Subgroups — C₁₉×#18535 #18024494

Order 4864.

908 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1636	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1626	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#557	—	2	2	no	—
11	C₁₉×#557	—	2	2	no	—
12	C₁₉×#557	—	2	2	no	—
13	C₁₉×#557	C₂²	1	4	yes	—
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	—	2	2	no	—
18	C₂×C₁₉×#125	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#489	—	2	2	no	—
24	C₁₉×#487	C₂²	1	2	yes	—
25	C₁₉×#486	C₂²	1	2	yes	—
26	C₁₉×#480	—	2	1	no	—
27	C₁₉×#480	—	2	1	no	—
28	C₁₉×#477	C₂²	1	2	yes	—
29	C₁₉×#477	C₂²	1	2	yes	—
30	C₁₉×#460	C₂²	1	2	yes	—
31	C₁₉×#460	C₂²	1	2	yes	—
32	C₁₉×#448	—	2	1	no	—
33	C₁₉×#448	—	2	1	no	—
34	C₁₉×#440	—	2	2	no	—
35	C₁₉×#440	—	2	2	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#417	—	2	2	no	—
39	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#332	C₂²	1	4	yes	—
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₁₉	—	2	2	no	—
48	C₂×SD₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	—	2	4	no	—
51	C₁₉×C₄⋊Q₈	—	2	4	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₁₉×#127	C₂³	1	1	yes	characteristic
58	C₁₉×#125	—	2	8	no	—
59	C₁₉×#125	—	2	4	no	—
60	C₁₉×#125	—	2	8	no	—
61	C₁₉×#125	—	2	4	no	—
62	C₁₉×#124	—	2	1	no	—
63	C₁₉×#121	—	2	1	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	4	no	—
66	C₄×Q₈×C₁₉	—	2	4	no	—
67	C₄×Q₈×C₁₉	—	2	4	no	—
68	C₄×Q₈×C₁₉	—	2	4	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	D₄	1	2	yes	—
74	C₄×Q₈×C₁₉	D₄	1	2	yes	—
75	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
76	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	—	2	2	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#107	—	2	2	no	—
93	C₁₉×#107	—	2	2	no	—
94	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
95	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×#102	—	2	2	no	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	—	2	1	no	—
104	C₁₉×#97	—	2	1	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	C₂³	1	2	yes	—
108	#41×C₁₉	—	4	4	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	4	4	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	SD₁₆×C₁₉	—	4	4	no	—
133	SD₁₆×C₁₉	—	4	4	no	—
134	M₁₆×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	8	no	—
139	C₄⋊C₄×C₁₉	—	2	8	no	—
140	C₄⋊C₄×C₁₉	—	2	8	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	—	2	8	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
166	#18535	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	#120	1	1	yes	characteristic
169	Q₈×C₁₉	—	2	4	no	—
170	Q₈×C₁₉	—	2	2	no	—
171	Q₈×C₁₉	—	2	2	no	—
172	Q₈×C₁₉	—	2	2	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	4	4	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	4	4	no	—
177	Q₈×C₁₉	#137	1	4	yes	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	4	2	no	—
180	D₄×C₁₉	—	4	2	no	—
181	D₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₁₉	—	4	2	no	—
204	C₈×C₁₉	—	4	2	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₂×#557	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#3141	C₂×C₁₉	1	1	yes	characteristic
208	#3112	C₂×C₁₉	1	1	yes	characteristic
209	#3112	C₂×C₁₉	1	1	yes	characteristic
210	#1636	C₂×C₁₉	1	4	yes	complemented
211	#1626	C₂×C₁₉	1	4	yes	complemented
212	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	#454	1	2	yes	—
221	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
222	C₄×C₁₉	—	2	4	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	8	1	no	—
232	C₄×C₁₉	C₂×#137	1	2	yes	—
233	C₄×C₁₉	#575	1	2	yes	—
234	#557	—	2	2	no	—
235	#557	—	2	2	no	—
236	#557	—	2	2	no	—
237	#557	C₂²×C₁₉	1	4	yes	—
238	#532	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	—	2	1	no	—
240	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#125	—	2	2	no	—
242	C₂×#125	—	2	1	no	—
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×Q₈	—	2	1	no	—
