Subgroups — C₁₉×#34958 #18040917

Order 4864.

2226 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2608	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2607	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2569	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2549	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2437	C₂	1	4	yes	maximal
6	C₁₉×#2396	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₉×C₂²⋊Q₈	C₂	1	8	yes	maximal, complemented
8	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
13	C₂×C₁₉×#117	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
16	C₁₉×#400	C₂²	1	4	yes	complemented
17	C₁₉×#399	C₂²	1	4	yes	—
18	C₁₉×#398	C₂²	1	8	yes	complemented
19	C₁₉×#396	C₂²	1	8	yes	—
20	C₁₉×#395	C₂²	1	4	yes	complemented
21	C₁₉×#393	C₂²	1	4	yes	—
22	C₁₉×#391	C₂²	1	8	yes	complemented
23	C₁₉×#389	C₂²	1	8	yes	complemented
24	C₁₉×#387	C₂²	1	8	yes	complemented
25	C₁₉×#387	C₂²	1	8	yes	complemented
26	C₁₉×#385	C₂²	1	8	yes	—
27	C₁₉×#385	C₂²	1	8	yes	—
28	C₁₉×#381	C₂²	1	1	yes	characteristic
29	C₁₉×#381	C₂²	1	1	yes	characteristic
30	C₁₉×#380	C₂²	1	8	yes	—
31	C₁₉×#380	C₂²	1	4	yes	—
32	C₁₉×#379	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	complemented
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
35	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
37	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
41	C₂×C₁₉×#95	C₂²	1	4	yes	—
42	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₉	—	4	4	no	—
45	C₂³×C₄×C₁₉	Q₈	1	8	yes	complemented
46	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×C₂²⋊Q₈	—	2	32	no	—
52	C₄×Q₈×C₁₉	—	4	8	no	—
53	C₁₉×#117	—	4	4	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
64	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₄²×C₁₉	—	4	8	no	—
68	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
72	C₁₉×#95	C₂³	1	8	yes	—
73	C₁₉×#95	C₂³	1	4	yes	—
74	C₁₉×#95	C₂³	1	4	yes	—
75	C₁₉×#95	C₂³	1	4	yes	—
76	C₁₉×#95	C₂³	1	4	yes	—
77	C₁₉×#95	C₂³	1	4	yes	—
78	C₁₉×#95	C₂³	1	8	yes	—
79	C₁₉×#95	C₂³	1	8	yes	—
80	C₁₉×#95	C₂³	1	4	yes	—
81	C₂⁴×C₁₉	—	2	8	no	—
82	C₂⁴×C₁₉	—	4	2	no	—
83	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
84	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
85	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
86	C₂×Q₈×C₁₉	—	2	16	no	—
87	C₂×Q₈×C₁₉	—	4	4	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	16	no	—
91	C₂²×C₄×C₁₉	—	2	16	no	—
92	C₂²×C₄×C₁₉	—	4	16	no	—
93	C₂²×C₄×C₁₉	—	4	8	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	4	no	—
96	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
98	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
101	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₄⋊C₄×C₁₉	—	2	16	no	—
108	C₄⋊C₄×C₁₉	—	2	16	no	—
109	C₄⋊C₄×C₁₉	—	2	16	no	—
110	C₄⋊C₄×C₁₉	—	4	4	no	—
111	C₄⋊C₄×C₁₉	—	4	8	no	—
112	C₄⋊C₄×C₁₉	—	4	4	no	—
113	C₂²⋊C₄×C₁₉	—	2	8	no	—
114	C₂²⋊C₄×C₁₉	—	2	16	no	—
115	C₂²⋊C₄×C₁₉	—	2	16	no	—
116	C₂²⋊C₄×C₁₉	—	4	2	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	#41	1	16	yes	—
119	C₄²×C₁₉	—	2	16	no	—
120	C₄²×C₁₉	—	2	8	no	—
121	C₄²×C₁₉	—	4	4	no	—
122	C₄²×C₁₉	—	4	4	no	—
123	#34958	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₁₉	—	2	4	no	—
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	2	16	no	—
127	C₂³×C₁₉	—	2	4	no	—
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	—	4	4	no	—
130	C₂³×C₁₉	—	4	16	no	—
131	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
132	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
133	C₂³×C₁₉	C₂×#41	1	8	yes	—
134	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
135	Q₈×C₁₉	—	4	16	no	—
136	C₂×C₄×C₁₉	—	2	8	no	—
137	C₂×C₄×C₁₉	—	2	8	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	16	no	—
141	C₂×C₄×C₁₉	—	2	8	no	—
142	C₂×C₄×C₁₉	—	2	8	no	—
143	C₂×C₄×C₁₉	—	2	8	no	—
144	C₂×C₄×C₁₉	—	2	8	no	—
145	C₂×C₄×C₁₉	—	2	8	no	—
146	C₂×C₄×C₁₉	—	2	8	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	4	8	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	4	32	no	—
