Subgroups — #18074470

Order 4864.

772 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564559	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563655	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562316	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	C₂×#10597292	—	2	2	no	—
13	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	#11926303	—	2	1	no	—
15	#11926293	—	2	2	no	—
16	#11926290	—	2	1	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	—	2	1	no	—
22	C₁₉×#555	C₄	1	2	yes	complemented
23	C₁₉×#554	C₄	1	2	yes	complemented
24	C₁₉×#553	—	2	2	no	—
25	C₁₉×#548	—	2	2	no	—
26	C₁₉×#547	—	2	1	no	—
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	D₄	1	2	yes	—
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	2	no	—
48	C₁₉×#124	—	2	4	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	2	no	—
53	C₁₉×C₂²⋊Q₈	—	2	2	no	—
54	C₁₉×C₂²⋊Q₈	—	2	4	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₁₉×#121	—	2	4	no	—
57	C₁₉×#121	—	2	2	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	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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	#10597292	—	4	4	no	—
89	C₁₉⋊#95	—	2	1	no	—
90	C₂²⋊(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	C₄×C₁₉⋊C₈	—	2	1	no	—
97	#41×C₁₉	—	2	1	no	—
98	#41×C₁₉	—	2	1	no	—
99	#41×C₁₉	—	2	1	no	—
100	#41×C₁₉	—	2	1	no	—
101	#41×C₁₉	—	4	1	no	—
102	#41×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	4	1	no	—
104	#41×C₁₉	—	4	1	no	—
105	#41×C₁₉	—	8	2	no	—
106	#41×C₁₉	—	8	2	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	4	2	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×Dic₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	2	4	no	—
131	C₄⋊C₄×C₁₉	—	2	4	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	2	4	no	—
144	C₂²⋊C₄×C₁₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₉	—	2	1	no	—
146	C₂²⋊C₄×C₁₉	—	2	1	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	2	1	no	—
149	C₂²⋊C₄×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	4	no	—
151	C₄²×C₁₉	—	2	1	no	—
152	C₄²×C₁₉	—	2	1	no	—
153	C₄²×C₁₉	—	2	1	no	—
154	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊Dic₁₉	—	2	2	no	—
159	C₄⋊Dic₁₉	—	4	1	no	—
160	C₄×Dic₁₉	—	4	1	no	—
161	C₄×Dic₁₉	—	4	1	no	—
162	#64520	—	4	1	no	—
163	#64520	—	4	1	no	—
164	C₂×C₁₉⋊C₈	—	4	2	no	—
165	C₂×C₁₉⋊C₈	—	4	1	no	—
166	C₂×C₁₉⋊C₈	—	4	1	no	—
167	C₂×C₁₉⋊C₈	—	4	1	no	—
168	#8423	—	19	1	no	maximal, Sylow
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	#120	1	1	yes	characteristic
172	Q₈×C₁₉	—	2	1	no	—
173	Q₈×C₁₉	—	2	1	no	—
174	Q₈×C₁₉	—	4	4	no	—
175	Q₈×C₁₉	—	4	1	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	2	1	no	—
180	D₄×C₁₉	—	2	1	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	1	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	1	no	—
187	D₄×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	4	1	no	—
189	D₄×C₁₉	—	4	1	no	—
190	D₄×C₁₉	—	8	4	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	8	2	no	—
207	C₂×C₄×C₁₉	—	8	4	no	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
216	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
218	C₂×Dic₁₉	—	4	2	no	—
219	C₂×Dic₁₉	—	8	1	no	—
220	C₂×Dic₁₉	—	8	1	no	—
221	C₁₉⋊C₈	—	8	1	no	—
222	C₁₉⋊C₈	—	8	1	no	—
223	C₁₉⋊C₈	—	8	1	no	—
224	#3511	D₁₉	1	1	yes	characteristic
225	#1981	—	19	1	no	—
226	#1806	—	19	1	no	—
227	#1548	—	19	1	no	—
228	#1547	—	19	1	no	—
229	#1502	—	19	1	no	—
230	#1477	—	19	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	4	1	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	1	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	#379	1	1	yes	characteristic
240	C₂²×C₁₉	#449	1	1	yes	characteristic
241	C₂²×C₁₉	#452	1	1	yes	characteristic
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	4	1	no	—
246	C₄×C₁₉	—	4	4	no	—
247	C₄×C₁₉	—	4	1	no	—
248	C₄×C₁₉	—	4	1	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	#416	1	1	yes	characteristic
251	C₄×C₁₉	#417	1	1	yes	characteristic
252	C₄×C₁₉	#449	1	1	yes	characteristic
253	C₄×C₁₉	#452	1	1	yes	characteristic
254	C₄×C₁₉	#453	1	1	yes	characteristic
255	C₄×C₁₉	#455	1	1	yes	characteristic
256	Dic₁₉	—	8	2	no	—
257	#556	—	2	1	no	—
258	#555	Dic₁₉	1	2	yes	complemented
259	#554	Dic₁₉	1	2	yes	complemented
260	#553	—	2	2	no	—
261	#548	—	2	2	no	—
262	#547	—	2	1	no	—
263	#542	—	2	2	no	—
264	#537	—	2	1	no	—
265	#533	—	2	1	no	—
266	#532	—	2	1	no	—
267	#532	C₂×D₁₉	1	1	yes	characteristic
268	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
269	#520	—	2	1	no	—
270	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
271	#431	—	19	1	no	—
272	#423	—	19	1	no	—
273	C₂×C₄⋊C₈	—	19	1	no	—
274	C₂×#104	—	38	1	no	—
275	C₂×#103	—	38	2	no	—
276	C₄×C₄⋊C₄	—	19	1	no	—
277	#339	—	38	1	no	—
278	#333	—	38	2	no	—
279	#332	—	38	1	no	—
280	#331	—	38	1	no	—
281	#327	—	38	2	no	—
282	Q₈⋊C₈	—	38	1	no	—
283	D₄⋊C₈	—	38	1	no	—
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	8	1	no	—
