Subgroups — C₁₉×#18298 #18024257

Order 4864.

1024 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3188	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1618	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1617	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1616	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1599	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1598	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1516	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#544	C₂²	1	1	yes	characteristic
13	C₁₉×#542	—	2	2	no	—
14	C₁₉×#540	—	2	2	no	—
15	C₁₉×#538	—	2	1	no	—
16	C₁₉×#538	C₂²	1	2	yes	—
17	C₁₉×#537	C₂²	1	1	yes	characteristic
18	C₁₉×#535	—	2	1	no	—
19	C₁₉×#532	—	2	2	no	—
20	C₁₉×#529	—	2	2	no	—
21	C₁₉×#525	—	2	1	no	—
22	C₁₉×#525	C₂²	1	2	yes	—
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₉	—	2	1	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#484	C₂²	1	2	yes	—
27	C₁₉×#482	—	2	2	no	—
28	C₁₉×#481	C₂²	1	2	yes	—
29	C₁₉×#466	—	2	2	no	—
30	C₁₉×#465	—	2	2	no	—
31	C₁₉×#450	C₂²	1	2	yes	—
32	C₁₉×#449	—	2	2	no	—
33	C₁₉×#447	C₂²	1	2	yes	—
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₁₉×#400	C₂²	1	1	yes	characteristic
36	C₁₉×#399	C₂²	1	1	yes	characteristic
37	C₁₉×#394	—	2	1	no	—
38	C₁₉×#394	C₂²	1	1	yes	characteristic
39	C₁₉×#392	—	2	1	no	—
40	C₁₉×#392	C₂²	1	1	yes	characteristic
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#386	—	2	1	no	—
43	C₁₉×#381	C₂²	1	1	yes	characteristic
44	C₁₉×#328	C₂²	1	2	yes	—
45	C₁₉×#328	C₂²	1	2	yes	—
46	C₁₉×#327	C₂²	1	2	yes	—
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#324	C₂²	1	1	yes	characteristic
49	C₁₉×#324	C₂²	1	1	yes	characteristic
50	C₁₉×#323	C₂²	1	2	yes	—
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	D₄	1	2	yes	complemented
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×D₈×C₁₉	—	2	2	no	—
62	C₂²×C₈×C₁₉	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	—	2	2	no	—
64	C₁₉×#127	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	—	2	2	no	—
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	complemented
79	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	D₄	1	2	yes	complemented
90	C₁₉×#121	C₂³	1	2	yes	—
91	C₁₉×#120	—	2	2	no	—
92	C₁₉×#120	—	2	2	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	D₄	1	2	yes	complemented
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₉	—	2	2	no	—
119	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
120	C₁₉×#107	—	2	2	no	—
121	C₁₉×#106	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	—	2	2	no	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	C₂³	1	1	yes	characteristic
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
137	#41×C₁₉	—	4	2	no	—
138	#41×C₁₉	—	4	2	no	—
139	#41×C₁₉	—	8	2	no	—
140	#41×C₁₉	—	8	2	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	4	1	no	—
155	C₂×D₄×C₁₉	—	4	2	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	—	8	1	no	—
158	C₂×D₄×C₁₉	—	8	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	—	8	1	no	—
162	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	8	1	no	—
172	C₂²×C₄×C₁₉	—	8	1	no	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	SD₁₆×C₁₉	—	8	2	no	—
181	D₈×C₁₉	—	8	2	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	8	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	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	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	—	8	1	no	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₂²⋊C₄×C₁₉	—	8	1	no	—
213	C₂²⋊C₄×C₁₉	—	8	1	no	—
214	C₂²⋊C₄×C₁₉	—	8	1	no	—
215	C₂²⋊C₄×C₁₉	—	8	1	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	2	2	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	2	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	#18298	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	2	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	#120	1	2	yes	—
240	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₁₉	—	4	2	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	8	1	no	—
244	D₄×C₁₉	—	4	4	no	—
245	D₄×C₁₉	—	4	2	no	—
246	D₄×C₁₉	—	4	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	8	2	no	—
253	D₄×C₁₉	—	8	2	no	—
