Subgroups — C₁₉×#21345 #18027304

Order 4864.

746 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1984	C₂	1	2	yes	maximal
3	C₁₉×#1939	C₂	1	2	yes	maximal
4	C₁₉×#1917	C₂	1	4	yes	maximal
5	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1767	C₂	1	2	yes	maximal
7	C₁₉×#1745	C₂	1	2	yes	maximal
8	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₉×#97	C₂²	1	2	yes	—
15	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#97	C₂²	1	2	yes	—
17	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
19	C₄×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
20	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₄³×C₁₉	C₂²	1	1	yes	characteristic
26	C₄³×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#336	C₂²	1	2	yes	—
28	C₁₉×#336	C₂²	1	4	yes	—
29	C₁₉×#336	C₂²	1	4	yes	—
30	C₁₉×#336	C₂²	1	4	yes	—
31	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
33	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
35	C₄×Q₈×C₁₉	—	2	4	no	—
36	C₄×Q₈×C₁₉	—	2	4	no	—
37	C₄×Q₈×C₁₉	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×C₄⋊C₈	—	2	8	no	—
58	C₁₉×C₄⋊C₈	—	2	4	no	—
59	C₁₉×#97	—	2	4	no	—
60	C₁₉×#97	—	2	2	no	—
61	C₁₉×#97	—	2	4	no	—
62	C₁₉×#97	Q₈	1	4	yes	complemented
63	C₄×C₈×C₁₉	—	2	4	no	—
64	C₁₉×#95	C₂×C₄	1	2	yes	—
65	C₁₉×#95	C₂×C₄	1	2	yes	—
66	C₁₉×#95	C₂×C₄	1	2	yes	—
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	2	2	no	—
69	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
70	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₁₉	—	2	2	no	—
82	C₂×C₈×C₁₉	—	2	2	no	—
83	C₂×C₈×C₁₉	—	2	2	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	2	4	no	—
86	C₂×C₈×C₁₉	—	2	4	no	—
87	C₂×C₈×C₁₉	—	2	4	no	—
88	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
89	C₂×C₈×C₁₉	#41	1	4	yes	—
90	C₄⋊C₄×C₁₉	—	2	4	no	—
91	C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₄⋊C₄×C₁₉	—	2	4	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	M₁₆	1	4	yes	—
96	C₄²×C₁₉	—	2	4	no	—
97	C₄²×C₁₉	—	2	4	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	—	2	2	no	—
100	C₄²×C₁₉	—	2	4	no	—
101	C₄²×C₁₉	—	2	2	no	—
102	C₄²×C₁₉	—	2	4	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	4	2	no	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	2	no	—
107	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
108	C₄²×C₁₉	#41	1	4	yes	—
109	C₄²×C₁₉	#41	1	2	yes	—
110	#21345	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
112	Q₈×C₁₉	—	2	8	no	—
113	C₂×C₄×C₁₉	—	2	2	no	—
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	#117	1	2	yes	—
136	C₂×C₄×C₁₉	#117	1	2	yes	—
137	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
138	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
139	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
140	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
141	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
142	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
143	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
146	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
147	C₈×C₁₉	—	2	4	no	—
148	C₈×C₁₉	—	2	4	no	—
149	C₈×C₁₉	—	4	4	no	—
150	C₄²×Q₈	C₂×C₁₉	1	1	yes	characteristic
151	#1984	C₂×C₁₉	1	2	yes	—
152	#1939	C₂×C₁₉	1	2	yes	—
153	#1917	C₂×C₁₉	1	4	yes	—
154	#1767	C₂×C₁₉	1	1	yes	characteristic
155	#1767	C₂×C₁₉	1	2	yes	—
156	#1745	C₂×C₁₉	1	2	yes	—
157	C₄×#97	C₂×C₁₉	1	1	yes	characteristic
158	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
159	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
160	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
161	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
162	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
163	C₂²×C₁₉	#568	1	1	yes	characteristic
164	C₂²×C₁₉	#568	1	1	yes	characteristic
165	C₄×C₁₉	—	2	4	no	—
166	C₄×C₁₉	—	2	2	no	—
167	C₄×C₁₉	—	2	2	no	—
168	C₄×C₁₉	—	2	2	no	—
169	C₄×C₁₉	—	2	4	no	—
170	C₄×C₁₉	—	4	2	no	—
171	C₄×C₁₉	—	4	1	no	—
172	C₄×C₁₉	—	4	1	no	—
173	C₄×C₁₉	—	4	2	no	—
174	C₄×C₁₉	#432	1	4	yes	—
175	C₄×C₁₉	#529	1	2	yes	—
176	C₄×C₁₉	#533	1	2	yes	—
177	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
179	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
180	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
181	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
182	C₂×#97	C₂²×C₁₉	1	2	yes	—
183	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
184	C₂×#97	C₂²×C₁₉	1	2	yes	—
