Subgroups — #18077225

Order 4864.

934 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572659	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563545	C₂	1	2	yes	maximal, complemented
3	#14561953	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561483	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#120	C₂	1	1	yes	maximal, characteristic
6	D₄×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
12	#11926270	—	2	1	no	—
13	#11926268	—	2	1	no	—
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#120	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#386	—	2	1	no	—
19	C₁₉×#386	C₄	1	1	yes	characteristic
20	C₁₉×#385	—	2	1	no	—
21	C₁₉×#385	C₄	1	1	yes	characteristic
22	C₁₉×#379	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	2	no	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	—	4	4	no	—
33	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₁₉×#120	—	2	2	no	—
37	C₁₉×#120	C₈	1	4	yes	complemented
38	C₄×D₄×C₁₉	—	2	2	no	—
39	C₄×D₄×C₁₉	—	2	2	no	—
40	C₄×D₄×C₁₉	—	4	4	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₂²×C₁₉⋊C₈	—	2	2	no	—
55	C₂²×C₁₉⋊C₈	D₄	1	4	yes	complemented
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	4	8	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
66	C₄×C₁₉⋊C₈	—	2	2	no	—
67	C₂⁴×C₁₉	—	2	1	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	1	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	4	2	no	—
72	C₂⁴×C₁₉	—	4	2	no	—
73	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₁₉	C₂×C₈	1	2	yes	complemented
75	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	2	2	no	—
78	C₂×D₄×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	—	4	2	no	—
80	C₂×D₄×C₁₉	—	4	2	no	—
81	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
82	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	8	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	4	4	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	4	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	4	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	2	2	no	—
116	C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	4	2	no	—
119	C₂²⋊C₄×C₁₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₉	C₂×C₈	1	2	yes	complemented
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	4	2	no	—
124	C₂×C₁₉⋊C₈	—	2	4	no	—
125	C₂×C₁₉⋊C₈	—	4	4	no	—
126	C₂×C₁₉⋊C₈	—	4	4	no	—
127	C₂×C₁₉⋊C₈	—	4	2	no	—
128	C₂×C₁₉⋊C₈	—	8	2	no	—
129	#8965	—	19	1	no	maximal, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	4	no	—
146	C₂³×C₁₉	—	4	8	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	complemented
153	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂³×C₁₉	C₄×D₄	1	2	yes	—
155	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
156	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
157	C₂³×C₁₉	#131	1	2	yes	—
158	D₄×C₁₉	—	2	4	no	—
159	D₄×C₁₉	—	2	4	no	—
160	D₄×C₁₉	—	4	8	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	8	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	1	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	—	8	1	no	—
187	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	complemented
188	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#121	1	2	yes	—
190	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
191	C₁₉⋊C₈	—	4	4	no	—
192	C₁₉⋊C₈	—	8	2	no	—
193	#2972	—	19	1	no	—
194	C₄×#120	D₁₉	1	1	yes	characteristic
195	#1779	—	19	2	no	—
196	#1459	—	19	1	no	—
197	#1282	—	19	2	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	4	no	—
203	C₂²×C₁₉	—	2	8	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	4	no	—
213	C₂²×C₁₉	—	4	4	no	—
214	C₂²×C₁₉	—	4	4	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	#386	1	1	yes	characteristic
222	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
223	C₂²×C₁₉	#408	1	1	yes	characteristic
224	C₂²×C₁₉	C₈×D₄	1	2	yes	—
225	C₂²×C₁₉	#435	1	2	yes	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	2	2	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	4	1	no	—
232	C₄×C₁₉	—	4	1	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	B(4,𝔽₂)	1	2	yes	—
235	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
236	C₂×#120	Dic₁₉	1	1	yes	characteristic
237	C₂×C₄×D₄	—	2	1	no	—
238	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
239	C₈×D₄	—	38	4	no	—
240	#431	—	38	1	no	—
241	C₂×C₂²⋊C₈	—	19	2	no	—
242	C₂×C₂²⋊C₈	—	19	2	no	—
243	C₂×C₂²⋊C₈	—	38	1	no	—
