Subgroups — C₁₉×#3516 #14561373

Order 2432.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#556	C₂	1	3	yes	maximal, complemented
3	C₁₉×#554	C₂	1	3	yes	maximal, complemented
4	C₁₉×#553	C₂	1	3	yes	maximal, complemented
5	C₁₉×#552	C₂	1	3	yes	maximal, complemented
6	D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#542	C₂	1	3	yes	maximal, complemented
10	C₁₉×#541	C₂	1	3	yes	maximal, complemented
11	C₁₉×#529	C₂	1	3	yes	maximal, complemented
12	C₁₉×#529	C₂	1	3	yes	maximal, complemented
13	C₁₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
20	C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
21	C₁₉×#126	C₂²	1	6	yes	—
22	C₁₉×#126	C₂²	1	3	yes	—
23	C₁₉×#126	C₂²	1	3	yes	—
24	C₁₉×#126	C₂²	1	6	yes	—
25	C₁₉×#125	C₂²	1	3	yes	—
26	C₁₉×#125	C₂²	1	3	yes	—
27	C₁₉×#125	C₂²	1	6	yes	—
28	C₁₉×#125	C₂²	1	3	yes	—
29	C₁₉×#124	C₂²	1	3	yes	—
30	C₁₉×#124	C₂²	1	3	yes	—
31	C₁₉×#124	C₂²	1	3	yes	—
32	C₁₉×#123	C₂²	1	1	yes	characteristic
33	C₁₉×#123	C₂²	1	3	yes	—
34	C₁₉×#123	C₂²	1	6	yes	—
35	C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
36	C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
37	C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
38	C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
39	C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
40	C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
41	C₁₉×#121	C₂²	1	3	yes	—
42	C₁₉×#121	C₂²	1	3	yes	—
43	C₁₉×#121	C₂²	1	3	yes	—
44	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×Q₈×C₁₉	C₂²	1	3	yes	—
46	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×Q₈×C₁₉	C₂²	1	3	yes	—
48	C₄×Q₈×C₁₉	C₂²	1	3	yes	—
49	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×Q₈×C₁₉	C₂²	1	3	yes	—
51	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×Q₈×C₁₉	C₂²	1	3	yes	—
53	C₄×D₄×C₁₉	C₂²	1	3	yes	—
54	C₄×D₄×C₁₉	C₂²	1	3	yes	—
55	C₄×D₄×C₁₉	C₂²	1	3	yes	—
56	C₄×D₄×C₁₉	C₂²	1	3	yes	—
57	C₄×D₄×C₁₉	C₂²	1	3	yes	—
58	C₄×D₄×C₁₉	C₂²	1	6	yes	—
59	C₁₉×#117	C₂²	1	3	yes	—
60	C₁₉×#117	C₂²	1	3	yes	—
61	C₁₉×#117	C₂²	1	3	yes	—
62	C₁₉×#117	C₂²	1	6	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
65	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
66	#41×C₁₉	—	2	4	no	—
67	C₂×Q₈×C₁₉	—	2	4	no	—
68	C₂×Q₈×C₁₉	—	2	4	no	—
69	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
70	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
71	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
72	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×D₄×C₁₉	C₂³	1	3	yes	—
74	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×D₄×C₁₉	C₂³	1	3	yes	—
76	C₂×D₄×C₁₉	C₂³	1	3	yes	—
77	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
79	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
80	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
81	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
82	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
83	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
84	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
85	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
86	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
87	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
88	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
90	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
91	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
92	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
93	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
94	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
95	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
96	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
97	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
98	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
100	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
101	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
103	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
104	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
105	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
106	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
108	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
110	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
111	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
112	C₄²×C₁₉	C₂³	1	3	yes	—
113	C₄²×C₁₉	C₂³	1	3	yes	—
114	C₄²×C₁₉	C₂³	1	3	yes	—
115	C₄²×C₁₉	C₂³	1	3	yes	—
116	C₄²×C₁₉	C₂³	1	6	yes	—
117	C₄²×C₁₉	C₂³	1	3	yes	—
118	C₄²×C₁₉	C₂³	1	3	yes	—
119	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
120	C₂³×C₁₉	C₂⁴	1	3	yes	—
121	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
122	Q₈×C₁₉	—	2	6	no	—
123	Q₈×C₁₉	—	2	6	no	—
124	Q₈×C₁₉	—	4	3	no	—
125	Q₈×C₁₉	#41	1	4	yes	—
