Subgroups — C₁₉×#60646 #18066605

Order 4864.

3250 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#577	C₂	1	4	yes	maximal, complemented
2	C₁₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3154	C₂	1	12	yes	maximal, complemented
5	C₁₉×#3152	C₂	1	3	yes	maximal, complemented
6	C₁₉×#3151	C₂	1	3	yes	maximal, complemented
7	C₁₉×#3147	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₉×#492	C₂	1	3	yes	maximal, complemented
9	C₄×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	—
11	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	2	yes	—
12	C₁₉×#577	—	2	32	no	—
13	C₂×C₁₉×#137	C₂²	1	12	yes	complemented
14	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
15	C₂×C₁₉×#135	C₂²	1	12	yes	complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	12	yes	complemented
17	C₂×C₁₉×#131	C₂²	1	2	yes	—
18	C₁₉×#550	—	2	2	no	—
19	D₄×Q₈×C₁₉	—	2	2	no	—
20	C₁₉×#547	—	2	6	no	—
21	D₄²×C₁₉	—	2	6	no	—
22	C₁₉×#536	C₂²	1	6	yes	complemented
23	C₁₉×#535	C₂²	1	6	yes	—
24	C₁₉×#532	C₂²	1	3	yes	—
25	C₁₉×#532	C₂²	1	3	yes	complemented
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	complemented
27	C₂×C₁₉×#127	C₂²	1	3	yes	—
28	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#497	C₂²	1	12	yes	complemented
30	C₁₉×#496	C₂²	1	12	yes	complemented
31	C₁₉×#495	C₂²	1	12	yes	complemented
32	C₁₉×#494	C₂²	1	3	yes	complemented
33	C₁₉×#493	C₂²	1	3	yes	complemented
34	C₁₉×#492	C₂²	1	3	yes	complemented
35	C₁₉×#492	C₂²	1	6	yes	complemented
36	C₁₉×#492	C₂²	1	12	yes	complemented
37	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#405	C₂²	1	6	yes	complemented
39	C₄×M₁₆×C₁₉	C₂²	1	3	yes	complemented
40	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	complemented
41	C₁₉×2₋¹⁺⁴	—	2	16	no	—
42	C₁₉×H(5,𝔽₂)	—	2	16	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	—	2	6	no	—
45	C₂×#41×C₁₉	C₂³	1	6	yes	—
46	C₂×#41×C₁₉	C₂³	1	6	yes	—
47	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₉	—	2	2	no	—
49	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
50	C₂²×D₄×C₁₉	—	2	6	no	—
51	C₂²×D₄×C₁₉	—	2	6	no	—
52	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
53	C₁₉×#137	—	2	48	no	—
54	C₁₉×AGL(1,ℤ/8)	—	2	48	no	—
55	C₁₉×#135	—	2	48	no	—
56	C₂×Q₁₆×C₁₉	C₂³	1	12	yes	—
57	C₂×SD₁₆×C₁₉	—	2	48	no	—
58	C₂×SD₁₆×C₁₉	C₂³	1	12	yes	—
59	C₂×SD₁₆×C₁₉	C₂³	1	24	yes	—
60	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
61	C₂×D₈×C₁₉	C₂³	1	12	yes	—
62	C₁₉×#131	D₄	1	16	yes	complemented
63	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
64	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
65	C₁₉×C₄⋊Q₈	—	2	6	no	—
66	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
68	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₉×#127	—	2	6	no	—
70	C₁₉×#127	C₂³	1	3	yes	—
71	C₁₉×#127	C₂³	1	6	yes	—
72	C₁₉×#127	C₂³	1	1	yes	characteristic
73	C₁₉×#124	C₂³	1	6	yes	—
74	C₁₉×#124	C₂³	1	6	yes	—
75	C₁₉×#123	—	2	12	no	—
76	C₁₉×C₂²⋊Q₈	—	2	12	no	—
77	C₁₉×#121	—	2	6	no	—
78	C₁₉×#121	—	2	6	no	—
79	C₁₉×#121	—	2	12	no	—
80	C₁₉×#120	—	2	12	no	—
81	C₄×Q₈×C₁₉	D₄	1	2	yes	—
