Subgroups — #18074463

Order 4864.

756 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564584	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563655	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562320	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562312	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562022	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3511	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597294	—	2	1	no	—
12	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926306	—	2	2	no	—
14	#11926303	—	2	1	no	—
15	#11926290	—	2	1	no	—
16	#11926290	—	2	2	no	—
17	#11926288	—	2	1	no	—
18	#11926278	—	2	2	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	C₁₉×#556	C₄	1	2	yes	complemented
22	C₁₉×#555	—	2	1	no	—
23	C₁₉×#554	—	2	1	no	—
24	C₁₉×#553	—	2	2	no	—
25	C₁₉×#548	—	2	2	no	—
26	C₁₉×#547	C₄	1	2	yes	complemented
27	C₁₉×#542	—	2	2	no	—
28	C₁₉×#537	—	2	1	no	—
29	C₁₉×#533	—	2	1	no	—
30	C₁₉×#532	—	2	1	no	—
31	C₁₉×#532	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₉×#520	—	2	1	no	—
34	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
42	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
43	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
44	C₁₉×#127	D₄	1	1	yes	characteristic
45	C₁₉×#126	—	2	4	no	—
46	C₁₉×#125	—	2	2	no	—
47	C₁₉×#124	—	2	4	no	—
48	C₁₉×#124	—	2	2	no	—
49	C₁₉×#124	—	2	1	no	—
50	C₁₉×#123	—	2	4	no	—
51	C₁₉×C₂²⋊Q₈	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	—	2	4	no	—
53	C₁₉×C₂²⋊Q₈	—	2	2	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	1	no	—
60	C₁₉×#121	D₄	1	2	yes	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×C₁₉	—	2	2	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
74	C₁₉×#117	—	2	2	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊Dic₁₉	—	2	1	no	—
84	C₂×C₄×Dic₁₉	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	—	2	1	no	—
87	#10597294	—	4	2	no	—
88	C₁₉⋊#95	—	2	1	no	—
89	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
90	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
91	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
92	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
93	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
94	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
95	C₄×C₁₉⋊C₈	—	2	1	no	—
96	#41×C₁₉	—	2	1	no	—
97	#41×C₁₉	—	2	1	no	—
98	#41×C₁₉	—	2	1	no	—
99	#41×C₁₉	—	2	1	no	—
100	#41×C₁₉	—	4	1	no	—
101	#41×C₁₉	—	4	1	no	—
102	#41×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	4	1	no	—
104	#41×C₁₉	—	8	4	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	8	2	no	—
109	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	4	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×Dic₁₉	—	4	1	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
137	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
138	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
139	C₂²⋊C₄×C₁₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	1	no	—
143	C₂²⋊C₄×C₁₉	—	2	1	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	1	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	4	no	—
148	C₄²×C₁₉	—	2	1	no	—
149	C₄²×C₁₉	—	2	1	no	—
150	C₄²×C₁₉	—	2	1	no	—
151	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄⋊Dic₁₉	—	2	2	no	—
156	C₄⋊Dic₁₉	—	4	1	no	—
157	C₄×Dic₁₉	—	4	1	no	—
158	C₄×Dic₁₉	—	4	1	no	—
159	#64520	—	4	1	no	—
160	#64520	—	4	1	no	—
161	C₂×C₁₉⋊C₈	—	4	2	no	—
162	C₂×C₁₉⋊C₈	—	4	1	no	—
163	C₂×C₁₉⋊C₈	—	4	1	no	—
164	C₂×C₁₉⋊C₈	—	4	1	no	—
165	#8422	—	19	1	no	maximal, Sylow
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	#120	1	1	yes	characteristic
169	Q₈×C₁₉	—	2	1	no	—
170	Q₈×C₁₉	—	2	1	no	—
171	Q₈×C₁₉	—	4	4	no	—
