Subgroups — #18078876

Order 4864.

514 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572670	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562233	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562078	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561987	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561505	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#463	C₂	1	1	yes	maximal, characteristic
8	#11926622	—	2	1	no	—
9	#11926616	—	2	2	no	—
10	D₄×C₁₉⋊C₈	—	2	1	no	—
11	#11926601	C₂²	1	1	yes	characteristic
12	#11926601	C₂²	1	1	yes	characteristic
13	#11926597	C₂²	1	1	yes	characteristic
14	#11926508	—	2	1	no	—
15	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₄×#64520	C₂²	1	1	yes	characteristic
17	#11926284	—	2	2	no	—
18	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
20	#11926268	—	2	1	no	—
21	#11926268	—	2	1	no	—
22	C₂²×SD₁₆×C₁₉	C₄	1	1	yes	characteristic
23	C₂²×D₈×C₁₉	C₄	1	1	yes	characteristic
24	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#463	—	2	1	no	—
27	C₁₉×#463	—	2	1	no	—
28	C₁₉×#463	—	2	1	no	—
29	C₁₉×#463	—	2	1	no	—
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₄	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₄	1	1	yes	characteristic
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂×SD₁₆×C₁₉	—	2	1	no	—
38	C₂×SD₁₆×C₁₉	—	2	1	no	—
39	C₂×SD₁₆×C₁₉	—	4	2	no	—
40	C₂×D₈×C₁₉	—	2	1	no	—
41	C₂×D₈×C₁₉	—	2	1	no	—
42	C₂×D₈×C₁₉	—	4	2	no	—
43	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₁₉×#124	—	2	1	no	—
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#124	—	2	1	no	—
49	C₄×D₄×C₁₉	—	2	1	no	—
50	C₄×D₄×C₁₉	—	2	1	no	—
51	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
53	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
54	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×#64520	—	2	2	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂²×C₁₉⋊C₈	—	2	2	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×#102	—	2	1	no	—
69	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
70	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
74	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
75	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
78	#10597260	—	2	1	no	—
79	#10597260	—	2	1	no	—
80	#10597260	D₄	1	2	yes	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₄×C₁₉⋊C₈	—	2	1	no	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	4	1	no	—
88	C₂×Q₈×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	8	2	no	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	SD₁₆×C₁₉	—	4	2	no	—
109	SD₁₆×C₁₉	—	4	2	no	—
110	D₈×C₁₉	—	4	2	no	—
111	D₈×C₁₉	—	4	2	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	#41	1	1	yes	characteristic
131	#64520	—	2	2	no	—
132	#64520	—	4	1	no	—
133	#64520	—	8	2	no	—
134	C₂×C₁₉⋊C₈	—	2	1	no	—
135	C₂×C₁₉⋊C₈	—	2	1	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	8	2	no	—
140	#9243	—	19	1	no	maximal, Sylow
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	8	1	no	—
150	C₂³×C₁₉	—	8	1	no	—
151	C₂³×C₁₉	—	8	1	no	—
152	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₁₉	—	4	1	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	2	1	no	—
157	D₄×C₁₉	—	2	1	no	—
158	D₄×C₁₉	—	2	1	no	—
159	D₄×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	#100	1	2	yes	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	8	1	no	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
184	C₈×C₁₉	—	4	1	no	—
185	C₈×C₁₉	—	4	1	no	—
186	C₁₉⋊C₈	—	4	1	no	—
187	C₁₉⋊C₈	—	4	2	no	—
188	C₁₉⋊C₈	—	4	1	no	—
189	C₁₉⋊C₈	—	4	2	no	—
190	C₁₉⋊C₈	—	8	1	no	—
191	C₂×#463	D₁₉	1	1	yes	characteristic
192	#2974	—	19	1	no	—
193	#1527	—	19	1	no	—
194	#1490	—	19	1	no	—
195	#1469	—	19	1	no	—
196	#1290	—	19	1	no	—
197	#1283	—	19	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	4	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	8	2	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	16	1	no	—
212	C₂²×C₁₉	—	16	1	no	—
213	C₂²×C₁₉	#386	1	1	yes	characteristic
214	C₂²×C₁₉	#443	1	1	yes	characteristic
215	C₂²×C₁₉	#444	1	1	yes	characteristic
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	—	4	1	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
225	C₄×C₁₉	#413	1	1	yes	characteristic
226	C₂²×SD₁₆	Dic₁₉	1	1	yes	characteristic
227	C₂²×D₈	Dic₁₉	1	1	yes	characteristic
228	C₂×#124	C₂×D₁₉	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
230	#463	—	2	1	no	—
231	#463	—	2	1	no	—
232	#463	—	2	1	no	—
233	#463	—	2	1	no	—
234	#436	—	38	1	no	—
235	#435	—	38	2	no	—
236	C₈×D₄	—	38	1	no	—
237	#432	—	19	1	no	—
238	#432	—	19	1	no	—
239	#431	—	19	1	no	—
240	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
