Subgroups — C₁₉×#18557 #18024516

Order 4864.

900 conjugacy classes of subgroups.

The subgroup lattice has 712 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	C₁₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3116	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1633	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic
16	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#557	—	2	1	no	—
18	C₁₉×#557	C₂²	1	1	yes	characteristic
19	C₁₉×#554	—	2	2	no	—
20	C₁₉×#554	—	2	1	no	—
21	C₁₉×#554	—	2	1	no	—
22	C₁₉×#554	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₁₉	—	2	1	no	—
24	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#533	—	2	2	no	—
26	C₁₉×#533	—	2	1	no	—
27	C₁₉×#533	—	2	1	no	—
28	C₁₉×#533	C₂²	1	1	yes	characteristic
29	C₁₉×#533	C₂²	1	1	yes	characteristic
30	C₄×#41×C₁₉	—	2	1	no	—
31	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
33	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#498	C₂²	1	1	yes	characteristic
35	C₁₉×#494	C₂²	1	1	yes	characteristic
36	C₁₉×#487	C₂²	1	1	yes	characteristic
37	C₁₉×#487	C₂²	1	1	yes	characteristic
38	C₁₉×#485	—	2	1	no	—
39	C₁₉×#479	—	2	1	no	—
40	C₁₉×#479	—	2	1	no	—
41	C₁₉×#477	C₂²	1	1	yes	characteristic
42	C₁₉×#477	C₂²	1	1	yes	characteristic
43	C₁₉×#477	C₂²	1	1	yes	characteristic
44	C₁₉×#476	C₂²	1	1	yes	characteristic
45	C₁₉×#475	C₂²	1	1	yes	characteristic
46	C₁₉×#475	C₂²	1	1	yes	characteristic
47	C₁₉×#470	—	2	2	no	—
48	C₁₉×#462	C₂²	1	1	yes	characteristic
49	C₁₉×#461	C₂²	1	1	yes	characteristic
50	C₁₉×#452	—	2	1	no	—
51	C₁₉×#441	—	2	2	no	—
52	C₁₉×#441	—	2	1	no	—
53	C₁₉×#440	—	2	1	no	—
54	C₁₉×#432	C₂²	1	1	yes	characteristic
55	C₁₉×#428	—	2	1	no	—
56	C₁₉×#423	C₂²	1	1	yes	characteristic
57	C₁₉×#419	—	2	1	no	—
58	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
72	C₂²×Q₈×C₁₉	—	2	1	no	—
73	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
74	C₂×Q₁₆×C₁₉	—	2	1	no	—
75	C₂×Q₁₆×C₁₉	—	2	2	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	—	2	1	no	—
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	2	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	—	2	2	no	—
82	C₁₉×C₄⋊Q₈	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	1	no	—
84	C₁₉×C₄⋊Q₈	—	2	1	no	—
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×#125	—	2	2	no	—
90	C₁₉×#125	—	2	2	no	—
91	C₁₉×#125	—	2	2	no	—
92	C₁₉×#125	—	2	1	no	—
93	C₁₉×#125	—	2	1	no	—
94	C₁₉×#125	—	2	1	no	—
95	C₁₉×#125	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×C₂²⋊Q₈	—	2	2	no	—
103	C₁₉×C₂²⋊Q₈	—	2	1	no	—
104	C₁₉×C₂²⋊Q₈	—	2	1	no	—
105	C₁₉×C₂²⋊Q₈	—	2	2	no	—
106	C₁₉×C₂²⋊Q₈	—	2	1	no	—
107	C₁₉×C₂²⋊Q₈	—	2	1	no	—
108	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
109	C₄×Q₈×C₁₉	—	2	2	no	—
110	C₄×Q₈×C₁₉	—	2	2	no	—
111	C₄×Q₈×C₁₉	—	2	2	no	—
112	C₄×Q₈×C₁₉	—	2	1	no	—
113	C₄×Q₈×C₁₉	—	2	1	no	—
114	C₄×Q₈×C₁₉	—	2	1	no	—
115	C₄×Q₈×C₁₉	—	2	1	no	—
116	C₄×Q₈×C₁₉	—	2	1	no	—
117	C₄×Q₈×C₁₉	—	2	1	no	—
118	C₄×Q₈×C₁₉	—	2	1	no	—
119	C₄×Q₈×C₁₉	—	2	1	no	—
120	C₄×Q₈×C₁₉	—	2	1	no	—
121	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
122	C₄×Q₈×C₁₉	D₄	1	2	yes	—
123	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
125	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₁₉	—	2	2	no	—
129	C₄×D₄×C₁₉	—	2	2	no	—
130	C₄×D₄×C₁₉	—	2	1	no	—
131	C₄×D₄×C₁₉	—	2	1	no	—
132	C₄×D₄×C₁₉	—	2	1	no	—
133	C₄×D₄×C₁₉	—	2	1	no	—
134	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
