Subgroups — C₁₉×#34373 #18040332

Order 4864.

1998 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2378	C₂	1	4	yes	maximal
3	C₁₉×#2362	C₂	1	4	yes	maximal
4	C₁₉×#2355	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2355	C₂	1	4	yes	maximal, complemented
6	Q₈×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2336	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2331	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2327	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2314	C₂	1	4	yes	maximal
11	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#533	C₄	1	16	yes	complemented
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#125	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#391	C₂²	1	4	yes	—
26	C₁₉×#391	C₂²	1	8	yes	—
27	C₁₉×#389	C₂²	1	4	yes	—
28	C₁₉×#389	C₂²	1	8	yes	—
29	C₁₉×#388	C₂²	1	8	yes	—
30	C₁₉×#388	C₂²	1	8	yes	—
31	C₁₉×#387	C₂²	1	8	yes	—
32	C₁₉×#387	C₂²	1	8	yes	—
33	C₁₉×#387	C₂²	1	8	yes	—
34	C₁₉×#387	C₂²	1	8	yes	—
35	C₁₉×#387	C₂²	1	8	yes	—
36	C₁₉×#384	C₂²	1	2	yes	—
37	C₁₉×#384	C₂²	1	4	yes	—
38	C₁₉×#383	C₂²	1	2	yes	—
39	C₁₉×#382	C₂²	1	2	yes	—
40	C₁₉×#382	C₂²	1	2	yes	—
41	C₁₉×#382	C₂²	1	4	yes	—
42	C₁₉×#381	C₂²	1	2	yes	—
43	C₁₉×#380	C₂²	1	2	yes	—
44	C₁₉×#380	C₂²	1	2	yes	—
45	C₁₉×#380	C₂²	1	2	yes	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
55	C₁₉×#376	C₂²	1	2	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	—
62	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	—
63	C₁₉×#125	C₂×C₄	1	16	yes	—
64	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
65	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
66	C₄×Q₈×C₁₉	—	4	8	no	—
67	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
68	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
69	C₁₉×#117	—	4	4	no	—
70	C₁₉×#117	C₂×C₄	1	16	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	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	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	4	yes	—
102	C₁₉×#95	C₂³	1	4	yes	—
103	C₁₉×#95	C₂³	1	2	yes	—
104	C₁₉×#95	C₂³	1	2	yes	—
105	C₁₉×#95	C₂³	1	8	yes	—
106	C₁₉×#95	C₂³	1	8	yes	—
107	C₁₉×#95	C₂³	1	8	yes	—
108	C₁₉×#95	C₂³	1	8	yes	—
109	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	4	4	no	—
113	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
114	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
133	C₄⋊C₄×C₁₉	—	2	8	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	8	no	—
137	C₄⋊C₄×C₁₉	—	4	4	no	—
138	C₄⋊C₄×C₁₉	—	4	8	no	—
139	C₄⋊C₄×C₁₉	—	4	8	no	—
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
141	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
142	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
143	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
144	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
145	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
146	C₂²⋊C₄×C₁₉	—	4	4	no	—
147	C₂²⋊C₄×C₁₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
149	C₄²×C₁₉	—	2	4	no	—
150	C₄²×C₁₉	—	2	4	no	—
151	C₄²×C₁₉	—	4	8	no	—
152	C₄²×C₁₉	—	4	4	no	—
153	C₄²×C₁₉	—	4	8	no	—
154	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
155	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
156	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
157	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
158	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
159	#34373	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
165	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	16	no	—
167	Q₈×C₁₉	—	4	8	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	8	no	—
178	C₂×C₄×C₁₉	—	2	8	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	8	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	8	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
193	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
194	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
195	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
198	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
199	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
200	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
201	#2378	C₂×C₁₉	1	4	yes	—
202	#2362	C₂×C₁₉	1	4	yes	—
203	#2355	C₂×C₁₉	1	2	yes	complemented
204	#2355	C₂×C₁₉	1	4	yes	complemented
205	Q₈×C₄⋊C₄	C₂×C₁₉	1	2	yes	complemented
206	#2336	C₂×C₁₉	1	4	yes	complemented
207	#2331	C₂×C₁₉	1	2	yes	complemented
208	#2327	C₂×C₁₉	1	2	yes	complemented
209	#2314	C₂×C₁₉	1	4	yes	—
210	#2285	C₂×C₁₉	1	1	yes	characteristic
211	#2283	C₂×C₁₉	1	1	yes	characteristic
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
220	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	C₂²×C₁₉	#585	1	2	yes	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	2	8	no	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	2	8	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	4	8	no	—
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	#519	1	4	yes	—
232	C₄×C₁₉	#520	1	4	yes	—
233	#533	C₄×C₁₉	1	16	yes	complemented
234	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#125	C₂²×C₁₉	1	2	yes	—
237	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
238	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
239	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
240	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
241	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
242	C₂×#117	C₂²×C₁₉	1	2	yes	—
243	C₂×#117	C₂²×C₁₉	1	2	yes	—
244	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
245	#391	C₂²×C₁₉	1	4	yes	—
246	#391	C₂²×C₁₉	1	8	yes	—
247	#389	C₂²×C₁₉	1	4	yes	—
248	#389	C₂²×C₁₉	1	8	yes	—
249	#388	C₂²×C₁₉	1	8	yes	—
250	#388	C₂²×C₁₉	1	8	yes	—
