Subgroups — C₁₉×#34993 #18040952

Order 4864.

2866 conjugacy classes of subgroups.

The subgroup lattice has 498 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	C₂×C₁₉×#534	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2850	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2639	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2488	C₂	1	8	yes	maximal, complemented
6	C₁₉×#2472	C₂	1	8	yes	maximal, complemented
7	C₁₉×#2308	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#543	—	2	8	no	—
13	C₁₉×#534	—	2	8	no	—
14	C₂×C₁₉×#124	C₂²	1	4	yes	complemented
15	C₂×C₁₉×#123	C₂²	1	4	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
18	C₂×C₁₉×#121	C₂²	1	4	yes	—
19	C₂×C₁₉×#120	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
24	C₂²×C₄²×C₁₉	C₂²	1	2	yes	complemented
25	C₁₉×#400	C₂²	1	8	yes	complemented
26	C₁₉×#397	C₂²	1	8	yes	complemented
27	C₁₉×#394	C₂²	1	8	yes	complemented
28	C₁₉×#393	C₂²	1	8	yes	complemented
29	C₁₉×#391	C₂²	1	4	yes	complemented
30	C₁₉×#390	C₂²	1	4	yes	complemented
31	C₁₉×#388	C₂²	1	8	yes	complemented
32	C₁₉×#388	C₂²	1	8	yes	complemented
33	C₁₉×#386	C₂²	1	8	yes	—
34	C₁₉×#386	C₂²	1	8	yes	—
35	C₁₉×#386	C₂²	1	4	yes	complemented
36	C₁₉×#386	C₂²	1	4	yes	complemented
37	C₁₉×#386	C₂²	1	8	yes	complemented
38	C₁₉×#382	C₂²	1	4	yes	complemented
39	C₁₉×#381	C₂²	1	4	yes	complemented
40	C₁₉×#379	C₂²	1	4	yes	complemented
41	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
42	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
43	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
44	C₂⁵×C₁₉	C₂³	1	2	yes	—
45	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
47	C₂²×D₄×C₁₉	—	2	8	no	—
48	C₂²×D₄×C₁₉	—	2	8	no	—
49	C₂²×D₄×C₁₉	—	2	8	no	—
50	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₉	—	2	4	no	—
54	C₂³×C₄×C₁₉	—	4	4	no	—
55	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₁₉×#124	—	4	8	no	—
63	C₁₉×#123	—	2	16	no	—
64	C₁₉×C₂²⋊Q₈	—	2	16	no	—
65	C₁₉×C₂²⋊Q₈	—	2	32	no	—
66	C₁₉×#121	—	2	16	no	—
67	C₁₉×#120	—	2	16	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₉	—	4	4	no	—
85	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
87	C₁₉×#95	C₂³	1	8	yes	—
88	C₁₉×#95	C₂³	1	8	yes	—
89	C₁₉×#95	C₂³	1	8	yes	—
90	C₁₉×#95	C₂³	1	8	yes	—
91	C₁₉×#95	C₂³	1	8	yes	—
92	C₂⁴×C₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	4	no	—
94	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	4	2	no	—
96	C₂⁴×C₁₉	—	4	2	no	—
97	C₂⁴×C₁₉	—	4	4	no	—
98	C₂⁴×C₁₉	—	4	4	no	—
99	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
100	C₂⁴×C₁₉	#41	1	4	yes	—
101	C₂⁴×C₁₉	#41	1	4	yes	—
102	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
103	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
104	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂×Q₈×C₁₉	—	2	8	no	—
106	C₂×Q₈×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	2	8	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	8	no	—
111	C₂×D₄×C₁₉	—	2	8	no	—
112	C₂×D₄×C₁₉	—	2	8	no	—
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	4	4	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	32	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	8	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	8	no	—
127	C₂²×C₄×C₁₉	—	2	8	no	—
128	C₂²×C₄×C₁₉	—	4	2	no	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	4	2	no	—
132	C₂²×C₄×C₁₉	—	4	2	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	4	4	no	—
135	C₂²×C₄×C₁₉	—	4	4	no	—
136	C₂²×C₄×C₁₉	—	4	16	no	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
144	C₄⋊C₄×C₁₉	—	2	8	no	—
145	C₄⋊C₄×C₁₉	—	2	8	no	—
146	C₄⋊C₄×C₁₉	—	2	16	no	—
147	C₂²⋊C₄×C₁₉	—	2	8	no	—
148	C₂²⋊C₄×C₁₉	—	2	8	no	—
