Subgroups — #18082077

Order 4864.

552 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564621	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564472	C₂	1	1	yes	maximal, characteristic
3	#14563664	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563411	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562207	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562203	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#465	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597275	—	2	1	no	—
9	C₂×#10597291	—	2	2	no	—
10	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597272	—	2	1	no	—
12	#11926404	C₂²	1	1	yes	characteristic
13	#11926404	C₂²	1	1	yes	characteristic
14	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926311	—	2	2	no	—
16	#11926307	—	2	1	no	—
17	#11926298	—	2	1	no	—
18	#11926281	—	2	2	no	—
19	#11926278	—	2	2	no	—
20	C₂²×SD₁₆×C₁₉	C₄	1	1	yes	characteristic, complemented
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₁₉×#465	—	2	1	no	—
25	C₁₉×#465	—	2	1	no	—
26	C₁₉×#465	—	2	1	no	—
27	C₁₉×#465	—	2	1	no	—
28	C₂×C₁₉×#106	C₄	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#103	C₄	1	1	yes	characteristic, complemented
30	C₂×C₁₉×#102	C₄	1	1	yes	characteristic, complemented
31	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×SD₁₆×C₁₉	—	2	1	no	—
36	C₂×SD₁₆×C₁₉	—	2	1	no	—
37	C₂×SD₁₆×C₁₉	—	4	2	no	—
38	C₂²×C₈×C₁₉	—	4	2	no	—
39	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₁₉×C₂²⋊Q₈	—	2	1	no	—
46	C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₁₉×#121	—	2	1	no	—
52	C₁₉×#121	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	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⋊Dic₁₉	—	2	1	no	—
59	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
60	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄×Dic₁₉	—	2	1	no	—
64	C₂²×C₁₉⋊C₈	—	2	1	no	—
65	C₁₉×#106	—	2	1	no	—
66	C₁₉×#106	—	2	1	no	—
67	C₁₉×#103	—	2	1	no	—
68	C₁₉×#103	—	2	1	no	—
69	C₁₉×#102	—	2	1	no	—
70	C₁₉×#102	—	2	1	no	—
71	#10597291	—	4	4	no	—
72	C₁₉⋊#95	—	2	1	no	—
73	C₁₉⋊#95	—	2	1	no	—
74	C₁₉⋊#95	—	2	1	no	—
75	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
77	#10597275	—	4	2	no	—
78	#10597272	—	4	2	no	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	4	1	no	—
84	C₂×Q₈×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×Dic₁₉	—	2	2	no	—
105	C₂²×Dic₁₉	—	4	1	no	—
106	C₂²×Dic₁₉	—	4	1	no	—
107	SD₁₆×C₁₉	—	4	2	no	—
108	SD₁₆×C₁₉	—	4	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊Dic₁₉	—	2	2	no	—
130	C₂²⋊Dic₁₉	—	2	2	no	—
131	C₂²⋊Dic₁₉	—	4	2	no	—
132	C₂²⋊Dic₁₉	—	4	2	no	—
133	C₄⋊Dic₁₉	—	4	1	no	—
134	C₄⋊Dic₁₉	—	4	1	no	—
135	C₄⋊Dic₁₉	—	4	1	no	—
136	C₄⋊Dic₁₉	—	4	1	no	—
137	C₄×Dic₁₉	—	4	1	no	—
138	C₄×Dic₁₉	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	#9786	—	19	1	no	maximal, Sylow
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	8	1	no	—
148	C₂³×C₁₉	—	8	1	no	—
149	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
150	C₂³×C₁₉	#121	1	1	yes	characteristic
151	C₂³×C₁₉	#127	1	1	yes	characteristic
152	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
153	C₂³×C₁₉	#137	1	2	yes	—
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	8	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	2	no	—
