Subgroups — C₄×C₁₉×#458 #18027439

Order 4864.

1538 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#458	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#123	C₂	1	3	yes	maximal, complemented
4	C₁₉×#1890	C₂	1	3	yes	maximal, complemented
5	C₁₉×#1867	C₂	1	3	yes	maximal, complemented
6	C₁₉×#1790	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₉×#99	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#123	C₂²	1	3	yes	—
10	C₁₉×#520	—	2	3	no	—
11	C₁₉×#518	—	2	3	no	—
12	C₁₉×#518	C₂²	1	3	yes	—
13	C₄×#41×C₁₉	—	2	3	no	—
14	C₂×C₄×D₄×C₁₉	—	2	3	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×#458	C₄	1	8	yes	direct product factor
18	C₂×C₁₉×#99	C₂²	1	3	yes	—
19	C₂×C₁₉×#99	C₂²	1	3	yes	—
20	C₁₉×#388	—	2	3	no	—
21	C₁₉×#387	—	2	3	no	—
22	C₁₉×#386	C₂²	1	3	yes	—
23	C₁₉×#385	C₂²	1	3	yes	complemented
24	C₁₉×#381	C₂²	1	3	yes	complemented
25	C₄×C₄⋊C₄×C₁₉	—	2	3	no	—
26	C₄×C₂²⋊C₄×C₁₉	—	2	3	no	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	complemented
28	C₁₉×#342	C₂²	1	6	yes	complemented
29	C₁₉×H(5,𝔽₂)	—	2	6	no	—
30	C₁₉×H(5,𝔽₂)	C₂×C₄	1	4	yes	—
31	C₂×#41×C₁₉	—	2	3	no	—
32	C₂²×D₄×C₁₉	—	2	3	no	—
33	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	D₄	1	3	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₁₉×#123	—	2	6	no	—
40	C₁₉×#123	C₂×C₄	1	12	yes	complemented
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₄×Q₈×C₁₉	—	2	3	no	—
43	C₄×D₄×C₁₉	—	2	3	no	—
44	C₄×D₄×C₁₉	—	2	6	no	—
45	C₄×D₄×C₁₉	—	2	3	no	—
46	C₄×D₄×C₁₉	—	2	6	no	—
47	C₄×D₄×C₁₉	—	2	6	no	—
48	C₄×D₄×C₁₉	—	2	6	no	—
49	C₄×D₄×C₁₉	—	2	6	no	—
50	C₁₉×#117	—	2	6	no	—
51	C₁₉×#117	—	2	3	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
60	C₂×C₂²⋊C₄×C₁₉	D₄	1	3	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
62	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
64	C₂×C₄²×C₁₉	—	2	3	no	—
65	C₂×C₄²×C₁₉	—	2	3	no	—
66	C₂×C₄²×C₁₉	—	2	3	no	—
67	C₂×C₄²×C₁₉	—	2	3	no	—
68	C₂×C₄²×C₁₉	D₄	1	3	yes	—
69	C₁₉×#99	—	2	6	no	—
70	C₁₉×#99	C₂×C₄	1	12	yes	complemented
71	C₁₉×#95	—	2	3	no	—
72	C₁₉×#95	—	2	3	no	—
73	C₁₉×#95	—	2	3	no	—
74	C₁₉×#95	—	2	3	no	—
75	C₁₉×#95	—	2	3	no	—
76	C₂⁴×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
78	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
79	#41×C₁₉	—	2	12	no	—
80	#41×C₁₉	—	2	12	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	3	no	—
83	C₂×D₄×C₁₉	—	2	12	no	—
84	C₂×D₄×C₁₉	—	2	12	no	—
85	C₂×D₄×C₁₉	—	2	6	no	—
86	C₂×D₄×C₁₉	—	2	6	no	—
87	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
88	C₂×D₄×C₁₉	#41	1	6	yes	—