251	#387	C₂²×C₁₉	1	8	yes	—
252	#387	C₂²×C₁₉	1	8	yes	—
253	#387	C₂²×C₁₉	1	8	yes	—
254	#387	C₂²×C₁₉	1	8	yes	—
255	#387	C₂²×C₁₉	1	8	yes	—
256	#384	C₂²×C₁₉	1	4	yes	—
257	#384	C₂²×C₁₉	1	2	yes	—
258	#383	C₂²×C₁₉	1	2	yes	—
259	#382	C₂²×C₁₉	1	4	yes	—
260	#382	C₂²×C₁₉	1	2	yes	—
261	#382	C₂²×C₁₉	1	2	yes	—
262	#381	C₂²×C₁₉	1	2	yes	—
263	#380	C₂²×C₁₉	1	2	yes	—
264	#380	C₂²×C₁₉	1	2	yes	—
265	#380	C₂²×C₁₉	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
267	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
268	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
269	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
270	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
274	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
275	#376	C₂²×C₁₉	1	2	yes	—
276	C₂×C₁₉	—	4	2	no	—
277	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
278	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
279	C₂×C₁₉	#3428	1	1	yes	characteristic
280	C₂×C₁₉	#3554	1	2	yes	—
281	C₂×C₁₉	#3555	1	2	yes	—
282	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
283	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
284	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
288	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
289	#125	C₂×C₄×C₁₉	1	16	yes	—
290	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
291	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
292	C₄×Q₈	—	4	8	no	—
293	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
294	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
295	#117	—	4	4	no	—
296	#117	C₂×C₄×C₁₉	1	16	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
313	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
314	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
316	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
317	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
318	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
319	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
320	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
324	#95	C₂³×C₁₉	1	4	yes	—
325	#95	C₂³×C₁₉	1	4	yes	—
326	#95	C₂³×C₁₉	1	4	yes	—
327	#95	C₂³×C₁₉	1	4	yes	—
328	#95	C₂³×C₁₉	1	4	yes	—
329	#95	C₂³×C₁₉	1	2	yes	—
330	#95	C₂³×C₁₉	1	2	yes	—
331	#95	C₂³×C₁₉	1	8	yes	—
332	#95	C₂³×C₁₉	1	8	yes	—
333	#95	C₂³×C₁₉	1	8	yes	—
334	#95	C₂³×C₁₉	1	8	yes	—
335	C₁₉	#34373	1	1	yes	characteristic, direct product factor, Sylow
336	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	4	4	no	—
340	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
341	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
347	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
352	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
356	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	4	8	no	—
366	C₄⋊C₄	—	4	8	no	—
367	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
368	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
369	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
370	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
371	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
372	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
376	C₄²	—	2	4	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	4	8	no	—
379	C₄²	—	4	4	no	—
380	C₄²	—	4	8	no	—
381	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
382	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
383	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
384	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
385	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
391	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
392	Q₈	—	2	16	no	—
393	Q₈	—	4	8	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
417	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
418	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
419	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
420	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
421	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
422	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
423	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
425	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
432	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
434	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
435	C₂²	C₁₉×#585	1	2	yes	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	8	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	8	no	—
444	C₄	—	4	4	no	—
445	C₄	C₁₉×#519	1	4	yes	—
446	C₄	C₁₉×#520	1	4	yes	—
447	C₂	—	4	2	no	—
448	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
449	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
450	C₂	C₁₉×#3428	1	1	yes	characteristic
451	C₂	C₁₉×#3554	1	2	yes	—
452	C₂	C₁₉×#3555	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂⁴
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
4. C₁₉×#2355	C₂	semidirect
5. C₁₉×#2355	C₂	semidirect
6. Q₈×C₄⋊C₄×C₁₉	C₂	semidirect
7. C₁₉×#2336	C₂	semidirect
8. C₁₉×#2331	C₂	semidirect
9. C₁₉×#2327	C₂	semidirect
13. C₁₉×#533	C₄	semidirect
159. #34373	C₁₉	direct (N × H)
203. #2355	C₂×C₁₉	semidirect
204. #2355	C₂×C₁₉	semidirect
205. Q₈×C₄⋊C₄	C₂×C₁₉	semidirect
206. #2336	C₂×C₁₉	semidirect
207. #2331	C₂×C₁₉	semidirect
208. #2327	C₂×C₁₉	semidirect
233. #533	C₄×C₁₉	semidirect
335. C₁₉	#34373	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×#533	2
C₁₉×#2378	2
C₁₉×#2362	2
C₁₉×#2355	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2336	2
C₁₉×#2331	2
C₁₉×#2327	2
C₁₉×#2314	2
C₁₉×#2285	2
C₁₉×#2283	2
#34373	19

Subgroups — C19×#34373 #18040332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34373 #18040332