287	C₂×C₁₉	—	8	2	no	—
288	C₂×C₁₉	#1788	1	1	yes	characteristic
289	C₂×C₁₉	#1792	1	1	yes	characteristic
290	C₂×C₁₉	#1796	1	1	yes	characteristic
291	C₂×#41	—	2	2	no	—
292	C₂×#41	—	2	1	no	—
293	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
294	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
295	C₂×M₁₆	—	38	1	no	—
296	C₂²×C₈	—	38	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
300	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
301	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
302	#127	C₂²⋊D₁₉	1	1	yes	characteristic
303	#126	—	2	4	no	—
304	#125	—	2	2	no	—
305	#124	—	2	2	no	—
306	#124	—	2	4	no	—
307	#124	—	2	1	no	—
308	#123	—	2	4	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	2	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	#121	—	2	2	no	—
314	#121	—	2	4	no	—
315	#121	—	2	2	no	—
316	#121	—	2	2	no	—
317	#121	—	2	1	no	—
318	#121	C₂²⋊D₁₉	1	2	yes	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
322	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
330	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
331	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	#117	—	2	1	no	—
335	#117	C₂²⋊D₁₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	38	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	38	1	no	—
342	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
343	C₄⋊C₈	—	38	1	no	—
344	C₄⋊C₈	—	38	1	no	—
345	C₄⋊C₈	—	38	1	no	—
346	C₄⋊C₈	—	38	1	no	—
347	C₄⋊C₈	—	38	1	no	—
348	#104	—	76	2	no	—
349	#103	—	76	4	no	—
350	C₂²⋊C₈	—	38	1	no	—
351	C₄×C₈	—	38	1	no	—
352	#95	—	38	1	no	—
353	C₁₉	#8423	1	1	yes	characteristic, complemented, Sylow
354	#41	—	2	1	no	—
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	4	1	no	—
359	#41	—	4	1	no	—
360	#41	—	4	1	no	—
361	#41	—	4	1	no	—
362	#41	—	8	2	no	—
363	#41	—	8	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	—	4	2	no	—
368	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
369	C₂×Q₈	C₂²⋊Dic₁₉	1	4	yes	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
376	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	76	1	no	—
384	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
387	M₁₆	—	76	1	no	—
388	M₁₆	—	76	1	no	—
389	C₂×C₈	—	76	2	no	—
390	C₂×C₈	—	76	1	no	—
391	C₂×C₈	—	76	1	no	—
392	C₂×C₈	—	76	1	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	38	2	no	—
403	C₄⋊C₄	—	76	1	no	—
404	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
405	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
406	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₄²	—	2	4	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	76	1	no	—
420	C₄²	—	76	1	no	—
421	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
422	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
423	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
424	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
425	C₂³	—	2	1	no	—
426	C₂³	—	2	2	no	—
427	C₂³	#10597399	1	1	yes	characteristic
428	Q₈	—	2	1	no	—
429	Q₈	—	2	1	no	—
430	Q₈	—	4	4	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	1	no	—
446	D₄	—	8	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	—	8	4	no	—
464	C₂×C₄	—	76	2	no	—
465	C₂×C₄	—	152	1	no	—
466	C₂×C₄	—	152	1	no	—
467	C₂×C₄	#10597395	1	1	yes	characteristic
468	C₂×C₄	#10597396	1	1	yes	characteristic
469	C₂×C₄	#10597396	1	1	yes	characteristic
470	C₂×C₄	#10597397	1	1	yes	characteristic
471	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
474	C₂×C₄	#10597399	1	1	yes	characteristic
475	C₂×C₄	#10597399	1	1	yes	characteristic
476	C₂×C₄	#10597399	1	1	yes	characteristic
477	C₈	—	152	1	no	—
478	C₈	—	152	1	no	—
479	C₈	—	152	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	2	no	—
488	C₂²	#11926400	1	1	yes	characteristic
489	C₂²	#11926689	1	1	yes	characteristic
490	C₂²	#11926706	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	152	2	no	—
500	C₄	#11926540	1	1	yes	characteristic
501	C₄	#11926545	1	1	yes	characteristic
502	C₄	#11926689	1	1	yes	characteristic
503	C₄	#11926706	1	1	yes	characteristic
504	C₄	#11926712	1	1	yes	characteristic
505	C₄	#11926722	1	1	yes	characteristic
506	C₂	—	2	1	no	—
507	C₂	—	2	1	no	—
508	C₂	—	8	1	no	—
509	C₂	—	8	2	no	—
510	C₂	#14563575	1	1	yes	characteristic
511	C₂	#14563589	1	1	yes	characteristic
512	C₂	#14563610	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	#8423
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. #14564559	C₂	semidirect
2. #14563655	C₂	semidirect
3. #14562316	C₂	semidirect
4. #14562312	C₂	semidirect
5. #14562130	C₂	semidirect
6. #14562022	C₂	semidirect
22. C₁₉×#555	C₄	semidirect
23. C₁₉×#554	C₄	semidirect
258. #555	Dic₁₉	semidirect
259. #554	Dic₁₉	semidirect
353. C₁₉	#8423	semidirect

Maximal subgroups

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

subgroup	index
#14564559	2
#14563655	2
#14562316	2
#14562312	2
#14562130	2
#14562022	2
C₁₉×#3511	2
#8423	19