Subgroups — C₁₉×#19095 #18025054

Order 4864.

834 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3568	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1659	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1535	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1535	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	C₂²	1	1	yes	characteristic
13	C₁₉×#563	C₂²	1	1	yes	characteristic
14	C₁₉×#563	C₂²	1	1	yes	characteristic
15	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic
16	C₁₉×#556	—	2	1	no	—
17	C₁₉×#556	—	2	1	no	—
18	C₁₉×#556	—	2	1	no	—
19	C₁₉×#551	—	2	1	no	—
20	C₁₉×#551	—	2	1	no	—
21	C₁₉×#551	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#542	—	2	1	no	—
24	C₁₉×#542	—	2	1	no	—
25	C₁₉×#538	—	2	1	no	—
26	C₁₉×#538	—	2	1	no	—
27	C₁₉×#538	—	2	1	no	—
28	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#529	C₂²	1	1	yes	characteristic
30	C₁₉×#529	C₂²	1	1	yes	characteristic
31	C₁₉×#529	C₂²	1	1	yes	characteristic
32	C₁₉×#501	C₂²	1	2	yes	complemented
33	C₁₉×#501	C₂²	1	2	yes	complemented
34	C₁₉×#497	C₂²	1	2	yes	—
35	C₁₉×#491	C₂²	1	2	yes	complemented
36	C₁₉×#489	C₂²	1	2	yes	—
37	C₁₉×#489	C₂²	1	2	yes	—
38	C₁₉×#484	—	2	1	no	—
39	C₁₉×#483	—	2	1	no	—
40	C₁₉×#481	—	2	1	no	—
41	C₁₉×#480	—	2	1	no	—
42	C₁₉×#477	—	2	1	no	—
43	C₁₉×#476	—	2	1	no	—
44	C₁₉×#475	—	2	1	no	—
45	C₁₉×#474	—	2	1	no	—
46	C₁₉×#462	—	2	1	no	—
47	C₁₉×#461	—	2	1	no	—
48	C₁₉×#451	—	2	1	no	—
49	C₁₉×#448	—	2	1	no	—
50	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#330	C₂²	1	2	yes	complemented
54	C₁₉×#330	C₂²	1	2	yes	complemented
55	C₁₉×#330	C₂²	1	2	yes	complemented
56	C₁₉×#329	C₂²	1	2	yes	—
57	C₁₉×#329	C₂²	1	2	yes	—
58	C₁₉×#329	C₂²	1	2	yes	—
59	C₂²×Q₈×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×#126	—	2	1	no	—
70	C₁₉×#126	—	2	1	no	—
71	C₁₉×#126	—	2	1	no	—
72	C₁₉×#126	—	2	1	no	—
73	C₁₉×#126	—	2	1	no	—
74	C₁₉×#126	—	2	1	no	—
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#126	—	2	1	no	—
78	C₁₉×#126	—	2	1	no	—
79	C₁₉×#126	—	2	1	no	—
80	C₁₉×#126	—	2	1	no	—
81	C₁₉×#126	—	2	1	no	—
82	C₁₉×#125	C₂³	1	1	yes	characteristic
83	C₁₉×#125	C₂³	1	1	yes	characteristic
84	C₁₉×#125	C₂³	1	1	yes	characteristic
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#124	—	2	1	no	—
92	C₁₉×#124	—	2	1	no	—
93	C₁₉×#124	—	2	1	no	—
94	C₁₉×#124	C₂³	1	1	yes	characteristic
95	C₁₉×#124	C₂³	1	1	yes	characteristic
96	C₁₉×#124	C₂³	1	1	yes	characteristic
97	C₁₉×#123	—	2	1	no	—
98	C₁₉×#123	—	2	1	no	—
99	C₁₉×#123	—	2	1	no	—
100	C₁₉×#123	—	2	1	no	—
101	C₁₉×#123	—	2	1	no	—
102	C₁₉×#123	—	2	1	no	—
103	C₁₉×#123	—	2	1	no	—
104	C₁₉×#123	—	2	1	no	—
105	C₁₉×#123	—	2	1	no	—
106	C₁₉×C₂²⋊Q₈	—	2	1	no	—
107	C₁₉×C₂²⋊Q₈	—	2	1	no	—
108	C₁₉×C₂²⋊Q₈	—	2	1	no	—