172	Q₈×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	8	2	no	—
175	D₄×C₁₉	—	2	1	no	—
176	D₄×C₁₉	—	2	1	no	—
177	D₄×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	4	2	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	4	1	no	—
184	D₄×C₁₉	—	4	1	no	—
185	D₄×C₁₉	—	4	1	no	—
186	D₄×C₁₉	—	8	4	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	—	8	4	no	—
204	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
212	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
214	C₂×Dic₁₉	—	4	2	no	—
215	C₂×Dic₁₉	—	8	1	no	—
216	C₂×Dic₁₉	—	8	1	no	—
217	C₁₉⋊C₈	—	8	1	no	—
218	C₁₉⋊C₈	—	8	1	no	—
219	C₁₉⋊C₈	—	8	1	no	—
220	#3511	D₁₉	1	1	yes	characteristic
221	#1987	—	19	1	no	—
222	#1806	—	19	1	no	—
223	#1549	—	19	1	no	—
224	#1547	—	19	1	no	—
225	#1502	—	19	1	no	—
226	#1477	—	19	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	4	1	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	1	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	#379	1	1	yes	characteristic
236	C₂²×C₁₉	#449	1	1	yes	characteristic
237	C₂²×C₁₉	#452	1	1	yes	characteristic
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	4	1	no	—
242	C₄×C₁₉	—	4	1	no	—
243	C₄×C₁₉	—	4	4	no	—
244	C₄×C₁₉	—	4	1	no	—
245	C₄×C₁₉	—	4	2	no	—
246	C₄×C₁₉	#416	1	1	yes	characteristic
247	C₄×C₁₉	#417	1	1	yes	characteristic
248	C₄×C₁₉	#449	1	1	yes	characteristic
249	C₄×C₁₉	#452	1	1	yes	characteristic
250	C₄×C₁₉	#454	1	1	yes	characteristic
251	C₄×C₁₉	#456	1	1	yes	characteristic
252	Dic₁₉	—	8	2	no	—
253	#556	Dic₁₉	1	2	yes	complemented
254	#555	—	2	1	no	—
255	#554	—	2	1	no	—
256	#553	—	2	2	no	—
257	#548	—	2	2	no	—
258	#547	Dic₁₉	1	2	yes	complemented
259	#542	—	2	2	no	—
260	#537	—	2	1	no	—
261	#533	—	2	1	no	—
262	#532	—	2	1	no	—
263	#532	C₂×D₁₉	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
265	#520	—	2	1	no	—
266	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
267	#431	—	19	1	no	—
268	#423	—	19	1	no	—
269	C₂×C₄⋊C₈	—	19	1	no	—
270	C₂×#104	—	38	1	no	—
271	C₄×C₄⋊C₄	—	19	1	no	—
272	#340	—	38	2	no	—
273	#339	—	38	1	no	—
274	#332	—	38	1	no	—
275	#332	—	38	2	no	—
276	#331	—	38	1	no	—
277	#327	—	38	2	no	—
278	Q₈⋊C₈	—	38	1	no	—
279	D₄⋊C₈	—	38	1	no	—
280	C₂×C₁₉	—	2	1	no	—
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	8	1	no	—
283	C₂×C₁₉	—	8	2	no	—
284	C₂×C₁₉	#1788	1	1	yes	characteristic
285	C₂×C₁₉	#1793	1	1	yes	characteristic
286	C₂×C₁₉	#1795	1	1	yes	characteristic
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	1	no	—
289	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
290	C₂²×Q₈	—	2	1	no	—
291	C₂×M₁₆	—	38	1	no	—
292	C₂²×C₈	—	38	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
296	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
297	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
298	#127	C₂²⋊D₁₉	1	1	yes	characteristic
299	#126	—	2	4	no	—
300	#125	—	2	2	no	—
301	#124	—	2	4	no	—
302	#124	—	2	2	no	—
303	#124	—	2	1	no	—
304	#123	—	2	4	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	#121	—	2	2	no	—
310	#121	—	2	2	no	—
311	#121	—	2	4	no	—
312	#121	—	2	2	no	—
313	#121	—	2	1	no	—
314	#121	C₂²⋊D₁₉	1	2	yes	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
318	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
326	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
327	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
328	#117	—	2	2	no	—
329	#117	—	2	2	no	—
330	#117	—	2	1	no	—
331	#117	C₂²⋊D₁₉	1	1	yes	characteristic
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	38	1	no	—
335	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	38	1	no	—
338	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
339	C₄⋊C₈	—	38	1	no	—
340	C₄⋊C₈	—	38	1	no	—
