Subgroups — #18074386

Order 4864.

714 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563619	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562292	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562284	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562038	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562034	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561949	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3455	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
13	#11926299	—	2	1	no	—
14	#11926293	—	2	1	no	—
15	#11926290	—	2	1	no	—
16	#11926290	—	2	1	no	—
17	#11926288	—	2	1	no	—
18	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
20	#11926270	—	2	1	no	—
21	#11926268	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#542	—	2	1	no	—
24	C₁₉×#541	—	2	1	no	—
25	C₁₉×#540	—	2	1	no	—
26	C₁₉×#539	—	2	1	no	—
27	C₁₉×#539	C₄	1	2	yes	—
28	C₁₉×#538	—	2	1	no	—
29	C₁₉×#538	C₄	1	2	yes	—
30	C₁₉×#533	C₂²	1	1	yes	characteristic
31	C₁₉×#532	C₂²	1	1	yes	characteristic
32	C₁₉×#529	—	2	2	no	—
33	C₁₉×#529	—	2	2	no	—
34	C₁₉×#525	—	2	1	no	—
35	C₄×#41×C₁₉	—	2	1	no	—
36	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
41	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
42	C₁₉×#127	D₄	1	1	yes	characteristic
43	C₁₉×#126	—	2	2	no	—
44	C₁₉×#126	—	2	2	no	—
45	C₁₉×#126	—	2	2	no	—
46	C₁₉×#126	—	2	2	no	—
47	C₁₉×#125	—	2	2	no	—
48	C₁₉×#125	—	2	2	no	—
49	C₁₉×#125	—	2	1	no	—
50	C₁₉×#124	—	2	2	no	—
51	C₁₉×#124	—	2	2	no	—
52	C₁₉×#124	—	2	1	no	—
53	C₁₉×#123	—	2	2	no	—
54	C₁₉×#123	—	2	2	no	—
55	C₁₉×#123	—	2	2	no	—
56	C₁₉×#123	—	2	2	no	—
57	C₁₉×#123	—	2	2	no	—
58	C₁₉×C₂²⋊Q₈	—	2	1	no	—
59	C₁₉×C₂²⋊Q₈	—	2	1	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	2	1	no	—
69	C₁₉×#121	C₂×C₄	1	2	yes	—
70	C₁₉×#120	—	2	2	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	D₄	1	2	yes	—
75	C₄×D₄×C₁₉	—	2	1	no	—
76	C₄×D₄×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	D₄	1	2	yes	—
83	C₁₉×#117	—	2	2	no	—
84	C₁₉×#117	—	2	1	no	—
85	C₁₉×#117	—	2	1	no	—
86	C₁₉×#117	—	2	1	no	—
87	C₁₉×#117	—	2	1	no	—
88	C₁₉×#117	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	—	2	2	no	—
94	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×C₁₉⋊C₈	—	2	1	no	—
97	C₂²×C₁₉⋊C₈	—	2	1	no	—
98	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
99	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
100	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
101	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
102	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
103	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
104	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
105	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
106	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
107	C₄×C₁₉⋊C₈	—	2	1	no	—
108	C₄×C₁₉⋊C₈	—	2	1	no	—
109	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
110	#41×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	—	4	1	no	—
113	#41×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	2	2	no	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	2	1	no	—
162	C₂²⋊C₄×C₁₉	—	2	1	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	1	no	—