135	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₁₉×#117	—	2	2	no	—
137	C₁₉×#117	—	2	1	no	—
138	C₁₉×#117	—	2	1	no	—
139	C₁₉×#117	—	2	1	no	—
140	C₁₉×#117	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
145	C₂×C₄²×C₁₉	—	2	2	no	—
146	C₂×C₄²×C₁₉	—	2	1	no	—
147	C₂×C₄²×C₁₉	—	2	1	no	—
148	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
149	C₁₉×#107	—	2	1	no	—
150	C₁₉×#107	—	2	1	no	—
151	C₁₉×#107	—	2	1	no	—
152	C₁₉×#106	—	2	1	no	—
153	C₁₉×#106	—	2	1	no	—
154	C₁₉×#106	—	2	2	no	—
155	C₁₉×#106	—	2	1	no	—
156	C₁₉×C₄⋊C₈	—	2	1	no	—
157	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₉×#103	—	2	1	no	—
162	C₁₉×#103	—	2	1	no	—
163	C₁₉×#103	—	2	1	no	—
164	C₁₉×#103	—	2	1	no	—
165	C₁₉×#103	—	2	1	no	—
166	C₁₉×#103	—	2	2	no	—
167	C₁₉×#103	—	2	1	no	—
168	C₁₉×#103	—	2	1	no	—
169	C₁₉×#103	—	2	2	no	—
170	C₁₉×#102	—	2	1	no	—
171	C₁₉×C₂²⋊C₈	—	2	1	no	—
172	C₁₉×#97	—	2	1	no	—
173	C₁₉×#97	—	2	1	no	—
174	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
176	#41×C₁₉	—	2	2	no	—
177	#41×C₁₉	—	2	2	no	—
178	C₂×Q₈×C₁₉	—	2	2	no	—
179	C₂×Q₈×C₁₉	—	2	2	no	—
180	C₂×Q₈×C₁₉	—	2	1	no	—
181	C₂×Q₈×C₁₉	—	2	1	no	—
182	C₂×Q₈×C₁₉	—	2	2	no	—
183	C₂×Q₈×C₁₉	—	2	1	no	—
184	C₂×Q₈×C₁₉	—	2	1	no	—
185	C₂×Q₈×C₁₉	—	4	1	no	—
186	C₂×Q₈×C₁₉	—	4	2	no	—
187	C₂×Q₈×C₁₉	—	4	2	no	—
188	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₁₉	—	2	1	no	—
193	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	2	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	2	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	Q₁₆×C₁₉	—	4	4	no	—
205	Q₁₆×C₁₉	—	4	2	no	—
206	SD₁₆×C₁₉	—	4	2	no	—
207	M₁₆×C₁₉	—	4	2	no	—
208	M₁₆×C₁₉	—	4	2	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	—	2	1	no	—
211	C₂×C₈×C₁₉	—	2	1	no	—
212	C₂×C₈×C₁₉	—	2	1	no	—
213	C₂×C₈×C₁₉	—	2	1	no	—
214	C₂×C₈×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	2	no	—
216	C₄⋊C₄×C₁₉	—	2	2	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₄⋊C₄×C₁₉	—	2	2	no	—
220	C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₄⋊C₄×C₁₉	—	2	2	no	—
222	C₄⋊C₄×C₁₉	—	2	2	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	2	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	2	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	2	1	no	—
233	C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₄⋊C₄×C₁₉	—	2	1	no	—
236	C₄⋊C₄×C₁₉	—	2	1	no	—
237	C₄⋊C₄×C₁₉	—	2	1	no	—
238	C₄⋊C₄×C₁₉	—	2	1	no	—
239	C₄⋊C₄×C₁₉	—	4	1	no	—
240	C₄⋊C₄×C₁₉	—	4	1	no	—
241	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₁₉	—	2	2	no	—
247	C₂²⋊C₄×C₁₉	—	2	2	no	—
248	C₂²⋊C₄×C₁₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₉	—	2	1	no	—
250	C₂²⋊C₄×C₁₉	—	2	1	no	—
251	C₂²⋊C₄×C₁₉	—	2	1	no	—
252	C₂²⋊C₄×C₁₉	—	4	1	no	—
253	C₄²×C₁₉	—	2	2	no	—
254	C₄²×C₁₉	—	2	2	no	—
255	C₄²×C₁₉	—	2	1	no	—
256	C₄²×C₁₉	—	2	2	no	—
257	C₄²×C₁₉	—	2	1	no	—
258	C₄²×C₁₉	—	2	1	no	—
259	C₄²×C₁₉	—	2	1	no	—
260	C₄²×C₁₉	—	2	1	no	—
261	C₄²×C₁₉	—	2	1	no	—
262	C₄²×C₁₉	—	2	1	no	—
263	C₄²×C₁₉	—	4	1	no	—
264	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
268	#18557	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂³×C₁₉	—	2	1	no	—
270	C₂³×C₁₉	#120	1	1	yes	characteristic
271	Q₈×C₁₉	—	2	1	no	—
272	Q₈×C₁₉	—	2	1	no	—
273	Q₈×C₁₉	—	2	1	no	—
274	Q₈×C₁₉	—	2	1	no	—
275	Q₈×C₁₉	—	4	2	no	—
276	Q₈×C₁₉	—	4	2	no	—
277	Q₈×C₁₉	—	4	4	no	—
278	Q₈×C₁₉	—	4	2	no	—
279	Q₈×C₁₉	—	4	1	no	—
280	Q₈×C₁₉	—	4	1	no	—
281	Q₈×C₁₉	—	4	1	no	—
282	Q₈×C₁₉	—	4	1	no	—
