Subgroups — #18070844

Order 4864.

584 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563703	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563615	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561458	C₂	1	2	yes	maximal, complemented
4	#14561456	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	#11926299	—	2	1	no	—
10	#11926299	C₂²	1	2	yes	—
11	#11926299	C₂²	1	2	yes	—
12	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₉	—	2	1	no	—
14	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#390	C₂²	1	1	yes	characteristic
17	C₁₉×#389	C₂²	1	1	yes	characteristic
18	C₁₉×#388	—	2	1	no	—
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#380	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₁₉×#121	—	2	2	no	—
30	C₁₉×#121	—	2	2	no	—
31	C₄×D₄×C₁₉	—	4	2	no	—
32	C₄×D₄×C₁₉	—	4	2	no	—
33	C₄×D₄×C₁₉	—	4	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	4	2	no	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
57	C₂⁴×C₁₉	—	2	1	no	—
58	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×D₄×C₁₉	—	2	4	no	—
60	C₂×D₄×C₁₉	—	2	1	no	—
61	C₂×D₄×C₁₉	—	4	1	no	—
62	C₂×D₄×C₁₉	—	4	1	no	—
63	C₂×D₄×C₁₉	—	4	2	no	—
64	C₂×D₄×C₁₉	—	4	2	no	—
65	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	—	4	2	no	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	D₈	1	2	yes	—
85	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
95	C₂²⋊C₄×C₁₉	—	2	4	no	—
96	C₂²⋊C₄×C₁₉	—	4	2	no	—
97	C₂²⋊C₄×C₁₉	—	4	2	no	—
98	C₂²⋊C₄×C₁₉	—	4	1	no	—
99	C₂²⋊C₄×C₁₉	—	4	1	no	—
100	C₂²⋊C₄×C₁₉	—	4	2	no	—
101	C₄²×C₁₉	—	2	2	no	—
102	C₄²×C₁₉	—	2	2	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	4	2	no	—
106	C₂×C₁₉⋊C₈	—	4	2	no	—
107	C₂×C₁₉⋊C₈	—	4	2	no	—
108	C₂×C₁₉⋊C₈	—	4	2	no	—
109	C₂×C₁₉⋊C₈	—	4	2	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	#7647	—	19	1	no	maximal, Sylow
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	4	1	no	—
121	C₂³×C₁₉	—	4	1	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	#102	1	2	yes	—
127	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	D₄×C₁₉	—	4	2	no	—
129	D₄×C₁₉	—	4	2	no	—
130	D₄×C₁₉	—	4	8	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	8	4	no	—
159	C₂×C₄×C₁₉	#99	1	2	yes	—
160	C₂×C₄×C₁₉	#102	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#135	1	2	yes	—
166	C₁₉⋊C₈	—	8	2	no	—
167	C₁₉⋊C₈	—	8	2	no	—
168	C₄×#121	D₁₉	1	1	yes	characteristic
169	#1817	—	19	1	no	—
170	#1797	—	19	1	no	—
171	#1271	—	19	2	no	—
172	#1270	—	19	2	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	4	1	no	—
177	C₂²×C₁₉	—	4	1	no	—
178	C₂²×C₁₉	—	4	1	no	—
179	C₂²×C₁₉	—	4	1	no	—
180	C₂²×C₁₉	—	4	2	no	—
181	C₂²×C₁₉	—	4	2	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	—	8	1	no	—
184	C₂²×C₁₉	—	8	1	no	—
185	C₂²×C₁₉	—	8	1	no	—
186	C₂²×C₁₉	—	8	1	no	—
187	C₂²×C₁₉	#407	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
189	C₂²×C₁₉	#413	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
191	C₂²×C₁₉	#416	1	1	yes	characteristic
192	C₂²×C₁₉	#421	1	1	yes	characteristic
193	C₂²×C₁₉	#421	1	1	yes	characteristic
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	4	1	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	8	1	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₂×#121	Dic₁₉	1	1	yes	characteristic
206	C₂×C₄×D₄	—	2	1	no	—
207	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
208	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
209	C₂×C₄⋊C₈	—	38	1	no	—
210	C₂×C₂²⋊C₈	—	38	1	no	—
211	C₂×C₂²⋊C₈	—	38	1	no	—
212	#390	C₂×D₁₉	1	1	yes	characteristic
