Subgroups — C₂×C₁₉×#1615 #18024065

Order 4864.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#539	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#481	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1615	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#539	—	2	2	no	—
10	C₁₉×#539	—	2	2	no	—
11	C₁₉×#539	—	2	2	no	—
12	C₁₉×#539	C₂²	1	4	yes	—
13	C₂×C₁₉×#126	—	2	1	no	—
14	C₂×C₁₉×#125	—	2	1	no	—
15	C₂×C₁₉×#123	—	2	1	no	—
16	C₂×C₁₉×#123	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#484	—	2	2	no	—
24	C₁₉×#484	C₂²	1	4	yes	complemented
25	C₁₉×#481	—	2	2	no	—
26	C₁₉×#481	C₂²	1	4	yes	—
27	C₂×C₁₉×#107	—	2	1	no	—
28	C₂×C₁₉×#106	—	2	1	no	—
29	C₂×C₁₉×#103	—	2	1	no	—
30	C₂×C₁₉×#102	—	2	1	no	—
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₉×#400	—	2	2	no	—
34	C₁₉×#400	C₂²	1	4	yes	complemented
35	C₂×C₁₉×#95	—	2	1	no	—
36	C₂×C₁₉×#95	—	2	1	no	—
37	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
38	C₁₉×#328	C₂²	1	4	yes	complemented
39	C₁₉×#327	C₂²	1	4	yes	—
40	C₁₉×#324	C₂²	1	4	yes	complemented
41	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₁₉×#126	—	2	4	no	—
53	C₁₉×#126	—	2	4	no	—
54	C₁₉×#125	—	2	4	no	—
55	C₁₉×#125	—	2	4	no	—
56	C₁₉×#123	—	2	4	no	—
57	C₁₉×#123	—	2	4	no	—
58	C₁₉×#123	—	2	4	no	—
59	C₁₉×#123	—	2	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
65	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	D₄	1	2	yes	—
69	C₁₉×#121	C₂³	1	2	yes	—
70	C₄×D₄×C₁₉	—	2	4	no	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	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×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₁₉×#107	—	2	4	no	—
97	C₁₉×#106	—	2	4	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×C₂²⋊C₈	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
103	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
104	C₁₉×#95	—	2	4	no	—
105	C₁₉×#95	—	2	4	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	C₂³	1	2	yes	—
108	C₂⁴×C₁₉	—	2	1	no	—
109	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	4	2	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	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	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	4	2	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	4	2	no	—
135	C₂²×C₄×C₁₉	—	4	2	no	—
136	C₂²×C₄×C₁₉	—	4	4	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	—	8	2	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	4	2	no	—
152	C₂×C₈×C₁₉	—	4	2	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	—	2	4	no	—
178	C₂×#1615	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	#120	1	1	yes	characteristic
186	C₂³×C₁₉	#120	1	1	yes	characteristic
187	C₂³×C₁₉	#135	1	2	yes	—
188	C₂³×C₁₉	#137	1	2	yes	—
189	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₉	—	4	2	no	—
191	Q₈×C₁₉	—	8	1	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	4	no	—
196	D₄×C₁₉	—	8	1	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	4	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	8	1	no	—
223	C₂×C₄×C₁₉	—	8	4	no	—
224	C₂×C₄×C₁₉	—	8	4	no	—
225	C₂×C₄×C₁₉	—	8	2	no	—
226	C₂×C₄×C₁₉	—	8	2	no	—
227	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₁₉	—	4	2	no	—
232	C₈×C₁₉	—	4	2	no	—
233	C₂×#539	C₂×C₁₉	1	1	yes	characteristic
234	C₂×#484	C₂×C₁₉	1	1	yes	characteristic, complemented
235	C₂×#481	C₂×C₁₉	1	1	yes	characteristic
236	C₂×#400	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#1615	C₂×C₁₉	1	8	yes	direct product factor
238	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂×#327	C₂×C₁₉	1	1	yes	characteristic
240	C₂×#324	C₂×C₁₉	1	1	yes	characteristic, complemented
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	8	4	no	—
251	C₂²×C₁₉	#452	1	2	yes	—
252	C₂²×C₁₉	#452	1	2	yes	—
253	C₂²×C₁₉	#454	1	2	yes	—
254	C₂²×C₁₉	#458	1	2	yes	—
255	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
256	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	8	2	no	—
268	C₄×C₁₉	—	8	2	no	—
269	#539	—	2	2	no	—
270	#539	—	2	2	no	—
271	#539	—	2	2	no	—
272	#539	C₂²×C₁₉	1	4	yes	—
273	C₂×#126	—	2	1	no	—
274	C₂×#125	—	2	1	no	—
275	C₂×#123	—	2	1	no	—
276	C₂×#123	—	2	1	no	—
277	C₂×C₂²⋊Q₈	—	2	1	no	—
278	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
283	#484	—	2	2	no	—
284	#484	C₂²×C₁₉	1	4	yes	complemented