254	D₄×C₁₉	—	8	1	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	8	4	no	—
257	D₄×C₁₉	—	8	4	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	4	no	—
271	C₂×C₄×C₁₉	—	4	4	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	8	1	no	—
284	C₂×C₄×C₁₉	—	8	2	no	—
285	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
286	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
287	C₂×C₄×C₁₉	#135	1	2	yes	—
288	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
289	C₈×C₁₉	—	4	2	no	—
290	C₈×C₁₉	—	4	2	no	—
291	#3460	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#3188	C₂×C₁₉	1	2	yes	complemented
293	#2635	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1618	C₂×C₁₉	1	2	yes	complemented
295	#1617	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1616	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1600	C₂×C₁₉	1	2	yes	complemented
298	#1599	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1598	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1516	C₂×C₁₉	1	2	yes	complemented
301	#1459	C₂×C₁₉	1	1	yes	characteristic, complemented
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	2	no	—
305	C₂²×C₁₉	—	2	2	no	—
306	C₂²×C₁₉	—	2	2	no	—
307	C₂²×C₁₉	—	4	2	no	—
308	C₂²×C₁₉	—	4	2	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	4	2	no	—
311	C₂²×C₁₉	—	4	1	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	2	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	—	8	1	no	—
318	C₂²×C₁₉	—	8	1	no	—
319	C₂²×C₁₉	—	8	1	no	—
320	C₂²×C₁₉	—	8	1	no	—
321	C₂²×C₁₉	—	8	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
325	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
326	C₂²×C₁₉	#575	1	1	yes	characteristic
327	C₄×C₁₉	—	2	2	no	—
328	C₄×C₁₉	—	2	2	no	—
329	C₄×C₁₉	—	2	1	no	—
330	C₄×C₁₉	—	2	1	no	—
331	C₄×C₁₉	—	4	2	no	—
332	C₄×C₁₉	—	4	1	no	—
333	C₄×C₁₉	—	4	2	no	—
334	C₄×C₁₉	—	4	1	no	—
335	C₄×C₁₉	—	4	2	no	—
336	C₄×C₁₉	—	8	1	no	—
337	C₄×C₁₉	—	8	1	no	—
338	C₄×C₁₉	—	8	1	no	—
339	#544	C₂²×C₁₉	1	1	yes	characteristic
340	#542	—	2	2	no	—
341	#540	—	2	2	no	—
342	#538	—	2	1	no	—
343	#538	C₂²×C₁₉	1	2	yes	—
344	#537	C₂²×C₁₉	1	1	yes	characteristic
345	#535	—	2	1	no	—
346	#532	—	2	2	no	—
347	#529	—	2	2	no	—
348	#525	—	2	1	no	—
349	#525	C₂²×C₁₉	1	2	yes	—
350	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
351	C₄×#41	—	2	1	no	—
352	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
353	#484	C₂²×C₁₉	1	2	yes	—
354	#482	—	2	2	no	—
355	#481	C₂²×C₁₉	1	2	yes	—
356	#466	—	2	2	no	—
357	#465	—	2	2	no	—
358	#450	C₂²×C₁₉	1	2	yes	—
359	#449	—	2	2	no	—
360	#447	C₂²×C₁₉	1	2	yes	—
361	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
362	#400	C₂²×C₁₉	1	1	yes	characteristic
363	#399	C₂²×C₁₉	1	1	yes	characteristic
364	#394	—	2	1	no	—
365	#394	C₂²×C₁₉	1	1	yes	characteristic
366	#392	—	2	1	no	—
367	#392	C₂²×C₁₉	1	1	yes	characteristic
368	#388	—	2	1	no	—
369	#386	—	2	1	no	—
370	#381	C₂²×C₁₉	1	1	yes	characteristic
371	#328	C₂²×C₁₉	1	2	yes	—
372	#328	C₂²×C₁₉	1	2	yes	—
373	#327	C₂²×C₁₉	1	2	yes	—
374	#327	C₂²×C₁₉	1	2	yes	—
375	#324	C₂²×C₁₉	1	1	yes	characteristic
376	#324	C₂²×C₁₉	1	1	yes	characteristic
377	#323	C₂²×C₁₉	1	2	yes	—
378	C₂×C₁₉	—	2	1	no	—
379	C₂×C₁₉	—	2	1	no	—
380	C₂×C₁₉	—	4	2	no	—
381	C₂×C₁₉	—	8	2	no	—
382	C₂×C₁₉	—	8	1	no	—
383	C₂×C₁₉	—	16	1	no	—
384	C₂×C₁₉	#3002	1	1	yes	characteristic
385	C₂×C₁₉	#3021	1	1	yes	characteristic
386	C₂×C₁₉	#3026	1	1	yes	characteristic
387	C₂×#41	—	2	1	no	—
388	C₂×#41	—	2	1	no	—
389	C₂×#41	D₄×C₁₉	1	2	yes	complemented
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
396	C₂×SD₁₆	—	2	2	no	—
397	C₂×D₈	—	2	2	no	—
398	C₂²×C₈	—	2	2	no	—
399	C₄⋊Q₈	—	2	2	no	—
400	#127	—	2	2	no	—
401	#126	—	2	2	no	—
402	#126	—	2	2	no	—
403	#125	—	2	2	no	—
404	#124	—	2	2	no	—
405	#124	—	2	2	no	—
406	#124	—	2	2	no	—
407	#123	—	2	2	no	—
408	#123	—	2	2	no	—
409	#123	—	2	2	no	—
410	#123	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	complemented
415	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
416	#121	—	2	1	no	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#121	—	2	2	no	—
420	#121	—	2	2	no	—
421	#121	—	2	2	no	—
422	#121	—	2	1	no	—
423	#121	—	2	2	no	—
424	#121	—	2	2	no	—
