Subgroups — C₂×C₁₉×#1445 #18019804

Order 4864.

2942 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#95	C₂	1	4	yes	maximal
3	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1445	C₂	1	8	yes	maximal, direct product factor
6	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
7	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₁₉	—	2	4	no	—
12	C₂²×C₄⋊C₄×C₁₉	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂×C₁₉×#95	—	2	16	no	—
15	C₂×C₁₉×#95	—	2	4	no	—
16	C₂×C₁₉×#95	—	2	4	no	—
17	C₂×C₁₉×#95	C₂²	1	16	yes	—
18	C₂×C₁₉×#95	C₂²	1	4	yes	—
19	C₂×C₁₉×#95	C₂²	1	4	yes	—
20	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	—	2	8	no	—
22	C₂³×C₄×C₁₉	—	2	8	no	—
23	C₂³×C₄×C₁₉	—	2	4	no	—
24	C₂³×C₄×C₁₉	—	2	4	no	—
25	C₂³×C₄×C₁₉	—	2	8	no	—
26	C₂³×C₄×C₁₉	—	2	4	no	—
27	C₂³×C₄×C₁₉	—	2	4	no	—
28	C₂³×C₄×C₁₉	—	2	8	no	—
29	C₂³×C₄×C₁₉	—	2	4	no	—
30	C₂³×C₄×C₁₉	—	2	8	no	—
31	C₂³×C₄×C₁₉	—	2	4	no	—
32	C₂³×C₄×C₁₉	—	2	8	no	—
33	C₂³×C₄×C₁₉	—	2	8	no	—
34	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
35	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₉	D₄	1	8	yes	—
37	C₂³×C₄×C₁₉	D₄	1	4	yes	—
38	C₂³×C₄×C₁₉	D₄	1	4	yes	—
39	C₂³×C₄×C₁₉	Q₈	1	8	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₉	—	2	32	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	complemented
48	C₁₉×#95	—	2	32	no	—
49	C₁₉×#95	—	2	8	no	—
50	C₁₉×#95	—	2	8	no	—
51	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
52	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
53	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
54	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
55	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
56	C₂⁴×C₁₉	#41	1	8	yes	—
57	C₂⁴×C₁₉	#41	1	4	yes	—
58	C₂⁴×C₁₉	#41	1	4	yes	—
59	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	—	2	16	no	—
61	C₂²×C₄×C₁₉	—	2	16	no	—
62	C₂²×C₄×C₁₉	—	2	16	no	—
63	C₂²×C₄×C₁₉	—	2	8	no	—
64	C₂²×C₄×C₁₉	—	2	16	no	—
65	C₂²×C₄×C₁₉	—	2	32	no	—
66	C₂²×C₄×C₁₉	—	2	16	no	—
67	C₂²×C₄×C₁₉	—	2	32	no	—
68	C₂²×C₄×C₁₉	—	2	16	no	—
69	C₂²×C₄×C₁₉	—	2	32	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	8	no	—
73	C₂²×C₄×C₁₉	—	2	4	no	—
74	C₂²×C₄×C₁₉	—	2	4	no	—
75	C₂²×C₄×C₁₉	—	2	8	no	—
76	C₂²×C₄×C₁₉	—	2	8	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	8	no	—
81	C₂²×C₄×C₁₉	—	2	8	no	—
82	C₂²×C₄×C₁₉	—	4	16	no	—
83	C₂²×C₄×C₁₉	—	4	8	no	—
84	C₂²×C₄×C₁₉	—	4	8	no	—
85	C₂²×C₄×C₁₉	—	4	16	no	—
86	C₂²×C₄×C₁₉	—	4	8	no	—
87	C₂²×C₄×C₁₉	—	4	8	no	—
88	C₂²×C₄×C₁₉	—	4	16	no	—
89	C₂²×C₄×C₁₉	—	4	8	no	—
90	C₂²×C₄×C₁₉	—	4	8	no	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
98	C₄⋊C₄×C₁₉	—	2	32	no	—
99	C₂×#1445	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
101	C₂³×C₁₉	#117	1	8	yes	—
102	C₂³×C₁₉	C₄×D₄	1	8	yes	—
103	C₂³×C₁₉	C₄×Q₈	1	8	yes	—
104	C₂³×C₁₉	#121	1	8	yes	—
105	C₂³×C₁₉	C₂²⋊Q₈	1	16	yes	—
106	C₂³×C₁₉	C₂²⋊Q₈	1	8	yes	—
107	C₂³×C₁₉	#123	1	8	yes	—
108	C₂³×C₁₉	#123	1	8	yes	—
109	C₂³×C₁₉	#123	1	16	yes	—
110	C₂³×C₁₉	#124	1	4	yes	—
111	C₂³×C₁₉	#124	1	4	yes	—
112	C₂³×C₁₉	#125	1	16	yes	—
113	C₂³×C₁₉	#126	1	16	yes	—
114	C₂³×C₁₉	#127	1	4	yes	—
115	C₂³×C₁₉	C₄⋊Q₈	1	4	yes	—
116	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
117	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
118	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
119	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
120	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
121	C₂³×C₁₉	C₂×#41	1	4	yes	—
122	C₂³×C₁₉	C₂×#41	1	2	yes	—
123	C₂³×C₁₉	C₂×#41	1	2	yes	—
124	C₂×C₄×C₁₉	—	2	8	no	—
125	C₂×C₄×C₁₉	—	2	8	no	—
126	C₂×C₄×C₁₉	—	2	8	no	—
127	C₂×C₄×C₁₉	—	2	32	no	—
128	C₂×C₄×C₁₉	—	2	8	no	—
129	C₂×C₄×C₁₉	—	2	16	no	—
130	C₂×C₄×C₁₉	—	2	8	no	—
131	C₂×C₄×C₁₉	—	2	16	no	—
132	C₂×C₄×C₁₉	—	2	8	no	—
133	C₂×C₄×C₁₉	—	2	16	no	—
134	C₂×C₄×C₁₉	—	4	8	no	—
135	C₂×C₄×C₁₉	—	4	4	no	—
136	C₂×C₄×C₁₉	—	4	8	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	4	no	—
140	C₂×C₄×C₁₉	—	4	8	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	32	no	—