285	#481	—	2	2	no	—
286	#481	C₂²×C₁₉	1	4	yes	—
287	C₂×#107	—	2	1	no	—
288	C₂×#106	—	2	1	no	—
289	C₂×#103	—	2	1	no	—
290	C₂×#102	—	2	1	no	—
291	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
293	#400	—	2	2	no	—
294	#400	C₂²×C₁₉	1	4	yes	complemented
295	C₂×#95	—	2	1	no	—
296	C₂×#95	—	2	1	no	—
297	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
298	#328	C₂²×C₁₉	1	4	yes	complemented
299	#327	C₂²×C₁₉	1	4	yes	—
300	#324	C₂²×C₁₉	1	4	yes	complemented
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	2	2	no	—
304	C₂×C₁₉	—	8	2	no	—
305	C₂×C₁₉	#1615	1	4	yes	direct product factor
306	C₂×C₁₉	C₂×#452	1	1	yes	characteristic
307	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
308	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
309	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	2	1	no	—
320	#126	—	2	4	no	—
321	#126	—	2	4	no	—
322	#125	—	2	4	no	—
323	#125	—	2	4	no	—
324	#123	—	2	4	no	—
325	#123	—	2	4	no	—
326	#123	—	2	4	no	—
327	#123	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	4	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
333	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	D₄×C₁₉	1	2	yes	—
337	#121	C₂³×C₁₉	1	2	yes	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	—	2	4	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
354	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	#107	—	2	4	no	—
365	#106	—	2	4	no	—
366	#103	—	2	4	no	—
367	#102	—	2	4	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	C₂²⋊C₈	—	2	1	no	—
370	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
371	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
372	#95	—	2	4	no	—
373	#95	—	2	4	no	—
374	#95	—	2	1	no	—
375	#95	C₂³×C₁₉	1	2	yes	—
376	C₁₉	C₂×#1615	1	1	yes	characteristic, direct product factor, Sylow
377	C₂⁴	—	2	1	no	—
378	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	8	2	no	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	4	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	4	1	no	—
436	C₄⋊C₄	—	4	1	no	—
437	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₄²	—	2	4	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	C₁₉×#120	1	1	yes	characteristic
454	C₂³	C₁₉×#120	1	1	yes	characteristic
455	C₂³	C₁₉×#135	1	2	yes	—
456	C₂³	C₁₉×#137	1	2	yes	—
457	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
458	Q₈	—	4	2	no	—
459	Q₈	—	8	1	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	8	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	8	1	no	—
491	C₂×C₄	—	8	4	no	—
492	C₂×C₄	—	8	4	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
496	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
499	C₈	—	4	2	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	8	4	no	—
511	C₂²	C₁₉×#452	1	2	yes	—
512	C₂²	C₁₉×#452	1	2	yes	—
513	C₂²	C₁₉×#454	1	2	yes	—
514	C₂²	C₁₉×#458	1	2	yes	—
515	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
516	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
517	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	2	no	—
529	C₂	—	2	1	no	—
530	C₂	—	2	2	no	—
531	C₂	—	2	1	no	—
532	C₂	—	8	2	no	—
533	C₂	C₁₉×#1615	1	4	yes	direct product factor
534	C₂	C₂×C₁₉×#452	1	1	yes	characteristic
535	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
536	C₂	C₂×C₁₉×#458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#484	C₂	semidirect
4. C₂×C₁₉×#400	C₂	semidirect
5. C₁₉×#1615	C₂	direct (N × H)
6. C₂×C₁₉×#328	C₂	semidirect
8. C₂×C₁₉×#324	C₂	semidirect
24. C₁₉×#484	C₂²	semidirect
34. C₁₉×#400	C₂²	semidirect
38. C₁₉×#328	C₂²	semidirect
40. C₁₉×#324	C₂²	semidirect
178. C₂×#1615	C₁₉	direct (N × H)
234. C₂×#484	C₂×C₁₉	semidirect
236. C₂×#400	C₂×C₁₉	semidirect
237. #1615	C₂×C₁₉	direct (N × H)
238. C₂×#328	C₂×C₁₉	semidirect
240. C₂×#324	C₂×C₁₉	semidirect
284. #484	C₂²×C₁₉	semidirect
294. #400	C₂²×C₁₉	semidirect
298. #328	C₂²×C₁₉	semidirect
300. #324	C₂²×C₁₉	semidirect
305. C₂×C₁₉	#1615	direct (N × H)
376. C₁₉	C₂×#1615	direct (N × H)
533. C₂	C₁₉×#1615	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×#539	2
C₂×C₁₉×#484	2
C₂×C₁₉×#481	2
C₂×C₁₉×#400	2
C₁₉×#1615	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₂×C₁₉×#324	2
C₂×#1615	19

Subgroups — C2×C19×#1615 #18024065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1615 #18024065