Subgroups — C₁₉×#20633 #18026592

Order 4864.

1690 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	2	yes	maximal
3	C₁₉×#2315	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1799	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₉×#342	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#518	—	2	8	no	—
8	C₂×C₄×D₄×C₁₉	C₄	1	4	yes	complemented
9	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
10	C₂×C₁₉×#117	C₄	1	2	yes	complemented
11	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	complemented
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#99	—	2	8	no	—
16	C₂×C₁₉×#99	C₂²	1	8	yes	—
17	C₁₉×#385	—	2	8	no	—
18	C₁₉×#380	C₂²	1	8	yes	complemented
19	C₁₉×#342	C₂²	1	8	yes	complemented
20	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	—	2	4	no	—
23	C₂²×D₄×C₁₉	—	2	4	no	—
24	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂²×D₄×C₁₉	D₄	1	4	yes	—
26	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
27	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
28	C₂³×C₄×C₁₉	—	2	4	no	—
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	complemented
32	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
33	C₄×D₄×C₁₉	—	2	16	no	—
34	C₄×D₄×C₁₉	—	2	16	no	—
35	C₁₉×#117	—	2	8	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
38	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
43	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
47	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
48	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
49	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	complemented
51	C₁₉×#99	—	2	16	no	—
52	C₁₉×#95	—	2	8	no	—
53	C₂⁴×C₁₉	—	2	2	no	—
54	C₂⁴×C₁₉	—	2	2	no	—
55	C₂⁴×C₁₉	—	8	2	no	—
56	C₂⁴×C₁₉	—	8	2	no	—
57	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	complemented
58	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
59	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
62	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
63	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
64	C₂⁴×C₁₉	#41	1	4	yes	—
65	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	4	no	—
67	C₂×D₄×C₁₉	—	2	4	no	—
68	C₂×D₄×C₁₉	—	2	16	no	—
69	C₂×D₄×C₁₉	—	2	16	no	—
70	C₂×D₄×C₁₉	—	2	4	no	—
71	C₂×D₄×C₁₉	—	2	4	no	—
72	C₂×D₄×C₁₉	C₄⋊C₄	1	8	yes	complemented
73	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
74	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	2	8	no	—
80	C₂²×C₄×C₁₉	—	4	8	no	—
81	C₂²×C₄×C₁₉	—	8	2	no	—
82	C₂²×C₄×C₁₉	—	8	8	no	—
83	C₂²×C₄×C₁₉	—	8	2	no	—
84	C₂²×C₄×C₁₉	—	8	4	no	—
85	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	complemented
86	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
90	C₄⋊C₄×C₁₉	—	2	8	no	—
91	C₄⋊C₄×C₁₉	—	8	8	no	—
92	C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₂²⋊C₄×C₁₉	—	2	4	no	—
94	C₂²⋊C₄×C₁₉	—	2	8	no	—
95	C₂²⋊C₄×C₁₉	—	2	8	no	—
96	C₂²⋊C₄×C₁₉	—	2	8	no	—
97	C₂²⋊C₄×C₁₉	—	4	8	no	—
98	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
99	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
100	C₄²×C₁₉	—	2	8	no	—
101	#20633	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂³×C₁₉	—	2	2	no	—
103	C₂³×C₁₉	—	2	2	no	—
104	C₂³×C₁₉	—	2	8	no	—
105	C₂³×C₁₉	—	4	2	no	—
106	C₂³×C₁₉	—	4	8	no	—
107	C₂³×C₁₉	—	4	2	no	—
108	C₂³×C₁₉	—	4	2	no	—
109	C₂³×C₁₉	—	4	4	no	—
110	C₂³×C₁₉	—	8	4	no	—
111	C₂³×C₁₉	—	8	2	no	—
112	C₂³×C₁₉	—	8	2	no	—
113	C₂³×C₁₉	—	8	4	no	—
114	C₂³×C₁₉	—	8	4	no	—
115	C₂³×C₁₉	—	8	4	no	—
116	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
118	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
119	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
120	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₁₉	#117	1	2	yes	—
122	C₂³×C₁₉	#117	1	2	yes	—
123	C₂³×C₁₉	#121	1	8	yes	—
124	C₂³×C₁₉	C₂²⋊Q₈	1	8	yes	—
125	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
126	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
127	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
128	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
129	C₂³×C₁₉	C₂×#41	1	2	yes	—
130	D₄×C₁₉	—	2	8	no	—