109	C₁₉×C₂²⋊Q₈	—	2	1	no	—
110	C₁₉×C₂²⋊Q₈	—	2	1	no	—
111	C₁₉×C₂²⋊Q₈	—	2	1	no	—
112	C₁₉×C₂²⋊Q₈	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	—	2	1	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
116	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
117	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₉×#121	—	2	1	no	—
119	C₁₉×#121	—	2	1	no	—
120	C₁₉×#121	—	2	1	no	—
121	C₁₉×#121	D₄	1	1	yes	characteristic
122	C₁₉×#121	D₄	1	1	yes	characteristic
123	C₁₉×#121	D₄	1	1	yes	characteristic
124	C₁₉×#120	—	2	1	no	—
125	C₁₉×#120	—	2	1	no	—
126	C₁₉×#120	—	2	1	no	—
127	C₁₉×#120	—	2	1	no	—
128	C₄×Q₈×C₁₉	—	2	1	no	—
129	C₄×Q₈×C₁₉	—	2	1	no	—
130	C₄×Q₈×C₁₉	—	2	1	no	—
131	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
132	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
133	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
134	C₄×D₄×C₁₉	—	2	1	no	—
135	C₄×D₄×C₁₉	—	2	1	no	—
136	C₄×D₄×C₁₉	—	2	1	no	—
137	C₄×D₄×C₁₉	—	2	1	no	—
138	C₄×D₄×C₁₉	—	2	1	no	—
139	C₄×D₄×C₁₉	—	2	1	no	—
140	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
141	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
142	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
143	C₁₉×#117	—	2	1	no	—
144	C₁₉×#117	—	2	1	no	—
145	C₁₉×#117	—	2	1	no	—
146	C₁₉×#117	—	2	1	no	—
147	C₁₉×#117	—	2	1	no	—
148	C₁₉×#117	—	2	1	no	—
149	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
154	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
155	C₁₉×#107	—	2	2	no	—
156	C₁₉×#107	—	2	2	no	—
157	C₁₉×#106	—	2	2	no	—
158	C₁₉×#106	—	2	2	no	—
159	C₁₉×C₄⋊C₈	—	2	1	no	—
160	C₁₉×C₄⋊C₈	—	2	1	no	—
161	C₁₉×C₄⋊C₈	—	2	1	no	—
162	C₁₉×#103	—	2	2	no	—
163	C₁₉×#103	—	2	2	no	—
164	C₁₉×#103	—	2	2	no	—
165	C₁₉×#103	—	2	2	no	—
166	C₁₉×#102	—	2	2	no	—
167	C₁₉×#102	—	2	2	no	—
168	C₁₉×C₂²⋊C₈	—	2	1	no	—
169	C₁₉×C₂²⋊C₈	—	2	1	no	—
170	C₁₉×C₂²⋊C₈	—	2	1	no	—
171	C₁₉×#97	C₂³	1	2	yes	—
172	C₁₉×#97	C₂³	1	2	yes	—
173	C₁₉×#97	C₂³	1	2	yes	—
174	C₂⁴×C₁₉	—	2	1	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	1	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	—	2	2	no	—
179	C₂×Q₈×C₁₉	—	4	1	no	—
180	C₂×Q₈×C₁₉	—	8	2	no	—
181	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	4	1	no	—
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	Q₁₆×C₁₉	—	8	2	no	—
204	SD₁₆×C₁₉	—	8	2	no	—
205	C₂×C₈×C₁₉	—	2	2	no	—
206	C₂×C₈×C₁₉	—	2	2	no	—
207	C₂×C₈×C₁₉	—	2	2	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	2	no	—
227	C₄⋊C₄×C₁₉	—	2	2	no	—
228	C₄⋊C₄×C₁₉	—	4	1	no	—
229	C₄⋊C₄×C₁₉	—	4	1	no	—
230	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₂²⋊C₄×C₁₉	—	2	1	no	—
237	C₂²⋊C₄×C₁₉	—	2	1	no	—
238	C₂²⋊C₄×C₁₉	—	2	1	no	—
239	C₂²⋊C₄×C₁₉	—	2	1	no	—
240	C₂²⋊C₄×C₁₉	—	2	1	no	—
241	C₂²⋊C₄×C₁₉	—	2	1	no	—
