Subgroups — #18087764

Order 4864.

1670 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926299	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	—	2	8	no	—
6	C₂³×C₁₉⋊C₈	—	2	2	no	—
7	C₂³×C₁₉⋊C₈	—	2	2	no	—
8	C₂³×C₁₉⋊C₈	C₄	1	4	yes	complemented
9	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
10	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
13	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	4	yes	complemented
14	#11926299	—	2	8	no	—
15	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
18	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
19	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₁₉×#95	C₄	1	2	yes	—
21	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	4	no	—
23	C₂³×C₄×C₁₉	—	2	4	no	—
24	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₉	D₄	1	2	yes	—
29	C₂³×C₄×C₁₉	D₄	1	2	yes	—
30	C₂³×C₄×C₁₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂×C₂²⋊C₄×C₁₉	C₈	1	8	yes	complemented
36	C₂×C₄²×C₁₉	—	2	4	no	—
37	C₂×C₄²×C₁₉	—	2	2	no	—
38	C₂×C₄²×C₁₉	—	2	2	no	—
39	C₂×C₄²×C₁₉	—	2	4	no	—
40	C₂²×C₁₉⋊C₈	—	2	16	no	—
41	C₂²×C₁₉⋊C₈	—	2	16	no	—
42	C₂²×C₁₉⋊C₈	—	2	8	no	—
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₂²×C₁₉⋊C₈	—	2	4	no	—
45	C₂²×C₁₉⋊C₈	—	2	2	no	—
46	C₂²×C₁₉⋊C₈	—	2	16	no	—
47	C₂²×C₁₉⋊C₈	—	2	4	no	—
48	C₂²×C₁₉⋊C₈	—	2	2	no	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	4	no	—
51	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
52	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
53	C₂²×C₁₉⋊C₈	D₄	1	8	yes	—
54	C₁₉×#95	—	2	4	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
56	C₂⁴×C₁₉	—	2	4	no	—
57	C₂⁴×C₁₉	—	2	4	no	—
58	C₂⁴×C₁₉	C₄²	1	2	yes	—
59	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
61	C₂⁴×C₁₉	C₂×C₈	1	4	yes	—
62	C₂⁴×C₁₉	M₁₆	1	4	yes	—
63	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	2	4	no	—
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	2	8	no	—
68	C₂²×C₄×C₁₉	—	2	4	no	—
69	C₂²×C₄×C₁₉	—	2	4	no	—
70	C₂²×C₄×C₁₉	—	2	8	no	—
71	C₂²×C₄×C₁₉	—	2	8	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	4	no	—
74	C₂²×C₄×C₁₉	—	2	4	no	—
75	C₂²×C₄×C₁₉	—	2	8	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	8	no	—
78	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂×C₈	1	8	yes	complemented
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	4	yes	—
94	C₂²⋊C₄×C₁₉	—	2	16	no	—
95	C₄²×C₁₉	—	4	2	no	—
96	C₄²×C₁₉	—	4	4	no	—
97	C₄²×C₁₉	—	4	2	no	—
98	C₂×C₁₉⋊C₈	—	2	32	no	—
99	C₂×C₁₉⋊C₈	—	2	4	no	—
100	C₂×C₁₉⋊C₈	—	2	4	no	—
101	C₂×C₁₉⋊C₈	—	2	8	no	—
102	C₂×C₁₉⋊C₈	—	2	8	no	—
103	C₂×C₁₉⋊C₈	—	2	4	no	—
104	C₂×C₁₉⋊C₈	—	2	8	no	—
105	C₂×C₁₉⋊C₈	—	4	2	no	—
106	C₂×C₁₉⋊C₈	—	4	4	no	—
107	C₂×C₁₉⋊C₈	—	4	2	no	—
108	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	8	yes	complemented
109	#10714	—	19	1	no	maximal, Sylow
110	C₂³×C₁₉	—	2	4	no	—
111	C₂³×C₁₉	—	2	4	no	—
112	C₂³×C₁₉	—	2	4	no	—
113	C₂³×C₁₉	—	2	4	no	—
114	C₂³×C₁₉	—	2	4	no	—
115	C₂³×C₁₉	—	2	4	no	—
116	C₂³×C₁₉	—	2	16	no	—
117	C₂³×C₁₉	—	2	16	no	—
118	C₂³×C₁₉	#95	1	4	yes	—
119	C₂³×C₁₉	C₄×C₈	1	4	yes	—
120	C₂³×C₁₉	#97	1	4	yes	—
121	C₂³×C₁₉	C₂²⋊C₈	1	8	yes	—
122	C₂³×C₁₉	C₄⋊C₈	1	8	yes	—
123	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
124	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂³×C₁₉	C₄×D₄	1	4	yes	—
127	C₂³×C₁₉	C₂²×C₈	1	2	yes	—
128	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
129	C₂³×C₁₉	#131	1	4	yes	—
130	C₂×C₄×C₁₉	—	2	4	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	4	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	8	no	—
138	C₂×C₄×C₁₉	—	2	8	no	—
139	C₂×C₄×C₁₉	—	2	16	no	—
140	C₂×C₄×C₁₉	—	4	4	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	8	no	—
