Subgroups — C₁₉×#34985 #18040944

Order 4864.

2866 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2855	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2848	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2627	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2626	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2450	C₂	1	8	yes	maximal, complemented
8	C₁₉×#2449	C₂	1	8	yes	maximal, complemented
9	C₁₉×#2315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2308	C₂	1	2	yes	maximal
11	C₂×C₁₉×#385	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#543	—	2	8	no	—
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	4	yes	complemented
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₁₉	—	2	8	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#400	C₂²	1	4	yes	complemented
31	C₁₉×#399	C₂²	1	4	yes	complemented
32	C₁₉×#398	C₂²	1	8	yes	complemented
33	C₁₉×#396	C₂²	1	8	yes	complemented
34	C₁₉×#395	C₂²	1	4	yes	complemented
35	C₁₉×#393	C₂²	1	4	yes	complemented
36	C₁₉×#391	C₂²	1	4	yes	complemented
37	C₁₉×#389	C₂²	1	4	yes	complemented
38	C₁₉×#387	C₂²	1	8	yes	complemented
39	C₁₉×#386	C₂²	1	4	yes	—
40	C₁₉×#386	C₂²	1	8	yes	—
41	C₁₉×#386	C₂²	1	4	yes	—
42	C₁₉×#385	C₂²	1	4	yes	—
43	C₁₉×#385	C₂²	1	4	yes	—
44	C₁₉×#385	C₂²	1	8	yes	complemented
45	C₁₉×#385	C₂²	1	8	yes	complemented
46	C₁₉×#385	C₂²	1	8	yes	complemented
47	C₁₉×#381	C₂²	1	4	yes	—
48	C₁₉×#380	C₂²	1	2	yes	—
49	C₁₉×#380	C₂²	1	2	yes	—
50	C₁₉×#380	C₂²	1	4	yes	complemented
51	C₁₉×#379	C₂²	1	4	yes	—
52	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
53	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₉	—	2	4	no	—
58	C₂²×D₄×C₁₉	—	2	4	no	—
59	C₂²×D₄×C₁₉	Q₈	1	8	yes	complemented
60	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₉	—	2	4	no	—
62	C₂³×C₄×C₁₉	—	2	4	no	—
63	C₂³×C₄×C₁₉	—	4	4	no	—
64	C₂³×C₄×C₁₉	—	4	4	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×C₂²⋊Q₈	—	2	8	no	—
76	C₁₉×C₂²⋊Q₈	—	2	8	no	—
77	C₁₉×C₂²⋊Q₈	—	2	16	no	—
78	C₁₉×C₂²⋊Q₈	—	2	16	no	—
79	C₁₉×C₂²⋊Q₈	—	4	8	no	—
80	C₄×D₄×C₁₉	—	2	32	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
96	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
104	C₂×C₄²×C₁₉	—	2	4	no	—
105	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
106	C₁₉×#95	C₂³	1	8	yes	—
107	C₁₉×#95	C₂³	1	8	yes	—
108	C₁₉×#95	C₂³	1	4	yes	—
109	C₁₉×#95	C₂³	1	4	yes	—
110	C₁₉×#95	C₂³	1	8	yes	—
111	C₁₉×#95	C₂³	1	8	yes	—
112	C₂⁴×C₁₉	—	2	2	no	—
113	C₂⁴×C₁₉	—	2	2	no	—
114	C₂⁴×C₁₉	—	4	2	no	—
115	C₂⁴×C₁₉	—	4	2	no	—
116	C₂⁴×C₁₉	—	4	2	no	—
117	C₂⁴×C₁₉	—	4	2	no	—
118	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
119	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
120	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
121	C₂⁴×C₁₉	#41	1	4	yes	—
122	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
123	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
124	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
125	C₂×Q₈×C₁₉	—	2	4	no	—
126	C₂×Q₈×C₁₉	—	2	4	no	—
127	C₂×Q₈×C₁₉	—	4	4	no	—
128	C₂×Q₈×C₁₉	—	4	4	no	—
129	C₂×D₄×C₁₉	—	2	32	no	—
130	C₂×D₄×C₁₉	—	2	8	no	—
131	C₂×D₄×C₁₉	—	2	8	no	—
132	C₂×D₄×C₁₉	C₂×Q₈	1	16	yes	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	8	no	—
139	C₂²×C₄×C₁₉	—	2	8	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	8	no	—
143	C₂²×C₄×C₁₉	—	2	8	no	—
144	C₂²×C₄×C₁₉	—	2	8	no	—
145	C₂²×C₄×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	4	2	no	—
147	C₂²×C₄×C₁₉	—	4	4	no	—
148	C₂²×C₄×C₁₉	—	4	4	no	—
149	C₂²×C₄×C₁₉	—	4	2	no	—
150	C₂²×C₄×C₁₉	—	4	2	no	—
151	C₂²×C₄×C₁₉	—	4	4	no	—
152	C₂²×C₄×C₁₉	—	4	4	no	—
153	C₂²×C₄×C₁₉	—	4	4	no	—
154	C₂²×C₄×C₁₉	—	4	16	no	—
155	C₂²×C₄×C₁₉	—	4	16	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
159	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
161	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
167	C₄⋊C₄×C₁₉	—	2	8	no	—
168	C₄⋊C₄×C₁₉	—	2	8	no	—