89	C₂²×C₄×C₁₉	—	2	3	no	—
90	C₂²×C₄×C₁₉	—	2	3	no	—
91	C₂²×C₄×C₁₉	—	2	3	no	—
92	C₂²×C₄×C₁₉	—	2	3	no	—
93	C₂²×C₄×C₁₉	—	2	3	no	—
94	C₂²×C₄×C₁₉	—	2	3	no	—
95	C₂²×C₄×C₁₉	—	2	3	no	—
96	C₂²×C₄×C₁₉	—	2	3	no	—
97	C₂²×C₄×C₁₉	—	2	3	no	—
98	C₂²×C₄×C₁₉	—	2	3	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	6	no	—
102	C₂²×C₄×C₁₉	—	8	2	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	complemented
104	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
109	C₄⋊C₄×C₁₉	—	2	3	no	—
110	C₄⋊C₄×C₁₉	—	2	3	no	—
111	C₄⋊C₄×C₁₉	—	2	12	no	—
112	C₄⋊C₄×C₁₉	—	2	6	no	—
113	C₄⋊C₄×C₁₉	—	4	6	no	—
114	C₂²⋊C₄×C₁₉	—	2	6	no	—
115	C₂²⋊C₄×C₁₉	—	2	12	no	—
116	C₂²⋊C₄×C₁₉	—	2	6	no	—
117	C₂²⋊C₄×C₁₉	—	2	3	no	—
118	C₂²⋊C₄×C₁₉	—	2	6	no	—
119	C₂²⋊C₄×C₁₉	—	2	6	no	—
120	C₂²⋊C₄×C₁₉	—	4	6	no	—
121	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	complemented
122	C₄²×C₁₉	—	2	6	no	—
123	C₄²×C₁₉	—	2	3	no	—
124	C₄²×C₁₉	—	2	3	no	—
125	C₄²×C₁₉	—	4	6	no	—
126	C₄²×C₁₉	—	4	3	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	C₄×#458	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	2	4	no	—
130	C₂³×C₁₉	—	2	3	no	—
131	C₂³×C₁₉	—	2	3	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	3	no	—
135	C₂³×C₁₉	—	4	3	no	—
136	C₂³×C₁₉	—	8	1	no	—
137	C₂³×C₁₉	—	8	1	no	—
138	C₂³×C₁₉	C₄×D₄	1	6	yes	—
139	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
140	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
141	C₂³×C₁₉	C₂×#41	1	3	yes	—
142	Q₈×C₁₉	—	2	4	no	—
143	D₄×C₁₉	—	2	12	no	—
144	D₄×C₁₉	—	2	12	no	—
145	D₄×C₁₉	—	2	12	no	—
146	C₂×C₄×C₁₉	—	2	12	no	—
147	C₂×C₄×C₁₉	—	2	3	no	—
148	C₂×C₄×C₁₉	—	2	3	no	—
149	C₂×C₄×C₁₉	—	2	6	no	—
150	C₂×C₄×C₁₉	—	2	6	no	—
151	C₂×C₄×C₁₉	—	2	6	no	—
152	C₂×C₄×C₁₉	—	2	6	no	—
153	C₂×C₄×C₁₉	—	2	3	no	—
154	C₂×C₄×C₁₉	—	2	3	no	—
155	C₂×C₄×C₁₉	—	4	3	no	—
156	C₂×C₄×C₁₉	—	4	3	no	—
157	C₂×C₄×C₁₉	—	4	3	no	—
158	C₂×C₄×C₁₉	—	4	3	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	3	no	—
162	C₂×C₄×C₁₉	—	4	6	no	—
163	C₂×C₄×C₁₉	—	4	3	no	—
164	C₂×C₄×C₁₉	—	4	3	no	—
165	C₂×C₄×C₁₉	—	4	3	no	—
166	C₂×C₄×C₁₉	—	4	3	no	—
167	C₂×C₄×C₁₉	—	4	3	no	—
168	C₂×C₄×C₁₉	—	8	3	no	—
169	C₂×C₄×C₁₉	—	8	3	no	—
170	C₂×C₄×C₁₉	—	8	3	no	—
171	C₂×C₄×C₁₉	C₄×D₄	1	6	yes	—
172	C₂×C₄×C₁₉	#120	1	3	yes	—
173	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
174	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
175	C₂×#458	C₂×C₁₉	1	1	yes	characteristic
176	C₄×#123	C₂×C₁₉	1	3	yes	complemented
177	#1890	C₂×C₁₉	1	3	yes	complemented
178	#1867	C₂×C₁₉	1	3	yes	complemented
