Subgroups — C₁₉×#21877 #18027836

Order 4864.

1098 conjugacy classes of subgroups.

The subgroup lattice has 426 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	C₁₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2313	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1996	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1964	C₂	1	2	yes	maximal
6	C₁₉×#1899	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1799	C₂	1	4	yes	maximal, complemented
8	C₁₉×#539	—	2	4	no	—
9	C₁₉×#539	—	2	4	no	—
10	C₂×C₁₉×#126	C₄	1	2	yes	complemented
11	C₂×C₁₉×#125	C₄	1	2	yes	complemented
12	C₂×C₁₉×#123	C₄	1	2	yes	complemented
13	C₂×C₁₉×#123	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	complemented
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#99	C₂²	1	8	yes	—
21	C₁₉×#389	—	2	4	no	—
22	C₁₉×#387	—	2	4	no	—
23	C₁₉×#381	C₂²	1	2	yes	—
24	C₁₉×#380	C₂²	1	2	yes	—
25	C₁₉×#380	C₂²	1	2	yes	—
26	C₁₉×#380	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#342	C₂²	1	8	yes	—
29	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₁₉×#126	—	2	8	no	—
37	C₁₉×#125	—	2	8	no	—
38	C₁₉×#123	—	2	4	no	—
39	C₁₉×#123	—	2	4	no	—
40	C₁₉×#123	—	2	8	no	—
41	C₁₉×C₂²⋊Q₈	—	2	2	no	—
42	C₁₉×C₂²⋊Q₈	—	2	2	no	—
43	C₁₉×C₂²⋊Q₈	—	2	8	no	—
44	C₁₉×#121	—	2	2	no	—
45	C₁₉×#121	—	2	2	no	—
46	C₄×D₄×C₁₉	—	2	4	no	—
47	C₄×D₄×C₁₉	—	2	4	no	—
48	C₁₉×#117	—	4	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
73	C₁₉×#99	—	4	8	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	4	no	—
79	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
80	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	8	1	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	8	1	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	8	1	no	—
95	C₂²×C₄×C₁₉	—	8	1	no	—
96	C₂²×C₄×C₁₉	—	8	2	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	4	4	no	—
117	C₄⋊C₄×C₁₉	—	8	2	no	—
118	C₄⋊C₄×C₁₉	—	8	2	no	—
119	C₄⋊C₄×C₁₉	—	8	2	no	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
122	C₂²⋊C₄×C₁₉	—	2	2	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	4	no	—
127	C₂²⋊C₄×C₁₉	—	2	4	no	—
128	C₂²⋊C₄×C₁₉	—	2	8	no	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₄²×C₁₉	—	2	4	no	—
132	C₄²×C₁₉	—	4	4	no	—
133	C₄²×C₁₉	—	8	2	no	—
134	#21877	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
142	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
143	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
145	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
146	Q₈×C₁₉	—	8	2	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	4	2	no	—
149	D₄×C₁₉	—	4	4	no	—
150	D₄×C₁₉	—	8	2	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	8	4	no	—
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×#539	C₂×C₁₉	1	1	yes	characteristic
180	#2316	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#2313	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#1996	C₂×C₁₉	1	2	yes	complemented
183	#1964	C₂×C₁₉	1	2	yes	—
184	#1899	C₂×C₁₉	1	4	yes	complemented
185	#1799	C₂×C₁₉	1	4	yes	complemented
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	8	4	no	—
198	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₉	#520	1	2	yes	—
200	C₂²×C₁₉	#535	1	1	yes	characteristic
201	C₂²×C₁₉	#536	1	1	yes	characteristic
202	C₂²×C₁₉	#537	1	2	yes	—
203	C₄×C₁₉	—	2	4	no	—
204	C₄×C₁₉	—	2	4	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	8	4	no	—
211	C₄×C₁₉	—	8	4	no	—
212	#539	—	2	4	no	—
213	#539	—	2	4	no	—
214	C₂×#126	C₄×C₁₉	1	2	yes	complemented
215	C₂×#125	C₄×C₁₉	1	2	yes	complemented
216	C₂×#123	C₄×C₁₉	1	2	yes	complemented
217	C₂×#123	C₂²×C₁₉	1	2	yes	—
218	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	complemented
219	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