283	Q₈×C₁₉	—	8	2	no	—
284	Q₈×C₁₉	#137	1	2	yes	—
285	Q₈×C₁₉	#137	1	2	yes	—
286	D₄×C₁₉	—	2	4	no	—
287	D₄×C₁₉	—	2	1	no	—
288	D₄×C₁₉	#137	1	2	yes	—
289	C₂×C₄×C₁₉	—	2	4	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	2	1	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	1	no	—
296	C₂×C₄×C₁₉	—	2	1	no	—
297	C₂×C₄×C₁₉	—	2	1	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	2	no	—
305	C₂×C₄×C₁₉	—	4	4	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	8	1	no	—
311	C₂×C₄×C₁₉	—	8	1	no	—
312	C₂×C₄×C₁₉	—	8	2	no	—
313	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
314	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
315	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
316	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
319	C₈×C₁₉	—	2	2	no	—
320	C₈×C₁₉	—	4	1	no	—
321	C₈×C₁₉	—	4	1	no	—
322	C₈×C₁₉	—	4	1	no	—
323	C₈×C₁₉	—	4	1	no	—
324	C₈×C₁₉	—	4	1	no	—
325	Q₈×#41	C₂×C₁₉	1	1	yes	characteristic
326	#3185	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#3116	C₂×C₁₉	1	1	yes	characteristic
328	#3078	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1651	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1645	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1643	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1637	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1636	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1633	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1632	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#1489	C₂×C₁₉	1	1	yes	characteristic
340	C₂²×C₁₉	—	2	1	no	—
341	C₂²×C₁₉	—	2	2	no	—
342	C₂²×C₁₉	—	2	1	no	—
343	C₂²×C₁₉	—	2	1	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
347	C₄×C₁₉	—	2	1	no	—
348	C₄×C₁₉	—	2	2	no	—
349	C₄×C₁₉	—	2	1	no	—
350	C₄×C₁₉	—	2	2	no	—
351	C₄×C₁₉	—	2	1	no	—
352	C₄×C₁₉	—	2	1	no	—
353	C₄×C₁₉	—	4	1	no	—
354	C₄×C₁₉	—	4	2	no	—
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	2	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	1	no	—
360	C₄×C₁₉	—	8	1	no	—
361	C₄×C₁₉	—	8	1	no	—
362	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
363	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
364	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
365	C₄×C₁₉	#575	1	1	yes	characteristic
366	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
367	#557	—	2	1	no	—
368	#557	C₂²×C₁₉	1	1	yes	characteristic
369	#554	—	2	2	no	—
370	#554	—	2	1	no	—
371	#554	—	2	1	no	—
372	#554	C₂²×C₁₉	1	1	yes	characteristic
373	D₄×Q₈	—	2	1	no	—
374	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
375	#533	—	2	2	no	—
376	#533	—	2	1	no	—
377	#533	—	2	1	no	—
378	#533	C₂²×C₁₉	1	1	yes	characteristic
379	#533	C₂²×C₁₉	1	1	yes	characteristic
380	C₄×#41	—	2	1	no	—
381	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×C₄×Q₈	—	2	1	no	—
383	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
384	#498	C₂²×C₁₉	1	1	yes	characteristic
385	#494	C₂²×C₁₉	1	1	yes	characteristic
386	#487	C₂²×C₁₉	1	1	yes	characteristic
387	#487	C₂²×C₁₉	1	1	yes	characteristic
388	#485	—	2	1	no	—
389	#479	—	2	1	no	—
390	#479	—	2	1	no	—
391	#477	C₂²×C₁₉	1	1	yes	characteristic
392	#477	C₂²×C₁₉	1	1	yes	characteristic
393	#477	C₂²×C₁₉	1	1	yes	characteristic
394	#476	C₂²×C₁₉	1	1	yes	characteristic
395	#475	C₂²×C₁₉	1	1	yes	characteristic
396	#475	C₂²×C₁₉	1	1	yes	characteristic
397	#470	—	2	2	no	—
398	#462	C₂²×C₁₉	1	1	yes	characteristic