179	#1790	C₂×C₁₉	1	1	yes	characteristic
180	C₄×#99	C₂×C₁₉	1	3	yes	complemented
181	C₂²×C₁₉	—	2	3	no	—
182	C₂²×C₁₉	—	2	3	no	—
183	C₂²×C₁₉	—	2	6	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	3	no	—
186	C₂²×C₁₉	—	4	6	no	—
187	C₂²×C₁₉	—	4	3	no	—
188	C₂²×C₁₉	—	4	3	no	—
189	C₂²×C₁₉	—	8	3	no	—
190	C₂²×C₁₉	—	8	4	no	—
191	C₂²×C₁₉	C₂×C₄×D₄	1	3	yes	—
192	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
193	C₂²×C₁₉	#525	1	3	yes	—
194	C₄×C₁₉	—	2	3	no	—
195	C₄×C₁₉	—	2	6	no	—
196	C₄×C₁₉	—	4	6	no	—
197	C₄×C₁₉	—	4	3	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	4	3	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	8	3	no	—
202	C₄×C₁₉	#458	1	2	yes	direct product factor
203	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×#123	C₂²×C₁₉	1	3	yes	—
205	#520	—	2	3	no	—
206	#518	—	2	3	no	—
207	#518	C₂²×C₁₉	1	3	yes	—
208	C₄×#41	—	2	3	no	—
209	C₂×C₄×D₄	—	2	3	no	—
210	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
211	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
212	#458	C₄×C₁₉	1	8	yes	direct product factor
213	C₂×#99	C₂²×C₁₉	1	3	yes	—
214	C₂×#99	C₂²×C₁₉	1	3	yes	—
215	#388	—	2	3	no	—
216	#387	—	2	3	no	—
217	#386	C₂²×C₁₉	1	3	yes	—
218	#385	C₂²×C₁₉	1	3	yes	complemented
219	#381	C₂²×C₁₉	1	3	yes	complemented
220	C₄×C₄⋊C₄	—	2	3	no	—
221	C₄×C₂²⋊C₄	—	2	3	no	—
222	C₄×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	complemented
223	#342	C₂²×C₁₉	1	6	yes	complemented
224	C₂×C₁₉	—	2	3	no	—
225	C₂×C₁₉	—	2	3	no	—
226	C₂×C₁₉	—	4	6	no	—
227	C₂×C₁₉	C₄×#120	1	1	yes	characteristic
228	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
229	C₂×C₁₉	#3025	1	1	yes	characteristic
230	H(5,𝔽₂)	—	2	6	no	—
231	H(5,𝔽₂)	C₂×C₄×C₁₉	1	4	yes	—
232	C₂×#41	—	2	3	no	—
233	C₂²×D₄	—	2	3	no	—
234	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	D₄×C₁₉	1	3	yes	—
237	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
240	#123	—	2	6	no	—
241	#123	C₂×C₄×C₁₉	1	12	yes	complemented
242	C₄×Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	3	no	—
244	C₄×D₄	—	2	3	no	—
245	C₄×D₄	—	2	6	no	—
246	C₄×D₄	—	2	3	no	—
247	C₄×D₄	—	2	6	no	—
248	C₄×D₄	—	2	6	no	—
249	C₄×D₄	—	2	6	no	—
250	C₄×D₄	—	2	6	no	—
251	#117	—	2	6	no	—
252	#117	—	2	3	no	—
253	C₂×C₄⋊C₄	—	2	3	no	—
254	C₂×C₄⋊C₄	—	2	3	no	—
255	C₂×C₄⋊C₄	—	2	3	no	—
256	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
257	C₂×C₂²⋊C₄	—	2	3	no	—
258	C₂×C₂²⋊C₄	—	2	3	no	—
259	C₂×C₂²⋊C₄	—	2	3	no	—
260	C₂×C₂²⋊C₄	—	2	3	no	—
261	C₂×C₂²⋊C₄	D₄×C₁₉	1	3	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