126	D₄×C₁₉	—	2	6	no	—
127	D₄×C₁₉	—	2	2	no	—
128	D₄×C₁₉	—	2	6	no	—
129	D₄×C₁₉	—	4	3	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	6	no	—
132	C₂×C₄×C₁₉	—	2	6	no	—
133	C₂×C₄×C₁₉	—	2	6	no	—
134	C₂×C₄×C₁₉	—	4	6	no	—
135	C₂×C₄×C₁₉	—	4	3	no	—
136	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
139	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
141	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
143	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
144	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
145	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
146	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
148	#3516	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂²×C₁₉	—	2	1	no	—
150	C₂²×C₁₉	—	2	1	no	—
151	C₂²×C₁₉	—	2	1	no	—
152	C₂²×C₁₉	—	2	3	no	—
153	C₂²×C₁₉	—	2	1	no	—
154	C₂²×C₁₉	—	2	3	no	—
155	C₂²×C₁₉	—	2	3	no	—
156	C₂²×C₁₉	—	2	1	no	—
157	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
158	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
159	C₄×C₁₉	—	2	1	no	—
160	C₄×C₁₉	—	2	3	no	—
161	C₄×C₁₉	—	2	3	no	—
162	C₄×C₁₉	—	2	1	no	—
163	C₄×C₁₉	—	2	1	no	—
164	C₄×C₁₉	—	2	3	no	—
165	C₄×C₁₉	—	2	1	no	—
166	C₄×C₁₉	—	2	3	no	—
167	C₄×C₁₉	—	2	3	no	—
168	C₄×C₁₉	—	2	3	no	—
169	C₄×C₁₉	—	2	1	no	—
170	C₄×C₁₉	C₂×#41	1	6	yes	—
171	#557	C₂×C₁₉	1	1	yes	characteristic, complemented
172	#556	C₂×C₁₉	1	3	yes	complemented
173	#554	C₂×C₁₉	1	3	yes	complemented
174	#553	C₂×C₁₉	1	3	yes	complemented
175	#552	C₂×C₁₉	1	3	yes	complemented
176	D₄×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#548	C₂×C₁₉	1	1	yes	characteristic, complemented
178	#548	C₂×C₁₉	1	1	yes	characteristic, complemented
179	#542	C₂×C₁₉	1	3	yes	complemented
180	#541	C₂×C₁₉	1	3	yes	complemented
181	#529	C₂×C₁₉	1	3	yes	complemented
182	#529	C₂×C₁₉	1	3	yes	complemented
183	#520	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#519	C₂×C₁₉	1	1	yes	characteristic, complemented
185	C₂×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂×C₁₉	—	2	2	no	—
187	C₂×C₁₉	—	4	1	no	—
188	C₂×C₁₉	—	4	3	no	—
189	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
190	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
191	C₂×C₁₉	#585	1	1	yes	characteristic
192	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
193	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
194	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
195	C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
196	C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
197	#126	C₂²×C₁₉	1	6	yes	—
198	#126	C₂²×C₁₉	1	3	yes	—
199	#126	C₂²×C₁₉	1	3	yes	—
200	#126	C₂²×C₁₉	1	6	yes	—
201	#125	C₂²×C₁₉	1	3	yes	—
202	#125	C₂²×C₁₉	1	3	yes	—
203	#125	C₂²×C₁₉	1	6	yes	—
204	#125	C₂²×C₁₉	1	3	yes	—
205	#124	C₂²×C₁₉	1	3	yes	—
206	#124	C₂²×C₁₉	1	3	yes	—
207	#124	C₂²×C₁₉	1	3	yes	—
208	#123	C₂²×C₁₉	1	1	yes	characteristic
209	#123	C₂²×C₁₉	1	3	yes	—
210	#123	C₂²×C₁₉	1	6	yes	—
211	C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
212	C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
213	C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
214	C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
215	C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
216	C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
217	#121	C₂²×C₁₉	1	3	yes	—
218	#121	C₂²×C₁₉	1	3	yes	—
219	#121	C₂²×C₁₉	1	3	yes	—
220	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₄×Q₈	C₂²×C₁₉	1	3	yes	—
222	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
223	C₄×Q₈	C₂²×C₁₉	1	3	yes	—
224	C₄×Q₈	C₂²×C₁₉	1	3	yes	—
225	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
226	C₄×Q₈	C₂²×C₁₉	1	3	yes	—
227	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
228	C₄×Q₈	C₂²×C₁₉	1	3	yes	—
229	C₄×D₄	C₂²×C₁₉	1	3	yes	—
230	C₄×D₄	C₂²×C₁₉	1	3	yes	—
231	C₄×D₄	C₂²×C₁₉	1	3	yes	—
232	C₄×D₄	C₂²×C₁₉	1	3	yes	—
233	C₄×D₄	C₂²×C₁₉	1	3	yes	—
234	C₄×D₄	C₂²×C₁₉	1	6	yes	—
235	#117	C₂²×C₁₉	1	3	yes	—
236	#117	C₂²×C₁₉	1	3	yes	—
237	#117	C₂²×C₁₉	1	3	yes	—
238	#117	C₂²×C₁₉	1	6	yes	—
239	C₂×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
240	C₂×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
241	C₂×C₄²	C₂²×C₁₉	1	3	yes	—
242	C₁₉	#3516	1	1	yes	characteristic, direct product factor, Sylow
243	#41	—	2	4	no	—
244	C₂×Q₈	—	2	4	no	—
245	C₂×Q₈	—	2	4	no	—
246	C₂×Q₈	C₂³×C₁₉	1	3	yes	—
247	C₂×Q₈	C₂³×C₁₉	1	3	yes	—
248	C₂×Q₈	C₂³×C₁₉	1	3	yes	—
249	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
250	C₂×D₄	C₂³×C₁₉	1	3	yes	—
251	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×D₄	C₂³×C₁₉	1	3	yes	—
253	C₂×D₄	C₂³×C₁₉	1	3	yes	—
254	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
255	C₂²×C₄	C₂³×C₁₉	1	3	yes	—
256	C₂²×C₄	C₂³×C₁₉	1	3	yes	—
257	C₂²×C₄	C₂³×C₁₉	1	3	yes	—
