Subgroups — C₁₉×#18352 #18024311

Order 4864.

996 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3193	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2635	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1617	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1614	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1599	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1596	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1511	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#554	—	2	4	no	—
11	C₁₉×#554	—	2	2	no	—
12	D₄×Q₈×C₁₉	—	2	2	no	—
13	C₁₉×#544	C₂²	1	2	yes	—
14	C₁₉×#543	—	2	1	no	—
15	C₁₉×#543	C₂²	1	2	yes	—
16	C₁₉×#533	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₁₉×#518	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#484	C₂²	1	4	yes	—
23	C₁₉×#480	—	2	2	no	—
24	C₁₉×#468	—	2	4	no	—
25	C₁₉×#450	C₂²	1	4	yes	—
26	C₁₉×#448	—	2	2	no	—
27	C₁₉×#407	C₂²	1	2	yes	—
28	C₁₉×#400	C₂²	1	1	yes	characteristic
29	C₁₉×#399	C₂²	1	1	yes	characteristic
30	C₁₉×#394	—	2	1	no	—
31	C₁₉×#394	C₂²	1	1	yes	characteristic
32	C₁₉×#392	—	2	1	no	—
33	C₁₉×#392	C₂²	1	1	yes	characteristic
34	C₁₉×#388	—	2	1	no	—
35	C₁₉×#386	—	2	1	no	—
36	C₁₉×#381	C₂²	1	1	yes	characteristic
37	C₁₉×#328	C₂²	1	4	yes	—
38	C₁₉×#328	C₂²	1	4	yes	—
39	C₁₉×#324	C₂²	1	2	yes	—
40	C₁₉×#323	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	D₄	1	2	yes	complemented
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	4	no	—
54	C₁₉×#125	—	2	2	no	—
55	C₁₉×#125	—	2	4	no	—
56	C₁₉×C₂²⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	2	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	4	no	—
66	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	complemented
67	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	4	no	—
73	C₄×D₄×C₁₉	—	2	4	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
95	C₁₉×#107	—	2	4	no	—
96	C₁₉×#103	—	2	4	no	—
97	C₁₉×#102	—	2	4	no	—
98	C₁₉×C₂²⋊C₈	—	2	2	no	—
99	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	C₂³	1	1	yes	characteristic
104	C₁₉×#95	C₂³	1	1	yes	characteristic
105	C₂⁴×C₁₉	—	2	1	no	—
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	8	2	no	—
112	C₂×Q₈×C₁₉	—	8	2	no	—
113	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	—	8	1	no	—
121	C₂×D₄×C₁₉	—	8	1	no	—
122	C₂×D₄×C₁₉	—	8	1	no	—
123	C₂×D₄×C₁₉	—	8	1	no	—
124	C₂×D₄×C₁₉	—	8	1	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	8	1	no	—
135	C₂²×C₄×C₁₉	—	8	1	no	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	SD₁₆×C₁₉	—	8	4	no	—
144	M₁₆×C₁₉	—	8	2	no	—
145	C₂×C₈×C₁₉	—	2	4	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	4	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	8	1	no	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₂²⋊C₄×C₁₉	—	4	1	no	—
166	C₂²⋊C₄×C₁₉	—	4	2	no	—
167	C₂²⋊C₄×C₁₉	—	8	1	no	—
168	C₂²⋊C₄×C₁₉	—	8	1	no	—
169	C₂²⋊C₄×C₁₉	—	8	1	no	—
170	C₂²⋊C₄×C₁₉	—	8	1	no	—
171	C₄²×C₁₉	—	2	4	no	—
172	C₄²×C₁₉	—	2	1	no	—
173	C₄²×C₁₉	—	2	1	no	—
174	#18352	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	4	1	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	#120	1	2	yes	—
191	C₂³×C₁₉	#137	1	2	yes	—
192	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₉	—	4	4	no	—
194	Q₈×C₁₉	—	4	4	no	—
195	Q₈×C₁₉	—	8	2	no	—