263	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
264	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
265	C₂×C₄²	—	2	3	no	—
266	C₂×C₄²	—	2	3	no	—
267	C₂×C₄²	—	2	3	no	—
268	C₂×C₄²	—	2	3	no	—
269	C₂×C₄²	D₄×C₁₉	1	3	yes	—
270	#99	—	2	6	no	—
271	#99	C₂×C₄×C₁₉	1	12	yes	complemented
272	#95	—	2	3	no	—
273	#95	—	2	3	no	—
274	#95	—	2	3	no	—
275	#95	—	2	3	no	—
276	#95	—	2	3	no	—
277	C₁₉	C₄×#458	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	—	2	1	no	—
279	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
280	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
281	#41	—	2	12	no	—
282	#41	—	2	12	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×D₄	—	2	3	no	—
285	C₂×D₄	—	2	12	no	—
286	C₂×D₄	—	2	12	no	—
287	C₂×D₄	—	2	6	no	—
288	C₂×D₄	—	2	6	no	—
289	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
290	C₂×D₄	#41×C₁₉	1	6	yes	—
291	C₂²×C₄	—	2	3	no	—
292	C₂²×C₄	—	2	3	no	—
293	C₂²×C₄	—	2	3	no	—
294	C₂²×C₄	—	2	3	no	—
295	C₂²×C₄	—	2	3	no	—
296	C₂²×C₄	—	2	3	no	—
297	C₂²×C₄	—	2	3	no	—
298	C₂²×C₄	—	2	3	no	—
299	C₂²×C₄	—	2	3	no	—
300	C₂²×C₄	—	2	3	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	6	no	—
304	C₂²×C₄	—	8	2	no	—
305	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	complemented
306	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
307	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
311	C₄⋊C₄	—	2	3	no	—
312	C₄⋊C₄	—	2	3	no	—
313	C₄⋊C₄	—	2	12	no	—
314	C₄⋊C₄	—	2	6	no	—
315	C₄⋊C₄	—	4	6	no	—
316	C₂²⋊C₄	—	2	6	no	—
317	C₂²⋊C₄	—	2	12	no	—
318	C₂²⋊C₄	—	2	6	no	—
319	C₂²⋊C₄	—	2	3	no	—
320	C₂²⋊C₄	—	2	6	no	—
321	C₂²⋊C₄	—	2	6	no	—
322	C₂²⋊C₄	—	4	6	no	—
323	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	complemented
324	C₄²	—	2	6	no	—
325	C₄²	—	2	3	no	—
326	C₄²	—	2	3	no	—
327	C₄²	—	4	6	no	—
328	C₄²	—	4	3	no	—
329	C₄²	—	4	1	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	3	no	—
332	C₂³	—	2	3	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	4	3	no	—
336	C₂³	—	4	3	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	C₄×D₄×C₁₉	1	6	yes	—
340	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
341	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
342	C₂³	C₂×#41×C₁₉	1	3	yes	—
343	Q₈	—	2	4	no	—
344	D₄	—	2	12	no	—
345	D₄	—	2	12	no	—
346	D₄	—	2	12	no	—
347	C₂×C₄	—	2	12	no	—
348	C₂×C₄	—	2	3	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	6	no	—
351	C₂×C₄	—	2	6	no	—
352	C₂×C₄	—	2	6	no	—
353	C₂×C₄	—	2	6	no	—
354	C₂×C₄	—	2	3	no	—
355	C₂×C₄	—	2	3	no	—
356	C₂×C₄	—	4	3	no	—
357	C₂×C₄	—	4	3	no	—
