Subgroups — C₁₉×#18121 #18024080

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 628 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
2	C₁₉×#3091	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2395	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×#1612	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1611	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1610	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1501	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	C₄×#41×C₁₉	—	2	1	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
26	C₁₉×#485	—	2	2	no	—
27	C₁₉×#484	C₂²	1	2	yes	—
28	C₁₉×#483	C₂²	1	2	yes	—
29	C₁₉×#482	—	2	2	no	—
30	C₁₉×#481	C₂²	1	2	yes	—
31	C₁₉×#480	C₂²	1	2	yes	—
32	C₁₉×#427	—	2	2	no	—
33	C₁₉×#416	—	2	2	no	—
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×#398	C₂²	1	1	yes	characteristic
38	C₁₉×#397	—	2	1	no	—
39	C₁₉×#397	C₂²	1	1	yes	characteristic
40	C₁₉×#394	—	2	1	no	—
41	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₄×C₂²⋊C₄×C₁₉	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	—
54	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	2	2	no	—
59	C₁₉×#127	—	2	2	no	—
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#125	—	2	2	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
74	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#121	—	2	2	no	—
81	C₁₉×#121	—	2	1	no	—
82	C₁₉×#121	D₄	1	2	yes	—
83	C₁₉×#121	C₂³	1	2	yes	—
84	C₁₉×#120	—	2	2	no	—
85	C₁₉×#120	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	2	2	no	—
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	D₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₉	—	2	2	no	—
114	C₂×C₄²×C₁₉	—	2	1	no	—
115	C₂×C₄²×C₁₉	—	2	1	no	—
116	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
117	C₁₉×#107	—	2	2	no	—
118	C₁₉×#107	—	2	2	no	—
119	C₁₉×#106	—	2	2	no	—
120	C₁₉×#106	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×#95	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	4	no	—
138	#41×C₁₉	—	4	2	no	—
139	#41×C₁₉	—	8	2	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	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	1	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	4	1	no	—
153	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	4	4	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	4	2	no	—
187	C₄⋊C₄×C₁₉	—	4	2	no	—
188	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	—	4	2	no	—
202	C₂²⋊C₄×C₁₉	—	4	2	no	—
203	C₂²⋊C₄×C₁₉	—	4	2	no	—
204	C₂²⋊C₄×C₁₉	—	4	2	no	—
205	C₄²×C₁₉	—	2	2	no	—
206	C₄²×C₁₉	—	2	2	no	—
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	2	2	no	—
210	C₄²×C₁₉	—	4	2	no	—
211	C₄²×C₁₉	—	4	1	no	—
212	C₄²×C₁₉	—	4	1	no	—
213	#18121	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	#120	1	2	yes	—
225	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₁₉	—	4	2	no	—
227	Q₈×C₁₉	—	4	2	no	—
228	Q₈×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	4	4	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	2	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	8	2	no	—
235	D₄×C₁₉	—	8	2	no	—
236	D₄×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	8	1	no	—
238	D₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	4	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	4	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	8	1	no	—
268	C₂×C₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#135	1	2	yes	—
272	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
273	C₈×C₁₉	—	4	2	no	—
274	C₈×C₁₉	—	4	2	no	—
275	#3460	C₂×C₁₉	1	1	yes	characteristic
276	#3091	C₂×C₁₉	1	2	yes	complemented
277	#2395	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1618	C₂×C₁₉	1	2	yes	complemented
279	#1617	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1616	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1612	C₂×C₁₉	1	2	yes	complemented
282	#1611	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1610	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1501	C₂×C₁₉	1	2	yes	complemented
285	#1459	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
302	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
303	C₂²×C₁₉	#575	1	1	yes	characteristic
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	4	2	no	—
308	C₄×C₁₉	—	4	2	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	2	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₄×C₁₉	—	8	1	no	—
314	C₄×C₁₉	—	8	1	no	—
315	C₄×C₁₉	—	8	1	no	—
316	C₄×C₁₉	#458	1	2	yes	—
317	#544	C₂²×C₁₉	1	1	yes	characteristic
318	#542	—	2	2	no	—
319	#540	—	2	2	no	—
320	#538	—	2	1	no	—
321	#538	C₂²×C₁₉	1	2	yes	—
322	#537	C₂²×C₁₉	1	1	yes	characteristic
323	#535	—	2	1	no	—
324	#532	—	2	2	no	—
325	#529	—	2	2	no	—
326	#525	—	2	1	no	—
327	#525	C₂²×C₁₉	1	2	yes	—
328	C₄×#41	—	2	1	no	—
329	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
