Subgroups — #18072210

Order 4864.

1058 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926508	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#14561481	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64520	C₄	1	2	yes	complemented
6	C₂²×C₂²⋊Dic₁₉	C₄	1	2	yes	—
7	C₂²×C₄×Dic₁₉	—	2	1	no	—
8	#11926508	—	2	1	no	—
9	#11926508	—	2	1	no	—
10	#11926508	—	2	1	no	—
11	#11926508	—	2	1	no	—
12	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	complemented
13	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	C₄×C₂²⋊Dic₁₉	—	2	1	no	—
15	C₄×C₂²⋊Dic₁₉	—	2	1	no	—
16	C₄×C₂²⋊Dic₁₉	C₄	1	2	yes	—
17	C₄×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉⋊#95	—	2	1	no	—
19	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	—	2	1	no	—
21	C₁₉×#407	—	2	1	no	—
22	C₁₉×#407	—	2	1	no	—
23	C₁₉×#407	C₄	1	2	yes	complemented
24	C₁₉×#407	C₄	1	2	yes	complemented
25	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	—	4	4	no	—
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×Dic₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	4	4	no	—
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
49	C₂×C₂²⋊Dic₁₉	—	2	8	no	—
50	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
51	C₂×C₄×Dic₁₉	—	2	2	no	—
52	C₂×C₄×Dic₁₉	—	2	2	no	—
53	C₂×C₄×Dic₁₉	—	4	4	no	—
54	C₂×#64520	—	2	2	no	—
55	C₂×#64520	—	2	2	no	—
56	C₂×#64520	—	4	4	no	—
57	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	complemented
58	C₁₉×C₂²⋊C₈	—	2	2	no	—
59	C₁₉×C₂²⋊C₈	—	2	2	no	—
60	C₁₉×C₂²⋊C₈	—	2	2	no	—
61	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
62	C₁₉⋊#95	—	2	2	no	—
63	C₁₉⋊#95	—	2	2	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	4	2	no	—
70	C₂⁴×C₁₉	—	4	2	no	—
71	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
72	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
73	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	—	4	2	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	—	4	2	no	—
88	C₂²×C₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
120	C₂²×Dic₁₉	—	2	8	no	—
121	C₂²×Dic₁₉	—	2	4	no	—
122	C₂²×Dic₁₉	—	4	4	no	—
123	C₂²×Dic₁₉	—	4	4	no	—
124	M₁₆×C₁₉	—	4	4	no	—
125	M₁₆×C₁₉	—	4	4	no	—
126	C₂×C₈×C₁₉	—	2	4	no	—
127	C₂×C₈×C₁₉	—	4	4	no	—
128	C₂²⋊Dic₁₉	—	2	8	no	—
129	C₂²⋊Dic₁₉	—	2	4	no	—
130	C₂²⋊Dic₁₉	M₁₆	1	8	yes	complemented
131	C₄×Dic₁₉	—	4	4	no	—
132	C₄×Dic₁₉	—	4	4	no	—
133	#64520	—	4	4	no	—
134	#64520	—	4	4	no	—
135	C₂×C₁₉⋊C₈	—	2	4	no	—
136	C₂×C₁₉⋊C₈	—	4	4	no	—
137	#7929	—	19	1	no	maximal, Sylow
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	16	no	—
159	C₂³×C₁₉	#95	1	1	yes	characteristic
160	C₂³×C₁₉	#95	1	1	yes	characteristic
161	C₂³×C₁₉	#95	1	1	yes	characteristic
162	C₂³×C₁₉	#95	1	1	yes	characteristic
163	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
164	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#99	1	4	yes	—
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×Dic₁₉	—	2	8	no	—
204	C₂×Dic₁₉	—	4	4	no	—
205	C₂×Dic₁₉	—	4	16	no	—
206	C₂×Dic₁₉	—	4	4	no	—
207	C₈×C₁₉	—	4	4	no	—
208	C₁₉⋊C₈	—	4	4	no	—
209	C₂×#407	—	19	1	no	—
210	C₂×#407	D₁₉	1	1	yes	characteristic
211	C₂×C₄×C₂²⋊C₄	—	19	1	no	—
212	#1282	—	19	4	no	—
213	C₂²×C₁₉	—	2	8	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	4	4	no	—
231	C₂²×C₁₉	—	4	4	no	—
232	C₂²×C₁₉	—	4	4	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	4	no	—
235	C₂²×C₁₉	—	4	4	no	—
236	C₂²×C₁₉	#342	1	2	yes	—
237	C₂²×C₁₉	#344	1	2	yes	—
238	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
239	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
240	C₂²×C₁₉	#407	1	2	yes	—
241	C₂²×C₁₉	#423	1	2	yes	—
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	#342	1	2	yes	—
249	C₄×C₁₉	C₂×#99	1	2	yes	—
250	Dic₁₉	—	4	8	no	—
251	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
252	C₂²×M₁₆	—	2	1	no	—
253	C₂²×M₁₆	—	19	2	no	—
254	C₂²×C₂²⋊C₄	—	19	2	no	—
255	C₂²×C₄²	—	38	1	no	—
256	#407	—	2	1	no	—
257	#407	—	2	1	no	—
258	#407	—	38	1	no	—
259	#407	—	38	1	no	—
260	#407	—	38	1	no	—
261	#407	—	38	1	no	—
262	#407	Dic₁₉	1	2	yes	complemented
263	#407	Dic₁₉	1	2	yes	complemented
264	C₂×C₂²⋊C₈	—	2	1	no	—
265	C₂×C₂²⋊C₈	—	19	2	no	—
266	C₂×C₂²⋊C₈	—	19	2	no	—
267	C₂×C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
268	C₄×C₂²⋊C₄	—	19	2	no	—
269	C₄×C₂²⋊C₄	—	19	2	no	—
270	C₄×C₂²⋊C₄	—	38	1	no	—
271	C₄×C₂²⋊C₄	—	38	1	no	—
272	C₂×#95	—	38	1	no	—
273	C₂×C₁₉	—	2	2	no	—
274	C₂×C₁₉	—	2	2	no	—
275	C₂×C₁₉	—	2	2	no	—
276	C₂×C₁₉	—	2	2	no	—
277	C₂×C₁₉	—	2	2	no	—
278	C₂×C₁₉	—	4	1	no	—
279	C₂×C₁₉	—	4	1	no	—
280	C₂×C₁₉	#1728	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#342	1	1	yes	characteristic
282	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
283	C₂⁵	C₄×D₁₉	1	1	yes	characteristic
284	C₂³×C₄	—	4	4	no	—
285	C₂³×C₄	—	38	2	no	—
286	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
287	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
288	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
289	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
290	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
