Subgroups — C₁₉×#18432 #18024391

Order 4864.

940 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2641	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1599	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1597	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1470	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#564	—	2	1	no	—
11	C₁₉×#563	—	2	1	no	—
12	C₁₉×#557	—	2	1	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#552	—	2	1	no	—
15	C₁₉×#552	—	2	1	no	—
16	C₁₉×#552	—	2	2	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#544	C₂²	1	2	yes	—
19	C₁₉×#541	—	2	1	no	—
20	C₁₉×#541	—	2	2	no	—
21	C₁₉×#539	C₂²	1	2	yes	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
26	C₁₉×#496	—	2	1	no	—
27	C₁₉×#492	—	2	1	no	—
28	C₁₉×#490	—	2	1	no	—
29	C₁₉×#486	—	2	1	no	—
30	C₁₉×#460	—	2	2	no	—
31	C₁₉×#460	—	2	1	no	—
32	C₁₉×#459	—	2	1	no	—
33	C₁₉×#450	C₂²	1	4	yes	—
34	C₁₉×#450	C₂²	1	2	yes	—
35	C₁₉×#447	C₂²	1	2	yes	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#394	—	2	2	no	—
39	C₁₉×#394	C₂²	1	4	yes	—
40	C₁₉×#390	—	2	1	no	—
41	C₁₉×#390	—	2	1	no	—
42	C₁₉×#376	C₂²	1	1	yes	characteristic
43	C₁₉×#328	C₂²	1	2	yes	—
44	C₁₉×#328	C₂²	1	4	yes	—
45	C₁₉×#327	C₂²	1	2	yes	—
46	C₁₉×#324	C₂²	1	4	yes	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
50	C₂×SD₁₆×C₁₉	—	2	4	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×D₈×C₁₉	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	—	2	1	no	—
60	C₁₉×#127	—	2	1	no	—
61	C₁₉×#127	—	2	1	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	1	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	1	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	D₄	1	1	yes	characteristic
82	C₁₉×#124	D₄	1	1	yes	characteristic
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	1	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
95	C₁₉×#121	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	2	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₉	D₄	1	2	yes	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
105	C₁₉×#117	—	2	2	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	2	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
117	C₂×C₄²×C₁₉	—	2	1	no	—
118	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	—	2	1	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	4	no	—
124	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
125	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
126	C₁₉×#97	—	2	1	no	—
127	C₄×C₈×C₁₉	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₂⁴×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	4	4	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	—	8	2	no	—
144	C₂×D₄×C₁₉	—	8	2	no	—
145	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	SD₁₆×C₁₉	—	8	2	no	—
155	SD₁₆×C₁₉	—	8	4	no	—
156	D₈×C₁₉	—	8	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	8	4	no	—
197	C₂²⋊C₄×C₁₉	—	8	4	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	2	no	—
200	C₄²×C₁₉	—	2	2	no	—
201	C₄²×C₁₉	—	2	2	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	4	2	no	—
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	#18432	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	4	4	no	—
211	C₂³×C₁₉	—	4	4	no	—
212	C₂³×C₁₉	—	4	2	no	—
213	C₂³×C₁₉	—	4	4	no	—
214	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	2	no	—
217	Q₈×C₁₉	—	4	2	no	—
218	Q₈×C₁₉	—	8	2	no	—
219	D₄×C₁₉	—	4	1	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	2	no	—
222	D₄×C₁₉	—	4	4	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	8	2	no	—
225	D₄×C₁₉	—	8	2	no	—
226	D₄×C₁₉	—	8	2	no	—
227	D₄×C₁₉	—	8	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	8	2	no	—
245	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₈×C₁₉	—	4	2	no	—
252	C₈×C₁₉	—	4	2	no	—
253	#3563	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#3217	C₂×C₁₉	1	1	yes	characteristic
255	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2641	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1599	C₂×C₁₉	1	4	yes	complemented
258	#1597	C₂×C₁₉	1	4	yes	complemented
259	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1500	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1470	C₂×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	8	8	no	—
268	C₂²×C₁₉	—	8	2	no	—
269	C₂²×C₁₉	—	8	2	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
272	C₂²×C₁₉	#577	1	2	yes	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	8	2	no	—
286	C₄×C₁₉	#454	1	2	yes	—
287	#564	—	2	1	no	—
288	#563	—	2	1	no	—
289	#557	—	2	1	no	—
290	#554	—	2	1	no	—
291	#552	—	2	1	no	—
292	#552	—	2	1	no	—
293	#552	—	2	2	no	—
294	#544	—	2	1	no	—
295	#544	C₂²×C₁₉	1	2	yes	—
296	#541	—	2	1	no	—
297	#541	—	2	2	no	—
298	#539	C₂²×C₁₉	1	2	yes	—
299	#533	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
301	#529	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
303	#496	—	2	1	no	—