149	C₂²⋊C₄×C₁₉	—	2	8	no	—
150	C₂²⋊C₄×C₁₉	—	2	16	no	—
151	C₂²⋊C₄×C₁₉	—	2	16	no	—
152	C₂²⋊C₄×C₁₉	—	4	8	no	—
153	C₂²⋊C₄×C₁₉	—	4	8	no	—
154	C₂²⋊C₄×C₁₉	—	4	8	no	—
155	C₂²⋊C₄×C₁₉	C₂×D₄	1	16	yes	—
156	C₄²×C₁₉	—	2	8	no	—
157	C₄²×C₁₉	—	4	4	no	—
158	#34993	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	4	no	—
163	C₂³×C₁₉	—	2	4	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	2	4	no	—
166	C₂³×C₁₉	—	2	8	no	—
167	C₂³×C₁₉	—	2	8	no	—
168	C₂³×C₁₉	—	4	4	no	—
169	C₂³×C₁₉	—	4	8	no	—
170	C₂³×C₁₉	—	4	8	no	—
171	C₂³×C₁₉	—	4	4	no	—
172	C₂³×C₁₉	—	4	16	no	—
173	C₂³×C₁₉	—	4	8	no	—
174	C₂³×C₁₉	—	8	4	no	—
175	C₂³×C₁₉	—	8	4	no	—
176	C₂³×C₁₉	—	8	8	no	—
177	C₂³×C₁₉	#124	1	16	yes	complemented
178	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
179	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
180	C₂³×C₁₉	C₂×#41	1	4	yes	—
181	C₂³×C₁₉	C₂×#41	1	4	yes	—
182	C₂³×C₁₉	C₂×#41	1	2	yes	—
183	C₂³×C₁₉	C₂×#41	1	2	yes	—
184	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
185	Q₈×C₁₉	—	8	8	no	—
186	D₄×C₁₉	—	4	16	no	—
187	D₄×C₁₉	—	4	16	no	—
188	D₄×C₁₉	—	8	8	no	—
189	C₂×C₄×C₁₉	—	2	8	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	8	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	8	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	8	no	—
205	C₂×C₄×C₁₉	—	4	8	no	—
206	C₂×C₄×C₁₉	—	4	16	no	—
207	C₂×C₄×C₁₉	—	4	8	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	8	no	—
210	C₂×C₄×C₁₉	—	8	8	no	—
211	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
212	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
213	C₂×#543	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂×#534	C₂×C₁₉	1	1	yes	characteristic
215	#2850	C₂×C₁₉	1	4	yes	complemented
216	#2639	C₂×C₁₉	1	4	yes	complemented
217	#2488	C₂×C₁₉	1	8	yes	complemented
218	#2472	C₂×C₁₉	1	8	yes	complemented
219	#2308	C₂×C₁₉	1	2	yes	complemented
220	C₂×#386	C₂×C₁₉	1	2	yes	complemented
221	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂²×C₁₉	—	2	4	no	—
223	C₂²×C₁₉	—	2	8	no	—
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	—	2	4	no	—
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	4	no	—
229	C₂²×C₁₉	—	2	8	no	—
230	C₂²×C₁₉	—	4	16	no	—
231	C₂²×C₁₉	—	4	4	no	—
232	C₂²×C₁₉	—	4	8	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	4	no	—
235	C₂²×C₁₉	—	4	8	no	—
236	C₂²×C₁₉	—	8	16	no	—
237	C₂²×C₁₉	C₂×#124	1	8	yes	—
238	C₂²×C₁₉	C₂×#124	1	4	yes	—
239	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
240	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
241	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
242	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
243	C₂²×C₁₉	#585	1	2	yes	—
244	C₄×C₁₉	—	2	4	no	—
245	C₄×C₁₉	—	2	8	no	—
246	C₄×C₁₉	—	4	4	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	2	no	—
249	C₄×C₁₉	—	4	8	no	—
250	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
251	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
252	#543	—	2	8	no	—
253	#534	—	2	8	no	—
254	C₂×#124	C₂²×C₁₉	1	4	yes	complemented
255	C₂×#123	C₂²×C₁₉	1	4	yes	—
256	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
257	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
258	C₂×#121	C₂²×C₁₉	1	4	yes	—
259	C₂×#120	C₂²×C₁₉	1	4	yes	—
260	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
262	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
264	C₂²×C₄²	C₂²×C₁₉	1	2	yes	complemented
265	#400	C₂²×C₁₉	1	8	yes	complemented
266	#397	C₂²×C₁₉	1	8	yes	complemented
267	#394	C₂²×C₁₉	1	8	yes	complemented
268	#393	C₂²×C₁₉	1	8	yes	complemented
269	#391	C₂²×C₁₉	1	4	yes	complemented
270	#390	C₂²×C₁₉	1	4	yes	complemented
271	#388	C₂²×C₁₉	1	8	yes	complemented