291	C₂³×C₄	D₇₆	1	1	yes	characteristic
292	C₂³×C₄	D₇₆	1	1	yes	characteristic
293	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
294	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
295	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
297	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
298	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
299	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	4	4	no	—
303	C₂×M₁₆	—	38	2	no	—
304	C₂×M₁₆	—	38	2	no	—
305	C₂×M₁₆	—	76	4	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	19	4	no	—
308	C₂×C₂²⋊C₄	—	19	4	no	—
309	C₂×C₂²⋊C₄	—	38	8	no	—
310	C₂×C₂²⋊C₄	—	38	2	no	—
311	C₂×C₄²	—	38	2	no	—
312	C₂×C₄²	—	38	2	no	—
313	C₂×C₄²	—	76	4	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	38	2	no	—
318	C₂²⋊C₈	—	38	2	no	—
319	C₂²⋊C₈	—	38	2	no	—
320	C₂²⋊C₈	—	38	2	no	—
321	C₂²⋊C₈	C₂×Dic₁₉	1	4	yes	complemented
322	#95	—	38	2	no	—
323	#95	—	38	2	no	—
324	C₁₉	#7929	1	1	yes	characteristic, complemented, Sylow
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	4	2	no	—
327	C₂⁴	—	4	2	no	—
328	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
329	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
330	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
331	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
332	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
333	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
334	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	38	8	no	—
350	C₂²×C₄	—	38	4	no	—
351	C₂²×C₄	—	76	4	no	—
352	C₂²×C₄	—	76	4	no	—
353	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
355	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
356	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
357	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
358	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
359	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
360	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
361	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
363	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
364	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
365	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
368	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
369	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
370	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
378	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
381	M₁₆	—	4	4	no	—
382	M₁₆	—	4	4	no	—
383	M₁₆	—	76	4	no	—
384	M₁₆	—	76	4	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	4	4	no	—
387	C₂×C₈	—	38	4	no	—
388	C₂×C₈	—	76	4	no	—
389	C₂²⋊C₄	—	19	8	no	—
390	C₂²⋊C₄	—	38	8	no	—
391	C₂²⋊C₄	—	38	4	no	—
392	C₄²	—	76	4	no	—
393	C₄²	—	76	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	16	no	—
415	C₂³	C₁₉⋊#95	1	1	yes	characteristic
416	C₂³	C₁₉⋊#95	1	1	yes	characteristic
417	C₂³	C₁₉⋊#95	1	1	yes	characteristic
418	C₂³	C₁₉⋊#95	1	1	yes	characteristic
419	C₂³	M₁₆×D₁₉	1	4	yes	—
420	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
421	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
422	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	38	8	no	—
451	C₂×C₄	—	76	4	no	—
452	C₂×C₄	—	76	16	no	—
453	C₂×C₄	—	76	4	no	—
454	C₂×C₄	#10597263	1	4	yes	—
455	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
456	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
457	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
458	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
459	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
461	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
463	C₈	—	4	4	no	—
464	C₈	—	76	4	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	#11926310	1	2	yes	—
489	C₂²	#11926316	1	2	yes	—
490	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
491	C₂²	M₁₆×Dic₁₉	1	2	yes	—
492	C₂²	#11926507	1	2	yes	—
493	C₂²	#11926567	1	2	yes	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	76	8	no	—
501	C₄	#11926310	1	2	yes	—
502	C₄	C₂×#10597263	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	2	2	no	—
506	C₂	—	2	2	no	—
507	C₂	—	2	2	no	—
508	C₂	—	4	1	no	—
509	C₂	—	4	1	no	—
510	C₂	#14563328	1	1	yes	characteristic
511	C₂	C₂×#11926310	1	1	yes	characteristic
512	C₂	C₂×#11926316	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#407	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁵×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#407	D₁₉
hypocenter	C₁₉	#7929
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. #14561481	C₂	semidirect
5. C₂²×#64520	C₄	semidirect
12. C₂×C₂²⋊(C₁₉⋊C₈)	C₄	semidirect
23. C₁₉×#407	C₄	semidirect
24. C₁₉×#407	C₄	semidirect
57. C₂²×C₁₉⋊C₈	C₂×C₄	semidirect
61. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
130. C₂²⋊Dic₁₉	M₁₆	semidirect
262. #407	Dic₁₉	semidirect
263. #407	Dic₁₉	semidirect
321. C₂²⋊C₈	C₂×Dic₁₉	semidirect
324. C₁₉	#7929	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926508	2
C₂×C₄×C₂²⋊Dic₁₉	2
#14561481	2
C₂×C₁₉×#407	2
#7929	19