82	C₄×D₄×C₁₉	—	2	6	no	—
83	C₄×D₄×C₁₉	—	2	6	no	—
84	C₄×D₄×C₁₉	D₄	1	6	yes	—
85	C₁₉×#117	C₂³	1	3	yes	—
86	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
87	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
88	C₁₉×#97	C₂³	1	6	yes	—
89	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₉	C₂³	1	3	yes	—
91	C₄×C₈×C₁₉	C₂³	1	6	yes	—
92	C₂⁴×C₁₉	—	2	6	no	—
93	#41×C₁₉	—	2	24	no	—
94	#41×C₁₉	—	2	24	no	—
95	#41×C₁₉	—	4	8	no	—
96	#41×C₁₉	—	4	24	no	—
97	#41×C₁₉	C₂×D₄	1	8	yes	—
98	C₂×Q₈×C₁₉	—	2	6	no	—
99	C₂×Q₈×C₁₉	—	2	24	no	—
100	C₂×Q₈×C₁₉	—	4	8	no	—
101	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
103	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
104	C₂×D₄×C₁₉	—	2	6	no	—
105	C₂×D₄×C₁₉	—	2	6	no	—
106	C₂×D₄×C₁₉	—	2	24	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	6	no	—
109	C₂×D₄×C₁₉	—	2	6	no	—
110	C₂×D₄×C₁₉	—	2	12	no	—
111	C₂×D₄×C₁₉	—	4	24	no	—
112	C₂×D₄×C₁₉	—	8	12	no	—
113	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
114	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
115	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
116	C₂²×C₄×C₁₉	—	2	6	no	—
117	C₂²×C₄×C₁₉	—	2	6	no	—
118	C₂²×C₄×C₁₉	—	2	6	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
121	Q₁₆×C₁₉	—	2	24	no	—
122	SD₁₆×C₁₉	—	2	24	no	—
123	SD₁₆×C₁₉	—	2	48	no	—
124	SD₁₆×C₁₉	—	2	8	no	—
125	D₈×C₁₉	—	2	24	no	—
126	M₁₆×C₁₉	C₂×D₄	1	24	yes	complemented
127	C₂×C₈×C₁₉	C₂×D₄	1	24	yes	complemented
128	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
129	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
130	C₄⋊C₄×C₁₉	—	2	6	no	—
131	C₄⋊C₄×C₁₉	—	2	12	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
134	C₂²⋊C₄×C₁₉	—	2	12	no	—
135	C₂²⋊C₄×C₁₉	—	2	12	no	—
136	C₂²⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
137	C₄²×C₁₉	C₂×D₄	1	6	yes	—
138	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
139	C₄²×C₁₉	C₂⁴	1	3	yes	—
140	#60646	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	6	no	—
143	C₂³×C₁₉	—	4	12	no	—
144	C₂³×C₁₉	—	8	12	no	—
145	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
146	Q₈×C₁₉	—	2	12	no	—
147	Q₈×C₁₉	—	2	4	no	—
148	Q₈×C₁₉	—	4	12	no	—
149	Q₈×C₁₉	#127	1	4	yes	—
150	D₄×C₁₉	—	2	4	no	—
151	D₄×C₁₉	—	2	12	no	—
152	D₄×C₁₉	—	4	12	no	—
153	D₄×C₁₉	—	4	12	no	—
154	D₄×C₁₉	—	4	12	no	—
155	D₄×C₁₉	—	4	4	no	—
156	D₄×C₁₉	—	4	12	no	—
157	D₄×C₁₉	—	8	12	no	—
158	D₄×C₁₉	#127	1	12	yes	—
159	C₂×C₄×C₁₉	—	2	12	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	6	no	—
162	C₂×C₄×C₁₉	—	4	12	no	—
163	C₂×C₄×C₁₉	—	4	12	no	—
164	C₂×C₄×C₁₉	—	4	12	no	—
165	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
166	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
167	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
168	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
170	C₈×C₁₉	C₂²×D₄	1	4	yes	—
171	C₈×C₁₉	C₂²×D₄	1	12	yes	—
172	C₂×#577	C₂×C₁₉	1	4	yes	complemented
173	#3499	C₂×C₁₉	1	1	yes	characteristic, complemented
174	#3498	C₂×C₁₉	1	1	yes	characteristic, complemented
175	#3154	C₂×C₁₉	1	12	yes	complemented
176	#3152	C₂×C₁₉	1	3	yes	complemented
