Subgroups — C₁₉×#18563 #18024522

Order 4864.

1060 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3519	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1634	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1632	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1631	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1629	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	2	no	—
13	C₁₉×#555	C₂²	1	1	yes	characteristic
14	C₁₉×#554	C₂²	1	1	yes	characteristic
15	C₁₉×#553	—	2	1	no	—
16	C₁₉×#553	—	2	1	no	—
17	C₁₉×#550	C₂²	1	1	yes	characteristic
18	C₁₉×#546	—	2	2	no	—
19	C₁₉×#546	—	2	1	no	—
20	D₄²×C₁₉	—	2	1	no	—
21	D₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#540	—	2	1	no	—
23	C₁₉×#538	—	2	2	no	—
24	C₁₉×#532	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₁₉×#525	—	2	1	no	—
28	C₂×C₁₉×#121	—	2	1	no	—
29	C₁₉×#518	—	2	1	no	—
30	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#501	—	2	1	no	—
32	C₁₉×#497	—	2	2	no	—
33	C₁₉×#494	C₂²	1	2	yes	complemented
34	C₁₉×#492	C₂²	1	2	yes	complemented
35	C₁₉×#489	—	2	1	no	—
36	C₁₉×#483	—	2	1	no	—
37	C₁₉×#480	—	2	1	no	—
38	C₁₉×#477	C₂²	1	2	yes	complemented
39	C₁₉×#476	—	2	1	no	—
40	C₁₉×#476	—	2	1	no	—
41	C₁₉×#476	C₂²	1	2	yes	—
42	C₁₉×#476	C₂²	1	2	yes	complemented
43	C₁₉×#476	C₂²	1	2	yes	complemented
44	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₉×#106	—	2	1	no	—
46	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₉×#102	—	2	1	no	—
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#333	C₂²	1	2	yes	complemented
50	C₁₉×#331	C₂²	1	2	yes	complemented
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	D₄	1	2	yes	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	2	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₁₉×#137	—	4	8	no	—
64	C₂×Q₁₆×C₁₉	—	2	4	no	—
65	C₂×SD₁₆×C₁₉	—	2	4	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#127	C₂³	1	1	yes	characteristic
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	D₄	1	1	yes	characteristic
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	D₄	1	1	yes	characteristic
81	C₁₉×#124	D₄	1	2	yes	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	D₄	1	1	yes	characteristic
102	C₁₉×#120	—	2	2	no	—
103	C₁₉×#120	—	2	2	no	—
104	C₁₉×#120	—	2	2	no	—
105	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₉	—	2	2	no	—
107	C₄×D₄×C₁₉	—	2	2	no	—
108	C₄×D₄×C₁₉	—	2	2	no	—
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	—	2	1	no	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	—	2	1	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
117	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
118	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#117	—	2	1	no	—
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#107	—	2	2	no	—
133	C₁₉×#106	—	2	2	no	—
134	C₁₉×#106	—	2	2	no	—
135	C₁₉×#106	—	2	2	no	—
136	C₁₉×C₄⋊C₈	—	2	1	no	—
137	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
139	C₁₉×#103	—	2	2	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×#102	—	2	2	no	—
142	C₁₉×#102	—	2	2	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×#97	—	2	1	no	—
145	C₁₉×#97	—	2	1	no	—
146	C₄×C₈×C₁₉	C₂³	1	2	yes	—
147	C₂⁴×C₁₉	—	2	2	no	—
148	C₂⁴×C₁₉	—	2	1	no	—
149	#41×C₁₉	—	4	4	no	—
150	#41×C₁₉	—	8	2	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	4	4	no	—
153	C₂×Q₈×C₁₉	—	4	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	2	1	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	4	1	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	4	2	no	—
170	C₂×D₄×C₁₉	—	8	2	no	—
171	C₂×D₄×C₁₉	—	8	4	no	—
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	4	1	no	—
186	C₂²×C₄×C₁₉	—	8	2	no	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	Q₁₆×C₁₉	—	4	8	no	—
191	SD₁₆×C₁₉	—	4	8	no	—
192	M₁₆×C₁₉	—	2	4	no	—
193	C₂×C₈×C₁₉	—	2	2	no	—