399	#461	C₂²×C₁₉	1	1	yes	characteristic
400	#452	—	2	1	no	—
401	#441	—	2	1	no	—
402	#441	—	2	2	no	—
403	#440	—	2	1	no	—
404	#432	C₂²×C₁₉	1	1	yes	characteristic
405	#428	—	2	1	no	—
406	#423	C₂²×C₁₉	1	1	yes	characteristic
407	#419	—	2	1	no	—
408	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
409	#333	C₂²×C₁₉	1	1	yes	characteristic
410	#333	C₂²×C₁₉	1	1	yes	characteristic
411	#332	C₂²×C₁₉	1	1	yes	characteristic
412	#332	C₂²×C₁₉	1	1	yes	characteristic
413	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
414	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
415	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
416	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
417	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
418	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
419	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
420	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×C₁₉	—	4	1	no	—
422	C₂×C₁₉	—	4	2	no	—
423	C₂×C₁₉	#3004	1	1	yes	characteristic
424	C₂×C₁₉	#3007	1	1	yes	characteristic
425	C₂×C₁₉	#3018	1	1	yes	characteristic
426	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
429	C₂×Q₁₆	—	2	1	no	—
430	C₂×Q₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	1	no	—
432	C₂×M₁₆	—	2	1	no	—
433	C₂×M₁₆	—	2	1	no	—
434	C₄⋊Q₈	—	2	2	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	2	no	—
437	C₄⋊Q₈	—	2	1	no	—
438	C₄⋊Q₈	—	2	1	no	—
439	C₄⋊Q₈	—	2	1	no	—
440	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	2	no	—
447	#125	—	2	1	no	—
448	#125	—	2	1	no	—
449	#125	—	2	1	no	—
450	#125	—	2	1	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	2	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	—	2	1	no	—
463	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	1	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×Q₈	—	2	1	no	—
474	C₄×Q₈	—	2	1	no	—
475	C₄×Q₈	—	2	1	no	—
476	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
477	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
478	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
479	C₄×Q₈	D₄×C₁₉	1	2	yes	—
480	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
481	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
482	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	2	1	no	—
488	C₄×D₄	—	2	1	no	—
489	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
490	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
491	#117	—	2	2	no	—
492	#117	—	2	1	no	—
493	#117	—	2	1	no	—
494	#117	—	2	1	no	—
495	#117	D₄×C₁₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	—	2	2	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
500	C₂×C₄²	—	2	2	no	—
501	C₂×C₄²	—	2	1	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
504	#107	—	2	1	no	—
505	#107	—	2	1	no	—
506	#107	—	2	1	no	—
507	#106	—	2	1	no	—
508	#106	—	2	1	no	—
509	#106	—	2	2	no	—
510	#106	—	2	1	no	—
511	C₄⋊C₈	—	2	1	no	—
512	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
513	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
514	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
515	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
516	#103	—	2	1	no	—
517	#103	—	2	1	no	—
518	#103	—	2	1	no	—
519	#103	—	2	1	no	—
520	#103	—	2	1	no	—
521	#103	—	2	2	no	—
522	#103	—	2	1	no	—
523	#103	—	2	1	no	—
524	#103	—	2	2	no	—
525	#102	—	2	1	no	—
526	C₂²⋊C₈	—	2	1	no	—
527	#97	—	2	1	no	—
528	#97	—	2	1	no	—