152	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
153	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
154	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
155	C₂×C₄×C₁₉	C₂×#41	1	16	yes	—
156	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
157	#2608	C₂×C₁₉	1	2	yes	complemented
158	#2607	C₂×C₁₉	1	2	yes	complemented
159	#2569	C₂×C₁₉	1	4	yes	complemented
160	#2549	C₂×C₁₉	1	4	yes	complemented
161	#2437	C₂×C₁₉	1	4	yes	—
162	#2396	C₂×C₁₉	1	4	yes	complemented
163	C₄×C₂²⋊Q₈	C₂×C₁₉	1	8	yes	complemented
164	#2280	C₂×C₁₉	1	1	yes	characteristic
165	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	2	yes	—
166	C₂²×C₁₉	—	2	4	no	—
167	C₂²×C₁₉	—	2	4	no	—
168	C₂²×C₁₉	—	2	16	no	—
169	C₂²×C₁₉	—	2	4	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	4	16	no	—
172	C₂²×C₁₉	—	4	4	no	—
173	C₂²×C₁₉	#533	1	8	yes	—
174	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
175	C₂²×C₁₉	C₂²×#41	1	4	yes	—
176	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
177	C₄×C₁₉	—	2	4	no	—
178	C₄×C₁₉	—	2	2	no	—
179	C₄×C₁₉	—	2	16	no	—
180	C₄×C₁₉	—	4	4	no	—
181	C₄×C₁₉	—	4	8	no	—
182	C₄×C₁₉	—	4	4	no	—
183	C₄×C₁₉	#543	1	4	yes	—
184	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
185	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	—
186	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
187	C₂×#117	C₂²×C₁₉	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
189	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
190	#400	C₂²×C₁₉	1	4	yes	complemented
191	#399	C₂²×C₁₉	1	4	yes	—
192	#398	C₂²×C₁₉	1	8	yes	complemented
193	#396	C₂²×C₁₉	1	8	yes	—
194	#395	C₂²×C₁₉	1	4	yes	complemented
195	#393	C₂²×C₁₉	1	4	yes	—
196	#391	C₂²×C₁₉	1	8	yes	complemented
197	#389	C₂²×C₁₉	1	8	yes	complemented
198	#387	C₂²×C₁₉	1	8	yes	complemented
199	#387	C₂²×C₁₉	1	8	yes	complemented
200	#385	C₂²×C₁₉	1	8	yes	—
201	#385	C₂²×C₁₉	1	8	yes	—
202	#381	C₂²×C₁₉	1	1	yes	characteristic
203	#381	C₂²×C₁₉	1	1	yes	characteristic
204	#380	C₂²×C₁₉	1	8	yes	—
205	#380	C₂²×C₁₉	1	4	yes	—
206	#379	C₂²×C₁₉	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
208	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
209	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
210	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
211	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
212	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
214	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
215	C₂×#95	C₂²×C₁₉	1	4	yes	—
216	C₂×C₁₉	—	2	8	no	—
217	C₂×C₁₉	—	4	2	no	—
218	C₂×C₁₉	C₂×#533	1	2	yes	—
219	C₂×C₁₉	C₂×#543	1	1	yes	characteristic
220	C₂×C₁₉	#3481	1	4	yes	—
221	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
222	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
223	C₂³×C₄	—	4	4	no	—
224	C₂³×C₄	Q₈×C₁₉	1	8	yes	complemented
225	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
226	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
228	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
229	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
230	C₂²⋊Q₈	—	2	32	no	—
231	C₄×Q₈	—	4	8	no	—
232	#117	—	4	4	no	—
233	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
234	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
239	C₂×C₂²⋊C₄	—	2	16	no	—
240	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
241	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
246	C₂×C₄²	—	4	8	no	—
247	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
248	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
249	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
250	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
251	#95	C₂³×C₁₉	1	8	yes	—
252	#95	C₂³×C₁₉	1	4	yes	—
253	#95	C₂³×C₁₉	1	4	yes	—
254	#95	C₂³×C₁₉	1	4	yes	—
255	#95	C₂³×C₁₉	1	4	yes	—
256	#95	C₂³×C₁₉	1	4	yes	—
257	#95	C₂³×C₁₉	1	8	yes	—
258	#95	C₂³×C₁₉	1	8	yes	—
259	#95	C₂³×C₁₉	1	4	yes	—
260	C₁₉	#34958	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	—	2	8	no	—
262	C₂⁴	—	4	2	no	—
263	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