143	C₂×C₄×C₁₉	#95	1	4	yes	—
144	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#117	1	2	yes	—
150	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₁₉	#120	1	2	yes	—
152	C₂×C₄×C₁₉	#120	1	2	yes	—
153	C₂×C₄×C₁₉	#121	1	4	yes	—
154	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₁₉	#123	1	2	yes	—
156	C₂×C₄×C₁₉	#123	1	2	yes	—
157	C₁₉⋊C₈	—	2	8	no	—
158	C₁₉⋊C₈	—	4	4	no	—
159	C₂⁴×C₈	—	19	1	no	—
160	C₂²×C₂²⋊C₈	—	19	1	no	—
161	C₂×C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
162	C₂×#336	—	19	4	no	—
163	C₂²×C₁₉	—	2	16	no	—
164	C₂²×C₁₉	—	2	16	no	—
165	C₂²×C₁₉	—	2	4	no	—
166	C₂²×C₁₉	—	2	4	no	—
167	C₂²×C₁₉	—	2	8	no	—
168	C₂²×C₁₉	—	2	8	no	—
169	C₂²×C₁₉	#336	1	8	yes	complemented
170	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
171	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
172	C₂²×C₁₉	#385	1	2	yes	—
173	C₂²×C₁₉	#386	1	2	yes	—
174	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
176	C₂²×C₁₉	#405	1	2	yes	—
177	C₂²×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
178	C₂²×C₁₉	#408	1	2	yes	—
179	C₂²×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
180	C₂²×C₁₉	#424	1	2	yes	—
181	C₂²×C₁₉	C₈×D₄	1	8	yes	—
182	C₂²×C₁₉	#435	1	8	yes	—
183	C₄×C₁₉	—	2	4	no	—
184	C₄×C₁₉	—	4	8	no	—
185	C₄×C₁₉	#379	1	1	yes	characteristic
186	C₄×C₁₉	#380	1	2	yes	—
187	C₄×C₁₉	#381	1	1	yes	characteristic
188	C₄×C₁₉	#385	1	2	yes	—
189	C₄×C₁₉	#386	1	2	yes	—
190	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
191	C₂³×C₈	—	19	2	no	—
192	C₂³×C₈	—	19	4	no	—
193	C₂³×C₈	—	19	2	no	—
194	C₂³×C₈	—	38	8	no	—
195	C₂³×C₈	—	38	2	no	—
196	C₂³×C₈	—	38	2	no	—
197	C₂²×C₂²⋊C₄	Dic₁₉	1	2	yes	—
198	C₂²×C₄²	C₂×D₁₉	1	2	yes	—
199	C₂×C₂²⋊C₈	—	19	4	no	—
200	C₂×C₂²⋊C₈	—	38	2	no	—
201	C₂×C₂²⋊C₈	—	38	2	no	—
202	C₄×C₂²⋊C₄	—	2	2	no	—
203	C₄×C₂²⋊C₄	—	2	2	no	—
204	C₂×#95	Dic₁₉	1	2	yes	—
205	#336	—	38	8	no	—
206	C₂×C₁₉	—	2	8	no	—
207	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
208	C₂×C₁₉	C₂×#336	1	1	yes	characteristic
209	C₂×C₁₉	#1729	1	1	yes	characteristic
210	C₂×C₁₉	C₈×C₂²⋊C₄	1	2	yes	—
211	C₂×C₁₉	#1752	1	2	yes	—
212	C₂×C₁₉	#1850	1	4	yes	—
213	C₂×C₁₉	#1869	1	4	yes	—
214	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	Dic₃₈	1	2	yes	—
218	C₂³×C₄	C₄×D₁₉	1	2	yes	—
219	C₂³×C₄	C₄×D₁₉	1	2	yes	—
220	C₂³×C₄	D₇₆	1	2	yes	—
221	C₂³×C₄	C₂×Dic₁₉	1	4	yes	—
222	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
223	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
224	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
225	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
226	C₂²×C₈	—	19	4	no	—
227	C₂²×C₈	—	19	8	no	—
228	C₂²×C₈	—	19	4	no	—
229	C₂²×C₈	—	38	16	no	—
230	C₂²×C₈	—	38	16	no	—
231	C₂²×C₈	—	38	16	no	—
232	C₂²×C₈	—	38	8	no	—
233	C₂²×C₈	—	38	2	no	—
234	C₂²×C₈	—	38	4	no	—
235	C₂²×C₈	—	38	2	no	—
236	C₂²×C₈	—	38	2	no	—
237	C₂²×C₈	—	38	4	no	—
238	C₂²×C₈	—	38	4	no	—
239	C₂²×C₈	—	38	2	no	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	C₁₉⋊C₈	1	8	yes	complemented
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂²⋊C₈	—	38	8	no	—
248	#95	—	2	4	no	—
249	C₁₉	#10714	1	1	yes	characteristic, complemented, Sylow
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	C₂×C₁₉⋊C₈	1	4	yes	—
253	C₂⁴	#64520	1	4	yes	—
254	C₂⁴	C₄×Dic₁₉	1	2	yes	—
255	C₂⁴	C₄⋊Dic₁₉	1	2	yes	—
256	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
257	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	C₂×C₁₉⋊C₈	1	8	yes	complemented
273	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
274	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
275	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
