Subgroups — C₁₉×#34359 #18040318

Order 4864.

2406 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2378	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2368	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2344	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2342	C₂	1	4	yes	maximal
6	C₁₉×#2332	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2329	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2313	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2310	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×#381	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	C₄	1	16	yes	complemented
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#117	C₂²	1	2	yes	—
20	C₂×C₁₉×#117	C₂²	1	4	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#391	C₂²	1	8	yes	complemented
26	C₁₉×#391	C₂²	1	8	yes	complemented
27	C₁₉×#389	C₂²	1	8	yes	complemented
28	C₁₉×#388	C₂²	1	8	yes	—
29	C₁₉×#388	C₂²	1	8	yes	—
30	C₁₉×#387	C₂²	1	8	yes	complemented
31	C₁₉×#387	C₂²	1	8	yes	complemented
32	C₁₉×#387	C₂²	1	8	yes	complemented
33	C₁₉×#387	C₂²	1	8	yes	complemented
34	C₁₉×#385	C₂²	1	8	yes	—
35	C₁₉×#381	C₂²	1	2	yes	—
36	C₁₉×#381	C₂²	1	2	yes	—
37	C₁₉×#381	C₂²	1	2	yes	—
38	C₁₉×#381	C₂²	1	2	yes	—
39	C₁₉×#381	C₂²	1	2	yes	—
40	C₁₉×#381	C₂²	1	4	yes	—
41	C₁₉×#380	C₂²	1	2	yes	—
42	C₁₉×#380	C₂²	1	2	yes	—
43	C₁₉×#380	C₂²	1	4	yes	—
44	C₁₉×#379	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	complemented
46	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
47	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
48	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
49	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
50	C₂×C₁₉×#95	C₂²	1	2	yes	—
51	C₂×C₁₉×#95	C₂²	1	2	yes	—
52	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₉	—	4	4	no	—
54	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
55	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	—	4	4	no	—
58	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
69	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
70	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
71	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
72	C₁₉×#117	—	4	8	no	—
73	C₁₉×#117	—	4	4	no	—
74	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	complemented
75	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
83	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
84	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
95	C₁₉×#95	C₂³	1	4	yes	—
96	C₁₉×#95	C₂³	1	4	yes	—
97	C₁₉×#95	C₂³	1	4	yes	—
98	C₁₉×#95	C₂³	1	4	yes	—
99	C₁₉×#95	C₂³	1	4	yes	—
100	C₁₉×#95	C₂³	1	4	yes	—
101	C₁₉×#95	C₂³	1	8	yes	—
102	C₁₉×#95	C₂³	1	8	yes	—
103	C₁₉×#95	C₂³	1	8	yes	—
104	C₁₉×#95	C₂³	1	8	yes	—
105	C₂⁴×C₁₉	—	2	4	no	—
106	C₂⁴×C₁₉	—	2	4	no	—
107	C₂⁴×C₁₉	—	4	2	no	—
108	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
109	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	—	4	16	no	—
113	C₂×Q₈×C₁₉	—	4	2	no	—
114	C₂×Q₈×C₁₉	—	4	4	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
117	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	8	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	8	no	—
122	C₂²×C₄×C₁₉	—	4	16	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	—	4	2	no	—
125	C₂²×C₄×C₁₉	—	4	2	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
131	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₄⋊C₄×C₁₉	—	4	8	no	—
147	C₄⋊C₄×C₁₉	—	4	4	no	—
148	C₄⋊C₄×C₁₉	—	4	8	no	—
149	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
150	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
151	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
152	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
153	C₂²⋊C₄×C₁₉	—	2	8	no	—
154	C₂²⋊C₄×C₁₉	—	2	8	no	—
155	C₂²⋊C₄×C₁₉	—	2	8	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₉	—	4	4	no	—
158	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
159	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
160	C₄²×C₁₉	—	4	8	no	—
161	C₄²×C₁₉	—	4	4	no	—
162	C₄²×C₁₉	—	4	8	no	—
163	#34359	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	8	no	—
169	C₂³×C₁₉	—	2	8	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	4	4	no	—
174	C₂³×C₁₉	—	4	16	no	—
175	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
176	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
177	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
178	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
179	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
180	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
181	Q₈×C₁₉	—	4	8	no	—
182	Q₈×C₁₉	—	4	8	no	—
183	C₂×C₄×C₁₉	—	2	8	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	16	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	8	no	—
