Subgroups — C₁₉×#18366 #18024325

Order 4864.

1048 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1600	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1599	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1598	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1512	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#556	—	2	2	no	—
10	C₁₉×#555	—	2	2	no	—
11	C₁₉×#553	—	2	2	no	—
12	C₁₉×#552	—	2	2	no	—
13	C₁₉×#544	C₂²	1	1	yes	characteristic
14	C₁₉×#538	—	2	1	no	—
15	C₁₉×#538	C₂²	1	2	yes	—
16	C₁₉×#537	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₁₉×#529	—	2	1	no	—
19	C₁₉×#529	C₂²	1	2	yes	—
20	C₁₉×#525	—	2	1	no	—
21	C₂×C₁₉×#121	—	2	1	no	—
22	C₁₉×#520	—	2	1	no	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#496	—	2	2	no	—
25	C₁₉×#490	—	2	2	no	—
26	C₁₉×#460	—	2	2	no	—
27	C₁₉×#459	—	2	2	no	—
28	C₁₉×#450	C₂²	1	4	yes	—
29	C₁₉×#447	C₂²	1	4	yes	—
30	C₁₉×#432	C₂²	1	2	yes	—
31	C₁₉×#394	—	2	1	no	—
32	C₁₉×#394	C₂²	1	2	yes	—
33	C₁₉×#392	—	2	1	no	—
34	C₁₉×#392	C₂²	1	2	yes	—
35	C₁₉×#390	—	2	1	no	—
36	C₁₉×#382	C₂²	1	1	yes	characteristic
37	C₁₉×#328	C₂²	1	4	yes	—
38	C₁₉×#327	C₂²	1	4	yes	—
39	C₁₉×#324	C₂²	1	2	yes	—
40	C₁₉×#323	C₂²	1	2	yes	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₁₉	—	2	4	no	—
48	C₂×D₈×C₁₉	—	2	4	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×#127	—	2	2	no	—
51	C₁₉×#127	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#126	—	2	2	no	—
54	C₁₉×#126	—	2	2	no	—
55	C₁₉×#126	—	2	2	no	—
56	C₁₉×#125	—	2	1	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×#125	D₄	1	2	yes	complemented
59	C₁₉×#124	—	2	1	no	—
60	C₁₉×#124	—	2	2	no	—
61	C₁₉×#124	—	2	2	no	—
62	C₁₉×#124	D₄	1	2	yes	complemented
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
71	C₁₉×#121	—	2	1	no	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	1	no	—
77	C₁₉×#121	—	4	4	no	—
78	C₁₉×#121	C₂³	1	2	yes	—
79	C₁₉×#120	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	1	no	—
93	C₁₉×#117	—	2	2	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×C₄⋊C₈	—	2	2	no	—
108	C₁₉×#102	—	2	4	no	—
109	C₁₉×#102	—	2	4	no	—
110	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
111	C₁₉×#97	—	2	2	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	C₂³	1	2	yes	—
114	C₂⁴×C₁₉	—	2	2	no	—
115	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
116	#41×C₁₉	—	4	2	no	—
117	#41×C₁₉	—	4	2	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	4	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	4	2	no	—
133	C₂×D₄×C₁₉	—	8	2	no	—
134	C₂×D₄×C₁₉	—	8	2	no	—
135	C₂×D₄×C₁₉	—	8	2	no	—
136	C₂×D₄×C₁₉	—	8	2	no	—
137	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	4	1	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
152	SD₁₆×C₁₉	—	8	4	no	—
153	D₈×C₁₉	—	8	4	no	—
154	C₂×C₈×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	4	2	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	4	4	no	—
182	C₂²⋊C₄×C₁₉	—	8	2	no	—
183	C₂²⋊C₄×C₁₉	—	8	2	no	—
184	C₄²×C₁₉	—	2	2	no	—
185	C₄²×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	C₂×D₄	1	2	yes	—
190	C₄²×C₁₉	C₂×D₄	1	2	yes	—
191	#18366	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	—	2	1	no	—
