Subgroups — C₁₉×#34209 #18040168

Order 4864.

2854 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#519	C₂	1	2	yes	maximal
3	C₁₉×#2365	C₂	1	8	yes	maximal, complemented
4	C₁₉×#2344	C₂	1	8	yes	maximal
5	C₁₉×#2327	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2310	C₂	1	2	yes	maximal
7	C₄×C₁₉×C₄⋊Q₈	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×C₄⋊Q₈	C₄	1	16	yes	complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	4	yes	—
15	C₁₉×#519	—	2	16	no	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	8	yes	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	8	yes	—
18	C₂×C₁₉×#117	C₂²	1	2	yes	—
19	C₂×C₁₉×#117	C₂²	1	8	yes	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#391	C₂²	1	8	yes	—
25	C₁₉×#391	C₂²	1	8	yes	—
26	C₁₉×#389	C₂²	1	16	yes	—
27	C₁₉×#387	C₂²	1	32	yes	—
28	C₁₉×#384	C₂²	1	2	yes	—
29	C₁₉×#382	C₂²	1	2	yes	—
30	C₁₉×#381	C₂²	1	8	yes	—
31	C₁₉×#380	C₂²	1	4	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	16	yes	—
35	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
36	C₁₉×#376	C₂²	1	2	yes	—
37	C₄³×C₁₉	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₉	—	2	8	no	—
39	C₂²×Q₈×C₁₉	—	2	8	no	—
40	C₂²×Q₈×C₁₉	C₂×C₄	1	16	yes	—
41	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	32	yes	—
49	C₄×Q₈×C₁₉	—	2	32	no	—
50	C₄×Q₈×C₁₉	—	2	32	no	—
51	C₁₉×#117	—	2	8	no	—
52	C₁₉×#117	—	2	4	no	—
53	C₁₉×#117	—	2	32	no	—
54	C₁₉×#117	D₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	32	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
75	C₁₉×#95	C₂³	1	8	yes	—
76	C₁₉×#95	C₂³	1	8	yes	—
77	C₁₉×#95	C₂³	1	32	yes	—
78	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	64	no	—
80	C₂×Q₈×C₁₉	—	2	8	no	—
81	C₂×Q₈×C₁₉	—	2	8	no	—
82	C₂×Q₈×C₁₉	—	2	8	no	—
83	C₂×Q₈×C₁₉	—	2	8	no	—
84	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
85	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
86	C₂²×C₄×C₁₉	—	2	8	no	—
87	C₂²×C₄×C₁₉	—	2	8	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₉	#41	1	4	yes	—
94	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
97	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
102	C₄⋊C₄×C₁₉	—	2	32	no	—
103	C₄⋊C₄×C₁₉	—	2	8	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	16	no	—
106	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
107	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
108	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
109	C₂²⋊C₄×C₁₉	—	2	8	no	—
110	C₂²⋊C₄×C₁₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
112	C₄²×C₁₉	—	2	32	no	—
113	C₄²×C₁₉	—	2	8	no	—
114	C₄²×C₁₉	—	2	4	no	—
115	C₄²×C₁₉	—	2	16	no	—
116	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
117	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
118	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
119	C₄²×C₁₉	C₂×D₄	1	8	yes	—
120	#34209	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
123	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
124	C₂³×C₁₉	C₂×#41	1	2	yes	—
125	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
126	Q₈×C₁₉	—	2	32	no	—
127	Q₈×C₁₉	—	2	32	no	—
128	C₂×C₄×C₁₉	—	2	32	no	—
129	C₂×C₄×C₁₉	—	2	8	no	—
130	C₂×C₄×C₁₉	—	2	8	no	—
131	C₂×C₄×C₁₉	—	2	8	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	16	no	—
134	C₂×C₄×C₁₉	—	2	8	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	8	no	—
137	C₂×C₄×C₁₉	—	2	16	no	—
138	C₂×C₄×C₁₉	C₄×D₄	1	16	yes	—
139	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
140	C₂×C₄×C₁₉	C₂³×C₄	1	16	yes	—
141	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
143	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
145	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
146	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
147	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
148	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
149	C₂×C₄×C₁₉	2₋¹⁺⁴	1	8	yes	—
150	C₂²×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
151	C₂×#519	C₂×C₁₉	1	2	yes	—
152	#2365	C₂×C₁₉	1	8	yes	complemented
153	#2344	C₂×C₁₉	1	8	yes	—
154	#2327	C₂×C₁₉	1	4	yes	complemented
155	#2310	C₂×C₁₉	1	2	yes	—
156	C₄×C₄⋊Q₈	C₂×C₁₉	1	4	yes	complemented
157	#2285	C₂×C₁₉	1	1	yes	characteristic
158	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
159	C₂²×C₁₉	—	2	4	no	—
160	C₂²×C₁₉	—	2	4	no	—
161	C₂²×C₁₉	—	2	4	no	—
162	C₂²×C₁₉	C₂×C₄×D₄	1	4	yes	—
163	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
164	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
165	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
166	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	4	yes	—
167	C₄×C₁₉	—	2	16	no	—
168	C₄×C₁₉	—	2	4	no	—
169	C₄×C₁₉	—	2	8	no	—
170	C₄×C₁₉	—	4	8	no	—
171	C₄×C₁₉	—	4	4	no	—
172	C₄×C₁₉	C₂×C₄×D₄	1	4	yes	—
173	C₄×C₁₉	C₂×C₄×D₄	1	4	yes	—
174	C₄×C₁₉	#519	1	8	yes	complemented
175	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
176	C₂×C₄⋊Q₈	C₄×C₁₉	1	16	yes	complemented
177	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
178	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
179	C₂×C₄⋊Q₈	C₂²×C₁₉	1	4	yes	—
180	#519	—	2	16	no	—
181	C₂×C₄×Q₈	C₂²×C₁₉	1	8	yes	—
182	C₂×C₄×Q₈	C₂²×C₁₉	1	8	yes	—
183	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
184	C₂×#117	C₂²×C₁₉	1	2	yes	—
185	C₂×#117	C₂²×C₁₉	1	8	yes	—
186	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
187	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
188	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
189	#391	C₂²×C₁₉	1	8	yes	—
190	#391	C₂²×C₁₉	1	8	yes	—
191	#389	C₂²×C₁₉	1	16	yes	—
192	#387	C₂²×C₁₉	1	32	yes	—
193	#384	C₂²×C₁₉	1	2	yes	—