194	C₂×C₈×C₁₉	—	2	2	no	—
195	C₂×C₈×C₁₉	—	2	2	no	—
196	C₂×C₈×C₁₉	—	4	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	2	no	—
207	C₄⋊C₄×C₁₉	—	2	2	no	—
208	C₄⋊C₄×C₁₉	—	4	1	no	—
209	C₄⋊C₄×C₁₉	—	4	1	no	—
210	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	2	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	2	1	no	—
230	C₄²×C₁₉	—	2	2	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
236	#18563	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	—	2	1	no	—
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	2	2	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	4	4	no	—
243	C₂³×C₁₉	—	4	2	no	—
244	C₂³×C₁₉	—	8	1	no	—
245	C₂³×C₁₉	—	8	2	no	—
246	C₂³×C₁₉	—	8	2	no	—
247	C₂³×C₁₉	#120	1	1	yes	characteristic
248	Q₈×C₁₉	—	2	2	no	—
249	Q₈×C₁₉	—	4	2	no	—
250	Q₈×C₁₉	—	4	4	no	—
251	Q₈×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	2	1	no	—
253	D₄×C₁₉	—	2	1	no	—
254	D₄×C₁₉	—	2	1	no	—
255	D₄×C₁₉	—	2	2	no	—
256	D₄×C₁₉	—	4	2	no	—
257	D₄×C₁₉	—	4	2	no	—
258	D₄×C₁₉	—	4	4	no	—
259	D₄×C₁₉	—	4	2	no	—
260	D₄×C₁₉	—	4	4	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	2	no	—
264	D₄×C₁₉	—	8	2	no	—
265	D₄×C₁₉	—	8	2	no	—
266	D₄×C₁₉	—	8	2	no	—
267	D₄×C₁₉	—	8	2	no	—
268	D₄×C₁₉	#137	1	2	yes	complemented
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	8	1	no	—
285	C₂×C₄×C₁₉	—	8	1	no	—
286	C₂×C₄×C₁₉	—	8	2	no	—
287	C₂×C₄×C₁₉	—	8	1	no	—
288	C₂×C₄×C₁₉	—	8	2	no	—
289	C₂×C₄×C₁₉	—	8	2	no	—
290	C₂×C₄×C₁₉	—	8	2	no	—
291	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
292	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
293	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
297	C₈×C₁₉	—	2	4	no	—
298	C₈×C₁₉	—	4	2	no	—
299	C₈×C₁₉	—	4	2	no	—
300	#3519	C₂×C₁₉	1	1	yes	characteristic
301	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#3152	C₂×C₁₉	1	1	yes	characteristic, complemented
303	C₂×#476	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1634	C₂×C₁₉	1	2	yes	complemented
305	#1632	C₂×C₁₉	1	2	yes	complemented
306	#1631	C₂×C₁₉	1	2	yes	complemented
307	#1629	C₂×C₁₉	1	2	yes	complemented
308	#1551	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1483	C₂×C₁₉	1	1	yes	characteristic, complemented
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	2	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	2	no	—
319	C₂²×C₁₉	—	4	1	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	8	4	no	—
326	C₂²×C₁₉	—	16	4	no	—
327	C₂²×C₁₉	#453	1	2	yes	—
328	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
329	C₄×C₁₉	—	2	1	no	—
330	C₄×C₁₉	—	2	1	no	—
331	C₄×C₁₉	—	2	1	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	4	1	no	—
334	C₄×C₁₉	—	4	1	no	—
335	C₄×C₁₉	—	4	1	no	—
336	C₄×C₁₉	—	4	1	no	—
337	C₄×C₁₉	—	4	1	no	—
338	C₄×C₁₉	—	4	2	no	—
339	C₄×C₁₉	—	8	2	no	—
340	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
341	C₄×C₁₉	#575	1	1	yes	characteristic
342	C₄×C₁₉	#577	1	2	yes	—
343	C₂×#137	—	2	2	no	—
344	#555	C₂²×C₁₉	1	1	yes	characteristic
345	#554	C₂²×C₁₉	1	1	yes	characteristic
346	#553	—	2	1	no	—
347	#553	—	2	1	no	—
348	#550	C₂²×C₁₉	1	1	yes	characteristic
349	#546	—	2	2	no	—
350	#546	—	2	1	no	—
351	D₄²	—	2	1	no	—
352	D₄²	C₂²×C₁₉	1	1	yes	characteristic
353	#540	—	2	1	no	—
354	#538	—	2	2	no	—
355	#532	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#529	C₂²×C₁₉	1	1	yes	characteristic
358	#525	—	2	1	no	—
359	C₂×#121	—	2	1	no	—
360	#518	—	2	1	no	—
361	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
362	#501	—	2	1	no	—
363	#497	—	2	2	no	—
364	#494	C₂²×C₁₉	1	2	yes	complemented
365	#492	C₂²×C₁₉	1	2	yes	complemented
366	#489	—	2	1	no	—
367	#483	—	2	1	no	—
368	#480	—	2	1	no	—
369	#477	C₂²×C₁₉	1	2	yes	complemented
370	#476	—	2	1	no	—
371	#476	—	2	1	no	—
372	#476	C₂²×C₁₉	1	2	yes	—
373	#476	C₂²×C₁₉	1	2	yes	complemented
374	#476	C₂²×C₁₉	1	2	yes	complemented