177	#3151	C₂×C₁₉	1	3	yes	complemented
178	#3147	C₂×C₁₉	1	3	yes	complemented
179	C₂×#492	C₂×C₁₉	1	3	yes	complemented
180	C₄×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
181	C₂²×C₁₉	—	2	6	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	—	4	6	no	—
184	C₂²×C₁₉	—	4	12	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	16	12	no	—
187	C₂²×C₁₉	C₂×#127	1	6	yes	—
188	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
189	C₄×C₁₉	—	2	6	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₄×C₁₉	—	4	6	no	—
192	C₄×C₁₉	C₂×#127	1	6	yes	—
193	C₄×C₁₉	#577	1	4	yes	complemented
194	C₄×C₁₉	C₂³×D₄	1	2	yes	—
195	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
196	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	—
197	#577	—	2	32	no	—
198	C₂×#137	C₂²×C₁₉	1	12	yes	complemented
199	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	12	yes	complemented
200	C₂×#135	C₂²×C₁₉	1	12	yes	complemented
201	C₂²×SD₁₆	C₂²×C₁₉	1	12	yes	complemented
202	C₂×#131	C₂²×C₁₉	1	2	yes	—
203	#550	—	2	2	no	—
204	D₄×Q₈	—	2	2	no	—
205	#547	—	2	6	no	—
206	D₄²	—	2	6	no	—
207	#536	C₂²×C₁₉	1	6	yes	complemented
208	#535	C₂²×C₁₉	1	6	yes	—
209	#532	C₂²×C₁₉	1	3	yes	—
210	#532	C₂²×C₁₉	1	3	yes	complemented
211	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	complemented
212	C₂×#127	C₂²×C₁₉	1	3	yes	—
213	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
214	#497	C₂²×C₁₉	1	12	yes	complemented
215	#496	C₂²×C₁₉	1	12	yes	complemented
216	#495	C₂²×C₁₉	1	12	yes	complemented
217	#494	C₂²×C₁₉	1	3	yes	complemented
218	#493	C₂²×C₁₉	1	3	yes	complemented
219	#492	C₂²×C₁₉	1	3	yes	complemented
220	#492	C₂²×C₁₉	1	6	yes	complemented
221	#492	C₂²×C₁₉	1	12	yes	complemented
222	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
223	#405	C₂²×C₁₉	1	6	yes	complemented
224	C₄×M₁₆	C₂²×C₁₉	1	3	yes	complemented
225	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	complemented
226	C₂×C₁₉	—	2	6	no	—
227	C₂×C₁₉	—	8	2	no	—
228	C₂×C₁₉	—	8	6	no	—
229	C₂×C₁₉	C₂²×#127	1	1	yes	characteristic
230	C₂×C₁₉	C₂×#577	1	2	yes	—
231	2₋¹⁺⁴	—	2	16	no	—
232	H(5,𝔽₂)	—	2	16	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	6	no	—
235	C₂×#41	C₂³×C₁₉	1	6	yes	—
236	C₂×#41	C₂³×C₁₉	1	6	yes	—
237	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
238	C₂²×Q₈	—	2	2	no	—
239	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
240	C₂²×D₄	—	2	6	no	—
241	C₂²×D₄	—	2	6	no	—
242	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
243	#137	—	2	48	no	—
244	AGL(1,ℤ/8)	—	2	48	no	—
245	#135	—	2	48	no	—
246	C₂×Q₁₆	C₂³×C₁₉	1	12	yes	—
247	C₂×SD₁₆	—	2	48	no	—
248	C₂×SD₁₆	C₂³×C₁₉	1	12	yes	—
249	C₂×SD₁₆	C₂³×C₁₉	1	24	yes	—
250	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
251	C₂×D₈	C₂³×C₁₉	1	12	yes	—
252	#131	D₄×C₁₉	1	16	yes	complemented
253	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
254	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
255	C₄⋊Q₈	—	2	6	no	—
256	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
257	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