244	C₂×C₂²⋊C₈	—	38	4	no	—
245	#386	—	2	1	no	—
246	#386	Dic₁₉	1	1	yes	characteristic
247	#385	—	2	1	no	—
248	#385	Dic₁₉	1	1	yes	characteristic
249	#379	Dic₁₉	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	—	2	1	no	—
251	C₄×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
252	#324	—	38	1	no	—
253	#323	—	38	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	2	no	—
257	C₂×C₁₉	—	2	2	no	—
258	C₂×C₁₉	—	4	4	no	—
259	C₂×C₁₉	—	4	2	no	—
260	C₂×C₁₉	#1869	1	1	yes	characteristic
261	C₂×C₁₉	#1889	1	1	yes	characteristic
262	C₂×C₁₉	#1891	1	1	yes	characteristic
263	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	4	4	no	—
271	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
272	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
273	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
274	C₂²×C₈	—	19	4	no	—
275	C₂²×C₈	—	38	2	no	—
276	C₂²×C₈	—	38	2	no	—
277	#120	—	2	2	no	—
278	#120	C₁₉⋊C₈	1	4	yes	complemented
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	4	4	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
294	C₄⋊C₈	—	38	2	no	—
295	C₂²⋊C₈	—	38	2	no	—
296	C₂²⋊C₈	—	38	2	no	—
297	C₂²⋊C₈	—	38	2	no	—
298	C₂²⋊C₈	—	38	2	no	—
299	C₂²⋊C₈	—	38	2	no	—
300	C₂²⋊C₈	—	76	8	no	—
301	C₄×C₈	—	38	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	C₁₉	#8965	1	1	yes	characteristic, complemented, Sylow
306	C₂⁴	—	2	2	no	—
307	C₂⁴	—	2	1	no	—
308	C₂⁴	—	2	2	no	—
309	C₂⁴	—	2	1	no	—
310	C₂⁴	—	4	2	no	—
311	C₂⁴	—	4	2	no	—
312	C₂⁴	C₂×C₁₉⋊C₈	1	2	yes	complemented
313	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
314	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	C₂×C₁₉⋊C₈	1	2	yes	—
321	C₂×D₄	#64520	1	2	yes	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₁₉	1	2	yes	—
346	C₂²×C₄	#64543	1	2	yes	—
347	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
349	C₂×C₈	—	38	4	no	—
350	C₂×C₈	—	76	4	no	—
351	C₂×C₈	—	76	4	no	—
352	C₂×C₈	—	76	2	no	—
353	C₂×C₈	—	152	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	C₂×C₁₉⋊C₈	1	2	yes	complemented
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	4	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	4	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	complemented
391	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
392	C₂³	C₂×#64520	1	1	yes	characteristic
393	C₂³	D₄×Dic₁₉	1	2	yes	—
394	C₂³	#10597394	1	2	yes	—
395	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
396	D₄	—	2	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	4	8	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	8	1	no	—
425	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	complemented
426	C₂×C₄	#10597381	1	1	yes	characteristic
427	C₂×C₄	#10597383	1	1	yes	characteristic
428	C₂×C₄	#10597385	1	2	yes	—
429	C₈	—	76	4	no	—
430	C₈	—	152	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	#11926424	1	1	yes	characteristic
455	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
456	C₂²	#11926511	1	1	yes	characteristic
457	C₂²	D₄×C₁₉⋊C₈	1	2	yes	—
458	C₂²	#11926616	1	2	yes	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	8	1	no	—
467	C₄	#11926730	1	2	yes	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	2	2	no	—
471	C₂	—	2	2	no	—
472	C₂	—	4	4	no	—
473	C₂	—	4	2	no	—
474	C₂	#14563928	1	1	yes	characteristic
475	C₂	#14564044	1	1	yes	characteristic
476	C₂	#14564054	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂³×C₁₉	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₄×C₁₉×#120	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×C₁₉×#120	C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄×#120	D₁₉
hypocenter	C₁₉	#8965
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₄×#120

Complements

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

N	H ≅ G/N	type
1. #14572659	C₂	semidirect
2. #14563545	C₂	semidirect
3. #14561953	C₂	semidirect
4. #14561483	C₂	semidirect
37. C₁₉×#120	C₈	semidirect
55. C₂²×C₁₉⋊C₈	D₄	semidirect
74. C₂⁴×C₁₉	C₂×C₈	semidirect
120. C₂²⋊C₄×C₁₉	C₂×C₈	semidirect
152. C₂³×C₁₉	C₂²⋊C₈	semidirect
187. C₂×C₄×C₁₉	C₂²⋊C₈	semidirect
278. #120	C₁₉⋊C₈	semidirect
305. C₁₉	#8965	semidirect
312. C₂⁴	C₂×C₁₉⋊C₈	semidirect
364. C₂²⋊C₄	C₂×C₁₉⋊C₈	semidirect
390. C₂³	C₂²⋊(C₁₉⋊C₈)	semidirect
425. C₂×C₄	C₂²⋊(C₁₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#14572659	2
#14563545	2
#14561953	2
#14561483	2
C₄×C₁₉×#120	2
#8965	19