×C₄²×C₁₉	—	2	1	no	—
122	C₂×C₄²×C₁₉	—	2	1	no	—
123	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
128	C₁₉×C₄⋊C₈	—	2	1	no	—
129	C₁₉×C₄⋊C₈	—	2	2	no	—
130	C₁₉×C₄⋊C₈	—	2	2	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×#104	—	2	2	no	—
133	C₁₉×#104	—	2	4	no	—
134	C₁₉×#104	Q₈	1	4	yes	complemented
135	C₁₉×#97	—	2	2	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₄×C₈×C₁₉	—	2	1	no	—
138	C₄×C₈×C₁₉	—	2	2	no	—
139	C₁₉×#95	—	2	2	no	—
140	C₁₉×#95	—	2	2	no	—
141	C₁₉×#95	—	2	1	no	—
142	C₁₉×#95	—	2	2	no	—
143	#41×C₁₉	—	2	1	no	—
144	#41×C₁₉	—	2	1	no	—
145	#41×C₁₉	C₂×Q₈	1	2	yes	—
146	#41×C₁₉	#41	1	2	yes	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	4	2	no	—
152	C₂×Q₈×C₁₉	—	4	4	no	—
153	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
156	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₁₉	—	2	1	no	—
173	M₁₆×C₁₉	—	2	1	no	—
174	M₁₆×C₁₉	—	2	2	no	—
175	M₁₆×C₁₉	—	2	1	no	—
176	M₁₆×C₁₉	—	2	2	no	—
177	M₁₆×C₁₉	C₂×Q₈	1	2	yes	complemented
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	—	4	4	no	—
197	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
200	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
201	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
202	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
203	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
206	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	2	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	2	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	2	no	—
225	C₄²×C₁₉	—	4	2	no	—
226	C₄²×C₁₉	—	4	2	no	—
227	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
229	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
230	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₉	C₂×D₄	1	2	yes	—
233	C₄²×C₁₉	C₂×D₄	1	2	yes	—
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂×Q₈	1	2	yes	complemented
236	#22529	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₉	—	2	1	no	—
240	Q₈×C₁₉	—	2	2	no	—
241	Q₈×C₁₉	—	2	2	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	4	4	no	—
244	Q₈×C₁₉	—	4	2	no	—
245	Q₈×C₁₉	—	8	1	no	—
246	Q₈×C₁₉	—	8	2	no	—
247	Q₈×C₁₉	C₄×Q₈	1	2	yes	—
248	D₄×C₁₉	—	2	2	no	—
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	2	1	no	—
251	D₄×C₁₉	C₄×Q₈	1	2	yes	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	4	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	2	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	8	1	no	—
275	C₂×C₄×C₁₉	—	8	2	no	—
276	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
290	C₈×C₁₉	—	2	2	no	—
291	C₈×C₁₉	—	4	1	no	—
292	C₈×C₁₉	—	4	2	no	—
293	Q₈×#41	C₂×C₁₉	1	1	yes	characteristic
294	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#2295	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1995	C₂×C₁₉	1	2	yes	complemented
297	#1994	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1986	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1986	C₂×C₁₉	1	2	yes	complemented
300	#1806	C₂×C₁₉	1	1	yes	characteristic
301	#1806	C₂×C₁₉	1	2	yes	—
302	#1759	C₂×C₁₉	1	2	yes	—
303	C₄×#104	C₂×C₁₉	1	1	yes	characteristic
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	1	no	—
306	C₂²×C₁₉	—	2	2	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₁₉	#548	1	1	yes	characteristic
311	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	—	4	2	no	—
321	C₄×C₁₉	—	4	2	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	4	1	no	—
324	C₄×C₁₉	—	4	2	no	—
325	C₄×C₁₉	—	4	1	no	—
326	C₄×C₁₉	—	8	2	no	—
327	C₄×C₁₉	#421	1	2	yes	—
328	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
329	C₄×C₁₉	#519	1	1	yes	characteristic
330	C₄×C₁₉	#548	1	1	yes	characteristic
331	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
332	Q₈²	C₄×C₁₉	1	1	yes	characteristic, complemented
333	#557	C₄×C₁₉	1	2	yes	complemented
334	#557	C₄×C₁₉	1	1	yes	characteristic, complemented
335	#554	—	2	2	no	—
336	#554	—	2	1	no	—
337	#554	C₄×C₁₉	1	1	yes	characteristic, complemented
338	#554	C₄×C₁₉	1	2	yes	complemented
339	D₄×Q₈	—	2	1	no	—