196	Q₈×C₁₉	—	8	2	no	—
197	D₄×C₁₉	—	2	8	no	—
198	D₄×C₁₉	—	4	4	no	—
199	D₄×C₁₉	—	8	4	no	—
200	D₄×C₁₉	—	8	4	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	8	1	no	—
224	C₂×C₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	—	8	2	no	—
226	C₂×C₄×C₁₉	—	8	2	no	—
227	C₂×C₄×C₁₉	—	8	2	no	—
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#137	1	2	yes	—
231	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
232	C₈×C₁₉	—	4	4	no	—
233	#3501	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#3193	C₂×C₁₉	1	2	yes	complemented
235	#2635	C₂×C₁₉	1	1	yes	characteristic
236	#1617	C₂×C₁₉	1	2	yes	complemented
237	#1614	C₂×C₁₉	1	2	yes	complemented
238	#1599	C₂×C₁₉	1	2	yes	complemented
239	#1596	C₂×C₁₉	1	2	yes	complemented
240	#1511	C₂×C₁₉	1	2	yes	complemented
241	#1465	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	—	2	2	no	—
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	2	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	8	1	no	—
252	C₂²×C₁₉	—	8	1	no	—
253	C₂²×C₁₉	—	8	1	no	—
254	C₂²×C₁₉	—	8	1	no	—
255	C₂²×C₁₉	—	8	1	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	1	no	—
258	C₂²×C₁₉	—	8	1	no	—
259	C₂²×C₁₉	—	8	1	no	—
260	C₂²×C₁₉	—	8	1	no	—
261	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
263	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	2	2	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	4	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	4	4	no	—
272	C₄×C₁₉	—	8	1	no	—
273	C₄×C₁₉	—	8	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	#554	—	2	4	no	—
276	#554	—	2	2	no	—
277	D₄×Q₈	—	2	2	no	—
278	#544	C₂²×C₁₉	1	2	yes	—
279	#543	—	2	1	no	—
280	#543	C₂²×C₁₉	1	2	yes	—
281	#533	—	2	1	no	—
282	C₂×C₂²⋊Q₈	—	2	1	no	—
283	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
284	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
285	#518	—	2	1	no	—
286	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
287	#484	C₂²×C₁₉	1	4	yes	—
288	#480	—	2	2	no	—
289	#468	—	2	4	no	—
290	#450	C₂²×C₁₉	1	4	yes	—
291	#448	—	2	2	no	—
292	#407	C₂²×C₁₉	1	2	yes	—
293	#400	C₂²×C₁₉	1	1	yes	characteristic
294	#399	C₂²×C₁₉	1	1	yes	characteristic
295	#394	—	2	1	no	—
296	#394	C₂²×C₁₉	1	1	yes	characteristic
297	#392	—	2	1	no	—
298	#392	C₂²×C₁₉	1	1	yes	characteristic
299	#388	—	2	1	no	—
300	#386	—	2	1	no	—
301	#381	C₂²×C₁₉	1	1	yes	characteristic
302	#328	C₂²×C₁₉	1	4	yes	—
303	#328	C₂²×C₁₉	1	4	yes	—
304	#324	C₂²×C₁₉	1	2	yes	—
305	#323	C₂²×C₁₉	1	2	yes	—
306	C₂×C₁₉	—	2	1	no	—
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	4	2	no	—
309	C₂×C₁₉	—	4	2	no	—
310	C₂×C₁₉	—	16	1	no	—
311	C₂×C₁₉	#3004	1	1	yes	characteristic
312	C₂×C₁₉	#3021	1	1	yes	characteristic
313	C₂×C₁₉	#3026	1	1	yes	characteristic
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	D₄×C₁₉	1	2	yes	complemented
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	4	no	—
327	#125	—	2	2	no	—
328	#125	—	2	4	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	complemented
340	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
341	#121	—	2	2	no	—
342	#121	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	#117	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
368	#107	—	2	4	no	—
369	#103	—	2	4	no	—
370	#102	—	2	4	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