258	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
259	#127	—	2	6	no	—
260	#127	C₂³×C₁₉	1	3	yes	—
261	#127	C₂³×C₁₉	1	6	yes	—
262	#127	C₂³×C₁₉	1	1	yes	characteristic
263	#124	C₂³×C₁₉	1	6	yes	—
264	#124	C₂³×C₁₉	1	6	yes	—
265	#123	—	2	12	no	—
266	C₂²⋊Q₈	—	2	12	no	—
267	#121	—	2	6	no	—
268	#121	—	2	6	no	—
269	#121	—	2	12	no	—
270	#120	—	2	12	no	—
271	C₄×Q₈	D₄×C₁₉	1	2	yes	—
272	C₄×D₄	—	2	6	no	—
273	C₄×D₄	—	2	6	no	—
274	C₄×D₄	D₄×C₁₉	1	6	yes	—
275	#117	C₂³×C₁₉	1	3	yes	—
276	C₂×C₄⋊C₄	—	2	6	no	—
277	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
278	#97	C₂³×C₁₉	1	6	yes	—
279	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₁₉	1	3	yes	—
281	C₄×C₈	C₂³×C₁₉	1	6	yes	—
282	C₁₉	#60646	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁴	—	2	6	no	—
284	#41	—	2	24	no	—
285	#41	—	2	24	no	—
286	#41	—	4	8	no	—
287	#41	—	4	24	no	—
288	#41	C₂×D₄×C₁₉	1	8	yes	—
289	C₂×Q₈	—	2	6	no	—
290	C₂×Q₈	—	2	24	no	—
291	C₂×Q₈	—	4	8	no	—
292	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
294	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
295	C₂×D₄	—	2	6	no	—
296	C₂×D₄	—	2	6	no	—
297	C₂×D₄	—	2	24	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	6	no	—
300	C₂×D₄	—	2	6	no	—
301	C₂×D₄	—	2	12	no	—
302	C₂×D₄	—	4	24	no	—
303	C₂×D₄	—	8	12	no	—
304	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
305	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
306	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
307	C₂²×C₄	—	2	6	no	—
308	C₂²×C₄	—	2	6	no	—
309	C₂²×C₄	—	2	6	no	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
311	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
312	Q₁₆	—	2	24	no	—
313	SD₁₆	—	2	24	no	—
314	SD₁₆	—	2	48	no	—
315	SD₁₆	—	2	8	no	—
316	D₈	—	2	24	no	—
317	M₁₆	C₂×D₄×C₁₉	1	24	yes	complemented
318	C₂×C₈	C₂×D₄×C₁₉	1	24	yes	complemented
319	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
320	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
321	C₄⋊C₄	—	2	6	no	—
322	C₄⋊C₄	—	2	12	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
325	C₂²⋊C₄	—	2	12	no	—
326	C₂²⋊C₄	—	2	12	no	—
327	C₂²⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
328	C₄²	C₂×D₄×C₁₉	1	6	yes	—
329	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
330	C₄²	C₂⁴×C₁₉	1	3	yes	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	6	no	—
333	C₂³	—	4	12	no	—
334	C₂³	—	8	12	no	—
335	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
336	Q₈	—	2	12	no	—
337	Q₈	—	2	4	no	—
338	Q₈	—	4	12	no	—
339	Q₈	C₁₉×#127	1	4	yes	—
340	D₄	—	2	4	no	—
341	D₄	—	2	12	no	—
342	D₄	—	4	12	no	—
343	D₄	—	4	12	no	—
344	D₄	—	4	12	no	—
345	D₄	—	4	12	no	—
346	D₄	—	4	4	no	—
347	D₄	—	8	12	no	—
348	D₄	C₁₉×#127	1	12	yes	—
349	C₂×C₄	—	2	12	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	6	no	—
352	C₂×C₄	—	4	12	no	—
353	C₂×C₄	—	4	12	no	—
354	C₂×C₄	—	4	12	no	—
355	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
356	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
357	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
358	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