340	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
341	#533	—	2	1	no	—
342	#533	—	2	2	no	—
343	#533	C₂²×C₁₉	1	1	yes	characteristic
344	#533	C₂²×C₁₉	1	2	yes	—
345	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
346	C₄×#41	C₂²×C₁₉	1	2	yes	—
347	C₂×C₄×Q₈	—	2	1	no	—
348	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
349	#446	—	2	1	no	—
350	#446	—	2	2	no	—
351	C₈×Q₈	—	2	1	no	—
352	#423	C₂²×C₁₉	1	1	yes	characteristic
353	#423	C₂²×C₁₉	1	2	yes	—
354	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#104	C₂²×C₁₉	1	2	yes	—
356	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
357	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
358	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
359	#391	—	2	1	no	—
360	#389	—	2	1	no	—
361	#387	—	2	2	no	—
362	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
363	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
364	#376	C₂²×C₁₉	1	2	yes	—
365	C₄³	C₂²×C₁₉	1	1	yes	characteristic
366	#339	C₂²×C₁₉	1	2	yes	—
367	#339	C₂²×C₁₉	1	2	yes	—
368	#339	C₂²×C₁₉	1	2	yes	—
369	#339	C₂²×C₁₉	1	1	yes	characteristic
370	#339	C₂²×C₁₉	1	2	yes	—
371	#339	C₂²×C₁₉	1	2	yes	—
372	#339	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₁₉	—	2	1	no	—
374	C₂×C₁₉	—	2	1	no	—
375	C₂×C₁₉	—	4	2	no	—
376	C₂×C₁₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
377	C₂×C₁₉	C₂×#421	1	1	yes	characteristic
378	C₂×C₁₉	#2901	1	1	yes	characteristic
379	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
380	C₂²×Q₈	—	2	1	no	—
381	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
382	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
383	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
385	C₄⋊Q₈	—	2	1	no	—
386	C₄⋊Q₈	—	2	2	no	—
387	C₄⋊Q₈	—	2	2	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
390	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
391	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
392	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
393	#125	—	2	2	no	—
394	#125	—	2	2	no	—
395	#125	—	2	2	no	—
396	#125	C₂×C₄×C₁₉	1	2	yes	—
397	#125	C₂×C₄×C₁₉	1	2	yes	—
398	#125	C₂×C₄×C₁₉	1	2	yes	—
399	C₂²⋊Q₈	—	2	1	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
418	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
419	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
420	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
421	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
422	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
423	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
424	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
425	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
426	C₄×Q₈	D₄×C₁₉	1	2	yes	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
432	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
433	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
434	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
435	#117	—	2	2	no	—
436	#117	—	2	1	no	—
437	#117	C₂³×C₁₉	1	1	yes	characteristic
438	#117	C₂³×C₁₉	1	2	yes	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	2	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
444	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	2	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
451	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
454	C₄⋊C₈	—	2	1	no	—
455	C₄⋊C₈	—	2	2	no	—
456	C₄⋊C₈	—	2	2	no	—
457	C₄⋊C₈	—	2	1	no	—
458	#104	—	2	2	no	—
459	#104	—	2	4	no	—
460	#104	Q₈×C₁₉	1	4	yes	complemented
461	#97	—	2	2	no	—
462	#97	—	2	1	no	—
463	C₄×C₈	—	2	1	no	—
464	C₄×C₈	—	2	2	no	—
465	#95	—	2	2	no	—
466	#95	—	2	2	no	—
467	#95	—	2	1	no	—
468	#95	—	2	2	no	—
469	C₁₉	#22529	1	1	yes	characteristic, direct product factor, Sylow
470	#41	—	2	1	no	—
471	#41	—	2	1	no	—
472	#41	C₂×Q₈×C₁₉	1	2	yes	—
473	#41	#41×C₁₉	1	2	yes	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	4	2	no	—
479	C₂×Q₈	—	4	4	no	—
480	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