245	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
247	#489	—	2	2	no	—
248	#487	C₂²×C₁₉	1	2	yes	—
249	#486	C₂²×C₁₉	1	2	yes	—
250	#480	—	2	1	no	—
251	#480	—	2	1	no	—
252	#477	C₂²×C₁₉	1	2	yes	—
253	#477	C₂²×C₁₉	1	2	yes	—
254	#460	C₂²×C₁₉	1	2	yes	—
255	#460	C₂²×C₁₉	1	2	yes	—
256	#448	—	2	1	no	—
257	#448	—	2	1	no	—
258	#440	—	2	2	no	—
259	#440	—	2	2	no	—
260	#432	C₂²×C₁₉	1	1	yes	characteristic
261	#432	C₂²×C₁₉	1	1	yes	characteristic
262	#417	—	2	2	no	—
263	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
264	#332	C₂²×C₁₉	1	4	yes	—
265	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
266	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
267	C₂×C₁₉	—	2	2	no	—
268	C₂×C₁₉	—	16	1	no	—
269	C₂×C₁₉	#3004	1	1	yes	characteristic
270	C₂×C₁₉	#3005	1	1	yes	characteristic
271	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
275	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₄⋊Q₈	—	2	4	no	—
280	C₄⋊Q₈	—	2	4	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
284	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
285	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
286	#127	C₂³×C₁₉	1	1	yes	characteristic
287	#125	—	2	8	no	—
288	#125	—	2	4	no	—
289	#125	—	2	8	no	—
290	#125	—	2	4	no	—
291	#124	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	4	no	—
297	C₄×Q₈	—	2	4	no	—
298	C₄×Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	D₄×C₁₉	1	2	yes	—
303	C₄×Q₈	D₄×C₁₉	1	2	yes	—
304	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
305	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	#107	—	2	2	no	—
323	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
324	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
325	#103	—	2	2	no	—
326	#103	—	2	2	no	—
327	#103	—	2	4	no	—
328	#102	—	2	4	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	C₂²⋊C₈	—	2	1	no	—
332	C₂²⋊C₈	—	2	1	no	—
333	#97	—	2	1	no	—
334	#97	—	2	1	no	—
335	#97	—	2	1	no	—
336	C₄×C₈	C₂³×C₁₉	1	2	yes	—
337	C₁₉	#18535	1	1	yes	characteristic, direct product factor, Sylow
338	#41	—	4	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
348	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
362	SD₁₆	—	4	4	no	—
363	SD₁₆	—	4	4	no	—
364	M₁₆	—	4	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
383	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₄²	—	2	8	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
396	C₂³	—	4	1	no	—
397	C₂³	C₁₉×#120	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	4	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	4	no	—
406	Q₈	C₁₉×#137	1	4	yes	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	8	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
427	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	C₁₉×#454	1	2	yes	—
441	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
442	C₄	—	2	4	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	8	1	no	—
452	C₄	C₂×C₁₉×#137	1	2	yes	—
453	C₄	C₁₉×#575	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	16	1	no	—
456	C₂	C₁₉×#3004	1	1	yes	characteristic
457	C₂	C₁₉×#3005	1	1	yes	characteristic
458	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ 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. C₂×C₁₉×#557	C₂	semidirect
5. C₁₉×#1636	C₂	semidirect
6. C₁₉×#1626	C₂	semidirect
7. C₁₉×#1556	C₂	semidirect
8. C₁₉×#1491	C₂	semidirect
9. C₁₉×#1491	C₂	semidirect
166. #18535	C₁₉	direct (N × H)
206. C₂×#557	C₂×C₁₉	semidirect
210. #1636	C₂×C₁₉	semidirect
211. #1626	C₂×C₁₉	semidirect
212. #1556	C₂×C₁₉	semidirect
213. #1491	C₂×C₁₉	semidirect
214. #1491	C₂×C₁₉	semidirect
337. C₁₉	#18535	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#557	2
C₁₉×#3141	2
C₁₉×#3112	2
C₁₉×#1636	2
C₁₉×#1626	2
C₁₉×#1556	2
C₁₉×#1491	2
#18535	19

Subgroups — C19×#18535 #18024494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18535 #18024494