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₁₉	—	4	2	no	—
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	8	1	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	2	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	4	4	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	8	2	no	—
216	D₄×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	8	4	no	—
218	D₄×C₁₉	—	8	2	no	—
219	D₄×C₁₉	—	8	1	no	—
220	D₄×C₁₉	—	8	2	no	—
221	D₄×C₁₉	—	8	8	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	4	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#120	1	2	yes	—
246	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₈×C₁₉	—	4	4	no	—
249	#3493	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#3217	C₂×C₁₉	1	2	yes	complemented
251	#2619	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1600	C₂×C₁₉	1	4	yes	complemented
253	#1599	C₂×C₁₉	1	2	yes	complemented
254	#1598	C₂×C₁₉	1	2	yes	complemented
255	#1512	C₂×C₁₉	1	2	yes	complemented
256	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	1	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	—	8	2	no	—
268	C₂²×C₁₉	—	8	2	no	—
269	C₂²×C₁₉	—	8	2	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	—	8	2	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
275	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₂²×C₁₉	#575	1	1	yes	characteristic
277	C₄×C₁₉	—	2	2	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	8	2	no	—
288	#556	—	2	2	no	—
289	#555	—	2	2	no	—
290	#553	—	2	2	no	—
291	#552	—	2	2	no	—
292	#544	C₂²×C₁₉	1	1	yes	characteristic
293	#538	—	2	1	no	—
294	#538	C₂²×C₁₉	1	2	yes	—
295	#537	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
297	#529	—	2	1	no	—
298	#529	C₂²×C₁₉	1	2	yes	—
299	#525	—	2	1	no	—
300	C₂×#121	—	2	1	no	—
301	#520	—	2	1	no	—
302	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
303	#496	—	2	2	no	—
304	#490	—	2	2	no	—
305	#460	—	2	2	no	—
306	#459	—	2	2	no	—
307	#450	C₂²×C₁₉	1	4	yes	—
308	#447	C₂²×C₁₉	1	4	yes	—
309	#432	C₂²×C₁₉	1	2	yes	—
310	#394	—	2	1	no	—
311	#394	C₂²×C₁₉	1	2	yes	—
312	#392	—	2	1	no	—
313	#392	C₂²×C₁₉	1	2	yes	—
314	#390	—	2	1	no	—
315	#382	C₂²×C₁₉	1	1	yes	characteristic
316	#328	C₂²×C₁₉	1	4	yes	—
317	#327	C₂²×C₁₉	1	4	yes	—
318	#324	C₂²×C₁₉	1	2	yes	—
319	#323	C₂²×C₁₉	1	2	yes	—
320	C₂×C₁₉	—	2	1	no	—
321	C₂×C₁₉	—	2	1	no	—
322	C₂×C₁₉	—	8	2	no	—
323	C₂×C₁₉	—	8	1	no	—
324	C₂×C₁₉	—	16	2	no	—
325	C₂×C₁₉	#3006	1	1	yes	characteristic
326	C₂×C₁₉	#3021	1	1	yes	characteristic
327	C₂×C₁₉	#3027	1	1	yes	characteristic
328	C₂×#41	—	2	1	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
333	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
334	C₂×SD₁₆	—	2	4	no	—
335	C₂×D₈	—	2	4	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	#127	—	2	2	no	—
338	#127	—	2	2	no	—
339	#126	—	2	2	no	—
340	#126	—	2	2	no	—
341	#126	—	2	2	no	—
342	#126	—	2	2	no	—
343	#125	—	2	1	no	—
344	#125	—	2	2	no	—
345	#125	D₄×C₁₉	1	2	yes	complemented
346	#124	—	2	1	no	—
347	#124	—	2	2	no	—
348	#124	—	2	2	no	—
349	#124	D₄×C₁₉	1	2	yes	complemented
350	#123	—	2	2	no	—
351	#123	—	2	2	no	—
352	#123	—	2	2	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	2	no	—