169	C₄⋊C₄×C₁₉	—	2	4	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	2	8	no	—
172	C₄⋊C₄×C₁₉	—	2	16	no	—
173	C₄⋊C₄×C₁₉	—	4	8	no	—
174	C₄⋊C₄×C₁₉	—	4	4	no	—
175	C₄⋊C₄×C₁₉	—	4	4	no	—
176	C₂²⋊C₄×C₁₉	—	2	8	no	—
177	C₂²⋊C₄×C₁₉	—	2	8	no	—
178	C₂²⋊C₄×C₁₉	—	2	8	no	—
179	C₂²⋊C₄×C₁₉	—	2	8	no	—
180	C₂²⋊C₄×C₁₉	—	2	8	no	—
181	C₂²⋊C₄×C₁₉	—	4	8	no	—
182	C₂²⋊C₄×C₁₉	—	4	8	no	—
183	C₂²⋊C₄×C₁₉	C₂×D₄	1	16	yes	—
184	C₄²×C₁₉	—	2	8	no	—
185	#34985	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	2	4	no	—
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	2	4	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	8	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	4	no	—
194	C₂³×C₁₉	—	2	4	no	—
195	C₂³×C₁₉	—	4	4	no	—
196	C₂³×C₁₉	—	4	4	no	—
197	C₂³×C₁₉	—	4	8	no	—
198	C₂³×C₁₉	—	4	8	no	—
199	C₂³×C₁₉	—	4	8	no	—
200	C₂³×C₁₉	—	4	4	no	—
201	C₂³×C₁₉	—	4	8	no	—
202	C₂³×C₁₉	—	4	4	no	—
203	C₂³×C₁₉	C₂²⋊Q₈	1	16	yes	complemented
204	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
205	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
206	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
207	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
208	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
209	C₂³×C₁₉	C₂×#41	1	2	yes	—
210	C₂³×C₁₉	C₂×#41	1	4	yes	—
211	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₉	—	8	4	no	—
213	Q₈×C₁₉	—	8	4	no	—
214	D₄×C₁₉	—	2	32	no	—
215	C₂×C₄×C₁₉	—	2	8	no	—
216	C₂×C₄×C₁₉	—	2	8	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	8	no	—
227	C₂×C₄×C₁₉	—	2	8	no	—
228	C₂×C₄×C₁₉	—	2	8	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	8	no	—
231	C₂×C₄×C₁₉	—	2	8	no	—
232	C₂×C₄×C₁₉	—	4	4	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	16	no	—
235	C₂×C₄×C₁₉	—	4	16	no	—
236	C₂×C₄×C₁₉	—	4	16	no	—
237	C₂×C₄×C₁₉	—	4	4	no	—
238	C₂×C₄×C₁₉	—	8	4	no	—
239	C₂×C₄×C₁₉	—	8	4	no	—
240	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
243	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
244	C₂×#543	C₂×C₁₉	1	1	yes	characteristic, complemented
245	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
246	#2855	C₂×C₁₉	1	2	yes	complemented
247	#2848	C₂×C₁₉	1	2	yes	complemented
248	#2627	C₂×C₁₉	1	2	yes	complemented
249	#2626	C₂×C₁₉	1	2	yes	complemented
250	#2450	C₂×C₁₉	1	8	yes	complemented
251	#2449	C₂×C₁₉	1	8	yes	complemented
252	#2315	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2308	C₂×C₁₉	1	2	yes	—
254	C₂×#385	C₂×C₁₉	1	2	yes	complemented
255	C₂²×C₁₉	—	2	8	no	—
256	C₂²×C₁₉	—	2	4	no	—
257	C₂²×C₁₉	—	2	2	no	—
258	C₂²×C₁₉	—	2	4	no	—
259	C₂²×C₁₉	—	2	2	no	—
260	C₂²×C₁₉	—	2	4	no	—
261	C₂²×C₁₉	—	2	4	no	—
262	C₂²×C₁₉	—	2	8	no	—
263	C₂²×C₁₉	—	2	4	no	—
264	C₂²×C₁₉	—	2	8	no	—
265	C₂²×C₁₉	—	4	16	no	—
266	C₂²×C₁₉	—	4	16	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	4	yes	—
271	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	8	yes	—
272	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
273	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
274	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
275	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
276	C₂²×C₁₉	#585	1	2	yes	—
277	C₄×C₁₉	—	2	4	no	—
278	C₄×C₁₉	—	2	4	no	—
279	C₄×C₁₉	—	2	4	no	—
280	C₄×C₁₉	—	2	4	no	—
281	C₄×C₁₉	—	4	8	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	4	no	—
284	C₄×C₁₉	—	4	4	no	—
285	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
286	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
287	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
288	#543	—	2	8	no	—
289	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
291	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
292	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
293	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
294	C₂×C₄×D₄	—	2	8	no	—
295	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
296	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