131	D₄×C₁₉	—	2	8	no	—
132	D₄×C₁₉	—	2	16	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	8	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	4	8	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	4	no	—
140	C₂×C₄×C₁₉	—	4	16	no	—
141	C₂×C₄×C₁₉	—	4	8	no	—
142	C₂×C₄×C₁₉	—	8	8	no	—
143	C₂×C₄×C₁₉	—	8	4	no	—
144	C₂×C₄×C₁₉	—	8	16	no	—
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
146	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
147	C₂×#518	C₂×C₁₉	1	1	yes	characteristic
148	C₂²×#99	C₂×C₁₉	1	2	yes	—
149	#2315	C₂×C₁₉	1	2	yes	complemented
150	#1799	C₂×C₁₉	1	8	yes	complemented
151	C₂×#342	C₂×C₁₉	1	2	yes	complemented
152	C₂²×C₁₉	—	2	4	no	—
153	C₂²×C₁₉	—	2	2	no	—
154	C₂²×C₁₉	—	2	4	no	—
155	C₂²×C₁₉	—	2	4	no	—
156	C₂²×C₁₉	—	2	4	no	—
157	C₂²×C₁₉	—	4	8	no	—
158	C₂²×C₁₉	—	4	2	no	—
159	C₂²×C₁₉	—	4	2	no	—
160	C₂²×C₁₉	—	4	2	no	—
161	C₂²×C₁₉	—	4	2	no	—
162	C₂²×C₁₉	—	4	8	no	—
163	C₂²×C₁₉	—	4	1	no	—
164	C₂²×C₁₉	—	4	1	no	—
165	C₂²×C₁₉	—	4	2	no	—
166	C₂²×C₁₉	—	4	4	no	—
167	C₂²×C₁₉	—	4	4	no	—
168	C₂²×C₁₉	—	4	4	no	—
169	C₂²×C₁₉	—	8	8	no	—
170	C₂²×C₁₉	#380	1	4	yes	—
171	C₂²×C₁₉	#380	1	4	yes	—
172	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×#121	1	2	yes	—
176	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
177	C₄×C₁₉	—	2	8	no	—
178	C₄×C₁₉	—	2	4	no	—
179	C₄×C₁₉	—	4	4	no	—
180	C₄×C₁₉	—	8	8	no	—
181	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
182	#518	—	2	8	no	—
183	C₂×C₄×D₄	C₄×C₁₉	1	4	yes	complemented
184	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
185	C₂×#117	C₄×C₁₉	1	2	yes	complemented
186	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	complemented
187	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
189	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
190	C₂×#99	—	2	8	no	—
191	C₂×#99	C₂²×C₁₉	1	8	yes	—
192	#385	—	2	8	no	—
193	#380	C₂²×C₁₉	1	8	yes	complemented
194	#342	C₂²×C₁₉	1	8	yes	complemented
195	C₂×C₁₉	—	2	2	no	—
196	C₂×C₁₉	—	2	1	no	—
197	C₂×C₁₉	—	2	1	no	—
198	C₂×C₁₉	—	2	4	no	—
199	C₂×C₁₉	—	2	2	no	—
200	C₂×C₁₉	—	2	4	no	—
201	C₂×C₁₉	—	4	4	no	—
202	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
203	C₂×C₁₉	#2883	1	2	yes	—
204	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
205	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
206	C₂²×D₄	—	2	4	no	—
207	C₂²×D₄	—	2	4	no	—
208	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
209	C₂²×D₄	D₄×C₁₉	1	4	yes	—
210	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
211	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
214	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
215	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	complemented
216	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
217	C₄×D₄	—	2	16	no	—
218	C₄×D₄	—	2	16	no	—
219	#117	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	8	no	—
221	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
222	C₂×C₂²⋊C₄	—	2	4	no	—
223	C₂×C₂²⋊C₄	—	2	8	no	—
224	C₂×C₂²⋊C₄	—	2	8	no	—
225	C₂×C₂²⋊C₄	—	2	8	no	—
226	C₂×C₂²⋊C₄	—	2	4	no	—
227	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
230	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
231	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
234	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	complemented
235	#99	—	2	16	no	—
236	#95	—	2	8	no	—
237	C₁₉	#20633	1	1	yes	characteristic, direct product factor, Sylow
238	C₂⁴	—	2	2	no	—
239	C₂⁴	—	2	2	no	—
240	C₂⁴	—	8	2	no	—
241	C₂⁴	—	8	2	no	—
242	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	complemented
243	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
244	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
245	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
246	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
247	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
248	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
249	C₂⁴	#41×C₁₉	1	4	yes	—
250	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	16	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	C₄⋊C₄×C₁₉	1	8	yes	complemented
