Subgroups — C₂×C₁₉×#2027 #18029418

Order 4864.

1454 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×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#418	C₂	1	2	yes	maximal
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2027	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#339	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#544	—	2	4	no	—
10	C₁₉×#544	—	2	2	no	—
11	C₁₉×#544	C₂²	1	4	yes	complemented
12	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
13	C₂×C₁₉×#125	—	2	2	no	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₁₉×#117	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#418	—	2	4	no	—
20	C₁₉×#418	C₂²	1	8	yes	—
21	C₂×C₁₉×#102	—	2	2	no	—
22	C₂×C₁₉×#102	—	2	2	no	—
23	C₁₉×#390	—	2	2	no	—
24	C₁₉×#390	C₂²	1	4	yes	—
25	C₁₉×#343	C₂²	1	4	yes	complemented
26	C₁₉×#339	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₉	—	2	1	no	—
28	C₂²×Q₈×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	2	no	—
30	C₂²×D₄×C₁₉	—	2	2	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	4	no	—
33	C₂²×D₄×C₁₉	—	2	2	no	—
34	C₂²×D₄×C₁₉	Q₈	1	4	yes	complemented
35	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	D₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₉	—	2	2	no	—
40	C₂×M₁₆×C₁₉	—	2	4	no	—
41	C₂×M₁₆×C₁₉	—	2	4	no	—
42	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
43	C₂²×C₈×C₁₉	—	2	2	no	—
44	C₁₉×C₄⋊Q₈	—	2	8	no	—
45	C₁₉×C₄⋊Q₈	—	2	8	no	—
46	C₁₉×#125	—	2	8	no	—
47	C₁₉×#125	—	2	8	no	—
48	C₁₉×C₂²⋊Q₈	—	2	8	no	—
49	C₁₉×C₂²⋊Q₈	—	2	8	no	—
50	C₁₉×#117	—	2	2	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₁₉×#117	D₄	1	4	yes	—
53	C₁₉×#117	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	—	2	4	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
69	C₁₉×#102	—	2	8	no	—
70	C₁₉×#102	—	2	8	no	—
71	C₂⁴×C₁₉	—	2	4	no	—
72	C₂⁴×C₁₉	—	2	2	no	—
73	C₂⁴×C₁₉	—	4	4	no	—
74	C₂⁴×C₁₉	—	4	4	no	—
75	C₂⁴×C₁₉	—	4	1	no	—
76	C₂⁴×C₁₉	—	4	1	no	—
77	C₂⁴×C₁₉	—	4	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	8	no	—
80	C₂×Q₈×C₁₉	—	8	4	no	—
81	C₂×D₄×C₁₉	—	2	8	no	—
82	C₂×D₄×C₁₉	—	2	8	no	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	4	no	—
89	C₂×D₄×C₁₉	—	4	4	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	complemented
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	4	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₁₉	#41	1	4	yes	—
107	C₂²×C₄×C₁₉	#41	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₁₉	—	2	4	no	—
110	M₁₆×C₁₉	—	2	4	no	—
111	M₁₆×C₁₉	—	4	4	no	—
112	C₂×C₈×C₁₉	—	2	4	no	—
113	C₂×C₈×C₁₉	—	4	4	no	—
114	C₄⋊C₄×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	16	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
121	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	4	16	no	—
125	C₄²×C₁₉	—	2	4	no	—
126	C₄²×C₁₉	—	2	4	no	—
127	C₄²×C₁₉	—	2	4	no	—
128	C₄²×C₁₉	—	4	2	no	—
129	C₂×#2027	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	4	4	no	—
135	C₂³×C₁₉	—	4	16	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	8	2	no	—
141	C₂³×C₁₉	—	8	2	no	—
142	C₂³×C₁₉	—	8	8	no	—
143	C₂³×C₁₉	—	8	2	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	#120	1	1	yes	characteristic
146	C₂³×C₁₉	#120	1	1	yes	characteristic
147	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
148	C₂³×C₁₉	#124	1	2	yes	—
149	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₉	—	8	8	no	—
151	D₄×C₁₉	—	2	8	no	—
152	D₄×C₁₉	—	4	4	no	—
153	D₄×C₁₉	—	4	8	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	#120	1	2	yes	—
167	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
169	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₁₉	#124	1	4	yes	—
171	C₂×C₄×C₁₉	#124	1	4	yes	—
172	C₂×C₄×C₁₉	#124	1	2	yes	—
173	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
176	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
177	C₈×C₁₉	—	4	4	no	—
178	C₂×#544	C₂×C₁₉	1	1	yes	characteristic, complemented
179	C₂×#418	C₂×C₁₉	1	2	yes	—
180	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
181	#2027	C₂×C₁₉	1	8	yes	direct product factor
182	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
183	C₂×#339	C₂×C₁₉	1	2	yes	complemented
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	4	8	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	8	4	no	—
193	C₂²×C₁₉	—	8	8	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	8	no	—
197	C₂²×C₁₉	#393	1	2	yes	—
198	C₂²×C₁₉	#393	1	2	yes	—
199	C₂²×C₁₉	#453	1	2	yes	—
200	C₂²×C₁₉	#454	1	2	yes	—
201	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
204	C₄×C₁₉	—	4	4	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	4	4	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	#393	1	4	yes	—
209	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
210	C₄×C₁₉	C₂×#124	1	2	yes	—
211	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
213	#544	—	2	4	no	—
214	#544	—	2	2	no	—
215	#544	C₂²×C₁₉	1	4	yes	complemented
216	C₂×C₄⋊Q₈	—	2	2	no	—
217	C₂×#125	—	2	2	no	—
218	C₂×C₂²⋊Q₈	—	2	2	no	—
219	C₂×#117	C₂²×C₁₉	1	2	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