165	C₂²⋊C₄×C₁₉	—	2	1	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	1	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₁₉⋊C₈	—	4	1	no	—
177	C₂×C₁₉⋊C₈	—	4	1	no	—
178	C₂×C₁₉⋊C₈	—	4	1	no	—
179	C₂×C₁₉⋊C₈	—	4	1	no	—
180	C₂×C₁₉⋊C₈	—	4	1	no	—
181	C₂×C₁₉⋊C₈	—	4	1	no	—
182	C₂×C₁₉⋊C₈	—	4	1	no	—
183	C₂×C₁₉⋊C₈	—	4	1	no	—
184	#8411	—	19	1	no	maximal, Sylow
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	1	no	—
188	C₂³×C₁₉	—	2	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	1	no	—
194	Q₈×C₁₉	—	4	1	no	—
195	Q₈×C₁₉	—	8	1	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	8	1	no	—
202	D₄×C₁₉	—	8	2	no	—
203	D₄×C₁₉	—	8	2	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×C₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
232	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
234	C₁₉⋊C₈	—	8	1	no	—
235	C₁₉⋊C₈	—	8	1	no	—
236	C₁₉⋊C₈	—	8	1	no	—
237	C₁₉⋊C₈	—	8	1	no	—
238	#3455	D₁₉	1	1	yes	characteristic
239	#1798	—	19	1	no	—
240	#1542	—	19	1	no	—
241	#1540	—	19	1	no	—
242	#1481	—	19	1	no	—
243	#1480	—	19	1	no	—
244	#1458	—	19	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	8	1	no	—
255	C₂²×C₁₉	#379	1	1	yes	characteristic
256	C₂²×C₁₉	#416	1	1	yes	characteristic
257	C₂²×C₁₉	#417	1	1	yes	characteristic
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	4	1	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	#449	1	1	yes	characteristic
269	C₄×C₁₉	#449	1	1	yes	characteristic
270	C₄×C₁₉	#452	1	1	yes	characteristic
271	C₄×C₁₉	#452	1	1	yes	characteristic
272	#542	—	2	1	no	—
273	#542	—	2	1	no	—
274	#541	—	2	1	no	—
275	#540	—	2	1	no	—
276	#539	—	2	1	no	—
277	#539	Dic₁₉	1	2	yes	—
278	#538	—	2	1	no	—
279	#538	Dic₁₉	1	2	yes	—
280	#533	C₂×D₁₉	1	1	yes	characteristic
281	#532	C₂×D₁₉	1	1	yes	characteristic
282	#529	—	2	2	no	—
283	#529	—	2	2	no	—
284	#525	—	2	1	no	—
285	C₄×#41	—	2	1	no	—
286	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
287	#431	—	19	1	no	—
288	#431	—	19	1	no	—
289	C₂×C₄⋊C₈	—	19	1	no	—
290	C₂×C₄⋊C₈	—	19	1	no	—
291	C₂×C₂²⋊C₈	—	38	1	no	—
292	#336	—	38	1	no	—
293	#333	—	38	1	no	—
294	#332	—	38	1	no	—
295	#332	—	38	1	no	—
296	#331	—	38	1	no	—
297	Q₈⋊C₈	—	38	2	no	—
298	D₄⋊C₈	—	38	2	no	—
299	#324	—	38	1	no	—
300	#323	—	38	1	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	8	2	no	—
304	C₂×C₁₉	—	8	1	no	—
305	C₂×C₁₉	#1788	1	1	yes	characteristic
306	C₂×C₁₉	#1791	1	1	yes	characteristic
307	C₂×C₁₉	#1794	1	1	yes	characteristic
308	C₂×#41	—	2	1	no	—
309	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
310	C₂²×C₈	—	38	1	no	—
311	C₂²×C₈	—	38	1	no	—
312	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
313	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
314	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
315	#127	C₂²⋊D₁₉	1	1	yes	characteristic
316	#126	—	2	2	no	—
317	#126	—	2	2	no	—
318	#126	—	2	2	no	—
319	#126	—	2	2	no	—
320	#125	—	2	2	no	—
321	#125	—	2	2	no	—
322	#125	—	2	1	no	—
323	#124	—	2	2	no	—
324	#124	—	2	2	no	—
325	#124	—	2	1	no	—
326	#123	—	2	2	no	—
327	#123	—	2	2	no	—
328	#123	—	2	2	no	—
329	#123	—	2	2	no	—
330	#123	—	2	2	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	2	1	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	C₂×Dic₁₉	1	2	yes	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	—	2	2	no	—