276	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
277	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
278	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
279	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
280	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₁₉	1	4	yes	—
285	C₂²×C₄	#64543	1	4	yes	—
286	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
288	C₂×C₈	—	19	8	no	—
289	C₂×C₈	—	38	32	no	—
290	C₂×C₈	—	38	8	no	—
291	C₂×C₈	—	38	4	no	—
292	C₂×C₈	—	38	8	no	—
293	C₂×C₈	—	38	4	no	—
294	C₂×C₈	—	38	8	no	—
295	C₂×C₈	—	38	4	no	—
296	C₂×C₈	—	76	4	no	—
297	C₂×C₈	—	76	2	no	—
298	C₂×C₈	—	76	2	no	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₄²	—	4	2	no	—
301	C₄²	—	4	2	no	—
302	C₄²	—	4	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	16	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	4	no	—
310	C₂³	—	2	4	no	—
311	C₂³	C₄×C₁₉⋊C₈	1	4	yes	—
312	C₂³	#10597260	1	4	yes	—
313	C₂³	C₄⋊(C₁₉⋊C₈)	1	8	yes	—
314	C₂³	C₂²⋊(C₁₉⋊C₈)	1	8	yes	—
315	C₂³	C₁₉⋊#95	1	4	yes	—
316	C₂³	C₂²×C₁₉⋊C₈	1	2	yes	—
317	C₂³	C₂×#64520	1	2	yes	—
318	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
319	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
320	C₂³	D₄×Dic₁₉	1	4	yes	—
321	C₂³	#10597394	1	4	yes	—
322	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	16	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₁₉⋊#95	1	4	yes	—
337	C₂×C₄	#10597323	1	2	yes	—
338	C₂×C₄	#10597324	1	4	yes	—
339	C₂×C₄	C₂²⋊C₄×D₁₉	1	2	yes	—
340	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	4	yes	—
341	C₂×C₄	#10597328	1	2	yes	—
342	C₂×C₄	#10597332	1	2	yes	—
343	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
347	C₂×C₄	#10597381	1	2	yes	—
348	C₂×C₄	#10597383	1	2	yes	—
349	C₂×C₄	#10597385	1	4	yes	—
350	C₈	—	38	8	no	—
351	C₈	—	76	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	8	no	—
355	C₂²	—	2	8	no	—
356	C₂²	—	2	16	no	—
357	C₂²	—	2	16	no	—
358	C₂²	#11926299	1	8	yes	complemented
359	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
360	C₂²	C₂²⋊C₄×Dic₁₉	1	2	yes	—
361	C₂²	#11926419	1	2	yes	—
362	C₂²	#11926424	1	2	yes	—
363	C₂²	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
364	C₂²	C₂×#10597260	1	1	yes	characteristic
365	C₂²	#11926500	1	2	yes	—
366	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
367	C₂²	#11926511	1	2	yes	—
368	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
369	C₂²	#11926571	1	2	yes	—
370	C₂²	D₄×C₁₉⋊C₈	1	8	yes	—
371	C₂²	#11926616	1	8	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	4	8	no	—
374	C₄	#11926399	1	1	yes	characteristic
375	C₄	#11926402	1	2	yes	—
376	C₄	#11926405	1	1	yes	characteristic
377	C₄	#11926416	1	2	yes	—
378	C₄	#11926421	1	2	yes	—
379	C₂	—	2	8	no	—
380	C₂	#14561857	1	1	yes	characteristic
381	C₂	C₂×#11926299	1	1	yes	characteristic
382	C₂	#14563332	1	1	yes	characteristic
383	C₂	C₂²⋊C₄×C₁₉⋊C₈	1	2	yes	—
384	C₂	#14563413	1	2	yes	—
385	C₂	#14563815	1	4	yes	—
386	C₂	#14563928	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Fitting	C₂×C₄×C₂²⋊C₄×C₁₉	C₂
socle	C₂⁴×C₁₉	C₂²×C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#10714
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×#11926299	C₂	semidirect
8. C₂³×C₁₉⋊C₈	C₄	semidirect
13. C₂×C₂²⋊(C₁₉⋊C₈)	C₄	semidirect
35. C₂×C₂²⋊C₄×C₁₉	C₈	semidirect
85. C₂²×C₄×C₁₉	C₂×C₈	semidirect
108. C₂×C₁₉⋊C₈	C₂²⋊C₄	semidirect
169. C₂²×C₁₉	#336	semidirect
242. C₂×C₂²⋊C₄	C₁₉⋊C₈	semidirect
249. C₁₉	#10714	semidirect
272. C₂²×C₄	C₂×C₁₉⋊C₈	semidirect
358. C₂²	#11926299	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₁₉⋊C₈	2
C₂²×C₂²⋊(C₁₉⋊C₈)	2
C₂×#11926299	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#10714	19