Subgroups — #18081532

Order 4864.

700 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563397	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926281	C₂	1	2	yes	maximal, complemented
3	C₂×#11926278	C₂	1	2	yes	maximal
4	#14561865	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×#10597260	—	2	1	no	—
9	C₂×C₁₉⋊#95	—	2	1	no	—
10	C₂×C₁₉⋊#95	C₂²	1	2	yes	—
11	#11926299	—	2	1	no	—
12	#11926281	—	2	4	no	—
13	#11926278	—	2	4	no	—
14	C₂×C₁₉×#124	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#391	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#390	C₄	1	1	yes	characteristic, complemented
20	C₁₉×#388	—	2	1	no	—
21	C₁₉×#388	—	2	1	no	—
22	C₁₉×#386	—	2	1	no	—
23	C₁₉×#386	—	2	1	no	—
24	C₁₉×#382	C₄	1	1	yes	characteristic, complemented
25	C₂²×Q₈×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	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×Dic₁₉	—	2	2	no	—
32	C₁₉×#124	—	4	2	no	—
33	C₁₉×C₂²⋊Q₈	—	2	2	no	—
34	C₁₉×C₂²⋊Q₈	—	2	2	no	—
35	C₁₉×#121	—	2	2	no	—
36	C₁₉×#121	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	4	2	no	—
47	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₉	—	2	4	no	—
52	C₂×C₄⋊Dic₁₉	—	4	2	no	—
53	C₂×C₄⋊Dic₁₉	—	4	2	no	—
54	C₂²×C₁₉⋊C₈	—	2	2	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	C₁₉⋊#95	—	2	2	no	—
60	C₁₉⋊#95	—	2	2	no	—
61	C₁₉⋊#95	—	4	2	no	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
64	#10597260	—	4	2	no	—
65	C₂⁴×C₁₉	—	2	1	no	—
66	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	4	1	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	—	4	1	no	—
72	C₂×D₄×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂²⋊C₄	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	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	2	yes	—
100	C₂²×Dic₁₉	—	2	4	no	—
101	C₂²×Dic₁₉	—	4	2	no	—
102	C₂²×Dic₁₉	—	4	2	no	—
103	C₂²×Dic₁₉	—	4	2	no	—
104	C₂²×Dic₁₉	—	4	2	no	—
105	C₂²×Dic₁₉	—	4	2	no	—
106	C₂²×Dic₁₉	—	4	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	4	2	no	—
110	C₂²⋊C₄×C₁₉	—	4	2	no	—
111	C₂²⋊C₄×C₁₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₂²⋊C₄×C₁₉	—	4	2	no	—
115	C₂²⋊C₄×C₁₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₉	—	4	2	no	—
117	C₄²×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	4	8	no	—
122	C₂×C₁₉⋊C₈	—	2	4	no	—
123	C₂×C₁₉⋊C₈	—	4	2	no	—
124	C₂×C₁₉⋊C₈	—	4	2	no	—
125	#9682	—	19	1	no	maximal, Sylow
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	—	2	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₁₉	#124	1	1	yes	characteristic
139	C₂³×C₁₉	#127	1	1	yes	characteristic
140	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂³×C₁₉	#137	1	1	yes	characteristic
143	C₂³×C₁₉	#137	1	1	yes	characteristic
144	Q₈×C₁₉	—	8	2	no	—
145	D₄×C₁₉	—	8	2	no	—
146	D₄×C₁₉	—	8	1	no	—
147	D₄×C₁₉	—	8	1	no	—
148	D₄×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	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	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	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	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	#99	1	2	yes	—
180	C₂×C₄×C₁₉	#104	1	2	yes	—
181	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₉	#121	1	2	yes	—
183	C₂×Dic₁₉	—	4	4	no	—
184	C₂×Dic₁₉	—	4	4	no	—
185	C₂×Dic₁₉	—	4	4	no	—
186	C₂×Dic₁₉	—	8	2	no	—
187	C₂×Dic₁₉	—	8	2	no	—
188	C₂×Dic₁₉	—	8	2	no	—
189	C₂×Dic₁₉	—	8	2	no	—
190	C₁₉⋊C₈	—	4	4	no	—
191	#2850	D₁₉	1	1	yes	characteristic
192	#1749	—	19	1	no	—
193	C₂×#328	—	19	2	no	—
194	C₂×#327	—	19	2	no	—
195	C₄⋊#95	—	19	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	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	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	#390	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
217	C₂²×C₁₉	#410	1	1	yes	characteristic
218	C₂²×C₁₉	#417	1	1	yes	characteristic
219	C₂²×C₁₉	#417	1	1	yes	characteristic
220	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
221	C₂²×C₁₉	#421	1	1	yes	characteristic
222	C₂²×C₁₉	#489	1	1	yes	characteristic
223	C₂²×C₁₉	#489	1	1	yes	characteristic
224	C₂²×C₁₉	#496	1	1	yes	characteristic
225	C₂²×C₁₉	#497	1	1	yes	characteristic
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	2	2	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	4	1	no	—
231	C₄×C₁₉	—	4	1	no	—
232	C₄×C₁₉	—	8	1	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	—	8	1	no	—
235	Dic₁₉	—	8	4	no	—
236	C₂×#124	Dic₁₉	1	1	yes	characteristic, complemented
237	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
238	C₂×#121	C₂×D₁₉	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	—	38	1	no	—
240	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
241	C₂×C₂²⋊C₈	—	19	2	no	—
242	C₂×#97	—	38	1	no	—
243	#391	Dic₁₉	1	1	yes	characteristic, complemented
244	#390	Dic₁₉	1	1	yes	characteristic, complemented
245	#388	—	2	1	no	—
246	#388	—	2	1	no	—