194	#382	C₂²×C₁₉	1	2	yes	—
195	#381	C₂²×C₁₉	1	8	yes	—
196	#380	C₂²×C₁₉	1	4	yes	—
197	C₄×C₄⋊C₄	C₂²×C₁₉	1	16	yes	—
198	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
199	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
200	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
201	#376	C₂²×C₁₉	1	2	yes	—
202	C₄³	C₂²×C₁₉	1	2	yes	—
203	C₂×C₁₉	—	2	4	no	—
204	C₂×C₁₉	C₂²×C₄×D₄	1	1	yes	characteristic
205	C₂×C₁₉	C₂×#519	1	2	yes	—
206	C₂×C₁₉	#3499	1	2	yes	—
207	C₂×C₁₉	#3509	1	2	yes	—
208	C₂²×Q₈	—	2	8	no	—
209	C₂²×Q₈	—	2	8	no	—
210	C₂²×Q₈	C₂×C₄×C₁₉	1	16	yes	—
211	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
212	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
213	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
214	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
215	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
216	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
217	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
218	C₄⋊Q₈	C₂×C₄×C₁₉	1	32	yes	—
219	C₄×Q₈	—	2	32	no	—
220	C₄×Q₈	—	2	32	no	—
221	#117	—	2	8	no	—
222	#117	—	2	4	no	—
223	#117	—	2	32	no	—
224	#117	D₄×C₁₉	1	8	yes	—
225	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	32	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
228	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
231	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
232	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
236	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
237	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
238	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
239	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
240	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
241	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
244	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
245	#95	C₂³×C₁₉	1	8	yes	—
246	#95	C₂³×C₁₉	1	8	yes	—
247	#95	C₂³×C₁₉	1	32	yes	—
248	C₁₉	#34209	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
250	C₂×Q₈	—	2	64	no	—
251	C₂×Q₈	—	2	8	no	—
252	C₂×Q₈	—	2	8	no	—
253	C₂×Q₈	—	2	8	no	—
254	C₂×Q₈	—	2	8	no	—
255	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
256	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
264	C₂²×C₄	#41×C₁₉	1	4	yes	—
265	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
266	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
267	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
273	C₄⋊C₄	—	2	32	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
278	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
279	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
280	C₂²⋊C₄	—	2	8	no	—
281	C₂²⋊C₄	—	2	4	no	—
282	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
283	C₄²	—	2	32	no	—
284	C₄²	—	2	8	no	—
285	C₄²	—	2	4	no	—
286	C₄²	—	2	16	no	—
287	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
288	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
289	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
290	C₄²	C₂×D₄×C₁₉	1	8	yes	—
291	C₂³	—	2	4	no	—
292	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
293	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
294	C₂³	C₂×#41×C₁₉	1	2	yes	—
295	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
296	Q₈	—	2	32	no	—
297	Q₈	—	2	32	no	—
298	C₂×C₄	—	2	32	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	16	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	16	no	—
308	C₂×C₄	C₄×D₄×C₁₉	1	16	yes	—
309	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
310	C₂×C₄	C₂³×C₄×C₁₉	1	16	yes	—
311	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
312	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
313	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
314	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
315	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
316	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
317	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
318	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
319	C₂×C₄	C₁₉×2₋¹⁺⁴	1	8	yes	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	4	no	—
323	C₂²	C₂×C₄×D₄×C₁₉	1	4	yes	—
324	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
325	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
326	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
327	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	4	yes	—
328	C₄	—	2	4	no	—
329	C₄	—	2	8	no	—
330	C₄	—	2	16	no	—
331	C₄	—	4	8	no	—
332	C₄	—	4	4	no	—
333	C₄	C₂×C₄×D₄×C₁₉	1	4	yes	—
334	C₄	C₂×C₄×D₄×C₁₉	1	4	yes	—
335	C₄	C₁₉×#519	1	8	yes	complemented
336	C₂	—	2	4	no	—
337	C₂	C₂²×C₄×D₄×C₁₉	1	1	yes	characteristic
338	C₂	C₂×C₁₉×#519	1	2	yes	—
339	C₂	C₁₉×#3499	1	2	yes	—
340	C₂	C₁₉×#3509	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2365	C₂	semidirect
5. C₁₉×#2327	C₂	semidirect
7. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
11. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
120. #34209	C₁₉	direct (N × H)
152. #2365	C₂×C₁₉	semidirect
154. #2327	C₂×C₁₉	semidirect
156. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
174. C₄×C₁₉	#519	semidirect
176. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
248. C₁₉	#34209	direct (N × H)
335. C₄	C₁₉×#519	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₄⋊Q₈	2
C₂×C₁₉×#519	2
C₁₉×#2365	2
C₁₉×#2344	2
C₁₉×#2327	2
C₁₉×#2310	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2285	2
C₄×C₁₉×#117	2
#34209	19

Subgroups — C19×#34209 #18040168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34209 #18040168