213	#389	C₂×D₁₉	1	1	yes	characteristic
214	#388	—	2	1	no	—
215	#386	—	2	1	no	—
216	#380	Dic₁₉	1	1	yes	characteristic
217	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
218	C₄×C₂²⋊C₄	—	2	1	no	—
219	#336	—	19	2	no	—
220	#336	—	19	2	no	—
221	#336	—	38	1	no	—
222	C₂×C₁₉	—	4	2	no	—
223	C₂×C₁₉	—	8	2	no	—
224	C₂×C₁₉	#1465	1	1	yes	characteristic
225	C₂×C₁₉	#1486	1	1	yes	characteristic
226	C₂×C₁₉	#1488	1	1	yes	characteristic
227	C₂×C₁₉	#1516	1	1	yes	characteristic
228	C₂×C₁₉	#1519	1	1	yes	characteristic
229	C₂×C₁₉	#1535	1	1	yes	characteristic
230	C₂×C₁₉	#1540	1	1	yes	characteristic
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
236	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
237	C₂²×C₈	—	38	2	no	—
238	C₂²×C₈	—	38	2	no	—
239	#121	—	2	2	no	—
240	#121	—	2	2	no	—
241	C₄×D₄	—	4	2	no	—
242	C₄×D₄	—	4	2	no	—
243	C₄×D₄	—	4	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	—	4	2	no	—
255	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
256	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
257	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
259	C₄⋊C₈	—	76	2	no	—
260	C₂²⋊C₈	—	76	2	no	—
261	C₂²⋊C₈	—	76	2	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	C₁₉	#7647	1	1	yes	characteristic, complemented, Sylow
266	C₂⁴	—	2	1	no	—
267	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	#64520	1	2	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	#64525	1	2	yes	—
291	C₂²×C₄	#64526	1	2	yes	—
292	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
298	C₂×C₈	—	76	2	no	—
299	C₂×C₈	—	76	2	no	—
300	C₂×C₈	—	76	2	no	—
301	C₂×C₈	—	76	2	no	—
302	C₂×C₈	—	76	2	no	—
303	C₂×C₈	—	76	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	#64520	1	2	yes	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	2	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	#10597289	1	2	yes	—
335	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	8	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	#10597289	1	2	yes	—
368	C₂×C₄	#10597291	1	2	yes	—
369	C₂×C₄	C₂×#64520	1	1	yes	characteristic
370	C₂×C₄	C₂×#64520	1	1	yes	characteristic
371	C₂×C₄	C₂×#64525	1	1	yes	characteristic
372	C₂×C₄	C₂×#64526	1	1	yes	characteristic
373	C₂×C₄	#10597396	1	2	yes	—
374	C₈	—	152	2	no	—
375	C₈	—	152	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	#11926508	1	1	yes	characteristic
391	C₂²	C₂×#10597291	1	1	yes	characteristic
392	C₂²	#11926528	1	1	yes	characteristic
393	C₂²	C₂×#10597289	1	1	yes	characteristic
394	C₂²	#11926540	1	1	yes	characteristic
395	C₂²	#11926561	1	1	yes	characteristic
396	C₂²	#11926561	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	1	no	—
408	C₂	—	4	2	no	—
409	C₂	—	8	2	no	—
410	C₂	#14561973	1	1	yes	characteristic
411	C₂	#14562060	1	1	yes	characteristic
412	C₂	#14562069	1	1	yes	characteristic
413	C₂	#14562191	1	1	yes	characteristic
414	C₂	#14562203	1	1	yes	characteristic
415	C₂	#14562266	1	1	yes	characteristic
416	C₂	#14562284	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#121	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#121	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#121	D₁₉
hypocenter	C₁₉	#7647
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. #14563703	C₂	semidirect
2. #14563615	C₂	semidirect
3. #14561458	C₂	semidirect
4. #14561456	C₂	semidirect
265. C₁₉	#7647	semidirect

Maximal subgroups

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

subgroup	index
#14563703	2
#14563615	2
#14561458	2
#14561456	2
C₄×C₁₉×#121	2
#7647	19