341	C₄⋊C₈	—	38	1	no	—
342	C₄⋊C₈	—	38	1	no	—
343	C₄⋊C₈	—	38	1	no	—
344	#104	—	76	2	no	—
345	C₂²⋊C₈	—	38	1	no	—
346	C₄×C₈	—	38	1	no	—
347	#95	—	38	1	no	—
348	C₁₉	#8422	1	1	yes	characteristic, complemented, Sylow
349	#41	—	2	1	no	—
350	#41	—	2	1	no	—
351	#41	—	2	1	no	—
352	#41	—	2	1	no	—
353	#41	—	4	1	no	—
354	#41	—	4	1	no	—
355	#41	—	4	1	no	—
356	#41	—	4	1	no	—
357	#41	—	8	4	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	8	2	no	—
362	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
369	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	76	1	no	—
377	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
380	M₁₆	—	76	1	no	—
381	M₁₆	—	76	1	no	—
382	C₂×C₈	—	76	2	no	—
383	C₂×C₈	—	76	1	no	—
384	C₂×C₈	—	76	1	no	—
385	C₂×C₈	—	76	1	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	38	2	no	—
395	C₄⋊C₄	—	76	1	no	—
396	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
397	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
398	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
399	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	76	1	no	—
413	C₄²	—	76	1	no	—
414	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
415	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
416	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
417	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
418	C₂³	—	2	1	no	—
419	C₂³	—	2	2	no	—
420	C₂³	#10597399	1	1	yes	characteristic
421	Q₈	—	2	1	no	—
422	Q₈	—	2	1	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	4	1	no	—
426	Q₈	—	8	2	no	—
427	D₄	—	2	1	no	—
428	D₄	—	2	1	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	1	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	8	4	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	—	8	4	no	—
456	C₂×C₄	—	76	2	no	—
457	C₂×C₄	—	152	1	no	—
458	C₂×C₄	—	152	1	no	—
459	C₂×C₄	#10597395	1	1	yes	characteristic
460	C₂×C₄	#10597396	1	1	yes	characteristic
461	C₂×C₄	#10597396	1	1	yes	characteristic
462	C₂×C₄	#10597397	1	1	yes	characteristic
463	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
466	C₂×C₄	#10597399	1	1	yes	characteristic
467	C₂×C₄	#10597399	1	1	yes	characteristic
468	C₂×C₄	#10597399	1	1	yes	characteristic
469	C₈	—	152	1	no	—
470	C₈	—	152	1	no	—
471	C₈	—	152	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	2	no	—
480	C₂²	#11926400	1	1	yes	characteristic
481	C₂²	#11926689	1	1	yes	characteristic
482	C₂²	#11926706	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	152	2	no	—
492	C₄	#11926540	1	1	yes	characteristic
493	C₄	#11926545	1	1	yes	characteristic
494	C₄	#11926689	1	1	yes	characteristic
495	C₄	#11926706	1	1	yes	characteristic
496	C₄	#11926717	1	1	yes	characteristic
497	C₄	#11926727	1	1	yes	characteristic
498	C₂	—	2	1	no	—
499	C₂	—	2	1	no	—
500	C₂	—	8	1	no	—
501	C₂	—	8	2	no	—
502	C₂	#14563575	1	1	yes	characteristic
503	C₂	#14563594	1	1	yes	characteristic
504	C₂	#14563605	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3511	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3511	D₁₉
hypocenter	C₁₉	#8422
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3511

Complements

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

N	H ≅ G/N	type
1. #14564584	C₂	semidirect
2. #14563655	C₂	semidirect
3. #14562320	C₂	semidirect
4. #14562312	C₂	semidirect
5. #14562130	C₂	semidirect
6. #14562022	C₂	semidirect
21. C₁₉×#556	C₄	semidirect
26. C₁₉×#547	C₄	semidirect
253. #556	Dic₁₉	semidirect
258. #547	Dic₁₉	semidirect
348. C₁₉	#8422	semidirect

Maximal subgroups

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

subgroup	index
#14564584	2
#14563655	2
#14562320	2
#14562312	2
#14562130	2
#14562022	2
C₁₉×#3511	2
#8422	19