161	D₄×C₁₉	—	8	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	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	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
182	C₂×Dic₁₉	—	4	2	no	—
183	C₂×Dic₁₉	—	4	2	no	—
184	C₂×Dic₁₉	—	4	2	no	—
185	C₂×Dic₁₉	—	8	1	no	—
186	C₂×Dic₁₉	—	8	1	no	—
187	C₂×Dic₁₉	—	8	1	no	—
188	C₂×Dic₁₉	—	8	1	no	—
189	C₂×Dic₁₉	—	8	1	no	—
190	C₂×Dic₁₉	—	8	1	no	—
191	C₈×C₁₉	—	2	1	no	—
192	C₈×C₁₉	—	2	1	no	—
193	C₈×C₁₉	—	2	1	no	—
194	C₈×C₁₉	#99	1	2	yes	complemented
195	C₁₉⋊C₈	—	4	2	no	—
196	C₂×#465	D₁₉	1	1	yes	characteristic
197	#1996	—	19	1	no	—
198	#1964	—	19	1	no	—
199	#1808	—	19	1	no	—
200	#1752	—	19	1	no	—
201	#1520	—	19	1	no	—
202	#1519	—	19	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	16	2	no	—
215	C₂²×C₁₉	#390	1	1	yes	characteristic
216	C₂²×C₁₉	#440	1	2	yes	—
217	C₂²×C₁₉	#468	1	2	yes	—
218	C₂²×C₁₉	#496	1	1	yes	characteristic
219	C₂²×C₁₉	#497	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
227	C₄×C₁₉	#410	1	1	yes	characteristic
228	Dic₁₉	—	8	2	no	—
229	Dic₁₉	—	16	1	no	—
230	Dic₁₉	—	16	1	no	—
231	C₂²×SD₁₆	Dic₁₉	1	1	yes	characteristic, complemented
232	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
234	C₂×#121	C₂×D₁₉	1	1	yes	characteristic
235	#465	—	2	1	no	—
236	#465	—	2	1	no	—
237	#465	—	2	1	no	—
238	#465	—	2	1	no	—
239	C₂×#107	—	38	1	no	—
240	C₂×#106	Dic₁₉	1	1	yes	characteristic, complemented
241	C₂×#103	Dic₁₉	1	1	yes	characteristic, complemented
242	C₂×#102	Dic₁₉	1	1	yes	characteristic, complemented
243	C₂×#99	—	38	2	no	—
244	C₂×C₂²⋊C₈	—	19	1	no	—
245	C₂×#97	—	38	1	no	—
246	#380	—	19	1	no	—
247	#380	—	19	1	no	—
248	C₄×C₂²⋊C₄	—	19	1	no	—
249	#342	—	38	2	no	—
250	#340	—	38	1	no	—
251	#336	—	38	1	no	—
252	#328	—	38	2	no	—
253	#327	—	38	2	no	—
254	C₂×C₁₉	—	2	2	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	2	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	16	1	no	—
259	C₂×C₁₉	#1964	1	1	yes	characteristic
260	C₂×C₁₉	#1973	1	1	yes	characteristic
261	C₂×C₁₉	#1976	1	1	yes	characteristic
262	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
265	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	4	2	no	—
269	C₂²×C₈	—	4	2	no	—
270	C₂²×C₈	—	38	1	no	—
271	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
272	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
273	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
274	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
276	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	#121	—	2	1	no	—
284	#121	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	38	1	no	—
287	C₂×C₄⋊C₄	—	38	1	no	—
288	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	19	2	no	—
293	C₂×C₂²⋊C₄	—	38	1	no	—
294	C₂×C₂²⋊C₄	—	38	1	no	—
295	C₂×C₄²	—	38	1	no	—
296	#107	—	76	2	no	—
297	#106	—	2	1	no	—
298	#106	—	2	1	no	—
299	#103	—	2	1	no	—
300	#103	—	2	1	no	—
301	#102	—	2	1	no	—
302	#102	—	2	1	no	—
303	#99	—	76	4	no	—
304	C₂²⋊C₈	—	19	2	no	—
305	C₂²⋊C₈	—	38	1	no	—
306	#97	—	76	2	no	—
307	#95	—	38	1	no	—
308	#95	—	38	1	no	—
309	#95	—	38	1	no	—
310	C₁₉	#9786	1	1	yes	characteristic, complemented, Sylow
311	C₂⁴	—	2	1	no	—
312	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	4	1	no	—
316	C₂×Q₈	—	4	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	38	2	no	—
331	C₂²×C₄	—	76	1	no	—
332	C₂²×C₄	—	76	1	no	—
333	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