242	C₂²⋊C₄×C₁₉	—	2	1	no	—
243	C₂²⋊C₄×C₁₉	—	2	1	no	—
244	C₂²⋊C₄×C₁₉	—	2	1	no	—
245	C₂²⋊C₄×C₁₉	—	2	1	no	—
246	C₂²⋊C₄×C₁₉	—	2	1	no	—
247	C₂²⋊C₄×C₁₉	—	2	1	no	—
248	C₂²⋊C₄×C₁₉	—	2	1	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	—	2	1	no	—
253	C₂²⋊C₄×C₁₉	—	2	1	no	—
254	C₂²⋊C₄×C₁₉	—	2	1	no	—
255	C₂²⋊C₄×C₁₉	—	2	1	no	—
256	C₂²⋊C₄×C₁₉	—	2	1	no	—
257	C₂²⋊C₄×C₁₉	—	2	1	no	—
258	C₂²⋊C₄×C₁₉	—	2	1	no	—
259	C₂²⋊C₄×C₁₉	—	2	1	no	—
260	C₂²⋊C₄×C₁₉	—	2	1	no	—
261	C₂²⋊C₄×C₁₉	—	2	1	no	—
262	C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₄²×C₁₉	—	2	1	no	—
264	C₄²×C₁₉	—	2	1	no	—
265	C₄²×C₁₉	—	2	1	no	—
266	C₄²×C₁₉	—	2	1	no	—
267	C₄²×C₁₉	—	2	1	no	—
268	C₄²×C₁₉	—	2	1	no	—
269	C₄²×C₁₉	—	2	1	no	—
270	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
274	#19095	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₁₉	—	2	1	no	—
276	C₂³×C₁₉	—	2	1	no	—
277	C₂³×C₁₉	—	2	1	no	—
278	C₂³×C₁₉	—	8	1	no	—
279	C₂³×C₁₉	—	8	1	no	—
280	C₂³×C₁₉	—	8	1	no	—
281	C₂³×C₁₉	#120	1	1	yes	characteristic
282	Q₈×C₁₉	—	4	1	no	—
283	Q₈×C₁₉	—	4	1	no	—
284	Q₈×C₁₉	—	4	1	no	—
285	Q₈×C₁₉	—	4	2	no	—
286	Q₈×C₁₉	—	4	2	no	—
287	Q₈×C₁₉	—	8	2	no	—
288	Q₈×C₁₉	—	8	1	no	—
289	Q₈×C₁₉	—	8	1	no	—
290	Q₈×C₁₉	—	8	1	no	—
291	D₄×C₁₉	—	4	1	no	—
292	D₄×C₁₉	—	4	1	no	—
293	D₄×C₁₉	—	4	1	no	—
294	D₄×C₁₉	—	8	1	no	—
295	D₄×C₁₉	—	8	1	no	—
296	D₄×C₁₉	—	8	1	no	—
297	D₄×C₁₉	—	8	1	no	—
298	D₄×C₁₉	—	8	1	no	—
299	D₄×C₁₉	—	8	1	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	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	2	no	—
313	C₂×C₄×C₁₉	—	8	1	no	—
314	C₂×C₄×C₁₉	—	8	1	no	—
315	C₂×C₄×C₁₉	—	8	1	no	—
316	C₂×C₄×C₁₉	—	8	1	no	—
317	C₂×C₄×C₁₉	—	8	1	no	—
318	C₂×C₄×C₁₉	—	8	1	no	—
319	C₂×C₄×C₁₉	—	8	2	no	—
320	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
321	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
322	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
323	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
326	C₈×C₁₉	—	4	2	no	—
327	C₈×C₁₉	—	4	2	no	—
328	C₈×C₁₉	—	4	2	no	—
329	#3568	C₂×C₁₉	1	1	yes	characteristic
330	#3239	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1664	C₂×C₁₉	1	2	yes	complemented
334	#1664	C₂×C₁₉	1	2	yes	complemented
335	#1660	C₂×C₁₉	1	2	yes	complemented
336	#1659	C₂×C₁₉	1	2	yes	complemented
337	#1535	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#1535	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#1535	C₂×C₁₉	1	1	yes	characteristic, complemented
340	C₂²×C₁₉	—	2	1	no	—
341	C₂²×C₁₉	—	2	1	no	—
342	C₂²×C₁₉	—	2	1	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	1	no	—
349	C₂²×C₁₉	—	4	1	no	—
350	C₂²×C₁₉	—	4	1	no	—
351	C₂²×C₁₉	—	4	1	no	—
352	C₂²×C₁₉	—	16	2	no	—
353	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