258	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
259	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	4	8	no	—
266	C₂²×C₄	—	8	2	no	—
267	C₂²×C₄	—	8	8	no	—
268	C₂²×C₄	—	8	2	no	—
269	C₂²×C₄	—	8	4	no	—
270	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	complemented
271	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
274	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	8	8	no	—
277	C₂²⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₂²⋊C₄	—	2	8	no	—
280	C₂²⋊C₄	—	2	8	no	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	4	8	no	—
283	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
284	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
285	C₄²	—	2	8	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	4	2	no	—
290	C₂³	—	4	8	no	—
291	C₂³	—	4	2	no	—
292	C₂³	—	4	2	no	—
293	C₂³	—	4	4	no	—
294	C₂³	—	8	4	no	—
295	C₂³	—	8	2	no	—
296	C₂³	—	8	2	no	—
297	C₂³	—	8	4	no	—
298	C₂³	—	8	4	no	—
299	C₂³	—	8	4	no	—
300	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
301	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
302	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
303	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
304	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
305	C₂³	C₁₉×#117	1	2	yes	—
306	C₂³	C₁₉×#117	1	2	yes	—
307	C₂³	C₁₉×#121	1	8	yes	—
308	C₂³	C₁₉×C₂²⋊Q₈	1	8	yes	—
309	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
310	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
311	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
312	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
313	C₂³	C₂×#41×C₁₉	1	2	yes	—
314	D₄	—	2	16	no	—
315	D₄	—	2	8	no	—
316	D₄	—	2	8	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	16	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	8	8	no	—
327	C₂×C₄	—	8	4	no	—
328	C₂×C₄	—	8	16	no	—
329	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
330	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	8	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	8	8	no	—
349	C₂²	C₁₉×#380	1	4	yes	—
350	C₂²	C₁₉×#380	1	4	yes	—
351	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
352	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
353	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
354	C₂²	C₂×C₁₉×#121	1	2	yes	—
355	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
356	C₄	—	2	4	no	—
357	C₄	—	2	8	no	—
358	C₄	—	4	4	no	—
359	C₄	—	8	8	no	—
360	C₂	—	2	2	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	2	4	no	—
364	C₂	—	2	4	no	—
365	C₂	—	2	2	no	—
366	C₂	—	4	4	no	—
367	C₂	C₂×C₁₉×#380	1	1	yes	characteristic
368	C₂	C₁₉×#2883	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2315	C₂	semidirect
4. C₁₉×#1799	C₂	semidirect
5. C₂×C₁₉×#342	C₂	semidirect
8. C₂×C₄×D₄×C₁₉	C₄	semidirect
10. C₂×C₁₉×#117	C₄	semidirect
11. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
18. C₁₉×#380	C₂²	semidirect
19. C₁₉×#342	C₂²	semidirect
31. C₂³×C₄×C₁₉	C₂×C₄	semidirect
37. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
46. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
50. C₂×C₄²×C₁₉	C₂×C₄	semidirect
57. C₂⁴×C₁₉	C₄⋊C₄	semidirect
72. C₂×D₄×C₁₉	C₄⋊C₄	semidirect
85. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
101. #20633	C₁₉	direct (N × H)
149. #2315	C₂×C₁₉	semidirect
150. #1799	C₂×C₁₉	semidirect
151. C₂×#342	C₂×C₁₉	semidirect
183. C₂×C₄×D₄	C₄×C₁₉	semidirect
185. C₂×#117	C₄×C₁₉	semidirect
186. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
193. #380	C₂²×C₁₉	semidirect
194. #342	C₂²×C₁₉	semidirect
215. C₂³×C₄	C₂×C₄×C₁₉	semidirect
221. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
230. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
234. C₂×C₄²	C₂×C₄×C₁₉	semidirect
237. C₁₉	#20633	direct (N × H)
242. C₂⁴	C₄⋊C₄×C₁₉	semidirect
257. C₂×D₄	C₄⋊C₄×C₁₉	semidirect
270. C₂²×C₄	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#518	2
C₂²×C₁₉×#99	2
C₁₉×#2315	2
C₁₉×#1799	2
C₂×C₁₉×#342	2
#20633	19

Subgroups — C19×#20633 #18026592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20633 #18026592