193	C₂×C₄×C₁₉	—	2	8	no	—
194	C₂×C₄×C₁₉	—	2	8	no	—
195	C₂×C₄×C₁₉	—	2	8	no	—
196	C₂×C₄×C₁₉	—	2	8	no	—
197	C₂×C₄×C₁₉	—	2	8	no	—
198	C₂×C₄×C₁₉	—	2	8	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	4	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	8	no	—
204	C₂×C₄×C₁₉	—	8	8	no	—
205	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
206	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
207	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
209	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
211	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
212	#2378	C₂×C₁₉	1	4	yes	complemented
213	#2368	C₂×C₁₉	1	4	yes	complemented
214	#2344	C₂×C₁₉	1	4	yes	complemented
215	#2342	C₂×C₁₉	1	4	yes	—
216	#2332	C₂×C₁₉	1	4	yes	complemented
217	#2329	C₂×C₁₉	1	4	yes	complemented
218	#2313	C₂×C₁₉	1	2	yes	complemented
219	#2310	C₂×C₁₉	1	2	yes	complemented
220	#2280	C₂×C₁₉	1	1	yes	characteristic
221	C₂×#381	C₂×C₁₉	1	1	yes	characteristic
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	8	no	—
227	C₂²×C₁₉	—	2	8	no	—
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	4	16	no	—
232	C₂²×C₁₉	—	4	4	no	—
233	C₂²×C₁₉	#518	1	4	yes	—
234	C₂²×C₁₉	#519	1	4	yes	—
235	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
236	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
237	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
238	C₂²×C₁₉	#585	1	2	yes	—
239	C₄×C₁₉	—	2	2	no	—
240	C₄×C₁₉	—	2	2	no	—
241	C₄×C₁₉	—	2	2	no	—
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	2	8	no	—
244	C₄×C₁₉	—	2	8	no	—
245	C₄×C₁₉	—	4	8	no	—
246	C₄×C₁₉	—	4	8	no	—
247	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₄×C₁₉	1	16	yes	complemented
250	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
251	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
254	C₂×#117	C₂²×C₁₉	1	4	yes	—
255	C₂×#117	C₂²×C₁₉	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
259	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
260	#391	C₂²×C₁₉	1	8	yes	complemented
261	#391	C₂²×C₁₉	1	8	yes	complemented
262	#389	C₂²×C₁₉	1	8	yes	complemented
263	#388	C₂²×C₁₉	1	8	yes	—
264	#388	C₂²×C₁₉	1	8	yes	—
265	#387	C₂²×C₁₉	1	8	yes	complemented
266	#387	C₂²×C₁₉	1	8	yes	complemented
267	#387	C₂²×C₁₉	1	8	yes	complemented
268	#387	C₂²×C₁₉	1	8	yes	complemented
269	#385	C₂²×C₁₉	1	8	yes	—
270	#381	C₂²×C₁₉	1	2	yes	—
271	#381	C₂²×C₁₉	1	2	yes	—
272	#381	C₂²×C₁₉	1	4	yes	—
273	#381	C₂²×C₁₉	1	2	yes	—
274	#381	C₂²×C₁₉	1	2	yes	—
275	#381	C₂²×C₁₉	1	2	yes	—
276	#380	C₂²×C₁₉	1	4	yes	—
277	#380	C₂²×C₁₉	1	2	yes	—
278	#380	C₂²×C₁₉	1	2	yes	—
279	#379	C₂²×C₁₉	1	2	yes	—
280	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
281	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
282	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
283	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
284	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
285	C₂×#95	C₂²×C₁₉	1	2	yes	—
286	C₂×#95	C₂²×C₁₉	1	2	yes	—
287	C₂×C₁₉	—	2	4	no	—
288	C₂×C₁₉	—	2	4	no	—
289	C₂×C₁₉	—	4	2	no	—
290	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
292	C₂×C₁₉	#3428	1	1	yes	characteristic
293	C₂×C₁₉	#3535	1	4	yes	—
294	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×Q₈	—	4	4	no	—
296	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
297	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
298	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
299	C₂³×C₄	—	4	4	no	—
300	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
301	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
302	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
305	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
311	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
312	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
313	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
314	#117	—	4	8	no	—
315	#117	—	4	4	no	—
316	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	complemented
317	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
325	C₂×C₂²⋊C₄	—	4	4	no	—
326	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
334	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
335	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
336	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
337	#95	C₂³×C₁₉	1	4	yes	—
338	#95	C₂³×C₁₉	1	4	yes	—
339	#95	C₂³×C₁₉	1	4	yes	—
340	#95	C₂³×C₁₉	1	4	yes	—
341	#95	C₂³×C₁₉	1	4	yes	—
342	#95	C₂³×C₁₉	1	4	yes	—
343	#95	C₂³×C₁₉	1	8	yes	—
344	#95	C₂³×C₁₉	1	8	yes	—
345	#95	C₂³×C₁₉	1	8	yes	—
346	#95	C₂³×C₁₉	1	8	yes	—
347	C₁₉	#34359	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	4	2	no	—
351	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
352	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