354	C₄×C₁₉	—	2	1	no	—
355	C₄×C₁₉	—	2	1	no	—
356	C₄×C₁₉	—	2	1	no	—
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	2	1	no	—
359	C₄×C₁₉	—	2	1	no	—
360	C₄×C₁₉	—	4	1	no	—
361	C₄×C₁₉	—	4	1	no	—
362	C₄×C₁₉	—	4	1	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	4	1	no	—
366	C₄×C₁₉	—	4	1	no	—
367	C₄×C₁₉	—	4	1	no	—
368	C₄×C₁₉	—	4	1	no	—
369	C₄×C₁₉	—	8	2	no	—
370	#563	C₂²×C₁₉	1	1	yes	characteristic
371	#563	C₂²×C₁₉	1	1	yes	characteristic
372	#563	C₂²×C₁₉	1	1	yes	characteristic
373	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
374	#556	—	2	1	no	—
375	#556	—	2	1	no	—
376	#556	—	2	1	no	—
377	#551	—	2	1	no	—
378	#551	—	2	1	no	—
379	#551	—	2	1	no	—
380	#542	—	2	1	no	—
381	#542	—	2	1	no	—
382	#542	—	2	1	no	—
383	#538	—	2	1	no	—
384	#538	—	2	1	no	—
385	#538	—	2	1	no	—
386	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
387	#529	C₂²×C₁₉	1	1	yes	characteristic
388	#529	C₂²×C₁₉	1	1	yes	characteristic
389	#529	C₂²×C₁₉	1	1	yes	characteristic
390	#501	C₂²×C₁₉	1	2	yes	complemented
391	#501	C₂²×C₁₉	1	2	yes	complemented
392	#497	C₂²×C₁₉	1	2	yes	—
393	#491	C₂²×C₁₉	1	2	yes	complemented
394	#489	C₂²×C₁₉	1	2	yes	—
395	#489	C₂²×C₁₉	1	2	yes	—
396	#484	—	2	1	no	—
397	#483	—	2	1	no	—
398	#481	—	2	1	no	—
399	#480	—	2	1	no	—
400	#477	—	2	1	no	—
401	#476	—	2	1	no	—
402	#475	—	2	1	no	—
403	#474	—	2	1	no	—
404	#462	—	2	1	no	—
405	#461	—	2	1	no	—
406	#451	—	2	1	no	—
407	#448	—	2	1	no	—
408	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
409	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
410	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
411	#330	C₂²×C₁₉	1	2	yes	complemented
412	#330	C₂²×C₁₉	1	2	yes	complemented
413	#330	C₂²×C₁₉	1	2	yes	complemented
414	#329	C₂²×C₁₉	1	2	yes	—
415	#329	C₂²×C₁₉	1	2	yes	—
416	#329	C₂²×C₁₉	1	2	yes	—
417	C₂×C₁₉	—	4	1	no	—
418	C₂×C₁₉	—	8	1	no	—
419	C₂×C₁₉	—	8	1	no	—
420	C₂×C₁₉	—	8	1	no	—
421	C₂×C₁₉	#3021	1	1	yes	characteristic
422	C₂×C₁₉	#3022	1	1	yes	characteristic
423	C₂×C₁₉	#3022	1	1	yes	characteristic
424	C₂²×Q₈	—	2	1	no	—
425	C₂×Q₁₆	—	2	2	no	—
426	C₂×SD₁₆	—	2	2	no	—
427	C₄⋊Q₈	—	2	1	no	—
428	C₄⋊Q₈	—	2	1	no	—
429	C₄⋊Q₈	—	2	1	no	—
430	C₄⋊Q₈	—	2	1	no	—
431	C₄⋊Q₈	—	2	1	no	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
434	#126	—	2	1	no	—
435	#126	—	2	1	no	—
436	#126	—	2	1	no	—
437	#126	—	2	1	no	—
438	#126	—	2	1	no	—
439	#126	—	2	1	no	—
440	#126	—	2	1	no	—
441	#126	—	2	1	no	—
442	#126	—	2	1	no	—
443	#126	—	2	1	no	—
444	#126	—	2	1	no	—
445	#126	—	2	1	no	—
446	#126	—	2	1	no	—
447	#125	C₂³×C₁₉	1	1	yes	characteristic
448	#125	C₂³×C₁₉	1	1	yes	characteristic
449	#125	C₂³×C₁₉	1	1	yes	characteristic
450	#124	—	2	1	no	—
451	#124	—	2	1	no	—
452	#124	—	2	1	no	—
453	#124	—	2	1	no	—