258	C₂²×C₄	C₂³×C₁₉	1	3	yes	—
259	C₂²×C₄	C₂³×C₁₉	1	6	yes	—
260	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
261	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
262	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
263	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
264	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
265	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
267	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
268	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
269	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
270	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
271	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
272	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
273	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
274	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
275	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
277	C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
278	C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
279	C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
280	C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
281	C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
282	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
283	C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
284	C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
285	C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
287	C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
288	C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
289	C₄²	C₂³×C₁₉	1	3	yes	—
290	C₄²	C₂³×C₁₉	1	3	yes	—
291	C₄²	C₂³×C₁₉	1	3	yes	—
292	C₄²	C₂³×C₁₉	1	3	yes	—
293	C₄²	C₂³×C₁₉	1	6	yes	—
294	C₄²	C₂³×C₁₉	1	3	yes	—
295	C₄²	C₂³×C₁₉	1	3	yes	—
296	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
297	C₂³	C₂⁴×C₁₉	1	3	yes	—
298	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
299	Q₈	—	2	6	no	—
300	Q₈	—	2	6	no	—
301	Q₈	—	4	3	no	—
302	Q₈	#41×C₁₉	1	4	yes	—
303	D₄	—	2	6	no	—
304	D₄	—	2	2	no	—
305	D₄	—	2	6	no	—
306	D₄	—	4	3	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	6	no	—
309	C₂×C₄	—	2	6	no	—
310	C₂×C₄	—	2	6	no	—
311	C₂×C₄	—	4	6	no	—
312	C₂×C₄	—	4	3	no	—
313	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
314	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
315	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
316	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
317	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
318	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
319	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
320	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
321	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
322	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
323	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	3	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	3	no	—
331	C₂²	—	2	3	no	—
332	C₂²	—	2	1	no	—
333	C₂²	C₁₉×2₋¹⁺⁴	1	2	yes	—
334	C₂²	C₂⁵×C₁₉	1	1	yes	characteristic
335	C₄	—	2	1	no	—
336	C₄	—	2	3	no	—
337	C₄	—	2	3	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	3	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	3	no	—
343	C₄	—	2	3	no	—
344	C₄	—	2	3	no	—
345	C₄	—	2	1	no	—
346	C₄	C₂×#41×C₁₉	1	6	yes	—
347	C₂	—	2	2	no	—
348	C₂	—	4	1	no	—
349	C₂	—	4	3	no	—
350	C₂	C₂²×#41×C₁₉	1	1	yes	characteristic
351	C₂	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
352	C₂	C₁₉×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#557	C₂	semidirect
2. C₁₉×#556	C₂	semidirect
3. C₁₉×#554	C₂	semidirect
4. C₁₉×#553	C₂	semidirect
5. C₁₉×#552	C₂	semidirect
6. D₄×Q₈×C₁₉	C₂	semidirect
7. C₁₉×#548	C₂	semidirect
8. C₁₉×#548	C₂	semidirect
9. C₁₉×#542	C₂	semidirect
10. C₁₉×#541	C₂	semidirect
11. C₁₉×#529	C₂	semidirect
12. C₁₉×#529	C₂	semidirect
13. C₁₉×#520	C₂	semidirect
14. C₁₉×#519	C₂	semidirect
15. C₂×C₄×Q₈×C₁₉	C₂	semidirect
148. #3516	C₁₉	direct (N × H)
171. #557	C₂×C₁₉	semidirect
172. #556	C₂×C₁₉	semidirect
173. #554	C₂×C₁₉	semidirect
174. #553	C₂×C₁₉	semidirect
175. #552	C₂×C₁₉	semidirect
176. D₄×Q₈	C₂×C₁₉	semidirect
177. #548	C₂×C₁₉	semidirect
178. #548	C₂×C₁₉	semidirect
179. #542	C₂×C₁₉	semidirect
180. #541	C₂×C₁₉	semidirect
181. #529	C₂×C₁₉	semidirect
182. #529	C₂×C₁₉	semidirect
183. #520	C₂×C₁₉	semidirect
184. #519	C₂×C₁₉	semidirect
185. C₂×C₄×Q₈	C₂×C₁₉	semidirect
242. C₁₉	#3516	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×#557	2
C₁₉×#556	2
C₁₉×#554	2
C₁₉×#553	2
C₁₉×#552	2
D₄×Q₈×C₁₉	2
C₁₉×#548	2
C₁₉×#542	2
C₁₉×#541	2
C₁₉×#529	2
C₁₉×#520	2
C₁₉×#519	2
C₂×C₄×Q₈×C₁₉	2
#3516	19

Subgroups — C19×#3516 #14561373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3516 #14561373