222	C₂×#117	C₂²×C₁₉	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#99	C₂²×C₁₉	1	8	yes	—
225	#389	—	2	4	no	—
226	#387	—	2	4	no	—
227	#381	C₂²×C₁₉	1	2	yes	—
228	#380	C₂²×C₁₉	1	2	yes	—
229	#380	C₂²×C₁₉	1	2	yes	—
230	#380	C₂²×C₁₉	1	2	yes	—
231	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
232	#342	C₂²×C₁₉	1	8	yes	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	2	no	—
235	C₂×C₁₉	—	2	2	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	8	2	no	—
238	C₂×C₁₉	#2311	1	1	yes	characteristic
239	C₂×C₁₉	#2883	1	1	yes	characteristic
240	C₂×C₁₉	#2884	1	1	yes	characteristic
241	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
242	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
243	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
244	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
245	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	#126	—	2	8	no	—
249	#125	—	2	8	no	—
250	#123	—	2	4	no	—
251	#123	—	2	4	no	—
252	#123	—	2	8	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	2	8	no	—
256	#121	—	2	2	no	—
257	#121	—	2	2	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	4	no	—
260	#117	—	4	4	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
273	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
275	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
278	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
285	#99	—	4	8	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	4	no	—
291	C₁₉	#21877	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
293	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	8	1	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	8	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	8	1	no	—
308	C₂²×C₄	—	8	1	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	8	2	no	—
331	C₄⋊C₄	—	8	2	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
334	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	4	4	no	—
346	C₄²	—	8	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
354	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
355	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
356	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
357	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
358	Q₈	—	8	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	8	4	no	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	4	no	—
403	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
404	C₂²	C₁₉×#520	1	2	yes	—
405	C₂²	C₁₉×#535	1	1	yes	characteristic
406	C₂²	C₁₉×#536	1	1	yes	characteristic
407	C₂²	C₁₉×#537	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	4	no	—
416	C₄	—	8	4	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	2	no	—
419	C₂	—	2	2	no	—
420	C₂	—	2	1	no	—
421	C₂	—	8	2	no	—
422	C₂	C₁₉×#2311	1	1	yes	characteristic
423	C₂	C₁₉×#2883	1	1	yes	characteristic
424	C₂	C₁₉×#2884	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2316	C₂	semidirect
3. C₁₉×#2313	C₂	semidirect
4. C₁₉×#1996	C₂	semidirect
6. C₁₉×#1899	C₂	semidirect
7. C₁₉×#1799	C₂	semidirect
10. C₂×C₁₉×#126	C₄	semidirect
11. C₂×C₁₉×#125	C₄	semidirect
12. C₂×C₁₉×#123	C₄	semidirect
14. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
134. #21877	C₁₉	direct (N × H)
180. #2316	C₂×C₁₉	semidirect
181. #2313	C₂×C₁₉	semidirect
182. #1996	C₂×C₁₉	semidirect
184. #1899	C₂×C₁₉	semidirect
185. #1799	C₂×C₁₉	semidirect
214. C₂×#126	C₄×C₁₉	semidirect
215. C₂×#125	C₄×C₁₉	semidirect
216. C₂×#123	C₄×C₁₉	semidirect
218. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
291. C₁₉	#21877	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
C₁₉×#2316	2
C₁₉×#2313	2
C₁₉×#1996	2
C₁₉×#1964	2
C₁₉×#1899	2
C₁₉×#1799	2
#21877	19

Subgroups — C19×#21877 #18027836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21877 #18027836