425	#121	D₄×C₁₉	1	2	yes	complemented
426	#121	C₂³×C₁₉	1	2	yes	—
427	#120	—	2	2	no	—
428	#120	—	2	2	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	#117	—	2	2	no	—
440	#117	—	2	1	no	—
441	#117	—	2	1	no	—
442	#117	D₄×C₁₉	1	2	yes	complemented
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄²	—	2	2	no	—
455	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
456	#107	—	2	2	no	—
457	#106	—	2	2	no	—
458	#103	—	2	2	no	—
459	#102	—	2	2	no	—
460	#102	—	2	2	no	—
461	#102	—	2	2	no	—
462	C₂²⋊C₈	—	2	2	no	—
463	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
464	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	C₂³×C₁₉	1	1	yes	characteristic
469	#95	C₂³×C₁₉	1	1	yes	characteristic
470	C₁₉	#18298	1	1	yes	characteristic, direct product factor, Sylow
471	C₂⁴	—	2	1	no	—
472	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
474	#41	—	4	2	no	—
475	#41	—	4	2	no	—
476	#41	—	8	2	no	—
477	#41	—	8	2	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	4	1	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	—	8	1	no	—
495	C₂×D₄	—	8	1	no	—
496	C₂×D₄	—	8	1	no	—
497	C₂×D₄	—	8	1	no	—
498	C₂×D₄	—	8	1	no	—
499	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	8	1	no	—
509	C₂²×C₄	—	8	1	no	—
510	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
515	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
517	SD₁₆	—	8	2	no	—
518	D₈	—	8	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	8	2	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	8	1	no	—
533	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
534	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	8	1	no	—
550	C₂²⋊C₄	—	8	1	no	—
551	C₂²⋊C₄	—	8	1	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	2	no	—
557	C₄²	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	2	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	C₁₉×#120	1	2	yes	—
576	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	Q₈	—	4	2	no	—
578	Q₈	—	4	2	no	—
579	Q₈	—	8	1	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	8	2	no	—
588	D₄	—	8	2	no	—
589	D₄	—	8	1	no	—
590	D₄	—	8	2	no	—
591	D₄	—	8	2	no	—
592	D₄	—	8	4	no	—
593	D₄	—	8	4	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	8	1	no	—
620	C₂×C₄	—	8	2	no	—
621	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
622	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
623	C₂×C₄	C₁₉×#135	1	2	yes	—
624	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
625	C₈	—	4	2	no	—
626	C₈	—	4	2	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
650	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
651	C₂²	C₁₉×#575	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	2	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	8	1	no	—
668	C₂	—	8	2	no	—
669	C₂	—	16	1	no	—
670	C₂	C₁₉×#3002	1	1	yes	characteristic
671	C₂	C₁₉×#3021	1	1	yes	characteristic
672	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
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×#3460	C₂	semidirect
2. C₁₉×#3188	C₂	semidirect
3. C₁₉×#2635	C₂	semidirect
4. C₁₉×#1618	C₂	semidirect
5. C₁₉×#1617	C₂	semidirect
6. C₁₉×#1616	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1599	C₂	semidirect
9. C₁₉×#1598	C₂	semidirect
10. C₁₉×#1516	C₂	semidirect
11. C₁₉×#1459	C₂	semidirect
53. C₂×#41×C₁₉	D₄	semidirect
78. C₁₉×C₂²⋊Q₈	D₄	semidirect
89. C₁₉×#121	D₄	semidirect
106. C₁₉×#117	D₄	semidirect
221. #18298	C₁₉	direct (N × H)
291. #3460	C₂×C₁₉	semidirect
292. #3188	C₂×C₁₉	semidirect
293. #2635	C₂×C₁₉	semidirect
294. #1618	C₂×C₁₉	semidirect
295. #1617	C₂×C₁₉	semidirect
296. #1616	C₂×C₁₉	semidirect
297. #1600	C₂×C₁₉	semidirect
298. #1599	C₂×C₁₉	semidirect
299. #1598	C₂×C₁₉	semidirect
300. #1516	C₂×C₁₉	semidirect
301. #1459	C₂×C₁₉	semidirect
389. C₂×#41	D₄×C₁₉	semidirect
414. C₂²⋊Q₈	D₄×C₁₉	semidirect
425. #121	D₄×C₁₉	semidirect
442. #117	D₄×C₁₉	semidirect
470. C₁₉	#18298	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×#3460	2
C₁₉×#3188	2
C₁₉×#2635	2
C₁₉×#1618	2
C₁₉×#1617	2
C₁₉×#1616	2
C₁₉×#1600	2
C₁₉×#1599	2
C₁₉×#1598	2
C₁₉×#1516	2
C₁₉×#1459	2
#18298	19

Subgroups — C19×#18298 #18024257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18298 #18024257