185	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
187	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
188	C₄×C₄⋊C₄	C₄×C₁₉	1	2	yes	—
189	C₄×C₄⋊C₄	C₄×C₁₉	1	2	yes	—
190	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
191	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
192	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
193	C₄³	C₂²×C₁₉	1	1	yes	characteristic
194	C₄³	C₂²×C₁₉	1	2	yes	—
195	#336	C₂²×C₁₉	1	2	yes	—
196	#336	C₂²×C₁₉	1	4	yes	—
197	#336	C₂²×C₁₉	1	4	yes	—
198	#336	C₂²×C₁₉	1	4	yes	—
199	C₂×C₁₉	#2295	1	1	yes	characteristic
200	C₂×C₁₉	C₂×#432	1	1	yes	characteristic
201	C₂×C₁₉	#2923	1	1	yes	characteristic
202	C₂×C₁₉	Q₈×M₁₆	1	1	yes	characteristic
203	C₂×C₁₉	Q₈×M₁₆	1	1	yes	characteristic
204	C₂×C₁₉	#2970	1	1	yes	characteristic
205	C₂×C₁₉	#2971	1	1	yes	characteristic
206	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
208	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
209	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
210	C₄×Q₈	—	2	4	no	—
211	C₄×Q₈	—	2	4	no	—
212	C₄×Q₈	—	2	4	no	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
227	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
228	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
230	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
232	C₄⋊C₈	—	2	8	no	—
233	C₄⋊C₈	—	2	4	no	—
234	#97	—	2	4	no	—
235	#97	—	2	2	no	—
236	#97	—	2	4	no	—
237	#97	Q₈×C₁₉	1	4	yes	complemented
238	C₄×C₈	—	2	4	no	—
239	#95	C₂×C₄×C₁₉	1	2	yes	—
240	#95	C₂×C₄×C₁₉	1	2	yes	—
241	#95	C₂×C₄×C₁₉	1	2	yes	—
242	C₁₉	#21345	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	2	2	no	—
245	C₂×Q₈	M₁₆×C₁₉	1	4	yes	—
246	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
256	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
265	C₂×C₈	#41×C₁₉	1	4	yes	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	M₁₆×C₁₉	1	4	yes	—
272	C₄²	—	2	4	no	—
273	C₄²	—	2	4	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	4	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	4	1	no	—
280	C₄²	—	4	2	no	—
281	C₄²	—	4	1	no	—
282	C₄²	—	4	2	no	—
283	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
284	C₄²	#41×C₁₉	1	4	yes	—
285	C₄²	#41×C₁₉	1	2	yes	—
286	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
287	Q₈	—	2	8	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	C₁₉×#117	1	2	yes	—
311	C₂×C₄	C₁₉×#117	1	2	yes	—
312	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
313	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
314	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
315	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
316	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
317	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
318	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
319	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
321	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
322	C₈	—	2	4	no	—
323	C₈	—	2	4	no	—
324	C₈	—	4	4	no	—
325	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
326	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
327	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
328	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
329	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
330	C₂²	C₁₉×#568	1	1	yes	characteristic
331	C₂²	C₁₉×#568	1	1	yes	characteristic
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	2	no	—
336	C₄	—	2	4	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	1	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	2	no	—
341	C₄	C₁₉×#432	1	4	yes	—
342	C₄	C₁₉×#529	1	2	yes	—
343	C₄	C₁₉×#533	1	2	yes	—
344	C₂	C₁₉×#2295	1	1	yes	characteristic
345	C₂	C₂×C₁₉×#432	1	1	yes	characteristic
346	C₂	C₁₉×#2923	1	1	yes	characteristic
347	C₂	Q₈×M₁₆×C₁₉	1	1	yes	characteristic
348	C₂	Q₈×M₁₆×C₁₉	1	1	yes	characteristic
349	C₂	C₁₉×#2970	1	1	yes	characteristic
350	C₂	C₁₉×#2971	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle, prime radical	C₂³×C₁₉	C₂³×C₄
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
62. C₁₉×#97	Q₈	semidirect
110. #21345	C₁₉	direct (N × H)
237. #97	Q₈×C₁₉	semidirect
242. C₁₉	#21345	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×Q₈×C₁₉	2
C₁₉×#1984	2
C₁₉×#1939	2
C₁₉×#1917	2
C₁₉×#1767	2
C₁₉×#1745	2
C₄×C₁₉×#97	2
#21345	19

Subgroups — C19×#21345 #18027304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21345 #18027304