481	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
482	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
483	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	C₂×Q₈×C₁₉	1	2	yes	complemented
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	4	2	no	—
523	C₄⋊C₄	—	4	4	no	—
524	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
525	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
527	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
528	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
529	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
530	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
533	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	4	2	no	—
553	C₄²	—	4	2	no	—
554	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
555	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
556	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
557	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
558	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₄²	C₂×D₄×C₁₉	1	2	yes	—
560	C₄²	C₂×D₄×C₁₉	1	2	yes	—
561	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₄²	C₂×Q₈×C₁₉	1	2	yes	complemented
563	C₂³	—	2	1	no	—
564	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	1	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	4	4	no	—
570	Q₈	—	4	2	no	—
571	Q₈	—	8	1	no	—
572	Q₈	—	8	2	no	—
573	Q₈	C₄×Q₈×C₁₉	1	2	yes	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	1	no	—
577	D₄	C₄×Q₈×C₁₉	1	2	yes	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	8	1	no	—
601	C₂×C₄	—	8	2	no	—
602	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
603	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
604	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
605	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
606	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
607	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
608	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
610	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
612	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
613	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
614	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
615	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
625	C₂²	C₁₉×#548	1	1	yes	characteristic
626	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
627	C₄	—	2	2	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	8	2	no	—
642	C₄	C₁₉×#421	1	2	yes	—
643	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
644	C₄	C₁₉×#519	1	1	yes	characteristic
645	C₄	C₁₉×#548	1	1	yes	characteristic
646	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	4	2	no	—
650	C₂	Q₈×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
651	C₂	C₂×C₁₉×#421	1	1	yes	characteristic
652	C₂	C₁₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#2295	C₂	semidirect
4. C₁₉×#1995	C₂	semidirect
5. C₁₉×#1994	C₂	semidirect
6. C₁₉×#1986	C₂	semidirect
7. C₁₉×#1986	C₂	semidirect
12. Q₈²×C₁₉	C₄	semidirect
13. C₁₉×#557	C₄	semidirect
14. C₁₉×#557	C₄	semidirect
17. C₁₉×#554	C₄	semidirect
18. C₁₉×#554	C₄	semidirect
20. D₄×Q₈×C₁₉	C₄	semidirect
134. C₁₉×#104	Q₈	semidirect
177. M₁₆×C₁₉	C₂×Q₈	semidirect
235. C₄²×C₁₉	C₂×Q₈	semidirect
236. #22529	C₁₉	direct (N × H)
294. Q₈×M₁₆	C₂×C₁₉	semidirect
295. #2295	C₂×C₁₉	semidirect
296. #1995	C₂×C₁₉	semidirect
297. #1994	C₂×C₁₉	semidirect
298. #1986	C₂×C₁₉	semidirect
299. #1986	C₂×C₁₉	semidirect
332. Q₈²	C₄×C₁₉	semidirect
333. #557	C₄×C₁₉	semidirect
334. #557	C₄×C₁₉	semidirect
337. #554	C₄×C₁₉	semidirect
338. #554	C₄×C₁₉	semidirect
340. D₄×Q₈	C₄×C₁₉	semidirect
460. #104	Q₈×C₁₉	semidirect
469. C₁₉	#22529	direct (N × H)
504. M₁₆	C₂×Q₈×C₁₉	semidirect
562. C₄²	C₂×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41×C₁₉	2
Q₈×M₁₆×C₁₉	2
C₁₉×#2295	2
C₁₉×#1995	2
C₁₉×#1994	2
C₁₉×#1986	2
C₁₉×#1806	2
C₁₉×#1759	2
C₄×C₁₉×#104	2
#22529	19

Subgroups — C19×#22529 #18028488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22529 #18028488