264	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
265	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
266	C₂×Q₈	—	2	16	no	—
267	C₂×Q₈	—	4	4	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	16	no	—
272	C₂²×C₄	—	4	16	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
277	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
278	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
279	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
280	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
281	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
282	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
283	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
286	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	4	8	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	2	8	no	—
294	C₂²⋊C₄	—	2	16	no	—
295	C₂²⋊C₄	—	2	16	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	#41×C₁₉	1	16	yes	—
299	C₄²	—	2	16	no	—
300	C₄²	—	2	8	no	—
301	C₄²	—	4	4	no	—
302	C₄²	—	4	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	16	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	16	no	—
310	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
311	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
312	C₂³	C₂×#41×C₁₉	1	8	yes	—
313	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
314	Q₈	—	4	16	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	16	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	32	no	—
331	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
332	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
333	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
334	C₂×C₄	C₂×#41×C₁₉	1	16	yes	—
335	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	2	16	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	4	16	no	—
342	C₂²	—	4	4	no	—
343	C₂²	C₁₉×#533	1	8	yes	—
344	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
345	C₂²	C₂²×#41×C₁₉	1	4	yes	—
346	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
347	C₄	—	2	4	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	16	no	—
350	C₄	—	4	8	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	4	no	—
353	C₄	C₁₉×#543	1	4	yes	—
354	C₂	—	2	8	no	—
355	C₂	—	4	2	no	—
356	C₂	C₂×C₁₉×#533	1	2	yes	—
357	C₂	C₂×C₁₉×#543	1	1	yes	characteristic
358	C₂	C₁₉×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2608	C₂	semidirect
2. C₁₉×#2607	C₂	semidirect
3. C₁₉×#2569	C₂	semidirect
4. C₁₉×#2549	C₂	semidirect
6. C₁₉×#2396	C₂	semidirect
7. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
12. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
16. C₁₉×#400	C₂²	semidirect
18. C₁₉×#398	C₂²	semidirect
20. C₁₉×#395	C₂²	semidirect
22. C₁₉×#391	C₂²	semidirect
23. C₁₉×#389	C₂²	semidirect
24. C₁₉×#387	C₂²	semidirect
25. C₁₉×#387	C₂²	semidirect
33. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
34. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
45. C₂³×C₄×C₁₉	Q₈	semidirect
123. #34958	C₁₉	direct (N × H)
157. #2608	C₂×C₁₉	semidirect
158. #2607	C₂×C₁₉	semidirect
159. #2569	C₂×C₁₉	semidirect
160. #2549	C₂×C₁₉	semidirect
162. #2396	C₂×C₁₉	semidirect
163. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
186. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
190. #400	C₂²×C₁₉	semidirect
192. #398	C₂²×C₁₉	semidirect
194. #395	C₂²×C₁₉	semidirect
196. #391	C₂²×C₁₉	semidirect
197. #389	C₂²×C₁₉	semidirect
198. #387	C₂²×C₁₉	semidirect
199. #387	C₂²×C₁₉	semidirect
207. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
208. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
224. C₂³×C₄	Q₈×C₁₉	semidirect
260. C₁₉	#34958	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2608	2
C₁₉×#2607	2
C₁₉×#2569	2
C₁₉×#2549	2
C₁₉×#2437	2
C₁₉×#2396	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2280	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#34958	19

Subgroups — C19×#34958 #18040917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34958 #18040917