247	#386	—	2	1	no	—
248	#386	—	2	1	no	—
249	#382	Dic₁₉	1	1	yes	characteristic, complemented
250	C₂×#95	—	19	2	no	—
251	C₂×#95	—	38	1	no	—
252	#336	—	38	1	no	—
253	#328	—	38	4	no	—
254	#327	—	38	4	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	16	1	no	—
260	C₂×C₁₉	#1504	1	1	yes	characteristic
261	C₂×C₁₉	#1509	1	1	yes	characteristic
262	C₂×C₁₉	#1512	1	1	yes	characteristic
263	C₂×C₁₉	#1513	1	1	yes	characteristic
264	C₂×C₁₉	#1959	1	1	yes	characteristic
265	C₂×C₁₉	#1964	1	1	yes	characteristic
266	C₂×C₁₉	#1980	1	1	yes	characteristic
267	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
270	C₂³×C₄	—	38	2	no	—
271	C₂³×C₄	C₂²⋊D₁₉	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	—	38	2	no	—
275	#124	—	4	2	no	—
276	C₂²⋊Q₈	—	2	2	no	—
277	C₂²⋊Q₈	—	2	2	no	—
278	#121	—	2	2	no	—
279	#121	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	38	4	no	—
282	C₂×C₄⋊C₄	—	76	2	no	—
283	C₂×C₄⋊C₄	—	76	2	no	—
284	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₄²	—	4	2	no	—
293	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
294	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
295	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
297	C₂²⋊C₈	—	19	4	no	—
298	C₂²⋊C₈	—	38	2	no	—
299	#97	—	76	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	38	2	no	—
305	#95	—	38	2	no	—
306	#95	—	76	2	no	—
307	C₁₉	#9682	1	1	yes	characteristic, complemented, Sylow
308	C₂⁴	—	2	1	no	—
309	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	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	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	38	4	no	—
336	C₂²×C₄	—	76	2	no	—
337	C₂²×C₄	—	76	2	no	—
338	C₂²×C₄	—	76	2	no	—
339	C₂²×C₄	—	76	2	no	—
340	C₂²×C₄	—	76	2	no	—
341	C₂²×C₄	—	76	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	C₂²⋊Dic₁₉	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₁₉	1	2	yes	—
347	C₂²×C₄	#64543	1	2	yes	—
348	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
350	C₂×C₈	—	38	4	no	—
351	C₂×C₈	—	76	2	no	—
352	C₂×C₈	—	76	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	76	8	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	#10597382	1	1	yes	characteristic
380	C₂³	#10597386	1	1	yes	characteristic
381	C₂³	#10597395	1	1	yes	characteristic
382	C₂³	#10597395	1	1	yes	characteristic
383	C₂³	#10597397	1	1	yes	characteristic
384	C₂³	#10597397	1	1	yes	characteristic
385	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
386	Q₈	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	1	no	—
389	D₄	—	8	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	1	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	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	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	76	4	no	—
422	C₂×C₄	—	76	4	no	—
423	C₂×C₄	—	76	4	no	—
424	C₂×C₄	—	152	2	no	—
425	C₂×C₄	—	152	2	no	—
426	C₂×C₄	—	152	2	no	—
427	C₂×C₄	—	152	2	no	—
428	C₂×C₄	#10597291	1	2	yes	—
429	C₂×C₄	#10597294	1	2	yes	—
430	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
431	C₂×C₄	#10597384	1	2	yes	—
432	C₈	—	76	4	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	#11926447	1	1	yes	characteristic
453	C₂²	C₂×#10597291	1	1	yes	characteristic
454	C₂²	#11926518	1	1	yes	characteristic
455	C₂²	#11926545	1	1	yes	characteristic
456	C₂²	#11926545	1	1	yes	characteristic
457	C₂²	C₂×#10597294	1	1	yes	characteristic
458	C₂²	#11926561	1	1	yes	characteristic
459	C₂²	#11926903	1	1	yes	characteristic
460	C₂²	#11926903	1	1	yes	characteristic
461	C₂²	#11926934	1	1	yes	characteristic
462	C₂²	#11926939	1	1	yes	characteristic
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	152	4	no	—
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	16	1	no	—
478	C₂	#14562139	1	1	yes	characteristic
479	C₂	#14562160	1	1	yes	characteristic
480	C₂	#14562173	1	1	yes	characteristic
481	C₂	#14562178	1	1	yes	characteristic
482	C₂	#14564452	1	1	yes	characteristic
483	C₂	#14564472	1	1	yes	characteristic
484	C₂	#14564555	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2850	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#121	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2850	D₁₉
hypocenter	C₁₉	#9682
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2850

Complements

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

N	H ≅ G/N	type
1. #14563397	C₂	semidirect
2. C₂×#11926281	C₂	semidirect
4. #14561865	C₂	semidirect
14. C₂×C₁₉×#124	C₄	semidirect
18. C₁₉×#391	C₄	semidirect
19. C₁₉×#390	C₄	semidirect
24. C₁₉×#382	C₄	semidirect
236. C₂×#124	Dic₁₉	semidirect
243. #391	Dic₁₉	semidirect
244. #390	Dic₁₉	semidirect
249. #382	Dic₁₉	semidirect
307. C₁₉	#9682	semidirect

Maximal subgroups

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

subgroup	index
#14563397	2
C₂×#11926281	2
C₂×#11926278	2
#14561865	2
C₁₉×#2850	2
#9682	19