375	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	C₂×#106	—	2	1	no	—
377	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	C₂×#102	—	2	1	no	—
379	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
380	#333	C₂²×C₁₉	1	2	yes	complemented
381	#331	C₂²×C₁₉	1	2	yes	complemented
382	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
383	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
384	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
385	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
386	C₂×C₁₉	—	2	2	no	—
387	C₂×C₁₉	—	4	2	no	—
388	C₂×C₁₉	—	8	1	no	—
389	C₂×C₁₉	—	8	2	no	—
390	C₂×C₁₉	—	8	1	no	—
391	C₂×C₁₉	#3007	1	1	yes	characteristic
392	C₂×C₁₉	#3009	1	1	yes	characteristic
393	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
394	C₂×#41	—	2	1	no	—
395	C₂×#41	D₄×C₁₉	1	2	yes	—
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×D₄	—	2	2	no	—
398	C₂²×D₄	—	2	1	no	—
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
401	C₂³×C₄	—	2	1	no	—
402	#137	—	4	8	no	—
403	C₂×Q₁₆	—	2	4	no	—
404	C₂×SD₁₆	—	2	4	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₄⋊Q₈	—	2	1	no	—
408	C₄⋊Q₈	—	2	1	no	—
409	C₄⋊Q₈	—	2	1	no	—
410	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
411	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
412	#127	—	2	1	no	—
413	#127	C₂³×C₁₉	1	1	yes	characteristic
414	#126	—	2	2	no	—
415	#126	—	2	1	no	—
416	#125	—	2	1	no	—
417	#125	D₄×C₁₉	1	1	yes	characteristic
418	#124	—	2	2	no	—
419	#124	D₄×C₁₉	1	1	yes	characteristic
420	#124	D₄×C₁₉	1	2	yes	—
421	#123	—	2	2	no	—
422	#123	—	2	2	no	—
423	#123	—	2	2	no	—
424	#123	—	2	1	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
428	#121	—	2	2	no	—
429	#121	—	2	2	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	—	2	1	no	—
433	#121	—	2	2	no	—
434	#121	—	2	1	no	—
435	#121	—	2	1	no	—
436	#121	—	2	1	no	—
437	#121	—	2	1	no	—
438	#121	—	2	1	no	—
439	#121	—	2	1	no	—
440	#121	D₄×C₁₉	1	1	yes	characteristic
441	#120	—	2	2	no	—
442	#120	—	2	2	no	—
443	#120	—	2	2	no	—
444	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
456	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
457	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
458	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
459	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
460	#117	—	2	1	no	—
461	#117	—	2	1	no	—
462	#117	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	2	1	no	—
466	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	—	2	2	no	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
471	#107	—	2	2	no	—
472	#106	—	2	2	no	—
473	#106	—	2	2	no	—
474	#106	—	2	2	no	—
475	C₄⋊C₈	—	2	1	no	—
476	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
477	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
478	#103	—	2	2	no	—
479	#102	—	2	2	no	—
480	#102	—	2	2	no	—
481	#102	—	2	2	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	#97	—	2	1	no	—
484	#97	—	2	1	no	—
485	C₄×C₈	C₂³×C₁₉	1	2	yes	—
486	C₁₉	#18563	1	1	yes	characteristic, direct product factor, Sylow
487	C₂⁴	—	2	2	no	—
488	C₂⁴	—	2	1	no	—
489	#41	—	4	4	no	—
490	#41	—	8	2	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	4	4	no	—
493	C₂×Q₈	—	4	1	no	—
494	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	4	1	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	8	2	no	—
511	C₂×D₄	—	8	4	no	—
512	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	8	2	no	—
527	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	Q₁₆	—	4	8	no	—
531	SD₁₆	—	4	8	no	—
532	M₁₆	—	2	4	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	2	2	no	—
535	C₂×C₈	—	2	2	no	—
536	C₂×C₈	—	4	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	4	1	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	2	1	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	1	no	—