359	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
360	C₈	C₂²×D₄×C₁₉	1	4	yes	—
361	C₈	C₂²×D₄×C₁₉	1	12	yes	—
362	C₂²	—	2	6	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	6	no	—
365	C₂²	—	4	12	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	16	12	no	—
368	C₂²	C₂×C₁₉×#127	1	6	yes	—
369	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
370	C₄	—	2	6	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	6	no	—
373	C₄	C₂×C₁₉×#127	1	6	yes	—
374	C₄	C₁₉×#577	1	4	yes	complemented
375	C₄	C₂³×D₄×C₁₉	1	2	yes	—
376	C₂	—	2	6	no	—
377	C₂	—	8	6	no	—
378	C₂	—	8	2	no	—
379	C₂	C₂²×C₁₉×#127	1	1	yes	characteristic
380	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#577	C₂	semidirect
2. C₁₉×#3499	C₂	semidirect
3. C₁₉×#3498	C₂	semidirect
4. C₁₉×#3154	C₂	semidirect
5. C₁₉×#3152	C₂	semidirect
6. C₁₉×#3151	C₂	semidirect
7. C₁₉×#3147	C₂	semidirect
8. C₂×C₁₉×#492	C₂	semidirect
9. C₄×C₁₉×#131	C₂	semidirect
13. C₂×C₁₉×#137	C₂²	semidirect
14. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂×C₁₉×#135	C₂²	semidirect
16. C₂²×SD₁₆×C₁₉	C₂²	semidirect
22. C₁₉×#536	C₂²	semidirect
25. C₁₉×#532	C₂²	semidirect
26. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
29. C₁₉×#497	C₂²	semidirect
30. C₁₉×#496	C₂²	semidirect
31. C₁₉×#495	C₂²	semidirect
32. C₁₉×#494	C₂²	semidirect
33. C₁₉×#493	C₂²	semidirect
34. C₁₉×#492	C₂²	semidirect
35. C₁₉×#492	C₂²	semidirect
36. C₁₉×#492	C₂²	semidirect
37. C₁₉×#492	C₂²	semidirect
38. C₁₉×#405	C₂²	semidirect
39. C₄×M₁₆×C₁₉	C₂²	semidirect
40. C₂×C₄×C₈×C₁₉	C₂²	semidirect
62. C₁₉×#131	D₄	semidirect
126. M₁₆×C₁₉	C₂×D₄	semidirect
127. C₂×C₈×C₁₉	C₂×D₄	semidirect
140. #60646	C₁₉	direct (N × H)
172. C₂×#577	C₂×C₁₉	semidirect
173. #3499	C₂×C₁₉	semidirect
174. #3498	C₂×C₁₉	semidirect
175. #3154	C₂×C₁₉	semidirect
176. #3152	C₂×C₁₉	semidirect
177. #3151	C₂×C₁₉	semidirect
178. #3147	C₂×C₁₉	semidirect
179. C₂×#492	C₂×C₁₉	semidirect
180. C₄×#131	C₂×C₁₉	semidirect
193. C₄×C₁₉	#577	semidirect
198. C₂×#137	C₂²×C₁₉	semidirect
199. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
200. C₂×#135	C₂²×C₁₉	semidirect
201. C₂²×SD₁₆	C₂²×C₁₉	semidirect
207. #536	C₂²×C₁₉	semidirect
210. #532	C₂²×C₁₉	semidirect
211. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
214. #497	C₂²×C₁₉	semidirect
215. #496	C₂²×C₁₉	semidirect
216. #495	C₂²×C₁₉	semidirect
217. #494	C₂²×C₁₉	semidirect
218. #493	C₂²×C₁₉	semidirect
219. #492	C₂²×C₁₉	semidirect
220. #492	C₂²×C₁₉	semidirect
221. #492	C₂²×C₁₉	semidirect
222. #492	C₂²×C₁₉	semidirect
223. #405	C₂²×C₁₉	semidirect
224. C₄×M₁₆	C₂²×C₁₉	semidirect
225. C₂×C₄×C₈	C₂²×C₁₉	semidirect
252. #131	D₄×C₁₉	semidirect
282. C₁₉	#60646	direct (N × H)
317. M₁₆	C₂×D₄×C₁₉	semidirect
318. C₂×C₈	C₂×D₄×C₁₉	semidirect
374. C₄	C₁₉×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#577	2
C₁₉×#3499	2
C₁₉×#3498	2
C₁₉×#3154	2
C₁₉×#3152	2
C₁₉×#3151	2
C₁₉×#3147	2
C₂×C₁₉×#492	2
C₄×C₁₉×#131	2
#60646	19

Subgroups — C19×#60646 #18066605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60646 #18066605