340	#121	—	2	2	no	—
341	#121	—	2	1	no	—
342	#121	C₂×Dic₁₉	1	2	yes	—
343	#120	—	2	2	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
356	#117	—	2	2	no	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
368	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
369	C₄⋊C₈	—	38	1	no	—
370	C₄⋊C₈	—	38	1	no	—
371	C₄⋊C₈	—	38	1	no	—
372	C₄⋊C₈	—	38	1	no	—
373	C₄⋊C₈	—	38	1	no	—
374	C₄⋊C₈	—	38	1	no	—
375	C₂²⋊C₈	—	38	1	no	—
376	C₂²⋊C₈	—	38	1	no	—
377	C₂²⋊C₈	—	76	2	no	—
378	C₄×C₈	—	38	1	no	—
379	C₄×C₈	—	38	1	no	—
380	C₁₉	#8411	1	1	yes	characteristic, complemented, Sylow
381	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
382	#41	—	4	1	no	—
383	#41	—	4	1	no	—
384	#41	—	4	1	no	—
385	#41	—	4	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
410	C₂×C₈	—	76	1	no	—
411	C₂×C₈	—	76	1	no	—
412	C₂×C₈	—	76	1	no	—
413	C₂×C₈	—	76	1	no	—
414	C₂×C₈	—	76	1	no	—
415	C₂×C₈	—	76	1	no	—
416	C₂×C₈	—	76	1	no	—
417	C₂×C₈	—	76	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
433	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
453	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
454	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
455	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
463	Q₈	—	4	2	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	8	1	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	1	no	—
471	D₄	—	4	1	no	—
472	D₄	—	8	1	no	—
473	D₄	—	8	2	no	—
474	D₄	—	8	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	#10597395	1	1	yes	characteristic
496	C₂×C₄	#10597396	1	1	yes	characteristic
497	C₂×C₄	#10597396	1	1	yes	characteristic
498	C₂×C₄	#10597397	1	1	yes	characteristic
499	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
500	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
501	C₂×C₄	#10597399	1	1	yes	characteristic
502	C₂×C₄	#10597399	1	1	yes	characteristic
503	C₂×C₄	#10597399	1	1	yes	characteristic
504	C₂×C₄	#10597399	1	1	yes	characteristic
505	C₈	—	152	1	no	—
506	C₈	—	152	1	no	—
507	C₈	—	152	1	no	—
508	C₈	—	152	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	8	1	no	—
519	C₂²	#11926400	1	1	yes	characteristic
520	C₂²	#11926540	1	1	yes	characteristic
521	C₂²	#11926545	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	2	no	—
532	C₄	#11926689	1	1	yes	characteristic
533	C₄	#11926689	1	1	yes	characteristic
534	C₄	#11926706	1	1	yes	characteristic
535	C₄	#11926706	1	1	yes	characteristic
536	C₂	—	2	1	no	—
537	C₂	—	2	1	no	—
538	C₂	—	8	1	no	—
539	C₂	—	8	2	no	—
540	C₂	#14563575	1	1	yes	characteristic
541	C₂	#14563586	1	1	yes	characteristic
542	C₂	#14563599	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3455	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3455	D₁₉
hypocenter	C₁₉	#8411
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3455

Complements

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

N	H ≅ G/N	type
1. #14563619	C₂	semidirect
2. #14562292	C₂	semidirect
3. #14562284	C₂	semidirect
4. #14562038	C₂	semidirect
5. #14562034	C₂	semidirect
6. #14561949	C₂	semidirect
380. C₁₉	#8411	semidirect

Maximal subgroups

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

subgroup	index
#14563619	2
#14562292	2
#14562284	2
#14562038	2
#14562034	2
#14561949	2
C₁₉×#3455	2
#8411	19