144	C₂×C₄×C₁₉	—	4	32	no	—
145	C₂×C₄×C₁₉	—	4	32	no	—
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
147	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
148	C₂²×#95	C₂×C₁₉	1	4	yes	—
149	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
150	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
151	#1445	C₂×C₁₉	1	8	yes	direct product factor
152	C₂²×C₁₉	#381	1	8	yes	—
153	C₂²×C₁₉	#387	1	32	yes	—
154	C₂²×C₁₉	#390	1	8	yes	—
155	C₂²×C₁₉	#391	1	8	yes	—
156	C₂²×C₁₉	#397	1	16	yes	—
157	C₂²×C₁₉	#398	1	16	yes	—
158	C₂²×C₁₉	#399	1	16	yes	—
159	C₂²×C₁₉	#400	1	16	yes	—
160	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₁₉	C₂×#117	1	2	yes	—
162	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
163	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
164	C₂²×C₁₉	C₂×#121	1	2	yes	—
165	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	4	yes	—
166	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
167	C₂²×C₁₉	C₂×#123	1	2	yes	—
168	C₂²×C₁₉	C₂×#123	1	4	yes	—
169	C₂²×C₁₉	C₂×#123	1	2	yes	—
170	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
171	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
172	C₂²×C₁₉	C₂×#125	1	4	yes	—
173	C₂²×C₁₉	C₂×#126	1	4	yes	—
174	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
176	C₄×C₁₉	—	2	8	no	—
177	C₄×C₁₉	—	4	8	no	—
178	C₄×C₁₉	—	4	8	no	—
179	C₄×C₁₉	—	4	8	no	—
180	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
181	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
182	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
183	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	—	2	4	no	—
185	C₂²×C₄⋊C₄	—	2	4	no	—
186	C₂²×C₄⋊C₄	C₄×C₁₉	1	8	yes	complemented
187	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
188	C₂×#95	—	2	16	no	—
189	C₂×#95	—	2	4	no	—
190	C₂×#95	—	2	4	no	—
191	C₂×#95	C₂²×C₁₉	1	16	yes	—
192	C₂×#95	C₂²×C₁₉	1	4	yes	—
193	C₂×#95	C₂²×C₁₉	1	4	yes	—
194	C₂×C₁₉	#1445	1	16	yes	direct product factor
195	C₂×C₁₉	C₂×#381	1	1	yes	characteristic
196	C₂×C₁₉	C₂×#387	1	4	yes	—
197	C₂×C₁₉	C₂×#390	1	1	yes	characteristic
198	C₂×C₁₉	C₂×#391	1	1	yes	characteristic
199	C₂×C₁₉	C₂×#397	1	2	yes	—
200	C₂×C₁₉	C₂×#398	1	2	yes	—
201	C₂×C₁₉	C₂×#399	1	2	yes	—
202	C₂×C₁₉	C₂×#400	1	2	yes	—
203	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
204	C₂³×C₄	—	2	8	no	—
205	C₂³×C₄	—	2	4	no	—
206	C₂³×C₄	—	2	4	no	—
207	C₂³×C₄	—	2	8	no	—
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	—	2	8	no	—
211	C₂³×C₄	—	2	8	no	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	—	2	8	no	—
214	C₂³×C₄	—	2	4	no	—
215	C₂³×C₄	—	2	8	no	—
216	C₂³×C₄	—	2	8	no	—
217	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
218	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
219	C₂³×C₄	D₄×C₁₉	1	8	yes	—
220	C₂³×C₄	D₄×C₁₉	1	4	yes	—
221	C₂³×C₄	D₄×C₁₉	1	4	yes	—
222	C₂³×C₄	Q₈×C₁₉	1	8	yes	—
223	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
224	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
225	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
226	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
227	C₂×C₄⋊C₄	—	2	32	no	—
228	C₂×C₄⋊C₄	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	8	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	complemented
231	#95	—	2	32	no	—
232	#95	—	2	8	no	—
233	#95	—	2	8	no	—
234	C₁₉	C₂×#1445	1	1	yes	characteristic, direct product factor, Sylow
235	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
236	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
237	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
238	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
239	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
240	C₂⁴	#41×C₁₉	1	8	yes	—
241	C₂⁴	#41×C₁₉	1	4	yes	—
242	C₂⁴	#41×C₁₉	1	4	yes	—
243	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
244	C₂²×C₄	—	2	16	no	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	16	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	16	no	—