373	#95	—	2	1	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	#95	C₂³×C₁₉	1	1	yes	characteristic
377	#95	C₂³×C₁₉	1	1	yes	characteristic
378	C₁₉	#18352	1	1	yes	characteristic, direct product factor, Sylow
379	C₂⁴	—	2	1	no	—
380	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	8	2	no	—
386	C₂×Q₈	—	8	2	no	—
387	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	8	1	no	—
395	C₂×D₄	—	8	1	no	—
396	C₂×D₄	—	8	1	no	—
397	C₂×D₄	—	8	1	no	—
398	C₂×D₄	—	8	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	8	1	no	—
409	C₂²×C₄	—	8	1	no	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
417	SD₁₆	—	8	4	no	—
418	M₁₆	—	8	2	no	—
419	C₂×C₈	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	8	1	no	—
432	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	4	1	no	—
439	C₂²⋊C₄	—	4	1	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	8	1	no	—
442	C₂²⋊C₄	—	8	1	no	—
443	C₂²⋊C₄	—	8	1	no	—
444	C₂²⋊C₄	—	8	1	no	—
445	C₄²	—	2	4	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	C₁₉×#120	1	2	yes	—
464	C₂³	C₁₉×#137	1	2	yes	—
465	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
466	Q₈	—	4	4	no	—
467	Q₈	—	4	4	no	—
468	Q₈	—	8	2	no	—
469	Q₈	—	8	2	no	—
470	D₄	—	2	8	no	—
471	D₄	—	4	4	no	—
472	D₄	—	8	4	no	—
473	D₄	—	8	4	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	8	1	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	—	8	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
502	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
503	C₂×C₄	C₁₉×#137	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
505	C₈	—	4	4	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	8	1	no	—
521	C₂²	—	8	1	no	—
522	C₂²	—	8	1	no	—
523	C₂²	—	8	1	no	—
524	C₂²	—	8	1	no	—
525	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
526	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
527	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	4	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	2	1	no	—
541	C₂	—	4	2	no	—
542	C₂	—	4	2	no	—
543	C₂	—	16	1	no	—
544	C₂	C₁₉×#3004	1	1	yes	characteristic
545	C₂	C₁₉×#3021	1	1	yes	characteristic
546	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2635	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3501	C₂	semidirect
2. C₁₉×#3193	C₂	semidirect
4. C₁₉×#1617	C₂	semidirect
5. C₁₉×#1614	C₂	semidirect
6. C₁₉×#1599	C₂	semidirect
7. C₁₉×#1596	C₂	semidirect
8. C₁₉×#1511	C₂	semidirect
9. C₁₉×#1465	C₂	semidirect
42. C₂²×Q₈×C₁₉	D₄	semidirect
66. C₁₉×C₂²⋊Q₈	D₄	semidirect
81. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
174. #18352	C₁₉	direct (N × H)
233. #3501	C₂×C₁₉	semidirect
234. #3193	C₂×C₁₉	semidirect
236. #1617	C₂×C₁₉	semidirect
237. #1614	C₂×C₁₉	semidirect
238. #1599	C₂×C₁₉	semidirect
239. #1596	C₂×C₁₉	semidirect
240. #1511	C₂×C₁₉	semidirect
241. #1465	C₂×C₁₉	semidirect
315. C₂²×Q₈	D₄×C₁₉	semidirect
339. C₂²⋊Q₈	D₄×C₁₉	semidirect
354. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
378. C₁₉	#18352	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×#3501	2
C₁₉×#3193	2
C₁₉×#2635	2
C₁₉×#1617	2
C₁₉×#1614	2
C₁₉×#1599	2
C₁₉×#1596	2
C₁₉×#1511	2
C₁₉×#1465	2
#18352	19

Subgroups — C19×#18352 #18024311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18352 #18024311