363	#121	—	2	1	no	—
364	#121	—	4	4	no	—
365	#121	C₂³×C₁₉	1	2	yes	—
366	#120	—	2	2	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
377	#117	—	2	2	no	—
378	#117	—	2	2	no	—
379	#117	—	2	1	no	—
380	#117	—	2	2	no	—
381	#117	—	2	2	no	—
382	#117	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
394	C₄⋊C₈	—	2	2	no	—
395	#102	—	2	4	no	—
396	#102	—	2	4	no	—
397	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
398	#97	—	2	2	no	—
399	#95	—	2	1	no	—
400	#95	C₂³×C₁₉	1	2	yes	—
401	C₁₉	#18366	1	1	yes	characteristic, direct product factor, Sylow
402	C₂⁴	—	2	2	no	—
403	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
404	#41	—	4	2	no	—
405	#41	—	4	2	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	8	2	no	—
422	C₂×D₄	—	8	2	no	—
423	C₂×D₄	—	8	2	no	—
424	C₂×D₄	—	8	2	no	—
425	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
440	SD₁₆	—	8	4	no	—
441	D₈	—	8	4	no	—
442	C₂×C₈	—	2	4	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	8	2	no	—
471	C₂²⋊C₄	—	8	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	2	no	—
477	C₄²	C₂×D₄×C₁₉	1	2	yes	—
478	C₄²	C₂×D₄×C₁₉	1	2	yes	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
493	Q₈	—	4	2	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	8	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	4	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	D₄	—	8	4	no	—
505	D₄	—	8	2	no	—
506	D₄	—	8	1	no	—
507	D₄	—	8	2	no	—
508	D₄	—	8	8	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
532	C₂×C₄	C₁₉×#120	1	2	yes	—
533	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
535	C₈	—	4	4	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
554	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
555	C₂²	C₁₉×#575	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	2	no	—
566	C₄	—	8	2	no	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	8	1	no	—
570	C₂	—	8	2	no	—
571	C₂	—	16	2	no	—
572	C₂	C₁₉×#3006	1	1	yes	characteristic
573	C₂	C₁₉×#3021	1	1	yes	characteristic
574	C₂	C₁₉×#3027	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 ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3493	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#2619	C₂	semidirect
4. C₁₉×#1600	C₂	semidirect
5. C₁₉×#1599	C₂	semidirect
6. C₁₉×#1598	C₂	semidirect
7. C₁₉×#1512	C₂	semidirect
8. C₁₉×#1464	C₂	semidirect
58. C₁₉×#125	D₄	semidirect
62. C₁₉×#124	D₄	semidirect
82. C₄×Q₈×C₁₉	D₄	semidirect
89. C₄×D₄×C₁₉	D₄	semidirect
191. #18366	C₁₉	direct (N × H)
249. #3493	C₂×C₁₉	semidirect
250. #3217	C₂×C₁₉	semidirect
251. #2619	C₂×C₁₉	semidirect
252. #1600	C₂×C₁₉	semidirect
253. #1599	C₂×C₁₉	semidirect
254. #1598	C₂×C₁₉	semidirect
255. #1512	C₂×C₁₉	semidirect
256. #1464	C₂×C₁₉	semidirect
345. #125	D₄×C₁₉	semidirect
349. #124	D₄×C₁₉	semidirect
369. C₄×Q₈	D₄×C₁₉	semidirect
376. C₄×D₄	D₄×C₁₉	semidirect
401. C₁₉	#18366	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×#3493	2
C₁₉×#3217	2
C₁₉×#2619	2
C₁₉×#1600	2
C₁₉×#1599	2
C₁₉×#1598	2
C₁₉×#1512	2
C₁₉×#1464	2
#18366	19

Subgroups — C19×#18366 #18024325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18366 #18024325