221	C₂²×C₂²⋊C₄	—	2	2	no	—
222	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
223	#418	—	2	4	no	—
224	#418	C₂²×C₁₉	1	8	yes	—
225	C₂×#102	—	2	2	no	—
226	C₂×#102	—	2	2	no	—
227	#390	—	2	2	no	—
228	#390	C₂²×C₁₉	1	4	yes	—
229	#343	C₂²×C₁₉	1	4	yes	complemented
230	#339	C₂²×C₁₉	1	8	yes	complemented
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	2	2	no	—
234	C₂×C₁₉	—	8	4	no	—
235	C₂×C₁₉	#2027	1	4	yes	direct product factor
236	C₂×C₁₉	C₂×#393	1	1	yes	characteristic
237	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
238	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
239	C₂⁵	—	2	1	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	4	no	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	Q₈×C₁₉	1	4	yes	complemented
247	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	D₄×C₁₉	1	2	yes	—
250	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
255	C₂²×C₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	8	no	—
257	C₄⋊Q₈	—	2	8	no	—
258	#125	—	2	8	no	—
259	#125	—	2	8	no	—
260	C₂²⋊Q₈	—	2	8	no	—
261	C₂²⋊Q₈	—	2	8	no	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	D₄×C₁₉	1	4	yes	—
265	#117	C₂³×C₁₉	1	4	yes	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	—	4	8	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
281	#102	—	2	8	no	—
282	#102	—	2	8	no	—
283	C₁₉	C₂×#2027	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	2	2	no	—
286	C₂⁴	—	4	4	no	—
287	C₂⁴	—	4	4	no	—
288	C₂⁴	—	4	1	no	—
289	C₂⁴	—	4	1	no	—
290	C₂⁴	—	4	2	no	—
291	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
292	C₂×Q₈	—	2	8	no	—
293	C₂×Q₈	—	8	4	no	—
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	complemented
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
319	C₂²×C₄	#41×C₁₉	1	4	yes	—
320	C₂²×C₄	#41×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	4	4	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	4	4	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
334	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	4	16	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	4	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	16	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	8	2	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	8	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	C₁₉×#120	1	1	yes	characteristic
358	C₂³	C₁₉×#120	1	1	yes	characteristic
359	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
360	C₂³	C₁₉×#124	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
362	Q₈	—	8	8	no	—
363	D₄	—	2	8	no	—
364	D₄	—	4	8	no	—
365	D₄	—	4	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	C₁₉×#120	1	2	yes	—
379	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
380	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
381	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
382	C₂×C₄	C₁₉×#124	1	2	yes	—
383	C₂×C₄	C₁₉×#124	1	4	yes	—
384	C₂×C₄	C₁₉×#124	1	4	yes	—
385	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
386	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
388	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
389	C₈	—	4	4	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	8	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	8	4	no	—
399	C₂²	—	8	8	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	8	no	—
403	C₂²	C₁₉×#393	1	2	yes	—
404	C₂²	C₁₉×#393	1	2	yes	—
405	C₂²	C₁₉×#453	1	2	yes	—
406	C₂²	C₁₉×#454	1	2	yes	—
407	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
408	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
409	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
410	C₄	—	4	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	4	no	—
414	C₄	C₁₉×#393	1	4	yes	—
415	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
416	C₄	C₂×C₁₉×#124	1	2	yes	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	2	no	—
420	C₂	—	8	4	no	—
421	C₂	C₁₉×#2027	1	4	yes	direct product factor
422	C₂	C₂×C₁₉×#393	1	1	yes	characteristic
423	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
424	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
1. C₂×C₁₉×#544	C₂	semidirect
4. C₁₉×#2027	C₂	direct (N × H)
5. C₂×C₁₉×#343	C₂	semidirect
6. C₂×C₁₉×#339	C₂	semidirect
11. C₁₉×#544	C₂²	semidirect
25. C₁₉×#343	C₂²	semidirect
26. C₁₉×#339	C₂²	semidirect
34. C₂²×D₄×C₁₉	Q₈	semidirect
91. C₂×D₄×C₁₉	C₂×Q₈	semidirect
129. C₂×#2027	C₁₉	direct (N × H)
178. C₂×#544	C₂×C₁₉	semidirect
181. #2027	C₂×C₁₉	direct (N × H)
182. C₂×#343	C₂×C₁₉	semidirect
183. C₂×#339	C₂×C₁₉	semidirect
215. #544	C₂²×C₁₉	semidirect
229. #343	C₂²×C₁₉	semidirect
230. #339	C₂²×C₁₉	semidirect
235. C₂×C₁₉	#2027	direct (N × H)
246. C₂²×D₄	Q₈×C₁₉	semidirect
283. C₁₉	C₂×#2027	direct (N × H)
304. C₂×D₄	C₂×Q₈×C₁₉	semidirect
421. C₂	C₁₉×#2027	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×#544	2
C₂×C₁₉×#418	2
C₂×C₁₉×#390	2
C₁₉×#2027	2
C₂×C₁₉×#343	2
C₂×C₁₉×#339	2
C₂×#2027	19

Subgroups — C2×C19×#2027 #18029418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2027 #18029418