358	C₂×C₄	—	4	3	no	—
359	C₂×C₄	—	4	3	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	3	no	—
363	C₂×C₄	—	4	6	no	—
364	C₂×C₄	—	4	3	no	—
365	C₂×C₄	—	4	3	no	—
366	C₂×C₄	—	4	3	no	—
367	C₂×C₄	—	4	3	no	—
368	C₂×C₄	—	4	3	no	—
369	C₂×C₄	—	8	3	no	—
370	C₂×C₄	—	8	3	no	—
371	C₂×C₄	—	8	3	no	—
372	C₂×C₄	C₄×D₄×C₁₉	1	6	yes	—
373	C₂×C₄	C₁₉×#120	1	3	yes	—
374	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
375	C₂²	—	2	3	no	—
376	C₂²	—	2	3	no	—
377	C₂²	—	2	6	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	3	no	—
380	C₂²	—	4	6	no	—
381	C₂²	—	4	3	no	—
382	C₂²	—	4	3	no	—
383	C₂²	—	8	3	no	—
384	C₂²	—	8	4	no	—
385	C₂²	C₂×C₄×D₄×C₁₉	1	3	yes	—
386	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
387	C₂²	C₁₉×#525	1	3	yes	—
388	C₄	—	2	3	no	—
389	C₄	—	2	6	no	—
390	C₄	—	4	6	no	—
391	C₄	—	4	3	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	3	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	3	no	—
396	C₄	C₁₉×#458	1	2	yes	direct product factor
397	C₂	—	2	3	no	—
398	C₂	—	2	3	no	—
399	C₂	—	4	6	no	—
400	C₂	C₄×C₁₉×#120	1	1	yes	characteristic
401	C₂	C₂×C₁₉×#458	1	1	yes	characteristic
402	C₂	C₁₉×#3025	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₁₉×#123	C₂	semidirect
4. C₁₉×#1890	C₂	semidirect
5. C₁₉×#1867	C₂	semidirect
7. C₄×C₁₉×#99	C₂	semidirect
16. C₂²×C₄²×C₁₉	C₂²	semidirect
17. C₁₉×#458	C₄	direct (N × H)
23. C₁₉×#385	C₂²	semidirect
24. C₁₉×#381	C₂²	semidirect
27. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
28. C₁₉×#342	C₂²	semidirect
40. C₁₉×#123	C₂×C₄	semidirect
70. C₁₉×#99	C₂×C₄	semidirect
103. C₂²×C₄×C₁₉	C₂²×C₄	semidirect
121. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
128. C₄×#458	C₁₉	direct (N × H)
176. C₄×#123	C₂×C₁₉	semidirect
177. #1890	C₂×C₁₉	semidirect
178. #1867	C₂×C₁₉	semidirect
180. C₄×#99	C₂×C₁₉	semidirect
202. C₄×C₁₉	#458	direct (N × H)
211. C₂²×C₄²	C₂²×C₁₉	semidirect
212. #458	C₄×C₁₉	direct (N × H)
218. #385	C₂²×C₁₉	semidirect
219. #381	C₂²×C₁₉	semidirect
222. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
223. #342	C₂²×C₁₉	semidirect
241. #123	C₂×C₄×C₁₉	semidirect
271. #99	C₂×C₄×C₁₉	semidirect
277. C₁₉	C₄×#458	direct (N × H)
305. C₂²×C₄	C₂²×C₄×C₁₉	semidirect
323. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
396. C₄	C₁₉×#458	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₂×C₁₉×#458	2
C₄×C₁₉×#123	2
C₁₉×#1890	2
C₁₉×#1867	2
C₁₉×#1790	2
C₄×C₁₉×#99	2
C₄×#458	19

Subgroups — C4×C19×#458 #18027439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#458 #18027439