454	#124	—	2	1	no	—
455	#124	—	2	1	no	—
456	#124	—	2	1	no	—
457	#124	—	2	1	no	—
458	#124	—	2	1	no	—
459	#124	C₂³×C₁₉	1	1	yes	characteristic
460	#124	C₂³×C₁₉	1	1	yes	characteristic
461	#124	C₂³×C₁₉	1	1	yes	characteristic
462	#123	—	2	1	no	—
463	#123	—	2	1	no	—
464	#123	—	2	1	no	—
465	#123	—	2	1	no	—
466	#123	—	2	1	no	—
467	#123	—	2	1	no	—
468	#123	—	2	1	no	—
469	#123	—	2	1	no	—
470	#123	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	C₂²⋊Q₈	—	2	1	no	—
480	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
481	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
482	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
483	#121	—	2	1	no	—
484	#121	—	2	1	no	—
485	#121	—	2	1	no	—
486	#121	D₄×C₁₉	1	1	yes	characteristic
487	#121	D₄×C₁₉	1	1	yes	characteristic
488	#121	D₄×C₁₉	1	1	yes	characteristic
489	#120	—	2	1	no	—
490	#120	—	2	1	no	—
491	#120	—	2	1	no	—
492	#120	—	2	1	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×Q₈	—	2	1	no	—
495	C₄×Q₈	—	2	1	no	—
496	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
497	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
498	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
499	C₄×D₄	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
506	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
507	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
508	#117	—	2	1	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	—	2	1	no	—
513	#117	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
520	#107	—	2	2	no	—
521	#107	—	2	2	no	—
522	#106	—	2	2	no	—
523	#106	—	2	2	no	—
524	C₄⋊C₈	—	2	1	no	—
525	C₄⋊C₈	—	2	1	no	—
526	C₄⋊C₈	—	2	1	no	—
527	#103	—	2	2	no	—
528	#103	—	2	2	no	—
529	#103	—	2	2	no	—
530	#103	—	2	2	no	—
531	#102	—	2	2	no	—
532	#102	—	2	2	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	C₂²⋊C₈	—	2	1	no	—
535	C₂²⋊C₈	—	2	1	no	—
536	#97	C₂³×C₁₉	1	2	yes	—
537	#97	C₂³×C₁₉	1	2	yes	—
538	#97	C₂³×C₁₉	1	2	yes	—
539	C₁₉	#19095	1	1	yes	characteristic, direct product factor, Sylow
540	C₂⁴	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	4	1	no	—
546	C₂×Q₈	—	8	2	no	—
547	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	4	1	no	—
566	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	Q₁₆	—	8	2	no	—
570	SD₁₆	—	8	2	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	—	2	2	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	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	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	4	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
597	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
639	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	8	1	no	—
644	C₂³	—	8	1	no	—
645	C₂³	—	8	1	no	—