353	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
354	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
355	C₂×Q₈	—	4	16	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
360	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	4	16	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
374	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
375	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
378	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
379	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
382	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
383	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
389	C₄⋊C₄	—	4	8	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	8	no	—
392	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
393	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
394	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
395	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
402	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
403	C₄²	—	4	8	no	—
404	C₄²	—	4	4	no	—
405	C₄²	—	4	8	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	8	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	16	no	—
417	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
418	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
419	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
420	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
421	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
422	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
423	Q₈	—	4	8	no	—
424	Q₈	—	4	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	16	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	8	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	8	no	—
446	C₂×C₄	—	8	8	no	—
447	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
448	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
449	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
452	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	2	8	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	4	16	no	—
463	C₂²	—	4	4	no	—
464	C₂²	C₁₉×#518	1	4	yes	—
465	C₂²	C₁₉×#519	1	4	yes	—
466	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
467	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
468	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
469	C₂²	C₁₉×#585	1	2	yes	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	8	no	—
475	C₄	—	2	8	no	—
476	C₄	—	4	8	no	—
477	C₄	—	4	8	no	—
478	C₂	—	2	4	no	—
479	C₂	—	2	4	no	—
480	C₂	—	4	2	no	—
481	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
482	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
483	C₂	C₁₉×#3428	1	1	yes	characteristic
484	C₂	C₁₉×#3535	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2378	C₂	semidirect
3. C₁₉×#2368	C₂	semidirect
4. C₁₉×#2344	C₂	semidirect
6. C₁₉×#2332	C₂	semidirect
7. C₁₉×#2329	C₂	semidirect
8. C₁₉×#2313	C₂	semidirect
9. C₁₉×#2310	C₂	semidirect
14. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
25. C₁₉×#391	C₂²	semidirect
26. C₁₉×#391	C₂²	semidirect
27. C₁₉×#389	C₂²	semidirect
30. C₁₉×#387	C₂²	semidirect
31. C₁₉×#387	C₂²	semidirect
32. C₁₉×#387	C₂²	semidirect
33. C₁₉×#387	C₂²	semidirect
45. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
54. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
70. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
71. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
74. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
75. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
163. #34359	C₁₉	direct (N × H)
212. #2378	C₂×C₁₉	semidirect
213. #2368	C₂×C₁₉	semidirect
214. #2344	C₂×C₁₉	semidirect
216. #2332	C₂×C₁₉	semidirect
217. #2329	C₂×C₁₉	semidirect
218. #2313	C₂×C₁₉	semidirect
219. #2310	C₂×C₁₉	semidirect
249. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
260. #391	C₂²×C₁₉	semidirect
261. #391	C₂²×C₁₉	semidirect
262. #389	C₂²×C₁₉	semidirect
265. #387	C₂²×C₁₉	semidirect
266. #387	C₂²×C₁₉	semidirect
267. #387	C₂²×C₁₉	semidirect
268. #387	C₂²×C₁₉	semidirect
280. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
296. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
312. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
313. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
316. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
317. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
347. C₁₉	#34359	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₁₉×#2378	2
C₁₉×#2368	2
C₁₉×#2344	2
C₁₉×#2342	2
C₁₉×#2332	2
C₁₉×#2329	2
C₁₉×#2313	2
C₁₉×#2310	2
C₁₉×#2280	2
C₂×C₁₉×#381	2
#34359	19

Subgroups — C19×#34359 #18040318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34359 #18040318