272	#388	C₂²×C₁₉	1	8	yes	complemented
273	#386	C₂²×C₁₉	1	8	yes	—
274	#386	C₂²×C₁₉	1	8	yes	—
275	#386	C₂²×C₁₉	1	8	yes	complemented
276	#386	C₂²×C₁₉	1	4	yes	complemented
277	#386	C₂²×C₁₉	1	4	yes	complemented
278	#382	C₂²×C₁₉	1	4	yes	complemented
279	#381	C₂²×C₁₉	1	4	yes	complemented
280	#379	C₂²×C₁₉	1	4	yes	complemented
281	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
282	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
283	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
284	C₂×C₁₉	—	2	8	no	—
285	C₂×C₁₉	—	2	4	no	—
286	C₂×C₁₉	—	8	4	no	—
287	C₂×C₁₉	C₂²×#124	1	1	yes	characteristic
288	C₂×C₁₉	#3459	1	2	yes	—
289	C₂×C₁₉	#3490	1	1	yes	characteristic
290	C₂×C₁₉	#3491	1	1	yes	characteristic
291	C₂×C₁₉	#3496	1	2	yes	—
292	C₂⁵	C₂³×C₁₉	1	2	yes	—
293	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
295	C₂²×D₄	—	2	8	no	—
296	C₂²×D₄	—	2	8	no	—
297	C₂²×D₄	—	2	8	no	—
298	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
299	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
300	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
301	C₂³×C₄	—	2	4	no	—
302	C₂³×C₄	—	4	4	no	—
303	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
304	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
306	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
307	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
310	#124	—	4	8	no	—
311	#123	—	2	16	no	—
312	C₂²⋊Q₈	—	2	16	no	—
313	C₂²⋊Q₈	—	2	32	no	—
314	#121	—	2	16	no	—
315	#120	—	2	16	no	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
319	C₂×C₂²⋊C₄	—	2	8	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	4	8	no	—
322	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
332	C₂×C₄²	—	4	4	no	—
333	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
334	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
335	#95	C₂³×C₁₉	1	8	yes	—
336	#95	C₂³×C₁₉	1	8	yes	—
337	#95	C₂³×C₁₉	1	8	yes	—
338	#95	C₂³×C₁₉	1	8	yes	—
339	#95	C₂³×C₁₉	1	8	yes	—
340	C₁₉	#34993	1	1	yes	characteristic, direct product factor, Sylow
341	C₂⁴	—	2	4	no	—
342	C₂⁴	—	2	4	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	4	2	no	—
346	C₂⁴	—	4	4	no	—
347	C₂⁴	—	4	4	no	—
348	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
349	C₂⁴	#41×C₁₉	1	4	yes	—
350	C₂⁴	#41×C₁₉	1	4	yes	—
351	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
352	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
353	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
354	C₂×Q₈	—	2	8	no	—
355	C₂×Q₈	—	4	4	no	—
356	C₂×Q₈	—	4	4	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	4	32	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	16	no	—
386	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
387	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
389	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
391	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	16	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	16	no	—
400	C₂²⋊C₄	—	2	16	no	—
401	C₂²⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	4	8	no	—
404	C₂²⋊C₄	C₂×D₄×C₁₉	1	16	yes	—
405	C₄²	—	2	8	no	—
406	C₄²	—	4	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	8	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	16	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	8	4	no	—
423	C₂³	—	8	4	no	—
424	C₂³	—	8	8	no	—
425	C₂³	C₁₉×#124	1	16	yes	complemented
426	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
427	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
428	C₂³	C₂×#41×C₁₉	1	4	yes	—
429	C₂³	C₂×#41×C₁₉	1	4	yes	—
430	C₂³	C₂×#41×C₁₉	1	2	yes	—
431	C₂³	C₂×#41×C₁₉	1	2	yes	—
432	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