646	C₂³	C₁₉×#120	1	1	yes	characteristic
647	Q₈	—	4	1	no	—
648	Q₈	—	4	1	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	4	2	no	—
651	Q₈	—	4	2	no	—
652	Q₈	—	8	2	no	—
653	Q₈	—	8	1	no	—
654	Q₈	—	8	1	no	—
655	Q₈	—	8	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	8	1	no	—
660	D₄	—	8	1	no	—
661	D₄	—	8	1	no	—
662	D₄	—	8	1	no	—
663	D₄	—	8	1	no	—
664	D₄	—	8	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	8	1	no	—
679	C₂×C₄	—	8	1	no	—
680	C₂×C₄	—	8	1	no	—
681	C₂×C₄	—	8	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	—	8	2	no	—
685	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
686	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
687	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
691	C₈	—	4	2	no	—
692	C₈	—	4	2	no	—
693	C₈	—	4	2	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	16	2	no	—
707	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	8	2	no	—
724	C₂	—	4	1	no	—
725	C₂	—	8	1	no	—
726	C₂	—	8	1	no	—
727	C₂	—	8	1	no	—
728	C₂	C₁₉×#3021	1	1	yes	characteristic
729	C₂	C₁₉×#3022	1	1	yes	characteristic
730	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3568	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×#3239	C₂	semidirect
3. C₁₉×#3238	C₂	semidirect
4. C₁₉×#3218	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1664	C₂	semidirect
7. C₁₉×#1660	C₂	semidirect
8. C₁₉×#1659	C₂	semidirect
9. C₁₉×#1535	C₂	semidirect
10. C₁₉×#1535	C₂	semidirect
11. C₁₉×#1535	C₂	semidirect
28. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
32. C₁₉×#501	C₂²	semidirect
33. C₁₉×#501	C₂²	semidirect
35. C₁₉×#491	C₂²	semidirect
50. C₁₉×#432	C₂²	semidirect
51. C₁₉×#432	C₂²	semidirect
52. C₁₉×#432	C₂²	semidirect
53. C₁₉×#330	C₂²	semidirect
54. C₁₉×#330	C₂²	semidirect
55. C₁₉×#330	C₂²	semidirect
274. #19095	C₁₉	direct (N × H)
330. #3239	C₂×C₁₉	semidirect
331. #3238	C₂×C₁₉	semidirect
332. #3218	C₂×C₁₉	semidirect
333. #1664	C₂×C₁₉	semidirect
334. #1664	C₂×C₁₉	semidirect
335. #1660	C₂×C₁₉	semidirect
336. #1659	C₂×C₁₉	semidirect
337. #1535	C₂×C₁₉	semidirect
338. #1535	C₂×C₁₉	semidirect
339. #1535	C₂×C₁₉	semidirect
386. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
390. #501	C₂²×C₁₉	semidirect
391. #501	C₂²×C₁₉	semidirect
393. #491	C₂²×C₁₉	semidirect
408. #432	C₂²×C₁₉	semidirect
409. #432	C₂²×C₁₉	semidirect
410. #432	C₂²×C₁₉	semidirect
411. #330	C₂²×C₁₉	semidirect
412. #330	C₂²×C₁₉	semidirect
413. #330	C₂²×C₁₉	semidirect
539. C₁₉	#19095	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×#3568	2
C₁₉×#3239	2
C₁₉×#3238	2
C₁₉×#3218	2
C₁₉×#1664	2
C₁₉×#1660	2
C₁₉×#1659	2
C₁₉×#1535	2
#19095	19

Subgroups — C19×#19095 #18025054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19095 #18025054