529	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
530	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
531	C₁₉	#18557	1	1	yes	characteristic, direct product factor, Sylow
532	#41	—	2	2	no	—
533	#41	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	4	1	no	—
542	C₂×Q₈	—	4	2	no	—
543	C₂×Q₈	—	4	2	no	—
544	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	Q₁₆	—	4	4	no	—
561	Q₁₆	—	4	2	no	—
562	SD₁₆	—	4	2	no	—
563	M₁₆	—	4	2	no	—
564	M₁₆	—	4	2	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	—	4	1	no	—
597	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
599	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
600	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
601	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	4	1	no	—
620	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
621	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
622	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
623	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
624	C₂³	—	2	1	no	—
625	C₂³	C₁₉×#120	1	1	yes	characteristic
626	Q₈	—	2	1	no	—
627	Q₈	—	2	1	no	—
628	Q₈	—	2	1	no	—
629	Q₈	—	2	1	no	—
630	Q₈	—	4	2	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	4	no	—
633	Q₈	—	4	2	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	4	1	no	—
638	Q₈	—	8	2	no	—
639	Q₈	C₁₉×#137	1	2	yes	—
640	Q₈	C₁₉×#137	1	2	yes	—
641	D₄	—	2	4	no	—
642	D₄	—	2	1	no	—
643	D₄	C₁₉×#137	1	2	yes	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	8	1	no	—
666	C₂×C₄	—	8	1	no	—
667	C₂×C₄	—	8	2	no	—
668	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
669	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
670	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
671	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
673	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
674	C₈	—	2	2	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
687	C₄	—	2	1	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
703	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
704	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
705	C₄	C₁₉×#575	1	1	yes	characteristic
706	C₂	—	4	1	no	—
707	C₂	—	4	2	no	—
708	C₂	C₁₉×#3004	1	1	yes	characteristic
709	C₂	C₁₉×#3007	1	1	yes	characteristic
710	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3185	C₂	semidirect
4. C₁₉×#3078	C₂	semidirect
5. C₁₉×#1653	C₂	semidirect
6. C₁₉×#1651	C₂	semidirect
7. C₁₉×#1645	C₂	semidirect
8. C₁₉×#1643	C₂	semidirect
9. C₁₉×#1637	C₂	semidirect
10. C₁₉×#1636	C₂	semidirect
11. C₁₉×#1633	C₂	semidirect
12. C₁₉×#1632	C₂	semidirect
13. C₁₉×#1559	C₂	semidirect
14. C₁₉×#1491	C₂	semidirect
268. #18557	C₁₉	direct (N × H)
326. #3185	C₂×C₁₉	semidirect
328. #3078	C₂×C₁₉	semidirect
329. #1653	C₂×C₁₉	semidirect
330. #1651	C₂×C₁₉	semidirect
331. #1645	C₂×C₁₉	semidirect
332. #1643	C₂×C₁₉	semidirect
333. #1637	C₂×C₁₉	semidirect
334. #1636	C₂×C₁₉	semidirect
335. #1633	C₂×C₁₉	semidirect
336. #1632	C₂×C₁₉	semidirect
337. #1559	C₂×C₁₉	semidirect
338. #1491	C₂×C₁₉	semidirect
531. C₁₉	#18557	direct (N × H)

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
C₁₉×#3185	2
C₁₉×#3116	2
C₁₉×#3078	2
C₁₉×#1653	2
C₁₉×#1651	2
C₁₉×#1645	2
C₁₉×#1643	2
C₁₉×#1637	2
C₁₉×#1636	2
C₁₉×#1633	2
C₁₉×#1632	2
C₁₉×#1559	2
C₁₉×#1491	2
C₁₉×#1489	2
#18557	19

Subgroups — C19×#18557 #18024516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18557 #18024516