249	C₂²×C₄	—	2	32	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	32	no	—
252	C₂²×C₄	—	2	16	no	—
253	C₂²×C₄	—	2	32	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	4	16	no	—
267	C₂²×C₄	—	4	8	no	—
268	C₂²×C₄	—	4	8	no	—
269	C₂²×C₄	—	4	16	no	—
270	C₂²×C₄	—	4	8	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	16	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	—	4	8	no	—
275	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	—
276	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
278	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
279	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
281	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
282	C₄⋊C₄	—	2	32	no	—
283	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
284	C₂³	C₁₉×#117	1	8	yes	—
285	C₂³	C₄×D₄×C₁₉	1	8	yes	—
286	C₂³	C₄×Q₈×C₁₉	1	8	yes	—
287	C₂³	C₁₉×#121	1	8	yes	—
288	C₂³	C₁₉×C₂²⋊Q₈	1	16	yes	—
289	C₂³	C₁₉×C₂²⋊Q₈	1	8	yes	—
290	C₂³	C₁₉×#123	1	8	yes	—
291	C₂³	C₁₉×#123	1	8	yes	—
292	C₂³	C₁₉×#123	1	16	yes	—
293	C₂³	C₁₉×#124	1	4	yes	—
294	C₂³	C₁₉×#124	1	4	yes	—
295	C₂³	C₁₉×#125	1	16	yes	—
296	C₂³	C₁₉×#126	1	16	yes	—
297	C₂³	C₁₉×#127	1	4	yes	—
298	C₂³	C₁₉×C₄⋊Q₈	1	4	yes	—
299	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
300	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
301	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
302	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
303	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
304	C₂³	C₂×#41×C₁₉	1	4	yes	—
305	C₂³	C₂×#41×C₁₉	1	2	yes	—
306	C₂³	C₂×#41×C₁₉	1	2	yes	—
307	C₂×C₄	—	2	32	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	16	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	16	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	16	no	—
317	C₂×C₄	—	4	32	no	—
318	C₂×C₄	—	4	32	no	—
319	C₂×C₄	—	4	32	no	—
320	C₂×C₄	—	4	8	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
330	C₂²	C₁₉×#381	1	8	yes	—
331	C₂²	C₁₉×#387	1	32	yes	—
332	C₂²	C₁₉×#390	1	8	yes	—
333	C₂²	C₁₉×#391	1	8	yes	—
334	C₂²	C₁₉×#397	1	16	yes	—
335	C₂²	C₁₉×#398	1	16	yes	—
336	C₂²	C₁₉×#399	1	16	yes	—
337	C₂²	C₁₉×#400	1	16	yes	—
338	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
339	C₂²	C₂×C₁₉×#117	1	2	yes	—
340	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
341	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
342	C₂²	C₂×C₁₉×#121	1	2	yes	—
343	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	4	yes	—
344	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
345	C₂²	C₂×C₁₉×#123	1	2	yes	—
346	C₂²	C₂×C₁₉×#123	1	2	yes	—
347	C₂²	C₂×C₁₉×#123	1	4	yes	—
348	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
349	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
350	C₂²	C₂×C₁₉×#125	1	4	yes	—
351	C₂²	C₂×C₁₉×#126	1	4	yes	—
352	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
353	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
354	C₄	—	2	8	no	—
355	C₄	—	4	8	no	—
356	C₄	—	4	8	no	—
357	C₄	—	4	8	no	—
358	C₂	C₁₉×#1445	1	16	yes	direct product factor
359	C₂	C₂×C₁₉×#381	1	1	yes	characteristic
360	C₂	C₂×C₁₉×#387	1	4	yes	—
361	C₂	C₂×C₁₉×#390	1	1	yes	characteristic
362	C₂	C₂×C₁₉×#391	1	1	yes	characteristic
363	C₂	C₂×C₁₉×#397	1	2	yes	—
364	C₂	C₂×C₁₉×#398	1	2	yes	—
365	C₂	C₂×C₁₉×#399	1	2	yes	—
366	C₂	C₂×C₁₉×#400	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₁₉×#1445	C₂	direct (N × H)
12. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
47. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
99. C₂×#1445	C₁₉	direct (N × H)
151. #1445	C₂×C₁₉	direct (N × H)
186. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
194. C₂×C₁₉	#1445	direct (N × H)
230. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
234. C₁₉	C₂×#1445	direct (N × H)
358. C₂	C₁₉×#1445	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₉	2
C₂²×C₁₉×#95	2
C₁₉×#1445	2
C₂×#1445	19

Subgroups — C2×C19×#1445 #18019804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1445 #18019804