433	Q₈	—	8	8	no	—
434	D₄	—	4	16	no	—
435	D₄	—	4	16	no	—
436	D₄	—	8	8	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	16	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	8	8	no	—
459	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
460	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	8	no	—
469	C₂²	—	4	16	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	8	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	8	16	no	—
476	C₂²	C₂×C₁₉×#124	1	8	yes	—
477	C₂²	C₂×C₁₉×#124	1	4	yes	—
478	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
479	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
480	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
481	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
482	C₂²	C₁₉×#585	1	2	yes	—
483	C₄	—	2	4	no	—
484	C₄	—	2	8	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	8	no	—
489	C₂	—	2	8	no	—
490	C₂	—	2	4	no	—
491	C₂	—	8	4	no	—
492	C₂	C₂²×C₁₉×#124	1	1	yes	characteristic
493	C₂	C₁₉×#3459	1	2	yes	—
494	C₂	C₁₉×#3490	1	1	yes	characteristic
495	C₂	C₁₉×#3491	1	1	yes	characteristic
496	C₂	C₁₉×#3496	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#534	C₂
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×#2850	C₂	semidirect
4. C₁₉×#2639	C₂	semidirect
5. C₁₉×#2488	C₂	semidirect
6. C₁₉×#2472	C₂	semidirect
7. C₁₉×#2308	C₂	semidirect
8. C₂×C₁₉×#386	C₂	semidirect
9. C₂×C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
14. C₂×C₁₉×#124	C₂²	semidirect
16. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
17. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
24. C₂²×C₄²×C₁₉	C₂²	semidirect
25. C₁₉×#400	C₂²	semidirect
26. C₁₉×#397	C₂²	semidirect
27. C₁₉×#394	C₂²	semidirect
28. C₁₉×#393	C₂²	semidirect
29. C₁₉×#391	C₂²	semidirect
30. C₁₉×#390	C₂²	semidirect
31. C₁₉×#388	C₂²	semidirect
32. C₁₉×#388	C₂²	semidirect
35. C₁₉×#386	C₂²	semidirect
36. C₁₉×#386	C₂²	semidirect
37. C₁₉×#386	C₂²	semidirect
38. C₁₉×#382	C₂²	semidirect
39. C₁₉×#381	C₂²	semidirect
40. C₁₉×#379	C₂²	semidirect
41. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
42. C₂×C₁₉×#95	C₂²	semidirect
43. C₂×C₁₉×#95	C₂²	semidirect
158. #34993	C₁₉	direct (N × H)
177. C₂³×C₁₉	#124	semidirect
213. C₂×#543	C₂×C₁₉	semidirect
215. #2850	C₂×C₁₉	semidirect
216. #2639	C₂×C₁₉	semidirect
217. #2488	C₂×C₁₉	semidirect
218. #2472	C₂×C₁₉	semidirect
219. #2308	C₂×C₁₉	semidirect
220. C₂×#386	C₂×C₁₉	semidirect
221. C₂×C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
254. C₂×#124	C₂²×C₁₉	semidirect
256. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
257. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
263. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
264. C₂²×C₄²	C₂²×C₁₉	semidirect
265. #400	C₂²×C₁₉	semidirect
266. #397	C₂²×C₁₉	semidirect
267. #394	C₂²×C₁₉	semidirect
268. #393	C₂²×C₁₉	semidirect
269. #391	C₂²×C₁₉	semidirect
270. #390	C₂²×C₁₉	semidirect
271. #388	C₂²×C₁₉	semidirect
272. #388	C₂²×C₁₉	semidirect
275. #386	C₂²×C₁₉	semidirect
276. #386	C₂²×C₁₉	semidirect
277. #386	C₂²×C₁₉	semidirect
278. #382	C₂²×C₁₉	semidirect
279. #381	C₂²×C₁₉	semidirect
280. #379	C₂²×C₁₉	semidirect
281. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
282. C₂×#95	C₂²×C₁₉	semidirect
283. C₂×#95	C₂²×C₁₉	semidirect
340. C₁₉	#34993	direct (N × H)
425. C₂³	C₁₉×#124	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
C₂×C₁₉×#534	2
C₁₉×#2850	2
C₁₉×#2639	2
C₁₉×#2488	2
C₁₉×#2472	2
C₁₉×#2308	2
C₂×C₁₉×#386	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#34993	19

Subgroups — C19×#34993 #18040952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34993 #18040952