304	#492	—	2	1	no	—
305	#490	—	2	1	no	—
306	#486	—	2	1	no	—
307	#460	—	2	2	no	—
308	#460	—	2	1	no	—
309	#459	—	2	1	no	—
310	#450	C₂²×C₁₉	1	4	yes	—
311	#450	C₂²×C₁₉	1	2	yes	—
312	#447	C₂²×C₁₉	1	2	yes	—
313	#432	C₂²×C₁₉	1	1	yes	characteristic
314	#431	C₂²×C₁₉	1	1	yes	characteristic
315	#394	—	2	2	no	—
316	#394	C₂²×C₁₉	1	4	yes	—
317	#390	—	2	1	no	—
318	#390	—	2	1	no	—
319	#376	C₂²×C₁₉	1	1	yes	characteristic
320	#328	C₂²×C₁₉	1	4	yes	—
321	#328	C₂²×C₁₉	1	2	yes	—
322	#327	C₂²×C₁₉	1	2	yes	—
323	#324	C₂²×C₁₉	1	4	yes	—
324	C₂×C₁₉	—	2	2	no	—
325	C₂×C₁₉	—	8	1	no	—
326	C₂×C₁₉	—	16	2	no	—
327	C₂×C₁₉	#3010	1	1	yes	characteristic
328	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
329	C₂×C₁₉	#3027	1	1	yes	characteristic
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
333	C₂×SD₁₆	—	2	4	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×D₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
340	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
341	#127	—	2	1	no	—
342	#127	—	2	1	no	—
343	#127	—	2	1	no	—
344	#127	—	2	1	no	—
345	#126	—	2	2	no	—
346	#126	—	2	2	no	—
347	#126	—	2	2	no	—
348	#126	—	2	2	no	—
349	#126	—	2	1	no	—
350	#125	—	2	2	no	—
351	#125	—	2	2	no	—
352	#125	—	2	2	no	—
353	#125	—	2	2	no	—
354	#125	—	2	1	no	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#125	—	2	2	no	—
358	#125	—	2	2	no	—
359	#125	—	2	1	no	—
360	#125	—	2	1	no	—
361	#125	—	2	1	no	—
362	#125	—	2	1	no	—
363	#125	—	2	1	no	—
364	#125	D₄×C₁₉	1	1	yes	characteristic
365	#124	D₄×C₁₉	1	1	yes	characteristic
366	#123	—	2	2	no	—
367	#123	—	2	1	no	—
368	#123	—	2	2	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
378	#121	C₂³×C₁₉	1	1	yes	characteristic
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
384	C₄×Q₈	D₄×C₁₉	1	2	yes	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
388	#117	—	2	2	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#117	—	2	2	no	—
392	#117	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
396	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
398	C₂×C₂²⋊C₄	—	2	4	no	—
399	C₂×C₂²⋊C₄	—	2	4	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#102	—	2	4	no	—
407	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
408	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
409	#97	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	C₂³×C₁₉	1	2	yes	—
413	C₁₉	#18432	1	1	yes	characteristic, direct product factor, Sylow
414	C₂⁴	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
418	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	8	2	no	—
428	C₂×D₄	—	8	2	no	—
429	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
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	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
438	SD₁₆	—	8	2	no	—
439	SD₁₆	—	8	4	no	—
440	D₈	—	8	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	8	4	no	—
481	C₂²⋊C₄	—	8	4	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	4	2	no	—
488	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂³	—	2	1	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	4	no	—
497	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
498	Q₈	—	4	1	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	8	2	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	4	no	—
506	D₄	—	4	2	no	—
507	D₄	—	8	2	no	—
508	D₄	—	8	2	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
529	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
530	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
534	C₈	—	4	2	no	—
535	C₈	—	4	2	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	8	8	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	2	no	—
545	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
546	C₂²	C₁₉×#577	1	2	yes	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	8	2	no	—
560	C₄	C₁₉×#454	1	2	yes	—
561	C₂	—	2	2	no	—
562	C₂	—	8	1	no	—
563	C₂	—	16	2	no	—
564	C₂	C₁₉×#3010	1	1	yes	characteristic
565	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
566	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3217	C₂
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×#3563	C₂	semidirect
3. C₁₉×#3208	C₂	semidirect
4. C₁₉×#2641	C₂	semidirect
5. C₁₉×#1599	C₂	semidirect
6. C₁₉×#1597	C₂	semidirect
7. C₁₉×#1506	C₂	semidirect
8. C₁₉×#1500	C₂	semidirect
9. C₁₉×#1470	C₂	semidirect
208. #18432	C₁₉	direct (N × H)
253. #3563	C₂×C₁₉	semidirect
255. #3208	C₂×C₁₉	semidirect
256. #2641	C₂×C₁₉	semidirect
257. #1599	C₂×C₁₉	semidirect
258. #1597	C₂×C₁₉	semidirect
259. #1506	C₂×C₁₉	semidirect
260. #1500	C₂×C₁₉	semidirect
261. #1470	C₂×C₁₉	semidirect
413. C₁₉	#18432	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×#3563	2
C₁₉×#3217	2
C₁₉×#3208	2
C₁₉×#2641	2
C₁₉×#1599	2
C₁₉×#1597	2
C₁₉×#1506	2
C₁₉×#1500	2
C₁₉×#1470	2
#18432	19

Subgroups — C19×#18432 #18024391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18432 #18024391