241	C₂×#103	Dic₁₉	1	1	yes	characteristic
242	C₂×#102	Dic₁₉	1	1	yes	characteristic
243	#407	—	38	1	no	—
244	C₂×C₂²⋊C₈	—	38	1	no	—
245	C₄×M₁₆	—	19	1	no	—
246	#329	—	38	2	no	—
247	D₄⋊C₈	—	38	1	no	—
248	D₄⋊C₈	—	38	1	no	—
249	#323	—	38	1	no	—
250	#323	—	38	1	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	4	2	no	—
254	C₂×C₁₉	—	8	1	no	—
255	C₂×C₁₉	—	16	1	no	—
256	C₂×C₁₉	#1876	1	1	yes	characteristic
257	C₂×C₁₉	#1900	1	1	yes	characteristic
258	C₂×C₁₉	#1904	1	1	yes	characteristic
259	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
260	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
261	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂×SD₁₆	—	2	1	no	—
264	C₂×SD₁₆	—	2	1	no	—
265	C₂×SD₁₆	—	4	2	no	—
266	C₂×D₈	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×D₈	—	4	2	no	—
269	C₂×M₁₆	—	38	2	no	—
270	C₂×M₁₆	—	38	1	no	—
271	C₂²×C₈	—	38	2	no	—
272	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
273	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
274	#124	—	2	1	no	—
275	#124	—	2	1	no	—
276	#124	—	2	1	no	—
277	#124	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
281	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
282	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
283	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	38	1	no	—
292	C₄⋊C₈	—	38	1	no	—
293	C₄⋊C₈	—	38	1	no	—
294	#103	—	2	1	no	—
295	#103	—	2	1	no	—
296	#102	—	2	1	no	—
297	#102	—	2	1	no	—
298	C₂²⋊C₈	—	19	1	no	—
299	C₂²⋊C₈	—	19	1	no	—
300	C₂²⋊C₈	—	38	2	no	—
301	C₂²⋊C₈	—	38	2	no	—
302	C₂²⋊C₈	—	38	1	no	—
303	C₂²⋊C₈	—	38	1	no	—
304	#97	—	19	2	no	—
305	#97	—	38	1	no	—
306	#97	—	38	1	no	—
307	C₄×C₈	—	38	1	no	—
308	C₄×C₈	—	38	1	no	—
309	C₁₉	#9243	1	1	yes	characteristic, complemented, Sylow
310	C₂⁴	—	2	1	no	—
311	C₂⁴	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	4	1	no	—
315	C₂×Q₈	—	4	1	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
324	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
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	—	2	1	no	—
331	C₂²×C₄	—	8	2	no	—
332	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	#64543	1	1	yes	characteristic
334	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
335	SD₁₆	—	4	2	no	—
336	SD₁₆	—	4	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	4	2	no	—
339	M₁₆	—	38	2	no	—
340	M₁₆	—	76	1	no	—
341	M₁₆	—	152	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	38	1	no	—
347	C₂×C₈	—	38	1	no	—
348	C₂×C₈	—	38	2	no	—
349	C₂×C₈	—	76	1	no	—
350	C₂×C₈	—	76	1	no	—
351	C₂×C₈	—	152	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
354	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₄²	D₄×D₁₉	1	1	yes	characteristic
364	C₄²	#64543	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	8	1	no	—
376	C₂³	—	8	1	no	—
377	C₂³	—	8	1	no	—
378	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	8	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	2	1	no	—
384	D₄	—	2	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	8	1	no	—
389	D₄	#10597290	1	2	yes	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	8	1	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
405	C₂×C₄	#10597381	1	1	yes	characteristic
406	C₂×C₄	#10597383	1	1	yes	characteristic
407	C₂×C₄	#10597385	1	1	yes	characteristic
408	C₂×C₄	#10597385	1	1	yes	characteristic
409	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	76	1	no	—
413	C₈	—	76	2	no	—
414	C₈	—	76	1	no	—
415	C₈	—	76	2	no	—
416	C₈	—	152	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	16	1	no	—
431	C₂²	—	16	1	no	—
432	C₂²	#11926424	1	1	yes	characteristic
433	C₂²	#11926661	1	1	yes	characteristic
434	C₂²	#11926666	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂×#10597290	1	1	yes	characteristic
444	C₄	#11926528	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	4	2	no	—
448	C₂	—	8	1	no	—
449	C₂	—	16	1	no	—
450	C₂	#14563964	1	1	yes	characteristic
451	C₂	#14564099	1	1	yes	characteristic
452	C₂	#14564124	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#463	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₈×C₁₉	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#463	D₁₉
hypocenter	C₁₉	#9243
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#463

Complements

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

N	H ≅ G/N	type
1. #14572670	C₂	semidirect
2. #14562233	C₂	semidirect
3. #14562078	C₂	semidirect
4. #14561987	C₂	semidirect
5. #14561505	C₂	semidirect
6. #14561485	C₂	semidirect
309. C₁₉	#9243	semidirect

Maximal subgroups

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

subgroup	index
#14572670	2
#14562233	2
#14562078	2
#14561987	2
#14561505	2
#14561485	2
C₂×C₁₉×#463	2
#9243	19