331	#485	—	2	2	no	—
332	#484	C₂²×C₁₉	1	2	yes	—
333	#483	C₂²×C₁₉	1	2	yes	—
334	#482	—	2	2	no	—
335	#481	C₂²×C₁₉	1	2	yes	—
336	#480	C₂²×C₁₉	1	2	yes	—
337	#427	—	2	2	no	—
338	#416	—	2	2	no	—
339	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
340	#400	C₂²×C₁₉	1	1	yes	characteristic
341	#399	C₂²×C₁₉	1	1	yes	characteristic
342	#398	C₂²×C₁₉	1	1	yes	characteristic
343	#397	—	2	1	no	—
344	#397	C₂²×C₁₉	1	1	yes	characteristic
345	#394	—	2	1	no	—
346	C₄×C₄⋊C₄	—	2	1	no	—
347	C₄×C₂²⋊C₄	—	2	1	no	—
348	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
349	#328	C₂²×C₁₉	1	2	yes	—
350	#328	C₂²×C₁₉	1	2	yes	—
351	#327	C₂²×C₁₉	1	2	yes	—
352	#327	C₂²×C₁₉	1	2	yes	—
353	#324	C₂²×C₁₉	1	1	yes	characteristic
354	#324	C₂²×C₁₉	1	1	yes	characteristic
355	#323	C₂²×C₁₉	1	2	yes	—
356	C₂×C₁₉	—	2	1	no	—
357	C₂×C₁₉	—	2	1	no	—
358	C₂×C₁₉	—	4	2	no	—
359	C₂×C₁₉	—	8	2	no	—
360	C₂×C₁₉	—	8	1	no	—
361	C₂×C₁₉	#3002	1	1	yes	characteristic
362	C₂×C₁₉	#3018	1	1	yes	characteristic
363	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	D₄×C₁₉	1	2	yes	—
367	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×C₈	—	2	2	no	—
371	C₄⋊Q₈	—	2	2	no	—
372	#127	—	2	2	no	—
373	#126	—	2	2	no	—
374	#126	—	2	2	no	—
375	#125	—	2	2	no	—
376	#124	—	2	2	no	—
377	#124	—	2	2	no	—
378	#124	—	2	2	no	—
379	#123	—	2	2	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
387	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
388	#121	—	2	1	no	—
389	#121	—	2	2	no	—
390	#121	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	2	no	—
394	#121	—	2	1	no	—
395	#121	D₄×C₁₉	1	2	yes	—
396	#121	C₂³×C₁₉	1	2	yes	—
397	#120	—	2	2	no	—
398	#120	—	2	2	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	#117	—	2	2	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	D₄×C₁₉	1	2	yes	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×C₄²	—	2	2	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
430	#107	—	2	2	no	—
431	#107	—	2	2	no	—
432	#106	—	2	2	no	—
433	#106	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	C₂²⋊C₈	—	2	2	no	—
439	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
440	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	C₂³×C₁₉	1	1	yes	characteristic
446	#95	C₂³×C₁₉	1	1	yes	characteristic
447	C₁₉	#18121	1	1	yes	characteristic, direct product factor, Sylow
448	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
450	#41	—	4	2	no	—
451	#41	—	4	4	no	—
452	#41	—	4	2	no	—
453	#41	—	8	2	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	4	4	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
503	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	4	1	no	—
526	C₄²	—	4	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	C₁₉×#120	1	2	yes	—
538	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
539	Q₈	—	4	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	8	1	no	—
542	D₄	—	4	4	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	8	2	no	—
548	D₄	—	8	2	no	—
549	D₄	—	8	1	no	—
550	D₄	—	8	2	no	—
551	D₄	—	8	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	1	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
583	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
584	C₂×C₄	C₁₉×#135	1	2	yes	—
585	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
586	C₈	—	4	2	no	—
587	C₈	—	4	2	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
604	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
605	C₂²	C₁₉×#575	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	2	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	1	no	—
618	C₄	C₁₉×#458	1	2	yes	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	4	2	no	—
622	C₂	—	8	1	no	—
623	C₂	—	8	2	no	—
624	C₂	C₁₉×#3002	1	1	yes	characteristic
625	C₂	C₁₉×#3018	1	1	yes	characteristic
626	C₂	C₂×C₁₉×#458	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₁₉×#3460	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3091	C₂	semidirect
3. C₁₉×#2395	C₂	semidirect
4. C₁₉×#1618	C₂	semidirect
5. C₁₉×#1617	C₂	semidirect
6. C₁₉×#1616	C₂	semidirect
7. C₁₉×#1612	C₂	semidirect
8. C₁₉×#1611	C₂	semidirect
9. C₁₉×#1610	C₂	semidirect
10. C₁₉×#1501	C₂	semidirect
11. C₁₉×#1459	C₂	semidirect
213. #18121	C₁₉	direct (N × H)
276. #3091	C₂×C₁₉	semidirect
277. #2395	C₂×C₁₉	semidirect
278. #1618	C₂×C₁₉	semidirect
279. #1617	C₂×C₁₉	semidirect
280. #1616	C₂×C₁₉	semidirect
281. #1612	C₂×C₁₉	semidirect
282. #1611	C₂×C₁₉	semidirect
283. #1610	C₂×C₁₉	semidirect
284. #1501	C₂×C₁₉	semidirect
285. #1459	C₂×C₁₉	semidirect
447. C₁₉	#18121	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×#3091	2
C₁₉×#2395	2
C₁₉×#1618	2
C₁₉×#1617	2
C₁₉×#1616	2
C₁₉×#1612	2
C₁₉×#1611	2
C₁₉×#1610	2
C₁₉×#1501	2
C₁₉×#1459	2
#18121	19

Subgroups — C19×#18121 #18024080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18121 #18024080