298	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
301	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
303	#400	C₂²×C₁₉	1	4	yes	complemented
304	#399	C₂²×C₁₉	1	4	yes	complemented
305	#398	C₂²×C₁₉	1	8	yes	complemented
306	#396	C₂²×C₁₉	1	8	yes	complemented
307	#395	C₂²×C₁₉	1	4	yes	complemented
308	#393	C₂²×C₁₉	1	4	yes	complemented
309	#391	C₂²×C₁₉	1	4	yes	complemented
310	#389	C₂²×C₁₉	1	4	yes	complemented
311	#387	C₂²×C₁₉	1	8	yes	complemented
312	#386	C₂²×C₁₉	1	4	yes	—
313	#386	C₂²×C₁₉	1	8	yes	—
314	#386	C₂²×C₁₉	1	4	yes	—
315	#385	C₂²×C₁₉	1	4	yes	—
316	#385	C₂²×C₁₉	1	4	yes	—
317	#385	C₂²×C₁₉	1	8	yes	complemented
318	#385	C₂²×C₁₉	1	8	yes	complemented
319	#385	C₂²×C₁₉	1	8	yes	complemented
320	#381	C₂²×C₁₉	1	4	yes	—
321	#380	C₂²×C₁₉	1	2	yes	—
322	#380	C₂²×C₁₉	1	2	yes	—
323	#380	C₂²×C₁₉	1	4	yes	complemented
324	#379	C₂²×C₁₉	1	4	yes	—
325	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
326	C₂×C₁₉	—	2	4	no	—
327	C₂×C₁₉	—	2	8	no	—
328	C₂×C₁₉	—	4	4	no	—
329	C₂×C₁₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
330	C₂×C₁₉	#3459	1	2	yes	—
331	C₂×C₁₉	#3484	1	1	yes	characteristic
332	C₂×C₁₉	#3485	1	1	yes	characteristic
333	C₂×C₁₉	#3501	1	2	yes	—
334	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
335	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
337	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
338	C₂²×D₄	—	2	4	no	—
339	C₂²×D₄	—	2	4	no	—
340	C₂²×D₄	Q₈×C₁₉	1	8	yes	complemented
341	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
342	C₂³×C₄	—	2	4	no	—
343	C₂³×C₄	—	2	4	no	—
344	C₂³×C₄	—	4	4	no	—
345	C₂³×C₄	—	4	4	no	—
346	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
348	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
349	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
353	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂²⋊Q₈	—	2	8	no	—
357	C₂²⋊Q₈	—	2	8	no	—
358	C₂²⋊Q₈	—	2	16	no	—
359	C₂²⋊Q₈	—	2	16	no	—
360	C₂²⋊Q₈	—	4	8	no	—
361	C₄×D₄	—	2	32	no	—
362	C₂×C₄⋊C₄	—	2	4	no	—
363	C₂×C₄⋊C₄	—	4	8	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
373	C₂×C₂²⋊C₄	—	2	8	no	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
385	C₂×C₄²	—	2	4	no	—
386	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
387	#95	C₂³×C₁₉	1	8	yes	—
388	#95	C₂³×C₁₉	1	8	yes	—
389	#95	C₂³×C₁₉	1	4	yes	—
390	#95	C₂³×C₁₉	1	4	yes	—
391	#95	C₂³×C₁₉	1	8	yes	—
392	#95	C₂³×C₁₉	1	8	yes	—
393	C₁₉	#34985	1	1	yes	characteristic, direct product factor, Sylow
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	4	2	no	—
397	C₂⁴	—	4	2	no	—
398	C₂⁴	—	4	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
401	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
402	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
403	C₂⁴	#41×C₁₉	1	4	yes	—
404	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
405	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
406	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	—	4	4	no	—
411	C₂×D₄	—	2	32	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	C₂×Q₈×C₁₉	1	16	yes	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	—	4	4	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	16	no	—
437	C₂²×C₄	—	4	16	no	—
438	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
440	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
442	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	16	no	—
455	C₄⋊C₄	—	4	8	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	4	8	no	—
464	C₂²⋊C₄	—	4	8	no	—
465	C₂²⋊C₄	C₂×D₄×C₁₉	1	16	yes	—
466	C₄²	—	2	8	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	8	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	4	no	—
484	C₂³	C₁₉×C₂²⋊Q₈	1	16	yes	complemented
485	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
486	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
487	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