572	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
573	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
574	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
575	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	4	2	no	—
583	C₂³	—	8	1	no	—
584	C₂³	—	8	2	no	—
585	C₂³	—	8	2	no	—
586	C₂³	C₁₉×#120	1	1	yes	characteristic
587	Q₈	—	2	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	4	4	no	—
590	Q₈	—	8	2	no	—
591	D₄	—	2	1	no	—
592	D₄	—	2	1	no	—
593	D₄	—	2	1	no	—
594	D₄	—	2	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	4	no	—
598	D₄	—	4	2	no	—
599	D₄	—	4	4	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	2	no	—
603	D₄	—	8	2	no	—
604	D₄	—	8	2	no	—
605	D₄	—	8	2	no	—
606	D₄	—	8	2	no	—
607	D₄	C₁₉×#137	1	2	yes	complemented
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	8	1	no	—
624	C₂×C₄	—	8	1	no	—
625	C₂×C₄	—	8	2	no	—
626	C₂×C₄	—	8	1	no	—
627	C₂×C₄	—	8	2	no	—
628	C₂×C₄	—	8	2	no	—
629	C₂×C₄	—	8	2	no	—
630	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
631	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
632	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
633	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
636	C₈	—	2	4	no	—
637	C₈	—	4	2	no	—
638	C₈	—	4	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	8	4	no	—
654	C₂²	—	16	4	no	—
655	C₂²	C₁₉×#453	1	2	yes	—
656	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	8	2	no	—
668	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
669	C₄	C₁₉×#575	1	1	yes	characteristic
670	C₄	C₁₉×#577	1	2	yes	—
671	C₂	—	2	2	no	—
672	C₂	—	4	2	no	—
673	C₂	—	8	1	no	—
674	C₂	—	8	1	no	—
675	C₂	—	8	2	no	—
676	C₂	C₁₉×#3007	1	1	yes	characteristic
677	C₂	C₁₉×#3009	1	1	yes	characteristic
678	C₂	C₂×C₁₉×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3519	C₂
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×#3238	C₂	semidirect
3. C₁₉×#3152	C₂	semidirect
4. C₂×C₁₉×#476	C₂	semidirect
5. C₁₉×#1634	C₂	semidirect
6. C₁₉×#1632	C₂	semidirect
7. C₁₉×#1631	C₂	semidirect
8. C₁₉×#1629	C₂	semidirect
9. C₁₉×#1551	C₂	semidirect
10. C₁₉×#1490	C₂	semidirect
11. C₁₉×#1483	C₂	semidirect
25. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
33. C₁₉×#494	C₂²	semidirect
34. C₁₉×#492	C₂²	semidirect
38. C₁₉×#477	C₂²	semidirect
42. C₁₉×#476	C₂²	semidirect
43. C₁₉×#476	C₂²	semidirect
44. C₁₉×#432	C₂²	semidirect
46. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
48. C₄×M₁₆×C₁₉	C₂²	semidirect
49. C₁₉×#333	C₂²	semidirect
50. C₁₉×#331	C₂²	semidirect
51. C₁₉×Q₈⋊C₈	C₂²	semidirect
53. C₁₉×D₄⋊C₈	C₂²	semidirect
54. C₁₉×D₄⋊C₈	C₂²	semidirect
236. #18563	C₁₉	direct (N × H)
268. D₄×C₁₉	#137	semidirect
301. #3238	C₂×C₁₉	semidirect
302. #3152	C₂×C₁₉	semidirect
303. C₂×#476	C₂×C₁₉	semidirect
304. #1634	C₂×C₁₉	semidirect
305. #1632	C₂×C₁₉	semidirect
306. #1631	C₂×C₁₉	semidirect
307. #1629	C₂×C₁₉	semidirect
308. #1551	C₂×C₁₉	semidirect
309. #1490	C₂×C₁₉	semidirect
310. #1483	C₂×C₁₉	semidirect
356. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
364. #494	C₂²×C₁₉	semidirect
365. #492	C₂²×C₁₉	semidirect
369. #477	C₂²×C₁₉	semidirect
373. #476	C₂²×C₁₉	semidirect
374. #476	C₂²×C₁₉	semidirect
375. #432	C₂²×C₁₉	semidirect
377. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
379. C₄×M₁₆	C₂²×C₁₉	semidirect
380. #333	C₂²×C₁₉	semidirect
381. #331	C₂²×C₁₉	semidirect
382. Q₈⋊C₈	C₂²×C₁₉	semidirect
384. D₄⋊C₈	C₂²×C₁₉	semidirect
385. D₄⋊C₈	C₂²×C₁₉	semidirect
486. C₁₉	#18563	direct (N × H)
607. D₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3519	2
C₁₉×#3238	2
C₁₉×#3152	2
C₂×C₁₉×#476	2
C₁₉×#1634	2
C₁₉×#1632	2
C₁₉×#1631	2
C₁₉×#1629	2
C₁₉×#1551	2
C₁₉×#1490	2
C₁₉×#1483	2
#18563	19

Subgroups — C19×#18563 #18024522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18563 #18024522