334	C₂²×C₄	#64543	1	1	yes	characteristic
335	C₂²×C₄	#64543	1	1	yes	characteristic
336	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
339	SD₁₆	—	4	2	no	—
340	SD₁₆	—	4	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	38	2	no	—
348	C₂×C₈	—	76	1	no	—
349	C₂×C₈	—	76	1	no	—
350	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
351	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
352	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
353	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	76	1	no	—
361	C₄⋊C₄	—	76	1	no	—
362	C₄⋊C₄	—	76	1	no	—
363	C₄⋊C₄	—	76	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	38	2	no	—
369	C₂²⋊C₄	—	38	2	no	—
370	C₂²⋊C₄	—	76	2	no	—
371	C₂²⋊C₄	—	76	2	no	—
372	C₄²	—	76	1	no	—
373	C₄²	—	76	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	1	no	—
379	C₂³	—	8	1	no	—
380	C₂³	#10597360	1	2	yes	—
381	C₂³	#10597361	1	2	yes	—
382	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
383	C₂³	#10597384	1	1	yes	characteristic
384	C₂³	#10597386	1	1	yes	characteristic
385	Q₈	—	4	1	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	8	1	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	76	2	no	—
410	C₂×C₄	—	76	2	no	—
411	C₂×C₄	—	76	2	no	—
412	C₂×C₄	—	152	1	no	—
413	C₂×C₄	—	152	1	no	—
414	C₂×C₄	—	152	1	no	—
415	C₂×C₄	—	152	1	no	—
416	C₂×C₄	—	152	1	no	—
417	C₂×C₄	—	152	1	no	—
418	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
419	C₂×C₄	#10597382	1	1	yes	characteristic
420	C₂×C₄	#10597384	1	1	yes	characteristic
421	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	2	1	no	—
425	C₈	—	76	2	no	—
426	C₈	#10597291	1	2	yes	complemented
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	16	2	no	—
439	C₂²	#11926447	1	1	yes	characteristic
440	C₂²	#11926645	1	2	yes	—
441	C₂²	#11926787	1	2	yes	—
442	C₂²	#11926930	1	1	yes	characteristic
443	C₂²	#11926935	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₄	—	304	1	no	—
451	C₄	—	304	1	no	—
452	C₄	—	152	2	no	—
453	C₄	C₂×#10597291	1	1	yes	characteristic
454	C₄	#11926518	1	1	yes	characteristic
455	C₂	—	2	1	no	—
456	C₂	—	2	2	no	—
457	C₂	—	2	2	no	—
458	C₂	—	2	1	no	—
459	C₂	—	16	1	no	—
460	C₂	#14564472	1	1	yes	characteristic
461	C₂	#14564518	1	1	yes	characteristic
462	C₂	#14564534	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926447
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#465	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂×C₁₉×#121	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#465	D₁₉
hypocenter	C₁₉	#9786
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#465

Complements

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

N	H ≅ G/N	type
1. #14564621	C₂	semidirect
3. #14563664	C₂	semidirect
4. #14563411	C₂	semidirect
5. #14562207	C₂	semidirect
20. C₂²×SD₁₆×C₁₉	C₄	semidirect
28. C₂×C₁₉×#106	C₄	semidirect
29. C₂×C₁₉×#103	C₄	semidirect
30. C₂×C₁₉×#102	C₄	semidirect
194. C₈×C₁₉	#99	semidirect
231. C₂²×SD₁₆	Dic₁₉	semidirect
240. C₂×#106	Dic₁₉	semidirect
241. C₂×#103	Dic₁₉	semidirect
242. C₂×#102	Dic₁₉	semidirect
310. C₁₉	#9786	semidirect
426. C₈	#10597291	semidirect

Maximal subgroups

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

subgroup	index
#14564621	2
#14564472	2
#14563664	2
#14563411	2
#14562207	2
#14562203	2
C₂×C₁₉×#465	2
#9786	19