488	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
489	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
490	C₂³	C₂×#41×C₁₉	1	2	yes	—
491	C₂³	C₂×#41×C₁₉	1	4	yes	—
492	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
493	Q₈	—	8	4	no	—
494	Q₈	—	8	4	no	—
495	D₄	—	2	32	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	16	no	—
516	C₂×C₄	—	4	16	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	16	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	—	8	4	no	—
521	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
522	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
523	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
524	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
525	C₂²	—	2	8	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	4	16	no	—
536	C₂²	—	4	16	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	4	yes	—
541	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	8	yes	—
542	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
543	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
544	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
545	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
546	C₂²	C₁₉×#585	1	2	yes	—
547	C₄	—	2	4	no	—
548	C₄	—	2	4	no	—
549	C₄	—	2	4	no	—
550	C₄	—	2	4	no	—
551	C₄	—	4	8	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₂	—	2	4	no	—
556	C₂	—	2	8	no	—
557	C₂	—	4	4	no	—
558	C₂	C₂²×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
559	C₂	C₁₉×#3459	1	2	yes	—
560	C₂	C₁₉×#3484	1	1	yes	characteristic
561	C₂	C₁₉×#3485	1	1	yes	characteristic
562	C₂	C₁₉×#3501	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#543	C₂	semidirect
3. C₁₉×#2855	C₂	semidirect
4. C₁₉×#2848	C₂	semidirect
5. C₁₉×#2627	C₂	semidirect
6. C₁₉×#2626	C₂	semidirect
7. C₁₉×#2450	C₂	semidirect
8. C₁₉×#2449	C₂	semidirect
9. C₁₉×#2315	C₂	semidirect
11. C₂×C₁₉×#385	C₂	semidirect
18. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
19. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
20. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
30. C₁₉×#400	C₂²	semidirect
31. C₁₉×#399	C₂²	semidirect
32. C₁₉×#398	C₂²	semidirect
33. C₁₉×#396	C₂²	semidirect
34. C₁₉×#395	C₂²	semidirect
35. C₁₉×#393	C₂²	semidirect
36. C₁₉×#391	C₂²	semidirect
37. C₁₉×#389	C₂²	semidirect
38. C₁₉×#387	C₂²	semidirect
44. C₁₉×#385	C₂²	semidirect
45. C₁₉×#385	C₂²	semidirect
46. C₁₉×#385	C₂²	semidirect
50. C₁₉×#380	C₂²	semidirect
52. C₂×C₁₉×#95	C₂²	semidirect
59. C₂²×D₄×C₁₉	Q₈	semidirect
185. #34985	C₁₉	direct (N × H)
203. C₂³×C₁₉	C₂²⋊Q₈	semidirect
244. C₂×#543	C₂×C₁₉	semidirect
246. #2855	C₂×C₁₉	semidirect
247. #2848	C₂×C₁₉	semidirect
248. #2627	C₂×C₁₉	semidirect
249. #2626	C₂×C₁₉	semidirect
250. #2450	C₂×C₁₉	semidirect
251. #2449	C₂×C₁₉	semidirect
252. #2315	C₂×C₁₉	semidirect
254. C₂×#385	C₂×C₁₉	semidirect
291. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
292. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
293. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
297. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
303. #400	C₂²×C₁₉	semidirect
304. #399	C₂²×C₁₉	semidirect
305. #398	C₂²×C₁₉	semidirect
306. #396	C₂²×C₁₉	semidirect
307. #395	C₂²×C₁₉	semidirect
308. #393	C₂²×C₁₉	semidirect
309. #391	C₂²×C₁₉	semidirect
310. #389	C₂²×C₁₉	semidirect
311. #387	C₂²×C₁₉	semidirect
317. #385	C₂²×C₁₉	semidirect
318. #385	C₂²×C₁₉	semidirect
319. #385	C₂²×C₁₉	semidirect
323. #380	C₂²×C₁₉	semidirect
325. C₂×#95	C₂²×C₁₉	semidirect
340. C₂²×D₄	Q₈×C₁₉	semidirect
393. C₁₉	#34985	direct (N × H)
484. C₂³	C₁₉×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#543	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2855	2
C₁₉×#2848	2
C₁₉×#2627	2
C₁₉×#2626	2
C₁₉×#2450	2
C₁₉×#2449	2
C₁₉×#2315	2
C₁₉×#2308	2
C₂×C₁₉×#385	2
#34985	19

Subgroups — C19×#34985 #18040944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34985 #18040944